Line Emission from an Accretion Disk around a Rotating Black Hole: Toward a Measurement of Frame Dragging

TL;DR

This paper investigates spectral line emissions from accretion disks around rotating black holes to identify signatures of frame dragging, proposing a moment-mapping method to distinguish black hole spin states and suggesting observational strategies for detecting frame dragging effects.

Contribution

It introduces a moment-mapping scheme for line profiles to differentiate between Schwarzschild and Kerr black holes, and assesses observational signatures of frame dragging in accretion disk emissions.

Findings

Differences in line profiles are significant if the disk extends below 6GM/c^2 in Kerr black holes.

Moment analysis can indicate the presence of material close to the black hole's event horizon.

Line profile and hot spot light curves can potentially measure black hole spin and frame dragging effects.

Abstract

Line emission from an accretion disk and a corotating hot spot about a rotating black hole are considered for possible signatures of the frame-dragging effect. We explicitly compare integrated line profiles from a geometrically thin disk about a Schwarzschild and an extreme Kerr black hole, and show that the line profile differences are small if the inner radius of the disk is near or above the Schwarzschild stable-orbit limit of radius 6GM/c^2. However, if the inner disk radius extends below this limit, as is possible in the extreme Kerr spacetime, then differences can become significant, especially if the disk emissivity is stronger near the inner regions. We demonstrate that the first three moments of a line profile define a three-dimensional space in which the presence of material at small radii becomes quantitatively evident in broad classes of disk models. In the context of the simple, thin disk paradigm, this moment-mapping scheme suggests formally that the iron line detected by the Advanced Satellite for Cosmology and Astrophysics mission from MCG-6-30-15 (Tanaka et al. 1995) is 3 times more likely to originate from a disk about a rotating black hole than from a Schwarzschild system. A statistically significant detection of black hole rotation in this way may be achieved after only modest improvements in the quality of data. We also consider light curves and frequency shifts in line emission as a function of time for corotating hot spots in extreme Kerr and Schwarzschild geometries. Both the frequency-shift profile and the light curve from a hot spot are valuable measures of orbital parameters and might possibly be used to detect frame dragging even at radii approaching 6GM/c^2 if the inclination angle of the orbital plane is large.