THE SEARCH FOR TRANSITING EXTRASOLAR PLANETS
IN THE OPEN CLUSTER M52
A Thesis
Presented to the
Faculty of
San Diego State University
In Partial Fulfillment
of the Requirements for the Degree
Master of Sciences
in
Astronomy
by
Tiffany M. Borders
Summer 2008
SAN DIEGO STATE UNIVERSITY
The Undersigned Faculty Committee Approves the
Thesis of Tiffany M. Borders:
The Search for Transiting Extrasolar Planets
in the Open Cluster M52
Eric L. Sandquist, Chair
Department of Astronomy
William Welsh
Department of Astronomy
Calvin Johnson
Department of Physics
Approval Date
iii
Copyright 2008
by
Tiffany M. Borders
iv
DEDICATION
To all who seek new worlds.
v
Success is to be measured not so much by the position that one has reached in life as
by the obstacles which he has overcome.
–Booker T. Washington
All the world’s a stage, And all the men and women merely players. They have their
exits and their entrances; And one man in his time plays many parts...
–William Shakespeare, “As You Like It”, Act 2 Scene 7
vi
ABSTRACT OF THE THESIS
The Search for Transiting Extrasolar Planets
in the Open Cluster M52
by
Tiffany M. Borders
Master of Sciences in Astronomy
San Diego State University, 2008
In this survey we attempt to discover short-period Jupiter-size planets in the young
open cluster M52. Ten nights of R-band photometry were used to search for planetary transits.
We obtained light curves of 4,128 stars and inspected them for variability. No planetary
transits were apparent; however, some interesting variable stars were discovered. In total, 22
variable stars were discovered of which, 19 were not previously known as variable. Ten of our
variable stars were identified as eclipsing-type W Ursa Majoris contact binaries, 5 were
identified as detached binaries of the Algol type, 1 was identified as a slowly pulsating B star,
and 6 were irregular and require further investigation before they can be classified. A
color-magnitude diagram constructed from V and R photometry with fitted isochrones is also
presented to help determine cluster membership of our variable stars. We find that 3 of our W
Uma stars lie within a region of high cluster membership probability. Radial velocity follow
up observations are needed to confirm cluster membership. If confirmed, this would be highly
interesting as W Uma stars are not excepted to be found in such a young cluster.
vii
TABLE OF CONTENTS
PAGE
ABSTRACT . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
vi
LIST OF TABLES. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
ix
LIST OF FIGURES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
x
ACKNOWLEDGEMENTS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . xv
CHAPTER
1
INTRODUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.1
Planetary Transits . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
1
1.2
Fraction of Stars with Planets . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
5
1.3
Planet-Metallicity Correlation . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
6
1.4
Open Clusters . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
8
1.5
M52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
9
2
OBSERVATIONS OF M52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
3
DATA REDUCTION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
4
5
3.1
Overscan Correction and Trimming .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.2
Bias Removal . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 14
3.3
Flat Fielding . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.4
Correcting Bad Pixels . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.5
Header Corrections . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 15
3.6
Image Rejection . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 16
ISIS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.1
ISIS Setup . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.2
The interp.csh Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 17
4.3
The ref.csh Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
4.4
The subtract.csh Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
4.5
The detect.csh Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 23
4.6
The find.csh Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
4.7
The phot.csh Routine . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 24
PLANETARY TRANSIT SEARCH . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
viii
6
5.1
Box Least Square Algorithm . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 28
5.2
BLS Implementation .. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 30
5.3
SYSREM . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
5.4
Transit Selection Criteria . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 34
5.5
Planetary Transit Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 35
VARIABILITY . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 56
6.1
Period Determination . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
6.2
Variability Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.2.1 W UMa Variables . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 64
6.2.2 Slowly Pulsating B Stars . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.2.3 Detached Eclipsing Binaries . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 75
6.2.4 Irregular Variables or Unclassified . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 85
7
CONCLUSION . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 95
REFERENCES . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 96
ix
LIST OF TABLES
PAGE
Table 1.1 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
2
Table 2.1 R Filter Observations of M52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 11
Table 2.2 V Filter Observations of M52 . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 12
Table 4.1 ISIS Process Configuration File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 18
Table 4.2 ISIS Default Configuration File. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 20
Table 4.3 ISIS Phot Configuration File . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 21
Table 5.1 Input Parameters Used in BLS . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 33
Table 5.2 BLS Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Table 5.3 BLS Final Results . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 36
Table 6.1 Variable Star Information . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 57
x
LIST OF FIGURES
PAGE
Figure 1.1 Light curve of HD209458b from Brown et al. (2001) showing the
characteristic light curve of a planetary transit. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
4
Figure 1.2 Figure from Fischer & Valenti 2005 shows the occurrence of exoplanets vs iron abundance [Fe/H] of the host star measured spectroscopically. The occurrence of observed giant planets increases strongly with
stellar metallicity. The solid line is a power law fit for the probability
that a star has a detected planet. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . .
7
Figure 2.1 CMD with overlaid theoretical isochrones obtained from Cassisi et
al. (2006) . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 13
Figure 4.1 Composite reference image from ISIS.. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 19
Figure 4.2 var.fits produced from ISIS . Most of the really bright spots are saturated stars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 25
Figure 5.1 BLS example results from Kovacs et al. (2002) from a test set of
data. This shows the time series in the upper panel, the normalized BLS
frequency spectrum and the folded time series in the lower panel. The
signal parameters are displayed at the top where n is the number of bins,
P0 is the period, q is the fractional transit length, δ is the transit depth,
and δ/σ is the SNR. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 31
Figure 5.2 The top panel shows the RMS of the 4128 stars which appear on the
var.fits and have 323 out of 423 observations. The middle panel shows
the RMS of the 3935 stars remaining after filters have been applied. The
bottom panel shows the 1238 stars remaining which are suitable for BLS
study after filters were applied including an RMS < 0.015 magnitude cutoff. . . . . . 32
Figure 5.3 Binned phased plot for candidate ID 1956. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 38
Figure 5.4 Phase vs. unbinned delta magnitude of the points in transit for candidate ID 1956. Error bars have been added to convey the uncertainty in
the residual flux within the transit phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 39
Figure 5.5 Residuals of candidate ID 1956. Major time-axis tick marks are
spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian
Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first
observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 40
Figure 5.6 Normalized signal residue versus trial frequency for candidate ID
1956. The SR peak corresponds to a period of 1.5096 days. . . . . . . . . . . . . . . . . . . . . . . . . 41
Figure 5.7 Binned phased plot for candidate ID 2563. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 42
xi
Figure 5.8 Phase vs. unbinned delta magnitude of the points in transit for candidate ID 2563. Error bars have been added to convey the uncertainty in
the residual flux within the transit phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 43
Figure 5.9 Residuals for candidate ID 2563. Major time-axis tick marks are
spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian
Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first
observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 44
Figure 5.10 Normalized signal residue versus trial frequency for candidate ID
2563. The SR peak corresponds to a period of 1.5096 days. . . . . . . . . . . . . . . . . . . . . . . . . 45
Figure 5.11 Binned phased plot for candidate ID 1347. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 46
Figure 5.12 Phase vs. unbinned delta magnitude of the points in transit for
candidate ID 1347. Error bars have been added to convey the uncertainty
in the residual flux within the transit phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 47
Figure 5.13 Residuals for candidate ID 1347. Major time-axis tick marks are
spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian
Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first
observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 48
Figure 5.14 Normalized signal residue versus trials frequency for candidate ID
1347. The SR peak corresponds to a period of 1.4552 days. . . . . . . . . . . . . . . . . . . . . . . . . 49
Figure 5.15 Binned phased plot for candidate ID 1267. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 50
Figure 5.16 Phase vs. unbinned delta magnitude of the points in transit for
candidate ID 1267. Note that 1 “low” data point has been removed.
Error bars have been added to convey the uncertainty in the residual flux
within the transit phase. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 51
Figure 5.17 Phase vs. unbinned delta magnitude of the points in transit for
candidate ID 1267 including “low” data point. Error bars have been
added to convey the uncertainty in the residual flux within the transit phase. . . . . . . 53
Figure 5.18 Residuals for candidate ID 1267. Major time-axis tick marks are
spaced by 2.4 hours. The time-axis is defined as the Heliocentric Julian
Date (HJD(i)) subtracted from the Heliocentric Julian Date of the first
observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 54
Figure 5.19 Normalized signal residue versus trial frequency for candidate ID
1267. The SR peak corresponds to a period of 1.3598 days. . . . . . . . . . . . . . . . . . . . . . . . . 55
Figure 6.1 var.fits frame with location of variable stars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 58
Figure 6.2 Composite reference image with location of variable stars. . . . . . . . . . . . . . . . . . . . . . . 59
Figure 6.3 CMD highlighting the location of variable stars detected. . . . . . . . . . . . . . . . . . . . . . . 60
Figure 6.4 ID 0533 Lomb-Scargle period analysis. The peak of maximum
power corresponds to a P = 0.607 days. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 62
xii
Figure 6.5 ID 0533 Lafer-Kinman period analysis. Two of the lowest r values
corresponds to a period P = 0.607 days and P = 1.214 days. Lower r
values with larger periods can be ruled out based solely on the unphased
light curve. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 63
Figure 6.6 Phased light curves of suspected W UMa stars. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 65
Figure 6.7 Light curve of ID 0533. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 66
Figure 6.8 Light curve of ID 0981. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 67
Figure 6.9 Light curve of ID 1107. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 69
Figure 6.10 Light curve of ID 1133. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 70
Figure 6.11 Light curve of ID 1558. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 71
Figure 6.12 Light curve of ID 1834. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 72
Figure 6.13 Light curve of ID 2513. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 73
Figure 6.14 Light curve of ID 2673. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 74
Figure 6.15 Light curve of ID 2830. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 76
xiii
Figure 6.16 Light curve of ID 3727. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 77
Figure 6.17 Light curve of ID 1855. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 78
Figure 6.18 Phased light curves of suspected EA variables. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 80
Figure 6.19 Light curve of ID 0681. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 81
Figure 6.20 Light curve of ID 0980. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 82
Figure 6.21 Light curve of ID 1261. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 83
Figure 6.22 Light curve of ID 1284. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 84
Figure 6.23 Light curve of ID 4109. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 86
Figure 6.24 Light curve of ID 2409. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 88
Figure 6.25 Light curve of ID 2773. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 89
Figure 6.26 Light curve of ID 3096. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 90
xiv
Figure 6.27 Phased light curve of ID 3096. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 91
Figure 6.28 Light curve of ID 3928. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 92
Figure 6.29 Light curve of ID 4540. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 93
Figure 6.30 Light curve of ID 4762. Major time-axis tick marks are spaced
by 2.4 hours. The time-axis is defined as the Heliocentric Julian Date
(HJD(i)) subtracted from the Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th. . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . . 94
xv
ACKNOWLEDGEMENTS
First and foremost, my gracious thanks must be extended to my advisor Dr. Eric
Sandquist. I am exceedingly grateful for the 2 years of financial support you have provided
for me which has made this thesis possible. Thank you for your insight, patience, sense of
humor, endless advice, and for having a “test” for just about any situation. I have become a
better astronomer because of your guidance.
I would like to thank my family for their wholehearted support. A special thanks goes
to my loving and proud parents who always encourage me to fulfill my dreams.
Thank you to Matt Davis for being my motivation. I am thankful for all the
tremendous amounts of help and patience you’ve provided for me along the way.
I would like to thank Georgia Grossman and Azalee Bostroem for their friendship.
The support you’ve both provided for me is beyond words.
Thank you to De Marie Garcia for her insight, help, and for expanding my mind to
new possibilities of exploring the universe.
I would like to thank Leila Perello and Patty Baker for teaching me the beauty and
hard work required to dance ballet.
Thank you to the members of my thesis committee, Dr. William Welsh and Dr. Calvin
Johnson for their feedback on my thesis.
Thank you to Dr. Etzel for allowing me to complete my thesis with the use of his
computer “MEGADEATH.”
Finally, I would like to thank our department administrator, Margie Hoagland for all
her support and help.
1
CHAPTER 1
INTRODUCTION
The field of planet searches has grown tremendously since the first confirmed
extrasolar planet detections were made in the 1990s. One of the techniques for planet
detection that has had recent successes is the search for planets transiting their host stars. To
date, more than 2901 extrasolar planet candidates have been detected using various
techniques. There are 51 known transiting planets. Transits of bright stars have great scientific
potential, giving clues to information such as the internal structure of planets (Guillot 2005)
and their atmospheric composition (Charbonneau et al. 2002).
1.1 P LANETARY T RANSITS
The planetary transit method is based on the observation of the temporary dimming of
the apparent brightness of a parent star that occurs when a planet moves across the stellar
disk. One condition for the use of this method is, of course, that the planet should (from the
observer’s viewpoint) pass in front of its star. The probability of this occurring also depends
on the size of the star, and is greater when dealing with a large star. Another factor to consider
is the distance of the planet from the star since the nearer it is, the greater the chance that a
transit will occur.
So, what is the probability of being able to observe a planetary transit across a star at a
distance a? If the stars were indeed a point source, the transit would occur only if the star, the
planet, and the observer were in exact alignment. However, the star has a finite radius. In the
case of planetary-stellar transits one can estimate the probability to observe transits as a
function of three parameters, the star radius R∗ , the transiting planet radius Rp , and the
distance between both objects at the time of transit a. The probability to observe a transit
assuming random orientation of the orbit is (Sackett 1999):
P robability =
R∗ + Rp
a
(1.1)
In the case of planetary transits, this probability becomes close to R∗ /a showing that it is
more likely to observe a transiting planet at small orbital distances. In general, the nearer a
planet is to its star, the greater the possibility of a transit; and the larger the star, the greater the
chance that the planet will be seen to pass across it. However, the range of inclinations can
1
see J. Schneider’s Extrasolar Planets Encycolpedia at http://exoplanet.eu/ for an updated list.
2
change as the planet gets closer or further away from the parent star and this must also be
taken into account.
