Communications in Asteroseismology
Volume 146
June, 2005
Austrian Academy of Sciences Press
Vienna 2005
Editor: Michel Breger, Türkenschanzstraße 17, A - 1180 Wien, Austria
Layout and Production: Wolfgang Zima
Editorial Board: Gerald Handler, Don Kurtz, Jaymie Matthews, Ennio Poretti
http://www.deltascuti.net
COVER ILLUSTRATION: Selected sample screen shots of the program
Period04.
British Library Cataloguing in Publication data.
A Catalogue record for this book is available from the British Library.
All rights reserved
ISBN 3-7001-3505-X
ISSN 1021-2043
c 2005 by
Copyright Austrian Academy of Sciences
Vienna
Austrian Academy of Sciences Press
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Contents
Editorial
by M. Breger
4
New variable and multiple stars in the lower part of the Cepheid instability
strip
by Y. Frémat, P. Lampens, P. Van Cauteren and C.W. Robertson
6
OV And, a new field RRab Blazhko star?
by K. Kolenberg, E. Guggenberger, P. Lenz, P. Van Cauteren, P. Lampens
and P. Wils
11
Search for intrinsic variable stars in three open clusters: NGC 1664,
NGC 6811 and NGC 7209
by P. Van Cauteren, P. Lampens, C.W. Robertson and A. Strigachev
21
High-degree non-radial modes in the δ Scuti star AV Ceti
by L. Mantegazza and E. Poretti
33
Projected rotational velocities of some δ Scuti and γ Doradus stars
by L. Mantegazza and E. Poretti
37
Application of the Butterworth’s filter for excluding low-frequency trends
by T.N. Dorokhova and N.I. Dorokhov
40
PODEX – PhOtometric Data EXtractor
by T. Kallinger
45
Period04 User Guide
by P. Lenz and M. Breger
53
Comm. in Asteroseismology
Vol. 146, 2005
Editorial
This issue is the biggest one we have published so far. Once again, you can
find a number of articles with the latest research results.
Apart from the many new exciting discoveries, we have included the manual
for PERIOD04 - the latest incarnation of our multiple-period-finding software
package. This is the 25th anniversary of the first version. A long time ago, I
undertook a minisabbatical from the University Texas at Austin and went to
Vienna to write the program. The PERDET and MULTIPER versions were
simple Fortran programs not catering to the comforts of the users at all. But
they worked and are still used in some places. With time, more simultaneous
frequencies could be considered, and amplitude as well as phase variability
became an issue. With versions PERIOD90 and PERIOD95, the human brain
became too small to remember all the options and how to call them, e. g.,
Enter ’r’, then ’x’, etc.
So, Martin Sperl added a graphical interface and more options to the program, which became PERIOD98. This program was downloaded by many universities and observatories. His publication in the Communications became the
most widely quoted masters thesis we have had. His number of citations even
put some professors to shame! If your university persecutes you with the citation
index, learn from him.
For the last few years, we spent some of our time improving the program
and (horrors!) allowing for near-infinite combinations of a near-infinite number
of simultaneously present frequencies. (Of course, this also allows you to flaunt
all laws of statistics and significance, if you wish.)
So Patrick Lenz programmed all the changes and did a wonderful job. I used
dozens and dozens of new versions of the program on the Delta Scuti Network
data that came in and suggested/debugged more and more features. The
program even determined that over the years FG Vir with its 80+ frequencies
has no orbital light-time corrections larger than a few seconds! I just hope that
PERIOD04 with all the new features needed by our research has not emulated
a famous OFFICE suite ..... enough said.
Allow me a side comment. There exist a number of different programs
packages and approaches to help analyze the periodic content in photometric
data. I have participated in a number of successful blind and semi-blind tests.
The conclusion is that most programs and approaches work very well and give
M. Breger
5
correct as well as complete answers when used by cautious and experienced
astronomers. For Delta Scuti stars, the Merate and Vienna astronomers almost
routinely get the same answers with their different programs. Only a few approaches (may I mention CLEAN or earlier versions of Maximum Entropy?) are
controversial.
We hope you find PERIOD04 for WINDOWS, LINUX and Mac OS X useful.
Please give us your suggestions for PERIOD08.
Michel Breger
Editor
Comm. in Asteroseismology
Vol. 146, 2005
New variable and multiple stars in the lower part of the
Cepheid instability strip
Y. Frémat1 , P. Lampens1 , P. Van Cauteren2 and C.W. Robertson3
1
Royal Observatory of Belgium, 3 Ringlaan, 1180 Brussels, Belgium
2
Beersel Hills Observatory (BHO), Beersel, Belgium
3
SETEC Observatory, Goddard, Kansas, USA
Abstract
We obtained high-resolution spectra for 33 A-type stars during 4 consecutive
nights. All our targets are Hipparcos program stars located in the lower part
of the Cepheid instability strip which show hints for variability in radial velocity
of a yet unidentified nature.
CCD photometry was acquired for some of the most promising candidates
and used to further interpret the variability of several targets. A first result is
the discovery of two new pulsating variable stars.
In addition, five new binary or multiple systems were identified (one SB1,
three SB2 and one SB2 triple system).
1. Introduction
A very interesting region of the Hertzsprung-Russel diagram lies at the intersection of the main sequence and the classical Cepheid instability strip, where
a variety of phenomena are at play in the stellar atmospheres.
These phenomena include magnetism, diffusion, rotation and convection,
which are active in δ Scuti, SX Phe, γ Dor and roAp variable stars. The
latter processes may boost or, on the contrary, inhibit the presence of chemical
peculiarities (occurring in Ap, Am, ρ Puppis and λ Boo stars). The competition
between these processes and mechanisms thus leads to a large mix of stellar
groups of different atmospheric composition which also behave in different ways
with respect to pulsation and binarity. To address the issue of the interactions
between chemical composition, pulsation and multiplicity, we aim to perform a
Y. Frémat, P. Lampens, P. Van Cauteren and C.W. Robertson
7
systematic study of the chemical composition of a sample of poorly known mainsequence A- and F-type stars in this region. For this purpose, high-resolution
spectroscopic observations were carried out at the Observatoire de HauteProvence (OHP, France) in December 2004. We here give a brief account of
the present variability status in the observed sample.
2. Description of the sample
We selected 38 targets from the Hipparcos catalogue. The following criteria
have been adopted : 1) brightness larger than magnitude 8; 2) spectral type
ranging from A0 to F2; 3) showing some indication of radial velocity variability
in the catalogue of Grenier et al. (1999) and 4) having less than 10 references
in the bibliography recorded in the SIMBAD data base (CDS). Except for the
Hipparcos epoch photometry and because of the use selection criteria, very
little is known about the targets. The distribution in spectral type of the sample
of 33 observed stars is plotted in Fig. 1 (based on Grenier et al. 1999).
15
Number of Stars
12
9
6
3
0
A2
A3
A4
A5
A6
A7
A8
Spectral Type
A9
F2
Figure 1: Distribution in spectral type of the observed sample.
3. Observations
The spectroscopic observations were carried out at the 1.93 m telescope equipped
with the ELODIE spectrograph of the OHP (Baranne et al. 1996). Highresolution spectra were collected during 4 nights in 2004 (December 3–7). Each
target was observed 2 to 5 times in order to be able to detect rapid (periods
of order of a few hours) or slow (periods of order of a few days) line profile
8
New variable and multiple stars
variations (LPVs) and/or changes in radial velocity. However, due to circumstances (bad weather conditions) some of our targets were only observed 2–3
times successively, without the ability to reobserve at a later date. We adapted
the time exposures to ensure a S/N ratio per pixel (at 5000 Å) generally varying
from 80 to 100. The data were automatically reduced order by order at the end
of the night using the INTERTACOS pipeline. INTERTACOS was also used to
perform a cross-correlation with the F0 mask after each exposure.
For 4 promising candidates, we also acquired complementary CCD photometry in the period between December 2004 and February 2005. These observations were carried out using a 40cm Newton equipped with a SBIG ST10XME
camera (2 targets) at BHO, a 30cm telescope with SBIG ST8i camera (1 target) at SETEC Observatory (Kansas, USA) and a 25 cm telescope with a SBIG
ST10XME camera (1 target) at BHO on one more occasion. Depending on the
target’s magnitude, a B or V filter according to Bessell’s specifications (Bessell
1995) was used.
-1.90
0.96
-1.88
1.00
-100
0
100
Radial Velocity (km/s)
200
3.4
3.5
JD - 2453380
3.6
-1.86
3.7
-1.38
HIP 113790
-1.35
0.98
-1.32
-1.29
0.95
-200
Relative B Magnitude
0.99
0.93
-200
Normalized Intensity
-1.92
HIP 40361
Relative B Magnitude
Normalized Intensity
1.02
-1.26
-100
0
100
Radial Velocity (km/s)
2009.2
9.3
9.4
JD - 2453359
9.5
9.6
Figure 2: The left panels show some cross-correlation functions obtained during consecutive exposures while the right panels illustrate the corresponding light curves.
4. Detection of pulsation and/or multiplicity
The detection of the occurrence of pulsation and/or multiplicity is done by a
visual inspection of the shape and the variations of the cross-correlation functions (CCFs) for each target. The identification of several peaks in the CCFs
Y. Frémat, P. Lampens, P. Van Cauteren and C.W. Robertson
9
and/or the existence of day-to-day changes in radial velocity are interpreted as
the signature of binarity or multiplicity, while the appearance and disappearance
of bumps in the peaks of the CCFs collected during two consecutive exposures
are interpreted as the signature of intrinsic variability.
We classified the observed targets according to their likelihood to be effectively intrinsically variable. To this purpose four classes were defined (VAR1,
VAR2, VAR3, VAR4) among which the class VAR1 indicates a large probability. All VAR1 candidates were subsequently submitted to at least two (short)
photometric runs in order to verify whether they also show short-period light
variations (see new variable stars in Table 1). Fig. 1 illustrates the procedure as
applied to HIP 40361 and HIP 113790. Note that a simple frequency analysis
of the Hipparcos epoch photometric data confirms the listed main periodicity
for HIP 113790.
Table 1: Newly detected photometric-spectroscopic variable stars as well as multiple systems.
HIP
HD
Mag V
Sp. Type
Notes
New variable stars
confirmed by CCD photometry
9501
40361
113790
12389
68725
217860
7.99
6.94
7.30
A4V
F2
A8III
already known δ Scuti star
P ∼ 0.12 d
P ∼ 0.05 d, multiperiodic
unresolved Hipparcos variable
Newly detected multiple systems
3227
8581
46642
115200
116321
3777
11190
81995
219989
221774
7.44
7.88
7.35
7.35
7.38
A2III
A2III
A5
A2IV
A4IV
SB2
SB2
SB1
SB2
SB2
5. Conclusion
Among the 33 observed stars of our sample, 9 were found to be spectroscopically
variable on a timescale of several hours and are thus promising candidates for
the detection of pulsation(s). We classified these 9 candidates into two classes
VAR1 and VAR2. For 4 of these targets CCD light curves in the B or V passband
10
New variable and multiple stars
were obtained. The new photometric data confirm the variable nature of 3 stars,
one of which is the already known δ Scuti star HIP 9501 (Schutt 1991) and
another one is an unresolved Hipparcos variable star (ESA 1997). Five new
binary or multiple systems were further identified (one SB1, three SB2 and one
triple system). We are presently analyzing and exploiting the ELODIE spectra
in order to determine fundamental parameters for each observed target. These
results will be published in more details in the near future. We further plan
to organize a large photometric campaign next season in order to monitor the
light variations of the new intrinsic variable stars HIP 40361 and HIP 113790.
Acknowledgments.
This work is based on spectroscopic observations
made at the Observatoire de Haute-Provence (France) and on CCD photometric observations collected at Beersel Hills and SETEC observatories. Part
of the photometric data were acquired with equipment purchased thanks to a
research fund financed by the Belgian National Lottery (1999). Ample use was
made of the SIMBAD data base (Centre de Données Stellaires, Strasbourg).
References
Baranne, A., Queloz, D., Mayor, M., Adrianzyk, G., Knispel, G., Kohler, D., Lacroix,
D., Meunier, J.-P., Rimbaud, G., Vin, A. 1996, A&A Supp. Ser., 119, 373
Bessell, M.S. 1995, CCD Astronomy 2, No. 4, 20
ESA 1997, The Hipparcos and Tycho Catalogues ESA-SP 1200
Grenier, S., Burnage, R., Faraggiana, R., Gerbaldi, M., Delmas, F., Gómez, A. E.,
Sabas, V., Sharif, L. 1999, A&A Supp. Ser., 135, 503
Schutt R.L. 1991, AJ, 101, 2177
Comm. in Asteroseismology
Vol. 146, 2005
OV And, a new field RRab Blazhko star?
K. Kolenberg1 , E. Guggenberger1 , P. Lenz1 , P. Van Cauteren2 , P. Lampens3 ,
P. Wils4
1
3
Institut für Astronomie, Türkenschanzstr. 17, 1180 Vienna, Austria
2
Beersel Hills Observatory, Belgium
Koninklijke Sterrenwacht van België, Ringlaan 3, 1180 Ukkel, Belgium
4
Vereniging voor Sterrenkunde (VVS), Belgium
Abstract
Between 2004 November and 2005 January, we organized a small photometric
observing campaign dedicated to the RRab star OV And. This star lies very
close to other stars in the field. NSVS (Northern Sky Variability Survey) data
suggested the presence of the Blazhko effect in this star. The new data reveal
that the large discrepancies in pulsation amplitude of the star reported in the
literature can be reproduced by applying different reduction methods. We show
that only the data reduced with inclusion of the neighboring stars can be considered trustworthy. Nevertheless, we find some indications that the Blazhko
effect may exist in this star.
1. Introduction
The most intriguing subclass of the astrophysically important RR Lyrae stars
consists of stars showing the Blazhko effect, the phenomenon of amplitude
or phase modulation. These stars have light curves that are modulated on
timescales of typically tens to hundreds of days. Blazhko (1907) was the first
to report this phenomenon in RW Dra. The estimated incidence rate of Blazhko
variables among the galactic RRab stars (fundamental mode pulsators) is about
20-30 % (Szeidl 1988; Moskalik & Poretti 2002).
Though the Blazhko effect was discovered nearly a century ago, its physical
origin still remains a mystery. Two groups of possible models are proposed,
the magnetic models and the resonance models, but neither of them provides a
sufficient explanation for the variety of behavior observed in Blazhko stars (see
also Kolenberg 2004 for a concise general overview).
12
OV And, a new field RRab Blazhko star?
The number of brighter Blazhko stars in the field is limited, and most of
them have been known for a long time. For some, extensive photometric studies
have been published, often using data sets gathered over several decades (e.g.,
Borkowski 1980, Kovacs 1995, Szeidl & Kollath 2000, Smith et al. 2003, Jurcsik
et al. 2005). Long-term photometric surveys, often serving other aims than
studying only stellar variability (e.g., microlensing surveys like MACHO - Alcock
et al. 2003, and OGLE - Moskalik & Poretti 2002), have entailed the detection
of a multitude of new variable stars, among which also RR Lyrae Blazhko
stars. As a by-product of the Robotic Optical Transient Search Experiment
(ROTSE), the Northern Sky Variability Survey (NSVS) was established, offering
a temporal record of the sky over the optical magnitude range from 8 to 15.5.
This offers data for detecting new RR Lyrae Blazhko stars in the field. One of
such suspected Blazhko candidates is OV And.
2. The target star OV And
In the sky plane the RR Lyrae star OV And (NSV 134, RA2000: 00:20:44.42,
Dec2000: 40:49:41.6, V=10.4-11.0 according to GCVS 2003) lies close to a
few other stars (Rössiger 1987), which makes it difficult to resolve with the
classical photometric technique involving aperture photometry. Together with
its ’companion’ of almost equal brightness (at an angular separation of 7.5
arcsec) the star was previously denoted as BD+40 0060 = NSV 134 (Nikulina
1959) and was supposed to be a rapid irregular variable in the New Catalogue
of Suspected Variable Stars (Kukarkin & Kholopov 1982). Photometric data
from 1985-1986 revealed a light curve amplitude of about 0.5 mag, and led to
the conclusion that one of the stars must be an RR Lyrae star of type ’ab’,
meaning that it pulsates in the fundamental radial mode (Rössiger 1987).
From CCD images obtained by Prosser (1988) it was discovered that in
fact there are three other fainter stars located near the variable and its bright
’companion’. High-dispersion spectra obtained by the same author revealed a
large difference in radial velocities between OV And (about -194 km/s) and its
bright ’companion’ (-62 km/sec), indicating that the two brighter stars do not
form a physical pair. In his photometric data, which allowed resolution of OV
And and its ’companion’, no variability was detected in the ’companion’ nor in
any of the other neighboring stars. Prosser’s differential observations (featuring
‘variable minus ’companion’ magnitude’) point out an amplitude of 0.980 mag
(σ = 0.004 mag) in the star’s light variation, essentially twice the amplitude
found by Rossiger. According to Prosser this “could mean that the adopted
comparison star, BD+40 0056, may have some variation in brightness as well”.
Neither author mentioned a Blazhko effect.
K. Kolenberg et al.
13
2.1 NSVS data of OV And
The NSVS data of OV And were gathered by ROTSE-I in 1999-2000, and cover
a total time span of 254.8 days.
A frequency analysis of the 155 NSVS measurements with Period04 (see
Lenz & Breger 2005, this volume) yields the main frequency f to the expected
accuracy. We adopt the period P = 0.470581 d (frequency f = 2.12503
c/d) listed in the GEOS RR Lyrae database and determined from previous
measurements.
Figure 1: NSVS data phased with the main frequency f = 2.12504 c/d. For visibility
we chose phase 0.5 to be in the middle of the rising branch. Is the large scatter partly
due to a Blazhko effect?
In all our frequency analyses we adopt a 4σ significance criterion, σ being the
mean noise level in the Fourier periodogram at the relevant frequency (Breger et
al 1993). After prewhitening with the known main frequency and its significant
first 5 harmonics, a new frequency peak is found close to the main frequency,
however only at a level of 3.5 σ. Such closely-spaced frequency peaks are a
typical feature of Blazhko stars. However, due to its low signal-to-noise ratio,
we are not (yet) convinced that this peak is related to a real frequency.
As the pixel size of the CCD used for the NSVS corresponds to about
14 arcsec on the sky, the ROTSE-I cameras will always have measured the
combined magnitude of all five stars in the small group, resulting in a smaller
amplitude. Hence, the Blazhko effect should become harder to detect. The
light curve folded with the main period (Figure 1) shows a large scatter. The
average point to point photometric scatter of the NSVS data is reported to be
±0.02 mag for bright, unsaturated stars (Woźniak et al. 2004).
14
OV And, a new field RRab Blazhko star?
Table 1: Log of the photometric observations of OV And. BHO: Beersel Hills Observatory – vlt: Vienna Little Telescope.
Observatory
BHO
vlt
Detector
SBIG ST10XME
Apogee AP9E
Reduction Software
Mira AP (1)
MaxIm DL (2), IRAF (3)
Observers
PVC, PLa
KK, EG, PLe
(1) Produced by Axiom Research Inc. (2) Produced by Diffraction Limited.
(3) Image Reduction and Analysis Facility,
written and supported at the National Optical Astronomy Observatories (NOAO).
Date/HJD
Telescope Observatory
= 245 0000
19.11.04/3329
25-cm
BHO
24.11.04/3334
25-cm
BHO
24.11.04/3334
80-cm
vlt
25.11.04/3335
80-cm
vlt
03.12.04/3343
40-cm
BHO
20.12.04/3360
80-cm
vlt
21.12.04/3361
80-cm
vlt
11.01.05/3382
80-cm
vlt
17.01.05/3388
80-cm
vlt
Total time span: B 53.1 d, V 59.1 d.
Filters
V
V
V
B, V
V
B, V
B
B, V
B, V
Amount of data
Data
Hours
118
4.089
32
1.078
75
2.539
77, 80 7.576, 7.649
108
3.156
91, 91 4.937, 4.937
150
3.901
38, 35 3.788, 3.829
18, 21 2.627, 2.586
We decided to start a photometric monitoring of OV And in order to check
whether a Blazhko effect is indeed present.
3. Photometry of OV And
3.1 Observations
Photometric CCD observations were gathered from two different sites: the
80-cm telescope at the Vienna Observatory (Austria) yielded Johnson B and
V data, and the 25-cm and 40-cm telescopes at Beersel Hills Observatory
(Belgium) provided data in the filter V (following Bessell’s specifications, Bessell
1995) only.
