Luminosity of accretion disks in compact objects with quadrupole

TL;DR

This paper investigates how the quadrupole moment of a static, axially-symmetric compact object affects accretion disk properties, aiming to distinguish such objects from black holes through observational signatures.

Contribution

It provides detailed calculations of orbital parameters and luminosity profiles of accretion disks around objects described by the $q$-metric, extending understanding beyond Schwarzschild and Kerr black holes.

Findings

Orbital parameters depend on the quadrupole parameter q.

Luminosity spectra differ from those of black holes.

Potential observational signatures to distinguish compact objects.

Abstract

We consider the circular motion of test particles in the gravitational field of a static and axially-symmetric compact object described by the $q$-metric. To this end, we calculate orbital parameters of test particles on accretion disks such as angular velocity ($\Omega$), total energy ($E$), angular momentum ($L$), and radius of the innermost stable circular orbit ($r_{ISCO}$) as functions of the mass ($m$) and quadrupole ($q$) parameters of the source. The radiative flux, differential, and spectral luminosity of the accretion disk, which are quantities that can be experimentally measured, are then explored in detail. The obtained results are compared with the corresponding ones for the Schwarzschild and Kerr black holes in order to establish whether black holes may be distinguished from the $q$-metric via observations of the accretion disk's spectrum.