If R∗ = R⊙ , then for a planet at 1 AU (P = 365 days assuming a 1M⊙ star), the
probability of being able to observe a transit is 0.5%, rising to a not insignificant 10% if the
planet orbits at 0.05 AU (P = 4 days). As seen in Table 1.1, in the case of the solar system
observed by a person at a random orientation, the probability to observe a transit of Mercury
is of order 1% while it drops down to 0.1 % for Jupiter. For the configuration of “hot”
Jupiters, large planets close to their parent stars, such as 51 Pegasi b and HD209458 b they
favor the visibility of transits. The probability that the planet, as seen from Earth, will cross
the face of the star (assuming a solar-type star) attains 10%.
Table 1.1.
Probability of Transit % Duration of Transit (Hours)
Mercury
1.2
8
Venus
0.64
11
Earth
0.47
13
Jupiter
0.09
30
Saturn
0.05
41
51 Pegasi b
9.1
3
HD 209458 b
10.8
3
Variation in Flux %
1.2×10−3
7.6×10−3
8.4×10−3
1
0.75
1
1.6
The diminution in brightness due to the transit of the planet is easy to determine. It is
simply the ratio of the apparent surfaces of the planet and the star:
∆F =
Rp
R∗
2
(1.2)
Consequently, if the radius of the star can be estimated then the radius of the planet can be
deduced.
The duration of the transit depends firstly upon the period of revolution of the planet
around the star. The further away the planet is from the star, the longer it will take to pass
across the face. Secondly, the duration of the transit depends upon the inclination of the orbit.
It is possible from geometrical calculations to infer the duration of the transit event. The
maximum transit duration Tmax (when the planet crosses over the center of the stellar disk), in
front of a star of radius R∗ and mass M∗ , for a planet orbiting with a period P at a distance a
is (Lecavelier Des Etangs & Vidal-Madjar 2006):
Tmax
a 1/2
P × R∗
≈ 13.0
=
π×a
1AU
M∗
M⊙
−1/2 R∗
R⊙
hours
(1.3)
3
assuming a planet radius much smaller than R∗ . So, for a star with known mass and size, the
maximum transit duration is constrained by the orbital period and the size of the parent star.
For planets at different distances, the transit may last periods ranging from hours to several
days. The actual transit duration, however, depends on the inclination of the planetary orbit
with respect to the observer (Sackett 1999). For instance, if the planet’s orbit is at an inclined
angle then it might only graze a small region of the star therefore reducing the measured
transit duration. It is also worth mentioning that the transit duration becomes increasingly
more difficult to observe if the transit is long. A typical observation run is on average ∼10
hours and if the transit is longer than this, like in the case of Jupiter with a transit duration of
30 hours, an observer could easily miss the transit. Planets that have transit durations of less
than a day require rapid and continuous sampling to ensure high detection probabilities.
Another factor worth noting is that it is impossible to observe an object 24 hours a day from a
single site because of the alternation of night and day which produces yet another challenge to
finding transiting planets.
It is also possible to infer the shape of the photometric light curve. To calculate the
theoretical transit light curve, one must take into account the non-uniformity of the stellar flux
over the different parts of the stellar disk. It is in general affected by the limb darkening which
induces a curved bottom shape for the transit profile. This can be seen in Figure 1.1 showing
the high quality transit profile HD 209458b obtained by Brown et al. (2001) with the Hubble
Space Telescope. This observed profile can be very well fitted by a theoretical light curve
taking into account the limb darkening of the solar-type star HD209458.
To produce a detectable transit, most planets will require an orbital inclination of less
than a few degrees from edge-on (Sackett 1999). So, the planet’s orbit needs to be nearly
perpendicular to sky (inclination close to 90◦ ). While it is quite challenging to find this,
pre-selecting favorable inclination targets through measurement of the rotational spin of the
parent could be a way to favor transit discoveries. However, due to the precision of such
evaluations and to the probable spread of the planets’ orbital plane inclinations relative to the
star a gain of no more than a factor of three to five in detection probability is expected (Sackett
1999). Other proposed ways to favor transit detection are to select already transiting binary
star systems in which the orbital plane of the the binary is known to be close to edge-on and
by assuming that planets could be present in the orbital plane of the stellar system (Sackett
1999). However, the evolution and dynamics of double star systems are quite different from
single star systems which could affect the formation and frequency of planetary companions.
Also, the gain in probability remains of the order of a factor of three to five (Sackett 1999).
It should be noted that in order to detect an exoplanet by the transit method, the
luminous flux from the star has to be measured very accurately over an extended period, in the
4
Figure 1.1. Light curve of HD209458b from Brown et al. (2001) showing the characteristic
light curve of a planetary transit.
5
hope of being able to observe regular fluctuations as the star dims slightly for a certain
repeated amount of time. Accuracy to at least 1% in the measurement of the flux (0.01 mag) is
necessary for the detection of giant planets (Casoli & Encrenaz 2007). In the final analysis
from transit observations one can deduce the radius of the planet, its period, and the
inclination of its orbit but not its mass. Velometric observations are also needed to allow for
the minimum mass (Msini) of the planet to be determined.
Since there is no clear way to improve the probability of detecting planetary transits,
searches have to cope with probabilities in the range of 0.1 to 1%, except in the case of the
“very hot” Jupiter which can be detected with a much higher probability, up to ∼ 20% for the
shortest orbital period (Bouchy et al. 2004). The consequent strategies are to look for a large
number of targets such as fields containing thousands of stars to survey photometric
variations. Open clusters which contain up to a few thousand stars, for example, provide an
ideal environment for searching for transiting extrasolar planets. This strategy, however,
entails the analysis of lots of data. While hundreds of candidates stars may be found a vast
majority of these candidates will be revealed as variable stars or eclipsing binaries but even if
one planet is detected it will be a scientific treasure worth the hunt.
1.2 F RACTION OF S TARS WITH P LANETS
In order to answer the question “what fraction of stars have planets?” we must rely on
the analysis of statistical distributions of extrasolar planets (also known as exoplanets)
detected so far. To estimate the fraction of stars with planets it can be calculated from the raw
numbers of stars that host exoplanets divided by the number of stars monitored. For example,
Marcy & Butler (2000) report a fraction of 5% of main-sequence stars harbor companions of
0.5 to 8 Mjup within 3 AU. Lineweaver & Grether (2003) report an analysis from radial
velocitites of ∼1800 nearby Sun-like stars monitored by eight high-sensitivity Doppler
exoplanet surveys that approximately 90 of these stars host exoplanets massive enough to be
detectable. Thus, at least ∼5% of targets stars posses planets. Further analysis by Lineweaver
et al. (2003) estimate that at least ∼9% of Sun-like stars have planets in the mass and orbital
period ranges Msini > 0.3Mjup and P <13 years and at least ∼ 22% have planets in the
larger range Msini > 0.1Mjup and P < 60 years. Marcy et al. (2005) also report statistical
properties from the 152 exoplanets that have been discovered orbiting 13 normal stars using
the Doppler technique. They found that >7% of stars have giant planets within 5 AU (most
beyond 1 AU) and 1.2% of spectral type F,G, and K stars have hot Jupiters (a < 0.1 AU).
Lineweaver & Grether (2003) also attempt to answer the question of “what fraction of
Sun-like stars have Jupiter-like planets?” This fraction is important to consider because
Jupiter is a dominant orbiting body in our solar system and probably had a significant
influence on the formation of our planetary system. So, it is interesting to consider how
6
typical is Jupiter. Lineweaver & Grether (2003) estimate that the fraction of Sun-like stars
hosting planets to be ∼5% in a “Jupiter region” which is defined by orbital periods between
the period of the asteroid belt and Saturn with masses in the range MSat < Msini < 3MJup .
Using the transit method, the probability of detecting a transit in best in the case of a
hot Jupiter (as discussed in the previous section). Hot Jupiters typically have masses and radii
similar to that of Jupiter with short orbital periods between 1 - 10 days. So, what is the
probability of finding a transit of a hot Jupiter? The factors that need to be considered in order
to answer this question include the frequency of hot Jupiters around surveyed stars, the
likelihood of the geometrical alignment between the star and planet that is necessary to detect
transits, and the binary fraction (von Braun et al. 2005). von Braun et al. (2005) calculates the
probability by making several assumptions including a planet frequency around isolated stars
of 0.7% for planets with a semimajor axis of a ∼ 0.05. It is also assumed that approximately
10% - 20% of those hot Jupiter systems would have a favorable orientation (nearly edge-on)
that a transit would be visible from Earth. Since von Braun et al. (2005) assumes that planets
can only be detected around single stars a binary fraction of 50% is assumed. Under all these
assumptions, it is estimated that 1 star in 3000 (a ∼ 0.05 AU) has a transiting hot Jupiter
around a main-sequence star.
1.3 P LANET-M ETALLICITY C ORRELATION
Soon after the discovery of the first exoplanets, stellar spectroscopists noticed that the
stars hosting giant planets were systematically metal-rich (Udry & Santos 2007). Planet
occurrence appears to correlate strongly with the abundance of heavy elements in the host star
where the frequency of planets rises steeply as a function of the metallicity of the star (Figure
1.2). The frequency of planetary systems depends on the metallicity of the host star, with stars
of low metallicity having a lower probability of planetary formation. Current numbers suggest
that at least ∼25% of the stars with twice the metal content of the Sun( [Fe/H] ≥ +0.3) are
orbited by a giant planet, and this number decreases to below 5% for solar metallicity objects
(Udry & Santos 2007).
The correlation between planet occurrence and metallicity can be expressed as a
power law (Fischer & Valenti 2005):
P (planet) = 0.03 ×
(NF e /NH )
(NF e /NH )⊙
2
(1.4)
This correlation applies to FGK-type main sequence stars and is valid over the metallicity
range -0.5 < [Fe/H] < 0.5. This relationship (shown in Figure 1.2) quantifies the probability
P(planet) for forming a gas giant planet with orbital period shorter than 4 yrs as a function of
metallicity. Thus, from this power law, the probability of forming a gas giant planet is nearly
7
Figure 1.2. Figure from Fischer & Valenti 2005 shows the occurrence of exoplanets vs iron
abundance [Fe/H] of the host star measured spectroscopically. The occurrence of observed
giant planets increases strongly with stellar metallicity. The solid line is a power law fit for
the probability that a star has a detected planet.
8
proportional to the square number of the number of iron atoms. So, it appears that metallicity
seems to play a crucial role in the formation and/or evolution of planets. One explanation for
the physical mechanism for the observed planet-metallicity correlation is that the high
metallicity enhances planet formation because of the increased availability of small particle
condensates which are the building blocks of planetesimals. This high metallicity found in
planet-bearing stars is argued to be inherited from the primordial cloud, rather than an
acquired asset. Furthermore, planet-bearing stars with super-Solar metallicity are more than
twice as likely to have multiple planet systems than planets-bearing stars with sub-Solar
metallicity. The observed metallicity correlation does not imply that giant planets cannot be
formed around more metal-poor objects but rather that the probability of formation among
such systems is lower.
To test the dependence of metallicity on planets formation globular clusters can be
used as a direct study. These clusters are among the oldest of astronomical objects, and
therefore, their stars typically have very low metallicity. Gilliland et al. (2000) used WFPC2
on the Hubble Space Telescope (HST ) to search for transits on ∼34,000 main-sequence stars
in the globular cluster 47 Tucanae. While 47 Tuc is metal-rich as far as globular clusters are
concerned it is metal-poor ([Fe/H] = -0.76; Harris (1996)) compared with objects in the solar
neighborhood and has considerably lower metallicity of any star known to harbor an extrasolar
planet. Based on statistics from a sampling of planets in our local stellar neighborhood,
Gilliland expected that 1 out of 1,000 stars in the globular cluster should have planets transit
once every few days and predicted that HST should discover 17 hot Jupiter-class planets.
However, no planets were found. The lack of planets can be attributed to not only the low
metallicity but also the extreme environment of a globular cluster which might not be the best
place for planets to survive. Davies & Sigurdsson (2001) showed that a planet in the densest
core region of 47 Tuc, sampled by Gilliland et al. (2000), would survive disruption by stellar
encounters for ∼ 1×108 years with an orbital separation d ∼ 5 AU. Short period planets,
those to which transit surveys are sensitive, would survive for significantly longer.
1.4 O PEN C LUSTERS
As discussed in the previous sections, one way of overcoming the difficulties of
finding transits is to search for transits in dense stellar fields. While globular cluster do
contain thousands to millions of stars and seem like good laboratories for searching for
extrasolar planets the globular cluster’s low metallicity and harsh conditions may not support
planets (as discovered in the case of 47 Tuc). Other searches have undertaken a wide-field
search for transits in the Galactic plane since the Galactic plane provides a high density of
stars in a long narrow survey volume. Teams such as OGLE III (Optical Gravitational Lensing
Experiment) have monitored ∼52,000 galactic disk stars for 32 nights, and report 59 transit
9
candidates with periods ranging from 1 to 9 days (Udalski et al. 2002b,a). Open clusters (OC)
also provide a potentially ideal environment for the search of transiting extrasolar planets
since they feature relatively large number of stars (∼ 10,000 member stars) of the same
known age, metallicity, and distance. Open clusters are essentially at the same distance from
the Sun because the distance between member stars in the cluster is much smaller than the
distance to the cluster. The stars have nearly the same age since they formed together. Since
they all formed from the same nebula, cluster members should have virtually the same
chemical composition. However, cluster members do differ in mass.
Open clusters are less crowded and offer a range of metallicites which can further be
used to resolve the effects of metallicity and high-density environment on planet frequency.
With this motivation a number of open clusters have been monitored by different groups.
Examples of such teams include PISCES (Planets in Stellar Clusters Extensive Search;
(Mochejska et al. 2002, 2006)) and EXPLORE/OC von Braun et al. (2005), STEPPS (Survey
for Transiting Extrasolar Planets in Stellar Systems; Burke et al. (2004)) and UStAPS
(University of St. Andrews Planet Search; Street et al. (2003) which target selected open
clusters to find exoplanets. However, no cluster survey has yet confirmed the detection of a
planet. Despite no planets yet being confirmed, these surveys have provided promising
candidates awaiting follow-up, as well as cluster parameters and variable stars.
