Pith. sign in

REVIEW 4 major objections 5 minor 82 references

Survey of Radiative, Two-Temperature Magnetically Arrested Simulations of the Black Hole M87* I: Turbulent Electron Heating

T0 review · 4 major / 5 minor · reviewed 2026-08-10 · deepseek-v4-flash

Challenge this review Re-run · record.json Download PDF Read on arXiv ↗

Pith's one-line read Standard turbulent electron heating in two-temperature radiative simulations of M87* yields $R\approx 5$ and ~30% beam-scale linear polarization, far above the observed $<10\%$; matching M87* requires much cooler electrons.

desk verdict The first systematic 2TGRRMHD spin survey of M87* is a solid new resource, and the over-polarization result is a real challenge to K19 heating, though its force depends on a heating prescription whose validity in the near-horizon MAD regime remains unproven. read the letter →

arxiv 2501.12448 v3 pith:72GLBABQ submitted 2025-01-21 astro-ph.HE

Andrew Chael This is my paper · ORCID
classification astro-ph.HE
keywords M87*magneticallyarrestedaccretiontwo-temperatureGRMHDturbulentelectronheatingsub-gridprescriptionlinearpolarizationFaradaydepolarizationblackholespin-down
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

This paper tries to establish that the standard turbulent electron heating prescription adopted in two-temperature, radiative magnetically arrested simulations of M87* makes the electrons in the 230 GHz emitting region only moderately cooler than the ions, with $R = T_{\rm i}/T_{\rm e} \approx 5$. In that temperature state, simulated 20-microarcsecond-scale images carry roughly 30% linear polarization, while the Event Horizon Telescope measures less than 10%. The paper's core claim is therefore that this heating model cannot satisfy the polarization constraints on M87* without invoking much cooler electrons than it predicts. A sympathetic reader would take the main payoff to be a physically motivated prediction of electron temperature that conflicts sharply with post-processing models requiring $R_{\rm high} \approx 80$–$160$ for Faraday depolarization.

What carries the argument

The load-bearing object is the K19 sub-grid electron heating fraction $\delta_{\rm e}$, defined by $Q_{\rm i}/Q_{\rm e} = 35\,(\beta_{\rm i}/15)^{-1.4}\,e^{-0.1\,T_{\rm e}/T_{\rm i}}$ and $\delta_{\rm e} = 1/(1+Q_{\rm i}/Q_{\rm e})$. It partitions viscous dissipation between electrons and ions in each cell from the local ion plasma $\beta$ $\beta_{\rm i}$ and temperature ratio, and it is the sole electron heating input that sets why the simulated electrons stay at $R\approx 5$ instead of cooling further. The paper also relies on the $R(\beta_{\rm gas})$ fitting form of the standard post-processing temperature-ratio model to summarize the simulation data.

What would settle it

Run the same eleven-spin, two-temperature, radiative magnetically arrested suite with a reconnection-based electron heating prescription instead of the turbulent one, keeping the same black-hole mass, accretion-rate normalization, and magnetization cut; if any such model yields beam-scale linear polarization below 10% while keeping $R$ near 80–160 in the emitting region, the paper's central claim would be refuted.

Watch

Extended reading notes

Core claim

The paper reports eleven 3D magnetically arrested simulations around a $6.5\times 10^9\,M_\odot$ black hole, each evolved with separate electron and ion temperatures, radiative cooling, and the K19 electron heating fraction from gyrokinetic turbulence. It finds the emitting region sits at $R\approx 5$, with an effective adiabatic index $\Gamma_{\rm gas}\approx 1.55$, and that the images reproduce M87*'s total-intensity ring size, asymmetry, and position angle. The decisive result is polarimetric: the time-averaged, beam-blurred images have $\langle |m| \rangle \approx 30\%$, several times the observed $<10\%$, because the moderately warm electrons do not produce enough internal Faraday rotation to depolarize the ring. The paper concludes that producing the observed polarization requires $R_{\rm high}\approx 80$–$160$, more than an order of magnitude above what the turbulent heating prescription yields, and that this challenge is specific to the choice of sub-grid electron heating.

Load-bearing premise

The result assumes the K19 turbulent-heating formula correctly divides dissipated energy between electrons and ions everywhere in the flow, including the strongly magnetized jet; if the true electron share is smaller there, electrons would be cooler and the over-polarization would disappear.

Editorial extensions

If this is right

  • If the K19 prescription is right for M87*, the 230 GHz emission region sits at $R\approx 5$, so single-fluid libraries that tune $R_{\rm high}$ to 80–160 to match polarization are effectively invoking electron cooling physics that turbulent heating alone does not provide.
  • Because radiation feedback leaves $\phi_{\rm BH}$, $\eta$, and the spindown parameter nearly unchanged, conclusions about jet power and black-hole spin-down drawn from non-radiative MAD libraries remain valid even when two-temperature and radiative effects are added.
  • The larger effective adiabatic index ($\Gamma_{\rm gas}\approx 1.55$) than the usual $13/9$ makes simulated MAD discs about 15% thicker and jets about 10% narrower, so temperature modeling changes global disc structure, not just emissivity.
  • The polarization-spiral trend with spin persists in radiative two-temperature models; if one ignores the polarization-fraction mismatch, the observed $\angle\beta_2$ would select a spin around $a_*\in[-0.7,0.2]$, and for the weakly spinning retrograde case the image asymmetry is set by the accretion flow rather than the black-hole spin.

