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Revealing the Accretion Flow in M87*: Insights from Faraday Rotation

T0 review · 3 major / 3 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read M87's accretion flow is Faraday-thick at 43 GHz yet still shows a linear polarization-angle signal.

desk verdict Solid new qualitative prediction—Faraday-thick M87 screen can still yield linear EVPA—but the paper's own koral3D fits miss the code's Faraday depth by up to ~50x, so the quantitative RM-to-density/Mdot lower-limit pipeline is not established. read the letter →

arxiv 2504.13304 v1 pith:T6TBFHA5 submitted 2025-04-17 astro-ph.HE

Constanza Echiburú-Trujillo , Jason Dexter This is my paper · ORCID
classification astro-ph.HE
keywords accretionflowsFaradayrotationM87counter-jetradiativelyinefficientflowpolarizationsupermassiveblackholesmassrate
verification ladder T0 review T1 audit T2 compute T3 formal

The pith

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

The reading

The paper argues that the accretion flow onto M87's supermassive black hole is an external Faraday screen that is Faraday-thick at 43 GHz — the electric vector position angle (EVPA) rotates many times — yet it still produces the linear EVPA-versus-wavelength-squared relation usually taken as the hallmark of a Faraday-thin screen. Using an analytic cylindrical flow model and polarized ray-tracing radiative transfer through two accretion flow models, the paper finds rotation measures around $10^5$–$10^7$ rad m$^{-2}$ and Faraday depths far above unity in every case. The central consequence is that linearity alone cannot diagnose Faraday thinness in M87, and that resolved polarization measurements of the counter-jet, visible at 43 GHz, should reveal the accretion flow and place lower limits on electron density, magnetic field strength, and mass accretion rate. The same reasoning would apply to other low-luminosity active galaxies with resolved counter-jets, so a wrong assumption of Faraday thinness could bias RM-based accretion rate estimates elsewhere.

What carries the argument

The load-bearing element is the external Faraday screen: polarized synchrotron emission from a compact counter-jet blob at about 25 Schwarzschild radii passes through a geometrically thick, magnetized accretion flow whose Faraday depth $\tau_{\rho V}=2\,\mathrm{RM}\,\lambda^2$ is the line-of-sight integral of $n_e B_\parallel$. The paper combines an analytic cylindrical disk model with polarized radiative transfer through a semi-analytic RIAF and a turbulent MHD snapshot. The result that carries the argument is that a large mean Faraday depth does not randomize the position angle; the EVPA keeps rotating with $\lambda^2$, while the degree of depolarization is set by the fluctuation amplitude $\sigma_{\tau_{\rho V}}$ rather than by $\tau_{\rho V}$ itself, as shown by recovery of high polarization when the flow is made Faraday thin.

What would settle it

Resolved 43 GHz linear polarization observations of M87's counter-jet over multiple epochs would settle it: the models predict $|\mathrm{RM}|$ in the range roughly $10^5$–$10^7$ rad m$^{-2}$ with $\tau_{\rho V}\gg1$ and low linear polarization degree, so measuring $|\mathrm{RM}|$ well below $10^5$ rad m$^{-2}$ together with linear polarization above about 60 percent would rule out the assumed Faraday-thick screen.

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Extended reading notes

Core claim

The paper's claim is that M87's accretion flow is Faraday thick at 7 mm but leaves a clean linear EVPA–$\lambda^2$ signature. In the analytic cylindrical model, the screen gives $|\mathrm{RM}| \approx 9.93\times 10^6\,\mathrm{rad\,m^{-2}}$, i.e. Faraday depth $\tau_{\rho V}\approx 973$ at 43 GHz. In a semi-analytic radiatively inefficient accretion flow with a compact polarized blob as the counter-jet, the fit gives $|\mathrm{RM}| \approx 1.13\times 10^6\,\mathrm{rad\,m^{-2}}$, $\tau_{\rho V}\approx 111$. In a turbulent GRMHD snapshot, the screen remains Faraday thick with $\tau_{\rho V}\gg 1$ for all tested blob positions, the EVPA still tracks $\lambda^2$ linearly, and the emission is depolarized to a few percent by Faraday depth fluctuations. The paper reads this as showing that comparing the counter-jet and forward-jet polarization states can detect the accretion flow, and that linearity of EVPA with $\lambda^2$ is not by itself evidence of a Faraday-thin screen.

Load-bearing premise

The predictions assume the counter-jet is a small, compact patch of emission at a specific distance from the black hole, and that the surrounding gas has a particular density, temperature, and magnetic field strength; if the true emission region is larger or the gas thinner, the predicted Faraday-thick screen and linear signal weaken or disappear.