A log of the observations is given in Table 1. We used GSC 2787 1798
as the comparison star and GSC 2787 1777 as the check star. The errors on
individual data points varied between 0.010 mag and 0.030 mag as obtained
K. Kolenberg et al.
15
Table 2: Observed times of maximum (in Johnson B and V filters), and corresponding
O-C values for the elements T0 = HJD24539026.478 and P = 0.470581 d from the
GEOS RR Lyrae database. Errors in HJD(Max) are of order 0.001 d.
HJD(Max)
245 3329.306
245 3334.476
245 3335.418
245 3360.358
245 3361.300
O-C (±0.0014 d)
-0.0105
-0.0169
-0.0161
-0.0169
-0.0160
from the rms error on the differential magnitudes of the comparison star and
the check star.
3.2 Analysis of the data
On the CCD frames obtained with the 25-cm and 40-cm telescopes it was
impossible to resolve OV And and its ’companion’, and hence the reduced
data represent the combined light. For the CCD frames obtained in Vienna
we carried out the reductions twice: once with an aperture radius of 7 pixels
(i.e., about 0.5-0.8*FWHM depending on seeing conditions) which allowed to
(barely) separate both stars and once with an aperture radius of 19 pixels (about
3.5*FWHM) including both stars.
Rössiger (1987) found the following elements from his observations:
HJD(Max) = 2446764.241(±0.001) + 0.470568(±0.000002)E (d),
(1)
confirmed by Prosser (1988) based on data taken one year later. Adopting
Rössiger’s period, our observed times of maximum do no longer correspond
with his time T0 of maximum light. Adopting the period P =0.470581 d listed
in the GEOS database, we still obtain a systematic shift in the (O-C) values
(Table 2). As an updated ephemeris we propose:
HJD(Max) = 2453335.418(±0.001) + 0.470580(±0.000001)E (d).
(2)
3.2.1 How efficiently can the stars be resolved in the reduction?
For the night with the best seeing (JD 245 3361), we were able to separate OV
And from its ’companions’, as illustrated in Fig. 3 displaying the ’OV And group’
on representative frames for two different nights. The bright ’companion’ star
indeed proved to be constant, as was already reported by Prosser (1988).
16
OV And, a new field RRab Blazhko star?
Figure 2: OV And (star to the E) and its immediate neighborhood on representative
frames obtained at the 80-cm telescope in Vienna for HJD 2453361 (left) and HJD
2453335 (right). This figure demonstrates the effect of variable seeing. (North is up,
East is left.)
For all other nights, the differential data of the ’companion’ star showed
variations in brightness. However, we found evidence that these variations are
linked to those seen in the OV And data and therefore must be caused by
some contribution of the light of OV And itself. In the same way, the variable
contribution of the ’companion(s)’ in the ’separated’ OV And data (due to
variable seeing conditions) may not be neglected, as already indicated by the
larger scatter in the data, and hence these reduced data have to be interpreted
with caution!
The peak-to-peak B amplitude for the night of JD 2453361 amounts to
1.65 ± 0.03 mag. As we only obtained B data during this night, we can make
no statements on the V magnitude of OV And (without additional light).
3.2.2 Is OV And a Blazhko star?
Blazhko stars are typified by the occurrence of secondary frequencies close
to the main pulsation frequency and its harmonics. These frequencies are
thought to be related to nonradial modes in the mainly radially pulsating RR
Lyrae star, modes that, according to the currently plausible models, would cause
the observed amplitude and/or phase modulation.
A period analysis of the OV And B and V data, respectively with its ’companions’ and tentatively separated, and using Period04, always revealed the
main frequency f and its harmonics, up to high (8th) order. However, we did
not find any evidence of a secondary frequency close to the main pulsation
frequency above the 4σ significance level.
The main feature of the Blazhko effect is the variation of the light curve
shape and amplitude. Table 3(a) displays the total amplitude of the lightcurve
in different nights. From these data we cannot unambiguously conclude on the
presence of a Blazhko effect in OV And yet; at the level of 2σ the amplitudes
17
K. Kolenberg et al.
Table 3: Variation of the (peak-to-peak) light curve amplitude in the Johnson B and
V filter. The data in the upper panel are for OV And with its ’companions’; the lower
panel data for the reduced data in which we attempted to separate the light variation
of OV And. Note that the upper panel reproduces Rössiger’s (1987) values quite well,
whereas the lower panel agrees better with Prosser’s (1988) values. However, we call
for caution in interpreting the amplitudes in the lower panel!
(a)
Date
19.11.04
24.11.04
25.11.04
20.12.04
21.12.04
(b)
Date
24.11.04
25.11.04
20.12.04
21.12.04
OV And and ’companions’
AV (mag)
0.476
0.463
0.458
0.460
∆AV
0.015
0.015
0.015
0.015
AB (mag)
∆AB
0.865
0.894
0.893
0.015
0.015
0.015
OV And ’separated’
AV (mag)
1.015
1.053
1.179
1.179
∆AV
0.028
0.057
0.057
0.028
AB (mag)
∆AB
1.505
1.596
1.655
0.028
0.028
0.028
are stable. Though there may be an indication for a variation of the total
amplitude as suggested by the data in Table 3(b), we call for much caution
at this stage. We indeed cannot trust the values from Table 3(b) as it is very
difficult to obtain ”clean” measurements of OV And without influence of the
’companion”s light (and other neighboring stars)!
4. Conclusions
• Like previous authors who used small telescopes, we experienced difficulties separating OV And from its neighbors on the sky. Reduction of data
of OV And should include all neighboring stars in order to be trustworthy.
• The smaller amplitude reported by Rössiger (1987), about half of the
amplitude detected by Prosser (1988), can be explained by the fact that
Rössiger included the bright ’companion’ in his analysis, rather than due
to the comparison star’s behavior, as Prosser (1988) assumed. Additional
star light will reduce the total amplitude of the light curve, and also
influences its shape. The NSVS data show an even smaller amplitude.
The main reason for this, besides the inclusion of yet another star in the
reduction, is that the ROTSE camera (unfiltered CCD) is more sensitive
18
OV And, a new field RRab Blazhko star?
Figure 3: All our V data phased with the main frequency. OV And was reduced with
its ’companions’ included in the aperture. The amplitudes of the lightcurve are listed
in Table 3(a) (see columns for V ). The data suggest a small change in the light curve
shape and amplitude, but its significance needs to be proven.
in the red, the wavelength region where RR Lyrae stars emit less light
than in V .
• For the ’isolated’ OV And, we detected a light curve amplitude of 1.6±0.1
mag in the B filter. The light curve in the V filter is estimated to be
1.1 ± 0.1 mag.
• The present data don’t confirm the additional frequency suggested by the
NSVS data, but since we only observed 4 maxima we cannot disprove its
reality yet. Moreover, our observed light curves suggest that a Blazhko
effect may be present. We plan a follow-up action on OV And for next
autumn.
5. The Blazhko Project
These observations were carried out in the framework of the Blazhko Project,
an international collaboration, set up to join efforts in obtaining a better understanding of the Blazhko phenomenon in RR Lyrae stars. The project was
founded in Vienna and started its activities in the autumn of 2003. The starting
point for improving the modeling is an extensive data set, consisting of spectroscopy and photometry, of a limited sample of field RR Lyrae Blazhko stars,
and also some non-Blazhko stars for comparison. Besides the larger campaigns,
K. Kolenberg et al.
19
some small photometric campaigns – like this one – are organized to fine-tune
our knowledge of the frequency behavior of field Blazhko stars.
All interested colleagues – professionals and amateurs – are warmly invited
to join in the observational campaigns of the Blazhko Project. For more information we refer to the website dedicated to the Blazhko Project
(http://www.astro.univie.ac.at/˜ blazhko/)
or directly contact [email protected].
Acknowledgments.
The Blazhko Project, KK and EG are supported
by the Austrian Fonds zur Förderung der wissenschaftlichen Forschung, project
number P17097-N02. KK thanks Jacqueline Vandenbroere and Anton Paschke
for information on the data reported on the GEOS and BAV websites.
The data were partly gathered in the framework of the Observatoriumspraktikum, during which students at the Institute for Astronomy are taught to
use the telescope and CCD camera (see http://www.deltascuti.net/obsprak/
and http://www.astro.univie.ac.at/˜ blazhko/Winter.html). We thank all
the students who participated in the observations of OV And: Paul Beck, Daniel
Blaschke, Johannes Puschnig, Markus Hareter, Eveline Glassner, Pia Hecht,
Elisabeth Füllenhals, Sophie Aspöck, Vera Steinecker, Gerald Jungwirth, Hanns
Petsch, Jenny Feige, Adrian Partl, Mathias Jäger, Petra Zippe, Marius Halosar,
Florian Herzele. Part of the data was acquired with equipment purchased thanks
to a research fund financed by the Belgian National Lottery (1999).
References
Alcock, C., Allsman, R.A., Becker, A., et al., ApJ 598, 597
Bessell, M.S., 1995, CCD Astronomy 2, No. 4, 20
Blazhko, S., 1907, Astron. Nachr. 175, 325
Borkowski, K.J., 1980, Acta Astron. 30, 393
Breger, M., Stich, J., Garrido, R., et al., 1993, A&A 271, 482
GEOS RR Lyrae database: http://webast.ast.obs-mip.fr/people/leborgne/dbRR/
Kolenberg, K., 2004, CoAst 145, 16
Kukarkin, B.V., Kholopov, P.N., 1982, New Catalogue of Suspected Variable Stars
Jurcsik, J., Sódor, Á., V’aradi, M., et al., 2005, A&A 430, 1049
Kovacs, G., 1995, A&A 295, 693
Lenz, P., & Breger, M., 2005, CoAst 146, 53
Moskalik, P., & Poretti, E., 2002, A&A398, 213
Nikulina, T.G., 1959, Astron. Tsirk., 207, 14
NSVS, Northern Sky Variability Survey, http://skydot.lanl.gov/nsvs/nsvs.php
Prosser, C.F., 1988, Inform. Bull. Var. Stars, 3130, 1
Rossiger, S., 1987, Inform. Bull. Var. Stars, 2977, 1
ROTSE, Robotic Optical Transient Search Experiment,
http://rotse1.physics.lsa.umich.edu/
20
OV And, a new field RRab Blazhko star?
Szeidl, B., 1988, in ’Multimodal Stellar Pulsations’, Kultura, eds. Kovacs, G.,
Szabados, L., Szeidl, B., 45
Szeidl, B., Kollath, Z., 2000, ASP Conf. Ser. 203, 281
Smith, H.A., Church, J.A., Fournier, J., et al., 2003, PASP 115, 43
Woźniak, P. R., Vestrand, W. T., Akerlof, C. W., et al., 2004, The Astronomical
Journal, Vol. 127, 2436
Comm. in Asteroseismology
Vol. 146, 2005
Search for intrinsic variable stars in three open clusters:
NGC 1664, NGC 6811 and NGC 7209
P. Van Cauteren1 , P. Lampens2 , C.W. Robertson3 and A. Strigachev4 ,2
1
Beersel Hills Observatory, Beersel, Belgium
Royal Observatory of Belgium, 3 Ringlaan, 1180 Brussels, Belgium
3
SETEC Observatory, Goddard, Kansas, USA
Institute of Astronomy, Bulgarian Academy of Sciences, Sofia, Bulgaria
2
4
Abstract
We report on new time-series CCD observations for three poorly studied open
clusters from the STACC list. The collected light curves in the V filter of a
large number of stars per field have been examined in detail in search for shortperiodic variable stars. In particular we looked for new δ Scuti-type candidates.
First results for the open clusters NGC 1664, NGC 6811 and NGC 7209 are
presented.
1. Why study open clusters ?
The study of variable stars in open clusters presents various advantages for the
understanding of pulsation physics:
• open clusters with variable members provide comparative asteroseismological tests of stellar structure and evolution based on the implications
of a common origin and formation of their stellar members;
• open clusters are ideally suited for performing high-accuracy differential
photometry as well as ’CCD ensemble photometry’ based on a large sample of comparison stars in the field-of-view.
Such studies moreover require long baseline differential photometry (to detect
multiple frequencies combined with small amplitudes) as well as complementary multi-color photometry or high-resolution spectroscopy (to determine the
basic stellar parameters) if one wishes to take full profit of these observations
22
Search for intrinsic variable stars in three open clusters
(Freyhammer et al. 2001). We selected three poorly studied open clusters
from the STACC list (Frandsen & Arentoft 1998) in order to perform a CCD
survey using small telescopes (up to 1.3m) with the goal to search for intrinsic
variable stars. These open clusters are visible from the Northern hemisphere
and are furthermore prime targets for the detection of δ Scuti-type candidate
stars (Frandsen & Arentoft 1998).
On the other side, the presence of close neighboring stars in the (semi)crowded fields of the central parts of open clusters may affect the quality of
the results and this could imply the need for a different reduction technique
(point-spread function fitting instead of the aperture photometry approach).
2. General information about the observed clusters
2.1 NGC 1664
Is an extended open cluster of the STACC list with a rich central region (Frandsen & Arentoft 1998). A recent proper motion study was performed by Baumgardt et al. (2000). The cluster membership was also investigated by Missana
& Missana (1998). It is situated at a distance of about 1200 pc and has a
log age of 8.47 (Mermilliod 1995).
2.2 NGC 6811
Is an open cluster of the STACC list with many candidates in the instability
strip (Frandsen & Arentoft 1998). A proper motion study was performed by
Sanders (1971), yielding 97 probable members. Glushkova et al. (1999) collected radial velocities in the field and identified seven new members. From
their photoelectric photometric data they obtained a mean distance of 1040 pc
and an age of 0.7 Gyr based on 88 identified cluster members (log age = 8.85).
2.3 NGC 7209
Is an open cluster of the STACC list with a poorly populated color-magnitude
diagram (Frandsen & Arentoft 1998). Several studies of proper motions in
the cluster field exist: for example, Platais (1991) found 148 possible cluster
members down to mag 15 while recent proper motion studies were performed by
Baumgardt et al. (2000) and by Dias et al. (2001) based on the TYCHO-2 catalogue. Peña & Peniche (1994) proposed the existence of two clusters, NGC 7209
a and b, with a different reddening, age and distance based on Strömgren photometry of 54 stars in the cluster direction. Vancevicius et al. (1997) obtained
photoelectric photometry in the Vilnius system for 96 probable members but do
not support that conclusion: they estimated the mean reddening, the metalicity
P. Van Cauteren, P. Lampens, C.W. Robertson and A. Strigachev
23
and derived a median distance of 1026 ± 30 pc and an age of 0.45 Gyr (log
age = 8.65).
3. Observations and photometric reduction
The logbook of all observations, the telescopes and CCD cameras used are
listed in Table 1. Except for the observatory Hoher List (HL) where a selfbuilt camera was employed (2Kx2K; HoLiCam of the Observatorium Hoher
List, University of Bonn, Germany), the other cameras are from Photometrics
(1Kx1K; Skinakas, Crete) or SBIG (various ST’s), equipping instruments with
different focal lengths. We typically made use of a field-of-view with a size of
260 × 280 (e.g. BHO 40cm) or 340 × 230 (e.g. BHO 25cm).
Table 1: Log of the cluster observations
NGC
Obs/Tel
CCD
Start
End
Nr/hrs
Filter
1664
BHO40
BHO25
HL100
ST10E
ST7
HoLiCam
27-10-03
08-12-03
17-12-03
10-12-03
08-12-03
17-12-03
25.8
8.9
5.5
B,V
V
V
6811
BHO40
NAO70
ST10E
ST8
22-03-03
03-05-03
27-09-03
03-05-03
31.8
3.3
B,V
V
7209
BHO40
BHO25
SETEC
SKI130
ST10E
ST7
ST8i
CH360
29-07-02
01-08-03
12-08-02
19-08-03
20-08-03
10-08-03
05-09-02
04-10-03
25.9
31.9
42.6
9.2
B,V
V
V
V
All the frames were treated following the classical basic reduction scheme:
a median dark/bias was subtracted from each science frame and these were
then divided by a median flat-field. Aperture photometry was subsequently
performed using various packages. Consequently, we intentionally avoided the
stars with close neighbors on the collected images. First, for all the frames obtained at BHO, HL, SETEC and Skinakas, the aperture photometric package of
MIRA AP was applied. Differential magnitudes with respect to a pre-selected
comparison star were produced. For the frames acquired during one night in
0 The
MIRA AP software is produced by Axiom Research Inc.
24
Search for intrinsic variable stars in three open clusters
2003 with the Schmidt 50/70 telescope of the National Astronomical Observatory of Bulgaria (Tsvetkov et al. 1987), we gathered the differential data using
the MOMF code (Kjeldsen & Frandsen 1992). In a second step, CCD ensemble
photometry was applied in order to produce differential magnitudes with respect
to a comparison magnitude using a(n) (inhomogeneous) set of comparison stars
(Honeycutt 1992). The figures shown below are based on the latter data.
A V filter following Bessel’s (1995) specifications was used for the time-series
photometry. In addition, some nights were dedicated to the acquisition of the
B-magnitudes with the aim to produce updated color-magnitude diagrams in
the near future.
4. Results
4.1 NGC 1664
4.1.1 Analysis
The observed field of NGC 1664 is illustrated by Fig. 1. We used the numbering
of the (WE)BDA (Mermilliod 1995; cf. http://www.obswww.unige.ch/webda/)
database for identification purposes. 9 stars received an internal numbering.
284 stars were included in the reduction scheme and examined for rapid light
variations. The CCD data consist of more than 300 differential magnitudes in
the mean for most targets, with actual numbers varying between 39 (a few)
and 516 (many) depending on the position in the field.
4.1.2 Discussion of individual variable stars
We report the detection of two new short-periodic variable stars in the field:
V1 and V2. Both are possible δ Scuti variable stars. A period analysis of the
V-band data for star #100 = V1 indicates a main frequency of ≈ 4.48 c/d
and a semi-amplitude of 0.04 mag in V. Star #265 = V2 is probably a new
δ Sct star with a main frequency of ≈ 16.77 c/d and a semi-amplitude of 0.02
mag only in V. The light curves of two individual nights are presented in Fig. 2.
4.2 NGC 6811
4.2.1 Analysis
The observed field of NGC 6811 is illustrated by Fig. 3. We used the Lindoffnumbering for identification purposes (same as in (WE)BDA). 230 stars received
an internal numbering. 441 stars were included in the reduction scheme and
P. Van Cauteren, P. Lampens, C.W. Robertson and A. Strigachev
25
examined for rapid light variations. The CCD data consist of more than 200 differential magnitudes in the mean for most targets with actual numbers varying
between 56 (a few) and 355 (many) depending on the position in the field.
4.2.2 Discussion of individual variable stars
We report the detection of nine new variable stars in the field, of which six
are probably short-periodic variable stars of type δ Scuti and one is a suspected short-period variable. The light curves of the variable stars detected in
NGC6811 are presented in Fig. 4. Stars #18 = V1 and #37 = V2 are two δ Sct
type variables, with a main frequency of about 20 c/d and a semi-amplitude of
the order of 0.01 mag in V. Star #70 = V3 is a δ Sct type variable with a main
frequency of about 7.5 c/d and a semi-amplitude of 0.02 mag in V. The data
of star #39 = V4 indicate a frequency of about 8.4 c/d with a semi-amplitude
of 0.01-0.02 mag in V. Star #113 = V5 is a suspected variable of a similar type
with a possible frequency of 13 c/d of much smaller amplitude (< 0.01 mag).
Two δ Scuti variable stars were also detected among the new designations:
these are stars #489 = V6 and #491 = V7 (following the BDA-numbering)
with frequencies of ≈ 9.4 c/d and possibly 15 c/d and semi-amplitudes of 0.04
and 0.02 mag in V respectively. Two more variable stars of unknown type (V8
and V9) were discovered at the field edges (Fig. 5, left): they were only observed very shortly (for about 3 hrs) and do not show the characteristics typical
of δ Scuti stars as their periods are longer. The right panel of Fig. 5 shows the
observed light variations with a large amplitude in both cases.
4.3 NGC 7209
4.3.1 Analysis
The observed field of NGC 7209 is shown in Fig. 6. We used the Mäversnumbering for identification purposes (same as in (WE)BDA). 215 stars received
an internal numbering. 357 stars were included in the reduction scheme and
examined for rapid light variations. The CCD data consist of more than 900
differential magnitudes for most targets with actual numbers varying between
70 (a few) and 1100 (many) depending on the position in the field.