Reading between the lines

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

  • Inference: If reconnection-based heating also fails to cool electrons enough, the over-polarization may point to non-thermal electron populations, anisotropic electron distributions, or emission-region cuts rather than the heating fraction; the paper notes that several recent Sgr A* two-temperature studies with reconnection heating still find $R\approx 5$–$10$.
  • Inference: Because $R$ is not a single-valued function of $\beta_{\rm gas}$ in the simulations, with up to an order of magnitude of scatter, image libraries that parameterize $R(\beta)$ with one curve may mis-rank models; a history-dependent or two-parameter electron-temperature prescription could change which spins and heating models fit the polarization data.
  • Inference: The 30–50% of 230 GHz flux coming from the moderately magnetized region $1<\sigma_{\rm i}<25$ makes the magnetization cut a hidden lever on the polarization fraction; adopting a lower cut with a larger accretion rate could partly compensate the over-polarization, though the paper argues the effect is likely too small to fully resolve the mismatch.
  • Inference: If no heating prescription yields sufficiently cold electrons, the tension may point toward field configurations between standard turbulent and magnetically arrested states, or toward sub-Maxwellian electron distributions, rather than an error in the temperature ratio alone; the paper sketches these as alternatives.
Share X Bluesky LinkedIn Reddit HN

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

4 major / 5 minor

Summary. This paper presents eleven 3D two-temperature, radiative GRMHD (2TGRRMHD) simulations of M87* in the magnetically arrested state, covering spins a* = -0.9 to +0.9, together with eleven matched single-fluid runs in the KORAL code. The radiative runs adopt the Kawazura et al. (2019) turbulent electron-heating prescription and are calibrated to M87*'s mass, distance, and 230 GHz flux density, with small post hoc density rescaling factors tabulated (Table 2). The main results are: (i) radiation and two-temperature physics leave the horizon magnetic flux, jet efficiency, and spindown parameter nearly unchanged relative to single-fluid runs (Section 4.1); (ii) the radiative runs self-consistently produce R = Ti/Te ≈ 5 in the 230 GHz emitting region, well described by fitted Mościbrodzka et al. (2016) parameters R_low ≈ 2 and R_high ≈ 5, with an effective adiabatic index Γgas ≈ 1.55; (iii) the simulated images match EHT total-intensity statistics but are over-polarized (⟨|m|⟩ ≈ 30% against the EHT range of 5.7-10.7%); and (iv) the polarization mode β2 follows the Palumbo et al. (2020) trend with spin, parameterized by a two-parameter BZ-motivated fit. The paper interprets the over-polarization as a challenge to the turbulent-heating interpretation of M87*'s polarization and candidly lists the heating-prescription, numerical-dissipation, and magnetization-cutoff caveats.

Significance. The suite is the first systematic 2TGRRMHD spin survey of M87* and a practical resource for the EHT interpretation community: horizon fluxes, fitted R-beta parameters (Tables 1 and 3), per-simulation rescaling factors (Table 2), the β2(a*) fitting function (Eq. 37), and the public KORAL code are all provided. The manuscript is unusually candid about its own limitations; Section 5 explicitly flags the restricted regime of validity of the K19 prescription, the uncertain numerical heating rate, and the σ_cut choice. If the over-polarization result survives correction of Eq. (13) and alternative heating prescriptions, it is a substantive falsifiable challenge to the standard turbulent-heating interpretation of M87*'s polarization, implying much cooler electrons (R_high ≈ 80-160) or modifications to the aligned-MAD paradigm, and the follow-up R19 and compressive-driving tests are already specified. The secondary result that two-temperature and radiative effects leave φ_BH, η, and s unchanged strengthens the basis for spin inference from single-fluid MAD libraries.

major comments (4)
  1. [Eq. (13)-(14); Section 4.2] Equation (13) as printed is inconsistent with the rest of the paper, and since the heating partition drives the headline R ≈ 5 result, this is a load-bearing issue. With Q_i/Q_e = 35 (β_i/15)^(-1.4) e^(-0.1 Te/Ti), at β_i = 0.01 one gets Q_i/Q_e ≈ 10^6 and δ_e ≈ 10^-6; at β_i = 1, δ_e ≈ 7×10^-4; and δ_e exceeds 1/2 only for β_i ≳ 190. This is the opposite of the claim in Section 4.2 that the K19 prescription 'delivers most of the heat to electrons in the most highly magnetized regions (δ_e > 0.5 when β_i ≪ 1)'. It is also opposite to what the code must be doing: the moderate R ≈ 5 and weak Faraday depolarization reported in Sections 4.3-4.4 require substantial electron heating at low β_i, whereas the printed formula would leave electrons nearly unheated, producing R ≫ 5, strong depolarization, and ⟨|m|⟩ far below 30%. I suspect a sign error in the exponent or an inverted ratio in Eq. (13); the authors should correct the printed formula, verify it against the form actually implemented in KORAL, and check that Sections 4.2, 4.4, and 5 consistently describe the same δ_e(β_i, Te/Ti) behavior.
  2. [Section 5; Eqs. (13)-(14); Abstract] The stress-test concern about the K19 prescription's regime of validity lands. Even with a corrected Eq. (13), the model is calibrated from gyrokinetic simulations of Alfvénic turbulence, and the near-horizon MAD flow contains reconnection current sheets, compressive fluctuations, and relativistic electrons that are outside that calibration regime. Section 5 concedes that R19 or compressive-driving corrections (Satapathy et al. 2023, 2024) could lower δ_e at low β, raise R, and remove the tension with the EHT ⟨|m|⟩ < 10% constraint. Because this is load-bearing, I ask for a quantitative sensitivity test within the current pipeline: re-render a subset of snapshots with a modified heating partition (or with an R(β) profile spanning the R19/compressive-driving range) and recompute ⟨|m|⟩, m_net, and β2. The citations to Salas et al. (2024) and Liska et al. (2024), which found R ≈ 5-10 under R19-type heating, concern Sgr A* and X-ray binaries and do not substitute for a test in these M87* flows. Alternatively, the abstract and conclusions should state the tension as conditional on K19 rather than as a generic property of turbulent heating.
  3. [Section 5 (q_v discussion)] The paper's uncertainty about the numerical dissipation rate q_v is itself load-bearing, because the electron heating rate is δ_e q_v and R ≈ 5 is the quantity that creates the claimed polarization tension. The resolution-independence evidence cited from Mościbrodzka (2024) is an external test and does not directly bound q_v for this suite. The authors should provide, at minimum, the fractional contribution of the computed q_v to the electron internal-energy budget in the r ≲ 5 r_g emitting region, or a resolution study of R and ⟨|m|⟩ for one representative simulation, so the reader can judge how much of R ≈ 5 is set by the heating algorithm rather than physical dissipation. The call in Section 5 for a different numerical implementation is appropriate but is not a substitute for such a bound.
  4. [Section 3.2 (σ_cut = 25)] The choice σ_cut = 25 is non-standard (the community default is σ_cut = 1), and the paper reports that 30-50% of the 230 GHz flux originates from the region 1 < σ_i < 25. Since the polarization statistics in Figures 11-12 are computed over this emission, the over-polarization claim is partly defined by this choice. The paper's defense, that a lower σ_cut would require a higher accretion rate that is 'likely not sufficient' to depolarize the images, is plausible but qualitative. A quantitative check (recomputing ⟨|m|⟩ and m_net with σ_cut = 1 and the correspondingly rescaled density, or a short scan of ⟨|m|⟩ versus σ_cut for one simulation) would place this modeling choice on firmer ground and is well within the presented post-processing pipeline.
minor comments (5)
  1. [Section 4.4] The sentence 'the observed large degree of image polarization in M87*' is confusing, since the paper's argument is that the observed ⟨|m|⟩ = 5.7-10.7% is small compared with the simulated ≈30%; please rephrase, for example, 'the detected polarization signal in M87*'.
  2. [Section 4.4 (Eq. 37)] The claim that 'the ratio of the Kerr-Schild poloidal to radial magnetic field strength is proportional to Ω_H' should be 'azimuthal-to-radial' (or 'toroidal-to-poloidal'); as written the phrase is ambiguous given that the BZ monopole field is fundamentally radial. Showing explicitly how the argument of Eq. (37) follows from B_φ/B_r would make the zero-spin and high-spin limits of the fit transparent.
  3. [Section 3.1] The two density-rescaling steps (initial normalization to M_dot = 10^-6 M_dot_Edd at t = 10^4 t_g, the 500 t_g equilibration, and the second rescaling to median F230 = 0.5 Jy near t = 1.05×10^4 t_g, followed by the run to t = 2×10^4 t_g) are described in prose and are easy to misread; a short numbered timeline would improve clarity.
  4. [Figure 12] The fitted C0 and C1 values for Eq. (37) are given only in the text; adding them to the caption would make the figure self-contained.
  5. [Section 4.4] The prograde and retrograde fits to Eq. (37) differ by C1 = 17 deg versus -26 deg; one sentence explaining this offset (e.g., the contribution of the counter-rotating disc to the field pitch angle in the emission region) would help readers use the fit for spin inference.

