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XRISM forecast for the Coma cluster: stormy, with a steep power spectrum

T0 review · 4 major / 4 minor · reviewed 2026-08-16 · deepseek-v4-flash

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Pith's one-line read Using the XRISM Resolve microcalorimeter, this paper argues that the hot gas in the Coma cluster core is moving as a coherent large-scale wind while showing low small-scale turbulence, so its velocity power spectrum must be much steeper…

desk verdict The two XRISM velocity measurements are real, clean, and worth citing, but the steep power-spectrum conclusion leans on the gas-galaxy offset as a turbulent fluctuation—an assumption the paper's own wind interpretation undercuts. read the letter →

arxiv 2504.20928 v1 pith:4QGIDNZO submitted 2025-04-29 astro-ph.HE astro-ph.GA

XRISM Collaboration: Marc Audard , Hisamitsu Awaki , Ralf Ballhausen , Aya Bamba , Ehud Behar , Rozenn Boissay-Malaquin , Laura Brenneman , Gregory V. Brown
show 136 more authors
Lia Corrales Elisa Costantini Renata Cumbee Maria Diaz Trigo Chris Done Tadayasu Dotani Ken Ebisawa Megan E. Eckart Dominique Eckert Satoshi Eguchi Teruaki Enoto Yuichiro Ezoe Adam Foster Ryuichi Fujimoto Yutaka Fujita Yasushi Fukazawa Kotaro Fukushima Akihiro Furuzawa Luigi Gallo Javier A. Garcia Liyi Gu Matteo Guainazzi Kouichi Hagino Kenji Hamaguchi Isamu Hatsukade Katsuhiro Hayashi Takayuki Hayashi Natalie Hell Edmund Hodges-Kluck Ann Hornschemeier Yuto Ichinohe Daiki Ishi Manabu Ishida Kumi Ishikawa Yoshitaka Ishisaki Jelle Kaastra Timothy Kallman Erin Kara Satoru Katsuda Yoshiaki Kanemaru Richard Kelley Caroline Kilbourne Shunji Kitamoto Shogo Kobayashi Takayoshi Kohmura Aya Kubota Maurice Leutenegger Michael Loewenstein Yoshitomo Maeda Maxim Markevitch Hironori Matsumoto Kyoko Matsushita Dan McCammon Brian McNamara Francois Mernier Eric D. Miller Jon M. Miller Ikuyuki Mitsuishi Misaki Mizumoto Tsunefumi Mizuno Koji Mori Koji Mukai Hiroshi Murakami Richard Mushotzky Hiroshi Nakajima Kazuhiro Nakazawa Jan-Uwe Ness Kumiko Nobukawa Masayoshi Nobukawa Hirofumi Noda Hirokazu Odaka Shoji Ogawa Anna Ogorzalek Takashi Okajima Naomi Ota Stephane Paltani Robert Petre Paul Plucinsky Frederick S. Porter Katja Pottschmidt Kosuke Sato Toshiki Sato Makoto Sawada Hiromi Seta Megumi Shidatsu Aurora Simionescu Randall Smith Hiromasa Suzuki Andrew Szymkowiak Hiromitsu Takahashi Mai Takeo Toru Tamagawa Keisuke Tamura Takaaki Tanaka Atsushi Tanimoto Makoto Tashiro Yukikatsu Terada Yuichi Terashima Yohko Tsuboi Masahiro Tsujimoto Hiroshi Tsunemi Takeshi Tsuru Aysegul Tumer Hiroyuki Uchida Nagomi Uchida Yuusuke Uchida Hideki Uchiyama Shutaro Ueda Yoshihiro Ueda Shinichiro Uno Jacco Vink Shin Watanabe Brian J. Williams Satoshi Yamada Shinya Yamada Hiroya Yamaguchi Kazutaka Yamaoka Noriko Yamasaki Makoto Yamauchi Shigeo Yamauchi Tahir Yaqoob Tomokage Yoneyama Tessei Yoshida Mihoko Yukita Irina Zhuravleva Andrew Fabian Dylan Nelson Nobuhiro Okabe Annalisa Pillepich Cicely Potter Manon Regamey Kosei Sakai Mona Shishido Nhut Truong Daniel R. Wik John ZuHone
This is my paper · ORCID
classification astro-ph.HEastro-ph.GA
keywords galaxyclustersComaclusterintraclustermediumX-rayspectroscopymicrocalorimeterturbulencevelocitystructurefunctionpowerspectrum
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

