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arxiv: 2605.15502 · v1 · pith:RXOUPILJnew · submitted 2026-05-15 · 🌌 astro-ph.HE

Impacts of radiative cooling on the images of a black hole shadow and extended jets in two-temperature GRMHD simulations

Mingyuan Zhang , Yosuke Mizuno , Indu K. Dihingia , Christian M. Fromm , Ziri Younsi , Hai Yang , Alejandro Cruz-Osorio This is my paper

Pith reviewed 2026-05-19 15:30 UTC · model grok-4.3

classification 🌌 astro-ph.HE
keywords black hole shadowradiative coolingGRMHD simulationsM87*electron temperatureEvent Horizon Telescopejets
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The pith

Radiative cooling in GRMHD simulations of M87* makes the inner disk dimmer and the jets more extended and brighter.

A machine-rendered reading of the paper's core claim, the machinery that carries it, and where it could break.

This paper examines how including radiative cooling affects two-temperature GRMHD simulations of accreting black holes like M87*. Without cooling, electron temperatures stay higher in the dense inner regions near the equator. Adding cooling lowers those temperatures sharply, dimming the disk emission at 230 GHz while making the jets brighter and reach farther out. The total flux drops, and high-frequency parts of the spectrum weaken, though variability still comes mostly from the midplane and lessens at higher accretion rates.

Core claim

In two-temperature radiative GRMHD simulations of M87* accretion flows across mass accretion rates from 1 to 10 times 10^-6 Eddington, radiative cooling decreases electron temperature in the inner disk (r less than or equal to 10 r_g) and slightly in the jet sheath. This produces dimmer disks, more extended and brighter jets, and lower total flux in 230 GHz GRRT images compared to non-cooling models.

What carries the argument

Two-temperature GRMHD simulations including radiative cooling, combined with different electron heating prescriptions and nonthermal electron distribution functions, post-processed via general relativistic radiative transfer for synchrotron emission at 230 GHz.

If this is right

  • Black hole shadow images show reduced disk brightness but enhanced jet structures.
  • Total observed flux at 230 GHz is lower when cooling is included for the same accretion rate.
  • High-frequency flux in the SED is reduced.
  • Time variability in the images originates from the midplane and decreases with increasing accretion rate.

Where Pith is reading between the lines

These are editorial extensions of the paper, not claims the author makes directly.

  • Future higher-resolution arrays like ngEHT may detect these cooling-induced changes in jet extent and disk dimming.
  • Similar cooling effects could influence models for other low-luminosity active galactic nuclei.
  • Accounting for cooling might require adjustments in inferred accretion rates from observations.

Load-bearing premise

The chosen electron heating prescriptions and nonthermal distributions in the two-temperature GRMHD simulations capture the main processes determining electron temperatures at M87* accretion rates.

What would settle it

A direct comparison of observed 230 GHz images from next-generation Event Horizon Telescope arrays with the simulated jet extension and disk brightness in cooling versus non-cooling models.

Figures

Figures reproduced from arXiv: 2605.15502 by Alejandro Cruz-Osorio, Christian M. Fromm, Hai Yang, Indu K. Dihingia, Mingyuan Zhang, Yosuke Mizuno, Ziri Younsi.

