Photon Orbit Signatures in Spectra of Black Hole Accretion Disks

TL;DR

The paper tackles the problem of detecting photon ring signatures in unresolved spectra from black hole accretion disks, caused by long optical paths that photons traverse near the horizon. It develops a minimal unlensed one-zone, two-angle model to isolate the $n=0$ and $n=1$ sub-images and validates findings with ray-traced RIAF models and GRMHD snapshots. The results show that the $n=1$ image tends to push the synchrotron turnover to higher frequencies and can contribute a typical unresolved-spectrum correction of around $10\%$, growing with viewing inclination and sometimes dominating at high frequencies or producing kinks in the spectrum. This work implies that high-frequency spectroscopic studies (above $300$ GHz) of sources like M87* and Sgr A* can constrain the existence and properties of photon rings even without resolved imaging, with broader implications for other unresolved cores.

Abstract

Light orbiting an accreting black hole may impact the disk or jet multiple times before escaping to the observer, at a variety of angles with respect to the local magnetic field. In this letter, we characterize the imprints of these long path lengths and disparate magnetic field impacts in synchrotron spectra of hot accretion disks, as the strongly lensed ``photon ring'' exhibits a higher synchrotron turnover frequency in each lensed sub-image. We apply tools of varying complexity: first, we develop a minimal, unlensed one-zone model that isolates the first two sub-images of the accretion flow. By varying the magnetic field geometry encountered by each sub-image, we show that distinctive spectral signatures emerge in both total intensity and fractional linear polarization. Second, we examine a semi-analytic radiatively inefficient accretion flow (RIAF) model, in which we find that there is generally a frequency at which the first indirect image outshines the direct image even in total flux density. Lastly, we demonstrate that even general relativistic magnetohydrodynamic (GRMHD) simulation snapshots show this spectral character. We find a typical correction to the unresolved spectrum of order $10\%$ near the turnover frequency that grows with increasing viewing inclination, growing to order unity at higher frequencies. We predict sensitive spectral studies of the cores of Messier 87* and Sagittarius A* at frequencies exceeding $300$ GHz to constrain the existence of the photon ring even without imaging, with prospects for photon ring detection even in other sources with unresolved shadows.

Figures (5)

• Figure 1: Cross-section of the one-zone, two-angle model for the spectroscopy of the $n=0$ and $n=1$ images. Blue lines indicate field lines, while red rays show the optical path. The same uniform plasma occupies both cells, but the two cells make different angles of incidence with the rays, and the reduced on-sky area of the $n=1$ image is represented by shrinking one dimension of the cube by $e^{-\pi}$. In this example for a $5M$ cube emitter, the $n=0$ magnetic field incidence angle is $135^\circ$, while the $n=1$ is $45^\circ$; rays passing through the $n=1$ region still experience radiative transfer through the $n=0$ region. Both regions are assumed to be at rest.
• Figure 2: Spectroscopy of the photon ring as predicted by a one-zone model viewed from two angles, tuned to approximate the size and compact flux of the M87* accretion flow. Top row: thermal electron energy distribution with $\Theta_e = 10$ and $n_e=3\times10^4 {\rm cm}^{-3}$. Bottom row: power-law electron energy distribution with $p=3,\gamma_{\rm min}=100,\gamma_{\rm max}=10000$, and $n_e=5\times10^2 {\rm cm}^{-3}$. Both models have $B=30$ G. Left: an example spectrum from the model chosen to accentuate the effect, for which the $n=1$ image contributes a prominent spectral flattening beyond the turnover frequency. Middle: the range of ratios between the spectral peak of each sub-image as a function of the emission angles in each image. Right: same as the middle, but for the frequency offset between the peaks.
• Figure 3: Survey of power law index $p$ for the direct and indirect image magnetic field incidence angles $\theta_{B,0}=15^\circ$ and $\theta_{B,1}=45^\circ$ as shown in \ref{['fig:onezone_grid']}. Steeper power laws increase the relative contribution of the photon ring, leading to substructure in the spectrum of the polarization fraction.
• Figure 4: Dependence of the photon ring spectral feature on inclination and electron density in a RIAF model of Sgr A*. Left: 230 GHz images of the same model at $30^\circ$ and $70^\circ$ inclination, with a fixed peak number density of $3\times10^8{\rm cm}^{-3}$. Middle: spectral index maps at 230-235 GHz at each inclination. Right: spectra of the decomposed model at each inclination, varying the electron number density. The black star indicates the 230 GHz, 2.4 Jy value at the density used in the left figures.
• Figure 5: Spectral feature in ray-traced GRMHD, corresponding to a MAD $a=0.5$$R_\mathrm{high}=160$ model of M87*. Left: total intensity map. Center: spectral index map at 230 GHz revealing the elevated spectral index in the photon ring. Right: instantaneous spectrum, where the grey vertical band demarcates 230-345 GHz, and a circle marks the maximum of each contribution.