With two pointings of the XRISM Resolve microcalorimeter in the Coma cluster core, the paper delivers the first direct velocity measurements of hot intracluster gas in a cluster without a cool core. The iron emission lines show that the gas in both fields has only modest internal motion — line-of-sight velocity dispersions near 200 km/s, about Mach 0.24 — yet the gas as a whole is moving toward us at 450–730 km/s relative to the cluster's galaxies. The paper argues that no steady-state Kolmogorov turbulence spectrum can produce both facts at once: the same large-scale velocities that fit the line centroids would broaden the lines to about 475 km/s, far above what is observed. To match all the data, the velocity power spectrum must be steeper than Kolmogorov (slope $\alpha < -4.8$ at 68% confidence) or the dissipation scale must exceed about 240 kpc, either way suppressing small-scale turbulence relative to large-scale flows. That matters because turbulence is the leading candidate for reaccelerating the electrons that power Coma's giant radio halo.

What carries the argument

The load-bearing machinery is the velocity structure function (VSF), the mean squared difference of line-of-sight centroid velocities at a given projected separation $r$, tied to the 3D velocity power spectrum $P(k)$ by an integral involving the zeroth-order Bessel function, together with the line-of-sight velocity dispersion $\sigma_z$ as an independent constraint that integrates $P(k)$ over all wavenumbers. The paper adopts a phenomenological spectrum $P(k) = P_0 [1 + (k \ell_{\rm inj})^2]^{\alpha/2} \exp[-(k \ell_{\rm dis})^2]$ with an injection scale $\ell_{\rm inj} = 1$ Mpc, and creates Gaussian random-field realizations of the 3D velocity field, projected through the X-ray emissivity distribution, to compute the cosmic variance that comes from sampling only a few large eddies. This machinery lets two pointings constrain the whole spectrum: centroid differences between quadrants give VSF points at separations of roughly $1.8'$ and $6'$, the gas–galaxy offset supplies a point near 1 Mpc, and the narrow line widths cap the amount of power at small scales.

What would settle it

Take two additional XRISM pointings in Coma, one near the center and one at an intermediate projected separation of roughly $3'$–$10'$ from the existing fields, and measure the iron-line centroids and widths. The steep-spectrum model predicts that low dispersions near 200 km/s and large negative bulk offsets persist; if any new pointing shows a line-of-sight velocity dispersion above roughly 350 km/s, or a bulk velocity close to the cluster galaxy mean, the joint fit collapses and the rejection of Kolmogorov no longer stands.

Watch

Extended reading notes

Core claim

The paper's central claim is that the combination of low line-width dispersions and large bulk velocity offsets along two lines of sight through Coma rules out the standard Kolmogorov picture of steady-state turbulence in the intracluster medium. Resolve measured line-of-sight velocity dispersions $\sigma_z = 208 \pm 12$ km/s in the central $3' \times 3'$ field and $202 \pm 24$ km/s in a field 170 kpc to the south, while the centroids of the iron lines are blueshifted by $450 \pm 15$ and $730 \pm 30$ km/s relative to the mean velocity of cluster galaxies. Treating the centroid differences as points of a velocity structure function and including the $-590$ km/s gas–galaxy offset as a roughly 1 Mpc-scale point, the paper finds that a Kolmogorov spectrum with $\alpha = -11/3$ fits the structure function alone but predicts $\sigma_z \approx 475 \pm 53$ km/s, far above the observed line widths. A joint fit prefers a much steeper effective slope around $\alpha \approx -8$, with a 68% constraint $\alpha < -4.8$, equivalent to a dissipation scale $\ell_{\rm dis} > 240$ kpc. The paper interprets this as evidence either for an extremely high effective viscosity that damps motions before they cascade to small scales, or for a transient dynamical state in which large-scale merger-driven flows have not yet had time to cascade downward.