Careful cluster target selection is important in OC planet transit surveys. Some
challenges to consider suggested by von Braun et al. (2005) include the somewhat low
number of stars in an open cluster, determining OC cluster membership in the presence of
significant contamination, and differential reddening along the cluster field and long the line
of sight. To reduce some of these challenges careful selection can help maximize the number
of stars, maximize the probability of detecting transits, and reduce line-of-sight and
differential reddening. One of the biggest challenges in the selection of target clusters is the
lack of data on many OCs. The physical parameters of the cluster such as distance,
foreground reddening, age, and metallicity, are frequently either not determined or have large
uncertainties in the published values.
1.5 M52
The open cluster M52 was carefully selected for this photometric planetary transit
survey. M52 is relatively close at a distance of 1.4 ± 0.2 kpc (Bonatto & Bica 2006) and is
easily observable from our location and facilities available. M52 is located in the direction of
′
′′
Cassiopea at (J2000) α = 23h 24m 42s and δ = 61◦ 35 42 . It is a rich cluster that is strongly
concentrated and contains a moderate range of star brightnesses.
As discussed previously, metallicity is an important consideration in planetary
searches. We attempted to determine the metallicity of M52 for this project. However, there
10
are yet no spectroscopic measurements. We also attempted to determine [Fe/H] using
Stromgren photometry however, there is no Stromgren photometry in the F and G star range
where the metallicity calibrations are most trustworthy. Thus, we assume M52 is close to
solar metalicity based on the following reasons.
M52 is relatively young with an estimated age of 60 ± 10 Myr (Bonatto & Bica 2006).
It is presumed that because the cluster is young it has stars that are generally metal rich having
formed from remnants of previous supernovae explosions. During supernova detonations iron
is ejected, enriching the stellar medium and therefore, younger stars can be created with a
greater abundance of iron in their atmospheres. Thus, based on the youth of M52 we assume
that it is close to solar metallicity.
Younger clusters are typically concentrated in the center of the Galaxy and are close to
the Galactic plane. Within the Galactic plane the metallicity content is found to be higher.
Within the thin disk of the Galaxy, where open clusters reside, typical values of [Fe/H] range
from -0.5 to +0.3, while stars in the thick disk (further from the Galactic plane) range from
-0.6 to -0.4 (Carroll & Ostlie 2006). Also, in the Galaxy as a whole there is a general trend for
the metallicity to increase towards the central regions. Metal-rich stars are found to be more
common within the solar circle. Bonatto & Bica (2006) determined the location of M52 to be
7.9±0.2 kpc from the Galactic center which is ≈0.7 kpc outside the solar circle. Thus, also
based on the position of M52 within the Galaxy is likely that it is close to solar metallicity.
One caveat to this cluster is that it has a low Galactic latitude (ℓ = +112.81◦, b = 44◦ )
and is affected by Galactic star contamination. On average, the closer the OC is to the Galactic
disk, the higher the contamination due to Galactic field stars. However, transit detections
around main-sequence field stars are still possible and would also be scientifically valuable.
11
CHAPTER 2
OBSERVATIONS OF M52
Observations of M52 were obtained in 2001 between August and November and 2007
in December from Mount Laguna Observatory with the 40 inch telescope. Table 2.1 lists the
observations dates, the number of observed hours on the target source taken the in R band,
and the average seeing including the 1 σ uncertainty. Table 2.2 lists the observation dates, the
number of observed hours on the target source taken in the V band, and the average seeing
including the 1 σ uncertainty. Observations were taken in the V band for the construction of a
color-magnitude diagram (CMD).
A range of exposure times were taken for individual images from 60 seconds to 600
seconds. A total exposure time of 70.49 hours was taken in the R filter and a total exposure
time of 2.82 hours was taken in the V filter.
Table 2.1. R Filter Observations of M52
Date
Heliocentric Julian Day Duration (hr)
2001 Aug 24
2452146.0
4.94
2001 Aug 25
2452147.0
5.07
2001 Aug 26
2452148.0
4.88
2001 Sept 17
2452170.0
6.53
2001 Sept 18
2452171.0
6.02
2001 Sept 19
2452172.0
6.52
2001 Sept 20
2452173.0
6.52
2001 Oct 13
2452196.0
5.52
2001 Oct 14
2452197.0
5.73
2001 Oct 15
2452198.0
5.16
2001 Oct 16
2452199.0
5.91
2001 Nov 14
2452227.0
3.15
2001 Nov 15
2452228.0
0.29
2001 Nov 16
2452229.0
3.12
2007 Dec 06
2454444.0
1.13
Seeing (′′ )
3.08 ± 0.58
2.73 ± 0.26
2.92 ± 0.27
2.73 ± 0.26
2.71 ± 0.15
2.70 ± 0.16
2.76 ± 0.18
2.72 ± 0.22
2.82 ± 0.19
2.89 ± 0.28
2.84 ± 0.20
3.18 ± 0.43
2.67 ± 0.19
2.91 ± 0.33
2.51 ± 0.29
The color-magnitude diagram (CMD) was constructed from a DAOMATCH and
DAOMASTER combination of the R data and V data. Four images were used for the CMD
including two V band observations from September 17th and September 19th 2001 and two R
band observations from September 18th and September 19th 2001. Because the observed data
are uncalibrated, the magnitudes and colors were shifted to match calibrated data of M52
12
Table 2.2. V Filter Observations of M52
Date
Heliocentric Julian Day Duration (hr)
2001 Aug 25
2452147.0
0.24
2001 Aug 26
2452148.0
0.20
2001 Sept 17
2452170.0
0.18
2001 Sept 19
2452172.0
0.42
2001 Sept 20
2452173.0
0.83
2001 Oct 13
2452196.0
0.39
2001 Oct 14
2452197.0
0.42
2001 Oct 15
2452198.0
0.14
Seeing (′′ )
2.73 ± 0.26
2.92 ± 0.27
2.43 ± 0.02
2.70 ± 0.16
2.76 ± 0.18
2.72 ± 0.22
2.82 ± 0.19
2.89 ± 0.28
from Stetson (2000) obtained from the WEBDA1 online database. A star from our data was
matched to the same star from Stetson (2000) and an offset in both (V-R) and V was used to
shift the data. An offset of +2.0162 magnitudes was applied to the instrumental magnitudes
and an offset of +1.3213 was applied to the (V-R) color index. Figure 2.1 shows the CMD.
Overlaid on the observed CMD are theoretical isochrones obtained from the BASTI 2
interactive database of updated stellar evolution models from Cassisi et al. (2006). We
selected a metallicity of Z = 0.0198 since the cluster is assumed to be near solar and an age of
60 Myrs determined from Bonatto & Bica (2006). The CMD can be used as a tool for
estimating cluster membership for any detected variable stars in the cluster CMD. This will be
discussed in §6.
1
2
http://www.univie.ac.at/webda/
http://193.204.1.62/index.html
13
CMD of M52
8
10
V
12
14
16
18
0.2
0.4
0.6
0.8
(V - R)
1
1.2
1.4
Figure 2.1. CMD with overlaid theoretical isochrones obtained from Cassisi et al. (2006) .
14
CHAPTER 3
DATA REDUCTION
We must apply a series of corrections to each raw CCD image in order to seperate
instrumental signals and imperfections from the astronomical signals before photometric
analysis is implemented. Observations of the target object were reduced in the standard
fashion, using IRAF 1 routines to correct the raw data. Calibration images used for the image
reduction include dark frames and twilight flat fields which were taken on each night of an
observation. The basic processing steps are: overscan correction and trimming, bias removal,
flat-fielding and bad pixel corrections. Each is described below.
3.1 OVERSCAN C ORRECTION AND T RIMMING
The overscan strip is the narrow region of the CCD image usually running down either
side of the image and contains virtual pixels generated by the CCD electronics when the CCD
is read out. The overscan strip must be subtracted and trimmed from all target and calibration
images. The mean level of the pixels in the overscan region provides a measure of the average
signal introduced by reading the CCD. The values of the signal in the overscan strip may be
fitted as a function of row and subtracted from the value in each pixel in that row. Once this is
completed, the image is overscan corrected and the overscan region can thus be trimmed and
discarded.
The overscan region and trim section for this project is determined using the implot
IRAF routine. This plot provides a drop in the CCD pixel values in the region of the overscan
strip. We used the IRAF task COLBIAS to perform the overscan correction and trimming
using the chebyshev fitting function of order 25. A bias section of [2095:2195, 2:2045] and
trim section [21:2065, 2:2045] is used for all data sets.
3.2 B IAS R EMOVAL
The bias is the pixel-to-pixel structure in the read noise on an image. Since the bias
varies across the CCD, a bias frame must be used to remove the bias structure from other
images. The bias frames are zero second exposure where the the CCD is not exposed to any
light, so the measured signal is merely the bias. Multiple bias frames (typically 10 - 20) are
taken and then averaged to create a master bias frame to de-bias all the other images.
1
IRAF is distributed by the National Optical Astronomy Observatories, which are operated by the Association of Universities for Research in Astronomy, Inc., under cooperative agreement with the National Science
Foundation.
15
The IRAF routine IMCOMBINE is used to create the master bias frame with a median
combine for this project. We use the IMARITH task to subtract the master bias from the target
images and flat fields.
3.3 F LAT F IELDING
Since the sensitivity of individual pixels on the CCD is not constant the images need
to be corrected with flat-fielding. Flats (typically 5 - 10) using the twilight sky as the
illumination souce are used for this project. A seperate master flat is constructed for each
filter. The flat field correction is made with the master flat field, by dividing the image to be
corrected by the flat field. The individual flat field images are overscan corrected, trimmed,
and de-biased.
We use the IRAF task IMCOMBINE to median combine flats in each filter to create a
master flat. The master flat is then normalized. The normalized flat is then divided into the
target object frames of the corresponding filter.
3.4 C ORRECTING BAD P IXELS
Bad pixels can be replaced with an interpolated value based on the values in adjacent
non-bad pixels. Two flat field images of different exposure levels are used to create a pixel
mask in the IRAF routine CCDMASK. By using a ratio of two flat fields having different
exposures all features which would normally flat field properly are removed and only pixles
which are not corrected by flat fielding are found to make the pixel mask. This mask is then
used for the IRAF routine FIXPIX which replaces the bad pixels with a linear interpolation
along lines or columns using the nearest good pixels.
3.5 H EADER C ORRECTIONS
In a number of observations the header information was recorded incorrectly and
needed to be corrected or input into the header. For all observations the date needed to be
input in the header since this value is not the date in which the observation was taken but
instead the date in which the data was uploaded on the computer. The actual date the
observation was taken could not be recovered electronically.
For the dates of 2001 August 24th, September 20th, and October 15th and 16th the
time of observation was not recorded properly in the header. Based on times recorded in a log
during the observation the times were recreated based on the exposure times of the
observations and the beginning and end times recorded in the log. A program was written to
recreate these times and these new times were input in the header.
16
For the dates of 2001 August 24th, September 20th, October 15th, and October 16th
the RA and DEC were not recorded correctly. The correct RA of 23:24:48.00 and DEC of
+61:35:00.0 for M52 were input in the header for these observations.
3.6 I MAGE R EJECTION
Using the IMEXAM routine in IRAF, and average FWHM was determined for at least
5 stars on various locations of the image to determine the average seeing. Images with bad
seeing (seeing > 3.5′′ ) were not included in this survey. Images with bright satellite or meteor
tracks were also not included. Other images which were rejected were due to poor telescope
tracking or poor focus. In total 746 images were taken for this survey but after implementing
our image rejection we only used 423 images from August 2001, October 2002, and
November 2001.
While it appeared that our September observations were useable it was later
determined that these images were causing problems with our analysis. It was reported that
the telescope anti-reflection coating was damaged from bad UV flooding at the time. Our
September images were run in ISIS (to be discussed in §4) however, they were treated
separately from the rest of the observations. 165 images from September were processed
separately. Also, all of our December images were rejected in the end because they were too
noisy to be trustworthy.
17
CHAPTER 4
ISIS
We have implemented the Image Subtraction Method of Alard & Lupton (1998),
available in ISIS 2.1 1 , on our reduced images to identify variable candidates. We have
selected to use ISIS because it is one of the methods of choice to search for variability in
crowded fields. The entire process requires running six scripts: interp.csh, ref.csh,
subtract.csh, detect.csh, find.csh, and phot.csh. The basic steps involved in these scripts
include transforming all frames to a common grid, construction of a reference frame,
subtraction of each frame from the reference frame, construction of a median image of all
subtracted images, selection of stars to be photometered, and extraction of profile photometry
from the subtracted images. The following subsections will provide a detailed description of
each of the ISIS scripts. Before they are described, the general setup of the ISIS directories
will first be presented.
4.1 ISIS S ETUP
In order to run ISIS modifications need to be made to the configuration files in the
register folder. The configuration files include the process config, default config, and
phot config whose parameters are displayed in Tables 4.1, 4.2, and 4.3. In process config,
some basic parameters about the directory structures must be inputted. The keyword IM DIR
denotes the directory where the user’s images are located. MRJ DIR represents the location of
the installation directory. INFILE points to the location of the file where all the images and
their dates in Heliocentric Julian Day are housed. This file can be in the register directory and
is called dates. CONFIG DIR is the directory that houses the configuration files− the register
directory in other words. All other user specific inputs, especially those contained in
default config and phot config, will be discussed in later subsections. It should be noted that
there is no set formula to produce the best results, as the parameters need to be fine tuned over
and over again until satisfactory results are produced. We did find, however, that some
parameters did not effect our overall results and these parameters are mentioned in the
proceeding sections.
1
ISIS is available for download at: www2.iap.fr/users/alard/package.html
18
Table 4.1. ISIS Process Configuration File
Parameter
IM DIR
MRJ DIR ..