4.3.2 Discussion of individual variable stars
Although we did not (yet) systematically inspect all the material for this cluster,
we already report the detection of three possible δ Scuti variable stars in the
field: stars #24 = V1 (= GSC 3605 2253), #55 = V2 (= GSC 3605 2309)
and #59 = V3 (= GSC 3605 2247 1). Stars #24 and #55 are probably δ Scuti
26
Search for intrinsic variable stars in three open clusters
stars with rather small semi-amplitudes (< 0.01 mag). The data of star #59
clearly indicate a frequency of 7.7 c/d with a semi-amplitude of 0.01 mag in V.
The observed light variations of the detected variabe stars in NGC7209 are plotted in Fig. 7. In addition, star #112 = V4 (= GSC 3605 2721 = SAO 51648),
an infra-red source, appears to show small but irregular fluctuations.
We also noted the existence of slower fluctuations with observed amplitudes
of the order of 0.1-0.2 mag in the V magnitudes of a few stars which were however only occasionally observed: #91 (2 nights showing a (start of a) minimum
compared to the rest of the data), #122 (2 nights, ∆V = 0.3 mag), #179
(1 night, ∆V = 0.6 mag) and #3612 (1 night, ∆V = 0.6 mag) (using the
BDA-numbering).
5. Figures for three open clusters
Figure 1: Sample CCD frame of the open cluster NGC 1664. The newly detected
variable stars are indicated.
27
P. Van Cauteren, P. Lampens, C.W. Robertson and A. Strigachev
-0.46
0.12
-0.48
0.10
-0.50
0.08
∆ mag (#265 - comp)
∆ mag (#100 - comp)
-0.52
-0.54
-0.56
940.4
940.6
-0.46
-0.48
-0.50
-0.52
0.04
940.4
940.6
0.12
0.10
0.08
0.06
-0.54
-0.56
0.06
0.04
980.4
Julian date ( 2 452 000+)
980.6
980.2
980.4
Julian date ( 2 452 000+)
980.6
Figure 2: Light curves of NGC1664. Left panels: star #100. Right panels: star #265.
Figure 3: Sample CCD frame of the open cluster NGC 6811. The newly detected
variable stars are indicated
28
Search for intrinsic variable stars in three open clusters
-0.84
0.14
-0.82
0.16
-0.80
0.18
-0.78
0.22
0.24
747.2
747.4
747.6
0.14
0.16
∆ mag (#37 - comp)
∆ mag (#18 - comp)
0.20
0.18
-0.76
-0.74
-0.80
-0.78
0.22
-0.76
879.4
-0.74
879.6
Julian date ( 2 452 000+)
747.6
-0.82
0.20
0.24
747.4
-0.84
879.4
879.6
Julian date ( 2 452 000+)
-1.12
-0.48
-1.10
-0.44
-1.08
-0.40
-1.02
747.4
747.6
-1.12
-1.10
-1.08
∆ mag (#39 - comp)
∆ mag (#70 - comp)
-1.06
-1.04
-1.06
860.4
860.6
-0.48
-0.44
-0.40
-1.04
-0.36
-1.02
862.4
879.4
862.6
Julian date ( 2 452 000+)
879.6
Julian date ( 2 452 000+)
-0.46
-0.92
-0.44
-0.88
-0.42
-0.84
-0.40
-0.38
722.8
722.6
-0.46
-0.44
-0.42
∆ mag (#489 - comp)
∆ mag (#113 - comp)
-0.36
-0.32
-0.80
721.8
721.6
-0.92
-0.88
-0.84
-0.40
-0.80
-0.38
747.4
747.6
Julian date ( 2 452 000+)
860.4
Julian date ( 2 452 000+)
860.6
1.64
1.68
1.72
∆ mag (#491 - comp)
1.76
1.80
1.84
1.88
860.4
860.6
1.68
1.72
1.76
1.80
1.84
1.88
1.92
862.4
Julian date ( 2 452 000+)
862.6
Figure 4: Light curves of NGC6811. From top to bottom and left to right:
stars #18, #37, #70, #39, #113, #489, #491.
29
P. Van Cauteren, P. Lampens, C.W. Robertson and A. Strigachev
0.6
0.8
∆ mag (var - comp)
1.0
1.2
Star #288
1.4
0.3
0.4
0.5
0.6
1.5
2.0
2.5
3.0
Star #507
3.5
4.0
0.3
0.4
0.5
Julian date ( 2 452 762+)
0.6
Figure 5: Left panel: Extended field of the open cluster NGC 6811 (source: Digitized
Sky Survey). The newly detected variable stars are indicated. Right panels: Light
curves of NGC6811,V8-V9.
Figure 6: Sample CCD frame of the open cluster NGC 7209. The newly detected
variable stars are indicated.
Search for intrinsic variable stars in three open clusters
-0.82
0.20
-0.80
0.22
-0.78
0.24
Differential mag (#55 - comp)
Differential mag (#24 - comp)
30
-0.76
-0.74
871.4
871.6
-0.84
-0.82
-0.80
0.26
0.28
871.4
871.6
0.20
0.22
0.24
-0.78
0.26
-0.76
917.2
917.4
917.2
917.6
Julian date ( 2 452 000+)
-0.44
-0.42
0.86
∆ mag (#112 - comp)
Differential mag (#59 - comp)
0.84
0.88
871.4
871.6
0.80
0.82
0.84
-0.40
-0.38
504.4
504.6
-0.48
-0.46
-0.44
-0.42
0.86
-0.40
0.88
0.90
917.6
-0.46
0.82
0.90
917.4
Julian date ( 2 452 000+)
-0.48
0.80
917.2
917.4
917.6
Julian date ( 2 452 000+)
-0.38
855.4
Julian date ( 2 452 000+)
855.6
0.96
1.00
1.04
∆ mag (#91 - comp)
1.08
1.12
1.16
485.4
485.6
0.96
1.00
1.04
1.08
1.12
1.16
857.4
Julian date ( 2 452 000+)
857.6
Figure 7: Light curves of NGC7209.
stars #24, #55, #59, #112, #91.
From top to bottom and left to right:
P. Van Cauteren, P. Lampens, C.W. Robertson and A. Strigachev
31
6. Conclusions
We gathered new time-series CCD observations in two filters with the aim to
search for short-periodic variable stars in three poorly studied open clusters
from the STACC list: NGC 1664, NGC 6811 and NGC 7209. The time series
data are particularly extensive in the case of NGC 7209 (more than 100 hrs of
observations). Among our first results we report the detection of two possible
δ Scuti variable stars in the field centered on NGC 1664, the detection of nine
new variable stars in the field centered on NGC 6811 of which six are probably
of type δ Scuti and one is a suspected δ Scuti star as well as the detection of
three probable δ Scuti variable stars in the field centered on NGC 7209. The
search in NGC 7209 will be resumed as we did not (yet) systematically inspect
all the material available. It is also our intention to publish the BV-photometry
and to provide updated color-magnitude diagrams for these open clusters.
Acknowledgments. This work is based on CCD observations collected at
Beersel Hills (BHO 40cm, BHO 25cm), Hoher List (1m Cass.), NAO Rozhen
(Schmidt 50/70cm), SETEC (30cm Meade LX-200) and Skinakas (1.3m) observatories. The Skinakas Observatory is a collaborative project of the University
of Crete, the Foundation for Research and Technology – Hellas, and the MaxPlanck-Institut für Extraterrestrische Physik. We warmly thank Dr. P. Wils
for assistance with the reductions. We are grateful to the respective directors
Dr. K. Reif, Prof. K. Panov and Prof. I. Papamastorakis for the allocated
telescope time. Part of these data were acquired with equipment purchased
thanks to a research fund financed by the Belgian National Lottery (1999).
PL and AS acknowledge support from the Belgian Science Policy and from
the Bulgarian Academy of Sciences (project BL/33/B11). PVC is grateful to
the Royal Observatory of Belgium for putting at his disposal material acquired
by the Fund for Scientific Research - Flanders (Belgium) (project G.0178.02).
The Simbad (Centre de Données Astronomiques, Strasbourg, France) and
the (WE)BDA (Institut d’Astronomie, Lausanne, Switserland) databases were
extensively used.
References
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Bessell, M.S. 1995, CCD Astronomy 2, No. 4, 20
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Freyhammer, L. M., Arentoft, A. & Sterken, C. 2001, A&A 368, 580
Glushkova, E.V., Batyrshinova, V.M. & Ibragimov, M. A. 1999, Astron. Lett. 25, 86
Honeycutt, R.K. 1992, PASP, 104, 435
Kjeldsen, H. & Frandsen, S. 1992, PASP 104, 413
32
Search for intrinsic variable stars in three open clusters
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Eds D. Egret & M.A. Albrecht (Kluwer Academic Press, Dordrecht),127
Missana, M. & Missana, N. 1998, Astronomische Nachrichten 319, 187
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Platais, I. 1991, A&AS 87, 557
Sanders, W.L. 1971, A&A 15, 368
Tsvetkov, M.K., Georgiev, T. B., Bilkina, B.P., Tsvetkova, A. G. & Semkov, E.H.
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Comm. in Asteroseismology
Vol. 146, 2005
High-degree non-radial modes in the δ Scuti star
AV Ceti
L. Mantegazza and E. Poretti
INAF - Osservatorio Astronomico di Brera, Via E. Bianchi 46, 23807 Merate, Italy
Abstract
High-resolution spectroscopic observations taken during 5 consecutive nights of
the fast rotating δ Scuti star AV Ceti (v sin i = 188km/s) show the presence of
non-radial modes with ` ∼ 10 − 16 and very short periods (ν ∼ 40 − 70 c/d)
Introduction and Observations
The rapidly rotating δ Scuti star AV Ceti has been recently the target of a
simultaneous photometric and low-resolution spectroscopic international campaign (Dall et al. 20031). Seven low-degree modes were detected in the frequency range 10-31 c/d.
We observed this star with the Coudé Echelle Spectrograph attached at the
ESO CAT Telescope during 5 consecutive nights (October 24-30, 1994; Remote
Control from Garching headquarters) for about 2.5 consecutive hours per night
and 55 spectrograms were collected with exposure times of 10 min and a typical
S/N ratio at the continuum level of about 230. They had a resolution of 60000
and cover the region 4494-4513 Å. In this region we have two useful lines to
study line profile variations: TiII 4501Å and FeII 4508Å. Fig. 1 shows the
average continuum normalized spectrum (upper panel) and the pixel-by-pixel
standard deviation (lower panel).
1 Added by editor (MB): The Astronomy and Astrophysics publisher used an incorrect
name for the star (AV Cetei instead of AV Ceti) in the title and running head of the Dall
et al. paper. The authors of the present publication note: Cetus,-i belongs to the second
latin declination (as, for example, Cepheus,-i) : nominative and genitive cases are different
(Cephei, Ceti). On the other hand, Doradus,-us belongs to the fourth declination and the
genitive is the same as the nominative (γ Doradus, not γ Doradi). For a correct use of
abbreviations of constellations see http://www.iau.org/Activities/nomenclature/const.html
34
High-degree non-radial modes in the δ Scuti star AV Ceti
Figure 1: Average normalized spectrum (top panel); pixel-by-pixel data standard deviation (lower panel).
Data analysis and discussion
We can see that the line profiles have variations with a std.dev of about
0.002 of the continuum level. A non-linear least-squares fit of a rotationally
broadened Gaussian intrinsic profile, taking also into account the limb darkening,
on the two average line profiles supplies v sin i = 188 ± 1 km/s.
The line profile variations were analyzed by means of the Fourier Doppler
Imaging Technique (Kennelly et al. 1998; Hao 1998). Fig. 2 shows the twodimensional power spectrum obtained considering all the data in a single time
series and merging the information of the two spectral lines. We see that there
is a clear clump of modes in the region 10 ≤ ` ≤ 16, 35 ≤ ν ≤ 70 c/d. Because
of the very severe aliasing, due to the poor temporal coverage, it is not possible
to derive a detection of individual modes.
A CLEANed version of this power spectrum is shown in Fig. 3 (gain=0.9,
100 iterations). This figure should be considered only as indicative, and the
individual modes cannot be taken at face value, since the poor spectral window makes a correct deconvolution problematic. However it clearly shows that
we should expect a very complex pulsation pattern with several high-degree,
high-frequency modes. Can this be due to the fast rotation? More intensive
L. Mantegazza and E. Poretti
Figure 2: Two-dimensional Fourier power spectrum.
Figure 3: CLEANed two-dimensional Fourier power spectrum.
35
36
High-degree non-radial modes in the δ Scuti star AV Ceti
observations are necessary to get a more exhaustive picture of the stellar pulsation spectrum. We also note that the low-degree modes, photometrically
detected by Dall et al. (2003) do not produce relevant patterns in our power
spectrum. This does not necessarily mean that they are not present, since our
technique is more sensitive to high-degree modes (see also Mantegazza 2000).
References
Dall, T.H., Handler, G., Moalusi, M.B., Frandsen, S. 2003, A&A 410, 983
Hao, J. 1998, ApJ 500, 440
Kennelly,E.J. et al. 1998, ApJ 495, 440
Mantegazza, L. 2000, ASP Conf. Ser. 210, 138
Comm. in Asteroseismology
Vol. 146, 2005
Projected rotational velocities of some δ Scuti and
γ Doradus stars
L. Mantegazza1 , E. Poretti1
1
INAF - Osservatorio Astronomico di Brera, E. Bianchi 56, 23807 Merate, Italy
Abstract
We present the projected rotational velocities of some δ Scuti or γ Doradus
stars as derived from high-resolution spectrograms. For 6 stars the values are
the first determinations.
In the past years during our campaigns of monitoring of some selected
δ Scuti stars (see for example Mantegazza & Poretti 2002 and references
therein) we obtained spectra of a few δ Scuti or γ Doradus stars in order to
estimate their projected rotational velocities. Most of the spectra were taken
with the Coudé Echelle Spectrograph attached at the Coudé Auxiliary Telescope
at La Silla Observatory (ESO) in the 90’s. These spectra have a resolution of
60000 and cover the spectral range between 4490 and 4525 Å; their typical S/N
in the center is usually better than 200 at the continuum level. Few more spectrograms were taken with the FEROS spectrograph, then attached at the ESO
1.5 m telescope of La Silla Observatory in the years 2001-2002. These spectrograms have a resolution of 48000 and cover the spectral range 3600-9300 Å. For
the present work the useful lines between 4400-4600 Å were considered. All the
spectrograms were normalized to the continuum, defined by selecting a set of
continuum windows star by star and fitting them with a low-degree polynomial.
The unblended lines were then fitted by means of a non-linear least-squares
routine with a rotational profile convolved with a Gaussian intrinsic one taking
also into account the limb darkening. Limb darkening coefficients were derived from the paper by Diaz-Cordoves et al. (1995). The number of useful
lines varies from 2 to 7, depending upon rotational velocity, spectral type and
spectrograph. The typical rms uncertainties, resulting by averaging the values
obtained form different lines and/or spectrograms, are between 1-2 km/s. The
38
Projected rotational velocities of some δ Scuti and γ Doradus stars
results are reported in the following table, where for each star we give name,
spectral type, our v sin i, the number of spectrograms and a letter identifying
the spectrograph (C=CES, F=FEROS). In the 3 successive columns we give
for comparison the values derived by Royer et al. (2002), Abt & Morrel (1995),
and in the third those reported in the δ Scuti star catalog by Rodriguez et al.
(2000) or in other recent papers. The references are given in the next one.
There are only three γ Doradus stars in the sample: QW Pup, BT Psc, BU
Psc.
The agreement among the estimates of different authors is generally satisfactory with a few exceptions. The most striking is that regarding QQ Tel. We
observe that the estimate by Koen et al. (2002) is based on the correlation
profile (not directly on the line profiles), computed on spectrograms with a
lower resolution than ours (39000 vs. 60000), and maybe these are the causes
of the discrepancy.
Acknowledgments.
References
Abt, H.A., Morrell,N.I. 1995, ApJS 99, 135
Breger, M., Garrido, R., Handler, G. 2002, MNRAS 329, 531
Diaz-Cordoves, J., Claret, A., Gimenez, A. 1995, A&AS 110, 329
Koen, C., Balona, L., van Wyk, F., et al. 2002, MNRAS, 330, 567
Mantegazza, L., Poretti E. 2002, A&A 396, 211
Mathias, P., Le Contel, J.M., Capellier, E., et. al. 2004, A&A 417, 189
Rodriguez, E., Lopez-Gonzalez, M.J., Lopez de Coca, P. 2000, ASP
Conf.Ser. 210,499
Royer, F., Grenier, S., Bylac, M.O., Gomez A.E., Zorec, J. 2002 A&A 393, 897
39
L. Mantegazza and E. Poretti
Table 1: Measured v sin i and comparison with other determinations
HD
Name
Sp.Type
2724
BB Phe
F2II
3326
BG Cet
A5m
4849
AZ Phe
A9.5III
4919
ρ Phe
F2III
8511
AV Cet
F0V
“
“
9065
WZ Scl
F0IV
11413
BD Phe
A1V
11522
BK Cet
F0V
15634
TY For
A9V:n
“
“
16723
BS Cet
A7IV
55892 QW Pup
F0IV
66853
BI CMi
F2
160589 V703 Sco
A9V
182640
δ Aql
F0IV
185139
QQ Tel
F2IV
208435
BZ Gru F1III-IV
214441
CC Gru
F1III
215874
FM Aqr A9III-IV
223480
BF Phe
A9III
“
“
224638
BT Psc
F0
224639
BH Psc
F0
224945
BU Psc
A3
(1) Royer et al. (2002)
(2) Abt & Morrel (1995)
(3) Rodriguez et al. (2000)
(4) Breger et al. (2002)
(5) Koen et al. (2002)
(6) Mathias et al. (2004)
v sin i
km/s
83
91
92
84
190
188
33
126
129
128
124
52
56
78
≤10
89
65
148
123
94
83
83
19
108
58
1F
1C
1C
1C
1F
55C
1C
1C
2C
1C
3F
1C
2C
1F
13F
2C
2C
1C
1C
2C
1F
20C
16C
1F
26C
previous values
(1) (2) others
–
–
83
110
98
98
–
–
–
–
–
–
212 195
141
–
139
133
146
–
–
120
141
–
124
120
141
–
51
–
–
91
–
–
–
110
–
–
–
–
–
85
–
–
–
98
–
–
–
76
≤16
–
45
–
–
100
80
–
–
–
–
–
–
17
110
54
ref.
(3)
(3)
(3)
(3)
(3)
(3)
(4)
(3)
(5)
(3)
(3)
(6)
(3)
(6)
Comm. in Asteroseismology
Vol. 146, 2005
Application of the Butterworth’s filter for excluding
low-frequency trends
T.N. Dorokhova, N.I. Dorokhov
Astronomical Observatory, Odessa National University,
Shevchenko Park, Odessa 65014 Ukraine
Abstract
In the research of roAp stars low-frequency atmospheric and instrumental trends
of data can be removed by the application of Butterworth’s filter. Here we show
the validity of such a technique by using a data set in which we combined the
observed star’s data and an artificial frequency spectrum. It is shown that the
clearing of the data in the required frequency region is acquired due to the reduction of low-frequency noise, whereas the frequency solution practically does
not change. The cleaning enables an easier detection of dominant frequencies
in the investigated frequency region.
During some years we tested low-frequencies filters for reducing atmospheric
and instrumental trends from observations of roAp stars obtained under nonideal photometric conditions. We examined such techniques by using artificial
data series in the manner described by Breger (1990).
The programs PERIOD (Breger 1990), FOUR (Andronov 1994) and Period98 (Sperl 1998) were used for the analysis. The SPE package by Sergeev
(1992) was initially applied for data reducing and filtering.
We prepared a data set consisting of time series measurements of a comparison star (10th mag) during three long nights (8-10 hours) and incorporated
the artificial frequency spectrum with the parameters given in Table 1. The
resulting light curve is a combination of the observed atmospheric frequency
distribution with an ideal frequency spectrum. The frequency spectrum slightly
changed: the frequency at 112 c/d became 113 c/d (A ∼ 1mmag) and at 81
c/d a frequency appeared with A ∼ 2mmag.
The spectral window and amplitude Fourier spectrum of the combined pattern are presented in Fig. 1.
T.N. Dorokhova and N.I. Dorokhov
41
Figure 1: The spectral window and amplitude spectrum of the combined data set.
For the case of roAp stars the frequency region of interest ranges from 70
to 260 c/d Therefore, we are especially interested in the frequencies at 71, 81
and 113 c/d.
