Possibility of Detection of Exomoons with Inclined Orbits Orbiting Pulsar Planets Using the Time-of-Arrival Analysis

Abstract

The perturbation caused by planet-moon binarity on the time-of-arrival (TOA) signal of a pulsar with an orbiting planet is derived for the case of the orbit of the planet-moon system inclined of an angleαwith respect to the plane of the orbit of the planet-moon barycenter around the pulsar. We also consider both the orbits of the moon and the planet-moon barycenter as circular. The signal consists of three sinusoids with frequency, respectively, of(2np−3nb),(2np−nb), and(2np−3nb), wherenpandnbare, respectively, 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 fractionsin⁡I[9(Mp/Mm)/16(Mp+Mm)2][r/R]5(5 sin⁡2α/3−2sin⁡α/3−2 cos⁡2α/9)of the system crossing timeR/c, whereMpandMmare, respectively, the mass of the planet and the mass of the moon,ris their orbital separation,Ris the distance between the host pulsar and planet-moon barycenter,Iis the inclination of the orbital plane of the planet, andcis the speed of light.