Circularity Check

0 steps flagged · score 1.0 of 10

No significant circularity: the central over-polarization result is an output of externally anchored K19 electron heating and EHT polarization data, not a reducible fit.

full rationale

The paper's load-bearing claims are anchored to independent external inputs rather than to its own outputs. The electron heating fraction is taken from the Kawazura et al. (2019) gyrokinetic result (Eqs. 13-14), which is not derived from the present simulations or from the author's prior work; the polarization comparison uses EHT observational constraints on m_net, <|m|>, and beta_2; and the beta_2 spin trend is checked against the external Palumbo et al. (2020) result and the Blandford-Znajek wind-up picture. Quantities that are fitted, such as the R_low and R_high values in Table 3 and the C0, C1 parameters in Eq. 37, are explicitly presented as fits to simulation output or as fitting functions, not as predictions. The density rescaling to F230 = 0.5 Jy is disclosed and is a standard normalization; the claims about ring diameter, asymmetry, and polarization are not forced by that normalization. The paper's own Section 5 discussion acknowledges that the K19 prescription may not be valid in the low-beta MAD flow and calls for R19 and compressive-driving models as future work; this is a scientific caveat about input physics, not a circular substitution of the conclusion into the premises. Self-citations (Chael et al. 2019, Chael 2024, Narayan et al. 2022) support numerical setup, coordinate choices, and prior comparisons, but they do not carry the central argument, which rests on the externally given K19 model and on EHT data. No equation or fitted parameter reduces by construction to the claimed R about 5 or to the over-polarization result.

Assumptions & free parameters 7 free parameters · 6 assumptions · 0 invented entities

No new particles, mediators, forces, or conserved quantities are introduced. All physics inputs are drawn from existing literature (K19 gyrokinetic heating, Sądowski et al. 2017 radiation module) or from numerical stabilization choices (floors, sigma cuts, rescalings), which are listed as free parameters. The effective adiabatic index Gamma_gas about 1.55 is a derived output of the simulations, not an invented input.

free parameters (7)
  • Post-hoc density rescaling factor f230 per simulation = 0.91 to 1.27 (Table 2)
    Density and energy densities are rescaled in post-processing so the median 230 GHz flux equals the observed 0.5 Jy in the analysis window; total-intensity agreement with EHT is partly by construction. Disclosed in Section 3.2.
  • Initial density normalization to Mdot = 1e-6 Mdot_Edd = 1e-6 Mdot_Edd
    First normalization applied when restarting the two-temperature runs; fixes the physical density scale before the secondary F230-based rescaling. Section 3.1.
  • K19 electron heating coefficients (35, -1.4, -0.1) = Q_i/Q_e = 35 (beta_i/15)^-1.4 exp(-0.1 Te/Ti)
    Adopted from gyrokinetic simulations (Kawazura et al. 2019), not fitted here, but the R about 5 and over-polarization results hinge on this calibration. Eq. 13.
  • Magnetization ceiling sigma_max and sigma_cut = sigma_max = 100; sigma_cut = 25
    Numerical density floor caps sigma_i at 100, truncating the low-beta tail; the imaging cutoff at sigma_cut = 25 (field default is 1) discards emission from the most magnetized region, and 30-50% of 230 GHz flux comes from sigma between 1 and 25. Sections 3.1, 3.2, 5.
  • Fitted R_low and R_high per simulation = R_low 1.6-3.5, R_high 4.2-8.1 (Table 3)
    Two-parameter fits of the Moscibrodzka et al. (2016) R-beta model to the paper's own simulated cell distributions; summary statistics, not inputs.
  • beta_2 fitting function constants C0, C1 = Prograde C0 = 0.11, C1 = 17 deg; retrograde C0 = 0.26, C1 = -26 deg
    Two parameters per spin branch fit to the paper's own image statistics (Eq. 37); labeled a fitting function, motivated by BZ field wind-up, but not a prediction.
  • Initial electron energy fraction u_e = 0.05 u_gas = 0.05
    Restart condition setting R_init = 19 to 38; the author argues radiation and heating erase this memory but does not quantify the relaxation timescale. Section 3.1.
assumptions (6)
  • domain assumption Ideal MHD limit with infinite conductivity (fluid-frame electric field vanishes, e_mu = 0)
    Standard for GRMHD simulations; excludes non-ideal effects such as collisionless reconnection layers and electron inertia that could change electron heating and emission. Invoked in Section 2.2.
  • domain assumption Electrons and ions each follow relativistic Maxwell-Juttner distributions with temperature-dependent adiabatic index Gamma(Theta)
    Excludes non-thermal particle tails and anisotropic distributions, which are known to affect 230 GHz emission and Faraday rotation (the paper cites Galishnikova et al. 2023 as a caveat). Section 2.2, Eq. 1.
  • domain assumption M1 closure for the radiation field with gray frequency treatment (radiation energy plus photon number only) and Sądowski et al. (2017) opacities for synchrotron, bremsstrahlung, Thomson, and Compton processes
    Cooling and polarization transfer are frequency-dependent; Faraday rotation depth and synchrotron self-absorption are only approximated in the gray limit. Sections 2.2 and 3.2.
  • domain assumption Kawazura et al. (2019) sub-grid electron heating prescription (Eq. 13) remains valid in the near-horizon MAD plasma, including low-beta and high-sigma regions
    The central R about 5 result and the over-polarization claim depend on this external calibration being transferable to the global flow; the paper itself states microscopic electron heating is uncertain (Section 1).
  • domain assumption The numerically computed grid-scale viscous heating rate q_v (difference between adiabatic two-fluid evolution and the total fluid energy) equals the physical dissipation rate
    The author notes 2TGRRMHD codes can produce artificial or negative heating in some regions and that KORAL applies an entropy-mixing correction; cited resolution tests show no dependence, but no independent q_v scheme is tested in this paper. Section 5.
  • standard math Adopted astrophysical constants for M87*: M = 6.5e9 solar masses, D = 16.8 Mpc, eta_Edd = 0.1
    These EHT-recommended values set the physical scale of the radiative runs and the ring-size comparison; different values shift the projected ring diameter, especially at high spin. Section 2.1.

