Download LCM Analysis for PLATO 2.0

Bartlomiej Debski
Astronomical Observatory of the Jagiellonian University, Orla 171, 30-244 Krakow, Poland; [email protected]
Introduction
Light Curve Morphology Analysis is a quick method for studying the general properties of the surface phenomena in
close binary stars observed in a long-time base photometry (e.g. spaceborne missions like KEPLER, TESS, WFIRST,
PLATO). Its application to the Kepler data allowed us to find the indicators for starspot migration, the direction of the
starspot migration, constraints on the starspot co-latitude and size parameters and many other. One of the most
promising prospects for this method is the determination of which component of the contact binary is the more
massive one (which leads to the determination, which brightness minimum shall be called the primary one). In this
work we present some applications of the Analysis to the 422 objects with the EW-type light curves from the Kepler
Eclipsing Binary Catalogue.
The method is based on the analysis of the evolution of the light curve extrema. The analysis takes into account the
positions of the maxima (in orbital phase), their heights (in flux), the same for the minima (positions and depths) and
cross-correlates their combinations. To examine the expected correlations and signals, we made a grid of simulations
using a modified Wilson-Devinney code. The simulations covered a wide range od system parameters for contact
binaries (mass ratio, fill-out factor, temperatures ratio, inclination) and their starspots (co-latitude, longitude, size and
temperature).
Figure 1: naming convention in the analysis
Which minimum is the primary minimum?
Indicators of the starspot migration
Keywords: median maxima separation
Keywords: O'Connell effect, maxima separation
Separation of the brightness maxima in EW-type lightcurves produced by a (near) contact binary is affected mostly by the limb
darkening and stellar activity. Our simulations show that if in the primary minimum the more massive star is beeing eclipsed by a less
massive component, then the secondary maximum will occur more than 0.5 orbital phase after the primary maximum. The activity
represented by the migrating star spots will produce a distinctive pattern in the evolving maxima separation. That is why the median of
the separation should be measured, as it is almost unchanged and still larger than 0.5 orbital phase. This makes the median maxima
separation a very good indicator, which minimum shall be called the primary, and which the secondary one. This is not trivial task as the
minima may change their depths or shapes due to the ongoing stellar activity. Given the object is observed for many epochs, the median
maxima separation serve as the objective tracer of which minimum is the primary one.
Short version: choose your minima in such a way, that the median maxima separation will be larger than 0.5 ph.
A starspot that migrate along the stellar longitude will affect the height and position of the brightness maxima. During one
migration cycle (360˚ around the star) the maxima will be varying up and down, one after another. Thus the evolution of maxima
heights will be negatively correlated. In the same time, the separation of the maxima will be highest when spot reach the back of
the star and smallest for a spot sitting just between the stars. The separation, however, will evolve with a relatively small
amplitude. The diagram of the O'Connell effect vs maxima separation set with a similar scales on both axes shall display very
flattened circle, resembling a horizontal line. In fact, we found that most of the objects in our sample manifest the signal
attributable to the migrating starspot.
Short version: Changes in the O'Connell effect and the evolution of the maxima separation allows to select binaries with the
ongoing starspot migration.
Figure 2: The histogram of median maxima separations in
our sample taken directly from KEBC. The apparent bimodal
distribution is caused by randomly attributed primary
minima.
Figure 3: The histogram of median maxima separations after
re-phasing the binaries. Now primary minima are chosen in
such a way that the median maxima separation is larger than
0.5 ph.
Figure 4: Relation between the changes of the O’Connell
effect and the variations of maxima separation can be
explained with a migrating spot. Here a large spot moves
closely around the pole.
Figure 5: The longitudal migration of such a starspot will
affect the brightness maxima consecutively changing their
heights. It is visible as the negative correlation in maxima
heights diagram.
