Tidal effect on the gyroscopic precession around a compact star

Abstract

General relativistic effects around massive astrophysical objects can be captured using a test gyro orbiting the object in a circular geodesic. This paper discusses how the tidal field due to a companion object affects the spin precession frequency and orbital angular velocity of a spinning gyro orbiting around a compact astrophysical object. The precession frequency is studied in a region of space around the central object using a perturbative approach. The central object is either a neutron star or a white dwarf in this study. The test gyro is any planetary or asteroid-like object orbiting a neutron star or a white dwarf. Moreover, the companion object that causes the tidal field can be a neutron star, white dwarf or a stellar black hole. It is seen that the tidal effect significantly affects the spacetime around the central object, which affects the gyro precession frequency and the orbital angular velocity. Slow rotation approximation has been considered for the central object, which creates negligible deformation. The change in the gyro’s precession frequency and the orbital angular velocity due to the tidal field increases with an increase in the companion object’s mass and decreases as the separation between the central star and the companion star increases. The tidal effect also varies with the stiffness of the equation of state of matter describing the host star. The lower the compactness of the host star, the greater is the tidal response; thus the greater is the change in the gyro’s precession and angular velocity of the geodesic.