Editorial extensions

If this is right

  • A linear EVPA versus $\lambda^2$ relation measured in M87's counter-jet cannot by itself be taken as evidence for a Faraday-thin screen.
  • Comparing the counter-jet and forward-jet linear polarization at 43 GHz should reveal the accretion flow through rotation or depolarization and yield lower limits on electron density, magnetic field strength, and mass accretion rate.
  • Existing RM-based mass accretion rate limits for M87 that assumed a Faraday-thin spherical flow may instead be tracing the $\tau_{\rho V}=1$ surface, so the inferred rates would need reinterpretation.
  • The Faraday screen is time-variable in the turbulent model, so the measured RM and polarization degree should change with observing epoch and with position along the counter-jet.
  • Resolved polarized observations of other low-luminosity active galaxies with visible counter-jets, such as NGC 1052, could apply the same method.

Reading between the lines

Editorial extensions of the paper, not claims the author makes directly.

  • A testable extension would be to run the same radiative-transfer experiment with a time sequence of turbulent MHD snapshots; the paper's single-snapshot result leaves open whether the linear $\lambda^2$ relation persists across many realizations.
  • If the compact-blob assumption is relaxed, the linear pattern should break down for the turbulent screen, so multi-epoch, multi-frequency imaging could use the onset of nonlinearity to map the size of the counter-jet emission region.
  • The same Faraday-thick-but-linear behavior could occur along other lines of sight through radiatively inefficient flows, implying that unresolved RM measurements in low-luminosity active galactic nuclei may be more sensitive to screen fluctuations than to the mean magnetic field.
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Editorial analysis

A structured set of objections, weighed in public.

Desk editor's note, referee report, and a circularity audit.

Referee Report

3 major / 3 minor

Summary. The paper argues that resolved linear polarization observations of the M87 counter-jet at 43 GHz can probe the accretion flow via Faraday rotation. Using an analytic cylinder model and two numerical setups (a semi-analytic RIAF and a koral3D GRMHD snapshot) with the grtrans ray-tracing code, the authors find in all cases a Faraday-thick accretion flow (τ_ρV ≫ 1) with RM ~ 10^6 rad m^-2, yet the EVPA retains a linear wavelength-squared dependence. The koral3D model also yields strong depolarization due to Faraday-depth fluctuations. The authors propose that comparing counter-jet and forward-jet polarization can detect the accretion flow and place lower limits on electron density, magnetic field, and mass accretion rate.

Significance. The central result—that a linear EVPA–λ² relation can persist even when the Faraday screen is thick and depolarizing—is an important caution against the widespread assumption that linearity implies Faraday thinness. The paper is genuinely forward-modeling in spirit: the predicted RM is not fitted to M87's observed RM, the radiative transfer is done with an independent public code, and the density-scaling and blob-density tests cleanly isolate the accretion flow as the screen. If the claims hold, the work gives a concrete, falsifiable prediction for upcoming polarimetric VLBI observations. However, the quantitative inference from a measured RM to lower limits on density and Ṁ is weakened by an internal inconsistency between the fitted RM and the code's Faraday depths in the turbulent model, as detailed below.

