The Detectability Of Moons Of Extra Solar Planets

The detectability of moons of extra-solar planets is investigated, focussing on the time-of-arrival perturbation technique, a method for detecting moons of pulsar planets, and the photometric transit timing technique, a method for detecting moons of transiting planets. Realistic thresholds are derived and analysed in the in the context of the types of moons that are likely to form and be orbitally stable for the lifetime of the system.For the case of the time-of-arrival perturbation technique, the analysis is conducted in two stages. First, a preliminary investigation is conducted assuming that planet and moon's orbit are circular and coplanar. This analysis is then applied to the case of the pulsar planet PSR B1620-26 b, and used to conclude that a stable moon orbiting this pulsar planet could be detected, if its mass was >5% of its planet's mass (2.5 Jupiter masses), and if the planet-moon distance was ~2% of the planet-pulsar separation (23 AU). Time-of-arrival expressions are then derived for mutually inclined as well as non-circular orbits.For the case of the photometric transit timing technique, a different approach is adopted. First, analytic expressions for the timing perturbation due to the moon are derived for the case where the orbit of the moon is circular and coplanar with that of the planet and where the planet's orbit is circular and aligned to the line-of-sight, circular and inclined with respect to the line-of-sight or eccentric and aligned to the line-of-sight. It is found that when the velocity of the moon is small with respect to the velocity at which the planet-moon barycenter transits the star, that the timing perturbation could be well approximated by a sinusoid. Second, the timing noise is investigated analytically, for the case of white photometric noise, and numerically, using SOHO lightcurves, for the case of realistic and filtered realistic photometric noise. It is found the timing noise is normally distributed and uncorrelated for planets likely to host large moons. In addition it is found that realistic stellar photometric noise results in a dramatic increase in the standard deviation of the timing noise, which is not entirely reversed by filtering. Finally, using the method of generalised likelihood ratio testing, the work on the form of the timing perturbation due to a moon, and the behaviour of the timing noise are combined to derive both approximate analytic, and exact numerical thresholds. In particular, a Monte Carlo simulation is run which investigates thresholds for the cases of aligned, inclined and eccentric planet orbits for white, filtered and realistic photometric noise for a range of planet masses (10 Jupiter masses, 1 Jupiter mass, 1 Uranus mass and 1 Earth mass) and semi-major axes (0.2AU, 0.4AU and 0.6AU). Assuming Kepler quality data, it is found that for the case where the photometric noise is white, physically realistic moons could be detected for gas giant host planets, while for the case where the photometric noise is dominated by intrinsic stellar noise, filtering allows the detection of physically realistic moons for planets with a mass of 10 Jupiter masses.