Abstract.The orbital parameters of extra-solar planets have a significant impact on the probability that the planet will transit the host star. This was recently demonstrated by the transit detection of HD 17156b whose favourable eccentricity and argument of periastron dramatically increased its transit likelihood. We present a study which provides a quantitative analysis of how these two orbital parameters affect the geometric transit probability as a function of period. Further, we apply these results to known radial velocity planets and show that there are unexpectedly high transit probabilities for planets at relatively long periods. For a photometric monitoring campaign which aims to determine if the planet indeed transits, we calculate the significance of a null result and the subsequent constraints that may be applied to orbital parameters.
Transit ProbabilityThere have been at least five cases in which planetary transits were detected through photometric follow-up of planets already known via their radial velocity (RV) discoveries. The case of HD 17156b (Barbieri et al. 2007) is of particular interest since it is a 21.2 day period planet which happens to have a large eccentricity (e = 0.67) and an argument of periastron which places the periapsis of its orbit in the direction toward the observer and close to parallel to the line of sight, resulting in an increased transit probability.Recent work by Barnes (2007) and Burke (2008) showed that higher eccentricities of planetary orbits will increase their transit probabilities and, consequently, expected yield for transit surveys. We demonstrate the combined effect of the eccentricity, e, and argument of periastron, ω, on transit probability. As shown by Kane (2007), the place in a planetary orbit where it is possible for a transit to occur (where the planet passes the star-observer plane perpendicular to the planetary orbit) is when ω + f = π/2. The probability of such a transit occurring, P t , is given bywhere R p and R are the radii of the planet and star respectively, and a is the semi-major axis. The orbital configuration, especially with regards to the values of e and ω, plays a major role in determining the likelihood of a planet transiting the parent star.