REFERENCE
REF SUB
INFILE
VARIABLES
DEGREE
CONFIG DIR
SIG THRESH
COSMIC THRESH
REF STACK
N REJECT
MESH SMOOTH
Value
../images
1
a2m52r13rbtzf.fits
ref.fits
../register/dates
phot.data
2
../register2
3.0
3
interp a2m52r13rbtzf.fits 5
2
3
Definition
Directory where the images are stored
Installation directory
Reference image for astrometry
Reference image for subtraction
Dates of the frames
Coordinates of objects to make light curves
Degree of the polynomial astrometric transform
between frames
Where to find the configuration files
Threshold for variable detection in var.fits
Parameter for cosmic ray rejection
Image for subtraction (only for sub image
If Nth brightest value in series too large, reject it
Size of smoothing mesh for var.fits
4.2 T HE interp.csh ROUTINE
The interp.csh routine is used for image registration and interpolation. It removes
translations and rotations in all the images by applying a reference image and astrometric
transform to each image. In other words, it essentially maps each frame onto a reference
image, so that all the stars are in the same place in each image. For the astrometric transform,
stars in the reference image are cataloged and then matched to a catalog of each image. Any
offset is identified, and finally the astrometric transform (a first order two-dimensional
polynomial) is fitted to the data. The astrometric transform then defines new grid points, and
interpolates the values in the original grid using bicubic splines. The new image frame that is
constructed is aligned with the reference frame as well as conserving the total flux.
The most important input in the process config for this process is the REFERENCE
keyword, which denotes the reference image to be used throughout the process. The reference
image (also referred to as the template image) should be an image of good seeing and good
cluster core position. We have selected to use image a2m52r13rbtzf.fits (taken on August 25th
2001) because the position of the cluster is among the best of our best seeing images (seeing
2.1′′ ). Also, the DEGREE keyword is the degree of the polynomial used in the astrometric
transform between the frames.
4.3 T HE ref.csh ROUTINE
The ref.csh builds a composite reference frame to transform all images to the same
seeing and background level. REF SUB is an important parameter for this routine. This
keyword indicates the name of the file that includes a list of reference frame images to be
stacked. These images are typically the best seeing images and should have a field similar to
19
Figure 4.1. Composite reference image from ISIS.
those of most of the images in the series, which will later be transformed to the same seeing
and background level as the best image (REF STACK). The images chosen to be stacked
should have no visible defects, or the images will throw off succeeding steps, as the stacked
reference image is further applied to all images.
We used 12 of our best seeing images to create the stacked reference frame called
ref.fits which is the placed in the images directory. We initially used a much larger set of
images to build the ref.fits however, a number of the images were contributing to problems
found in the ref.fits. Some of the images we initially selected did not get subtracted properly
when transformed in order to match the seeing and background level of REF STACK. By
looking at the convr interp images produced from this routine we selected only the best
seeing images which did not have subtraction problems to build our ref.fits. This step was an
important part for optimizing our results in ISIS. From the plethora of test runs we performed
to determine the best parameters in ISIS we have discovered that choosing the images for your
ref.fits is among the most important step for this process. Figure 4.1 shows our final ref.fits. It
should be noted that for our September images, which were processed separately due to
telescope complications, all parameters were kept the same as our big run except the ref.fits
was composed of only September images.
20
Table 4.2. ISIS Default Configuration File
Parameter
nstamps x
nstamps y
sub x
sub y
half mesh size
half stamp size
deg bg
saturation
pix min
min stamp center
ngauss
deg gauss1
deg gauss2
deg guass3
sigma gauss1
sigma gauss2
sigma gauss3
deg spatial
Value
15
15
1
1
12
15
3
45000
7
100
3
8
6
4
0.8
1.67
4
3
Definition
Number of stamps along X axis
Number of stamps along Y axis
Number of sub division of the image along X axis
Number of sub division of the image along the Y axis
Half kernel size
Half stamp size
Degree to fit differential background variations
Saturation value for eliminating pixels
Minimum value for the pixels to fit
Minimum value for objects to enter kernel fit
Number of Gaussians
Degree associated with 1st Gaussian
Degree associated with 2nd Gaussian
Degree associated with 3rd Gaussian
Sigma of 1st Gaussian
Sigma of 2nd Gaussian
Sigma of 3rd Gaussian
Degree of the fit of the spatial variations of the Kernel
4.4 T HE subtract.csh ROUTINE
Once we have built a composite reference frame, we can apply image subtraction to all
images. To do this, the ref.fits image will be convolved with a spatially varying kernel in order
to match the background and seeing of the reference frame to each image. This is done by
essentially fitting gaussians to each object. Then the convolved image is subtracted from each
image and stored in the images directory. According to Alard & Lupton (1998), the kernel
satisfies the following equation with x and y as coordinates:
Ref erence(x, y) ⊗ Kernel(u, v) = I(x, y)
(4.1)
The kernel(u, v) represents a transform over a region of pixels(u, v) that when convolved
with the Ref (x, y) pixels will match the seeing in those pixels on the image frame. Because
this non-linear equation is computationally expensive to solve it is thus not practical for
crowded fields where we are interested in measuring the flux in many pixels. By decomposing
the kernel using a set of basis functions a standard linear least squares method can be applied
and the solution for the kernel is computationally easier to solve:
Kernel(u, v) =
X
i
ai Bi (u, v).
(4.2)
21
Table 4.3. ISIS Phot Configuration File
Parameter
sub x
sub y
rad1 bg size
rad2 bg size
nstars
mesh
saturation
min
psf width
ngauss
radphot
nstars max
nb adu el
rmax
first
keep
Value
1
1
15
20
5
2
45000
7
100
23
5
8
0.5
0.5
1
5
Definition
Number of sub division of the image along X axis
Number of sub division of the image along the Y axis
Inner radius of annulus for background
Outer radius
Saturation value for eliminating pixels
Minimum value for the pixels to fit
Minimum value for objects to enter kernel fit
Radius of circle within the pixels will be fitted to estimate flux
Gain in units of ADU/electrons
The ai term is the contribution of the different basis functions describing the kernel(u, v). Bi
are the basis functions (a Gaussian) used to model the seeing differences with the form:
−
B(u, v) ≡ e
(u2 +v 2 )
2σn 2
x
udn v dn
y
(4.3)
Solving the least squares problem yields the following matrix equation for the ai coefficients:
Ma = V,
(4.4)
with:
Cj (x, y)
dxdy
σ(x, y)2
Z
Ci (x, y)
dxdy
Vi =
Ref (x, y)
σ(x, y)2
Ci (x, y) = I(x, y) ⊗ Bi (x, y),
Mij =
Z
Ci (x, y)
where the variance is defined as:
σ(x, y) = k
p
I(x, y)
where k is a constant set according to the gain of the detector.
The key is that this process allows for PSF variations by subdividing the image−
processing it in subsections so that different objects can have different profiles− and by
(4.5)
22
adding a polynomial weighting factor in the kernel decomposition. First we must understand
that in dense field, a transformation kernel can be determined in a small area− small enough
that we can ignore the PSF’s variations. Thus, it is easier to model variations of the PSF in a
crowded field (such as an OC). To modify the previous kernel, we must make the coefficients
spatially dependent, so that:
Kernel(u, v) =
X
n
an (x, y) · Bn (u, v).
(4.6)
This process is robust and explained in further detail in Alard (2000). It should be noted that
this takes the longest of all the ISIS processes (can take a day or two depending on the number
of images).
This method allows for self-consistent fitting of the kernel variations while imposing
constant flux scaling− that is, in solving our least squares we must add the condition that the
sum of the kernel must be constant at all points of the image. Rather than doing a messy
Lagrangian, Alard uses a slightly different form of the kernel expressed in equation (4.7). The
new set of basis functions is described in such a way that all basis vectors, except the first one,
have zero sums:
Kernel(u, v) = a0 · B0 (u, v) +
where
X
1,N
′
an (x, y) · Bn (u, v),
(4.7)
′
Bn = Bn − B0
′
(4.8)
′
Provided that Bn vectors are normalized, the Bn will all have zero sums except B0 which will
equal B0 .
The most important parameters for the image subtraction are in the process config file
in the register directory. The kernel size is represented by half mesh size, while the
half stamp size is the area taken by the program around each object. It should be slightly
larger than the kernel size. We used values of 12 and 15 respectively and found that this
produced the best results. We also discovered that by increasing the kernel size up to 12
improved some background issues in the reference image. This background problem might be
attributed to a smaller kernel size not having enough background in it to do accurate fits.
The number of stamps can be chosen by using the nstamps x and nstamps y keywords,
to control the number in the x and y directions. The program looks for a number of bright
objects (not necessarily stars) and defines a small window around each of them. The part of
the image in these small windows are called stamps and are used to model the kernel. By
increasing the nstamps x and nstamps y values, we also increase the total number of stamps:
T otal stamps = nstamps x · nstamps y
(4.9)
23
In doing so, we have more data to be processed, and thus the process becomes more CPU
intensive. However, better results are also produced, so more stamps are recommended. We
used 10 for both nstamps x and nstamps y. We did not see any significant improvement with
nstamps ≥ 15. ISIS also allows for the images to be processed in parts, by breaking up the
image into several sub-images. We used sub x and sub y set to 1. Typically increasing this
parameter reduces PSF variation across the modeled part of the subimage and generally helps
ISIS fit better. However, we found through many experiments with our data that sub x and
sub y set to 1 produces realistic photometric results not achieved with 3×3 or 2×2. Among
other benefits of using the 1×1 with our data set include a reduction in background problems
and a significant decrease in the RMS. We also have found that the frames that are poorly fit
in one run are not necessarily poorly fit in another run with just slightly different parameters,
which points to bad fitting routines in ISIS.
We can also control the degree of spatial variations through the deg spatial keyword,
which specifies the degree of fit of the spatial variations of the kernel within a subimage. We
used a second order variation. It is important to make sure that the total number of stamps is
high enough for the degree of spatial variations− the spatial variations involves:
[(deg spatial + 1) · (deg spatial + 2)]/2
(4.10)
coefficients, and needs a number of stamps that is at least 3 or 4 times larger than this number.
The degree of differential background variations within a subimage can also be
changed, which is represented by deg bg parameter. For our data, we use a value of 3. From
looking at our subtracted images (conv images) it appears that the kernel determination (least
squares fit) seems to have problems. There are a large number images whose background or
kernel seems to go wrong leaving a messy looking background on the subtracted image. This
background problem seems to vary significantly with different parameter choices. Using
deg bg = 3 seems to give a good fit for a larger number of images overall.
Some of the less important parameters are the saturation limit, the minimum value for
the pixels to be fitted, and the minimum value for the central pixel of a stamp. The keywords
are: saturation with a value of 45000 counts, pix min with a pixel value of 7, and
min stamp center with a pixel value of 100. Finally, sigma gauss1, sigma gauss2 and
sigma gauss3 represent the Gaussian sigmas of the kernel expansion; we have used values of
0.8, 1.67, and 4 pixels. Experimentation showed that the largest sigma gauss is not
particularly important.
4.5 T HE detect.csh ROUTINE
Once we have successfully applied this method to all the images, only variable stars
should have any significant correlated residual. The var.fits image shows positions of variable
24
stars and relative strength of their variability. A faint signature indicates that the star has small
amplitude brightness variations, while large amplitude brightness variations would result in a
bright signature on the var.fits. Cosmic rays, however, will produce false positives, so a
rejection of some sort needs to be performed. Thus to remove defects from the images, such
as cosmics and atmospheric disturbances the ISIS software builds a time series of the values
of corresponding pixels on each frame and removes data points more than a user defined
standard deviation values from the median residual flux. This means that the two
measurements with the largest deviations are removed since most cosmics are removed in
earlier steps. The pertinent keyword here is N REJECT in the process config file. We have
used a value of 2. The images are then smoothed using the user specified parameter
MESH SMOOTH, which specifies the size of the smoothing mesh; we used a value of 3 for
MESH SMOOTH. Running the detect.csh script produces two images: var.fits and abs.fits
and are stored in the images directory. The smoothed, composite image of all these pixels is
var.fits, shown in Figure 4.2. The var.fits represents the mean of absolute normalized deviation
from each of the convolution images while the image abs.fits is the mean absolute deviation.
Our original var.fits constructed using the detect routine had noticeable features which
could be attributed to our December observations which we initially tried using in our ISIS
run. The December frames made a pretty big contribution to the var.fits. For the purpose of
variable detection, December images were removed from the var.fits to search for variability.
It should also be noted that a number of residuals on the var.fits had broken or split like
features. The cause of this phenomenon was not determined but these residuals were of
suspect and disregarded for the rest of our survey. Figure 4.2 shows our final var.fits. Note that
most of the really bright features on the image are from saturated stars.
4.6 T HE find.csh ROUTINE
After inspecting the var.fits, one can select a threshold in order to identify the
variables. The parameter is represented by SIG THRESH. We have set this detection limit to
0.075. This value is the pixel value cutoff and should be chosen by looking at the size of the
background spikes and deciding what stars to be a significant detection. The higher the value
the less variables will be identified. Such a low value, however, produced many false
variables, mostly attributed to the noisy edges of var.fits but can be easily eliminated by other
means. This script determines the location of the stars to be used for the photometry by
recording the coordinates of each of the mean of the absolute normalized deviations on the
var.fits that are above a certain threshold. This routine outputs a file called phot.data, which
contains the position of the variables, and is stored in the register directory.
25
Figure 4.2. var.fits produced from ISIS . Most of the really
bright spots are saturated stars.
26
4.7 T HE phot.csh ROUTINE
Light curves are produced using the ISIS routine phot.csh. The necessary
configuration file for this process is phot config. Most importantly, one must specify a value
for the radius of the annulus in order to estimate the background. This is set by rad1 bg,
which represents the inner radius, and rad2 bg which represents the outer radius, and should
be chosen according to the mean size of the PSF in the images. We used values of 15 and 20
pixels for rad1 bg and rad2 bg respectively. Two other important parameters are rad phot
and rad aper, which we used values of 5 and 7 respectively. The keyword rad phot is the
photometric radius−the radius of the circle within which the pixels of the object will be fitted
in order to estimate the flux. The rad aper parameter represents the radius for flux
normalization. For all other values, we did not alter the original phot config configuration files
that comes with the ISIS package.