Due to the high noise level, f4 =113 c/d is undetectable and does not appear
even after 12 steps of the analysis.
After that we applied the low-frequency Butterworth’s filters of some different cutoff frequencies and removed the low-frequency trends of the data.
We define the low frequency Butterworth’s filter in the following way:
|H(f )|2 ≈ (B/f )2M
when f B
Table 1: Artificial frequency spectrum.
No
1
2
3
4
frq.(c/d)
7
34
71
112
Ampl
10
7
3
1
Phase
0.4
0.1
0.6
0
42
Application of the Butterworth’s filter
Figure 2: The amplitude spectrum of the data after removing the low-frequency trend
by Butterworth’s filter degree M=2 and cutoff frequency B = 5%. The revealed
frequencies are: 71.01±0.01 c/d (A=1.9±0.13); 81.26 ±0.02 c/d (A=1.6±0.1);
113.15±0.02 c/d (A=1.3±0.1).The first low frequency peak is at 34 c/d. Its amplitude has decreased by 8 times but the value of frequency is practically unchanged.
The filter with such parameters is close to ideal, i.e. passes only the required
region of frequencies (see Otnes & Enochson 1978).
From experience we selected the degree M=2 and cutoff frequency B from
2 to 5%. Here we present even more rigorous cutoff frequencies B=5% (Fig.2)
and B=7% (Fig.3) studying the filters’ influence to the investigated frequency
region.
As a result of filtering the low frequencies’ amplitudes became lower (the
frequencies are not changed). Figure 4. shows the noise spectrum for different
cutoff frequencies.
At 100 c/d the noise has been reduced by 20% for B=5%, by 35% for
B=7% and up to 70% for B=10%. The reduction of the noise level enables
the astronomer to find the intrinsic frequencies sooner and more reliable.
These simple examples show that the frequency solution for the investigated
region is not distorted even by adopting a rather rigorous filter. The application
of low frequency filters appears to be more efficient and a better procedure than
corrections with low degree polynomials.
T.N. Dorokhova and N.I. Dorokhov
43
Figure 3: The amplitude spectrum of the data after removing the low-frequency trend
by Butterworth’s filter degree M=2 and cutoff frequency B = 7%. The revealed frequencies are: 113.16±0.02 c/d (A=1.1±0.1); 72.02±0.01 c/d (A=1.06±0.1); 81.26
±0.02 c/d (A=1.0±0.1).
Figure 4: The noise spectrum for: solid – the unfiltered data; dotted – after the M=2
degree and B=5% cutoff frequency filter; dash-dot-dot - after B=7% cutoff frequency
filter; dashed – after B=10% cutoff frequency filter.
44
Application of the Butterworth’s filter
References
Andronov I.L. 1994, Odessa Astronomical Publications, 7, 49
Breger M. 1990, CoAst, 20, 1
Otnes R. K., Enochson L. 1978, Applied time series analysis V.1. Basic
Technologies, New York, p. 428
Sergeev 1992, private communication
Sperl 1998, CoAst, 111, 1
Comm. in Asteroseismology
Vol. 146, 2005
PODEX – PhOtometric Data EXtractor
T. Kallinger
Institut für Astronomie, Türkenschanzstr. 17, 1180 Vienna, Austria
Abstract
New reduction tools are required to handle the increasing amount of photometric CCD data within a reasonable time. podex is an IDL based tool developed
to optimize the time needed for extracting light curves out of photometric CCD
data. The GUI based semi-automatic reduction tool provides the possibility
to apply bias correction, flat fielding, and background modeling to the raw
data. After extracting magnitudes even in crowded fields, a color–dependent
extinction correction and a conversion to relative magnitudes is performed. The
output of podex are completely reduced light curves of an arbitrary number
of stars on the CCD images. As the conditions between various nights and
observing runs change continuously and sometimes dramatically, full interactivity throughout the entire reduction procedure via a powerful graphical user
interface is a big advantage over all black-box procedures known to us.
1. Introduction
The motivation for developing podex originates in the increasing amount of
photometric CCD data and in the need to reduce them as fast as possible and
with minimum effort. Therefore, a tool is needed providing all needed reduction
steps at once.
All black-box procedures known to us (like IRAF or MOMF) are complicated to handle and provide only the extraction of instrumental magnitudes.
For a complete reduction also a color dependent extinction correction and the
conversion to relative magnitudes is needed. podex provides it.
The podex source code can be found at
http://ams.astro.univie.ac.at/computer.php
46
PODEX – PhOtometric Data EXtractor
Figure 1: Graphical user interface of podex. top left: control field; middle left:
The actual image is displayed in the raw data field. The stars of interest are marked
with cross–hair symbols on the first image. bottom left: status line; top right: The
apertures and background annulus of all used stars can be displayed in the aperture
field to control the proper definition of the aperture radii. middle right: The grey–
scaled lines indicate the instrumental light curves of all used stars. The black symbols
represent the corresponding reference light curve. bottom right: The relative (or
absolute) light curve of the actual star is displayed in the light curve field.
2. Input
After starting IDL, type ”podex” to start the graphical interface of podex.
The main input for podex is a file containing the list of CCD images to reduce
(in FITS format). podex is able to handle compressed FITS images as well.
If the images are not stored in the same directory as the list file (because the
data are on a CD or DVD, e.g.) define the full path in the list file and use the
list includes path option in the main window.
T. Kallinger
47
2.1 Preferences
The preferences of the actual session are controlled via the preference menu
(click the Change Preferences button in the control field). There is also the
possibility to import a set of preferences from a file (Load Preferences). The
session preferences are:
• FITS header keywords for date, Universal Time and integration
time of the observations:
Date and time are needed for calculation of the Julian date. Intensities are
normalized to ADU per, i. e. dividing by integration time.
• Right ascension (h:m:s) and declination (d:m:s) of the image center:
Stellar coordinates at epoch 2000.0 are used for the heliocentric correction of
the Julian date and the determination of the zenith distance.
• Geographic latitude (d:m:s) and east longitude (h:m:s) of the observatory:
Geographic coordinates are used for calculation of the zenith distance needed
for the photometric extinction correction.
• Filename of bias and flat field image:
Bias correction and/or flat fielding can be activated by using the subtract bias
and/or divide by flat options in the main window.
• Center box (pixel) for image centering:
Size of the box in which podex searches for the center of the star used to
determine the telescope pointing offset of consecutive images.
• Radius of the aperture (pixel):
Aperture radius for the brightest used star on the image.
• Inner radius and width (pixel) of the background annulus.
• Scaling factor for individual apertures (pixel per mag):
The aperture radius for fainter stars decreases by the given scale factor.
• Magnitude of star #1:
In order to compensate transparency changes in consecutive nights, the magnitude of star #1 is used as a reference.
When using a preference file, the first line of the file indicates the actual working
path. Click Save Preferences to save the actual preferences.
2.2 Coordinates
The pixel coordinates of the stars of interest are imported from a three column
file. The first two columns contain the X– and Y–coordinates on the image. The
third column an arbitrary color index (Johnson B-V, e.g.) for the corresponding
star. The color index is used for the color–dependent extinction correction. If
no color index is known, the value should be zero.
48
PODEX – PhOtometric Data EXtractor
The first star (star #1) in the list plays a special part. This star is used
for determining coordinate offsets of consecutive images due to an insufficient
pointing stability of the telescope. The star is also used as a reference light
source (use the offset correction option in the main window) to calibrate relative
magnitudes to absolute magnitudes and to compensate transparency changes
in consecutive nights. Therefore this star has to meet some special conditions.
• Star #1 should be a bright and constant star.
• Star #1 should not be located near the borders of the CCD frame.
• Inside the defined box for image centering no brighter star should be present.
podex provides the possibility to create a list of pixel coordinates. When
moving the cursor onto a target (in the raw data field) and clicking the left
mouse button, the center of the star is determined and marked by a cross-hair
symbol. Click the right mouse button, and the actual X/Y position of the cursor
and the corresponding intensity (in ADU) are displayed in the status line. Using
the Save Coordinate File button, the produced list of pixel coordinates (with
color index equal to zero) is exported to a file.
3. What is going on?
The reduction process is started by clicking the START Reduction button.
First, the bias image is subtracted from the raw image and the residual image
is divided by the flat field image (optional). After these corrections the image
is divided by integration time to normalize the intensity to ADU per second. A
sub–image (the size is defined by the preference parameter center box) centered
on the pixel coordinates of star #1 is extracted from the image. The difference
between the given coordinates for star #1 and the center of a 2–D Gaussian fit
to the sub–image defines the pointing offset in X and Y direction of the actual
image. This offset is applied to all coordinates.
3.1 The first image
The first image is used to define the individual aperture radii for all stars listed
in the coordinate list. As illustrated in Fig. 1 and Fig. 2, there is a clear relation
between the brightness of a star and the optimum aperture size (determined
by minimization of the point–to–point scatter in the light curve). Following
increasing concentric circles from the center of a star’s PSF to the border, the
signal–to–background scatter ratio grows smaller. When this ratio falls below a
certain level, including further (less exposed) pixels decreases the signal to noise
ratio of the resulting light curve. The turning point, where including pixels at
the edge of the PSF starts to decrease the resulting quality, is reached earlier
for faint stars than for bright stars.
49
T. Kallinger
For all stars listed in the coordinate file, the total amount of ADUs inside the
default aperture (defined by the preference keyword aperture radius) gives the
stellar intensity. The mean background intensity is subtracted from the stellar
intensity (see next section), and the residuals are transformed into instrumental
magnitudes. The instrumental magnitudes are used to define the individual
aperture radii. If this option is not needed, set the preference keyword scale
factor to zero. In this case the default aperture radius is used for all stars.
Instrumental magnitudes and the corresponding aperture radii are listed in the
terminal window. This list can be used to acquire color indices when starting
with images obtained with different filters.
10
scatter / minimal scatter
7.7mag
12.8mag
10.3mag
8.5mag
11.8mag
12.5mag
1
5
10
15
aperture radius (pixel)
20
Figure 2: Point–to–point scatter versus aperture radius for stars with different magnitudes. The scatter decreases with increasing aperture radius, reaches a minimum,
and starts to increase again. The size of the aperture with the least scatter in the
light curve depends on the brightness of the star. For fainter stars, smaller apertures
yield to optimum photometric quality.
3.2 Background correction
To use an annulus around the aperture to determine the background level is
sometimes problematic in crowded fields when one or more stars are located in
the background annulus. Nevertheless, podex uses such a background annulus
50
PODEX – PhOtometric Data EXtractor
22
aperture radius (pixel)
20
18
16
14
12
10
8
7
8
9
10
11
magnitude
12
13
14
Figure 3: Mean instrumental magnitude versus aperture radius associated to minimum
point–to–point scatter in the resulting light curve. The solid line represents a linear
regression, illustrating the high degree of linearity in the relation between aperture
radius and stellar brightness. Here the individual aperture radius decreases with about
2 pixel per magnitude.
but tries to ignore pixels exposed to stellar light (or cosmics). Hence the mean
intensity level and standard deviation of all stars inside the background annulus
(defined by the preference keywords inner radius and width) is determined. If
a pixel intensity exceeds the mean level by more than three times the standard
deviation, the corresponding pixel is rejected. The mean intensity and standard
deviation of all accepted pixels is re–calculated. The procedure is repeated until
no pixels are rejected but only up to 5 times.
3.3 Extraction of instrumental light curves
After defining the individual aperture radii, the reduction procedure extracts the
total intensity for all apertures, subtracts the corresponding mean background
level (multiplied by the number of pixels inside the aperture), and transforms
the residuals into instrumental magnitudes for all images given in the input file.
T. Kallinger
51
Figure 4: Left: Background annulus with containing a star. Right: Pixels exposed to
stellar light are not used to determine the mean background level around the aperture
(the star of interest is located inside the inner circle).
3.4 Color–dependent extinction correction
If a color index (CI) is given in the coordinate file and the option extinc. cor. in
the control field is selected a color dependent extinction correction is performed
for all instrumental light curves. First, the mean magnitude is subtracted from
all instrumental light curves. Then the extinction coefficient for an individual
light curve is computed as the slope of a linear regression in the Bouguer plot
(magnitude versus airmass X). There is a linear relation between the extinction coefficients and the corresponding CI. Again, a linear regression is used to
define the coefficients k0 and k1 . The instrumental light curves are corrected by
magcorr = maginstrumental − X · (k0 + CI · k1 ).
If no color indices are given, the extinction correction is not necessary because the differential extinction for different stars is too small to effect the
resulting light curves. (The typical field of view of a CCD images is not larger
than a few arcminutes). The average extinction of the field of view is corrected
by subtracting the reference light curve.
3.5 Reference light curve
The reference light curve corresponds to the weighted mean of all instrumental
light curves. The weight of an individual light curve is defined by the inverse
D–value divided by the variance of the corresponding light curve. The D–value
is the ratio between the standard deviation and the point–to–point scatter of
a light curve. The D–value is used as an estimator for variability in the light
curve. A light curve with a high D–value and/or a high variance has low weight
52
PODEX – PhOtometric Data EXtractor
for the reference light curve. Clicking the Calc Va-Cp button, the reference
light curve is determined and subtracted from the light curve of star #1. The
resulting relative (or absolute, if the offset cor. option is used) light curve
is displayed in the light curve field. The > (<) button switches to the light
curve of the next (previous) star in the coordinate list. The reference light
curve is determined without the star currently displayed. podex also provides
the possibility to exclude stars from calculation of the reference light curve.
The stars to be encountered are selected in the use menu. Mean magnitude,
variance, D–value, and weight of all light curves are listed in the terminal
window. Mean magnitude, standard deviation, and D–value of the currently
displayed star are listed in the status line.
3.6 Outlier rejection
Outliers can be rejected from the light curve by moving the cursor onto the
data point in the light curve field and press the left mouse button. The recently
rejected data point can be included again with the undo button.
4. Output
With the Save current star button the heliocentric Julian date, relative (or
absolute if the offset cor. option is used) magnitude, reference magnitude and
the airmass of the actual star are saved in a file. With the Save all stars
button the heliocentric Julian date and the instrumental magnitudes of all stars
are saved in a single file.
Acknowledgments.
This work is supported by the Austrian Fonds zur
Förderung der wissenschaftlichen Forschung (FWF) within the project Stellar Atmospheres and Pulsating Stars (P14984), and the Bundesministerium
für Verkehr, Innovation und Technologie (BMVIT) via the Austrian Space
Agency (ASA).
Comm. in Asteroseismology
Vol. 146, 2005
Period04 User Guide
P. Lenz, M. Breger
Department of Astronomy, Univ. Vienna, Türkenschanzstrasse 17,
1180 Vienna, Austria
Abstract
Period04, an extended version of Period98 by Sperl (1998), is a software
package designed for sophisticated time string analysis. In this article we
present the User Guide for Period04.
Contents
1.
Introduction
1.1
1.2
1.3
2.
. . . . . . . . . . . . . . . . . . . . .
The Graphical User Interface
2.1
2.2
2.3
2.4
2.5
2.6
2.7
2.8
55
Backwards compatibility . . . . . . . . . . . . . . . . .
Obtaining Period04 . . . . . . . . . . . . . . . . . . . .
Requirements . . . . . . . . . . . . . . . . . . . . . . .
. . . . . . . . . . . .
The main window . . . . . . . . . . . . . . . . . . . .
The menu bar . . . . . . . . . . . . . . . . . . . . . .
2.2.1
The ’File’ menu . . . . . . . . . . . . . . . .
2.2.2
The ’Special’ menu . . . . . . . . . . . . . .
2.2.3
The ’Options’ menu (available in expert mode
only) . . . . . . . . . . . . . . . . . . . . . .
2.2.4
The ’Help’ menu . . . . . . . . . . . . . . .
The status bar . . . . . . . . . . . . . . . . . . . . . .
The ’Time string’ tab . . . . . . . . . . . . . . . . . .
The ’Fit’ tab . . . . . . . . . . . . . . . . . . . . . . .
2.5.1
The Main tab . . . . . . . . . . . . . . . . .
2.5.2
The ’Goodness of Fit’ tab . . . . . . . . . .
The ’Fourier’ tab . . . . . . . . . . . . . . . . . . . .
The ’Log’ tab . . . . . . . . . . . . . . . . . . . . . .
Dialogs . . . . . . . . . . . . . . . . . . . . . . . . . .
2.8.1
The ’Weight selection’ dialog . . . . . . . . .
2.8.2
The ’Subdivide time string’ dialog . . . . . .
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2.8.3
2.8.4
2.8.5
2.9
2.10
2.11
2.12
2.13
2.14
3.
Getting Started . . . . . . . . . . . . . . . . . . . . 105
3.1
3.2
4.
The ’Combine substrings’ dialog . . . . . . . . 78
The ’Show time structuring’ dialog . . . . . . 79
The ’Calculate specific Nyquist frequency’ dialog (available in expert mode only) . . . . . 80
2.8.6
The ’Adjust time string’ dialog . . . . . . . . . 80
2.8.7
The ’Set default label for deleted points’ dialog 82
2.8.8
The ’Relabel data point’ dialog . . . . . . . . 82
2.8.9
The ’Edit substring’ dialog . . . . . . . . . . . 83
2.8.10
The ’Calculate epoch’ dialog . . . . . . . . . . 83
2.8.11
The ’Recalculate residuals’ dialog . . . . . . . 84
2.8.12
The ’Predict signal’ dialog . . . . . . . . . . . 85
2.8.13
The ’Create artificial data’ dialog . . . . . . . 85
2.8.14
The ’Set alias-gap’ dialog . . . . . . . . . . . 86
2.8.15
The ’Show analytical uncertainties’ dialog . . . 86
2.8.16
The ’Improve special’ dialog . . . . . . . . . . 87
2.8.17
The ’Calculate amplitude/phase variations’ dialog . . . . . . . . . . . . . . . . . . . . . . . 88
2.8.18
The ’Monte Carlo simulation’ dialog . . . . . . 89
2.8.19
The ’Calculate noise at frequency’ dialog . . . 90
2.8.20
The ’Calculate noise spectrum’ dialog . . . . . 91
Plots . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
2.9.1
Time string plots . . . . . . . . . . . . . . . . 94
2.9.2
Phase plots . . . . . . . . . . . . . . . . . . . 95
2.9.3
Fourier plots . . . . . . . . . . . . . . . . . . 96
Tables . . . . . . . . . . . . . . . . . . . . . . . . . . . 97
Period04 preferences . . . . . . . . . . . . . . . . . . . 98
The expert mode . . . . . . . . . . . . . . . . . . . . . 100
The Data Manager (expert mode only) . . . . . . . . . 101
Overview of Shortcuts: . . . . . . . . . . . . . . . . . . 104
Tutorial 1: A first example . . . . . . . . . . . . . . . . 105
Tutorial 2: Least-squares fitting of data including a periodic time shift . . . . . . . . . . . . . . . . . . . . . . 112
Using Period04 . . . . . . . . . . . . . . . . . . . . 118
4.1
4.2
4.3
Topics related to time string data . . . . . . . . .
4.1.1
Importing time strings . . . . . . . . . .
4.1.2
Exporting time string data . . . . . . . .
4.1.3
Creating artificial data . . . . . . . . . .
Topics related to Fourier calculations . . . . . . . .
4.2.1
Calculation of Fourier spectra . . . . . .
4.2.2
Significance of frequencies . . . . . . . .
Topics related to least-squares calculations . . . . .
4.3.1
Calculation of least-squares fits . . . . .
4.3.2
Calculation of amplitude/phase variations
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4.4
5.
4.3.3
Using the periodic time shift mode
4.3.4
Estimation of uncertainties . . . .
General topics . . . . . . . . . . . . . . . .
4.4.1
Using weights . . . . . . . . . . .
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Copyright notice . . . . . . . . . . . . . . . . . . . 135
5.1
Third party software . . . . . . . . . . . . . . . . . . . . 135
1. Introduction
Period04 is a computer program especially dedicated to the statistical analysis
of large astronomical time series containing gaps. As its predecessor, Period98,
the program offers tools to extract the individual frequencies from the multiperiodic content of time series and provides a flexible interface to perform
multiple-frequency fits.
Fundamentally, the program is composed of 3 modules:
• The Time String Module
Within this module the user administrates the time string data. The
module contains tools to split a data set into substrings, combine data
sets, set weights, etc.
• The Fit Module
Least-squares fits of a number of frequencies can be made in this module.
Apart from basic fitting techniques, Period04 also contains the possibility
to fit amplitude and/or phase variations, or to take into account a periodic
time shift. Furthermore, several tools for the calculation of uncertainties
of fit parameters, such as Monte Carlo simulations, are available.