how reviews work

0 comments
Cite this review

Pith. "Pith review of Survey of Radiative, Two-Temperature Magnetically Arrested Simulations of the Black Hole M87* I: Turbulent Electron Heating." pith.science (2026). https://pith.science/paper/72GLBABQ

@misc{pith2026250112448,
  author       = {Pith},
  title        = {Pith review of: Survey of Radiative, Two-Temperature Magnetically Arrested Simulations of the Black Hole M87* I: Turbulent Electron Heating},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/72GLBABQ}},
  note         = {Machine review of arXiv:2501.12448}
}
abstract

We present a set of eleven two-temperature, radiative, general relativistic magnetohydrodynamic (2TGRRMHD) simulations of the black hole M87* in the magnetically arrested (MAD) state, surveying different values of the black hole spin $a_*$. Our 3D simulations self-consistently evolve the temperatures of separate electron and ion populations under the effects of adiabatic compression/expansion, viscous heating, Coulomb coupling, and synchrotron, bremsstrahlung, and inverse Compton radiation. We adopt a sub-grid heating prescription from gyrokinetic simulations of plasma turbulence. Our simulations have accretion rates $\dot{M}=(0.5-1.5)\times10^{-6}\dot{M}_{\rm Edd}$ and radiative efficiencies $\epsilon_{\rm rad}=3-35\%$. We compare our simulations to a fiducial set of otherwise identical single-fluid GRMHD simulations and find no significant changes in the outflow efficiency or black hole spindown parameter. Our simulations produce an effective adiabatic index for the two-temperature plasma of $\Gamma_{\rm gas}\approx1.55$, larger than the $\Gamma_{\rm gas}=13/9$ value often adopted in single-fluid GRMHD simulations. We find moderate ion-to-electron temperature ratios in the 230 GHz emitting region of $R=T_{\rm i}/T_{\rm e}{\approx}5$. While total intensity 230 GHz images from our simulations are consistent with Event Horizon Telescope (EHT) results, our images have significantly more beam-scale linear polarization ($\langle|m|\rangle\approx 30\%$) than is observed in EHT images of M87* ($\langle|m|\rangle<10\%$). We find a trend of the average linear polarization pitch angle $\angle\beta_2$ with black hole spin consistent with what is seen in single-fluid GRMHD simulations, and we provide a simple fitting function for $\angle\beta_2(a_*)$ motivated by the wind-up of magnetic field lines by black hole spin in the Blandford-Znajek mechanism.

Figures

Figures reproduced from arXiv: 2501.12448 by the authors.