Load-bearing premise

The argument hinges on assuming that the average velocity of the cluster's galaxies equals the average velocity of the hot gas on large scales, so the measured $-590$ km/s gas–galaxy offset can be treated as a genuine point in the velocity structure function at about 1 Mpc; if gas and galaxies are not dynamically coupled that way, the steep-slope conclusion loses its footing.

Editorial extensions

If this is right

  • The ratio of small-scale kinetic pressure to thermal pressure in Coma is only about $3.1$–$3.3\%$, at the low end of cosmological simulation predictions for a merging cluster and close to the value measured in the relaxed core of A2029.
  • If the steep spectrum is real, most turbulent energy sits at scales of hundreds of kiloparsecs, so the cascade that could reaccelerate radio-halo electrons is suppressed and the standard turbulence-reacceleration model for Coma's radio halo faces a problem.
  • A dissipation scale above about 240 kpc would require an effective viscosity far larger than the Coulomb mean free path of roughly 10 kpc, implying poorly understood momentum transport in the intracluster plasma.
  • The transient-state interpretation would mean the cluster is still responding to a major merger, yet the galaxy velocity field shows no obvious merger substructure, so each explanation strains against the data in a different way.
  • Adding more XRISM pointings across the core would fill in the structure function at intermediate scales and can validate or refute both the steep-slope model and the assumption that X-ray surface brightness fluctuations trace velocities.

Reading between the lines

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

  • If the galaxy mean is a valid stand-in for the gas mean, the measured offsets mean the Coma core is not even approximately in hydrostatic equilibrium along the line of sight; repeating this measurement in other merging clusters would show whether such coherent winds are common.
  • A third XRISM pointing at an intermediate projected separation of a few arcminutes from the existing fields is the sharpest test: the steep-spectrum model predicts a line width near 200 km/s and a bulk offset near $-500$ to $-700$ km/s, while a near-zero offset would falsify the gas–galaxy coupling assumption.
  • The steep effective spectrum in the core could coexist with a Kolmogorov spectrum at small scales if the true spectrum has a break rather than a single power law; a broken power-law model with more VSF points would reconcile the XRISM data with fluctuation-based estimates.
  • A full VSF mapping over separations of roughly $1.5'$–$15'$ would effectively calibrate the conversion factor between density fluctuations and velocity fluctuations used in imaging-based turbulence measurements, turning a large body of existing X-ray imaging into velocity constraints.
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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

4 major / 4 minor

Summary. The paper reports XRISM Resolve measurements of the Fe line complex in two 3′×3′ pointings in the Coma cluster core: one at the center and one 6′ (170 kpc) to the south. The line-of-sight velocity dispersions are σz = 208±12 km/s and 202±24 km/s, while the gas bulk velocities are offset from the cluster galaxy mean by Δvz = −450±15 and −730±30 km/s. The authors build a velocity structure function from intra-Center quadrant differences, Center–South differences, and a gas–galaxy offset treated as a 1 Mpc VSF point; they fit a broken power-law model P(k) = P0[1+(k l_inj)^2]^{α/2} exp[−(k l_dis)^2] and conclude that a Kolmogorov spectrum is inconsistent with the joint VSF and line-width data, requiring a steeper effective slope (α < −4.8 at 68% confidence) or a large dissipation scale (l_dis > 240 kpc). They interpret this as evidence for either strong dissipation at large scales or a transient dynamical state of the cluster.

