Slow-Light Effect in the Jet-Launching Region of M87

TL;DR

This work demonstrates that slow-light general relativistic radiative transfer is crucial for modeling the jet-launching region of M87, where relativistic plasma acceleration affects observed morphology. By applying slow-light GRRT to four MAD GRMHD models with anisotropic nonthermal electrons, the authors show that slow-light images favor a double-edged, limb-brightened cone structure, in contrast to the loop-like features typical of fast-light images. They establish a loop–edge transition that tracks the plasma acceleration, finding that higher BH spin leads to earlier, sharper edge-dominated emission, thereby offering a potential diagnostic for BH spin. Multi-wavelength predictions and time-averaged behaviors indicate that future high-resolution VLBI (e.g., ngEHT, EHT, BHEX) can exploit these signatures to constrain spin and test the Blandford–Znajek jet-launch mechanism, with anisotropic electron distributions playing a key role in producing the observed limb-brightening.

Abstract

We explore the impact of "slow-light" radiative transfer - i.e., general relativistic radiative transfer (GRRT) calculations in which the simulated fluid evolves while light rays are propagating through it - in general relativistic magnetohydrodynamic (GRMHD) models of the M87 jet. Because the plasma in the jet-launching region is accelerated to relativistic velocities, and because the jet in M87 is nearly aligned with the line of sight (offset by ~17 degrees), a slow-light treatment is important for accurately modeling the observable structure. While fast-light images exhibit prominent helical or loop-shaped features in the jet - which we associate with narrow bundles of magnetic field lines - these features become stretched and smoothed-out in slow-light images. Our slow-light images instead exhibit a double-edged, cone-like morphology that is more consistent with observations of M87 than corresponding fast-light images. We find that the radius at which the plasma transitions from sub-relativistic to relativistic velocities is imprinted on slow-light images via a transition from loop-dominated at small distances from the black hole to edge-dominated at a larger distance, with the loop-edge transition occurring at larger distances for lower black hole spins. The jet image dynamics also vary with black hole spin, with low-spin models producing jets that exhibit substantial "wobbling", while high-spin models produce jets that are straighter and more stable in time. The spin-dependent jet morphology and variability are revealed by slow-light imaging because slow-light effects become more enhanced as the plasma velocity becomes more relativistic, and because the plasma acceleration is itself a strong function of the spin.

Figures (13)

• Figure 1: Left: an image at 86 GHz at $t = t_{\rm scn}$ ($= 22{,}250~t_{\rm g}$) obtained from the slow-light calculation for the high-spin case ($a_* = 0.9$). Right: three images from the fast-light calculations based on the GRMHD snapshots at $t = t_{\rm scn} - 1300~t_{\rm g}$, $t_{\rm scn} - 970~t_{\rm g}$, and $t_{\rm scn} - 640~t_{\rm g}$ (left to right). These three epochs correspond to the times when the light rays reaching $y = 0$, $-100~r_{\rm g}$, and $-200~r_{\rm g}$ in the slow-light image pass through the jet. The corresponding regions are extracted from the fast-light images and combined in a patchwork form (second panel from left) aligned with the slow-light image.
• Figure 2: A schematic illustration showing the correspondence between a slow-light image and a set of fast-light images, as shown in Figure \ref{['fig:slow_fast']}. The blue, orange, and green arrows represent the patchwork shown in Figure \ref{['fig:slow_fast']}. The blue ray passes through the jet or around the BH at $t = t_0 \sim t_{\rm scn} - 1300~t_{\rm g}$ and reaches the origin of the observer's screen at $r_{\rm scn} = 1300~r_{\rm g}$ and $t = t_{\rm scn}$. The orange (green) ray, which reaches $y = -100~r_{\rm g}$ ($-200~r_{\rm g}$) on the screen, passes near the jet axis at approximately $t \sim t_0 + \Delta t_1$ ($t_0 + \Delta t_2$). Here, the time delay $\Delta t_1$ ($\Delta t_2$) is geometrically obtained by tangentially deprojecting the corresponding distance $100~r_{\rm g}$ ($200~r_{\rm g}$) on the screen onto the light ray for an inclination of $i = 163^\circ$. This indicates that the light rays in the downstream region of the jet originate from later epochs.
• Figure 3: Profiles of the modified plasma bulk velocity, $\gamma\beta$, along the $z$-axis for the four spin models. Here, $\beta = v/c$ is the plasma bulk velocity normalized by the speed of light, and $\gamma = 1/\sqrt{1 - \beta^2}$ is the corresponding Lorentz factor. Note that $\gamma\beta = \sqrt{\gamma^2 - 1}$ ranges from 0 to infinity. The velocity is calculated within the jet region defined by $1 < \sigma < 300/\sqrt{r}$, using the GRMHD data averaged over $5000~t_{\rm g}$. Tick marks on the right side of the panel indicate the corresponding values of $\beta$.
• Figure 4: Eight snapshot images at 86 GHz from the slow-light (upper row) and fast-light (lower row) calculations for the GRMHD model with $a_* = 0.9$. The slow-light images are taken from $t_{\rm scn} = 22,000~t_{\rm g}$ to $26{,}200~t_{\rm g}$ with a cadence of $600~t_{\rm g}$. The fast-light images are based on the GRMHD snapshot data at $t = t_{\rm scn} - 1300~t_{\rm g}$ (see also Figure \ref{['fig:slow_fast']}). Movies are available in the online article and on https://youtu.be/VIzLOhfJFaI.
• Figure 5: Snapshot images at 86 GHz by slow-light (left) and fast-light (right) calculations for the $a_* = 0.3$ model. The slow light image is taken at $t = t_{\rm scn} = 24,650~t_{\rm g}$. The fast-light image is based on the GRMHD snapshot at $t = t_{\rm scn}-1015~t_{\rm g}$.