Possibility of Detecting Moons of Pulsar Planets Through Time-of-Arrival Analysis

Abstract

The perturbation caused by planet-moon binarity on the time-of-arrival signal of a pulsar with an orbiting planet is derived for the case in which the orbits of the moon and the planet-moon barycenter are both circular and coplanar. The signal consists of two sinusoids with frequency (2n_p - 3n_b) and (2n_p - n_b ), where n_p and n_b are the mean motions of the planet and moon around their barycenter, and the planet-moon system around the host, respectively. The amplitude of the signal is equal to the fraction sin I[9(M_p M_m)/16(M_p + M_m)^2] [r/R]^5 of the system crossing time R/c, where M_p and M_m are the the masses of the planet and moon, r is their orbital separation, R is the distance between the host pulsar and planet-moon barycenter, I is the inclination of the orbital plane of the planet, and c is the speed of light. The analysis is applied to the case of PSR B1620-26 b, a pulsar planet, to constrain the orbital separation and mass of any possible moons. We find that a stable moon orbiting this pulsar planet could be detected, if the moon had a separation of about one fiftieth of that of the orbit of the planet around the pulsar, and a mass ratio to the planet of ~5% or larger.