• The Fourier Module
For the extraction of new frequencies from the data, this module is provided. The Fourier analysis in Period04 is based on a discrete Fourier
transform algorithm. We do not use a Fast Fourier Transform (FFT)
algorithm as astronomical time string data sets usually are not equally
spaced.
Some tools or functions are only accessible when the program operates in
the so called ’Expert mode’. A detailed description of the expert mode can be
found in section 2.12.
Period04 is project oriented and saves all data (time string data, Fourier
spectra, frequencies and the log) in one central project file. The project file
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Period04 User Guide
itself is completely platform independent. This allows the user to switch between
various operating systems. As the program also stores the current program
settings along with the data, it is easy to resume work on a project.
1.1 Backwards compatibility
Period04 is based on Period98 by Sperl (1998). Period98 project files (.p98) can
be read by Period04 without any problems. The default extension for Period04
project files is .p04 though.
1.2 Obtaining Period04
Period04 is freely available and has been compiled for Linux, Windows and
MacOSX. The program can be downloaded from the Period04 website:
http://www.astro.univie.ac.at/ dsn/dsn/Period04/.
The installers will guide you through the installation process.
1.3 Requirements
Period04 is a Java/C++ hybrid program. Therefore, to run the program a
Java Runtime Environment (JRE) has to be installed. The JRE is already
preinstalled on every Mac OS X System. Windows and Linux users will have
to check if there already exists a JRE on their system. To do that simply
open a shell or a command prompt and type ’java -version’ If the command
is not found no Java is installed. In this case you have to download it from
http://java.sun.com/getjava. It is free. If the ’java’ command exists, please
check the version number. The Period04 binary works with all versions from
1.4.2.
P. Lenz and M. Breger
57
2. The Graphical User Interface
In this chapter the Period04 User Interface will be explained in detail.
2.1 The main window
The main window of Period04 consists of 3 parts: the menu bar at the top, the
status bar at the bottom and a tabbed frame in the center. The tabbed frame
contains 4 folders:
Time string
Fit
Fourier
Log
a module for the management of time string data
a flexible interface for least-square fitting
a module for the calculation of Fourier transforms
contains the protocol of all actions taken
The ’Time string’ folder is activated by default after start-up.
2.2 The menu bar
The menu bar gives access to 3 menus (File, Special and Help) in default mode,
whereas in the expert mode an additional menu entry, Options, is available. See
Section 2.12: ’The expert mode’ for more details on additional features.
2.2.1 The ’File’ menu
Figure 1: The ’File’ menu
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Period04 User Guide
• New Project
This command closes the current project and creates a new empty project.
• Load Project
Use this command to open an existing Period04 (or Period98) project
file. The file extension of Period04 projects is ’.p04’.
• Save Project
Save the complete project (time string data, frequencies, Fourier spectra,...) into a file. If you save the project for the first time you will be
asked to provide a name and a path for the file. Thereafter, each time
you save, the changes will automatically be written to this file.
• Save Project As
Provides the possibility to save the current project under a different name.
• Recent project-files
Gives instant access to up to 10 recently edited projects. The file paths
of projects are saved in a file named ’.period04-recentfiles’ which can be
found in the user directory.
• Import
This menu entry contains the following entries:
– Import time string:
Imports a time string from a file. If the project already contains
time string data the user will be asked whether he wants to erase
the old time string. Please see section 4.1.1 for further details on
this topic.
– Import frequencies:
Import frequencies, amplitudes and phases from a file.
• Export
The ’Export’ menu entry holds three items:
– Export time string:
Saves selected data columns into a file. Please see section 4.1.2 for
further details.
– Export frequencies:
Saves frequency data into a file.
– Export log file:
Saves the protocol into a file.
P. Lenz and M. Breger
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• Manage Data (available in expert mode only)
This command opens the Data Manager (section 2.13), a tool to edit
project data.
• Expert mode
If the ’Expert mode’ check box is selected, you will have access to additional tools (see section 2.12). This option is by default deselected.
• Quit
Quits the program. If the project has changed since the last backup the
user will be reminded to save the project before closing the program.
2.2.2 The ’Special’ menu
The special menu contains tools related to time string management, leastsquares fitting and Fourier noise calculations.
Figure 2: The ’Special’ menu in expert mode
• Weight selection
Starts a dialog for activating weights. The chosen weight selection will
be used in Fourier calculations as well as in least-squares calculations.
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Period04 User Guide
Time string related menu entries:
• Subdivide time string
Opens a dialog to divide the time string into substrings.
• Combine substrings
Opens a dialog to combine substrings.
• Calculate Nyquist frequency (available in expert mode only)
Calculate the Nyquist frequency for a user-defined time range.
• Show time structuring
Show some information on the time structuring of the current time string.
• Adjust time string
Opens a dialog for adjusting zero-point variations.
• Set default label for deleted points
Opens a dialog to define the default name and the attribute of the substring in which deleted data points will be put.
• Delete selected points
Deletes all points belonging to the currently selected time string irrevocably.
Menu entries related to least-squares fitting:
• Select all frequencies
Selects all frequencies in the Fit Module.
• Deselect all frequencies
Deselects all frequencies in the Fit Module.
• Clean all frequencies
Cleans the frequency list in the Fit Module.
• Calculate epochs
Calculates the times of epochs for every active frequency.
• Recalculate residuals
Recalculate the residuals using the current selection of time points and a
user-defined zero point.
• Predict signal
Predict the magnitude or intensity at a specific time according to the
current fit.
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• Create artificial data
Opens a dialog for creation of artificial data.
• Set alias-gap
Opens a dialog to set the step size for frequency adjustments.
• Show analytical uncertainties
Opens a window that displays the parameter uncertainties based on the
assumption of an ideal case.
Menu entries related to Fourier calculations:
• Calculate noise at frequency
Opens a dialog to calculate the noise at a specific frequency.
• Calculate noise spectrum
Provides a tool to calculate a noise spectrum.
2.2.3 The ’Options’ menu (available in expert mode only)
Figure 3: The ’Options’ menu
• Set fitting function
Period04 contains the possibility to change the fitting formula. Apart
from the default calculation mode, a fit including a periodic time shift
can be made.
2.2.4 The ’Help’ menu
• Period04 Help
Launches the Period04 help system.
• Topics
Gives access to certain Period04 topics in the help system.
• Tutorials
Launches the help system and shows the main page for the tutorials.
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Period04 User Guide
Figure 4: The ’Help’ menu
• Shortcuts
Opens a page that lists all shortcuts that are supported by Period04.
• Period04 - Homepage
Launches a web browser and navigates to the Period04 homepage.
• Report a bug
Provides instructions for the submission of bugs.
• Copyright
Displays the copyright notice.
• About
Displays some information (i.e., the version number) about your copy of
Period04.
2.3 The status bar
The status bar shows additional messages to inform the user of the status of the
program. In case of File I/O actions a progress bar is displayed that indicates
the progress of the task.
2.4 The ’Time string’ tab
The Time String Module is dedicated to edit time string data. In the upper
part of the ’Time string’ tab buttons for loading and saving time string data
are located:
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63
Figure 5: The status bar showing its default message.
Figure 6: The status bar showing the progress while loading a project.
• Import
Import time string data. If the current project is not empty, then the old
time string data will be replaced and the remaining project data (frequencies, Fourier spectra and the log) will be erased.
• Append
Add a time string to the time string of the current project.
• Export
Save time string data to a file.
The text box next to the buttons contains the full path-names of the files
from which the data have been imported. Below the text box some properties
of the currently selected time string are shown:
• Points selected
The number of points that are currently selected.
• Total points
The total number of points in the time string.
• Start time
The lowest time value of the currently selected time string.
• End time
The highest time value of the currently selected time string.
• Check box ’Time string is in magnitudes’
If your data are in magnitudes instead of intensity this option should
be selected. In case of magnitudes the y-axis of time string plots will be
reversed – it is also important for correct epoch calculation. By default the
program assumes that the data are in magnitudes. It is possible to change
the default setting by editing the Period04 preferences (section 2.11).
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Period04 User Guide
Figure 7: The ’Time string’ tab.
The main part of the ’Time string’ folder is made up of 4 list boxes. Each
list box represents an attribute for the time string data. If you did not read in
any attributes then the lists will show the entry ’unknown’. The names of the
attributes can be changed by clicking on the headings on the top of the lists.
You may also change the default names by editing the preferences file.
In the lower part of the Time String Module there are several buttons:
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65
• Edit substring
Click on this button to edit the properties (name, color and weight) of
the currently highlighted items (substrings) of the list. See section 2.8.9
for further details.
• Display table
Displays a list containing the full information on all data points of the
selected time string.
• Display graph
Plots the selected time string and, if the resolution of the viewport is high
enough, shows the current fit as well.
The columns in the Time String Module provide a pop-up menu too. The
following entries are currently available:
• Edit substring properties
Opens a dialog to edit the properties of a substring.
• Select all substrings
Selects all substrings in the current list box.
Figure 8: The pop-up menu for the list boxes in the Time String Module
2.5 The ’Fit’ tab
The ’Fit’ folder itself contains two tabs:
• Main
The ’Main’ tab contains the frequency list, a panel to define the settings
for least-squares calculations and several buttons to start calculations.
• Goodness of Fit
This tab provides tools for the calculation of uncertainties.
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Period04 User Guide
Figure 9: The ’Fit’ tab.
2.5.1 The Main tab
In the upper part of the ’Main’ folder buttons for loading or saving frequencies
are situated. If the frequencies are imported from an external file, the file to be
imported has to be formatted as shown below:
F1
F2
F3
8.245592
8.866320
(8.514142
0.036872
0.031595
0.009952
0.191925
0.201285
0.811823 )
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67
If the frequency parameters are enclosed by parentheses, the frequency will
appear inactive in the frequency list.
Furthermore, some information regarding the current fit is given:
• Selected frequencies
The total number of active frequencies. A frequency is active (and will
be included into calculations) when the respective check box is selected
in the frequency list.
• Zero point
The zero point of the magnitudes/intensities resulting from the last calculated fit.
• Residuals
The residuals (χ) for the last calculated fit.
To the left of the import/export buttons and to the right of the information
labels there is a toggle button, respectively.
Figure 10: The toggle buttons.
A click on the left hand side toggle button detaches the ’Time string’ tab
from the main frame and places the ’Time string’ panel to the left of the main
frame, whereas a click on the right hand side toggle button causes the ’Fourier’
tab to be detached and placed to the right of the main frame.
If your screen is wide enough this makes it possible to use Period04 without
having to switch between the different tabs.
Settings for least-squares fit calculations:
• Fitting formula
Displays the formula that is being used for least-squares fits.
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Period04 User Guide
• Calculations based on
This defines the type of data (Original or Adjusted) to be used for the
next least-squares calculation.
• Use weights
Displays a string that indicates which weights are being used for the
least-squares calculation. If no weights are used ’none’ will be displayed.
1
2
3
4
p
d
use
use
use
use
use
use
the weights assigned
the weights assigned
the weights assigned
the weights assigned
point weight
deviation weight
to
to
to
to
the
the
the
the
substrings
substrings
substrings
substrings
of
of
of
of
attribute
attribute
attribute
attribute
#1
#2
#3
#4
• Edit weight settings
Opens the weight-selection dialog.
The frequency list:
In the default mode the frequency list consists of input fields for frequency,
amplitude and phase values and corresponding check boxes. If a check box is
selected, then the respective non-zero frequency will be included in the next
least-squares calculation.
Input options for frequency fields:
It is possible to enter harmonics or frequency combinations into frequency
fields as shown in the examples below:
=2f1 or =2*f1
for the second harmonic of f1.
=f1+f3
for a combination frequency which is defined as
the sum of f1 and f3.
=2f1-3f4
or =2*f1-3*f4
for a combination frequency which is defined as
the difference of the second harmonic of f1 and
the third harmonic of f4.
Please note:
A reference to a frequency, which is a combination itself, will be rejected by the
program. If one of the frequencies listed in the combination is not active, the
combination is not active either.
P. Lenz and M. Breger
69
If a frequency is a combination, a little button showing the letter ’C’ will
appear between the frequency check box and the frequency input field. Click
on this button to show the frequency value instead of the combination string
and vice versa.
Figure 11: Example for an example combination frequency
Adding or subtracting the alias-gap value:
In order to add the alias-gap value to the frequency value, enter a trailing
’+’. Type ’-’ if you want to subtract the alias-gap value. Multiple ’+’ or ’-’
can also be used, e.g., ’34.11+++’ means 34.11 with three times the alias-gap
value added. The default value for the alias-gap can be set by using the ’Set
alias-gap dialog’ (section 2.8.14).
Extensions for the periodic time shift mode (available in expert mode only)
See also section 4.3.3: ’Using the periodic time shift mode’ for an instruction
on how to activate this option. If the periodic time shift (PTS) mode is active
the frequency list is extended to contain input fields for the periodic time shift
parameters.
Figure 12: The frequency panel in the periodic time shift mode.
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Period04 User Guide
Furthermore, two additional buttons are available:
• Search PTS start values
Searches for a good start value within a given range by means of Monte
Carlo shots.
• Improve PTS
Starts a least-squares calculation to improve the time shift parameters.
For this calculation all three parameters of the periodic time shift will be
improved, while the parameters of all other frequencies will be kept fixed.
Please note:
For the periodic time shift mode the buttons for showing the phase plot and
the calculation of amplitude and/or phase variations will not be available.
2.5.2 The ’Goodness of Fit’ tab
In this tab the uncertainties of the parameters can be calculated. See ’Estimation of uncertainties’ (section 4.3.4) for further details.
• Info
Launches the Period04 help system and shows a page with some information on how to use Period04 to estimate the uncertainties of fit
parameters.
• Calculate LS uncertainties
Calculates either correlated or uncorrelated uncertainties for the fitted
parameters via a least-squares calculation.
• Monte Carlo Simulation
Opens a dialog which allows for the calculation of uncertainties for the
fitted parameters by means of a Monte Carlo simulation.
• Print list
Prints the content of the text field.
• Export list
Opens a file-selector to save the content of the text field to a file.
P. Lenz and M. Breger
Figure 13: The ’Goodness of Fit’ Tab
2.6 The ’Fourier’ tab
The ’Fourier’ folder basically consists of two parts:
• a panel for the Fourier calculation settings
• a list box that contains all Fourier spectra calculated so far.
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Period04 User Guide
Figure 14: The ’Fourier’ tab.
The Fourier calculation settings panel
• Title
Defines the name of the Fourier spectrum.
• From / To
Defines the frequency range for the spectrum.
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• Step rate
Defines the accuracy of the frequency grid for the Fourier calculation.
Three default options for the step rate quality are available and can be
selected by the combo-box: High, Medium and Low. In order to set a
user-defined value, select ’Custom’ and type the desired value into the
input field next to the step rate combo-box.
Please note: The smaller the step rate the longer the calculation will take.
• Nyquist
Displays the Nyquist frequency for the time string that is currently selected. This value should be a good estimate for the upper frequency
limit due to the sampling pattern for the current data set. The algorithm
estimates the average time gap between neighboring points while ignoring
large gaps.
• Use weights
Displays a string that indicates which weights are being used for the
Fourier calculation. If no weights are used ’none’ will be displayed.
1
2
3
4
p
d
use
use
use
use
use
use
the weights assigned
the weights assigned
the weights assigned
the weights assigned
point weight
deviation weight
to
to
to
to
the
the
the
the
substrings
substrings
substrings
substrings
of
of
of
of
attribute
attribute
attribute
attribute
#1
#2
#3
#4
• Edit weight settings
Opens the weight-selection dialog.
• Calculations based on
Defines the type of data to be used for the calculation: ’Original data’,
’Adjusted data’, ’Residuals at original’ or ’Residuals at adjusted’. If ’Spectral window’ is chosen the program will calculate the spectral window
which is centered at zero frequency and reflects the pattern caused by
the structure of gaps in the time string.
• Compact mode
The output of the Fourier calculation can be quite extensive. To reduce
the output ’Peaks only’ can be selected. In this case only local maxima
and minima are saved. If ’All’ is selected, all data points of the spectrum
are stored.
To start the calculation based on the settings in the Fourier Module either
press the button ’Calculate’ or type the shortcut ’Alt+C’.
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Period04 User Guide
The Fourier list
All calculated Fourier spectra are listed in the Fourier list box. For every
spectrum the title of the spectrum and, in parentheses, the frequency and amplitude of the highest peak is given. By selecting a spectrum the settings for
that calculation will be loaded and displayed.
The buttons below the list provide the following functions:
• Rename spectrum
Change the title of the highlighted Fourier spectrum.
• Export spectrum
Save the data points of the highlighted Fourier spectrum into a file. In
order to export a set of spectra the Data Manager should be used.
• Delete spectrum
Erase the highlighted Fourier spectrum.
• Display table
Show the table of data points for the highlighted Fourier spectrum.
• Display graph
Show the highlighted Fourier spectrum as a plot on the monitor.
Please note:
The functions of these buttons are also accessible by a pop-up menu.
Figure 15: The pop-up menu for the Fourier list.
P. Lenz and M. Breger
2.7 The ’Log’ tab
Period04 logs all actions taken. It is possible to edit, print or save the log.
Figure 16: The ’Log’ Folder
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Period04 User Guide
2.8 Dialogs
2.8.1 The ’Weight selection’ dialog
In the ’Weight selection’ dialog the user selects the weights that should be used
for Fourier and least-squares calculations. Multiple selections are possible. See
’Using weights’ (section 4.4.1) for a detailed description of setting weights.
Figure 17: The ’Weight selection’ dialog
Period04 supports 3 types of weights:
• weights assigned to the substrings of an attribute
If you decided to give your substrings different weights in one or several
of the four attributes and you want to include them in the calculations,
then select the appropriate attribute weight.
• point weight
If you read in a point weight for each of your data points and want to
use them in your calculations, then select this weight.
• deviation weight
If this option is active the data points will be weighted based on their
residual value. ’Cutoff’ defines a limit residual value. If the residual of
the data point is within this limit, then its weight is set 1.0, otherwise
the weight will be calculated based on the residual and the cutoff value.
2.8.2 The ’Subdivide time string’ dialog
To split the time string into subgroups based on times of measurements select
’Subdivide time string’ in the ’Special’ menu. Period04 offers two alternative
ways of dividing a time string into substrings. The dialog box prompts the user
to choose the desired type of subdivision:
P. Lenz and M. Breger
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Figure 18: The ’Subdivide data’ dialog
• Subdivide by gaps
The program will search for time gaps between consecutive points that
are larger than a user-defined value. The data set is then subdivided by
these gaps.
• Subdivide by fixed intervals
If you want to divide the time string into substrings using a fixed time
interval then select this option.
According to your selection one of the dialogs shown in Figs. 19 and 20 will
open. Below the dialogs an appropriate time string plot shows the difference
between the two kinds of subdivisions applied to one and the same data set:
For a subdivision the following informations are needed:
• Size of the gap
Defines the minimum gap size (using the same time unit as your time
string). If two consecutive points are separated more than the given
value then a subdivision will be made.
• Start time
Only data points after this time value will be subdivided. Defaults to the
lowest time value of the time string.
• Time interval
Defines the length of the interval for the subdivision.
• Choose the attribute you want to subdivide
Defines the attribute (column) in which the subdivision should take place.
• Label prefix
The final labels of the substrings are constructed in the following way:
[prefix] + [average time of the substring]
Here you can define this prefix.
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Figure 19: Subdivide by
gaps
Figure 20: Subdivide by
fixed intervals
Figure 21: An example
for ’Subdivide by gaps’
Figure 22: An example
for ’Subdivide by fixed intervals’
• Use running counter
If this option is selected the program constructs the final label of the
substrings in the following way:
[prefix] + [a running counter]
• Decimal places to use from time
The number of digits that will be used for the labels of the substrings.
2.8.3 The ’Combine substrings’ dialog
This is the inverse operation to ’Subdivide time string’ (section 2.8.2). In order
to combine a number of substrings first highlight the substrings you want to join.
Then open the ’Combine substrings’ dialog (Special / Combine substrings).
Two values have to be defined:
• Attribute
Select the attribute in which the substrings should be combined.
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Figure 23: The ’Combine substrings’ dialog.
• New name
Enter the name for the resulting substring in this field.
2.8.4 The ’Show time structuring’ dialog
This dialog displays some information on the structure of the time string. For
every substring of the selected attribute the following data are given:
• Start / End time
• Length
• Mean time
• Number of points that belong to the substring
Figure 24: The ’Show time structuring’ dialog.
