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

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 ( -->2np − 3nb) and ( -->2np − nb), where -->np and -->nb 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 the fraction -->sin I [ 9(MpMm)/16(Mp + Mm)2][r/R]5 of the system crossing time -->R/c, where -->Mp and -->Mm are 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 B1620–26b, 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 its mass were >5% of its planet's mass, and if the planet-moon distance were ~2% of the planet-pulsar separation.