Maximum Observable Blueshift from Circular Equatorial Kerr Orbiters

TL;DR

This paper investigates the maximum observable blueshift from matter orbiting near a Kerr black hole, revealing how blueshift measurements can inform us about black hole spin and inclination, aiding astrophysical observations.

Contribution

It provides simple relations linking maximum blueshift to black hole spin and inclination, enhancing methods to infer black hole properties from emission line observations.

Findings

Maximum blueshift effectively probes inclination angles.

Higher blueshifts constrain black hole spin and inclination.

Results are relevant for interpreting line broadening in black hole observations.

Abstract

The region of spacetime near the event horizon of a black hole can be viewed as a deep potential well at large gravitational redshift relative to distant observers. However, matter orbiting in this region travels at relativistic speeds and can impart a significant Doppler shift to its electromagnetic emission, sometimes resulting in a net observed blueshift at infinity. Thus, a black hole broadens the line emission from monochromatic sources in its vicinity into a smoothly decaying "red wing"--whose flux vanishes at large redshift--together with a "blue blade" that retains finite flux up to a sharp edge corresponding to the maximum observable blueshift. In this paper, we study the blue blade produced by isotropic monochromatic emitters on circular equatorial orbits around a Kerr black hole, and obtain simple relations describing how the maximum blueshift encodes black hole spin and inclination. We find that small values of the maximum blueshift yield an excellent probe of inclination, while larger values provide strong constraints on spin or inclination in terms of the other. These results bear direct relevance to ongoing and future observations aiming to infer the angular momentum of supermassive black holes from the broadening of their surrounding line emission.