Semi-analytic studies of accretion disk and magnetic field geometry in M87*

TL;DR

This study uses a semi-analytic radiatively inefficient accretion flow (RIAF) model in Kerr spacetime, combined with general relativistic ray tracing and polarized radiative transfer, to explore how horizon-scale magnetic field geometry, black hole spin, disk dynamics, and geometric thickness affect M87*'s 230 GHz emission and EHT observables. By comparing seven magnetic-field geometries and various flow velocities against GRMHD simulations, the authors find that ring diameter is only weakly sensitive to thickness, while magnetic topology and inflow dynamics leave distinctive imprints on brightness asymmetry and polarization patterns; in particular, poloidal-dominated fields with partial radial inflow best match the data, with spin favored to be moderately or highly positive. The work highlights the utility and limits of stationary, semi-analytic models as complements to GRMHD, clarifying how polarization metrics such as β₂ andEVPA respond to field geometry and Faraday effects, and it suggests that a realistic M87* scenario likely requires a mixture of poloidal and toroidal fields and non-Kerr explorations. This framework provides a tractable path to interpret horizon-scale polarization and guides future refinements to include mixed-field geometries and nonideal plasma physics.

Abstract

Context: Magnetic fields play a pivotal role in dynamics of black hole accretion flows and formation of relativistic jets. Observations by the Event Horizon Telescope (EHT) provided unprecedented insights into accretion structures near black holes. Interpreting these observations requires a theoretical framework linking polarized emission to underlying system properties and magnetic field geometries. Aims: We investigate how system properties, particularly magnetic field geometry in the event horizon scale region, influence the structure of the observable synchrotron emission in M87*. Specifically, we aim to quantify the sensitivity of observables used by the EHT to black hole spin, plasma dynamics, accretion disk thickness, and magnetic field geometry. Methods: We adopt a semi-analytic radiatively inefficient accretion flow model in Kerr spacetime. We vary magnetic field geometry, black hole spin, accretion disk dynamics, and geometric thickness of the disk. We perform general relativistic ray tracing with a full polarized radiative transfer to obtain synthetic images of M87*. We extract EHT observables, such as disk diameter, asymmetry, and polarimetric metrics from synthetic models. We also consider a number of general relativistic magnetohydrodynamics simulations and compare them with the semi-analytical models. Results: We see limited impact of the disk thickness on observables. On the other hand, toroidal field dominated and poloidal field dominated magnetic configurations can be distinguished reliably. The flow dynamics, in particular presence of radial inflow, also significantly impacts the EHT observables. Conclusions: The M87* system is most consistent with a poloidal magnetic field dominated flow with partially radial inflow. While the spin remain elusive, moderate or large positive values are preferred.

Figures (8)

• Figure 1: Panels a-g: Schematic representation of the magnetic field configurations discussed in Sect. \ref{['sec:model']}. Last panel: Example number density map for an RIAF model with a default disk thickness parameter $H=0.5$.
• Figure 2: Left: Example of an RIAF model with $a_* > 0$ ray-traced at an inclination of $163^\circ$, blurred with a $15\, \mu\rm{as}$ circular Gaussian, indicated with a circle in the bottom right corner, before the 108$^\circ$ counterclockwise rotation to match it with the observed appearance of the M 87*. The ticks indicate the direction of polarization, vector $\vec{a}_*$ shows the observer's screen projection of the BH spin vector pointing away from the observer (into the screen). Right: Image of M 87* reconstructed from the EHT 2017 observations 2019ApJ...875L...4E. The axis shows the observed position angle of the jet, with the forward jet appearing toward the west at about 288$^\circ$Walker2018. The arrow shows the expected direction of the BH spin projection, pointing away from the observer. The $15\, \mu\rm{as}$ effective resolution of the image is indicated with a circle in the bottom right corner. Polarization ticks are shown in the region where $\mathcal{I}>0.1\mathcal{I}_{\rm max}$ and $\vert\mathcal{P}\rvert=\sqrt{\mathcal{Q}^2 + \mathcal{U}^2} >0.2\lvert\mathcal{P}\rvert_{\rm max}$, as shown in Fig. 1 of 2021ApJ...910L..13E.
• Figure 3: Ray-traced images of the fiducial RIAF model (Table \ref{['table:param']}) with various magnetic field geometries and different BH spin $a_*$ values, shown in units of brightness temperature. The conventions for the inclination angle $\theta_i$ and the position angle $\theta_{\rm PA}$ are described in Sect. \ref{['subsec:emission']}. The total flux density $\mathcal{I}_{\rm tot}$ and the net fractional polarization $|m_{\rm net}|$ are indicated. The convention for showing EVPA ticks is the same as in Fig. \ref{['fig:ratio']}.
• Figure 4: Time-averaged ray traced GRMHD images from the EHT image library 2019ApJ...875L...5E2021ApJ...910L..13EWong2022, representing different BH spin values $a_*$ and MAD or SANE states of magnetization. The conventions for the inclination angle $\theta_i$ and the position angle $\theta_{\rm PA}$ are described in Sect. \ref{['subsec:emission']}. The convention for showing EVPA ticks is the same as in Fig. \ref{['fig:ratio']}.
• Figure 5: Left: Diameter of the ring $\mathcal{D}$ and normalized diameter $\alpha$ for the fiducial RIAF model with various magnetic field configurations and for GRMHD images as a function of BH spin $a_*$. Right: Same for the brightness ratio parameter $\mathcal{I}_r$. The gray bands indicate constraints derived from the EHT observations of M 87*.