Changes of light curve
parameters of LPVs and
classification of Miras
and semiregular
variables
V.I. Marsakova,
Odessa National University
KOLOS-2015
T Cep
Mira-type variables:
pulsating red giants
AF Cyg
Semiregular variables:
pulsating red giants
and supergiants
Observations
We have used observations from the databases of the
 French Association of Variable Stars Observers (AFOEV)
 Variable Stars Observers League of Japan (VSOLJ)
 American Association of Variable Star Observers (AAVSO),
which allow to study the variability of these stars during the time
interval of about 100 years.
Methods
We have used:
 “Asymptotic parabolae” and “running parabolae” fitting to
determine the characteristics of extrema
 Trigonometrical polynomial to obtain the characteristics of
the mean phase light curves
 Wavelet analysis and “running sines” to study the stability of
the periods and the light curves
 Andronov I.L., AsAp Suppl., 1997, V. 124, 207.
 Andronov I.L. ASP Conf. Ser. 2003, V. 229 P.391
 Chinarova L.L. Odessa Astron. Publ. 2010. V. 23. P. 25.
 Marsakova V.I., Andronov I.L. ASP Conf. Ser. 2000. V. 203. P. 131.
 Andronov I.L., Marsakova V.I. Astrophysics. 2006. V.49. P. 370.
 Kudashkina L.S., Andronov I.L., Odessa Astron. Publ., 1996, V. 9, 108.
O-C
1. Small irregular period variations
(C
7)
Have some variables of C and S spectral classes
and variables with multiperiodicity
O-C
V Aur
J.D. -2400000
(C6)
R Cyg
O-C
(S2)
J.D. -2400000
2. Switching of similar values of the
period with sawtooth O-C curves
O-C
R Boo
J.D. -2400000
O-C
R Cas
J.D. -2400000
O-C
 Cyg X Cas
J.D. -2400000
O-C
R Dra
O-C
X Oph
J.D. -2400000
Switching of similar values of the
period with sawtooth O-C curves
There are not dependence on the main pulsational period
Variable Period Period(s) of
O-C
X Aur
164
20520, 9860
T Her
165
9000, 6500
RS Her
219
12600
R Boo
224
11340,7300
R Dra
246
12400, 7150
X Oph
332
16000
 Cyg
409
15400, 8500
R Cas
430
16600
Amplitude of the main
wave of O-C
32
10
17
11
11
24
15
20
3. Smooth cyclic at timescale
approximately 17000–22000 days
are acompanied changes of the shape
of the light curve
T Cep
Results of cross-correlation
analysis
Parameter
Period
Magnitude
of the hump
Magnitude
of the hump
Amplitude
Parameter
Correlation
Shift,
coefficient
cycles
0,80
0
Amplitude
0,85
0
Asymmetry
0,85
-4
Period
0,93
-3
Asymmetry
O-C
V Cas
J.D. -2400000
O-C
U Cyg
J.D. -2400000
O-C
R UMa
J.D. -2400000
O-C
U UMi
J.D. -2400000
Smooth cyclic at timescale
approximately 17000–23000 days
Variable Period Period(s) of O-C
W Lyr
V Cas
R UMA
S UMi
U UMi
Z Sco
T Cam
T Cep
T Cas
U Cyg
197
229
302
328
331
348
374
388
445
466
Amplitude of the main
wave of O-C
23900, 11900, 7900
30
22600, 10600
52
22900
26
14600,20600
29
17600, 9550
50
22500, 7100, 11050
48
22500, 11400
52
19700, 11300
82
18700
27
23200
60
For comparison:
Switching of similar values of the period
with sawtooth O-C curves
Variable Period Period(s) of
O-C
X Aur
164
20520, 9860
T Her
165
9000, 6500
RS Her
219
12600
R Boo
224
11340,7300
R Dra
246
12400, 7150
X Oph
332
16000
 Cyg
409
15400, 8500
R Cas
430
16600
Amplitude of the main
wave of O-C
32
10
17
11
11
24
15
20
4. Progressive changes
(continuous changes of the
same sign)
Residuals from parabola are sawtooth
Luminositiy variation during the helium-flash stage
Wood P.R., Zarro D.M. Astrophys. J., 1981, V. 247, P.
247.
AFOEV+VSOLJ
Superposition of the effects
J.D. -2400000
 Thomas Karlsson (Swedish Variable
Observations
database): http://var.astronet.se/
mirainfooc.
AFOEV+VSOLJ
The red dots are maxima that are fitted
from observations,
the lightblue are maxima published
by AAVSO and
the darkblue are maxima collected from
various other published sources.
The fitted maxima are based on
observation data from the organizations
AAVSO, AFOEV, VSOLJ and BAA/VSS using
approimation by 12 order polynomial fit to
the mean lightcurve at maximum
AFOEV+VSOLJ
J.D. -2400000
546.2
466.2
Smooth cyclic or progressive changes?
350.5
5.Multiperiodicity.
