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Jet Collimation Profile of Low-Luminosity AGN M84: Insight into the Jet Formation in the Low Accretion Regime

T0 review · 3 major / 5 minor · reviewed 2026-08-06 · deepseek-v4-flash

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Pith's one-line read The M84 jet switches from a semi-parabolic to a conical width profile at about 17,000 black-hole radii, far inside its Bondi radius.

desk verdict A useful VLBI measurement of the M84 jet collimation profile at the low-accretion extreme, but the parabolic-to-conical break radius needs a robustness check against frequency/epoch systematics before I trust it. read the letter →

arxiv 2507.21241 v1 pith:YPH6TYOW submitted 2025-07-28 astro-ph.HE

Elika Prameswari Fariyanto , Kazuhiro Hada , Yuzhu Cui , Mareki Honma , Masanori Nakamura , Keiichi Asada , Xuezheng Wang , Wu Jiang This is my paper
classification astro-ph.HE
keywords activegalacticnucleirelativisticjetsjetcollimationlow-luminosityAGNM84verylongbaselineinterferometrycoreshiftradiogalaxies
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 study sets out to measure how the jet of M84, one of the least luminous active galactic nuclei for which a jet collimation profile has been measured, widens with distance from its black hole. Combining phase-referenced VLBA images at six frequencies, supplementary archival VLBA data, and a 1980 VLA image, it finds that the jet width does not follow one power law: inside about $1.67\times10^4$ Schwarzschild radii the width grows as $r^{0.71}$, and outside it grows as $r^{1.16}$. The break is significant because it sits roughly 35 times closer to the black hole than M84's Bondi radius, undercutting the idea that the collimation transition happens where gravity captures the surrounding gas. If correct, M84 becomes the lowest-accretion example of a jet that loses collimation close to the black hole, and the tightest constraint yet on how accretion rate controls jet shaping.

What carries the argument

The load-bearing object is the jet collimation profile $W_j(r)$, the deconvolved Gaussian width of transverse radio slices plotted against deprojected distance from the black hole, fitted with a broken power law $W_j(r)=W_0\left[\left(r/r_0\right)^{n a_u}+\left(r/r_0\right)^{n a_d}\right]^{1/n}$. The upstream index $a_u$ and break radius $r_0$ are what carry the argument: they distinguish a collimated parabolic jet from a freely expanding cone and locate where the ambient pressure stops shaping the flow. The profile is anchored to the black hole by a frequency-dependent core-shift measurement, which sets an upper limit of $\lesssim14\,r_s$ on the distance from the 43 GHz core to the central engine.

What would settle it

Measure the M84 jet width at a single frequency (43 GHz) over the full range from $10^2$ to $10^7\,r_s$ with one epoch and matched resolution; if the width profile shows no break near $1.67\times10^4\,r_s$ within the quoted errors, the claimed transition is an artifact of blending multi-frequency data.

Watch

Extended reading notes

Core claim

The central claim is that the M84 jet has a two-part geometry: a semi-parabolic inner region $W(r)\propto r^{0.71\pm0.03}$ inside $r_0=15.8\pm3.0$ mas ($\approx1.67\times10^4\,r_s$) and a conical shape $W(r)\propto r^{1.16\pm0.01}$ beyond it, with the width at the break $W_0\approx1.46\times10^3\,r_s$. A single power law fits the data poorly ($\chi^2/{\rm dof}=2.59$), while the broken power law fits well ($\chi^2/{\rm dof}=1.09$). Compared with M87, whose break occurs near $2.5\times10^5\,r_s$, M84's break is almost two orders of magnitude closer, and since M84's Bondi radius is $\sim5.9\times10^5\,r_s$, the transition cannot be universally tied to the Bondi radius. The paper also derives a small core shift ($\lesssim1$ mas between 1.5 and 43 GHz) that places the black hole within $\lesssim14\,r_s$ of the 43 GHz core, and a magnetic field strength of $\sim6.5$ mG at 1 pc, which it argues is sufficient for a magnetically arrested accretion state.