Figure 1
Figure 1. Dimensionless simulation fluxes. The first panel shows the average value of the dimensionless magnetic flux, or “MAD parameter” 𝜙BH (Equation 19) for all simulations reported in this work as a function of black hole spin 𝑎∗. The second panel shows the outflow efficiency factor 𝜂 (Equation 22) for all simulations, and the third panel plots the spindown parameter 𝑠 (Equation 23). The final panel plots the bolometric r… view at source ↗
Figure 2
Figure 2. Poloidal profiles of prograde radiative simulations. From left to right, we plot poloidal profiles of the time- and azimuth-averaged quantities from the prograde radiative simulations ap9_radk, ap7_radk, ap5_radk, ap3_radk, and ap1_radk. From top to bottom, we plot the averaged rest mass density 𝜌/𝜌0 (where 𝜌0 = 1 g cm−3 ), the magnetization 𝜎𝑖 , ion temperature 𝑇i , electron temperature 𝑇e, and adiabatic index Γgas… view at source ↗
Figure 3
Figure 3. Poloidal profiles of retrograde radiative simulations. We plot the same quantities as in [PITH_FULL_IMAGE:figures/full_fig_p009_3.png] view at source ↗
Figures from the paper (10 more)
Figure 4
Figure 4. Figure 4: Radial profiles of time-averaged simulation quantities. From left to right, we plot radial profiles of the averaged ion number density ⟨𝑛i⟩, the fluid frame magnetic field strength in Gauss, √︁ 4𝜋⟨𝑏 2 ⟩, the gas internal energy density ⟨𝑢gas⟩, and the fluid-frame radia…
Figure 5
Figure 5. Figure 5: More radial profiles of time-averaged simulation quantities. From left to right, we plot radial profiles of the averaged ion temperature ⟨𝑇i⟩, the electron temperature ⟨𝑇e ⟩, the gas adiabatic index ⟨Γgas⟩ and the disc scale height ⟨ℎ/𝑟 ⟩. The first three quantities ar…
Figure 6
Figure 6. Figure 6: Radial profiles of time-averaged simulation velocities. From left to right, we plot radial profiles of the averaged fluid radial velocity ⟨𝑢 𝑟 ⟩, the averaged fluid azimuthal velocity ⟨𝑢 𝜙 ⟩, the averaged radiation frame radial velocity ⟨𝑢 𝑟 R ⟩ and the averaged radiat…
Figure 7
Figure 7. Figure 7: Dependence of disc height and jet width on magnetic flux. The left plot shows values of the disc scale height ⟨ℎ/𝑟 ⟩ computed at radius 𝑟 = 5 𝑟g with Equation 29 plotted against the corresponding simulation’s averaged value of dimensionless magnetic flux 𝜙BH (Equation …
Figure 8
Figure 8. Figure 8: Temperature ratio 𝑅 = 𝑇i/𝑇e versus 𝛽gas in simulation ap5_radk. In the left panel, we show a scatter plot of 𝑅 against 𝛽gas with points sampled randomly from all cells within 𝑟 < 25 𝑟g over the time range 15000 − 20000 𝑡g in the simulation. We exclude cells with 𝜎i > 2…
Figure 9
Figure 9. Figure 9: Snapshot images from the eleven radiative simulations. Synchrotron images were produced at 230 GHz using ipole; prograde simulations (top row) have an observer inclination 𝜃o = 163 deg and retrograde simulations (bottom row) have an observer inclination 𝜃o = 17 deg, su…
Figure 10
Figure 10. Figure 10: Averaged images from the eleven radiative simulations blurred to EHT resolution. Images from each simulation were blurred to the EHT 20 𝜇as resolution with a circular Gaussian kernel (indicated with the white circle in the upper left image) and time averaged over the …
Figure 11
Figure 11. Figure 11: Total intensity image statistics. From top to bottom we plot the ring diameter 𝑑 (Equation 31), image position angle 𝜑𝐴 (Equation 33) and image asymmetry parameter 𝐴 (Equation 32) for each radiative simulation as a function of spin 𝑎∗. We plot the mean value and 1𝜎 er…
Figure 12
Figure 12. Figure 12: Polarimetric image statistics. From top to bottom we plot the net linear polarization fraction 𝑚net (Equation 34), the EHT-scale average linear polarization fraction ⟨ |𝑚| ⟩ (Equation 35) and the phase of the linear polarization’s second Fourier coefficient ∠𝛽2 (Equat…
Figure 26
Figure 26. Figure 26: While the EHT has not yet claimed a measurement of [PITH_FULL_IMAGE:figures/full_fig_p016_26.png]

Discussion (0). Continue with ORCID to comment.

Reference graph

Works this paper leans on

82 extracted references · 2 canonical work pages

  1. [1]

    D., Payne D

    Blandford R. D., Payne D. G., 1982, @doi [ ] 10.1093/mnras/199.4.883 , https://ui.adsabs.harvard.edu/abs/1982MNRAS.199..883B 199, 883

    doi:10.1093/mnras/199.4.883 1982

  2. [2]

    D., Znajek R

    Blandford R. D., Znajek R. L., 1977, @doi [ ] 10.1093/mnras/179.3.433 , 179, 433

    doi:10.1093/mnras/179.3.433 1977

  3. [3]

    Chael A., 2024, @doi [ ] 10.1093/mnras/stae1692 , https://ui.adsabs.harvard.edu/abs/2024MNRAS.532.3198C 532, 3198

    doi:10.1093/mnras/stae1692 2024

  4. [4]

    Chael A., Rowan M., Narayan R., Johnson M., Sironi L., 2018, @doi [ ] 10.1093/mnras/sty1261 , 478, 5209

    doi:10.1093/mnras/sty1261 2018

  5. [5]

    D., 2019, @doi [ ] 10.1093/mnras/stz988 , 486, 2873

    Chael A., Narayan R., Johnson M. D., 2019, @doi [ ] 10.1093/mnras/stz988 , 486, 2873

    doi:10.1093/mnras/stz988 2019

  6. [6]

    D., Lupsasca A., 2021, @doi [ ] 10.3847/1538-4357/ac09ee , https://ui.adsabs.harvard.edu/abs/2021ApJ...918....6C 918, 6

    Chael A., Johnson M. D., Lupsasca A., 2021, @doi [ ] 10.3847/1538-4357/ac09ee , https://ui.adsabs.harvard.edu/abs/2021ApJ...918....6C 918, 6

    doi:10.3847/1538-4357/ac09ee 2021

  7. [7]

    N., Quataert E., 2023, @doi [ ] 10.3847/1538-4357/acf92d , https://ui.adsabs.harvard.edu/abs/2023ApJ...958...65C 958, 65

    Chael A., Lupsasca A., Wong G. N., Quataert E., 2023, @doi [ ] 10.3847/1538-4357/acf92d , https://ui.adsabs.harvard.edu/abs/2023ApJ...958...65C 958, 65

    doi:10.3847/1538-4357/acf92d 2023

  8. [8]

    Chatterjee K., et al., 2020, @doi [ ] 10.1093/mnras/staa2718 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.499..362C 499, 362

    doi:10.1093/mnras/staa2718 2020

Show all 82 references
  1. [9]

    D., 1918, Publications of Lick Observatory, http://adsabs.harvard.edu/abs/1918PLicO..13....9C 13, 9

    Curtis H. D., 1918, Publications of Lick Observatory, http://adsabs.harvard.edu/abs/1918PLicO..13....9C 13, 9

    1918

  2. [10]

    Dexter J., 2016, @doi [MNRAS] 10.1093/mnras/stw1526 , 462, 115

    2016 doi

  3. [12]

    Dexter J., et al., 2020, @doi [ ] 10.1093/mnras/staa922 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.494.4168D 494, 4168

    2020 doi

  4. [13]

    K., Das S., Prabhakar G., Mandal S., 2020, @doi [ ] 10.1093/mnras/staa1687 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.496.3043D 496, 3043

    Dihingia I. K., Das S., Prabhakar G., Mandal S., 2020, @doi [ ] 10.1093/mnras/staa1687 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.496.3043D 496, 3043

    2020 doi

  5. [14]

    K., Mizuno Y., Fromm C

    Dihingia I. K., Mizuno Y., Fromm C. M., Rezzolla L., 2023, @doi [ ] 10.1093/mnras/stac3165 , https://ui.adsabs.harvard.edu/abs/2023MNRAS.518..405D 518, 405