It should be noted that for this project we wanted to build light curves for all the stars
in the field and not just the variable stars that ISIS finds since the ISIS routines for variable
detection may not be sensitive to planets. In order to do this, we built a phot.data file from all
the stars found using the IRAF routine DAOFIND. After running phot.csh, 4128 light curves
for all the stars which appeared on the var.fits were produced.
As a final step, not included in the ISIS package, the light curves need to be converted
from flux residuals to magnitude with the template image flux as the zero-point. In order to do
this the template frame was reduced with the IRAF routine APPHOT to determine the relative
magnitude for each star’s zero-point. A program was used to extract the star number,
coordinates, magnitude, fluxes, and their uncertainties from the APPHOT output file. This file
is then read into the program which converts between the residual flux measured in ISIS into
their corresponding residual magnitudes using the reference zero-point magnitudes and fluxes
from APPHOT. Using the method described in Mochejska et al. (2002), the light curve is
converted point-by-point to magnitudes (mi ) by computing the total flux (ci ) as the sum of the
counts on the template (∆ctpl ), and the counts on the subtracted template (ctpl ), decreased by
the counts corresponding to the subtracted image (∆ci ):
ci = ctpl + ∆ctpl − ∆ci
(4.11)
The magnitude is then calculated using the following equation:
mi = 2.5 ∗ log 10mo −mtpl /2.5 + ∆ctpl − ∆ci + mo
(4.12)
27
To convert the photometric error in flux to magnitudes we used the following relation:
ci
m
σi = 2.5 ∗ log
(4.13)
ci + σic
The light curves have been plotted using a SM 2 script.
2
http://www.astro.princeton.edu:80/ rhl/sm/sm.html
28
CHAPTER 5
PLANETARY TRANSIT SEARCH
In this survey we have searched our data for transiting extrasolar planet candidates.
The following sections will describe this process in further detail including the method and
implementation which we have used to search for transiting planets. Also described in the
following sections is the attempted use of SYSREM for removing systematic errors, our
transit selection criteria and finally our results.
5.1 B OX L EAST S QUARE A LGORITHM
We implemented the Box Least Square (BLS) algorithm by Kovács et al. (2002) 1 to
search for planetary transits. This method effectively fits a box to photometric observations
using two levels; one high level to simulate the starlight outside the box (out-of-transit light
level), and a lower level of a small width to simulate the data points in the box. The advantage
of the BLS method is that transits have a nearly box-shaped form, which means that this
method gives a reasonably good fit. The BLS algorithm was chosen because it has been used
extensively in similar searches (Mochejska et al. 2002, 2005, 2006) and quantitative
comparisons indicate it is as good as others in literature (Tingley 2003).
BLS searches for the non-sinusoidal periodic signal by minimizing the following
equation:
iX
n
i2
1 −1
X
X
wi (xi − L)2
(5.1)
D=
wi (xi − H)2 +
wi(xi − H)2 +
i=1
i=i2 +1
i=i1
The boundaries of the transit are i1 and i2 within the phased binned data. The
observations i are sorted by phase using a trial period. The algorithm searches to minimize D
over all trial periods with all possible transit phases (i1 , i2 ). The points in the box are
represented by (i1 , i2 ) and xi are the light curve magnitude measurements. H is the magnitude
level out of transit on either side of the transit box ([1,i1 ) and (i2 ,n]). L is the in-transit level
([i1 , i2 ]). Since the magnitude scale is an inverse scale, L actually has a higher value than H. L
and H are defined as:
s
r
s
H = −
1−r
L =
1
The BLS code is available for download at: http://www.konkoly.hu/staff/kovacs.html
(5.2)
(5.3)
29
where r is the fraction of one period spent at level L (in transit) which is given by the sum of
the weights of these data points:
i2
X
wi
(5.4)
r=
i=i1
s is given as the sum of the product of the weights and the data points:
s=
i2
X
xi
(5.5)
i=i1
With these formulae, Kovacs shows that the minimization equation reduces to:
D=
n
X
i=1
wi x2i −
s2
r(1 − r)
(5.6)
Kovacs’ defines the BLS frequency spectrum by the amount of Signal Residue (SR)
defined as:
SR = MAX
s2 (i1 , i2 )
r(i1 , i2 )[1 − r(i1 , i2 )]
21
(5.7)
The SR is calculated over all trial periods with trial transits in the interval i1 , i2 . The
maximum value of SR minimizes D and therefore corresponds to a potential transit
observation. Over the entire spectrum of frequencies tested, the SR global maximum
corresponds to the period yielding the highest probability of an observed transit.
However, the SR alone is not enough to determine whether a candidate planetary
transit has been observed. Two additional quantities– the Signal Detection Efficiency (SDE)
and the signal-to-noise ratio (SNR(α)) help characterize the strength of the SR. The SDE is
defined as:
SDE =
SRpeak − < SR >
,
sd(SR)
(5.8)
where the SRpeak is the SR a the highest peak in the BLS spectra, < SR > is the average
signal residue, and sd(SR) is the standard deviation of the SR over the range of frequencies
tested. In other words, it looks at the “significance” of the peak to help determine the
likelihood of a planetary transit.
A transit that is theoretically visible is not necessarily detectable. Therefore, the SNR
(α) is used as a measure of the detectability of the transit. The SNR(α) is defined as:
α=
δ√
nq,
σ
(5.9)
30
where n is the number of data points, q is the fractional transit length, δ is the transit depth,
and σ is the RMS of the magnitude measurement. α and the SDE serve as a useful way to
gauge signal detection against the noise in the data. Adopting cutoff values of SDE and α can
be used to filter out false detections. This can be especially useful in the case where the SDE
might be high enough to suggest a likely transit but the noise is too high for the detection to be
trustworthy.
To demonstrate the power of the BLS method Figure 5.1 is provided. This example
shows a time series, the normalized BLS frequency spectrum and the folded time series in an
artificial dataset.
5.2 BLS I MPLEMENTATION
For our dataset the BLS program was only run on stars with an RMS scatter in
measurements < 0.015 mag. A star with an RMS greater than 0.015 mag would not have the
photometric precision required to detect a transit. The RMS for each star was calculated as:
RMS =
s
1
Npts − 1
X
i
(xi − < x >)2 ,
(5.10)
where xi is the magnitude at time i, Npts is the total number of data points, and < x > is the
average magnitude of the star. In order to remove any outlying data points a 3σ rejection was
applied in the calculation of the RMS.
Figure 5.2 shows three different RMS vs. magnitude plots of our data set. The top
panel show the RMS of the initial data set. These stars have at least 323 out of 423 total
observations and appear on the var.fits. We chose to keep only stars with at least 323 total
observations so that at most a star is missing 100 observations. The middle panel shows the
RMS of the stars remaining after the following filters were applied: saturated stars were
removed, stars with broken residuals on the var.fits were removed, and stars with less than 323
total observations were not included. The bottom panel shows the remaining 1238 stars
suitable for the BLS study. These stars have passed all the previously indicated filters and the
RMS is < 0.015 mag.
The BLS input parameters used in this survey are summarized in Table 5.1.
The number of frequency points nf, the frequency step df, and the minimum
frequency fmin, set the limits for the period range to be searched. The number of bins, nb,
was set to 100 (i.e. each bin covers 0.01 in phase). Setting the number of bins too low can
result in an overlooked transit. The disadvantage to setting the bins too high is computation
time. The minimum and maximum fractional transit lengths, qmi and qma respectively, were
selected because planetary transits of hot Jupiters are not expected to have fractional transit
lengths less than 0.01 or greater than 0.2. Also included in our implementation of BLS (not
31
Figure 5.1. BLS example results from Kovacs et al. (2002) from a test set of data. This shows
the time series in the upper panel, the normalized BLS frequency spectrum and the folded
time series in the lower panel. The signal parameters are displayed at the top where n is the
number of bins, P0 is the period, q is the fractional transit length, δ is the transit depth, and
δ/σ is the SNR.
32
RMS vs. Magnitude
1
0.1
0.01
0.001
0.0001
10
12
14
16
18
20
22
10
12
14
16
18
20
22
RMS
1
0.1
0.01
0.001
0.0001
0.1
0.01
0.001
0.0001
10
12
14
16
18
20
Magnitude
Figure 5.2. The top panel shows the RMS of the 4128 stars which appear on the var.fits and
have 323 out of 423 observations. The middle panel shows the RMS of the 3935 stars
remaining after filters have been applied. The bottom panel shows the 1238 stars remaining
which are suitable for BLS study after filters were applied including an RMS < 0.015
magnitude cutoff.
33
Table 5.1. Input Parameters Used in BLS
Parameter
nf
df
fmin
nb
qmi
qma
Definition
Value
Number of frequency points
200000
Frequency step (day−1 )
.00001
−1
Min frequency to be tested (day )
.1
Number bins in folded time series
100
Min fractional transit length
.01
Max fractional transit length
.2
included in the original code) was the inclusion of weights based on uncertainties in the
measured residual fluxes from ISIS.
BLS returns the Signal Residue (SR) for each frequency tested and for each transit
length, and records the maximum. The transit candidate frequency corresponds to the SR
global maximum found in the BLS spectrum. The BLS routine also returns the period, depth,
fractional transit length, and the bin index of the star at the beginning and end of the transit.
Included in our implementation of the code are a frequency spectrum, a normalized frequency
spectrum, average binned phase plots, the SDE, and the SNR(α).
5.3 SYSREM
Searching for transits involves finding a signal in noisy data. The signal is expected to
be weak for a planetary transit. It is therefore worthwhile to find a way to reduce the noise in
the data by removing systematic effects. The SYSREM (Tamuz et al. 2005) detrending
method works without prior knowledge of the effects as long as the effects appear linearly in
many stars of the sample. Basically, this algorithm identifies and subtracts out linear trends
that appear in a large portion of lightcurves in a given data set. The algorithm is especially
useful in cases where the uncertainties of the measurements are unequal. For equal
uncertainties, the algorithm reduces to the Principal Component Analysis (PCA) algorithm.
Consider a set of M observations with N stars. The residual of each observation, rij , is
defined to be the stellar magnitude after subtracting the average magnitude of the individual
star. The goal is to try to find an effective extinction coefficient for each star and an effective
airmass for every measurement, so we find sets {ci ; i = 1, ..., N} and {aj ; j = 1, ...M } that
minimize the global expression
S2 =
X (rij − ci aj )2
.
σij2
ij
First an estimate of the extinction coefficient is found by
P
2
j (rij aj /σij )
P
.
ci =
2
2
j (aj /σij )
(5.11)
(5.12)
34
The extinction coefficient, ci , are star or position-dependant factors while the airmass term,
aj , are frame-dependant factors. SYSREM can use random numbers as an initial guess for the
airmass. This is because SYSREM finds linear trends in the data which are not necessarily
airmasses so the airmass values have no special meaning for SYSREM.
The value of the effective “airmass” is then
P
(rij cj /σij2 )
(1)
aj = Pi 2 2 .
j (cj /σij )
(5.13)
(1)
We then recalculate the best-fitting coefficients, ci , and continue iteratively,
obtaining better approximations for both sets.
The effect is then removed by
(1)
(1) (1)
rij = rij − ci aj .
(5.14)
Additional linear trends can be fitted and removed with additional runs of SYSREM.
We did not apply our SYSREM results to our light curves in the end. We found that a
number of lightcurves with very large variations were creating problems by dominating the
identification of low level systematics. However, even when these stars with large variations
were removed the systematic effects that were found were at such a low level that even for our
stars with the largest correction the correction was so small the removal of the effect was
inconsequential. We found that our RMS was only improving for our dimmest stars with the
largest change of 0.004%. SYSREM was used to help identify strange features in some of our
stars but we did not apply the corrections to our stars.
5.4 T RANSIT S ELECTION C RITERIA
We selected criteria to help identify the most likely transit candidates. Each transit
candidate was ranked according to SDE. An SDE threshold > 4 and α > 9 was used for this
survey. Recall that the SDE determines the significance of the peak in the frequency spectrum
to help determine the likelihood of a planetary transit and α is the measure of the detectability
of the transit. According to Kovács et al. (2002) when α exceeds a value of 6 you can expect a
significant detection of a transit. For our data set, when α was set to 6 and and using an SDE
threshold > 4 it returned 257 planetary transits candidates so in order to narrow down our list
we have used an α threshold > 9. This is the also the same α cutoff used by Mochejska et al.
(2005) in one of a series of studies of open cluster stars.
In this work, we search the data set for periods between 1.05 and 10 days. This is
because the probability of finding planetary candidates in this period range is most probable.
Another limit imposed to filter out any false positives was to only keep transits with a transit
depth smaller than 0.08 mag because a potential planetary transit is unlikely to exceed this.
35
Also, any candidates that have a transit in only 1 transit phase bin (which corresponds to
transit durations of 0.1 days for a 10 day period) were required to have a high SDE and α.
Binned phase plots were created to show the average relative variability of the star
over the course of the observations according to the trial period. Stars which show evidence of
having two discrete levels in their brightness over the average phased observations were kept
as potential transit candidates. We also looked at the binned phase plots of each transit
candidate to determine whether or not the data points which fall in the transit phase were from
more than one night. However, we did not reject candidates based only on this. For each
transit candidate the light curve was also inspected.
5.5 P LANETARY T RANSIT R ESULTS
Using an initial criteria of an SDE threshold > 4, α > 9, and a period > 1.05 of the
1238 stars that were run on BLS we found 211 planetary candidates which required further
inspection. While this number is very high it is not surprising given the low SDE threshold
used. Each candidate required a second in-depth inspection of the binned phase plot and light
curve to try to identify any false positives.
After further inspection we found 21 transit candidates that were investigated further.