Figure 1
Figure 1. Figure 1: Accretion rates measured at the event horizon (top) and normalized magnetic flux at the horizon (bottom). The curves in different colors correspond to the different electron heating prescriptions, radiative cooling, and time-averaged accretion rates: without cooling of ˙m = 1 × 10−6 (black), the turbulent heating model with cooling of ˙m = 1 × 10−6 (blue), 5 × 10−6 (green), and 1 × 10−5 (red), and reconnec… view at source ↗
Figure 2
Figure 2. Figure 2: Logarithmic density distribution averaged in time and azimuth over the interval t = 12 000 tg to 15 000 tg. From left to right: without cooling (a), turbulent heating with cooling at ˙m = 1×10−6 (b), ˙m = 5×10−6 (c), and ˙m = 1×10−5 (e), and reconnection heating with cooling at ˙m = 5×10−6 (d). The dashed white and solid black curves represent the magnetization σ = 0.1 and 1, respectively. cooling of the e… view at source ↗
Figure 3
Figure 3. Figure 3: Panels (a) − (f) show the logarithm of the dimensionless electron temperature averaged in time and azimuth over the interval t = 12 000 tg to 15 000 tg. Panels (g) − (j) highlight the differences in linear scale by subtracting the dimensionless electron temperature in the corresponding non-cooling case. The solid black curves represent σ = 1. The dashed skyblue thin to thick curves represent Θe = 10, 32, a… view at source ↗
Figure 4
Figure 4. Figure 4: Angular distribution of time- and azimuthally-averaged dimen￾sionless electron temperature at the given radii on a logarithmic scale. From top to bottom: The radius increases from 7 rg to 20 rg. The curves in different colors correspond to the non-cooling or radiative cooling under different normalized mass accretion rates: the turbulent heating model without cooling (black), with cooling of ˙m = 1 × 10−6 … view at source ↗
Figure 5
Figure 5. Figure 5: Time-averaged GRRT decomposed images from MAD simulations in the interval t = 12 000 tg to 15 000 tg, assuming a black hole spin of a = 0.9375, observed at 230 GHz with an inclination angle of 163◦ . From top to bottom: the accretion rates are M˙ BH/M˙ Edd = 1 × 10−6 , 5 × 10−6 , 5 × 10−6 , and 1 × 10−5 , respectively. The electron heating prescriptions are used for turbulent heating and reconnection heati… view at source ↗
Figure 6
Figure 6. Figure 6: Same as [PITH_FULL_IMAGE:figures/full_fig_p009_6.png] view at source ↗
Figure 8
Figure 8. Figure 8: Light curves of flux at 230 GHz with a 163◦ inclination angle and spin a = 0.9375. Curves are plotted using accretion rates M˙ BH/M˙ Edd = 1×10−6 (top), 5×10−6 (middle), and 1×10−5 (bottom). The solid curves represent the cases without cooling, and the dashed curves correspond to those with radiative cooling. All curves are in turbulent heating and adopt the thermal/variable κ eDF. of time variability on t… view at source ↗
Figure 9
Figure 9. Figure 9: Total flux variation in turbulent heating without cooling (dots) and with radiative cooling (squares) at 230 GHz with a 163◦ inclination angle and spin a = 0.9375. The different colors correspond to the different accretion rates: M˙ BH/M˙ Edd = 1 × 10−6 (black), 5 × 10−6 (red), and 1 × 10−5 (blue). The labels on the x-axis denote the emissions that come from every region: the whole region is depicted first… view at source ↗
read the original abstract

The recent 230 GHz observations from the Event Horizon Telescope collaboration have successfully imaged the supermassive black hole shadow of the M87 galaxy. However, the relatively high radiative efficiency observed in the hot accretion flow suggests that radiative cooling is non-negligible and should be considered when calculating the electron temperature. In this study, we compare accretion models without and with radiative cooling across a range of mass accretion rates, $\dot{M}_{\mathrm{BH}} = (1.0 - 10) \times 10^{-6}\,\dot{M}_{\mathrm{Edd}}$, aiming to assess the impact of cooling on the disk structure, electron temperature distribution (eDF), black hole shadow morphology, broadband spectral energy distributions (SEDs), and flux variability. We performed general relativistic radiative transfer (GRRT) calculations on two-temperature, radiative, general relativistic magnetohydrodynamic (GRMHD) simulations, employing different electron heating prescriptions and nonthermal eDFs, analyzing the radiation transfer due to synchrotron emission at 230 GHz with inclination angle of $163^\circ$. These simulations are targeted toward M87$^{*}$. By comparing density profiles, eDFs, GRRT images, SEDs, and time variability between models, we find that the radiative cooling sharply decreases the electron temperature in the dense inner disk around the equatorial plane ($r\lesssim 10\,r_\mathrm{g}$), while slightly reducing jet sheath temperature. Cooling leads to a dimmer disk, more extended and brighter jets, and reduced total flux. For a given accretion rate, cooling reduces the high-frequency flux. Time variability originates primarily from the midplane in both non-cooling and cooling cases and decreases as accretion rates rise. Although currently below the dynamic range of EHT observations, the features identified in this study could be resolved by next-generation arrays such as the ngEHT.

Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, simulated authors' rebuttal, and a circularity audit. Tearing a paper down is the easy half of reading it; the pith above is the substance, this is the friction.

Referee Report

1 major / 3 minor

Summary. The paper compares two-temperature GRMHD simulations of M87* accretion flows with and without radiative cooling at fixed mass accretion rates Ṁ_BH = (1–10)×10^{-6} Ṁ_Edd. Using GRRT post-processing at 230 GHz and 163° inclination with varying electron heating prescriptions and nonthermal electron distribution functions, the authors report that cooling sharply lowers electron temperatures in the dense inner disk (r ≲ 10 r_g), slightly reduces jet-sheath temperatures, produces dimmer disks, more extended and brighter jets, lower total flux, and reduced high-frequency SED flux, while time variability remains midplane-dominated and decreases with rising Ṁ.

Significance. If the results hold after addressing the fixed-Ṁ framing, the work demonstrates that radiative cooling is non-negligible for electron thermodynamics and image morphology in hot accretion flows, with direct relevance to EHT and ngEHT interpretations of M87* shadows and extended jets. The systematic comparison across multiple heating prescriptions and nonthermal eDFs provides a useful robustness check.

major comments (1)
  1. [Abstract] Abstract and comparison setup: the central claims compare cooling versus non-cooling runs at identical Ṁ_BH = (1–10)×10^{-6} Ṁ_Edd and report dimmer disks plus brighter extended jets. Because cooling lowers the 230 GHz flux, matching the fixed observed EHT flux of M87* requires increasing Ṁ in the cooling runs; this rescaling raises densities and temperatures and can partially restore disk brightness while altering jet-sheath contrast, weakening the headline morphological differences. A flux-matched comparison (or explicit discussion of the required Ṁ adjustment) is needed to support the observable implications.
minor comments (3)
  1. [Abstract] The abstract states that simulations employ 'different electron heating prescriptions' but does not name them or reference the specific functional forms; this information should appear explicitly in the methods section with citations.
  2. [Methods] No numerical resolution, grid size, or convergence tests are mentioned in the abstract or summary; these details (including any resolution study) must be provided in §2 or §3 to allow assessment of the reported temperature and flux differences.
  3. [Results] Figure captions and text should clarify whether the reported 'more extended and brighter jets' are measured at fixed Ṁ or after any post-hoc normalization to observed flux.

Simulated Author's Rebuttal

1 responses · 0 unresolved

We thank the referee for the careful reading and constructive comments on our manuscript. The major comment raises an important point about the comparison framework. We address it point-by-point below, indicating where revisions have been made to strengthen the presentation of our results.

read point-by-point responses

  1. Referee: [Abstract] Abstract and comparison setup: the central claims compare cooling versus non-cooling runs at identical Ṁ_BH = (1–10)×10^{-6} Ṁ_Edd and report dimmer disks plus brighter extended jets. Because cooling lowers the 230 GHz flux, matching the fixed observed EHT flux of M87* requires increasing Ṁ in the cooling runs; this rescaling raises densities and temperatures and can partially restore disk brightness while altering jet-sheath contrast, weakening the headline morphological differences. A flux-matched comparison (or explicit discussion of the required Ṁ adjustment) is needed to support the observable implications.