    2023 doi

  6. [15]

    arXiv:2410.02986

    Event Horizon Telescope Collaboration 2024, @doi [arXiv e-prints] 10.48550/arXiv.2410.02986 , https://ui.adsabs.harvard.edu/abs/2024arXiv241002986T p. arXiv:2410.02986

    2024 doi arXiv

  7. [16]

    Event Horizon Telescope Collaboration et al., 2019a, @doi [ ] 10.3847/2041-8213/ab0e85 , 875, L4

    doi

  8. [17]

    Event Horizon Telescope Collaboration et al., 2019b, @doi [ ] 10.3847/2041-8213/ab0f43 , 875, L5

    doi

  9. [18]

    Event Horizon Telescope Collaboration et al., 2019c, @doi [ ] 10.3847/2041-8213/ab1141 , 875, L6

    doi

  10. [19]

    Event Horizon Telescope Collaboration et al., 2021a, @doi [ ] 10.3847/2041-8213/abe71d , https://ui.adsabs.harvard.edu/abs/2021ApJ...910L..12E 910, L12

    doi

  11. [20]

    Event Horizon Telescope Collaboration et al., 2021b, @doi [ ] 10.3847/2041-8213/abe4de , https://ui.adsabs.harvard.edu/abs/2021ApJ...910L..13E 910, L13

    doi

  12. [21]

    Event Horizon Telescope Collaboration et al., 2022a, @doi [ ] 10.3847/2041-8213/ac6429 , https://ui.adsabs.harvard.edu/abs/2022ApJ...930L..16E 930, L14

    doi

  13. [22]

    Event Horizon Telescope Collaboration et al., 2022b, @doi [ ] 10.3847/2041-8213/ac6672 , https://ui.adsabs.harvard.edu/abs/2022ApJ...930L..16E 930, L16

    doi

  14. [23]

    Event Horizon Telescope Collaboration et al., 2023, @doi [ ] 10.3847/2041-8213/acff70 , https://ui.adsabs.harvard.edu/abs/2023ApJ...957L..20E 957, L20

    2023 doi

  15. [24]

    Event Horizon Telescope Collaboration et al., 2024a, @doi [ ] 10.1051/0004-6361/202347932 , https://ui.adsabs.harvard.edu/abs/2024A&A...681A..79E 681, A79

    doi

  16. [25]

    Event Horizon Telescope Collaboration et al., 2024b, @doi [ ] 10.3847/2041-8213/ad2df1 , https://ui.adsabs.harvard.edu/abs/2024ApJ...964L..26E 964, L26

    doi

  17. [26]

    G., Moncrief V., 1976, @doi [ ] 10.1086/154565 , https://ui.adsabs.harvard.edu/abs/1976ApJ...207..962F 207, 962

    Fishbone L. G., Moncrief V., 1976, @doi [ ] 10.1086/154565 , https://ui.adsabs.harvard.edu/abs/1976ApJ...207..962F 207, 962

    1976 doi

  18. [27]

    Galishnikova A., Philippov A., Quataert E., Bacchini F., Parfrey K., Ripperda B., 2023, @doi [ ] 10.1103/PhysRevLett.130.115201 , https://ui.adsabs.harvard.edu/abs/2023PhRvL.130k5201G 130, 115201

    2023 doi

  19. [28]

    F., McKinney J

    Gammie C. F., McKinney J. C., T \'o th G., 2003, @doi [ ] 10.1086/374594 , 589, 444

    2003 doi

  20. [29]

    E., Ho L

    Greene J. E., Ho L. C., 2007, @doi [ ] 10.1086/520497 , 667, 131

    2007 doi

  21. [30]

    M., Quataert E., Kim C.-G., 2024, @doi [ ] 10.3847/1538-4357/ad5fe7 , https://ui.adsabs.harvard.edu/abs/2024ApJ...973..141G 973, 141

    Guo M., Stone J. M., Quataert E., Kim C.-G., 2024, @doi [ ] 10.3847/1538-4357/ad5fe7 , https://ui.adsabs.harvard.edu/abs/2024ApJ...973..141G 973, 141

    2024 doi

  22. [31]

    Hada K., Doi A., Kino M., Nagai H., Hagiwara Y., Kawaguchi N., 2011, @doi [ ] 10.1038/nature10387 , 477, 185

    2011 doi

  23. [32]

    C., 2008, @doi [ ] 10.1146/annurev.astro.45.051806.110546 , 46, 475

    Ho L. C., 2008, @doi [ ] 10.1146/annurev.astro.45.051806.110546 , 46, 475

    2008 arXiv

  24. [33]

    Howes G., 2010, @doi [ ] 10.1111/j.1745-3933.2010.00958.x , 409, L104

    2010

  25. [34]

    Ichimaru S., 1977, @doi [ ] 10.1086/155314 , 214, 840

    1977 doi

  26. [35]

    D., et al., 2020, @doi [Science Advances] 10.1126/sciadv.aaz1310 , https://ui.adsabs.harvard.edu/abs/2020SciA....6.1310J 6, eaaz1310

    Johnson M. D., et al., 2020, @doi [Science Advances] 10.1126/sciadv.aaz1310 , https://ui.adsabs.harvard.edu/abs/2020SciA....6.1310J 6, eaaz1310

    2020 doi

  27. [36]

    D., et al., 2023, @doi [Galaxies] 10.3390/galaxies11030061 , https://ui.adsabs.harvard.edu/abs/2023Galax..11...61J 11, 61

    Johnson M. D., et al., 2023, @doi [Galaxies] 10.3390/galaxies11030061 , https://ui.adsabs.harvard.edu/abs/2023Galax..11...61J 11, 61

    2023 doi

  28. [37]

    W., Hardee P

    Jones T. W., Hardee P. E., 1979, @doi [ ] 10.1086/156843 , https://ui.adsabs.harvard.edu/abs/1979ApJ...228..268J 228, 268

    1979 doi

  29. [38]

    A., 2019, @doi [Proceedings of the National Academy of Science] 10.1073/pnas.1812491116 , https://ui.adsabs.harvard.edu/abs/2019PNAS..116..771K 116, 771

    Kawazura Y., Barnes M., Schekochihin A. A., 2019, @doi [Proceedings of the National Academy of Science] 10.1073/pnas.1812491116 , https://ui.adsabs.harvard.edu/abs/2019PNAS..116..771K 116, 771

