Photon Emission from Circular Equatorial Kerr Orbiters

Abstract

We consider monochromatic and isotropic photon emission from circular equatorial Kerr orbiters. We derive analytic expressions for the photon escape probability and the redshift-dependent total flux collected on the celestial sphere as a function of emission radius and black hole parameters. These calculations crucially involve the critical curve delineating the region of photon escape from that of photon capture in each emitter's sky. This curve generalizes to finite orbital radius the usual Kerr critical curve and displays interesting features in the limit of high spin, which we investigate by developing a perturbative expansion about extremality. Although the innermost stable circular orbit appears to approach the event horizon for very rapidly spinning black holes, we find in this regime that the photon escape probability tends to 5/12 + 1/( √ 5π) arctan 5/3 ≈ 54.65%. We also obtain a simple formula for the flux distribution received on the celestial sphere, which is nonzero. This confirms that the near-horizon geometry of a high-spin black hole is in principle observable. These results require us to introduce a novel type of near-horizon double-scaling limit. We explain the dip observed in the total flux at infinity as an imprint of the black hole: the black hole "bite".

Polarized Image of Equatorial Emission in the Kerr Geometry

“…which holds in the limit where B eq → 0, even though (42) will not be well-defined. One can also show that this relation holds for nonzero β v , indicating that the primary effect of frame-dragging on polarization does not depend on the orbital speed of the accreting material.…”

“…Like the approximation (42) for the direct image, (45) holds for any magnetic field configuration and boost parameter. The correction sin −1 (a/b c ) is analogous to the "gravitational Faraday rotation" in the indirect image, thus extending the work of [46][47][48][49][50][51] to the strongly lensed regime.…”

“…The images of axisymmetric rings of radiating fluid are described by analyzing the local frame of an emitting point source in the Kerr geometry. The semi-analytic description of an unpolarized image from such an emitter has a long history going back to the 1970s with Cunningham and Bardeen, [38,39] and has recently been discussed in specific contexts such as the near-horizon-extreme-Kerr emission [40][41][42]. The polarized image has also been treated analytically for the high-spin case in [43].…”

Complete classification of photon escape in the Kerr black hole spacetime

“…For an emitter in a circular orbit of the extremal Kerr black hole, it was found that about 54.64% of photons escape to infinity in the limit where the orbital radius arbitrarily approaches the innermost stable circular orbit radius [7], which coincides with the horizon radius. Furthermore, the analytical value of the probability is recently found by use of the technique of the near-horizon geometry of the extremal Kerr [8]. In this case, the relativistic boost due to the source's proper motion causes such an increase in the escape probability and also the Doppler blueshift exceeding the gravitational redshift [7,9].…”

Photon emission from inside the innermost stable circular orbit

“…Recently, the escape probability of photons emitted isotropically from an emitter orbiting a circular geodesic near a Kerr black hole was shown to be more than 50% for an arbitrary black hole spin parameter and an arbitrary orbital radius [3,4]. Furthermore, depending on the direction of the emission, the Doppler shift cancels the gravitational redshift, and as a result, the signals can reach a distant observer in observable bands [3,5,6].…”