S Aql
S(f)
147
245
104.6
“semiregular”
interval
frequency
Mira-type variability of S Aql
before JD 2450000
Variability of S Aql : with trigonometric
polynomial fit (with two periods 146.7d (4
harmonics), 245.2d (2 harmonics))
Multiperiodicity: S Aql
Running sines:
smoothing curve
phase
J.D. -2400000
Phase trends
Multiperiodicity:
Y Per
769
245.3
253
149.4
247.3
Running sines
147.6
129
Phase trend
Multiperiodicity 250/150
Variable
P1 , (S)
P2, (S)
Period ratio GCVS
classification
GCVS
Spectral class
T Col
139.6 (0.06)
1.62
M
M3e-M6e
139.3 (0.13)
1.62
M
M6.5
143.3 (0.20)
1.65
1.61
1.68
1.62
1.70
M
ST Her
226.1 (0.60)
229.8 (0.11)
225.3 (0.52)
230.7 (0.18)
235.8 (0.57)
230.8 (0.31)
249.5 (0.16)
240.4 (0.08)
253 (0.32).
245.3 (0.08)
254.7 (0.32)
258.8 (0.26)
264.6 (0.20)
266.3 (0.59)
272.0 (0.6)
146.7(0.48)
234.3 (0.08)
245.7 (0.07)
257.5(0.49)
260 (0.17)
257.6 (0.37)
260.8 (0.07)
236.7 (0.24)
261.3 (0.05)
256.5 (0.07)
S Sct
268.6 (0.03)
DN Her
EL Lyr
S Tri
Y Per
S Sex
UZ Hya
AN Peg
S Aql
RU And
V Boo
X Mon
RR Her
148.1 (0.07)
M
M2e
M
C4,3e
M
M2-M5e
153.8 (0.2)
156.0 (0.26)
245.2 (0.18)
124,7 (0,03)
146,8 (0,02)
151 (0.07)
1.70
1.72
1.76
1.73
1.74
1.67
1.87
1.67
1.70
M
M
SRa
SRa
M4e
M5
M3-M5.5e
M5-M6e
SRa
M6e
151.1 (0.06)
1.71
SRa
M1e-M6ep
143.5 (0.05)
1.61
SRb
C5,7e-8,1e
150.8 (0.06)
152.1 (0.06)
151.3 (0.02)
1.70
1.68
1.77
SRb
M6-M7
SRb
C6,4
149.4 (0.04)
150 (0.15)
O-C
S Aql
J.D. -2400000
V Boo
O-C
Phase trend
J.D. -2400000
Amplitude changes
(SRA)
(M)
S PER, SRC
m
J.D. -2400000
A diagram of spectral type versus relative amplitude scatter. The
subtype increases rightwards.
S Tri
S Aql
W Hya
T Ari
T CVn,
BG Cyg
A diagram of the relative period scatter versus the relative
amplitude scatter.
S Aql,
S Tri
T CVn
S Per
T Ari
BG Cyg
W Hya
Main publications
 Marsakova V.I. Variations of light curve parameters in Miras with progressive period
changes.// Astron. Soc. Pacif. Conference Series. – 2000. – 203, 130
 Marsakova V.I., Andronov I.L. Unusual secondary variations in the Mira star T Cep.// Astron.
Soc. Pacif. Conference Series. – 2000. – 203, 131–132
 Marsakova V.I., Andronov I.L. Variability of long-period pulsating stars. II. Additional
parameters for classifying stars . – 2006 . – Astrophysics, 49, 506-522
 Marsakova V.I., Andronov I.L. Miras or SRa’s – the transient type variables. // Odessa
Astronomical Publications, 2012, 25, № 1, p. 60-64.
 Marsakova V.I. T Cep, U UMi, Z Sco – Mira-type variables with cyclic period changes //
Odessa Astronomical Publications, 2013, 26, № 1, p. 78-82.
 Marsakova V.I. Secular Variations of the Photometric Parameters of Mira Ceti Variables and
Semiregular Variables. Bulletin of the Crimean Astrophysical Observatory, 2014, 110, 23–29.
 Marsakova V.I. Characteristics of the Period Changes in Mira-type Variables// Odessa
Astronomical Publications, 2014, v.27, № 1, 225-234.
 Kudashkina L.S., Marsakova V.I. Statistical Studies of Long – Period Variable Stars in Odessa
// Częstochowski Kalendarz Astronomiczny-2015  Częstochowa, 2014.  .
 Andronov I. L., Marsakova V. I., Kudashkina L. S., Chinarova L. L.. Inter-Longitude Astronomy
project: long period variable stars // Advances in Astronomy and Space Physics, 4, 3-8
(2014).
Conclusion
1. Several types of period variations for Mira-type variables were
separated:
 small irregular period variations,
 switching of similar values of the period with sawtooth O-C curves
(amplitude is smaller),
 smooth cyclic at timescale approximately 17000–22000 days
(amplitude is higher, shape of curve is changed),
 progressive (continuous changes of the same sign),
 effects of multiperiodicity.
2. Some multiperiodic variables can be classified as ones belonging to a
transient type between Mira-type and semiregular variables
Author are grateful to L.S.
Kudashkina and I.L. Andronov for
collaboration and discussions.
Thank You for
attention!