Transit Detection of Radial Velocity Planets

Abstract

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.

Evidence for a planetary mass third body orbiting the binary star KIC 5095269

“…With a proposed inclination of 105.92 ± 1.45 • the probability of transits occurring needs to be considered. Kane & von Braun (2008) presented an analysis of the effect of orbital parameters, specifically eccentricity and argument of periastron, on the probability of a transit as a function of the orbital period. The probability of a transit occurring for a planet in a circular orbit drops dramatically as the orbital period of the planet increases.…”

Stability of planetary, single M dwarf, and binary star companions to Kepler detached eclipsing binaries and a possible five-body system

“…The set of orbital properties within a system jointly influence the potential for transits or eclipses to be seen in the light curve. The probability of a transit occurring decreases as the orbital period increases (Kane & von Braun 2008) so while KIC10268809, for example, has inclinations that may indicate the possibility of transits (84°and 94°for the binary stars and outer companion respectively), the very long orbital period of the outer companion results in transits being unlikely to occur. Extra events can be seen in the light curve of KIC5255552, indicating that transits occur, and there are also additional eclipses that a third body may not account for, thus indicating the possibility of a quadruple system (Zhang, J. et al 2018).…”