major comments (3)
  1. [§4.1, Figs. 4b and 5b] For the koral3D blob at φ=π/2, the fitted RM of 1.69×10^5 rad m^-2 implies τ_ρV ≈ 17 at 43 GHz, whereas the Faraday-depth map near the blob shows τ_ρV ≈ 640–780, a factor of 40–50 discrepancy. The paper states in §4.1 that 'the τρV values from the RM fit do not match the code calculations shown in the maps,' but it then proceeds in §4.2 to claim that 'a RM measurement implies a lower limit on τρV, density, and in turn, a lower limit on Mdot.' This is not justified: in a turbulent screen with large Faraday-depth fluctuations, the slope of the net EVPA is not the path-integrated Faraday depth. The authors should either provide a quantitative relation between the fitted RM and the screen properties, or soften the lower-limit claim to be only qualitative.
  2. [§3.1] The numerical setup states 'The simulation is conducted for a BH mass of 6.5×10^5 M⊙.' This contradicts the M87 mass of (6.5±0.7)×10^9 M⊙ used elsewhere in the paper. If the code genuinely used 10^5 M⊙, all physical scales (lengths, densities, magnetic fields from the model parametrization) would be wrong by orders of magnitude, and the predicted RM values would not apply to M87. Please correct the typo or, if the simulations actually used a different mass, restate the value explicitly and check the resulting RM normalization.
  3. [§3.3.2, Fig. 6] The text says the Faraday-thin limit is imposed 'by decreasing the accretion flow density by ∼ 100,' then reports that polarization is recovered 'while τρV ≫ 1.' The figure caption instead says the purple points correspond to 'imposing στρV = 1.' These are different statements: reducing n by 100 should reduce τ_ρV by roughly a factor of 100, while setting στρV = 1 acts on the fluctuations. Please clarify what was actually done, report the post-decrease τρV and στρV values, and reconcile the text and caption. This matters for the paper's conclusion that στρV rather than τρV controls depolarization.
minor comments (3)
  1. [Title page] The running header contains 'F araday Rotation'; the spacing appears to be a typesetting error.
  2. [§3.1] The mass '6 .5× 105M⊙' has irregular spacing and should be formatted as '6.5×10^5 M⊙' or, more likely, '6.5×10^9 M⊙' per the previous comment.
  3. [Fig. 6 caption] The phrase 'when imposing στρV = 1, marked by the vertical dotted line' is helpful, but the main text should use the same notation and explain how στρV = 1 is achieved in practice.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the predicted RMs are forward-modeled from explicit density and field assumptions, and no observed M87 RM is used as a fitting target.

full rationale

The paper's quantitative results are produced by solving the polarized radiative transfer equations in the public grtrans code with stated input parameters (n0_e,th = 3e4 cm^-3, Te = 5e9 K, beta = 10), not by fitting to M87's measured RM. The analytic RM of Section 2 is an integral over the assumed density and beta profiles, and the numerical RMs are the slopes of EVPA-vs-lambda^2 curves computed from those same models; hence the outputs are consequences of the inputs rather than restatements of a target quantity. The paper explicitly identifies where its own output is not forced: 'the τρV values from the RM fit do not match the code calculations shown in the maps' (Section 4.1), which is a flagged internal inconsistency and shows the chain is not circular. The self-citations to grtrans (Dexter & Agol 2009; Dexter 2016) are code and method references to an independent public code and to the standard relation τρV = 2 RM lambda^2; they are not invoked as an unverified uniqueness theorem. Assumptions about blob size, morphology, and normalization are acknowledged limitations in Section 4.3 ('because there is no real image of the counter-jet, we assume the size of the emission region and its morphology'), and such assumptions affect the strength of the predictions but do not make the predictions equal to their inputs by construction. No circular step satisfying the quoted-reduction criterion was found.

Assumptions & free parameters 5 free parameters · 5 assumptions · 0 invented entities

No new physical entities are introduced. The predictions rest on standard Faraday rotation theory plus assumed density, temperature, and magnetic field normalizations for M87, and on the counter-jet blob geometry. The number of free parameters is modest but they directly set the Faraday depth.

free parameters (5)
  • n* (density normalization) = 3e4 cm^-3
    Sets the electron density profile ne = n*(R*/R) in the analytic model and n0e,th in sariaf; directly controls RM and tau_rhoV. Chosen as 'typical', not from M87 observations.
  • beta (plasma beta) = 10
    Sets magnetic field strength from B^2/8pi = pgas/beta; enters RM as beta^{-1/2}. Default from prior RIAF modeling, not measured.
  • Te0 (electron temperature normalization) = 5e9 K
    Sets electron temperature in sariaf thermal model; chosen so electrons are non-relativistic because the accretion flow is not detected at radio wavelengths.
  • blob density and magnetic field = ne,blob=1e4 cm^-3, B=0.1 G
    Counter-jet blob parameters control the intrinsic synchrotron polarization. The RM result is shown to be insensitive to blob density.
  • blob size and position = 2 rg radius, at 100 rg vertical and 50 rg horizontal
    Emission region geometry; the paper shows this choice matters for linearity in koral3D.
assumptions (5)
  • standard math External Faraday rotation formula RM = (8.1e5) * integral ne B|| dl (Eq. 2)
    Standard definition used throughout; assumed valid for an external screen in front of the counter-jet.
  • domain assumption Accretion flow described by RIAF density/temperature profiles (Eqs. 9-11) with hydrostatic scale height
    Invoked in analytic and sariaf models; not directly measured for M87 at these radii.
  • domain assumption Counter-jet is a small, constant-density spherical blob with radial magnetic field and power-law electrons
    Section 3.1; simplification to isolate the Faraday screen, acknowledged as unconstrained in Section 4.3.
  • domain assumption Relativistic electrons in the forward-jet suppress its RM contribution
    Section 3.2.1: 'We do not consider the forward-jet, since relativistic electrons suppress the forward-jet contribution to the RM (Quataert & Gruzinov 2000)'.
  • ad hoc to paper Single koral3D snapshot represents M87 accretion flow at 50 rg
    Section 3.3 and 4.3; one snapshot, no time variability; parameters scaled to match M87 luminosity.