    2019 doi

  30. [39]

    A., Barnes M., TenBarge J

    Kawazura Y., Schekochihin A. A., Barnes M., TenBarge J. M., Tong Y., Klein K. G., Dorland W., 2020, @doi [Physical Review X] 10.1103/PhysRevX.10.041050 , https://ui.adsabs.harvard.edu/abs/2020PhRvX..10d1050K 10, 041050

    2020 doi

  31. [40]

    S., 1999, @doi [ ] 10.1046/j.1365-8711.1999.02244.x , 303, 343

    Komissarov S. S., 1999, @doi [ ] 10.1046/j.1365-8711.1999.02244.x , 303, 343

    1999

  32. [41]

    Liska M. T. P., Musoke G., Tchekhovskoy A., Porth O., Beloborodov A. M., 2022, @doi [ ] 10.3847/2041-8213/ac84db , https://ui.adsabs.harvard.edu/abs/2022ApJ...935L...1L 935, L1

    2022 doi

  33. [42]

    Liska M. T. P., Kaaz N., Chatterjee K., Emami R., Musoke G., 2024, @doi [ ] 10.3847/1538-4357/ad344a , https://ui.adsabs.harvard.edu/abs/2024ApJ...966...47L 966, 47

    2024 doi

  34. [43]

    C., Gammie C

    McKinney J. C., Gammie C. F., 2004, @doi [ ] 10.1086/422244 , https://ui.adsabs.harvard.edu/abs/2004ApJ...611..977M 611, 977

    2004 doi

  35. [44]

    C., Tchekhovskoy A., Blandford R

    McKinney J. C., Tchekhovskoy A., Blandford R. D., 2012, @doi [ ] 10.1111/j.1365-2966.2012.21074.x , 423, 3083

    2012

  36. [45]

    Medeiros L., Chan C.-K., Narayan R., \"O zel F., Psaltis D., 2022, @doi [ ] 10.3847/1538-4357/ac33a7 , https://ui.adsabs.harvard.edu/abs/2022ApJ...924...46M 924, 46

    2022 doi

  37. [46]

    P., Walker R

    Mertens F., Lobanov A. P., Walker R. C., Hardee P. E., 2016, @doi [ ] 10.1051/0004-6361/201628829 , 595, A54

    2016 doi

  38. [47]

    arXiv:2412.06492

    Mo\'scibrodzka M., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2412.06492 , https://ui.adsabs.harvard.edu/abs/2024arXiv241206492M p. arXiv:2412.06492

    2024 doi arXiv

  39. [48]

    F., 2018, ipole: Semianalytic scheme for relativistic polarized radiative transport , Astrophysics Source Code Library, record ascl:1804.002 ( @eprint ascl 1804.002 )

    Mo\'scibrodzka M., Gammie C. F., 2018, ipole: Semianalytic scheme for relativistic polarized radiative transport , Astrophysics Source Code Library, record ascl:1804.002 ( @eprint ascl 1804.002 )

    2018

  40. [49]

    Mo \'s cibrodzka M., Falcke H., Shiokawa H., 2016, @doi [ ] 10.1051/0004-6361/201526630 , 586, A38

    2016 doi

  41. [50]

    Narayan R., Yi I., 1994, @doi [ ] 10.1086/187381 , 428, L13

    1994 doi

  42. [51]

    V., Abramowicz M

    Narayan R., Igumenshchev I. V., Abramowicz M. A., 2003, @doi [ ] 10.1093/pasj/55.6.L69 , 55, L69

    2003 doi

  43. [52]

    Narayan R., Chael A., Chatterjee K., Ricarte A., Curd B., 2022, @doi [ ] 10.1093/mnras/stac285 , https://ui.adsabs.harvard.edu/abs/2022MNRAS.511.3795N 511, 3795

    2022 doi

  44. [53]

    Palumbo D. C. M., Wong G. N., Prather B. S., 2020, @doi [ ] 10.3847/1538-4357/ab86ac , https://ui.adsabs.harvard.edu/abs/2020ApJ...894..156P 894, 156

    2020 doi

  45. [54]

    Porth O., et al., 2019, @doi [ ] 10.3847/1538-4365/ab29fd , https://ui.adsabs.harvard.edu/abs/2019ApJS..243...26P 243, 26

    2019 doi

  46. [55]

    S., et al., 2023, @doi [ ] 10.3847/1538-4357/acc586 , https://ui.adsabs.harvard.edu/abs/2023ApJ...950...35P 950, 35

    Prather B. S., et al., 2023, @doi [ ] 10.3847/1538-4357/acc586 , https://ui.adsabs.harvard.edu/abs/2023ApJ...950...35P 950, 35

    2023 doi

  47. [56]

    J., Begelman M

    Rees M. J., Begelman M. C., Blandford R. D., Phinney E. S., 1982, @doi [ ] 10.1038/295017a0 , https://ui.adsabs.harvard.edu/abs/1982Natur.295...17R 295, 17

    1982 doi

  48. [57]

    M., Tchekhovskoy A., Quataert E., Chandra M., Gammie C

    Ressler S. M., Tchekhovskoy A., Quataert E., Chandra M., Gammie C. F., 2015, @doi [ ] 10.1093/mnras/stv2084 , 454, 1848

    2015 doi

  49. [58]

    M., Tchekhovskoy A., Quataert E., Gammie C

    Ressler S. M., Tchekhovskoy A., Quataert E., Gammie C. F., 2017, @doi [ ] 10.1093/mnras/stx364 , 467, 3604

    2017 doi

  50. [59]

    S., Wong G

    Ricarte A., Prather B. S., Wong G. N., Narayan R., Gammie C., Johnson M. D., 2020, @doi [ ] 10.1093/mnras/staa2692 , https://ui.adsabs.harvard.edu/abs/2020MNRAS.498.5468R 498, 5468

    2020 doi

  51. [60]

    Ricarte A., Narayan R., Curd B., 2023, @doi [ ] 10.3847/2041-8213/aceda5 , https://ui.adsabs.harvard.edu/abs/2023ApJ...954L..22R 954, L22

    2023 doi

  52. [61]

    Rowan M., Sironi L., Narayan R., 2017, @doi [ ] 10.3847/1538-4357/aa9380 , 850, 29

    2017 doi

  53. [62]