Direction of the starspot migration
Stationary, evolving starspots or not a contact binary at all
Keywords: secondary minimum depth, secondary minimum location
Keywords: O'Connell effect, maxima separation, maxima height
If a starspot is located on a primary star and migrates along the longitude, then the direction of
the migration can be traced by comparing the signals of changes in the secondary minimum
location and depth. This dependence is easy visible in case of a flat-bottom minima, because the
amplitude of minima shifts are large due to the geometry of the light curve. We found the direction
of a starspots migration in KIC 6118779 to be descending in the longitude (Debski, Zola, Baran
2014).
Short version: the longitudal migration of a starspot is tracabe by comparing the evolution of the
minimum depth and the changes in its location.
The confrontation between the evolution of the O’Connell effect and the maxima separiation may produce three results: 1) no correlation (no spot activity at all), 2)
horizontally flattened circle (starspot migration) and 3) vertical distribution. The last one is particularly interesting, since it implies no changes in the O'Connell effect
and fairly large variations in the maxima separation. In such situation, the spot model is constrained to just several possible locations of the evolving region: stellar pole,
back or in front of the second star. Such a stationary starspot must produce a positive correlation between changes in the height of the light curve maxima. In our
sample we found objects fulfilling these requirements, as shown in figures below. The problem is, all of those systems appear to have rather low inclination and fitting a
model is rather troublesome. Apart of that, there are also objects with a positive correlation of brightness maxima changes, but having no variations in maxima
separation and O'Connell effect whatsoever. These objects may experience radial pulsations of whole stars or not be contact binaries at all. One of the best examples is
the dwarf nova J1621 (Zola et al. 2016), which in queiescence is mimicing a contact binary light curve.
Short version: Some binaries manifest changes in the maxima height and location, which are allowed only in case of stationary spots, or exclude a contact binary
model.
Figure 7 (left): Stationary, large region
(radius r=45˚) located at the neck of the
contact binary changing ith brightness from
T=0.8 up to T=1.1 of the local surface
tmeperature. No O’Connell effect changes
occur , but the maxima separation is highly
variable.
Figure 8 (right): The same „pulsating” region
located at the neck is affecting both maxima
simultaneously. Here the inclination is very
low, therefore our model had to be rescaled,
but the slope has been preserved.
Figure 6. The evolution of the secondary minimum of KIC 6118779 (black dots) superimposed
with the changes of its depth in a timespan of almost three years. If the minimum gets deeper
during the ascention in phase location, it implies that a dark staspot migrates in the direction
of the descending longitude.
Summary: parameters of the system, parameters of the star spot
The key to the understanding what happens on the surface of the close binary is hidden in the evolution of its light curve. The typical timescale of surface activity in short-period
binaries last from several up to a few hundreds of orbital periods. Just because of that, it is crucial to conduct continuous observations lasting months or years and gather the information
about a complete process. This is particularly aplicable to the ongoing and planned spaceborne missions of the orbital observatories, as the method presented here provides a very fast
essesment for every potenetial object in the database. The analysis has been tested for contact binaries and can be extrapolated for the close, detached systems.
In this poster we are showing some interesting correlations between the evolving parameters of the light curve. Reading such characteristics of the curve, like the O'Connell effect or
maxima separation, allows to distinguish the binaries with different types of the surface activity manifestation. Moreover, the information about the median maxima separation can be
used as the fast and universal determinant of which component is more massive, thus which minimum is the primary one. The choice of proper minimum is very important for further
studies, as it, for example determines the geometry used in the WD code. This is extremely handy for making a preliminary catalogue with the light curve elements.
In our other study we show the constraints on the sparspot parameters which enforces the starspots located asymmetrically on the stellar poles (Debski, Zola, Bara, 2015). This has a
serious repercussions for most current contact binary models that place the modeled starspots on the stellar equator, as it influences the modeled system parametrs.
References
•
•
•
•
•
Debski, B.; Baran, A.; Zola, S.: 2014, CoSka, 43, 427
Debski, B., Zola, S., Baran, A., 2015, APSC, 496, 293
Wilson, R.E.; Devinney, E.J.: 1971, AJ, 166, 605
Wilson R.E.: 1979, ApJ, 23, 1054
Zola et al. 2016, ATel #9136