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Cite this review

Pith. "Pith review of Revealing the Accretion Flow in M87*: Insights from Faraday Rotation." pith.science (2026). https://pith.science/paper/T6TBFHA5

@misc{pith2026250413304,
  author       = {Pith},
  title        = {Pith review of: Revealing the Accretion Flow in M87*: Insights from Faraday Rotation},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/T6TBFHA5}},
  note         = {Machine review of arXiv:2504.13304}
}
abstract

The Faraday rotation measure (RM) is a commonly used tool to trace electron number density and magnetic fields in hot accretion flows, particularly in low-luminosity accreting supermassive black holes. We focus on the nuclear region of M87, which was observed at 230 GHz (1.3 mm) by the Event Horizon Telescope in 2019. It remains unclear whether this emission originates from the accretion flow, the jet base, or both. To probe the presence of an accretion flow, we explore the scenario where the linearly polarized emission from the counter-jet, visible at 43 GHz (7 mm), is Faraday-rotated by the accretion flow. We calculate theoretical predictions for counter-jet polarization using analytical and numerical models. In all cases, we find a Faraday-thick flow at 43 GHz (7 mm), with $\mathrm{RM} \sim 10^6$ rad m$^{-2}$, and a polarization angle that follows a linear relationship with wavelength squared, consistent with external Faraday rotation. The more realistic model, which includes turbulence and magnetic field fluctuations, predicts that the polarization pattern should be time-dependent, and that the counter-jet emission is depolarized due to Faraday depth fluctuations across the accretion flow. Despite the Faraday thick regime and strong depolarization, the linear relationship persists, enabling us to constrain the flow's physical properties. Comparing the counter-jet and forward-jet linear polarization states should enable detection of M87's accretion flow and provide lower limits on electron density, magnetic field strength, and mass accretion rate.

Figures

Figures reproduced from arXiv: 2504.13304 by the authors.

Figure 1
Figure 1. Illustration of our analytical model setup, where our line of sight defines a cylinder of radius R and height z. We consider emission originating from a small portion of the counter jet, located at 25 rS from the black hole. Note that relativistic electrons suppress the forward-jet contribution to the rotation measure, thus we ignore it in our model. In our second method, we employ a polarized radiative transfer cod… view at source ↗
Figure 2
Figure 2. We consider a face-on observer looking straight down into a geometrically thick accretion flow surrounding the black hole. The accretion flow electrons are assumed to be non-relativistic, while the observed synchrotron emission results from a radiating blob. The shaded area indicates where the blob will appear on the camera, with intensities calculated by backwards ray tracing. The blob’s radius is 2 rg, and it is p… view at source ↗
Figure 3
Figure 3. [PITH_FULL_IMAGE:figures/full_fig_p005_3.png] view at source ↗
Figures from the paper (5 more)
Figure 4
Figure 4. Figure 4: Polarization position angle measured at different frequencies, spanning the same range as in [PITH_FULL_IMAGE:figures/full_fig_p007_4.png]
Figure 5
Figure 5. Figure 5: Maps of τρV at 43 GHz for each position in azimuthal angle. Panel a is ϕblob = 0, panel b is ϕblob = π/2, panel c is ϕblob = π and panel d is ϕblob = −π/2, as in in [PITH_FULL_IMAGE:figures/full_fig_p008_5.png]
Figure 6
Figure 6. Figure 6: Linear polarization degree as a function of Fara￾day depth fluctuation στρV . The orange squares correspond to the blob positions displayed in Figures 4 and 5, where we averaged the degree of polarization over the range of frequen￾cies considered. The purple points cor…
Figure 7
Figure 7. Figure 7: Polarization position angle measured at different frequencies for the RIAF (black circles) and koral3D (blue squares) models with a larger blob size, and spanning the same range as in Figures 3 and 4. In these examples, the blob is positioned at ϕblob = π/2 with a radi…
Figure 8
Figure 8. Figure 8: Polarization position angle measured at different frequencies for the RIAF model with different camera inclinations. Using the setup from Section 3.1, the inclination is adjusted to 17◦ (black circles), 37◦ (dark grey squares), and 60◦ (light grey triangles) while main…

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