1. Spot Migration on Eclipsing Binary KIC9821078
Engin BAHAR, İbrahim ÖZAVCI and Hakan Volkan ŞENAVCI

2. Contents Summary KIC9821078 --> hereafter KIC98 :) Literature
Kepler Data
Light and Radial Velocity Curve Analysis
Spot Analysis via Light Curve Inversion Method
Results

3. Summary Main goal: Data : Technique :
to find out how spots or spot groups on the surface of the components behave.
Data :
Kepler light curves --> high-precision, almost continuous, covering a wide range of time (~4 years). 
Technique :
Phase each light curves cycle by cycle and obtain surface brightness map for each cycle using Light Curve Inversion method (LCI)
Examine how spots or spot groups behave throughout the time series surface brightness maps.
We aim to reveal the spot behavior of the system using Light Curve Inversion method. Kepler light curves were used during the analysis. The analysis perform via Light Curve Inversion method. We phased each light curve and obtain surface brightness maps for each cycle in order to understand the spot variations within the long-time interval.

4. About the System Vmag ~ 14.37 mag
Temperatures of the primary and the secondary  star approximately K and 4300 K, respectevly. 
The components are low mass stars
Ortbital period and inclination of the system about ~ 8.4 days and ~90 degrees, repectevly.
There are 17 long cadence and 4 short cadence quarter Kepler ligth curves.
Here is some information about the system. The brightness is about 14.3 magnitudes in V band and both components are late type stars with masses of approximately 0.7 and 0.5, respectevely. So, those are actually low mass stars. The orbital inclination of this long-period binary is near 90 degrees. We performed the analysis of 17 long cadence and 4 short cadence quarters of Kepler data.

5. Literature Some parameters of the system from literature Pourbaix vd.
2004
Slawson
vd.
2011
Prsa
Armstrong
2014
Gao
2016
Van Eylen
Morton
Spectral type
K5 / M0 -
Distance [pc]
180
Teff pri. ( / sec.)  [Ko]
4112 / 2950
4112 /  3050
4368 / 3667
4268
4385 / 3666
4128
E(B-V)
0.048
log g [cgs]
4.269
4.602
4.68
Mass pri. (/ sec.) [M☉]
0.61
Radius pri. (/ sec) [R☉]
0.59
r1 + r2 
0.094
a [R☉]
ecosw
0.0006
esinw
sini
[Fe/H]
-0.11
Age [Gyr]
9.59
Here are some parameters of the system derived in several studies in the literature, in which a large number of stars are analyzed, not specifically studying KIC98.

6. Literature Devor et al. (2008)
Stellar
Parameters
T1 [Ko]
4150
T2 [Ko]
3700
a [R☉]
18.54(9) q
0.7692(69) e
0 (fixed)
Vg [km/s]
-21.01(18)
i [o]
89.02(26)
Absolute Parameters
M1 [M☉]
0.6795(107)
M2 [M☉]
0.5226(61)
R1 [R☉]
0.634(43)
R2 [R☉]
0.525(52)
log g1 [cgs]
4.666(59)
log g2 [cgs]
4.718(86)
d [pc]
230(20)
First detailed study of the system was performed by Devor et al. They observed the system's light curves via ground based telescope and derived stellar and absolute parameters of the system as you can see on the left side. Because the light curves is quite scattered the presence of spots is not clear.
Some parameters of the system and observed light curve from Devor rt al. (2008)

7. Devor et al. (2008) Literature Synchronization of the System
Timescales of tsync ~ 0.56 and 1.02 Gyr for the primary and secondary components of KIC98.
Age of the system is assuming at least a few Gyr.
It would not be surprising if tidal forces between the components had already synchronized their rotations.
The synchronization parameter is significant for such spot analysis, since the rotational periods of the components have to precisely known in terms of phasing the light curves into cycle chunks. If the system is synchronized we can use orbital period for phasing. Devor et al. claim that the system should be synchronized since age of the system is at least a few Gyr.

8. Literature
Han et al. (2019)
Stellar
Parameters
T1 [Ko]
4000
T2 [Ko]
3300
a [R☉]
18.516(34) q
0.777(2) e
0.0314(2)
Vg [km/s]
-23.8(1)
i [o]
89.297(1)
Absolute Parameters
M1 [M☉]
0.67(1)
M2 [M☉]
0.52(1)
R1 [R☉]
0.662(1)
R2 [R☉]
0.478(1)
log g1 [cgs]
5.0
log g2 [cgs]
d [pc]
243.7
Another detailed study of the system was performed by Han et al. They derived parameters of the system using Kepler light curves and radial velocity curve. The parameters are convenient with those of obtained by Devor et al. Han et al removed out-of-eclipse variation of the light curves as you can see from the figure on right side, using Gaussian fits and modelled primary and secondary minima.
Some parameters of the system and light curve fits from Han et al. (2008)

9. Spot occultation effect on minima of the system (Han et al., 2019)
Literature
Han et al. (2019)
Secondary Residuals
Primary Residuals
Those figures present the residuals of the best-fit model and the Kepler short-cadence data where the positive deviations from zero indicate dark spots occulted during the eclipse. Position of these bump features change slightly.  This could be due to synchronized stars with their spots evolving, differential stellar rotation, or slightly sub-synchronous rotation of stars with their spots evolving.
Spot occultation effect on minima of the system (Han et al., 2019)