Load-bearing premise

The deconvolved Gaussian width of each radio slice is assumed to be the true jet diameter at that radius, although the data combine six frequencies and four epochs without a model for opacity or time variability.

Editorial extensions

If this is right

  • M84 becomes the least collimated LLAGN jet measured to date, extending the known relation between jet collimation and accretion rate down to an Eddington ratio of about $5\times10^{-7}$.
  • The parabolic-to-conical break at $\sim1.67\times10^4\,r_s$, well inside the Bondi radius, rules out a universal Bondi-radius transition and points instead to a steep drop in the confining gas density near the black hole.
  • If the tentative negative correlation between upstream power-law index and normalized accretion rate holds, lower-accretion jets should be systematically wider at a given radius, a prediction for the next generation of VLBI surveys.
  • The inferred magnetic flux approaching the magnetically arrested disk threshold implies that even very weakly accreting black holes can launch jets through a well-ordered magnetic field, giving low-power jets the same fundamental engine as powerful ones.

Reading between the lines

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

  • If the multi-frequency data are biased by opacity, the true break could be frequency-dependent; a single-frequency 43 GHz monitoring campaign would reveal whether the $r^{0.71}$ to $r^{1.16}$ transition is a structural feature or a spectral artifact.
  • The paper's interpretation implies that the ambient pressure profile at $\sim10^4\,r_s$ must fall steeply in M84; X-ray surface-brightness deprojection of the Bondi sphere could test this independently.
  • The same analysis applied to Sgr A*, an even lower-accretion black hole with no persistent jet, would be a direct test of the low-accretion trend, predicting that any jet there should break within a few hundred Schwarzschild radii.
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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 / 5 minor

Summary. The paper measures the jet collimation profile of the low-luminosity AGN M84 by combining multi-frequency VLBA observations from 2014 (VLBA I), supplementary VLBA data from 2020-2021 (VLBA II), and a 1980 VLA 1.4 GHz archival image. Using Gaussian deconvolution of transverse slices, the authors derive jet widths from ~10^2 to ~10^7 r_s and fit single and broken power-law models. They report a transition from a semi-parabolic profile (W ∝ r^0.71) to a conical shape (W ∝ r^1.16) at r0 = 15.8 ± 3.0 mas ≈ 1.67 × 10^4 r_s, with a reduced chi-square improvement from 2.59 to 1.09. They also measure a core shift between 1.4 and 43 GHz of ≲1 mas, use it to place an upper limit on the black hole position, and estimate a magnetic field strength of ~6.5 mG at 1 pc. The paper then compares M84 with other LLAGNs, finding a tentative anticorrelation between the upstream power-law index and normalized accretion rate, and concludes that the jet break occurs almost two orders of magnitude inside the Bondi radius, challenging a universal Bondi-radius transition.

Significance. If the central measurement is robust, the paper extends jet collimation studies to the lowest-accretion-rate regime yet probed and provides a concrete counterexample to the idea that the parabolic-to-conical transition occurs near the Bondi radius. The paper's strengths include a detailed error budget (Table 3), the use of atmosphere-corrected phase-referencing, a careful core-shift analysis, and an explicit comparison with M87. The authors also report all fitting parameters and make their statistical improvement quantitatively clear (χ²/dof from 2.59 to 1.09). The finding of a break at ~1.67 × 10^4 r_s, well inside the Bondi radius, is astrophysically interesting and, if confirmed, would support models where the collimation break is governed by the accretion-flow pressure profile rather than the Bondi scale alone. The paper is appropriately cautious in presenting the accretion-rate correlations as tentative (p-values are quoted), and the comparison across LLAGNs is a useful compilation for the community.