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Finally the total observing time and the total mean time of the time string
are given. If ’Time unit is in days’ is selected, the length of the substrings and
the total observing time will be converted into hours, otherwise they will be
given using the same time unit as your time string.
The content of the text area can be printed and saved to a file by clicking
on the appropriate button at the bottom of the dialog.
2.8.5 The ’Calculate specific Nyquist frequency’ dialog (available in expert
mode only)
Sometimes it is useful to calculate the Nyquist frequency based on data points
within a specified time range. To open the dialog choose ’Calculate specific
Nyquist frequency’ from the ’Special’ menu.
Figure 25: The ’Calculate Nyquist frequency’ dialog.
Enter the desired time range and press ’Calculate’ to get the appropriate
Nyquist frequency.
2.8.6 The ’Adjust time string’ dialog
It might occur that your substrings have marginally different zero-point offsets
in magnitude/intensity. This can be caused by different instrumentation, or
different observational conditions for these substrings.
Zero-point variations entail additional noise in the low frequency domain.
To reduce this noise source, one has to adjust the zero-point offsets. This can
be done through the ’Adjust time string’ dialog.
Before you open the dialog, however, you should calculate a fit as this routine uses the residuals to calculate the zero-point offsets. Select the appropriate
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Figure 26: The ’Adjust time string’ dialog.
attribute to show the set of given substrings. If weights should be used to calculate the average and the sigma values then select ’Use weights’.
In the list several columns are shown:
• Label
The name of the substring.
• Observed or Adjusted
Shows the mean value of Observed or Adjusted, respectively.
• Sigma(Obs./Adj.)
Shows the deviation of Observed or Adjusted.
• Points
The number of points that belong to the given substring
• Adjusted
If this column contains the entry ’Yes’ some or all points of the specific
substring have already been adjusted.
In order to adjust the data, select the substrings and press ’Adjust’. The
result will be displayed. You may export or print the content of the text box by
pressing the appropriate button.
Please note:
Remember to select ’Adjusted data’ for all further calculations!
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2.8.7 The ’Set default label for deleted points’ dialog
By default Period04 does not delete points directly, but adds them to a substring
labeled as ’deleted’ in the attribute ’Other’. As the user might prefer other
settings, the label and the position (that is the attribute) can be changed using
this dialog. To open the dialog select ’Set default label for deleted points’ in
the ’Special’ menu.
Figure 27: The ’Set default label for deleted points’ dialog.
• Put deleted points as attribute
Defines in which attribute the substring containing the deleted points will
appear.
• Label to use for deleted points
Defines the default name for the substring that contains the deleted
points.
After pressing ’OK’ the new settings will take effect.
2.8.8 The ’Relabel data point’ dialog
The ’Relabel data point’ dialog appears through a click with the right mouse
button on a data point in a time string plot. It is also accessible via the pop-up
menu of the time string data table.
Figure 28: The ’Relabel data point’ dialog.
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Using this dialog it is possible to change the labels for the chosen point in
each attribute. For clarification: the label refers to the name of the substring
that includes this point.
2.8.9 The ’Edit substring’ dialog
Figure 29: The ’Edit substring’ dialog.
The ’Edit substring’ dialog can be accessed through the ’Edit substring’
buttons on the ’Time string’ tab or by using the pop-up menu of the attribute
lists. This dialog (Fig. 29) shows the current properties (name, weight and
color) of the substring.
Name refers to the label of the substring that currently contains this point.
Weight assigns the given weight to all points of the selected substring. See
’Using weights’ (section 4.4.1) for more information on using weights for calculations. Color defines the color of this substring to be used for plots.
2.8.10 The ’Calculate epoch’ dialog
To calculate the epochs close to a given time open ’Calculate epoch’ in the
’Special’ menu. Please note that this calculation is based on the last fit.
It is possible to calculate the time of either
• Maximum light (maximum intensity, respectively)
• Minimum light (minimum intensity, respectively)
• Zero point, the time when the fit crosses the average of the fitted function
(1/4 period before the maximum light).
Note that the program already knows whether you are using magnitudes
(maximum light at minimum value) or intensities.
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Figure 30: The ’Calculate epoch’ dialog
The values for the epoch will be evaluated close to a given time, that has
to be entered into the respective input field.
After pressing ’Calculate’, the results will be displayed in the text box. The
first column is the frequency number, the second column shows the value for
the frequency and finally, in the last column the time of the epoch is displayed.
You may export or print the content of the text box by pressing the appropriate
button at the bottom of the dialog.
2.8.11 The ’Recalculate residuals’ dialog
For the purpose of recalculating the residuals using an other zero-point, select
’Recalculate residuals’ in the ’Special’ menu.
Figure 31: The ’Recalculate residuals’ dialog
Enter a new zero-point value into the input field and press ’OK’ to start the
calculation.
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2.8.12 The ’Predict signal’ dialog
If you want to calculate the signal at a given time, open the ’Predict signal’
dialog (Special / Predict signal).
Figure 32: The ’Predict signal’ dialog
The dialog displays the start time of the currently selected time string. Below this line a specific time can be entered at which the signal will be calculated
based upon the last fit. After pressing ’Calculate’ the result will be shown.
2.8.13 The ’Create artificial data’ dialog
Period04 also supports the creation of equally spaced artificial data. If desired
even a periodic time shift can be included. You may also refer to ’Creating
artificial data’ (section 4.1.3) for a step-by-step guide about how to use this
feature.
Figure 33: The ’Create artificial data’ dialog
• Start-time / End-time
Defines the time range for which data should be generated.
• Read time ranges from file
Press this button to read in multiple time ranges from a file. Such a file
should contain two columns: in the first column the start times should
be given and in the second column the respective end times.
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• Step
Period04 will create data points that are equally spaced in time. This
field defines the step size in time.
• Leading/trailing time
If this option is non-zero the time range(s) will be extended by the given
value.
Before the generation of the artificial data set starts, a file name has to be
specified in which the output will be written. Press ’Write data to the following
file’ and define the name and the path of the file in the file-selector dialog. If
the file already exists the user will be prompted whether he wants to append
the data to the existing file or to replace the file.
2.8.14 The ’Set alias-gap’ dialog
The alias-gap dialog allows for the definition of the step size for frequency adjustments. This value will be added or subtracted from a frequency when you
enter a trailing ’+’ or ’−’ to the respective frequency in the frequency list of
the Fit Module.
To open this dialog select ’Set alias-gap’ from the ’Special’ menu. After
changing the old value and pressing ’OK’ the new settings will take effect.
Figure 34: The ’Set alias-gap’ dialog
2.8.15 The ’Show analytical uncertainties’ dialog
This dialog displays the parameter uncertainties calculated from formulae which
assume an ideal case. See Breger et al. (1999) for the derivation of uncertainties
for frequency, phase and amplitude based on a mono periodic fit. If cross
terms can be neglected the equations can also be applied for each pulsation
frequency separately. See ’Estimation of uncertainties’ (section 4.3.4) for more
information.
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Figure 35: The ’Show analytical uncertainties’ dialog
You may export or print the content of the text area by pressing the appropriate button at the bottom.
Please note:
This option is only available when the standard fitting formula is being used.
2.8.16 The ’Improve special’ dialog
The ’Improve special’ dialog appears when you press the ’Improve special’ button in the Fit Module.
Figure 36: The ’Improve special’ dialog
The dialog consists of three list boxes that contain all currently available
frequency, amplitude and phase parameters. Select the parameters you want
to improve and press ’OK’ to start the least-squares calculation. Unselected
parameters will be kept fixed.
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2.8.17 The ’Calculate amplitude/phase variations’ dialog
This dialog opens up when you press the ’Calculate amplitude/phase variations’
button in the Fit Module. It offers the possibility to calculate amplitude and/or
phase variations. Please also see ’Calculating amplitude/phase variations’ (section 4.3.2) for a step-by-step guide on how to use this tool.
Figure 37: The ’Calculate amplitude/phase variations’ dialog
Calculation settings:
• Attribute to use:
Defines the attribute that contains the time string subdivision that should
be used for the calculation.
• Type of variations:
Select either ’amplitude variations’, ’phase variations’ and ’amplitude and
phase variations’ here.
• Parameters to improve:
By default option ’all ampl. & phases’ is selected. That means that for
this calculation the frequencies will be kept fixed and all amplitudes and
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phases are redetermined. To specify a different selection click on ’special’
and make your choice in the selection dialog that will be opened.
Press ’Calculate’ to start the calculation using the defined settings. The
results will be displayed in the text field. You may print or export the results to
a file by clicking the appropriate button at the bottom.
2.8.18 The ’Monte Carlo simulation’ dialog
This dialog is shown when you click on Monte Carlo Simulation in ’Goodness
of Fit’ tab in the Fit Module. It provides an interface for estimating the uncertainties of fit parameters by means of Monte Carlo simulations.
Figure 38: The ’Monte Carlo simulation’ dialog
For the Monte Carlo simulation the program generates a set of time strings.
Each data set is created as follows:
• The times of the data points are the same as for the original time string.
• The magnitudes (or intensity) of the data points are calculated from the
magnitudes predicted by the last fit plus Gaussian noise.
For every data set a least-squares calculation will be made. Based on the
distribution of fit parameters the program calculates the uncertainties of the
parameters.
• Number of processes
A ’process’ consists of the creation of time string data and a least-squares
calculation to determine the fit parameters. A low number of processes
results in a bad estimate of the uncertainties. Therefore, a high number
of processes is highly recommended to obtain reliable results.
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• Uncouple Frequency and Phase Uncertainties
Frequency and phase uncertainties are correlated. If this option is selected
the time string will be shifted in time so that the ’average time’ is zero.
If this condition is fulfilled, the frequency and phase uncertainties are no
longer correlated. This check box will only be visible if this option might
be useful, that is when both frequency and phase parameters are fitted
using the standard fitting formula.
• Use system time to initialize random generator
If this option is selected the random number generator that is used to
create the time string data sets will be initialized with the current system
time.
Please see ’Estimation of uncertainties’ (section 4.3.4) for further informations.
2.8.19 The ’Calculate noise at frequency’ dialog
In order to check the significance of a detected frequency it is necessary to
calculate the signal to noise ratio. For this purpose select ’Calculate noise at
frequency’ in the ’Special’ menu.
Figure 39: The ’Calculate Noise at Frequency’ dialog
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• Calculate noise at Frequency
Defines the frequency for which the noise should be calculated. The
frequencies that are stored in the frequency list in the Fit Module are
accessible by the combo-box below the frequency field. By default the
last frequency of the frequency list is activated.
• Box size
Determines the size of the frequency range to be used for the noise cal, f requency + boxsize
]
culation: [f requency − boxsize
2
2
• Step rate
Defines the accuracy of the frequency grid for the Fourier calculation.
Three default options for the step rate quality are available and can be
selected by the combo-box: High, Medium and Low. In order to set a
user-defined value, select ’Custom’ and type the value into the input field
next to the step rate combo-box.
Please note: The smaller the step rate the longer the calculation will take.
• Calculations based on
Defines the type of data to be used for the calculation: ’Original’ data,
’Adjusted’ data, ’Residuals at original’, ’Residuals at adjusted’ or ’Spectral
window’.
Click on ’Calculate’ to start the calculation. The results of the noise calculation will be shown in the text field below. If the frequency has been selected via
the combo-box then even a value for the signal to noise ratio will be calculated.
You can export or print the content of the text box by pressing the appropriate button.
2.8.20 The ’Calculate noise spectrum’ dialog
Period04 also provides a tool to calculate a noise spectrum. The corresponding
dialog can be accessed via the Special menu.
This dialog is very similar to the ’Calculate Noise at Frequency’ dialog.
However, for the noise spectrum the range and the step size have to be defined:
• Frequency range: from/to
Defines the frequency range for the noise spectrum.
• Spacing
In order to construct a noise spectrum the noise will be calculated for
certain frequencies in equidistant frequency steps. The ’spacing’ defines
the size of these frequency steps.
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Figure 40: The ’Calculate Noise Spectrum’ dialog
Click on ’Calculate’ to start the calculation. The resulting noise spectrum
data will be displayed in the text box below. To export or print the content of
this text box press the appropriate button at the bottom of the dialog.
2.9 Plots
Visual inspection of the data is very important. Period04 supports plotting on
the monitor of time string data, Fourier data and phase plots.
The menu bar for plot windows generally contains the following commands:
• The Graph menu:
– Print Graph
Opens a printer dialog for printing the plot using the current viewport.
– Export Graph As (EPS/JPG)
Save the current plot as an image in eps or jpg format.
– Close
Close the plot window.
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• The Colors menu (not available for Fourier plots)
Every attribute has substrings which are assigned to a color. Using this
menu option it is possible to switch between the different coloring of the
four attributes.
• The Data menu (not available for Fourier plots)
Here you can select the type of data to be plotted: ’Observed’, ’Adjusted’,
’Residuals at observed’ and ’Residuals at adjusted’.
• The Zoom menu:
– Display all
Resets the zoom.
– Select viewport
Opens a dialog to define the graph ranges.
– Freeze viewport (available for time string plots only)
If this option is selected the current viewport will be maintained,
unaffected of changes in the selection of substrings. Zooming functionality is not affected.
– Back
Undo the last zooming action.
• The Help menu
provides a link to the help page for the appropriate plot.
The status bar
In the status bar of plot windows the current coordinates of the cursor will
be displayed, provided that the mouse cursor is situated within the plot domain.
Editing plots
The Scientific Graphics Toolkit that is being used for the plots allows to
edit some properties of the design:
• Labels
Change the text, font, color or position of the plot title and/or the axis
titles.
• Axes
Change label font, tic properties or the range.
To open the appropriate dialog, make a right-click on the appropriate label
or axis to activate it, then a left-click to open the dialog.
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2.9.1 Time string plots
To plot the currently selected time string, press the button ’Display graph’ in
the ’Time string’ tab.
Figure 41: An example for a time string plot.
In this mode the menu bar is extended by an additional menu:
• The Display menu
In this menu the ’Display header’ option can be selected. If this option
is activated a header will be shown providing some information on the
current fit (number of frequencies, residuals, ...).
Editing the contents of time string plots:
• Relabel points
If you want to change the substring a particular point belongs to, click
on that point with the right mouse button. The ’Relabel data point’
dialog (section 2.8.8) will be shown. To prevent a wrong identification,
the dialog does only appear when the point is well separated from other
points.
• Deleting points
There are two ways to delete points:
– Press ’Ctrl’ and right-click on the point you want to delete.
– Draw a rectangle using the right mouse button. In contrast to zoomrectangles this rectangle is colored red. After releasing the button
the user will be prompted whether he wants to delete the points
within the rectangle or not.
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2.9.2 Phase plots
To show the phase plot press the ’Phase diagram’ button in the Fit Module.
By default the first found inactive frequency is being used for the plot. If no
inactive frequency can be found a default frequency value of 1.0 is chosen.
Please note: this option is not available within the periodic time shift mode.
Figure 42: A typical phase plot.
Phase plots provide the two additional options which are accessible via the
’File’ menu:
• Export phases
Opens a time string export dialog which allows for saving the phases along
with other data.
• Export binned phases
Same as ’Export phases’ apart from the fact that binned phases are exported instead of phases.
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The frequency panel
• The frequency combo-box
Defines the frequency that is used for the plot. The combo-box contains
all inactive frequencies that have been found in the Fit Module. To
use a user-defined frequency value select ’Other Frequency’ and type the
frequency into the input field next to the combo-box.
• Use binning
If this option is selected the data will be averaged for discrete phase
ranges. The input field next to the check-box defines the number of bins.
2.9.3 Fourier plots
To plot the currently selected Fourier spectrum, press the button ’Display graph’
spectrum in the Fourier Module.
Figure 43: A common Fourier plot.
In the Fourier mode the menu bar is extended by one item:
• The Display menu
– Display Power
If this option is selected power will be plotted instead of amplitude.
– Display header
If this check-box is activated a header will be displayed containing
the title of the spectrum and the values of the highest peak.
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2.10 Tables
Period04 allows to inspect the data in table format too.
To display the time string table, press ’Display table’ in the ’Time string’
tab. The table lists all selected data points along with information on residuals,
weights and the affiliation to substrings.
Figure 44: The time string table.
Within the Fourier Module it is also possible to inspect the values for frequency, amplitude and power of a Fourier spectrum in form of a table. To
open this table select the respective Fourier spectrum and click on the button
’Display table’.
As the tables are available only for informative purposes the table itself cannot be edited.
The menu bar for table windows contains the following entries:
• The Table menu
– Print Table
Use this command to print the complete table.
– Export Table
Save the content of the table to a file.
– Close
Close the table window.
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Figure 45: The data table for a Fourier spectrum.
• The Help menu
Provides a link to the appropriate help page.
Within time string tables a pop-up menu is available:
• Relabel point
Gives access to the ’Relabel data point’ dialog (section 2.8.8) for the
selected time point.
• Delete point
Deletes the currently highlighted time point.
2.11 Period04 preferences
A new feature of Period04 is the preferences file. It is located in the user directory and it is named ’.period04-pref’. At start-up Period04 searches for the
preferences file and reads in the default settings as defined in the file.
If the file is not found, the program shows a message reporting the problem
and creates a new file. The program also checks the file for defects. If the file
seems to be damaged or incomplete Period04 will ask the user if he wants to
delete the preferences file and to generate a new one or to proceed using the
internal default values.
By editing the ’.period04-pref’ file the user can set the following values:
• default program mode (standard mode or expert mode)
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• lower / upper bound for the default Fourier frequency range
• default compact mode for Fourier calculations
• default alias-gap value
• default scale (magnitudes or intensity)
• default names for the set of attribute names
• default file-format for time string files
The user may also add own comments provided that the line starts with
’#’. This character advises Period04 not to read that line.
The default preferences file in detail:
#
# .period04-pref
#
# This is the Period04 preferences file. You can set
# your personal settings by replacing the default values.
# If this file is not found, Period04 creates a new one
# using its original settings.
#
#-----------------------------------------PROGRAM_MODE
DEFAULT
#
# start the program in the given mode
# possible values: DEFAULT
#
EXPERT
#-----------------------------------------DEFAULT_FOURIER_LOWER_FREQUENCY
0.0
#
# defines the default lower boundary
# of the frequency range for
# Fourier calculations
#-----------------------------------------DEFAULT_FOURIER_UPPER_FREQUENCY
50.0
#
# defines the default upper boundary
# of the frequency range for
# Fourier calculations
#-----------------------------------------DEFAULT_FOURIER_COMPACT_MODE
ALL
#
# defines the default setting for
# Fourier calculations:
#
ALL = all data points of a Fourier
#
spectrum are saved
#
PEAKS_ONLY = only the maxima and
#
minima of the spectrum are saved
#-----------------------------------------DEFAULT_ALIAS_STEP
DEFAULT
#
# defines the default alias step rate:
#
DEFAULT = (1./365.)
#
a user-defined number
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#-----------------------------------------DEFAULT_SCALE_SETTING
MAG
#
# defines the default scale setting:
#
MAG = magnitudes
#
INT = intensity
#-----------------------------------------DEFAULT_NAME_SET[0]
Date
DEFAULT_NAME_SET[1]
Observatory
DEFAULT_NAME_SET[2]
Observer
DEFAULT_NAME_SET[3]
Other
#
# this defines the default attribute names
#-----------------------------------------DEFAULT_TIMESTRING_FILE_FORMAT
AUTO
#
# this defines the default file format for
# reading in time strings.
#
AUTO = try automatic determination
# You may also enter a user-defined string,
# composed of the following letters:
#
t ... time
#
o ... observed
#
a ... adjusted
#
c ... calculated
#
w ... point weight
#
r ... residuals(observed)
#
R ... residuals(adjusted)
#
1 ... attribute #1
#
2 ... attribute #2
#
3 ... attribute #3
#
4 ... attribute #4
#
5 ... weight(attribute #1)
#
6 ... weight(attribute #2)
#
7 ... weight(attribute #3)
#
8 ... weight(attribute #4)
#
i ... ignore
2.12 The expert mode
If the expert mode of Period04 is activated, additional tools are available such
as:
• the Data Manager (see section 2.13)
• the possibility to calculate fits considering periodic time shifts (see section 4.3.3)
• a tool to calculate the Nyquist frequency using specific time-ranges (see
section 2.8.5)
The expert mode can be activated by selecting the check-box ’Expert mode’
in the ’File’ menu. The expert mode setting is being saved in every Period04
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project file and will be reactivated automatically when the project is opened
again.
