A rapid black hole spin or emission from the plunging region?

TL;DR

This work demonstrates a spin-plunging region degeneracy in black hole spin measurements from X-ray continuum spectra: emission from within the ISCO can reproduce the spectrum of a high-spin disk around a Schwarzschild hole with modest ISCO stress. Using the fullkerr model, calibrated by GRMHD insights, the authors fit three soft-state X-ray binaries (M33 X-7, MAXI J1820+070, MAXI J0637-430) and show that spectra previously attributed to $a_ullet \approx 0.8$ can be equally well described by low spins ($a_ullet \sim 0.2$) with $ abla_{\,\cal J}$ in the range $10^{-1.5}$ to $10^{-1.0}$. The degeneracy in the $(a_ullet,\nabla_{\,\cal J})$ plane is sharp, and high-quality data from the MAXI sources disfavors the high-spin, low-stress branch, suggesting many EM spin inferences may be biased high if intra-ISCO emission is neglected. The findings underscore the need for simulations with full radiation physics and for multi-faceted observational approaches (including polarization and high-energy timing) to break the degeneracy and reliably constrain black hole spins.

Abstract

Emission from within the plunging region of black hole accretion flows has recently been detected in two X-ray binary systems. There is, furthermore, a possible discrepancy between the inferred spins of gravitational wave and electromagnetically detected black holes. Motivated by these two results we demonstrate, using theoretical calculations, numerical simulations and observational data, that the inclusion of emission from within the innermost stable circular orbit (ISCO) results in a black hole with a low spin producing a thermal continuum X-ray spectrum that mimics that produced by a much more rapidly rotating black hole surrounded by a disk with no emission from within the ISCO. We demonstrate this explicitly using the observed X-ray spectrum of a canonical soft-state high mass X-ray binary system M33 X-7. A vanishing ISCO temperature model requires a high spin $a_\bullet = 0.84\pm0.05$, as has been found previously in the literature. However, a disk around a Schwarzschild black hole can equally well (in fact slightly better) describe the data, provided that photons emitted from within the plunging region are included, and the ISCO stress is in line with that seen in numerical simulations of the accretion process. We then present an analysis of two further soft-state X-ray binaries (MAXI J1820+070 and MAXI J0637$-$430) which require the presence of intra-ISCO emission at high statistical significance. These two sources sit on the low-spin moderate-stress part of the degeneracy exhibited by M33 X-7, suggesting that when high quality data are available the high-spin low-stress region of parameter space is ruled out. We discuss how future advances in numerical simulations and data modelling will be essential to determining the spin of X-ray binary black holes which may well be systematically lower than current continuum fitting methods suggest.

Figures (12)

• Figure 1: The physics of angular momentum transport within the ISCO, as seen in GRMHD simulations of thin disks. The plunging region is denoted by vertical dotted lines. In the lower panel we show the specific angular momentum of fluid elements, density weighted and then averaged over time and angles, as a function of radius. Turbulence transports $\sim 5\%$ of the ISCO angular momentum back to the main body of the disk. This relatively small angular momentum flux, when coupled to the very large shear of the disk in these relativistic regions, produces a large energy flux near the ISCO, leading to a significant amount of thermal emission being produced. In the upper panel we show the "$\alpha$-parameter" one would infer from the magnetic stresses acting on the disk, at each radius. Flux-freezing, a purely magnetohydrodynamic effect, leads to amplified magnetic stresses in this region as field lines are dragged into the plunging region by the rapidly accelerating flow, and an "$\alpha$-parameter" which grows by over an order of magnitude. The drop below zero of $\alpha$ at the smallest radii is a simple consequence of causality at an event horizon, as angular momentum can only be transported inwards. The behavior of accretion disk models within the plunging region which assume constant-$\alpha$ lack physical content. Figure reproduced from Rule25.
• Figure 2: The locally emitted flux profiles of different black hole disks. By a green dotted curve we show a Schwarzschild disk with a (near) vanishing ISCO stress, while by a red dotted curve we show the same flux profile for a more rapidly rotating black hole $a_\bullet = 0.9$. By a black dashed curve we show the flux, generated in the fluid rest frame, from a Schwarzschild black hole disk with ISCO stress set to the value observed in the GRMHD simulation of Rule25. Not all of this flux escapes to the observer, and a significant fraction is lost into the black hole. The blue solid curve shows how much of this local flux does not end up in the black hole, and is therefore potentially observable. The moderate-stress Schwarzschild black hole looks much more similar to a rapidly spinning Kerr black hole disk than its vanishing stress counterpart. It will therefore be more difficult to distinguish these two profiles in the data.
• Figure 3: An example of spin-plunging region degeneracies. By red dashed curves we show three 0.3-10 keV disk spectra for vanishing ISCO stress disks around a black hole with mass $M_\bullet = 10 M_\odot$ and spin $a_\bullet = 0.85$, as observed at three different inclinations (denoted on plot). The solid curves show disks which include emission from within the plunging region, but now for Schwarzschild black holes of the same mass observed at the same inclinations. Clearly low-spin bright-plunging region disks can mimic rapidly rotating black holes with zero emission within the plunging region. The actual emission sourced from within the plunging region is shown by dotted curves, and makes up a small fraction of the bolometric luminosity of the disk.
• Figure 4: Left: The locally liberated flux, as measured in the fluid rest frame, for the Schwarzschild (spin $a=0$) simulations of Dhang25 (blue dashed curve) plotted against disk radius. This is compared to the classical NovikovThorne73 model (red dotted line) which clearly is an extremely poor approximation to the simulation results. The new model of MummeryBalbus2023 is shown by a black curve, which represents a much improved description. The ISCO is shown by the purple vertical dotted line. The right hand panel shows the amount of flux which escapes the black hole (i.e., is not captured) as a function of radius. These simulations were of thin disks, and are deemed "MAD" (i.e., they have strong magnetic fields).
• Figure 5: Left: the flux in the fluid rest frame, as a function of radius, for the six different spin values in Dhang25. They show minimal difference as the spin is varied. This is the exact opposite of what would be the case in a series of vanishing ISCO temperature disks (see e.g., the red and green curves in Figure \ref{['fig:fluxes']}). Right: the escaping fluxes from these disk systems as a function of radius. The different dynamical properties of plunging and circularly-orbiting material leads to some differences at radii $r \lesssim 3 r_g$. Photons emitted here are, however, extremely strongly gravitationally red-shifted (owing to the presence of a horizon $\sim 1r_g$ away), and will contribute minimally to the observed X-ray flux. The models of MummeryBalbus2023 are shown by solid curves, and reproduce all of the simulation data (dashed curves) well.