major comments (3)
  1. [Section 3.1, Figure 3] The width measurements used for the broken power-law fit are not tabulated, and the fit combines VLBA I (six frequencies, 2014), VLBA II (5–88 GHz, 2020–2021), and a 1980 VLA 1.4 GHz image as a single steady-state jet profile. The break radius r0 = 15.8 mas is close to the spatial scale where high-frequency VLBI measurements (sub-mas beams) give way to low-frequency and VLA measurements with much larger beams (Table 1 shows beams from 0.34 mas to 3860 mas). Because the radio core shifts by up to ~1 mas between 1.4 and 43 GHz (Section 3.2), the apparent jet width at a given de-projected radius may depend on observing frequency through opacity effects. The paper does not report Φ0 and Φb for each slice, nor does it test whether the break survives when the data are split by epoch or by frequency. I request that the authors tabulate all width measurements with their fitted Gaussian widths and beam sizes, and that they perform subset fits (e.g., VLBA I only, VLBA II only, high-frequency-only, low-frequency-only) to demonstrate that the broken power-law and its break radius are not an artifact of combining heterogeneous data.
  2. [Section 3.1, Section 4.1] The statement 'Despite many years of difference, the data set shows consistency and hence constrains the result' is an assertion that is not quantified. The reduced chi-square improvement from 2.59 to 1.09 is encouraging, but it does not by itself establish that multi-epoch and multi-frequency data trace the same intrinsic jet structure. To support this claim, the authors should compare width measurements at overlapping radii from different epochs (e.g., VLBA I 2014 versus VLBA II 2020/2021 at 5 and 22/24 GHz) and show that the residuals of the broken power-law fit do not correlate with observing frequency or epoch. Without such a test, the fitted indices and break radius may be biased by systematic differences between datasets.
  3. [Section 3.1, Section 3.2] The description of how the jet radius is referenced to the central engine is incomplete. The text says the jet radii are plotted 'with respect to the location of the central engine by assuming de-projected distance due to the inclination angle i = 74°' (Section 3.1), but it does not explicitly state whether the frequency-dependent core shift measured in Section 3.2 is applied to shift the origin for each frequency. The core shift is ≲1 mas, which is small compared with r0 = 15.8 mas but could be significant for the innermost points (r ≲ a few mas) that anchor the upstream power-law index a_u = 0.71. The authors should state clearly how the absolute position of the black hole was set for each dataset and, if no correction was applied, quantify the effect of a ~1 mas origin shift on a_u and r0.
minor comments (5)
  1. [Title] The title contains an apparent typesetting artifact: 'Jet F ormation' should read 'Jet Formation'.
  2. [Section 3.1] The broken power-law function is written with a sharpness parameter n, but the fit returns n = 75. The sharpness is not discussed in the text; a sentence explaining why such a large n is preferred (i.e., an almost sharp break) would improve readability.
  3. [Figure 3] The figure and table do not include the number of data points or the degrees of freedom explicitly; reporting dof alongside χ²/dof would allow the reader to judge the fit quality more directly.
  4. [Section 4.2] The Kendall tau p-values for the two correlations (0.23 and 0.48) are quoted, but the sample size (N ≈ 5–6) is not displayed in the figure; adding it would clarify the statistical weight of the tentative trends.
  5. [Appendix B] The footnotes in Table Appendix II.1 are helpful, but the superscript '3' on n_e(r_B) and T(r_B) is not explained in the table itself; please ensure the note appears in the table caption or as a footnote.

Circularity Check

0 steps flagged · score 0.0 of 10

No significant circularity: the central collimation break is a direct fit to observed jet widths, and self-citations are non-load-bearing.

full rationale

No circular step is present. The central claim, a parabolic-to-conical break at r0 ≈ 15.8 mas, is obtained by fitting Eq. (2) to directly measured deconvolved widths Wj = sqrt(Phi0^2 - Phi_b^2) described in Section 3.1, and that broken power-law is explicitly tested against a single power law (chi2/dof 2.59 vs 1.09). No fitted parameter is renamed as a prediction. The core-shift analysis in Section 3.2 uses the standard conical-core model rc(nu) proportional to nu^{-1/kr} from Lobanov (1998) to place an upper limit of ≲14 rs on the BH offset relative to the 43 GHz core; this offset is orders of magnitude smaller than the fitted break at 1.67 x 10^4 rs, so it cannot force the width fit. The broken power-law form is taken from Tseng et al. (2016), but it is used as a phenomenological fit function, not as a uniqueness or existence theorem, and the paper does not invoke same-author results to forbid alternatives. In Section 4.3, the opening angle phi_obs ≈ 4.6 deg is taken 'from our jet collimation analysis' and used as an input to the equipartition B1 estimate; that is a one-way propagation of a measured geometric quantity, not a self-referential definition, because B1 is not fed back into the collimation profile. Self-citations (Hada et al. 2011, 2013; Asada & Nakamura 2012; Wang et al. 2022) supply methods, calibrator parameters, and comparison values that are independently checked or externally falsifiable; the M84 result does not reduce to them. The paper's own caveat on viewing angle (Section 4.1, footnote 1) is a robustness check, not a circular step. Therefore the paper is self-contained with respect to circularity.