Many of our initial candidates were rejected because of large amounts of variance about the
mean magnitude, the points that fell into the transit bin were from only 1 night and also the
candidate had a low SDE and α, and also if many points outside the transit bin were at the
same depth as the points within the transit bin. The results of the planetary transit survey are
listed in Table 5.2. This table contains the star ID number, the coordinates of the star on the
var.fits, the Signal Detection Efficiency (SDE), the SR(α) which is the effective SNR, the
period is the trial period corresponding to the global maximum, Nt is the number of points in
the transit phase, depth is the depth of the transit in magnitudes, and qtran is the fractional
transit length according to the BLS output.
It should be mentioned that ID 1261 appeared to show variability in its light curve
characteristic of an eclipsing variable. ID 1261 was thus added to our list of variable stars and
dismissed as a transit. Also ID 3727 (not included in Table 5.2) was discovered to show
interesting variability from our BLS results. Because the period of ID 3727 is much shorter
than 1.05 days it was not included in our final BLS analysis, but it was added to the variability
section of this thesis.
From our list of 21 candidates 4 of these have been identified to have a box-shaped
light curve characteristic of a planetary transits and have points from multiple nights within
the transit. The properties of these best candidates are re-iterated in Table 5.3.
To better check the authenticity of the BLS output, these candidates were investigated
further. For each candidate 3 plots were examined: the binned phase plot, the frequency
36
spectrum, and the phased points within the transit. The output BLS spectrums are split into
1000 bins each with 100 points. The maximum SR in each bin was found and normalized
according to the global maximum SR. After closer inspection these 4 candidates were
dismissed, but a discussion of each is presented below.
Table 5.2. BLS Results
Star ID Coords. (x, y)
4522
623,1712
1722
855,706
1772
1422,722
1612
383,672
1956
994,781
0776
1397,349
3880
716,1464
4012
454, 1520
2563
1524, 997
1347
1344,566
1267
1806,535
2808
924,1081
2195
487,863
2232
1451,877
2801
1783,1079
4035
1214,1524
1051
464,456
3827
385,1411
1261
243,533
2202
916,866
4635
941,1755
SDE
7.429
6.587
6.481
6.377
6.269
6.039
5.936
5.751
5.295
5.236
5.149
4.852
4.811
4.621
4.502
4.501
4.464
4.400
4.376
4.327
4.304
SR(α) Period(days)
15.84
1.5555
22.26
1.1271
14.742
1.7299
14.274
1.0516
11.524
1.0972
13.787
2.4569
20.370
2.2614
13.789
1.9513
10.308
1.5096
19.141
1.4552
16.867
1.3598
14.016
1.4033
12.687
1.0913
10.391
1.135
14.344
2.761
18.038
1.3497
19.890
1.1457
9.608
1.376
19.224
1.524
16.422
2.263
10.183
2.457
Table 5.3. BLS Final Results
Star ID Coords. (x, y) SDE SR(α)
1956
994,781
6.269 11.52
2563
1524, 997
5.295 10.31
1347
1344,566
5.236 19.14
1267
1806,535
5.149 16.87
Period(days)
1.097
1.509
1.455
1.359
Nt
20
6
16
16
16
19
21
16
13
13
10
20
10
23
22
18
13
11
12
17
12
Depth
-0.024
-0.054
-0.021
-0.028
-0.013
-0.022
-0.016
-0.031
-0.024
-0.025
-0.060
-0.026
-0.015
-0.021
-0.032
-0.031
-0.007
-0.031
-0.058
-0.016
-0.0097
Nt
16
13
13
10
Depth
-0.013
-0.024
-0.025
-0.060
Qtran
0.0496
0.0142
0.0378
0.0378
0.0378
0.0142
0.0496
0.0378
0.0307
0.0307
0.0236
0.0473
0.0236
0.0402
0.0520
0.0426
0.0307
0.026
0.0284
0.0402
0.0284
Qtran
0.0378
0.0307
0.0307
0.0236
The binned phase plot of ID 1956 are shown in Figure 5.3. The binned phased plot
shows evidence of variability during the transit phase. However, the out-of-transit phases do
show variance about the mean magnitude. The points within the transit come from three
different nights. Figure 5.4 shows the points within the transit phase. This plot shows that the
variability is not on two discrete levels as would be expected for a transiting planet and thus
37
weakens the argument that candidate ID 1956 is an actual transit. It should be noted that there
are 3 “low” points which are most likely caused by bad measurements from ISIS that BLS
found to be in the transit phase. Figure 5.5 shows the residuals of ID 1956 where the points in
transit are coming from the August 26th, November 14th, and November 16th observations.
Figure 5.6 shows the normalized BLS spectrum for candidate ID 1956. The SR peak
corresponds to a period of 1.0972 days. The calibrated V magnitude of ID 1956 is 17.26 mag
and the calibrated (V-R) is 0.812.
The binned phase plot of ID 2563 is shown in Figure 5.7. The binned phased plot
shows evidence of variability during the transit phase. The points within the transit come from
only two different nights weakening the likelihood a transit has been detected. The
out-of-transit phases do not have a large variance about the mean magnitude. The points
within the transit phase shown in Figure 5.8 are not on two discrete levels thus further
weakening the argument that candidate ID 2563 is an actual transit. Figure 5.9 shows the
residuals of ID 2563 where the points within the BLS transit are coming from the October
15th and November 14th observations. The BLS spectrum is shown in Figure 5.10 with an SR
peak corresponding to a period of 1.5096 days. The calibrated V magnitude of ID 2563 is
17.19 mag and the calibrated (V-R) is 0.850.
The binned phase plot of ID 1347 are shown in Figure 5.11. The binned phased plots
do show evidence of variability during the transit phase. The points within the transit are
however only from only 2 different nights. The unbinned phased plot of the transit shown in
Figure 5.12 weakens any argument that ID 1347 is an actual transit because it is not at two
discrete levels. Also, reduced χ2 statistics revealed that the 13 points within the transit bin are
consistent with transit magnitudes. The reduced χ2 of the 13 points within the transit bin also
reveal that the points are also consistent with each other. Therefore, the points within the
transit are being contributed from points with large errors. Figure 5.13 shows the residuals of
ID 1347 where the points within the transit bin are coming from the October 16th and
November 14th observation. The BLS spectrum is shown in Figure 5.14 with an SR peak
corresponding to a period of 1.4552 days. The calibrated V magnitude of ID 1347 is 17.01
mag and the calibrated (V-R) is 0.875.
The binned phase plot of ID 1267 are shown in Figure 5.15. The binned phased plot
shows evidence of variability during the transit phase. The out-of-transit phases do not have a
large variance about the mean magnitude. The points within the transit are from only 2 nights.
The unbinned phased plot of the transit shown in Figure 5.16 is at a lower discrete level than
the other 3 transiting candidates and the transit is also on the larger side. However, 8 of the
points within the transit phase are coming from 1 night while only 1 point is coming from the
2nd night. This point is not at a lower discrete level with the other 8 points. Thus, the points
38
Figure 5.3. Binned phased plot for candidate ID 1956.
39
Figure 5.4. Phase vs. unbinned delta magnitude of the points in transit for candidate ID
1956. Error bars have been added to convey the uncertainty in the residual flux within the
transit phase.
40
-0.05
0
0.05
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
-0.05
0
0.05
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
-0.05
0
0.05
81
81.1
Nov14,01
81.9
Nov15,01
82.9
83 83.1
Nov16,01
Figure 5.5. Residuals of candidate ID 1956. Major time-axis tick marks are spaced by 2.4
hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
41
1
0.8
0.6
0.4
0
0.5
1
1.5
2
Figure 5.6. Normalized signal residue versus trial frequency for candidate ID 1956. The SR
peak corresponds to a period of 1.5096 days.
42
Figure 5.7. Binned phased plot for candidate ID 2563.
43
Figure 5.8. Phase vs. unbinned delta magnitude of the points in transit for candidate ID
2563. Error bars have been added to convey the uncertainty in the residual flux within the
transit phase.
44
-0.05
0
0.05
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
-0.05
0
0.05
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
-0.05
0
0.05
81
81.1
Nov14,01
81.9
Nov15,01
82.9
83 83.1
Nov16,01
Figure 5.9. Residuals for candidate ID 2563. Major time-axis tick marks are spaced by 2.4
hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
45
1
0.8
0.6
0.4
0.5
1
1.5
2
Figure 5.10. Normalized signal residue versus trial frequency for candidate ID 2563. The
SR peak corresponds to a period of 1.5096 days.
46
Figure 5.11. Binned phased plot for candidate ID 1347.
47
Figure 5.12. Phase vs. unbinned delta magnitude of the points in transit for candidate ID
1347. Error bars have been added to convey the uncertainty in the residual flux within the
transit phase.
48
0
0.05
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
0
0.05
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
0
0.05
81
81.1
Nov14,01
81.9
Nov15,01
82.9
83 83.1
Nov16,01
Figure 5.13. Residuals for candidate ID 1347. Major time-axis tick marks are spaced by 2.4
hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
49
1
0.8
0.6
0.4
0.2
0
0.5
1
1.5
2
Figure 5.14. Normalized signal residue versus trials frequency for candidate ID 1347. The
SR peak corresponds to a period of 1.4552 days.
50
Figure 5.15. Binned phased plot for candidate ID 1267.
51
Figure 5.16. Phase vs. unbinned delta magnitude of the points in transit for candidate ID
1267. Note that 1 “low” data point has been removed. Error bars have been added to convey
the uncertainty in the residual flux within the transit phase.
52
within the transit which appear at a lower level are actually only coming from only 1 night. It
should be noted that 1 “low” point has been removed in Figure 5.16 but this point is included
in Figure 5.17. It is very unlikely that this is an actual transit. Figure 5.18 shows the residuals
of ID 1267 where the points within the transit bin are coming from the October 15th
observation. The BLS spectrum is shown in Figure 5.19 with an SR peak corresponding to a
period of 1.3598 days. The calibrated V magnitude of ID 1267 is 17.36 mag and the
calibrated (V-R) is 0.845.
53
Figure 5.17. Phase vs. unbinned delta magnitude of the points in transit for candidate ID
1267 including “low” data point. Error bars have been added to convey the uncertainty in
the residual flux within the transit phase.
54
0
0.2
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
0
0.2
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
0
0.2
81
81.1
Nov14,01
81.9
Nov15,01
82.9
83 83.1
Nov16,01
Figure 5.18. Residuals for candidate ID 1267. Major time-axis tick marks are spaced by 2.4
hours. The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
55
1
0.8
0.6
0.4
0.5
1
1.5
2
Figure 5.19. Normalized signal residue versus trial frequency for candidate ID 1267. The
SR peak corresponds to a period of 1.3598 days.
56
CHAPTER 6
VARIABILITY
The side benefit of a transiting extrasolar planet survey are the number of variable
stars also discoved. We have identified 22 variable stars, 10 were identified as eclipsing-type
W Ursa Majoris contact binaries, 5 were identified as detached binaries of the Algol type, 1
was identified as a slowly pulsating B star, and 6 were irregular and require further
investigation before they can be classified. Previous studies by Viskum et al. (1997) and Choi
et al. (1998, 1999) identified 7 variable stars in the cluster. Of these 7 only 3 (ID 0980, ID
2673, and ID 1855) has been confirmed as variable in our survey. All 7 of these known
variable stars are in our field of view but, 2 are saturated (ID 1901, ID 2752) on our frames
and the other 2 (ID 2195, ID 2256) show no variability in their light curves.
A total of 19 new variable stars have thus been discovered. The position of these stars
have been identified on the composite ref.fits in Figure 6.1 and on the var.fits in Figure 6.2
from ISIS.
Table 6.1 lists the variable star number, pixel coordinates (x,y), variable type, average
relative V-band magnitude < Vrel >, the color (V-R), period, the approximate depth of the
primary and secondary minima, and a cluster membership estimation based on its position on
the CMD. The (V-R) and V-band magnitudes reported are the calibrated values (see §2.1 for
calibration explanation). It should be noted that 4 out of the 22 variable stars were too faint in
our V frames, and so a color could not be determined.
Figure 6.3 shows the location of our variable stars on a CMD constructed from this
survey. The location of the variables on the CMD is used to estimate likelihood of cluster
membership, as well as the star’s distance from the cluster center. However, any conclusive
membership determination will require radial velocities or proper motion measurements. In
order to help better distinguish possible cluster members we have overlaid theoretical
isochrones from Cassisi et al. (2006) along with the isochrone shifted by 0.75 magnitude. It is
well known that an unresolved binary system comprising of two identical stars has the same
color but twice the luminosity of an equivalent single star and such a system will appear in the
CMD vertically displaced by 0.75 mag (since 2.5 log2 = 0.75). The region between these two
isochrones represents the region within which a variable star has the greatest probability of
being a possible cluster member. Four of our W UMa variables including ID 2513, ID 1834,
ID 1558, and ID 2674 and 1 SPBs variable lie within the region having the highest probability
of being a cluster member while ID 0681, ID 980, ID 2938 and ID 3727 lie just outside this
57
region. This is interesting because it is not expected that W UMa stars would be found in such
a young cluster since the time scale expected for the stars to come into contact is larger than
the age of the cluster. It should be noted that the reliance on the colors determined should be
taken with some caution as the colors can be affected by what part of the light curve
measurements the color measurements were taken on (this is especially the case for W UMa
stars where they are characterized by continuous changes in their brightness).
Table 6.1. Variable Star Information
ID
0533
0981
1107
1133
1558
1834
2513
2673
2830
3727
0681
0980
1261
1284
4109
1855
2409
2773
3096
3928
4540
4762
(x, y)
1547,256
1541,433
828,481
1235,489
441,654
943,744
1223,976
1642,1030
876,1087
76,1403
708,324
1067,440
243,533
318,543
1219,1554
1101,751
833,944
1138,1065
782,1183
1809,1480
1104,1718
138,1810
Type
EW
EW
EW
EW
EW
EW
EW
EW
EW
EW
EA
EA
EA
EA
EA
SPBs
Irr.
Irr.
Irr.
Irr.
Irr.
Irr.