    E., Sironi L., Narayan R., 2019, @doi [ ] 10.3847/1538-4357/ab03d7 , 873, 2

    Rowan M. E., Sironi L., Narayan R., 2019, @doi [ ] 10.3847/1538-4357/ab03d7 , 873, 2

    2019 doi

  54. [63]

    R., Ressler S

    Ryan B. R., Ressler S. M., Dolence J. C., Gammie C., Quataert E., 2018, @doi [ ] 10.3847/1538-4357/aad73a , 864, 126

    2018 doi

  55. [64]

    Sadowski Sadowski S a dowski A., Narayan R., 2015, @doi [ ] 10.1093/mnras/stv2022 , 454, 2372

    2015 doi

  56. [65]

    Sadowski S a dowski A., Narayan R., Tchekhovskoy A., Zhu Y., 2013, @doi [ ] 10.1093/mnras/sts632 , 429, 3533

    2013 doi

  57. [66]

    C., Chael A., 2017, @doi [ ] 10.1093/mnras/stw3116 , 466, 705

    Sadowski S a dowski A., Wielgus M., Narayan R., Abarca D., McKinney J. C., Chael A., 2017, @doi [ ] 10.1093/mnras/stw3116 , 466, 705

    2017 doi

  58. [67]

    arXiv:2411.09556

    Salas L., et al., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2411.09556 , https://ui.adsabs.harvard.edu/abs/2024arXiv241109556S p. arXiv:2411.09556

    2024 doi arXiv

  59. [68]

    Satapathy K., Psaltis D., \"O zel F., 2023, @doi [ ] 10.3847/1538-4357/acef12 , https://ui.adsabs.harvard.edu/abs/2023ApJ...955...47S 955, 47

    2023 doi

  60. [69]

    Satapathy K., Psaltis D., \"O zel F., 2024, @doi [ ] 10.3847/1538-4357/ad444f , https://ui.adsabs.harvard.edu/abs/2024ApJ...969..100S 969, 100

    2024 doi

  61. [70]

    L., 2005, @doi [ ] 10.1086/427065 , https://ui.adsabs.harvard.edu/abs/2005ApJ...620...59S 620, 59

    Shapiro S. L., 2005, @doi [ ] 10.1086/427065 , https://ui.adsabs.harvard.edu/abs/2005ApJ...620...59S 620, 59

    2005 doi

  62. [71]

    L., Lightman A

    Shapiro S. L., Lightman A. P., Eardley D. M., 1976, @doi [ ] 10.1086/154162 , https://ui.adsabs.harvard.edu/abs/1976ApJ...204..187S 204, 187

    1976 doi

  63. [72]

    V., Penna R

    Shcherbakov R. V., Penna R. F., McKinney J. C., 2012, @doi [ ] 10.1088/0004-637X/755/2/133 , 755, 133

    2012 doi

  64. [73]

    W., 1983, @doi [ ] 10.1093/mnras/204.4.1269 , 204, 1269

    Stepney S., Guilbert P. W., 1983, @doi [ ] 10.1093/mnras/204.4.1269 , 204, 1269

    1983 doi

  65. [74]

    C., 2012, @doi [ ] 10.1111/j.1745-3933.2012.01256.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.423L..55T 423, L55

    Tchekhovskoy A., McKinney J. C., 2012, @doi [ ] 10.1111/j.1745-3933.2012.01256.x , https://ui.adsabs.harvard.edu/abs/2012MNRAS.423L..55T 423, L55

    2012

  66. [75]

    C., 2010, @doi [ ] 10.1088/0004-637X/711/1/50 , https://ui.adsabs.harvard.edu/abs/2010ApJ...711...50T 711, 50

    Tchekhovskoy A., Narayan R., McKinney J. C., 2010, @doi [ ] 10.1088/0004-637X/711/1/50 , https://ui.adsabs.harvard.edu/abs/2010ApJ...711...50T 711, 50

    2010 doi

  67. [76]

    C., 2011, @doi [ ] 10.1111/j.1745-3933.2011.01147.x , 418, L79

    Tchekhovskoy A., Narayan R., McKinney J. C., 2011, @doi [ ] 10.1111/j.1745-3933.2011.01147.x , 418, L79

    2011

  68. [77]

    T \'o th G., 2000, @doi [Journal of Computational Physics] 10.1006/jcph.2000.6519 , https://ui.adsabs.harvard.edu/abs/2000JCoPh.161..605T 161, 605

    2000

  69. [78]

    J., Quataert E., Blaes O., 2019, @doi [ ] 10.3847/1538-4357/ab089e , https://ui.adsabs.harvard.edu/abs/2019ApJ...878...51W 878, 51

    White C. J., Quataert E., Blaes O., 2019, @doi [ ] 10.3847/1538-4357/ab089e , https://ui.adsabs.harvard.edu/abs/2019ApJ...878...51W 878, 51

    2019 doi

  70. [79]

    N., Gammie C

    Wong G. N., Gammie C. F., 2022, @doi [ ] 10.3847/1538-4357/ac854d , https://ui.adsabs.harvard.edu/abs/2022ApJ...937...60W 937, 60

    2022 doi

  71. [80]

    Z., Dexter J., Chen A

    Yao P. Z., Dexter J., Chen A. Y., Ryan B. R., Wong G. N., 2021, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/stab2462 , 507, 4864

    2021 doi

  72. [81]

    B., vanEijnatten D., Younsi Z., Liska M., Tchekhovskoy A., 2020, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/staa3031 , 499, 3178

    Yoon D., Chatterjee K., Markoff S. B., vanEijnatten D., Younsi Z., Liska M., Tchekhovskoy A., 2020, @doi [Monthly Notices of the Royal Astronomical Society] 10.1093/mnras/staa3031 , 499, 3178

    2020 doi

  73. [82]

    Yuan F., Narayan R., 2014, @doi [ ] 10.1146/annurev-astro-082812-141003 , 52, 529

    2014 doi

  74. [83]

    A., et al., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2406.17754 , https://ui.adsabs.harvard.edu/abs/2024arXiv240617754Z p

    Zhang X. A., et al., 2024, @doi [arXiv e-prints] 10.48550/arXiv.2406.17754 , https://ui.adsabs.harvard.edu/abs/2024arXiv240617754Z p. arXiv:2406.17754

    2024 doi arXiv

Pith tools

Reviewed August 10, 2026 · model on record in the stance chip above.