It is possible to start Period04 in the expert mode by default. For this
purpose you have to edit the Period04 preferences file which is located in your
user directory. Change the setting for ’PROGRAM MODE’ from ’DEFAULT’
to ’EXPERT’ as shown in this excerpt:
PROGRAM_MODE
#
# start the program in the given mode
# possible values: DEFAULT
#
EXPERT
EXPERT
From now, the program will always start in expert mode right away.
2.13 The Data Manager (expert mode only)
The Data Manager is a tool that combines all import and export data options
Period04 is capable of. It can be accessed via the menu bar (File / Manage
data) or using the shortcut ’Ctrl+M’, provided that the expert mode is activated (see section 2.12).
Figure 46: The ’Data Manager’
The Data Manager dialog is divided into 2 columns: the left column provides options for import, export and rearrangement of data. The right column
shows some information on the current project. The project information panel
will hide if an option in the left column has been selected. Instead, an other
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panel will be displayed, showing additional options for the selected action.
The project information panel:
• Time string data:
Clean
Total points
Points selected
Delete the complete time string.
The total number of time points.
The number of currently selected time points.
• Frequency data:
Clean
Active frequencies
Delete all frequencies.
The number of selected frequencies.
• Fourier data:
Clean
Fourier spectra
Delete all Fourier spectra.
The number of spectra in the Fourier list.
• Project:
Save
Save as
Save the current project.
Save the current project using an other name.
If the project has changed since the last backup, a red warning label will be
displayed.
Options related to time string data:
• Append a new time string:
Choose this option if you want to add time string data to the current
project.
• Replace the old time string:
Erases the current time string and reads in a new time string. This option
does also provide the possibility prevent the automatic deletion of current
frequency data, Fourier spectra and the log.
• Rearrange time string data:
This option makes it possible to interchange time string data columns.
You may choose one of the following actions:
– replace ’Observed’ by ’Residuals(Observed)’
– replace ’Observed’ by ’Residuals(Adjusted)’
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– replace ’Observed’ by ’Calculated’
– replace ’Observed’ by ’Adjusted’
By default the ’Adjusted’ column will also be replaced by the chosen
values whereas the ’Calculated’ values will be set zero.
• Export time string data:
Choose this option if you want to export time string data from the current
project to a file.
Options related to frequency data:
• Import frequencies:
Import frequency data from a file. Make sure that the file is formatted
as shown in this example:
F1
F2
F3
F4
F5
12.716215
12.154121
24.227962
23.403372
(9.6562750
22.38070
4.034121
4.264320
3.816048
3.649441
0.953766
0.146566
0.688949
0.002060
0.998882 )
Unselected frequencies should be placed within parentheses.
• Export frequencies:
Export frequencies from the current project to a file.
Options related to Fourier data:
• Export Fourier spectra:
This option makes it possible to export either all or a specific selection of
Fourier spectra. According to the selection of the user, the program will
name the files either using the titles of the spectra or a composition of a
prefix and a running number.
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Figure 47: The ’Export Fourier spectra’ interface.
2.14 Overview of Shortcuts:
General Shortcuts:
Ctrl
Ctrl
Ctrl
Ctrl
Ctrl
Ctrl
Ctrl
Ctrl
Ctrl
F1
+
+
+
+
+
+
+
+
+
N
O
S
T
A
F
M
W
Q
Create a new project
Load an existing project
Save the active project
Import/append a time string
Adjust data
Import a set of frequencies
Launches the data manager (available in expert mode only)
Open the weight-selection dialog
Quit the program
Launch the Help System
Shortcuts only available in the ’Time string’ tab:
Alt + E
Alt + D
Export time string data
Display time string
Shortcuts only available in the ’Fit’ tab:
Alt + C
Alt + I
Improve amplitudes and phases
Improve all parameters
Shortcuts only available in the ’Fourier’ tab:
Alt + C
Alt + D
Calculate Fourier transformation
Display the selected Fourier spectrum
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3. Getting Started
The best way to learn how to use Period04 is by doing. For this reason we
created two example time strings which will be processed and discussed in the
tutorials below. The data files can be downloaded from the Period04 homepage:
http://www.astro.univie.ac.at/ dsn/dsn/Period04/
3.1 Tutorial 1: A first example
In this tutorial, we will use Period04 to examine a data set and determine the
frequencies by using Fourier analyses to give us rough values of the frequencies
and the Fit Module to refine these frequencies. Note that the Fourier analysis
cannot by itself solve the problem since it is a single-frequency method.
1. Start the program Period04.
You may wish to use the file ’Empty Period04 file.p04’ which is part of the
downloaded data package. The tab ’Time string’ is selected and active.
You will see four empty columns.
2. Import the data set.
We will now load the data file. It has the name ’Tutorial1.dat’. Click
on the button ’Import time string’ (left, near top). A window opens and
asks for the location of the data. Find the proper directory on your hard
disk and click on the file name. Click on the button ’Import’.
Figure 48: The ’Time string import’ dialog.
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A window opens and asks for the properties of each column. Since the
first data column is the time and the second columns contains the magnitude variations, everything is fine. Click on ’OK’.
(If not, under ’Column #1’ etc. you can select the contents of each column.)
You now have 1254 data points loaded with observing times ranging from
2720.81478 to 2740.92739. Do not worry about the ’unknown’ labels in
each of the four columns: it just means that you have not organized your
data into groups.
Save your data now (File, Save Project as) under, say, ’First’. It is now
stored as First.p04.
3. Look at the data.
In the same ’Time String’ window, click on ’Display Graph’ at the bottom
right. A new window opens with the light curves of the selected data,
which, by default, was all the data. You notice that the data strings are
spaced one (or more) days apart.
Let us examine a (any) single night. With your mouse select a part of
the data by drawing a rectangle around it. You may wish to increase the
scale of your selection by drawing more rectangles. If you make a mistake, open the ’Zoom’ dialog (top of ’Time string plot’) and use an option.
The single-night data indicates a variation lasting about 0.1d, with nonrepetitive light curves. This may already be a sign of multi periodicity.
Notice too that within each night, the data are taken about every 0.003d
or 5 minutes apart. This figure is approximate because the coverage differs from night to night. The sampling theorem suggests that periods
shorter than 10 minutes should not be determined with such a data set.
To put it differently, the Nyquist frequency is about (0.5 ∗ 1/0.003) or
167 cycles/day, abbreviated as c/d.
Furthermore, the data were taken one (or more) nights apart with daytime gaps. Consequently, 1 c/d aliasing is expected.
To summarize:
(a) we suspect that frequencies near 10 c/d exist,
(b) the Nyquist frequency should be near 167 c/d, and
(c) 1 c/d aliasing may exist.
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4. Perform a Fourier analysis of the data: Spectral Window
Make sure that you have selected all the data. Click on the ’Fourier’ tab.
A new window opens. Let us now enter all the necessary parameters.
Title: Spectral Window
From: 0
To: 5
(remember that the spectral window is centered on 0 c/d
and calculates the pattern caused by the observing gaps).
Use weights: Keep ’none’
Calculations based on: Spectral window
Compact Mode: All
(since there are no huge gaps in the data)
Now press the central button: Calculate.
Let us look at the answers. In the line above the ’Calculate’ button, we
see that the highest peak occurs at frequency 0 with an amplitude of 1.
This has to be the answer for a spectral window.
Click on ’Display Graph’ on the bottom right. A plot window opens. You
can see the 1 c/d structure. Keep it in mind for the frequency search of
the stellar variations. The true frequencies of the star should also show
the pattern, but centered on the true frequencies.
Figure 49: The spectral window.
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Close Fourier graph: Spectral Window.
5. Perform a Fourier analysis of the data: Periodic content of data
You are still in the Fourier window. If not, click on the ’Fourier’ tab. Let
us now enter all the necessary parameters:
Title: All data, incorrect zero-point
(the choice of this title will become clear below)
From: 0
Now see the Nyquist Frequency (167.778). Use this.
To: 167
Use weights: Keep ’none’
Calculations based on: Original data
Compact Mode: All
Now press the central button: Calculate.
Now a window opens asking you to select the zero-point shift. It allows
you to subtract the average brightness.
(a) INCORRECT OPTION:
Let us pick the incorrect option for the present data set. In the present
case, we select ’No’. This means that we assume that the measured average is not the true stellar average - this can indeed happen.
Let us look at the answers. In the line above the ’Calculate’ button, we
see that the highest peak occurs at frequency 0 with an amplitude of
0.4875. No, this is not the spectral window. It is a consequence of the
incorrect zero-point!
Do not include this frequency. Answer ’No’ to the question.
Click on ’Display Graph’ on the bottom right. A plot window opens. We
see two patterns, one centered on the frequency 0, the other one at 10.
Let us examine the structure at 0 in more detail: open the ’Zoom’ dialog
to the top of the plot and use option ’Select viewport’. Enter:
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Frequency min: -0.1
Frequency max: 5
Keep the chosen amplitudes. Click ’OK’.
Figure 50: An example for using a wrong zero-point
You see the peak with an amplitude of 0.49 (twice the incorrect zeropoint value) near frequency 0. You also see the spectral window pattern
associated with this peak (Fig. 50).
Close the graph and redo the Fourier analysis with the correct zero-point.
(b) CORRECT OPTION:
We redo the calculation (calling it ’All data’) and say ’Yes’. Now the
highest amplitude occurs at 10.0011883 with an amplitude of 0.20124.
Answer the question: ’Do you want to include this frequency?’ with ’Yes’.
It is now entered in the ’Fit’ window.
Look at the Fourier diagram again (button ’Display Graph’ at bottom
right). A nice pattern of peaks around the frequency 10 is visible. A
decision to try out this frequency for a fit appears reasonable. Let us do
it.
Close the plot.
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Figure 51: The Fourier spectrum using the correct zero-point
6. A One-frequency fit.
Click on the ’Fit’ tab (top). A window opens. You see the previously
suggested frequency.
(a) First calculation.
Select the first frequency F1 by clicking into the square to the left of
F1. A check mark appears. Click on ’Calculate’ at the bottom left. You
obtain the following result almost immediately:
Amplitude = 0.202266723 and Phase = 0.955286.
Near the top right you will see: Selected frequencies = 1. Yes, that is
true. Zero point: 0.2426. Yes, that is close to the average value already suggested by the program before the Fourier analysis. Residuals:
0.070878. We want to minimize this quantity, but we do not know what
the minimum value will be.
(b) Improve the frequency.
This option should be used carefully. Let us apply it (button bottom
middle). The frequency becomes 9.99988955, Amplitude = 0.202731263,
Phase = 0.501472. More importantly, the residuals have improved slightly.
7. Perform a Fourier analysis of the residuals
Let us see if the residuals contain more periodicities. Click on the ’Fourier’
tab.
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Title: Residuals, 1 frequency
From: 0
To: 167
Use weights: Keep ’none’
Calculations based on: Residuals at original (Note!)
Compact Mode: All
Now press the central button: Calculate.
A frequency of 14.5008529 and amplitude 0.0994119445 are found. Include the frequency (for the next fit).
Examine the plot. It looks very good.
8. A Two-frequency fit.
Click on the ’Fit’ tab (top). Now select both F1 and F2. Probably you
only need to click into the square to the left of F2 to see check marks
next to both frequencies.
Click on ’Calculate’. The residuals decrease. Click on ’Improve all’. We
obtain frequencies of 10 and 14.5, amplitudes of 0.2 and 0.1, respectively,
and essentially zero residuals. That’s it.
Do you want to see how the fit looks? Click on the ’Time string’ tab
and select ’Display Graph’. The program cannot show the fit for several
nights. Therefore, select a single night (rectangle....). You now see the
excellent fit.
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Figure 52: The final fit.
3.2 Tutorial 2: Least-squares fitting of data including a periodic time shift
This tutorial provides a basic introduction in how to find a multiple frequency
solution to a data set, taking into account a periodic time shift. Such a periodic
time shift could be the result of orbital light-time effects.
1. Start Period04.
2. Import the data file.
To read in the data set, press the button ’Import time string’. A fileselector dialog will be opened. Navigate to the directory that contains
the tutorial time strings and select the file ’Tutorial2.dat’.
In the next dialog, we are going to specify the properties of the columns
in the data file. The first column of our data file denotes time, whereas
the second column contains the observed magnitudes. Period04 should
already have assumed that, so just click on ’OK’.
Now press ’Display graph’ and examine the time string. You will observe
that a strong beating is present, which could be the result of two close
frequencies.
3. Extract the first frequency.
Click on the ’Fourier’ tab. In the ’Fourier Calculation Settings’ panel,
enter a title for the new Fourier spectrum. As you can see, the Nyquist
frequency of this time string is 139.806 cycles/day. Extend the upper
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limit of the frequency range to the lower integer part of this value (139).
Before you start the calculation, make sure that the option ’Original data’
is selected. Now press ’Calculate’.
A dialog will show up asking whether the zero point of magnitudes /
intensities should be subtracted. Press ’Yes’. After the calculation has
finished, the highest peak of the new spectrum is reported. Click on ’Yes’
to copy the values of the frequency peak into the Fit Module.
In the ’Fourier’ tab, press ’Display graph’ to inspect the plot of the Fourier
spectrum.
4. Calculate a first fit.
Switch to the ’Fit’ tab. You will notice that the new found frequency
has not yet been selected. Select frequency F1 and press ’Calculate’ to
improve amplitude and phase. Then, to improve all parameters press ’Improve all’.
To check how good this solution fits the data, move to the ’Time string’
tab and press ’Display graph’. As you see, there is still some work to do.
5. Find and fit further frequencies.
Switch back to the ’Fourier’ tab and calculate the next spectrum. From
now on the Fourier calculations should be based on the ’Residuals at original’, so make sure that this option is selected.
In the Fit Module, select the newly found frequency and press ’Calculate’.
Then click on ’Improve all’ to find the best least-squares solution.
Figure 53: The preliminary Four-frequency fit.
To detect further frequencies proceed as stated above. Extract two more
frequencies. The residuals will continue to decrease. Fig 53 shows the
frequency parameters you should obtain.
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6. Examining the data
Finally, after extraction of four frequencies the least-squares solution fits
quite well. Maximize the plot window and examine each night carefully.
You will notice that during the first and the last nights of the time string
the data points are shifted slightly to the right of the fit, whereas for the
nights in the middle of the data set the points are situated slightly left
of the fit. This may indicate that a periodic time shift is present with a
period that is approximately equal to the total length of the data set in
time, about 100 days. That corresponds to a frequency of 0.01 cycles/day.
Well, let us see if we can find any further frequencies. Switch to the
Fourier Module and extract the next frequency:
Frequency = 8.23515582 cycles/day and Amplitude = 0.00092585 magnitudes.
This is quite interesting, isn’t it? This frequency is quite close to the first
detected frequency (F1). The difference is only 0.010095 c/d which is
roughly the value for the frequency of the periodic time shift estimated
by visual inspection. It seems likely that the new frequency is an artefact
caused by a periodic time shift.
Now let us check whether our suspicion, viz. the presence of a periodic
time shift, can be confirmed. Leave the new frequency (F5) unselected
and do not change your four-frequency solution.
7. Activate the periodic time shift (PTS) mode.
Figure 54: The frequency panel in the periodic time shift mode.
Fitting a periodic time shift can only be done if Period04 runs in expert
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mode. To activate the expert mode, set the option ’Expert mode’ in the
File menu selected. A new menu entry, Options, will appear on the menu
bar. This menu contains the entry ’Set fitting function’ which provides
the alternative ’Standard formula with periodic time shift’. Select this
option. Now the program is enabled for calculating least-squares fits
including a periodic time shift. You will notice that the Fit Module has
slightly changed.
8. Determining the periodic time shift parameters.
For non-linear fitting good starting values are essential. In general, initial
values for the periodic time shift parameters can be estimated from visual
inspection of the data, as we did before. Period04 also provides a tool
to search for starting values within a user-defined range of frequencies
and amplitudes by means of Monte Carlo shots. Press the button ’Search
PTS start values’ to use this option.
Figure 55: The ’Search PTS start values’ dialog.
The lower frequency limit is calculated from the time base of the data
set. You should not search for frequencies with lower values. The reason
is that for such frequencies the time base of the data is too short to allow
a reliable determination of the periodic time shift.
The number of shots refers to the number of initial parameter values that
are being tested. We will keep the default values. However, we will deselect ’Use system time to initialize random generator’ in order to allow
the users to compare their results with the results given here. Press ’OK’
to start the calculation.
After the calculation has finished, the best set of starting values for the
periodic time shift parameters will be displayed (Frequency = 0.00975
cycles/day, Amplitude = 0.00104 days). Now let us improve these parameters by clicking on ’Improve PTS’.
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Figure 56: The fit after the determination of the periodic time shift parameters.
Finally, improve all frequencies together with the periodic time shift parameters by clicking on ’Improve all’. Do not use ’Calculate’, as for a
proper fit of a periodic time shift, the frequencies also have to be redetermined!
9. Extraction of further frequencies
Switch to the ’Fourier’ tab and calculate a new Fourier spectrum. Press
’Display graph’ and have a look at the plot. It is obvious that the detected frequency peak is not significant. Therefore, our analysis will stop
at this point.
Figure 57: The Fourier spectrum shows no significant peak.
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Please note:
Let us suppose that you have found a statistically significant frequency.
In this case you should use ’Improve all’ to obtain a new least-squares
solution. Furthermore, you do not have to use the ’Search PTS start values’ tool again, as you already have good starting values for the periodic
time shift which can be improved.
10. The final solution
Your final fit using the four extracted frequencies and including a periodic
time shift should be:
Figure 58: The final solution.
The residual noise is 0.000999 magnitudes.
Click on the ’Time string’ tab and press the button ’Display graph’. You
will notice that the solution fits the data very well. After having applied
the periodic time shift, the data points are distributed uniformly on both
sides of the fit.
Now let us compare the final parameters to the values that had been used
to generate this time string:
#
Frequency
Amplitude
Phase
-----------------------------------------------------PTSF
0.01
0.001
0.5
F1
8.24559
0.036872
0.19192
F2
8.86632
0.031595
0.20128
F3
8.51414
0.009952
0.81182
F4
7.42476
0.008187
0.76091
-----------------------------------------------------Desired residual noise: 0.001
Note the good agreement. The deviation from the initial values is caused
by noise.
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4. Using Period04
Within this section some of the key features of Period04 are discussed. In many
cases short step-by-step guides are given for easier comprehension.
4.1 Topics related to time string data
4.1.1 Importing time strings
1. Start the import
There are several different ways to start the import of a time string,
e.g. you can use the ’Import’ or ’Append’ buttons in the ’Time string’
folder. ’Import’ erases old project data and then loads the new time string.
’Append’ adds the time string to the current project without changing it
otherwise.
In addition, there are two more general approaches:
• The ’Import → time string’ command in the ’File’ menu.
(Shortcut ’Ctrl+T’)
This command checks whether the project already contains time
string data. If no time points are found the file-selector dialog is
shown, otherwise the program will display the dialog shown in Fig 59.
Figure 59: The selection dialog for time string imports.
’Append a new time string’ simply adds a data set to your existing
time string without any further changes in the project. If you select
’Replace the old time string’ you have the possibility to instruct Period04 not to erase the frequency data and/or the log.
• Importing a time string through the Data Manager (section 2.13).
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After having chosen one of the upper actions a file-selector is shown.
By default all files with the extension ’dat’ are shown. To display files
with another extension, please select ’All files’ in the file-selector dialog.
Navigate to the appropriate directory and select the file containing time
string data.
2. Set the file-format
The next step is to define the columns in your data file. For this purpose
the file-format dialog is opened.
Figure 60: The file-format dialog.
The dialog displays the first few lines of the selected file and provides an
initial guess for the column identification determined from the structure
of the columns in the file. The dialog shows the first four columns of the
file. In order to see the other columns, please use the scroll bar at the
bottom of the text box.
The following data can be read in by the program:
• Time
• Observed
• Adjusted
• Residuals to Observed
• Residuals to Adjusted
• Calculated
• Point weight
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• 4 attributes and 4 weights assigned to these attributes *)
• Ignore (column will not be read in)
*) The names of the attributes depend on the program settings and can
be changed by clicking on the heading buttons in the Time String Module. The default names are ’Date’, ’Observatory’, ’Observer’ and ’Other’.
In order to change the default names, the Period04 preferences file has
to be edited (see section 2.11).
3. Finally, press ’OK’
Please note:
Lines starting with ’#’, ’;’ or ’%’ will be treated as comment lines and are
ignored.