Assumptions & free parameters 10 free parameters · 5 assumptions · 0 invented entities

The central claim depends on fitted power-law parameters and adopted source parameters (viewing angle and black hole mass). The physical interpretation relies on standard VLBI core-shift, equipartition, and GRMHD jet assumptions from the literature. No new entities are introduced.

free parameters (10)
  • au (upstream power-law index) = 0.71 ± 0.03
    Fitted to the jet width versus de-projected distance profile in Section 3.1 using the broken power-law model.
  • ad (downstream power-law index) = 1.16 ± 0.01
    Fitted to the same broken power-law model.
  • r0 (break radius) = 15.8 ± 3.0 mas (~1.67e4 rs)
    Fitted break position in the broken power-law model.
  • W0 (jet radius at break) = 1.45 ± 0.28 mas
    Fitted jet width at the break position.
  • n (break sharpness) = 75
    Fitted sharpness parameter of the broken power-law; no uncertainty is quoted.
  • k (core shift power-law index) = 0.78 ± 0.23
    Fitted to the core position versus frequency relation in Section 3.2.
  • A (core shift amplitude) = 1.03 ± 0.53 mas GHz^(1/k)
    Amplitude in the core shift fit r_delta(nu) = A nu^-1/k + B.
  • B (core shift offset) = -0.012 ± 0.014 mas
    Offset in the core shift fit.
  • Viewing angle i = 74 degrees (adopted from Meyer et al. 2018)
    Used for de-projection of distances; the paper states that using 58 degrees instead shifts distances by about 10 percent.
  • Black hole mass MBH = 8.5e8 M_sun (adopted from Walsh et al. 2010)
    Used to convert angular scales to Schwarzschild radii and in the magnetic flux estimate; the allowed range is (4-26)e8 M_sun.
assumptions (5)
  • domain assumption The radio core position shifts with frequency as r_c(nu) proportional to nu^-1/k (Lobanov 1998), and the core shift can be used to locate the jet apex.
    Invoked in Section 3.2 to fit the core shift and set the distance origin for the jet profile.
  • domain assumption The jet is straight at a constant inclination angle i = 74 degrees, so the de-projected distance equals the apparent distance divided by sin(i).
    Used throughout Section 3.1 to convert angular offsets to physical de-projected radii.
  • domain assumption The deconvolved Gaussian FWHM of a transverse slice measures the true jet cross-section, and multi-frequency, multi-epoch data can be combined into a single steady-state profile.
    Section 3.1, eq. for Wj and Figure 3. This is the main systematic assumption behind the profile fit.
  • domain assumption Standard equipartition between magnetic field and radiating particles in the radio core (Lobanov 1998; O'Sullivan and Gabuzda 2009) applies to M84.
    Section 4.3, eqs. (5) and (6), used to derive the magnetic field strength B1 ~ 6.5 mG.
  • domain assumption GRMHD and RIAF jet models (e.g., McKinney 2006; Tchekhovskoy et al. 2008; Yuan et al. 2015) correctly describe wind-assisted collimation, so the break-before-Bondi-radius result is interpreted as weak confinement.
    Section 4.1 and 4.2, used to connect the measured jet shape to accretion rate physics.

