Constraining the quadrupole moment of stellar-mass black-hole candidates with the continuum fitting method

Black holes in General Relativity are known as Kerr black holes and are characterized solely by two parameters, the mass $M$ and the spin $J$. All the higher multipole moments of the gravitational field are functions of these two parameters. For instance, the quadrupole moment is $Q=-J^2/M$, which implies that a measurement of $M$, $J$, and $Q$ for black hole candidates would allow one to test whether these objects are really black holes as described by General Relativity. While future gravitational-wave experiments will be able to test the Kerr nature of these objects with very high accuracy, in this paper we show that it is possible to put constraints on the quadrupole moment of stellar-mass black hole candidates by using presently available X-ray data of the thermal spectrum of their accretion disk.