Additional options:
It is also possible to select multiple files in the file-selector dialog. In this
case, the program will ask the user for the file-format of the first data file. After
the specification of the file-format, a dialog will show up that allows to select
whether the program should apply the same file-format for all data files or to
show the file-format dialog for every file.
If the columns of most of your data files have a very special format, you
may find it useful to define a default file-format for reading in time strings. In
this case the file-format dialog will always propose the given default file-format
instead of trying to provide a guess about the file structure. This can be done
by editing the Period04 preferences file (see section 2.11).
4.1.2 Exporting time string data
1. Open the export dialog
To start the export you can either press the button ’Export time string’,
use the shortcut ’Alt+E’ or, if the program is running in expert mode,
start the Data Manager and select the option ’Export time string data’.
In any case the following dialog will show up:
2. Set the output format
The dialog contains two columns: the left text box lists all data columns
that can be exported. To the right there is another box, which defines
the structure of the columns in the resulting file. Now select the columns
to be exported from the list of available columns. Click on the button
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Figure 61: The time string export dialog.
’Add’ to add these columns to the list on the right. If you want to remove
a column that you have added before, simply select the column name in
the ’Columns to export’ list and press ’Remove’. Finally, when you have
finished your selection, press ’OK’.
Figure 62: The time string export dialog with an example of a selection.
In the example shown in Fig. 62, we have chosen the columns ’Time’,
’Observed’, ’Calculated’, ’Observer’ and the weights assigned to the substrings of attribute ’Observer’ for export.
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3. Choose a file name
Now, a file chooser will ask you for a name for the file. Enter a file name
and press ’Export’ to start the export of the data.
4.1.3 Creating artificial data
It is easy to generate an equally-spaced artificial data set using Period04. First,
make sure that there is a set of active frequencies – or at least one active
frequency – in the frequency list of the Fit Module. The current fit will be used
for the calculation of magnitude/intensity of the artificial data.
1. Select ’Create artificial data’ in the Special menu
The ’Create artificial data’ dialog will appear.
Figure 63: The ’Create artificial data’ dialog.
2. Setting the time range(s)
There are two options to define the start and end times of the time series
that will be generated:
• Definition of start and end time by the given input fields.
• Using the button ’Read time ranges from file’ for reading the definitions of start and end times from a file.
The latter option has the advantage that artificial data for an arbitrary
number of different start and end times can be created right away. Please
make sure that the file obeys the following format conditions:
• first column: start time
• second column: end time
3. Calculation settings
Now you have to define the step size. By default a value of 1/(20∗F max )
is given, which provides a good sampling even for the highest frequency.
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The input field ’Leading/trailing time’ gives you the possibility to extend
the time ranges by a certain value.
4. Start calculation and output of data
Click on the button ’Write data to the following file ...’ and choose a file
in which the data should be written. If the file already exists, you will be
prompted whether you want to append the data to the file, replace the
file or to cancel the task.
4.2 Topics related to Fourier calculations
4.2.1 Calculation of Fourier spectra
Let us suppose that you have already read in a time string.
1. Click on the ’Fourier’ tab.
As you can see, in the upper part of the window the settings for the
Fourier calculation can be defined.
2. Choose a title for the Fourier spectrum.
3. Define the frequency range for the spectrum.
Make sure that the upper frequency bound does not exceed the Nyquist
frequency.
4. Choose a step rate.
This value defines the step size in frequency. Usually the step rate quality
’High’ provides a good sampling.
5. If you want to use weighted data, set and activate the appropriate weights.
See section 4.4.1 for more information on this topic.
6. Choose the type of data you want to use.
If this is the first frequency to be extracted from the data set, ’Original
data’ is the right choice. For subsequent frequencies you would select
‘Residuals at original’. If you adjusted the zero-points of the time string
select ’Adjusted’ instead of ’Original’.
7. Select the compact mode.
If you want to reduce the output (the number of data points) of the
Fourier calculation, select ’Peaks only’. If this option is selected only the
local extrema of the spectrum will be saved.
8. Press ’Calculate’ to start the calculation.
A dialog will be opened and you will be asked whether you want to
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subtract the zero point of the magnitudes/intensities. Press ’Yes’. While
the program is calculating the ’Calculating’ tab is being shown. It reports
the progress of the calculation and shows the chosen settings. By clicking
on the button ’Cancel Calculation’ the calculation can be stopped.
9. After the calculation has been finished, a dialog is opened that informs
you about the value of the highest peak and asks you if you want to
include this frequency. Press ’Yes’ to add the frequency to the frequency
list in the ’Fit’ tab.
10. Inspect the Fourier spectrum visually by clicking on ’Display Graph’. The
next step is to make a least-squares fit. See ’Calculation of least-squares
fits’ for further details.
11. For extracting further frequencies proceed as stated above except that
you choose ’Residuals at original’ instead of ’Original data’.
4.2.2 Significance of frequencies
Every measurement is affected by noise that may be generated by many sources
(e.g., observations, instrumentation, undetected frequencies). For Fourier spectra, noise has the annoying effect that a peak that has been found may not be
real.
The signal to noise ratio
Therefore, a criterion is needed to ensure that the signal is a real feature.
Empirical results from observational analyses by Breger et al. (1993) and numerical simulations from Kuschnig et al. (1997) have shown that the ratio
between signal and noise in amplitude should not be lower than 4.0 for high
significance.
What is the signal?
As signal we define either the amplitude of the respective peak in the Fourier
spectrum or the amplitude of the least-squares solution for the peak.
What is the noise?
The noise is defined as the average amplitude in a frequency range that encloses
the detected peak. The noise may be calculated before or after prewhitening
the peak. The choice is beyond the scope of this manual.
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Checking the significance of a frequency
Let us assume that you have calculated a Fourier spectrum and detected a
new peak.
1. Select ’Calculate noise at frequency’ in the ’Special’ menu.
By default the program loads the last frequency value from the frequency
list in the Fit Module into the frequency field of the dialog. If you want to
calculate the noise for an other frequency, type the new frequency value
into the frequency field.
2. Define the box size for the noise calculation.
This value specifies the frequency range [f requency− boxsize
, f requency+
2
boxsize
]
which
is
being
used
for
the
calculation
of
the
noise.
2
3. Choose a step rate.
Usually the step rate quality ’High’ provides a very good sampling.
4. Select the type of data to use for the noise calculation.
In most cases ’Residuals at original’ is what you need, unless you work
with adjusted data.
5. Press ’Calculate’ to start the calculation.
After the calculation has been finished, the noise result will be displayed
in the text area in the lower part of the window. If the frequency has
been selected from the combo-box then even the signal to noise ratio will
be shown.
Period04 also contains the possibility to calculate a noise spectrum. See
section 2.8.20 for more details.
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4.3 Topics related to least-squares calculations
4.3.1 Calculation of least-squares fits
This is a step-by-step guide for calculating least-squares fits using the standard
fitting formula:
f (t) = Z +
X
Ai sin (2π (Ωi t + Φi ))
i
1. Click on the ’Fit’ tab.
2. After you have extracted a frequency by means of a Fourier calculation,
the frequency and amplitude are added to the frequency list. You may
also enter own frequency values.
3. Activate the new frequency by selecting the check box at the beginning
of the frequency line.
4. Select the type of data you want to use. By default ’Original data’ is
selected.
5. If you want to use weighted data, set the appropriate weights. See section 4.4.1 for more information on this topic.
6. Press ’Calculate’ to improve amplitude and phase.
7. Press ’Improve all’ to improve all parameters, including the value of the
frequency.
Period04 does also allow for more sophisticated least-squares fits:
• Improve special:
If you want to define a specific selection of parameters that should be
improved, then choose this option.
• Calculate amplitude/phase variations:
Use this if you suspect that the amplitude and/or phase of a parameter
is variable in different substrings.
• When the expert mode is active it is possible to calculate least-squares fits
that include a periodic time shift. See section 4.3.3 for more information
on this topic.
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4.3.2 Calculation of amplitude/phase variations
If you suspect that the amplitude and/or phase of a parameter is variable within
different substrings (e.g., representing different years), you might consider to
use this tool.
1. Prerequisites:
Let us assume that you have a set of frequencies and a certain subdivision
of your time string in the attribute ’Date’. By calculating a least-squares
fit for each substring separately you realized that the amplitude of a
frequency might be variable.
Figure 64: In this example a time string has been subdivided in attribute ’Date’.
2. Press the button ’Calculate amplitude/phase variations’ in the Fit Module.
3. In the dialog, select the attribute in which the subdivision of the time
string is located.
4. Choose the type of variation: ’amplitude variation’, ’phase variation’ or
’amplitude and phase variations’.
5. Select the frequency that shows the amplitude variation.
6. Decide whether you want to improve ’all amplitudes and phases’ while
keeping the frequencies fixed, or to define a special selection of variable
parameters. If you prefer the latter, then click on ’special’ to open a
dialog for the definition of the selection.
7. Press ’Calculate’ to start the calculation.
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8. After the calculation has finished the results are displayed in the text box
below.
4.3.3 Using the periodic time shift mode
In order to account for light time effects, Period04 does also allow to include
a periodic time shift in your least-squares calculations. In this case the fitting
formula is extended in the following way:
f (t) = Z +
X
Ai sin (2π (Ωi [t + αpts sin (2π (ωpts t + φpts ))] + Φi ))
i
The periodic time shift parameters are labeled with the subscript ’pts’. Z
denotes the zero point of f (t) and Ai , Ωi and Φi the parameters of frequency i.
Please note:
This calculation mode can only be selected when the expert mode is activated.
Let us assume that you already read in a data set and extracted some
frequencies. The visual inspection seems to indicate that the times are shifted
with a certain period.
1. Select the periodic time shift mode
First, activate the expert mode by selecting ’Expert mode’ in the ’File’
menu. You will notice that a new menu, ’Options’, has appeared. This
menu contains the entry ’Set fitting function’ which provides two choices:
Standard formula and Standard formula with periodic time shift. Click
on the latter.
2. Set parameters for the periodic time shift
By inspection of your data you might already have a rough estimate of
frequency and amplitude for the periodic time shift. You can either enter
these values into the respective field directly, or use the ’Search PTS start
values’ button to search for a good start value for the periodic time shift
parameters within a user-defined range of frequencies and amplitudes.
The lower frequency limit is calculated from the time base of the data
set. You should not search for frequencies with lower values since for
these frequencies the time base of the data is too short to allow a reliable
determination of the periodic time shift.
The number of shots refers to the number of initial parameter values that
are being tested.
P. Lenz and M. Breger
129
Figure 65: The ’Search PTS start values’ dialog.
3. Improving the parameters and the fit
The next step is to improve the periodic time shift parameters by means of
a least-squares fit. In order to start this calculation, press ’Improve PTS’.
Please note that the common frequency parameters will be kept fixed
during this calculation.
Now it is time to make a least-squares fit that considers all parameters
as variable. For this purpose press ’Improve all’. Do not use ’Calculate’,
as for a proper fit of a periodic time shift, the frequencies also have to
be redetermined!
Please note:
If the start values are not good enough it might occur that the least-squares
algorithm gets trapped in a false local minimum. Generally, nonlinear fitting
requires some judgment from the user!
Please see section 3.2 for a tutorial that explains the same matter using an
example time string.
4.3.4 Estimation of uncertainties
Period04 provides several tools to calculate the uncertainties of the parameters
of a fit:
• Calculation of uncertainties from the error matrix of a least-squares calculation
• Monte Carlo Simulation
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• Uncertainties calculated from analytically derived formulae assuming an
ideal case.
Please note:
The errors of frequency and phase are correlated. However, by an appropriate
choice of a zero point in time the uncertainties for frequency and phase can be
decoupled. This is the case when
N
X
ti = 0
i=1
(Breger et al., 1999). It is very likely that your data set does not fulfill this
condition. Therefore, Period04 provides the possibility to shift the data set
by the required value in time, for the purpose of determining the uncorrelated
parameter uncertainties when the standard fitting formula is being used.
1. Calculation of uncertainties from the error matrix of a least-squares
calculation
Period04 applies the curfit routine from Bevington (1969), which is a
Levenberg-Marquardt non-linear least-squares fitting procedure. As a
by-product of least-squares fits an error matrix is available from which
parameter uncertainties can be calculated. In some cases though (i.e.,
when the error matrix is ill-conditioned) this method does not provide a
good estimate of the uncertainties. In order to ensure that the calculated
uncertainties are reliable, Period04 performs checks for these cases.
The output of common least-squares fits are correlated uncertainties.
When the standard fitting formula is being used, Period04 additionally
offers the possibility to calculate uncorrelated uncertainties.
To calculate the uncertainties of the fit parameters, press ’Calculate LS
uncertainties’ in the ’Goodness of Fit’ tab. If you improved frequencies
and phases simultaneously, a dialog will ask you whether you want to uncouple the uncertainties of frequency and phase (in other words: whether
you want to calculate correlated or uncorrelated uncertainties). After you
made your choice, the uncertainties will be displayed in the text box.
2. Monte Carlo Simulation
Monte Carlo simulations are a very reliable way to determine parameter
uncertainties. The principle idea is to repeat an experiment (in our case
the optimization routine) on a generated set of samples.
For the Monte Carlo simulation Period04 generates a set of time strings.
Each data set is created as follows:
P. Lenz and M. Breger
131
• The times of the data points are the same as for the original time
string.
• The magnitudes of the data points are the magnitudes predicted by
the last fit plus Gaussian noise.
For every data set a least-squares calculation will be done. Based on the
distribution of fit parameters the program calculates the uncertainties of
the parameters.
A short step-by-step guide for making Monte Carlo simulations:
• The Monte Carlo simulation will use the same settings that have
been used for the last fit. So if you want to determine the uncertainties for all parameters, you will have to make a least-squares
calculation with all parameters variable first.
• Now click on ’Monte Carlo Simulation’ in the ’Goodness of Fit’ tab.
In the dialog you have to define some settings for the simulation:
Figure 66: The ’Monte Carlo Simulation’ dialog.
Number of processes
A ’process’ consists of the creation of time string data and a
least-squares calculation to determine the fit parameters. A low
number of processes results in a bad estimation of the uncertainties. Therefore, to obtain reliable results, a high number of
processes is necessary.
Uncouple Frequency and Phase Uncertainties
If this option is selected, the time string will be shifted in time
so that the ’average time’ is zero. In this case the frequency
and phase uncertainties are no longer correlated. This check
box will only be visible if this option might be useful, i.e., when
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both frequency and phase parameters are fitted using the standard fitting formula.
Use system time to initialize random generator
If this option is selected the random number generator that is
used to create the time string data sets will be initialized with
the current system time.
• Press ’OK’ to start the calculations. Depending on the number of
time points and the number of processes this might be a quite time
consuming task.
3. Uncertainties calculated from analytically derived formulae assuming an ideal case
Based on some assumptions one can derive a formula for the uncertainties in frequency, amplitude and phase. See Breger et al. (1999) for the
derivation based on a mono periodic fit. If cross terms can be neglected
then the following equations can also be applied for each pulsation frequency separately:
r
6 1 σ(m)
σ(f ) =
N πT a
r
2
σ(a) =
σ(m)
N
r
2 σ(m)
1
σ(φ) =
.
2π N a
N is the number of time points, T is the time length of the data set,
σ(m) denotes the residuals from the fit and a refers to the amplitude of
the frequency.
To show these parameter uncertainties, select ’Show analytical uncertainties’ in the ’Special’ menu.
Please note:
This option is only available when using the standard fitting formula.
4.4 General topics
4.4.1 Using weights
Period04 does also handle weighted data. It recognizes three different types of
weights:
P. Lenz and M. Breger
133
• Point weight
Each measurement has its own weight.
• Deviation weight
Filtering of poor data points.
• Attribute weights
Weights assigned to substrings of each of the four attributes (Date, Observer,...)
In order to use weights the user has to set or read in weights AND to activate them for calculations. This can be done in the ’Weight selection dialog’
which can be accessed by the ’Special’ menu or via the shortcut ’Ctrl+W’.
Figure 67: The ’Weight selection’ dialog
Using point weights:
As ’point weight’ we denote weights that are assigned to each of your data
points. Point weights can only be read in along with time string data. To
include these data proceed as described here:
1. Click on the button ’Import time string’ and select the file that contains
your data set in the file-selector dialog.
2. Now another dialog appears. It will show the columns in your data file
and asks you to label these columns correctly. Specify the column that
contains the point weight data as ’Pnt.weight’ and select appropriate
labels for the other columns too – at least ’Time’ and ’Observed’ are
required. Press ’OK’.
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3. Although your data set has been read in, the program does not yet include the point weights in calculations. They have to be activated in the
’Weight selection dialog’ first. So open the dialog, select ’Point weight’
and press ’OK’.
From this point the program will use the weighted data until you deselect
this option.
Using deviation weights:
The deviation weights are calculated from the residuals of data points:
residual = |observed − calculated|
(
1.0
if residual < cutoff
2
deviation weight =
cutoff
if residual ≥ cutoff
residual
In order to use deviation weights open the ’Weight selection dialog’, select
’Deviation weight’ and set an appropriate cutoff value.
Using attribute weights:
Each of the four list boxes in the ’Time string’ tab represents an attribute.
The default names of these attributes are ’Date’, ’Observatory’, ’Observer’ and
’Other’. If the time string has been subdivided in at least one attribute it is
possible to give each substring a certain weight.
1. If you have not done so already, read in a time string.
2. Subdivide the time string. Let us assume that you divided the time string
into several substrings in the attribute ’Date’.
3. Select a substring for which you want to change the weight. Open the
’Edit substring properties’ menu by pressing the ’Edit substring’ button at
the bottom of the ’Date’ list box. You can also access this dialog directly
via the pop-up menu.
4. Type the new weight value into the respective field and press ’OK’.
5. To enable the weights assigned to substrings of attribute ’Date’, open
the ’Weight selection dialog’, select ’Date’ and press ’OK’. Now these
weights will be included in all calculations.
P. Lenz and M. Breger
135
5. Copyright notice
c
Copyright 2004-2005
Patrick Lenz, Institute of Astronomy, University of Vienna
Permission to use, copy, modify, and distribute this software and its documentation for any purpose is hereby granted without fee, provided that the
above copyright notice, author statement and this permission notice appear in
all copies of this software and related documentation.
THE SOFTWARE IS PROVIDED ’AS-IS’ AND WITHOUT WARRANTY
OF ANY KIND, EXPRESS, IMPLIED OR OTHERWISE, INCLUDING WITHOUT LIMITATION, ANY WARRANTY OF MERCHANTABILITY OR FITNESS FOR A PARTICULAR PURPOSE. IN NO EVENT SHALL THE INSTITUTE OF ASTRONOMY OR THE UNIVERSITY OF VIENNA OR PATRICK
LENZ BE LIABLE FOR ANY SPECIAL, INCIDENTAL, INDIRECT OR CONSEQUENTIAL DAMAGES OF ANY KIND, OR ANY DAMAGES WHATSOEVER RESULTING FROM LOSS OF USE, DATA OR PROFITS, WHETHER
OR NOT ADVISED OF THE POSSIBILITY OF DAMAGE, AND ON ANY
THEORY OF LIABILITY, ARISING OUT OF OR IN CONNECTION WITH
THE USE OR PERFORMANCE OF THIS SOFTWARE.
c
Period04 is based on Period98 (Copyright 1996-1998
by Martin Sperl).
5.1 Third party software
Period04 makes use of the following third party software:
• Scientific Graphics Toolkit (SGT) - an open source library of Java graphics classes.
The SGT is provided by NOAA (National Oceanic and Atmospheric Administration) for full, free and open release and is available at
http:// www.epic.noaa.gov/java/sgt/sgt download.shtml.
• EpsGraphics2D - an open source package for creating high quality EPS
graphics
c
Copyright 2001-2004
by Paul James Mutton
http://www.jibble.org/epsgraphics/
• JavaHelpTM 2.0 01
Copyright 2003 Sun Microsystems, Inc.
http://java.sun.com/products/javahelp
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Acknowledgments.
We are grateful to M. Sperl for valuable comments. This work was supported by the Austrian Fonds zur Förderung der
wissenschaftlichen Forschung (Project P17441-N02).
References
Bevington, P. R., 1969, Data reduction and error analysis for the physical sciences,
McGraw-Hill (New York)
Breger M., Handler G., Garrido R., et al., 1999, A&A, 349, 225
Breger et al., 1993, A&A 271,482
Kuschnig et al., 1997, A&A 328, 544
Sperl, M. 1998, CoAst 111,1