Observational Properties of Near-Maximally Spinning Supermassive Black Holes

Abstract

Black holes described by the Kerr metric can have a theoretical maximum dimensionless spin parameter of $a_\bullet = 1$, but several effects may limit the maximum spin parameter in astrophysical systems. We perform general relativistic magnetohydrodynamics simulations of accretion flows around black holes with $a_\bullet = 0.9375$ and $a_\bullet = 0.998$, each corresponding to a proposed astrophysical limit in the literature. We then perform full polarized general relativistic ray-tracing to produce astrophysical movies of these simulations, as can be spatially resolved by the Event Horizon Telescope (EHT) and its extensions. Although many properties of black holes and accretion flows evolve rapidly as $a_\bullet \to 1$, we find that our $a_\bullet=0.9375$ and $a_\bullet=0.998$ simulations are remarkably similar, both in terms of their GRMHD fluid properties and their full-Stokes, time-variable images. This suggests that previous work using simulations with $a_\bullet \approx 0.9375$ may be representative of models with $a_\bullet \gtrsim 0.9375$ in most practical cases. Our calculations suggest that shape and size constraints on the photon ring, enabled by extensions of the EHT into space by missions such as the Black Hole Explorer (BHEX) may be the only practical way to distinguish between models with different spin parameters as $a\to 1$.

Figures (6)

• Figure 1: Above are vertical and midplane slices of the GRMHD snapshot from both the $a_\bullet=0.9375$ (left) run and the $a_\bullet=0.998$ (right) run. The color denotes the log density and the contour lines show the poloidal magnetic field.
• Figure 2: Above plots demonstrate the accretion rate, magnetization, jet power efficiency, and 230GHz flux as a function of time for both $a_\bullet=0.9375$ (blue) and $a_\bullet=0.998$ (red). The highlighted blue and red regions show the mean values $\pm 1\sigma$ (where $\sigma$ denotes a standard deviation) for $a_\bullet=0.9375$ and $0.998$ respectively. The dashed lines seen in the magnetization and jet power efficiency graphs demonstrate the expected mean values based on Narayan_etal_22 and Tchekhovskoy_Narayan_McKinney_10, where magnetization values are $\sim$ 54.735 and $\sim$ 51.612 for $a_\bullet=0.9375$ and $a_\bullet=0.998$ respectively. The reported 230GHz flux is for our Sgr A* model.
• Figure 3: The spin-up parameter (top) and jet power efficiency (bottom) as a function of spin. Green indicates previously calculated values and the predicted curve from Narayan_etal_22. The blue and red dots indicate our observed average jet power efficiency. The error bars indicate $\pm5\sigma_s$ based on our calculation of $\sigma_s$, which is shown in equation \ref{['eqn:sUncertainty']}, and $\pm5\sigma_\eta$ which is calculated similarly. (Note that $\sigma_s$ and $\sigma_\eta$ are distinct from the standard deviation shown in figure \ref{['fig:accretionRate']}.)
• Figure 4: Above are the time averaged images for the $a_\bullet=0.9375$ (left) and $a_\bullet=0.998$ (right) Sgr A$^*$ runs for a resolution of 0.625$\mu$as and inclination of $150^\circ$. The average is taken over the course of $15,000-30,000t_g$ and involves averaging all stokes parameters. The colorplot shows the average Stokes I in cgs units. The short lines show the average linear polarization direction and the color reflects the linear polarization fraction with darker green indicating a higher fraction. The navy dashed line indicates the critical curve and the white dashed line indicates the approximate lensed horizon Chael_Johnson_Lupsasca_21.
• Figure 5: Above are violin plots of observable parameters for the Sgr A$^*$ inclination $150^\circ$ and M87$^*$ inclination $163^\circ$ models compared to observational constraints. Note that the confidence interval for the Sgr A$^*$ models' $\angle \beta_2$ is the derotated range.