< Vrel >
16.54
16.41
16.59
17.28
18.29
14.89
14.73
12.90
17.01
13.56
14.82
14.04
16.54
15.45
16.28
13.53
16.43
18.14
14.08
17.62
15.12
15.70
RMS
0.0710
0.0562
0.1038
0.027
0.0755
0.0165
0.0126
0.0035
0.0278
0.0064
0.0069
0.0037
0.0125
0.0078
0.0375
0.0033
0.0111
0.0363
0.0075
0.0214
0.0111
0.0135
(V-R)
–
–
–
0.9481
0.9951
0.6163
0.5503
0.3885
0.6499
0.4973
0.6643
0.5675
0.5732
0.8057
–
0.4351
0.8513
0.6783
0.395
0.8192
0.4827
1.007
P (days)
1.214
0.6896
1.4826
1.2318
0.4617
0.83
1.44
–
1.028
0.4963
–
2.352
3.159
–
1.9651
–
–
–
2.23
–
–
–
Approx. Depth
0.2, 0.2
0.2 0.2
0.3, 0.3
0.1, 0.1
0.2, 0.2
0.05, 0.05
0.06
–
–
0.01, 0.02
–
0.05
0.25
0.52
0.71, 0.05
–
–
–
–
–
–
–
Memb.
–
–
–
medium
high/medium
high
high
high
low
low
high
high
low
medium
–
high
medium
low
medium
high/medium
low
low
6.1 P ERIOD D ETERMINATION
The periodicity search of our variable stars was carried out by two different period
search routines using the Lomb-Scargle and Lafler-Kinman methods. Both techniques are
sensitive to different kinds of periodic signals and compliment each other well.
The Lomb-Scargle period search used in this study was based on the work of Lomb
(1976) and Scargle (1982). This method is essentially a fitting of sine and cosine terms of
various frequencies that correspond to possible periodicites. The Lomb-Scargle normalized
power spectrum provides a measure of the spectral power in the signal as a function of
frequency (ω = 2π/T ) and is defined as,
58
Figure 6.1. var.fits frame with location of variable stars.
59
Figure 6.2. Composite reference image with location of
variable stars.
60
CMD of M52
8
EW Variables
EA Variables
Irregular/Unclassified
SPBs
10
1855
12
2673
3727
V
0980
14
0681
3096
1284
2513
2409
4540
1834
16
4762
1133
1261
1558
2830
18
2773
2938
20
0
0.2
0.4
0.8
0.6
(V - R)
1
Figure 6.3. CMD highlighting the location of variable stars detected.
1.2
1.4
61
P
P
1 [ ni Xi cos ω(ti − τ )]2 [ ni Xi sin ω(ti − τ )]2
+ Pn
},
P (ω) = { Pn
2
i Xi cos ω(ti − τ )
i Xi sin ω(ti − τ )
(6.1)
xi is the set of the measurements of a star’s light curve at times ti having n observations. Xi is
the difference between each individual measurement xi and the average value of the x.
For a range of frequencies, a time offset τ is computed for each value of the frequency,
by the equation
Pn
sin 2ωti
(6.2)
tan(2ωτ ) = Pni
i cos 2ωti
Typically the frequency with the most power in the frequency spectrum corresponds as the
frequency of variability or an alias of the period. The Lomb-Scargle routine will be more
sensitive to variability that is closer to sinusoidal.
The Lafler-Kinman search relies on the fact that for time series data folded on to the
correct period there will be a minimization of brightness differences between observations of
adjacent phases. In this method a trial period is chosen and the data are folded in phase and
then ordered. The absolute differences between successive observations are taken and added
together. This is expressed as,
S=
n−1
X
i=1
|xi − xi+1 | + |xn − x1 |
(6.3)
where xi is the ith data point, in order of phase for that particular trial period. S is determined
for all the different trial periods. If the trial period tested is correct then the summation will
become a minimum. An iterative process is used to refine the detected period. The
discriminant function is expressed as,
S
−2
(6.4)
Q
where Q is the total range of observations (absolute value of the difference between the
maximum magnitude and the minimum magnitude). The minimum of the discriminant
r=
function versus trial period is the location of the period. The frequency spectrum shows a
distinct drop or minimum near the value of r near the period. The Lafler-Kinman routines
tends to be more sensitive to the point-to-point correlations that arise in a light curve. The
validity of the period from either technique can be checked by simply folding the data and
examining the resulting phased plot.
Figure 6.4 and Figure 6.5 show an example of the Lomb-Scargle and the
Lafler-Kinman results that were run on star ID 0533. These techniques were run with trial
periods from 0 to 3 days with a spacing of 0.0001. The peak of maximum power for the
Lomb-Scargle results corresponds to a P = 0.607 days. The lowest r values correspond to
62
50
40
Power
30
20
10
0
0
0.5
1
1.5
Period (days)
2
2.5
Figure 6.4. ID 0533 Lomb-Scargle period analysis. The peak of maximum power
corresponds to a P = 0.607 days.
3
63
3
2.5
Power
2
1.5
1
0.5
0
0
0.5
1
1.5
Period (days)
2
2.5
Figure 6.5. ID 0533 Lafer-Kinman period analysis. Two of the lowest r values corresponds
to a period P = 0.607 days and P = 1.214 days. Lower r values with larger periods can be
ruled out based solely on the unphased light curve.
3
64
periods of P = 0.607 days and P = 1.214 days for the Lafer-Kinman period analysis. Since the
Lomb-Scargle technique could not distinguish between primary and secondary eclipses, the
period returned half the likely true period. Once the period was doubled the data were folded
correctly to P = 1.214 with a primary and secondary eclipse. The phased light curve be see in
Figure 6.6.
6.2 VARIABILITY R ESULTS
6.2.1 W UMa Variables
Eclipsing binary stars of W Ursae Majoris type are characterized by continuous
brightness changes due to eclipses and due to changing aspects of tidally distorted stars. The
minima in the light curves are of almost equal depth, indicating similar surface temperatures
of the components. The periods are short, almost exclusively ranging from about 7 hours up
to 1 day (Sterken 1997). W UMa stars are best explained by the assumptions that both stars
are in contact, and that the more massive component is transferring energy to the less massive
one via a common envelope, thus equalizing the surface temperatures (Sterken 1997).
Ten of our variable stars have been identified as probable W UMa variables. The
phased plots of our W UMa stars are shown in Figure 6.6. All December 2007 observations
and were removed from the phased light curves as the data were often too noisy and offset
from the rest of the observations. Also, because our September observations were processed
alone they are offset from the rest of the observations in our light curves. For the phased plot
of ID 0533 only September observations were used. Two of the previously known variables,
ID 2673 and ID 1855, are not phased because their variability is less present in the
non-September observations. It should also be be noted that because W UMa variables often
show nearly identical eclipse depths, the Lomb-Scargle search is sensitive to a period that
phases only one eclipse per orbit. The routine is not sensitive to the differences between
eclipses and finds each eclipse to be the same event therefore, the periods needs to be doubled
in this case.
The light curve data of ID 0533 are shown in Figure 6.7. Both primary and secondary
minima appear to be nearly identical in depth. The amplitude of variation is about 0.2
magnitude from peak to peak. Cluster membership could not be established for this star as it
appeared too faint in the V band for color determination.
The light curve data of ID 0981 are shown in Figure 6.8. The amplitude of variation is
about 0.2 magnitudes from peak to peak with primary and secondary eclipses being almost
identical depth. ID 0981 is particularly interesting because of the asymmetric shape of the
light curve. Cluster membership could not be established as there is no color determination
because it was too faint.
65
0981
0533
16.2
16.4
16.6
16.8
17
1107
16.2
16.3
16.4
16.5
16.6
0 0.2 0.4 0.6 0.8
1133
1
16.4
16.5
16.6
16.7
16.8
0 0.2 0.4 0.6 0.8
1558
1
Magnitude
1
0 0.2 0.4 0.6 0.8
3727
1
0 0.2 0.4 0.6 0.8
1
13.3
15.3
16.2
15.4
15.5
16.4
15.6
16.6
0 0.2 0.4 0.6 0.8
2513
13.2
13.22
13.24
13.26
13.28
13.3
0 0.2 0.4 0.6 0.8
1834
0 0.2 0.4 0.6 0.8
1
1
13.35
13.4
13.45
0 0.2 0.4 0.6 0.8
2830
15.3
15.35
15.4
15.45
15.5
15.55
1
13.5
12.2
12.22
12.24
0 0.2 0.4 0.6 0.8
Phase
Figure 6.6. Phased light curves of suspected W UMa stars.
1
66
16.4
16.6
16.8
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
16.4
16.6
16.8
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
16.4
16.6
16.8
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
16.4
16.6
16.8
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.7. Light curve of ID 0533. Major time-axis tick marks are spaced by 2.4 hours. The
time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
67
16.2
16.4
16.6
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
16.2
16.4
16.6
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
16.2
16.4
16.6
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
16.2
16.4
16.6
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.8. Light curve of ID 0981. Major time-axis tick marks are spaced by 2.4 hours. The
time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
68
The light curve data of ID 1107 are shown in Figure 6.9. The peak to peak amplitude
of variation is about 0.3 magnitudes. Maxima appears to be of similar heights, and minima are
of nearly identical depths. Cluster membership could not be determined because it was too
faint in V.
The light curve data of ID 1133 are shown in Figure 6.10. From the structure and
nightly variations in the light curve, it is likely that the variable is a W UMa variable. The
amplitude of the eclipse seems to change from the August and October observations. In the
phased plot, the depth of the eclipse appears to be changing. The period is slightly larger than
that would be expected of a W UMa but not too far off. It is possible that ID 1133 is a cluster
member based on its position on the CMD. It is located approximately 5′ from the cluster
center.
The light curve data of ID 1558 are shown in Figure 6.11. Variations from night to
night are present but the light curve changes noticeable from night to night. This may be due
to spotting of the surface which is common among this type. As with ID 1133 the minima
appears to be changing. The peak to peak variations are around 0.2 mag. The phased plot
shows a lot of scatter. Based on its location on the CMD it is a possible a cluster member but
it also located in a region of lots of scatter. It should also be noted that the color determination
for ID 1558 should be taken with some caution as larger amplitude W UMa stars are more
likely to be more effected by what part of the light curve measurements the color data are
taken on.
The light curve data of ID 1834 are shown in Figure 6.12. Both primary and
secondary minima appear to be similar in depth. The peak to peak variations are very small,
approx 0.05 magnitudes. While the phasing of the data looks slightly like the period could be
incorrect multiple trials with the data show that this period is the most likely period. The close
spatial position to the cluster center (approximate 3′ ) and the high membership probably
based on its located on the CMD indicates that this object could be a cluster member. M52 is
young to have a member W UMa making ID 1834 and interesting star for follow up work.
The light curve data of ID 2513 are shown in Figure 6.13. The light curve indicates it
is likely a W UMa variable. The amplitude of variation is small with peak to peak light
variations of approximately 0.06 magnitudes. The light curve shows and increase in
amplitude on the August 26th and September 19th observations. It is likely that ID 2513 is a
cluster member based on its location on the CMD and its close spatial position (approximately
1′ ) to the cluster center.
The light curve data of ID 2673 are shown in Figure 6.14. A previous study by
Viskum et al. (1997) have identified 6.14 as a δ scuti variable. Viskum et al. (1997) report ID
2673 is a main-sequence star near the hot border of the instability strip and could therefore be
69
16.5
17
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
16.5
17
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
16.5
17
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
16.5
17
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.9. Light curve of ID 1107. Major time-axis tick marks are spaced by 2.4 hours. The
time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
70
15.4
15.6
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
15.4
15.6
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
15.4
15.6
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
15.4
15.6
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.10. Light curve of ID 1133. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
71
16.2
16.4
16.6
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
16.2
16.4
16.6
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
16.2
16.4
16.6
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
16.2
16.4
16.6
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.11. Light curve of ID 1558. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
72
13.35
13.4
13.45
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
13.35
13.4
13.45
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
13.35
13.4
13.45
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
13.35
13.4
13.45
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.12. Light curve of ID 1834. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
73
13.2
13.25
13.3
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
13.2
13.25
13.3
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
13.2
13.25
13.3
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
13.2
13.25
13.3
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.13. Light curve of ID 2513. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
74
12.16
12.18
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
12.16
12.18
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
12.16
12.18
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
12.16
12.18
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.14. Light curve of ID 2673. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
75
a δ Scuti variable. However, the periodicity in our light curve does not seem characteristic of a
δ scuti star which is characterized by short pulsations (periods less than 0.3 days). We propose
that it is more likely that ID 2673 is a W UMa variable. Based on ID 2673’s position on the
CMD it is likely that it is a cluster member.
The light curve data of ID 2830 are shown in Figure 6.15. The continuous light curve
variations indicate that the star is likely a W UMa variable. Because the binary appears to
have a period very close to 1 day, the depth of the eclipse is difficult to determine. Due to ID
2830’s position on the CMD it is has a lower probability of being a cluster member however,
it does have a close spatial position (approximately 3′ ) to the center of the cluster.
The light curve data of ID 3727 are shown in Figure 6.16. It should be noted that ID
3727 was not identified as a variable from our ISIS results but was identified from our BLS
results. The variability in the light curve seems to indicates two eclipses which is more likely
to be a contact binary than a transiting planet. Also, the period is low for a transiting planet.
The peak to peak amplitude variations are very small only 0.02 magnitudes for the primary
eclipse and 0.01 for the secondary. The variability is more clearly present in our September
observations and only the September observations were used to phase the data. The position
of ID 3727 is near the edge of many frames, which probably effected our our August 24th
observations. The period used to phase the data was found from BLS as 0.49635 days. It is
unlikely that ID 3727 is a cluster member based on its position on the CMD.
6.2.2 Slowly Pulsating B Stars
Slowly pulsating B stars (hereafter SPBs) were first introduced by Waelkens (1991) as
a distinct group of variables with spectral types ranging from B2 to B9. The SPBs are situated
in the main sequence, with masses ranging from 3 to 7M⊙ . They have periods from 0.5 - 3
days and low amplitudes less than 0.1 mag. Their variability is interpreted in terms of
non-radial pulsations of higher-order g-modes (g-mode oscillations are found deep in the solar
interior) (Dziembowski et al. 1993).
