Supermassive black-hole imaging with a self-consistent electron-temperature prescription

TL;DR

This work addresses degeneracies in black-hole imaging caused by uncertain electron-energy distributions by introducing a first-principles, turbulence-informed electron distribution for M87*, derived from PIC simulations. It contrasts a conventional thermal $R-\beta$ model with a fully self-consistent PIC-TURB prescription that yields $\kappa(\sigma,\beta)$ and $\mathcal{T}(\sigma,\beta)$ without free parameters. The authors show that the self-consistent model can reproduce the 86 GHz jet morphology, the 230/345 GHz horizon-scale images, and the broadband SED with comparable or improved fidelity and with less degeneracy. This demonstrates the critical role of microscopic plasma physics, particularly magnetic reconnection heating, in shaping the observable signatures and provides a path toward more robust inference of plasma conditions from BH imagery.

Abstract

The recent 230 GHz observations by the Event Horizon Telescope have resolved the innermost structure of the M87 galaxy, revealing a ring-like feature consistent with thermal synchrotron emission from a magnetized torus surrounding a rotating supermassive black hole. Moreover, Global Millimeter VLBI Array observations at 86 GHz have revealed a larger-scale, edge-brightened jet with clear signatures of non-thermal emission. The theoretical modelling of these observations involves advanced general-relativistic magnetohydrodynamic simulations of magnetized accretion disks around rotating black holes, together with the associated synchrotron emission, which is normally treated with simplified expressions for the electron temperature and assuming a purely thermal distribution. However, an important non-thermal component is expected to be present, making the thermal-emission model not only an approximation, but also a source of degeneracy in the modelling. In view of this, we here present the first application of an ab-initio approach to the electron temperature derived from microscopic simulations of turbulent collisionless plasmas. The novel method, which has no tuneable coefficients and is fully specified by the thermodynamical and magnetic properties of the plasma, provides a better description of the jet morphology and width at 86 GHz, as well as of the broadband spectral emission. These findings highlight the importance of incorporating microscopic plasma physics in black-hole imaging and emphasise the crucial role of magnetic reconnection in electron heating and acceleration processes.

Figures (6)

• Figure 1: Top panels: Time and azimuthally averaged distributions of the power-law index $\kappa$ for accretion simulations onto a rotating BH with dimensionless spin $a_{\star}=0.9375$. The left panel refers to the PIC-CS kappa-model derived from Harris current sheets [Eq. \ref{['eq:kappa_ball']}], while the right panel exhibits the distribution for the PIC-TURB derived from decaying plasma turbulence [Eq. \ref{['eq:kappa2D_2']}]. Bottom panels: the same as on the top, but shown on a smaller scale near the event horizon. Despite the similarity in the functional dependence, the two models for the power-law index $\kappa$ can lead to differences, especially in the jet width (see also Fig. \ref{['fig:R-B_vs_PIC']}). The black solid lines represent the separation between the jet spine and jet sheath and are defined by $\log_{10}\sigma=\{-1,\, 0,\, 0.5\}$; the dashed white line refers instead to the Bernoulli parameter ${\rm Be}=1.02$ and separates the bound and unbound plasma, thus marking external surface of the jet.
• Figure 2: Comparison of the distributions in the electron temperature ratio, ${\cal T} := T_{e}/T_{p}$, using either the $R\!-\!\beta$ model with the PIC-CS model for the non-thermal component, or the fully self-consistent self-consistent prescription from turbulence simulations using the PIC-TURB model. More specifically, the left and middle columns report ${\cal T}$ with parameters $R_{\rm low}=1$ and $R_{\rm high}=\{10,\, 160\}$, while the right column refers to the self-consistent model. Note the considerable differences, especially in the core of the jet and near the torus surface. While the top row show the large-scale distributions, the bottom one offers a magnification near the event horizon. Also in this case, the black solid lines mark the separation between the jet spine and jet sheath, while the white dashed line the separation between bound and unbound plasma.
• Figure 3: Best-fit models for the jet morphology of M87* as obtained from the most recent GMVA observations at at 86 GHz Kim2018a (bottom-right panel). The left and middle columns refer to data that is azimuthally and time averaged over the interval $13,\!000 - 15,\!000,M$, for a BH with dimensionless spin $a_{\star}= 0.9375$. The top-left panel refers to the best-fit phenomenological model for the electron temperature, $\Theta_e = \Theta_e(R_{\rm low}, R_{\rm high}, \beta)$, corresponding to $R_{\rm low} = 1$ and $R_{\rm high} = 160$, and a $\kappa$-distribution from a current sheet with parameters $\epsilon = 0.5$, $\sigma_{\text{cut}} = 3.0$, $r_{\rm inj} = 10\,M$. The bottom-left panel shows instead the best-fit model using the self-consistent electron temperature, $\Theta_e = \Theta_e(\sigma,\beta)$, and a $\kappa$-distribution derived from a turbulent scenario. In this case, with $\epsilon = 1.0$, $\sigma_{\text{cut}} = 3, r_{\rm inj} = 10\,M$. The middle column displays the GRRT synthetic image convolved with a GMVA-like beam of $116\,\mu{\rm as} \times 307\,\mu{\rm as}$, to mimic the observational resolution.
• Figure 4: Jet-diameter comparison between observations and theoretical models. We report with solid lines the jet width measures from the convolved GRRT images covering a period of $2,\!000 M$, red line for the self-consistent $\Theta_e= \Theta_e(\sigma,\beta)$, and blue line for the phenomenological $\Theta_e = \Theta_e(R_{\rm low}, R_{\rm high}, \beta)$. We also show as shaded regions the variations within the standard deviation and with black circles the jet width as computed from the GMVA observation and the corresponding uncertainties. The uncertainties are obtained by assuming an uncertainty of 1/4 of the beam size at the $r = 0$ and a linear increase until 1/2 of the beam size is reached at $r = 2 \, \mu{\rm as}$.
• Figure 5: Broadband spectrum of the flux-density of M87*. Solid lines show the average spectra from simulations with different spins and numerical parameters, as computed over the time window between $13,\!000\, M$ and $15,\!000\,M$ for both non-thermal models and for an inclination $i = 160 ^{\circ}$. Note that the gray vertical lines refer to the most representative frequencies. For each observational data, the uncertainties indicate the variability during the observations. The inset shows a magnification of the low-frequency region.