    Authors: We agree that a flux-matched comparison would be valuable for direct observational interpretation. Our study deliberately fixes Ṁ_BH to isolate the thermodynamic and morphological effects of radiative cooling without introducing additional variations in accretion rate. The manuscript already states that cooling reduces the 230 GHz flux for a given Ṁ (see Section 3.3 and Figure 8). To address the referee's concern, we have added an explicit discussion in the revised Section 4.2 estimating the Ṁ adjustment needed to match the observed EHT flux (~0.5 Jy at 230 GHz) and qualitatively describing how higher densities in the rescaled cooling runs would affect disk brightness and jet contrast. We have also clarified the fixed-Ṁ framing in the abstract and introduction. Performing a full set of new simulations at flux-matched Ṁ values is computationally prohibitive at present, but the added discussion supports the observable implications while preserving the physical insight from the controlled comparison. revision: partial

Circularity Check

0 steps flagged

No circularity: direct numerical comparison of otherwise identical runs

full rationale

The paper executes two-temperature GRMHD simulations both with and without radiative cooling at identical fixed mass-accretion rates, then performs GRRT post-processing to compare density, electron temperature, 230 GHz images, SEDs, and variability. No central result is obtained by fitting a parameter to a subset of the same data and then relabeling the fit as a prediction; no self-citation supplies a uniqueness theorem or ansatz that is itself unverified; and no quantity is defined in terms of the very observable it is later said to predict. The fixed-Ṁ framing is an explicit modeling choice whose consequences are reported as such, not a definitional loop that forces the headline morphological differences.

Axiom & Free-Parameter Ledger

2 free parameters · 1 axioms · 0 invented entities

The comparison rests on standard two-temperature plasma modeling and numerical choices for heating and cooling that are not independently validated within the abstract.

free parameters (2)
  • mass accretion rate = (1.0-10) x 10^{-6} M_Edd
    Range (1.0-10) x 10^{-6} M_Edd chosen to match observed radiative efficiency where cooling becomes relevant.
  • electron heating prescription
    Multiple prescriptions tested but details not given in abstract; these control how energy is partitioned between ions and electrons.
axioms (1)
  • domain assumption Two-temperature approximation for ions and electrons
    Assumes separate temperatures for ions and electrons, standard for radiatively inefficient accretion flows.

pith-pipeline@v0.9.0 · 5908 in / 1360 out tokens · 58903 ms · 2026-05-19T15:30:11.184679+00:00 · methodology

discussion (0)

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Lean theorems connected to this paper

Citations machine-checked in the Pith Canon. Every link opens the source theorem in the public Lean library.

  • IndisputableMonolith/Foundation/Cost/FunctionalEquation.lean washburn_uniqueness_aczel unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    We performed general relativistic radiative transfer (GRRT) calculations on two-temperature, radiative, general relativistic magnetohydrodynamic (GRMHD) simulations, employing different electron heating prescriptions and nonthermal eDFs, analyzing the radiation transfer due to synchrotron emission at 230 GHz

  • IndisputableMonolith/Foundation/BlackBodyRadiationDeep.lean blackBodyRadiationDeepCert unclear
    ?
    unclear

    Relation between the paper passage and the cited Recognition theorem.

    radiative cooling sharply decreases the electron temperature in the dense inner disk around the equatorial plane (r ≲ 10 r_g), while slightly reducing jet sheath temperature, leading to a dimmer disk, more extended and brighter jets, and reduced total flux

What do these tags mean?
matches
The paper's claim is directly supported by a theorem in the formal canon.
supports
The theorem supports part of the paper's argument, but the paper may add assumptions or extra steps.
extends
The paper goes beyond the formal theorem; the theorem is a base layer rather than the whole result.
uses
The paper appears to rely on the theorem as machinery.
contradicts
The paper's claim conflicts with a theorem or certificate in the canon.
unclear
Pith found a possible connection, but the passage is too broad, indirect, or ambiguous to say the theorem truly supports the claim.

Reference graph

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