GRMHD modelling of accretion flow around Sagittarius A$^*$ constrained by EHT measurements

TL;DR

This work develops a steady-state GRMHD framework to model low-angular-momentum accretion onto a Kerr black hole, calibrated against Event Horizon Telescope measurements of magnetic field strengths near Sagittarius A*. By solving a family of global GRMHD solutions parameterized by energy, angular momentum, magnetic flux, and isorotation, the authors demonstrate that magnetic-field strengths inferred by the EHT at 7.3 r_g and 4 r_g can be reproduced to within about 10% for a near-extremal spin (a_k ≈ 0.94) and Ṁ ≈ 10^−8 M⊙ yr^−1. The analysis identifies regions in the L–Φ parameter space that simultaneously satisfy the radial magnetic-field constraints, providing a self-consistent magnetized flow description consistent with the MAD paradigm. The results have implications for interpreting near-horizon accretion physics and the role of magnetic fields in shaping emission from Sgr A*, while acknowledging simplifications such as the 1.5D geometry and ideal MHD assumptions that motivate future, more comprehensive studies.

Abstract

We study low angular momentum, advective accretion flows around a Kerr black hole within the framework of general relativistic magnetohydrodynamics (GRMHD) in the steady state. By solving the full set of GRMHD equations, we aim to provide a comprehensive understanding of the behavior of magnetized plasma in the strong gravity regime near a rotating black hole. The accretion solutions are obtained for a set of input parameters, namely energy (${\cal E}$), angular momentum (${\cal L}$), magnetic flux ($Φ$), and isorotation parameter ($I$). By systematically varying these parameters, we generate a family of global GRMHD accretion solutions that characterize the physical environment around the black hole. Using this approach, we investigate whether the inferred magnetic field strengths reported by the Event Horizon Telescope (EHT) for Sagittarius A$^*$ at various radii can be reproduced. We find that, for a broad range of parameter values, our model successfully recovers the EHT inferred magnetic field strengths with an accuracy of approximately $10\%$, offering a self-consistent framework for interpreting near-horizon accretion physics.

Figures (2)

• Figure 1: Example of a global GRMHD accretion solution around a Kerr black hole that accounts the EHT inferred magnetic fields at $7.3~r_{\rm g}$ and $4~r_{\rm g}$. In panel (a), variation of Mach number ($M$) is depicted with radial coordinate ($r$), where color denotes the flow velocity ($v$). Filled circle in black denotes the inner critical point ($r_{\rm in}$). Panel (b) shows the radial variation of density ($\rho$), whereas temperature ($T$) is shown using color. Panel (c) illustrates the magnetic field ($B$) variation with $r$, while plasma-$\beta$ is plotted using color. Thick grey and red horizontal lines denote the magnetic field strengths of $67 \pm 6.7$ G and $26 \pm 2.6$ G, respectively that intersect GRMHD accretion solution at $4~r_{\rm g}$ and $7.3~r_{\rm g}$. See the text for details.
• Figure 2: Effective domain of the parameter space in $\mathcal{L}-\Phi$ plane corresponding to GRMHD accretion solutions that reproduce EHT inferred magnetic field strength. The region shaded with cyan admits accretion solutions yielding magnetic field strength of $67 \pm 6.7$ G at $7.3 r_g$, while magenta shaded region corresponds to solutions matching $26 \pm 2.6$ G at $4r_{\rm g}$. Overlapping region (appeared as violet) provides accretion solutions that simultaneously satisfy magnetic fields constraints at both radii. See the text for details.