Dirk TerrellSouthwest Research Institute

terrell@boulder.swri.edu

Dirk TerrellSouthwest Research Institute

terrell@boulder.swri.edu

Eclipsing Binary Star Light Curve AnalysisEclipsing Binary Star Light Curve Analysis

Why Bother with Binaries?

• Provide accurate data that are very difficult to determine for single stars such as masses and radii.

• Are very common- the majority of stellar systems are binaries.

• They are interesting objects in and of themselves. Still many puzzles to solve about their structure and evolution.

Spectroscopic Binaries

Single-lined spectroscopic binary: spectral lines of one star are visible.

Double-lined spectroscopic binary: spectral lines of both stars are visible.

X-ray Binaries

Pulses from the neutron star act as a clock and can be used to measure the orbit.

Eclipsing Binaries

Stars orbital plane is oriented so that the two stars pass in front of one another as seen from Earth. The light curve is rich in information about the two stars.

Wide Variety of Light Curves

Light Curve Classification

EA, or Algol-type, light curves have deep minima with small variation between eclipses. May or may not be an Algol-type binary.

Lyrae-type Light Curves

EB, or Lyrae-type, light curves have unequal minima and substantial variation between eclipses. Most EB systems are nothing like Lyr.

Lyrae GSC 1534:0753

W UMa-type Light Curves

EW, or W UMa-type, light curves have nearly equal eclipse depths and large variation between eclipses. These are very common.

Terminology

a – semi-major axis of orbit (km or arcsec)

e – eccentricity of orbit (dimensionless)

i – inclination of orbit (deg or rad)

q – mass ratio of stars (dimensionless)

– longitude of periastron (deg or rad)

P – orbital period (days)

T0 – time of periastron passage (JD)

T1,T2 – temperatures of stars (K)

F1, F2 – rotation rates of stars (dimensionless)

V– center of mass radial velocity (km/sec)

r1, r2 – relative radii of stars (R/a)

L1/L2 – ratio of luminosities (dimensionless)

Spectroscopic Binaries

•Get a sin(i), e, , T0,P, V

•Get q (if double-lined) and some radius and rotation information (Rossiter Effect) if eclipsing

•a and i are perfectly correlated

•Gives absolute dimensions

Eclipsing Binaries

•Get e, i, P, T0

•Get r (therefore shapes), L1/L2

•Get F, q in favorable cases

•No information on absolute dimensions

Information in Light Curves

1. Eclipse durations give information on relative radii of stars.

2. Ratio of eclipse depths gives the ratio of the surface brightnesses of the stars for circular orbits.

3. Depths of total-annular eclipses give ratio of radii.

2'1

g

s

R

R

L

Lgs JRL 2'1 gg JRL 2

Information in Light Curves

1. Depth of a total eclipse gives ratio of monochromatic luminosities.

2. Shapes of the eclipses give information on the geometry of the system and limb darkening.

3. Outside eclipse variations give information on star shapes and reflection effect.

Eccentric Orbits

Displacement of secondary eclipse from phase 0.5 and difference in duration of eclipses give information on e and .

Additional Parameters for Light Curves

• x,y – monochromatic limb darkening coefficientsUse Van Hamme tables or my ld program which interpolatesthe Van Hamme tables. For detailed reflection treatment, you also need the bolometric coefficients.

• A – bolometric albedoUse 1.0 for radiative envelopes and 0.5 for convective ones

• g – gravity brightening (darkening) exponentUse 1.0 for radiative envelopes and 0.32 for convective ones

Modeling Binary Stars

Modeling binaries involves the usual steps in any sort of data analysis:

1. Develop the best theoretical model possible

2. Use the model to predict observables like light, radial velocity, X-ray pulse arrival times, etc.

3. Fit predicted observables to observations with an impersonal fitting scheme like least squares. Minimize residuals by adjusting model parameters.

The Wilson-Devinney Program

• First published in 1971 (ApJ vol 165, p. 229) by Bob Wilson and Ed Devinney

• Still being developed by Wilson. New version uses filter bandpasses rather than effective wavelengths. Adds Kurucz atmospheres.

• Uses modified Roche model to compute figures of the stars. Can model stars with eccentric orbits and non-synchronous rotation.

• Can do light curves, radial velocity curves, spectral line profiles, and X-ray pulses. Unpublished versions have added ability to model polarization curves and fluorescence.

• Consists of two programs:

• LC computes light curves given a set of parameters

• DC fits light curves to observations using the method of differential corrections

• Available at ftp://ftp.astro.ufl.edu/pub/wilson/lcdc2003/

The Roche Model

Assumptions in the standard Roche model:1. Stars are point masses2. Orbits are circular3. Stars rotate synchronously4. No radiation pressure effects5. Gas is in hydrostatic equilibrium

The extended Roche model:1. Eccentric orbits2. Non-synchronous rotation

Binary Star Morphology

Detached: both stars smaller than Roche lobe

Semidetached: one star fills Roche lobe, one is smaller

Binary Star Morphology

Overcontact: both stars larger than Roche lobe and share a common envelope of material whose surface is defined by a single equipotential.

Binary Star Morphology

Double contact: both stars fill critical surfaces but at least one rotates asynchronously.

Analyzing Data

1. Develop intuition about effects of various parameters on the light curve.

2. Use other types of observations to constrain parameters.

3. Do simultaneous solutions of multiple light curves (and radial velocity curves) where appropriate.

Effect of Inclination Changes

Decreasing inclination reduces depths of eclipses

Effect of Changing Star Sizes

Increasing the size of one star increases width of eclipses

Effect of Changing Temperatures

Changing the temperature of one star changes the ratio of eclipse depths

KT 60001

KT 59002 KT 49002

Effects of Changing e and

Changing e and causes eclipse widths and phases to change

e = 0.6

= 90º

= 270º

Effects of Changing e and

E = 0.6 and = 180º