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

Discovery, Study, Classification and Modeling

of Variable Stars

Natalia A. Virnina

Department of High and Applied Mathematics, Odessa National Maritime University, Ukraine,

[email protected]

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”: www.aavso.org/observing/charts/vsp/

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

Checking of the potential candidates

Check the discovery using VizieR-service http://vizier.u-strasbg.fr/viz-bin/VizieR

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 UBVRcIc 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 BVRcIc

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-pagehttp://sai.msu.su/groups/cluster/gcvs/gcvs/iii/vartype.txt

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

• Eclipsing • Pulsating

4. Determination of extrema timings

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=0.27123d

Input parametersMain parameters of the system:

i [80° .. 90°] – inclination

T1 4700 K (fixed) – temperature of the primary component

T2 [4100 K .. 5500 K] – temperature of the secondary component

q [1.5 .. 3.0] – mass ratio

Ω1 [3.95 .. 6.61] – potential of the primary component

Ω2 [3.95 .. 6.61] – potential of the secondary component

g1 0.32 (fixed) – gravity brightening of the primary component

A1 0.5 (fixed) – reflection effect for the primary component

g2 0.32 (fixed) – gravity brightening of the secondary component

A2 0.5 (fixed) – reflection effect for the primary component

e 0 (fixed) – eccentricity

p 90 (fixed) – periastron

[-0.02 .. 0.02] – phase shift

Results of modelingparameters:

Inclination 86.815 ± 0.005T2 4510 ± 10

mass ratio 1.858 ± 0.001Ω1 4.986 ± 0.001

Ω2 4.986 ± 0.001

fill-out factor10.7% 0.0017

r1pole 0.31

r1side 0.32

r1back 0.36

r2pole 0.41

r2side 0.44

r2back 0.47

WZ Crv – a binary system with asymmetric phase curves

Temperatures and relative radiuses

+ Spot

Super-WASP observations

Mwasp=0.3528R+0.6472V-0.1213

Mwasp=580nm

Fitting ParametersParameters WASP-2006 WASP-2007 WASP-2008 Our observ.

Inclination, ° 81.23 81.43 81.15 83.84

T1, K 12500 15000 14800 12830

T2, K 5650 5650 5650 5650

1 5.823 6.349 6.185 5.851

2 3.411 3.731 3.585 3.464

Mass ratio 0.796 0.958 0.898 0.807

Third light, % 7.4 11.6 8.7 2.9 (V-band)

Spot parameters

Co-latitude 69 62 30 160

Longitude 151 171 160 212

Radius 48 30 43 56

Temp. factor 0.89 0.53 0.61 0.73

Spot Changes on the Primary Component

Parameters WASP-2006 WASP-2007 WASP-2008

Co-latitude, ° 75±2 51±1 41.5±0.5

Longitude, ° 155±1 167±3 154±1

Radius, ° 45±2 28±1 57±1

Temp. factor 0.874±0.006 0.595±0.002 0.853±0.001

Fitting of WASP Data

2006 2007 2008

ConclusionsAdvantages 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!