Discovery, Study, Classification and Modeling of Variable Stars Natalia A. Virnina Department of High and Applied Mathematics, Odessa National Maritime University, Ukraine,

I. Discovery of Variable Stars

5 steps Choosing of the field and observations Searching for new variable stars Selection of comparison stars, photometry Photometric data analysis Publishing of the results

1. Choosing of the field and observations The best choice is rather small telescope with large field of view. The best region for searching for new variables is the one (nearly) free of variables. The chosen field could be checked with the “AAVSO variable stars plotter”: Where to begin to achieve the best results?

2. Search for new variable stars 1. Visual comparison of different frames (ineffective method) 2. Blinking of different frames (weakly effective method) 3. Statistical search (effective method): VAST – for the Linux platform C-Munipack – for the Windows platform

Working with C-Munipack…

Checking of the potential candidates

Check the discovery using VizieR-service

3. Comparison stars selection Important! The comparison stars have to be constant. Better to use several comparison stars than only one. The standard stars in the UBVR c I c photometric system were measured in the vicinities of some variable stars by A. Henden and the AAVSO group. In the absence of “standard” stars in the field, the SDSS database could be used as well, if to transform u, g, r, i, z photometric data into the standard BVR c I c One comparison star Five comparison stars

4. Photometric data analyzing 1. Heliocentric correction. 2. Search for the period (periodogram analysis). 3. Classification. 4. Determination of extrema timings and the initial epoch.

Search for the period “Peranso”, “WinEfk”, “Period 04”…

One of the most universal methods is Lafler & Kinman’s (1965) method Search for the period

Determination of variability type Classical classification is available on the web-page intense variable X-ray sources Groups of types of variability: eruptive variable stars pulsating variable stars rotating variable stars cataclysmic (explosive and nova-like) variables eclipsing binary systems

Determination of variability type The most frequent types EclipsingPulsating

4. Determination of extrema timings

Kwee-van Woerden (1956) method

4. Determination of extrema timings Kwee-van Woerden (1956) method

Referred in the ADS: «Variable Stars» («Переменные звёзды») OEJV (Open European Journal on Variable Stars) IBVS (International Bulletin of Variable Stars) Journal of the AAVSO (JAAVSO, eJAAVSO) Non-Referred Bulletin de l’AFOEV BAV Rundbrief The Astronomer VSNET Circular … 5. Publishing of the results

II. Modeling

Modeling using the Wilson-Devinney (W-D) code, Monte Carlo searching algorithm

How does the W-D code with the Monte Carlo searching algorithm work?

First (initial) iteration

Convergence of the iterations

BM UMa (V-band) P= d

Input parameters Main parameters of the system: i[80 °.. 90 ° ]– inclination T K (fixed)– temperature of the primary component T 2 [4100 K K] – temperature of the secondary component q[ ]– mass ratio Ω 1 [ ]– potential of the primary component Ω 2 [ ] – potential of the secondary component g ( fixed )– gravity brightening of the primary component A ( fixed ) – reflection effect for the primary component g ( fixed ) – gravity brightening of the secondary component A ( fixed ) – reflection effect for the primary component e0 ( fixed ) – eccentricity p 90 ( fixed ) – periastron  [ ] – phase shift

Results of modeling parameters: Inclination ± T ± 10 mass ratio1.858 ± Ω ± Ω ± fill-out factor10.7%  r 1 pole 0.31 r 1 side 0.32 r 1 back 0.36 r 2 pole 0.41 r 2 side 0.44 r 2 back 0.47

WZ Crv – a binary system with asymmetric phase curves

Temperatures and relative radiuses

+ Spot

Super-WASP observations M wasp =0.3528R V M wasp =580nm

Fitting Parameters ParametersWASP-2006WASP-2007WASP-2008Our observ. Inclination, ° T 1, K T 2, K   Mass ratio Third light, % (V-band) Spot parameters Co-latitude Longitude Radius Temp. factor

Spot Changes on the Primary Component ParametersWASP-2006WASP-2007WASP-2008 Co-latitude, °75 ± 251 ± ± 0.5 Longitude, ° 155 ± 1167 ± 3154 ± 1 Radius, ° 45 ± 228 ± 157 ± 1 Temp. factor0.874 ± ± ± 0.001

Fitting of WASP Data

Conclusions Advantages and Disadvantages of W-D code with MC searching algorithm + – The searching runs automatically; Only the borders of parameters are required; From the statistical point of view, the algorithm founds the best solution. Some parameters (mass ratio, inclination etc.) are too unsure; Sometimes statistically best solution is rather far from the real parameters.

Thanks for attention!