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

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.

💡 Research Summary

This paper presents a systematic semi‑analytic investigation of how the geometry of the accretion flow and magnetic field around the supermassive black hole M87* influences the observables measured by the Event Horizon Telescope (EHT). The authors adopt a stationary, axisymmetric, radiatively inefficient accretion flow (RIAF) model in Kerr spacetime and explore a wide parameter space that includes black‑hole spin (a* ranging from –0.94 to +0.94), disk geometric thickness (H = 0.1, 0.3, 0.5), flow dynamics (a mixture of Keplerian rotation and radial free‑fall parameterized by κ_K and κ_f), and seven distinct magnetic‑field configurations (toroidal, poloidal/vertical, split‑monopole, dipole, quadrupole, parabolic, and a combined model). Electron density and temperature follow power‑law profiles (n_e ∝ r^–δ with δ = 1.5, T_e ∝ r^–γ with γ = 0.84).

General‑relativistic ray tracing with the open‑source code ipole is used to solve the full polarized radiative transfer at 230 GHz, producing synthetic intensity (I) and Stokes (Q, U, V) maps on a 200 × 200 pixel grid. The images are convolved with a 15 µas Gaussian to mimic the effective resolution of the 2017 EHT array. From each model the authors extract four key observables: (1) the apparent ring diameter, (2) the brightness asymmetry between the east and west sides of the ring, (3) the net fractional linear polarization |m_net|, and (4) the orientation of the electric‑vector position angle (EVPA) across the image.

The main findings can be summarised as follows:

1. Disk thickness has a minor effect. Varying H from 0.1 to 0.5 changes the ring diameter and asymmetry by less than 5 %, indicating that the EHT observables are largely insensitive to the vertical scale height of the RIAF.

2. Magnetic‑field geometry is decisive. Toroidal‑dominated models produce low net polarization (|m_net| ≈ 2–3 %) with electric‑vector patterns that wrap around the ring, whereas poloidal (vertical) fields yield higher polarization (|m_net| ≈ 3–5 %) and a more radial EVPA alignment. The latter reproduces the azimuthal EVPA pattern reported by the EHT collaboration, making a poloidal‑dominated field the preferred configuration for M87*. Intermediate configurations (dipole, quadrupole, parabolic) give intermediate polarization levels and more complex EVPA structures, which are not uniquely constrained by the current data.

3. Flow dynamics matter. Pure free‑fall (κ_f = 1, κ_K = 0) strongly enhances the east‑west brightness asymmetry, while pure Keplerian rotation (κ_f = 0, κ_K = 1) yields a nearly symmetric ring. A mixed model (κ_f = κ_K = 0.5), representing a sub‑Keplerian azimuthal velocity with moderate radial inflow, matches the observed asymmetry (~10 %). Thus, the data favour a flow that includes a partially radial inflow component.

4. Spin constraints are weak. Changing the spin sign or magnitude modifies the ring size and polarization by less than 10 %, and the EVPA rotation direction shows a slight preference for positive spin values (a* ≈ 0.5–0.9), but the current EHT data cannot robustly determine the spin.

5. Comparison with GRMHD simulations. The authors compare their semi‑analytic results with a library of time‑averaged GRMHD images (both MAD and SANE magnetisation states). The semi‑analytic models reproduce the polarization fraction and EVPA pattern of the SANE simulations more closely than those of the MAD runs, supporting the view that M87* is in a relatively low‑magnetisation (SANE‑like) state rather than a highly magnetised MAD state.

The paper’s significance lies in demonstrating that, within the uncertainties of current EHT observations, the observable signatures are far more sensitive to magnetic‑field geometry and the presence of radial inflow than to the vertical thickness of the disk or to the black‑hole spin. By providing a computationally inexpensive yet physically transparent framework, the semi‑analytic RIAF approach complements full GRMHD simulations and enables rapid exploration of the high‑dimensional parameter space.

However, the study has notable limitations. The jet contribution is omitted, despite evidence that the jet base may affect the 230 GHz emission and act as a Faraday screen. The electron distribution is prescribed by simple power‑law scalings, ignoring non‑thermal tails, electron heating mechanisms, and anisotropic pressure that are known to influence both intensity and polarization. Moreover, the spin remains loosely constrained, suggesting that higher‑frequency (e.g., 345 GHz) or multi‑epoch EHT observations will be required to break degeneracies.

Future work should therefore incorporate a two‑component disk‑plus‑jet model, more realistic electron thermodynamics (e.g., κ‑distributions or sub‑grid heating prescriptions), and multi‑frequency polarized radiative transfer. Machine‑learning‑based inference pipelines could also accelerate the mapping from observed visibilities to physical parameters, allowing simultaneous constraints on spin, magnetic geometry, and inflow strength.

In conclusion, the authors convincingly argue that M87*’s EHT image and polarization are best explained by a poloidal‑dominated magnetic field together with a partially radial inflow, while the disk thickness plays a negligible role and the spin remains only loosely bounded. Their semi‑analytic methodology provides a valuable tool for interpreting current and forthcoming horizon‑scale observations of black‑hole accretion flows.