The light curve data of 1855 are shown in Figure 6.17. 1855 has been identified as a
variable in a previous study by Choi et al. (1999). Choi et al. (1999) proposes that 1855 is a
slowly pulsating B star with a pulsation period of 1.626 days. Choi et al. (1999) also reports
that 1855 is located near the SPBs instability strip. Based on 1855’s position on the CMD it is
likely that it is a cluster member.
6.2.3 Detached Eclipsing Binaries
The Algol type eclipsing binaries (EA) are a subgroup of eclipsing binaries with well
defined eclipses and the light remains rather constant between the eclipses. Orbital periods
range from extremely short (a fraction of a day) to very long (27 years for ǫ Aurigae) (Sterken
76
15.3
15.4
15.5
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
15.3
15.4
15.5
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
15.3
15.4
15.5
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
15.3
15.4
15.5
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.15. Light curve of ID 2830. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
77
12.2
12.22
12.24
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
12.2
12.22
12.24
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
12.2
12.22
12.24
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
12.2
12.22
12.24
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.16. Light curve of ID 3727. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
78
11.54
11.56
11.58
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
11.54
11.56
11.58
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
11.54
11.56
11.58
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
11.54
11.56
11.58
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.17. Light curve of ID 1855. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
79
1997). Eclipse depth can range from very shallow (0.01 magnitudes) if partial, to very deep
(several magnitudes) if total. The two eclipses can be comparable in depth or can be unequal
(Sterken 1997). Another classification of eclipsing binaries is EB, which also have well
defined eclipses and some variation between eclipses.
Five of our variables have been identified as EA variables. The phased plots of ID
0980, ID 4109, and ID 1261 are shown in Figure 6.18. ID 0681 would not be properly phased
because it was located near a bright star, which may have contaminated the light curve. ID
1284 is not phased because only one eclipse was observed and therefore no period could be
determined. Unfortunately, because the times were not properly recorded in our image headers
calculations of the eclipse ephemerides for all our EA variables are too inaccurate to be made.
The light curve data of ID 0681 are shown in Figure 6.19. The residual of ID 0681
appears strongly on the var.fits however, it is located near a bright star which appears to be
contaminating the light cuve. ID 0681 is a strong candidate for an eclipsing system with a
possibility of a totality but more data would be needed to verify this. It is possible that ID
0681 is a cluster member based on its position on the CMD.
The light curve data of ID 0980 are shown in Figure 6.20. This system has been
observed in the literature by Viskum et al. (1997) and has been identified as being located on
the main sequence within the stability strip. This star was initially identified as a δ Scuti, but
its light curve clearly indicates that it is an eclipsing variable. The depth of the primary
eclipse is about 0.5 magnitudes. Nothing is seen at the expected position of the secondary
eclipse. However, it could be possible that the period is actually 4.704 days and the secondary
and primary eclipse are of equal depth. It is very likely that ID 0980 is a cluster member
based on its location on the CMD.
The light curve of ID 1261 is shown in Figure 6.21. It should be noted that ID 1261
was not identified as a variable from our ISIS results but was identified from our BLS results.
Note that ID 1261 does not show up on our var.fits in Figure 4.2 The variability is clearer in
the September data that was not run in BLS. The returned period from BLS was 1.524 days
but with the September data the period is clearly closer to 3.159 days. The depth of the eclipse
is 0.25 magnitudes suggests that it is not a planetary transit. It is not likely that ID 1261 is a
cluster member based on its position on the CMD.
The light curve data of ID 1284 are shown in Figure 6.22. The depth of the eclipse is
0.52 magnitudes. The total eclipse lasts for almost 5 hours. This variable shows up very
strong on the var.fits. Because only one eclipse was observed no period determination can be
made. Based on ID 1284’s position on the CMD there is a medium possibility is it a cluster
member. Given the large eclipse, it isn’t unreasonable that the CMD position is off the MS.
80
0980
12.55
12.6
12.65
0
0.2
0.4
0.6
0.8
1
0.6
0.8
1
0.6
0.8
1
1261
Magnitude
15
15.1
15.2
15.3
0
0.2
0.4
4109
16
16.5
17
17.5
0
0.2
0.4
Phase
Figure 6.18. Phased light curves of suspected EA variables.
81
13.3
13.4
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
13.3
13.4
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
13.3
13.4
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
13.3
13.4
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.19. Light curve of ID 0681. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
82
12.55
12.6
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
12.55
12.6
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
12.55
12.6
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
12.55
12.6
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.20. Light curve of ID 0980. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
83
15.1
15.2
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
15.1
15.2
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
15.1
15.2
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
15.1
15.2
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.21. Light curve of ID 1261. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
84
13.8
14
14.2
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
13.8
14
14.2
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
13.8
14
14.2
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
13.8
14
14.2
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.22. Light curve of ID 1284. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
85
The light curve data of ID 4109 are shown in Figure 6.23. This binary system shows a
light curve of type EA. From the phase plot in Figure 6.18 it appears from the light curve that
there is one primary eclipse and one very low amplitude secondary eclipse. The secondary
eclipse is seen at 0.5 phase which is 0.3 phase away from the primary eclipse indicating that
the system is eccentric. The light curve of the primary eclipse does seem to change depth
slightly from the nights it was observed. Because the times of the October 15th and 16th
observations were not recorded in the header and an estimated time was used based on an
observation log recorded during the time of observation ID 4109 had some difficulties being
phased. The October 15th and 16th observations were removed for the phase plot.
6.2.4 Irregular Variables or Unclassified
Six of our variable stars have been identified as irregular or unclassified. Phase plots
of these irregular variables were not all included as an optimal period could not be
determined. A period search was attempted using both Lomb-Scargle and Lafler-Kinman
codes, but no adequate period was found.
The light curve data of ID 2409 are shown in Figure 6.24. Due to the variation in the
light curve it appears that ID 2409 is a likely W UMa variable candidate but this system could
not be phased properly. The variations do not appear consistent. The approximate amplitude
of variation is around 0.05. It is likely that ID 2409 is a cluster member based on its position
on the CMD and location to the center of the cluster (approximately 2′ ).
The light curve data of ID 2773 are shown in Figure 6.25. The night to night variations
indicate that this star is variable and possibly a W UMa variable. Attempts were made to
phase the data but no clear period could be determined. The light curve varies with a period
probably near a day. There is a small likelihood that ID 2773 is a cluster member based on its
position on the CMD. However, it is located near the cluster center (approximately 0.4 ′ ).
The light curve data of ID 3096 are shown in Figure 6.26. The light curve does not
provide clear evidence as to the classification of this star. The closest result which phases the
data is shown in Figure 6.27 with a period of P = 2.227 days . The nights phased include
August 25th, October 13th, 14th, 15th, and November 13th, 15th. The amplitude is about 0.02
magnitudes. There appears to be a significant amount of scatter in this light curve and in the
phased plot. ID 3096 could be a possible quasiperiodic variable since the nature of the
variation changes with a little variation within a night, to variation from night to night. There
is a medium likelihood that ID 3096 is associated with the cluster based on its location on the
CMD. It is located (approximately 2′ ) from the cluster center.
The light curve data of ID 3928 are shown in Figure 6.28. Variability appears to be
present but not clear or consistent. ID 3928 could be a possible W UMa or EB variable. ID
86
16.5
17
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
16.5
17
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
16.5
17
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
16.5
17
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.23. Light curve of ID 4109. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
87
3928 appears to have a little out of eclipse variation period near 2 days. The September
observations seem to indicate an eclipsing system but the October observations appear to be
unclear. It is possible that this could be a quasiperiodic variable. ID 3928 is spatially located
away from the center of the cluster but its location on the CMD suggest that there is a medium
likelihood is it associated with the cluster.
The light curve of ID 4540 are shown in Figure 6.29. The residual of ID 4540 is very
strong on the var.fits. However, because it is located so close to charge bleeding extending
from the brightest central star in the field it is likely that the light curve is somewhat
contaminated. Based on the variability in the light curve it appears that ID 4540 might be a
quasi periodic variable but it classification remains unclear. Based on ID 4540’s location on
the CMD there is little likelihood that it is associated with the cluster.
The light curve data of ID 4762 are shown in Figure 6.30. Variability is present in the
September and October observations. The variability in the September 17th and October 16th
observations indicate there is a possible eclipse. It should be noted that this star fell on a
column of bad pixels in all of our October observations which may be contaminating the
variability. The likelihood that ID 4762 is associated with the cluster is low since it lies offset
on the CMD and its spatial position is far from the center of the cluster.
88
14.65
14.7
14.75
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
14.65
14.7
14.75
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
14.65
14.7
14.75
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
14.65
14.7
14.75
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.24. Light curve of ID 2409. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
89
16.4
16.6
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
16.4
16.6
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
16.4
16.6
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
16.4
16.6
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.25. Light curve of ID 2773. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
90
12.74
12.76
12.78
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
12.74
12.76
12.78
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
12.74
12.76
12.78
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
12.74
12.76
12.78
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.26. Light curve of ID 3096. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
91
3096
12.72
12.74
12.76
12.78
12.8
0
0.2
0.4
Figure 6.27. Phased light curve of ID 3096.
0.6
0.8
1
92
15.8
16
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
15.8
16
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
15.8
16
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
15.8
16
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.28. Light curve of ID 3928. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
93
13.7
13.8
0
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
13.7
13.8
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
13.7
13.8
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
13.7
13.8
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.29. Light curve of ID 4540. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
94
14
14.2
0.1
0.2
0.3
1
1.1 1.2 1.3
2
2.1 2.2 2.3
Aug24,01
Aug25,01
Aug26,01
50
51
52
14
14.2
50.2
Oct13,01
51.2
Oct14,01
52.2
Oct15,01
53
53.2
Oct16,01
14
14.2
81
81.9
81.1
Nov14,01
Nov15,01
82.9
83 83.1
Nov16,01
14
14.2
23
23.2
Sept17,01
24
24.2
Sept18,01
25
25.2
Sept19,01
26 26.1 26.2
Sep20,01
Figure 6.30. Light curve of ID 4762. Major time-axis tick marks are spaced by 2.4 hours.
The time-axis is defined as the Heliocentric Julian Date (HJD(i)) subtracted from the
Heliocentric Julian Date of the first observation (HJD(1)) taken on August 24th.
95
CHAPTER 7
CONCLUSION
The probability for a planet to transit the host star is relatively small, so that large data
sets are needed to have a reasonable chance of finding a planet. Open clusters potentially
provide an ideal environment for finding extrasolar planets since they have a relatively large
number of stars. There have been many survey searching or planetary transits in star clusters
(see Weldrake (2007) for a review). While no planets have yet been confirmed within a star
cluster, these surveys have provided promising candidates awaiting follow-up observations, as
well as cluster parameters and variables stars.
Detecting transiting planets involves finding a faint signal in noisy data which is a very
challenging task. Only large planets in short orbits can be detected using ground-based
surveys. We have searched for planetary transits with a period range between 1.05 and 10
days using the BLS method searching 1,238 stars which have an RMS < 0.015 magnitude,
finding no likely transit candidates. While no planetary transits have been found in our survey
this does not rule out the possibility that there are not planets in M52. If, however, a planetary
transit candidate were found additional photometric observations in multiple filters would be
needed to check for transit consistency in order to rule out a possible eclipsing system.
We obtained lightcurves for 4,128 stars using the ISIS image subtraction software, and
identified 22 variable stars, of which 19 were not previously known as variable. Ten of our
variable stars were identified as eclipsing-type W Ursa Majoris contact binaries, 5 were
identified as detached binaries of the Algol type, 1 was identified as a slowly pulsating B star,
and 6 were irregular and require further investigation before they can be classified.
A color magnitude diagram was constructed from V and R photometry with fitted
isochrones from Cassisi et al. (2006). Our color magnitude diagram was used to help establish
cluster membership for our variable stars. We find that 3 of our W UMa stars lie within region
of high cluster membership probability. This is especially interesting because it is not
expected that W UMa stars would be found in such a young cluster. Radial velocity follow up
observations would be required to confirm whether or not they are actual cluster members.
96
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Alard, C. & Lupton, R. H. 1998, APJ, 503, 325
Bonatto, C. & Bica, E. 2006, A&A, 455, 931
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421, L13
Brown, T. M., Charbonneau, D., Gilliland, R. L., Noyes, R. W., & Burrows, A. 2001, APJ,
552, 699
Burke, C. J., Gaudi, B. S., DePoy, D. L., Pogge, R. W., & Pinsonneault, M. H. 2004, APJ,
127, 2382
Carroll, B. W. & Ostlie, D. A. 2006, Institute for Mathematics and Its Applications
Casoli, F. & Encrenaz, T. 2007, The New Worlds (The New Worlds, by F. Casoliand
T. Encrenaz Berlin: Springer, 2007. ISBN:978-0-387-44906-7)
Cassisi, S., Pietrinferni, A., Salaris, M., Castelli, F., Cordier, D., & Castellani, M. 2006,
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ABSTRACT OF THE THESIS
The Search for Transiting Extrasolar Planets
in the Open Cluster M52
by
Tiffany M. Borders
Master of Sciences in Astronomy
San Diego State University, 2008
In this survey we attempt to discover short-period Jupiter-size planets in the young
open cluster M52. Ten nights of R-band photometry were used to search for planetary transits.
We obtained light curves of 4,128 stars and inspected them for variability. No planetary
transits were apparent; however, some interesting variable stars were discovered. In total, 22
variable stars were discovered of which, 19 were not previously known as variable. Ten of our
variable stars were identified as eclipsing-type W Ursa Majoris contact binaries, 5 were
identified as detached binaries of the Algol type, 1 was identified as a slowly pulsating B star,
and 6 were irregular and require further investigation before they can be classified. A
color-magnitude diagram constructed from V and R photometry with fitted isochrones is also
presented to help determine cluster membership of our variable stars. We find that 3 of our W
Uma stars lie within a region of high cluster membership probability. Radial velocity follow
up observations are needed to confirm cluster membership. If confirmed, this would be highly
interesting as W Uma stars are not excepted to be found in such a young cluster.