Black-hole spin measurement ($a_{\ast }=cJ/(G{M}^2)$)

An inference of black-hole angular momentum, usually quoted through $a_{\ast }$. Accretion-based techniques use the dependence of the stable inner orbit and relativistic radiation transfer on spin in the Kerr black hole model. Disk truncation, inclination, illumination and atmosphere assumptions can imitate a change of spin and must enter the uncertainty model.

An inference from radiation reflected by an irradiated accretion disc, including iron-line and continuum features. Doppler effects, gravitational redshift and ray propagation determine its profile. Associating the innermost reflecting radius with the innermost stable circular orbit can constrain spin, conditional on illumination, ionization, abundance, inclination and disk structure.

A fit of a thermal accretion-disk spectrum that infers the inner emitting radius and identifies it with the innermost stable circular orbit. A relativistic thin-disk model requires independently constrained mass, distance and inclination, together with spectral hardening and absorption. Use of a suitable disk-dominated state is an essential physical check, not merely a statistical cut.