Eclipsing Binaries in Extra Solar Planet Research

Extrasolar planet research has similarities with EB studies in the sense that similar data, light, and radial velocity curves are used. A star-planet (or other low-luminosity object) system, with transits and radial velocities for the star only, is in many respects analogous to a single-lined spectroscopic and detached EB. As the number of detected transiting planets increases (on July 1, 2009, the Extrasolar Planet Encyclopedia22 listed 59 transiting planets), EB analyzing methods become more and more important to extrasolar planet researchers. In favorable cases they can give the mass ratio, inclination, as well as period, rate of period change, semimajor axis, stellar, and planetary radius.

As in a single-lined binary, the mass ratio q cannot be determined from the velocity curve, one can proceed as follows: The mass of the star, Ms, must be assumed, for instance, based on its spectral characteristics, from evolutionary models, e.g., assuming the star is on the main sequence. As for inclinations i between 80° and 90°, sin i and sin3 i vary only between 0.98 and 1, and 0.94 and 1, resp., and as q is usually small, e.g., q < 10-3, Kepler's third law

2 4n2a3

enables us to derive a good estimate of the semi-major axis, a, from the period P. Initially, adopting a reasonable value for the planetary mass, M p, q follows as q = M p/Ms.

Limb-darkening law and coefficients can be taken from Van Hamme (1993). The star's rotational period is most likely much smaller than P and requires the rotation parameter F\ to be set to values much smaller than unity. As the time of minima in planetary transits may not be well defined, it is an option to use time as an independent parameter and fit the ephemeris parameters (reference epoch T0, period P, and possibly rate of period change dP/dt) together with inclination i, a and systemic velocity, VY, and radii (or Roche potentials). As the triple (P, a, q) inserted in (1.4.1) might give different values for the stellar mass than the pregiven value Ms, some iterations are necessary. Examples are given in Sect.

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