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Cite this review

Pith. "Pith review of Jet Collimation Profile of Low-Luminosity AGN M84: Insight into the Jet Formation in the Low Accretion Regime." pith.science (2026). https://pith.science/paper/YPH6TYOW

@misc{pith2026250721241,
  author       = {Pith},
  title        = {Pith review of: Jet Collimation Profile of Low-Luminosity AGN M84: Insight into the Jet Formation in the Low Accretion Regime},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/YPH6TYOW}},
  note         = {Machine review of arXiv:2507.21241}
}
read the original abstract

Recent advancements in high-resolution Very Long Baseline Interferometry (VLBI) have significantly improved our understanding of jet collimation near supermassive black holes in active galactic nuclei (AGNs), particularly in high-power systems. However, the collimation properties of jets in low-luminosity AGNs (LLAGNs) remain poorly explored. In this study, we investigate the jet structure of M84, a nearby radio galaxy and a representative LLAGN, to probe jet collimation properties in a low-accretion regime. Utilizing astrometric phase-referencing observations from the Very Long Baseline Array (VLBA), supplemented by archival Very Large Array (VLA) data, we trace the jet geometry of M84 over a broad range of scales, from approximately 10^2 to 10^7 Schwarzschild radii (rs). Our analysis reveals a well-defined transition from a semi-parabolic profile, W(r) proportional to r^0.71, to a conical shape, W(r) proportional to r^1.16, occurring at approximately 1.67 x 10^4 rs. This indicates that the M84 jet is notably less collimated than those in other known LLAGN sources. Our findings provide new insights into the relationship between jet collimation and accretion rate, offering crucial constraints for jet formation models in LLAGNs.

Figures

Figures reproduced from arXiv: 2507.21241 by the authors.

Figure 1
Figure 1. (Top) Phase-referenced phases of M 84 at 15 GHz and fitted curves on five representative baselines. (Bottom) Zenith tropospheric delay value for each antenna derived from the phase-fitting method. The phase fitting was per￾formed on all 45 VLBA baselines simultaneously. improve our relative position measurements, we further took additional calibration steps. We applied essentially the same procedure used in Reid et … view at source ↗
Figure 2
Figure 2. Multifrequency images of M 84 from VLBA I and VLA observations. Contours are plotted at levels of (-1, 1, 2, 4, 8, 16, 32, 64, 128, 256) × 3Irms, where Irms represents the rms noise level of the image listed in [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. The upper panel shows the jet width of M 84 jets as a function of de-projected distances from the black hole in units of mas and rs. The solid black line represents the best fit of the double power-law model while the dotted line shows the best fit of the single power-law model. In the double power-law fitting, the jet transitions from a semi-parabolic profile (W ∝ r 0.71) in the upstream to a conical profile (W ∝ r… view at source ↗
Figures from the paper (3 more)
Figure 4
Figure 4. Figure 4: (Top) Core position of M 84 as a function of fre￾quency in declination direction. The shaded grey area rep￾resents uncertainties arising from the M 87 jet PA ≈ 270◦ − 320◦ . (Bottom) Core position of M 87 as a function of fre￾quency in right ascension direction compare…
Figure 5
Figure 5. Figure 5: Comparison between the jet collimation profiles of M 84 and M 87. The blue and grey ticks at the top axis mark the transition radius of M 84 and M 87. The blue and grey vertical line marks the location of Bondi radii of M 84 and M 87 (rB ∼ 4.0 × 105 rs; Allen et al. 20…
Figure 6
Figure 6. Figure 6: (Top) Upstream power-law indices to normalized accretion rate among various objects in the LLAGN class. (Bottom) Transition break locations to normalized accretion rate among various objects in the LLAGN class. The black￾capped error bar on the M 84 data point denotes …

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Reviewed papers in the Pith corpus that reference this work. Sorted by Pith novelty score. Full citation record

  1. Sub-Parsec Acceleration and Collimation of NGC 4261's Twin Jets

    astro-ph.GA 2025-06 conditional novelty 6.0 of 10

    NGC 4261's twin jets are collimated and accelerated in the same sub-parsec region, with a maximum Lorentz factor of about 2.6, evidence for a compact acceleration and collimation zone.

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