10. Lurie et al. (2017) Literature
SC - Q9
SC - Q7
     BJD
Lurie et al. examined about 2278 Kepler eclipsing binary stars and classified them according to out-of-eclipse light curve variations. You can see an example of spot modulation effect on the left side. The amplitude of the small bump decrease and finally disappear as the amplitude of the big bump increase. This is due to the combination of differential rotation of the star and the formation and dissipation of spots. Similarly, KIC98 (right side) also shows spot modulation effect. Lurie et al. also investigate rotational period of the program stars using auto-correlation function and Lomb-Scargle periodogram. They also found rotational periods of components of KIC98.
An Example of Spot Modulation on KIC Star (Lurie et al., 2017)
KIC
Porb (d)
Class
PACF (d)
P1min (d)
P1max (d)
8.429 sp
9.849
9.774
10.112
This work (KIC98)

11. Kepler Data Long cadence Short cadence
We use PyKE software for detrending and stitching processes and below are the results zoomed in the out-of-eclipse phases. 
PDC_SAP_FLUX obtained  from the Mikulski Archive for Space Telescopes (Upper panels)
Simple Aperture Photometry with Cotrending Basis Vector was performed and stitched by us (lower panels)

12. Kepler Data Normalized light curve Zoom in
We also performed light curve analysis of the system using a sample light curve of short cadence data. But we first remove spots effects on the light curve. To do this, we remove the eclipses and then fit a high degree polynomial to rest of light curve. You can see the fit on the left side and normalized light curve on the right side.
Zoom in
Spot effect was removed on the light curve using high degree polynomial model

13. Light and Radial Velocity Curve Analysis
Analysis was performed with the PHOEBE (Prsa & Zwitter 2005) code.
Primary
Secondary
Light curve solution was performed using the PHOEBE code. We use the RV data obtained by Han et al. Here you can see both the resultant light and radial velocity fits.

14. Light and Radial Velocity Curve Analysis
Stellar and orbital parameters
T1 [Ko]
4400
T2 [Ko]
3500(3)
i [o]
88.97(1)
q = M2/M1
0.7734(16) W1
29.89(6) W2
27.32(7)
a [R⊙]
18.69(2) e
(4) Vg
-24.02(5)
Absolute parameters​
M1 [M⊙]​
0.697(3)​
M2 [M⊙]​
0.539(3)​
L1 [L⊙]​
0.142(1)​
L2 [L⊙]​
0.041(1)​
R1 [R⊙]​
0.642(2)​
R2 [R⊙]​
0.552(1)​
log g1 [cgs]​
4.666(1)​
log g2 [cgs]​
4.687(1)​
Here are the parameters from the light curve solution of the system which are consistent with those of obtained in the literature.
Errors of the parameters, including ones obtained from PHOEBE code, are standard deviations!

15. Spot Analysis via Light Curve Inversion Method
Periodograms obtained from short and long cadence
Long cadence
Short cadence
Periods
Value (days)
Porb
Pmin
Pmax
In order to find out the orbital period precisely we use Lomb – Scargle periodogram and obtained three significant peaks. Assuming both synchronous and non-synchronous rotation, we use those three periods as well as the period obtained by Lurie et al. using ACF, during LCI.
Long cadence

16. Spot Analysis via Light Curve Inversion Method
Reconstruct surface brightness map
DoTS (Doppler Tomograph of Stars) code (Collier Cameron 1997)
LCI
We used the code DoTS by Andrew Collier Cameron for Light Curve Inversions. As the first analysis, we used the orbital period of the system. Here is an example of the fit and its resultant surface brightness map. Here, as you can see from the residual, there are discrepancies around minima due to the very small eccentric orbit of the system. Since it is not possible to consider the eccentricity in DoTS, we neglect minima phases by giving them very high errors.  e=

17. Spot Analysis via Light Curve Inversion Method
Porb = 8.430
Here you can see is the distribution of star spots in the form of latitudinally averaged mean spot filling factor as a function of longitude and time. The reconstructions performed using the orbital period generates unreliable drift structures as seen in the current slide. This may also be a consequence of non-synchronous rotation.

18. Spot Analysis via Light Curve Inversion Method
Reconstruct surface brightness map
DoTS (Doppler Tomograph of Stars) code (Collier Cameron 1997)
Pmin= 9.774
As the second attempt  we used the minimum period that we obtained from lomb-scargle periodograms. However it is not possible to phase correctly the binary light curve because the period is shorter than the orbital period. Therefore we remove all the eclipses and analyse the light curve as a single star. This time we obtained more realistic the drifts as you can see from the diagram on the right. 

19. Spot Analysis via Light Curve Inversion Method
Longitudinal spot pattern depends on time
Porb = 8.430
Pmin= 9.774
PACF = 9.849
Pmax = 10.112
Accordingly we performed the same for other periods and obtained the time-longitude diagrams as seen in the current slide. These results clearly show the significance of the period determination as the correct period allows us to clearly distinguish the spot distribution as well as their drifts and drift directions.
From long cadence light curves

20. Spot Analysis via Light Curve Inversion Method
Pmin= 9.774
PACF = 9.849
Pmax = 10.112
Longitudinal spot pattern from long cadence light curves
Here is a comparison of time-longitude diagram generated using long and short cadence data. The results are exactly the same.
 From short cadence light curves

21. Different slopes of migrating features
Results
Pmin= 9.774
Different slopes of migrating features
Two main drifts migrating towards lower and higher longitudes
Here the different slopes of migrating features corresponds to different drift rates. This can be interpreted as the presence of spots on different latitudes and also differential rotation. There are also two main drifts migrating towards lower and higher longitudes. This gave clues about the emerging and decaying spot groups on different latitudes.
We obtained a very similar spot behaviour from the analysis of KIC , an RSCVn type binary 0.5 days. Increasing the sample size of such long-term spot investigation of binary stars will give invaluable clues on understanding the binarity nature of magnetic activity.
Ozavci et al. (2018)

22. THANKS FOR YOUR ATTENTION