Significance. If the steep-spectrum conclusion holds, it is significant for ICM turbulence physics: it would challenge the Kolmogorov picture supported by fluctuation-based analyses, constrain the effective viscosity (l_dis > 240 kpc) with implications for radio-halo reacceleration, and demonstrate the power of microcalorimeter velocity measurements. The paper's strengths are the clean, well-characterized line-width measurements with a small gain systematic, the explicit forward modeling of the PSF and emission weighting, and the candid discussion of cosmic variance and sparse sampling. However, the central claim currently rests on the treatment of the gas–galaxy offset as a turbulent VSF point, an assumption that is in tension with the paper's own 'wind' interpretation and needs to be tested before the headline constraint can be considered secure.

major comments (4)
  1. [§4.3, VSF construction] The largest-scale VSF point is constructed by assuming that the cluster galaxy mean can stand in for the gas mean at r ≈ 1 Mpc, with the text stating: 'We can reasonably assume that the gas and galaxies fill the same potential well and have the same cluster-averaged velocities, and use the galaxy average as a substitute for the gas average.' This assumption is in tension with the paper's own §4.2 conclusion that the gas is a high-speed wind with M1D ≈ 0.3–0.5 flowing through the galaxies; if the gas and galaxies are dynamically decoupled, the −590 km/s offset is a coherent bulk flow rather than a turbulent velocity fluctuation and should not enter VSF(r). Because this point is the decisive anchor for the joint fit, the constraints α < −4.8 and l_dis > 240 kpc are not established without it. Please refit the model excluding this point, or model the bulk component separately, and report the resulting constraints.
  2. [§4.3, Eq. (2)] The conclusion that the effective slope is steeper than Kolmogorov is conditioned on fixing l_inj = 1 Mpc. The VSF points probe separations from roughly 50 kpc to 1 Mpc, comparable to the assumed injection scale, so the inferred α and l_dis are degenerate with l_inj. Please test the sensitivity of the α < −4.8 and l_dis > 240 kpc bounds to l_inj over a plausible range (e.g., 0.3–3 Mpc), or provide a quantitative physical argument that fixes l_inj at 1 Mpc.
  3. [§3.2, Fig. 4; §4.3] The small-scale VSF point at r ≈ 1.8′ is computed from quadrant velocities obtained from single-component fits, but the NW quadrant requires a two-component model whose main component is at −470 km/s with σz = 127±41 km/s and an additional 22% component at the cluster mean. If the single-component redshift for the NW quadrant is used in the VSF, that point may not represent the mean gas velocity. Please state explicitly which velocity was used for the NW quadrant and test the sensitivity of the fit to the two-component decomposition.
  4. [Appendix A] The quoted χ2 values and the F-test significance (98%) rely on the approximate cosmic-variance distribution derived from 1500 Gaussian random-field realizations and on the assumption that the observed field is one realization of a homogeneous, isotropic random process. With only three VSF points (one of which is the disputed gas–galaxy point) and two line-width measurements, the significance of the steepening is strongly model-dependent. Please present the constraints with and without the cosmic-variance approximation, or at least soften the 'F-test indicates 98% confidence' claim to reflect this dependence.
minor comments (4)
  1. [§4.4] Typo: 'exhist' should be 'exist'.
  2. [Acknowledgments] Typo: 'acnowledges' should be 'acknowledges'.
  3. [Fig. 3 caption] The caption would benefit from stating explicitly that the values inside the FOV are from single-component fits and that the NW quadrant's two-component decomposition is shown in Fig. 4; the spacing in '± 60 km s−1' is also inconsistent.
  4. [§4.2] The Mach numbers M1D = 0.14 and M1D = 0.3–0.5 are used without defining M1D; please define it as the ratio of the relevant line-of-sight velocity to the local sound speed.

Circularity Check

0 steps flagged · score 0.0 of 10

No circularity: the steep-spectrum claim is a model fit to independent XRISM velocity and line-width measurements, with the gas–galaxy offset used as an explicit, acknowledged assumption rather than a definitional input.

full rationale

The paper's derivation chain is not circular. The measured line-of-sight velocity dispersions (208±12 and 202±24 km/s) and the velocity offsets (450±15 and 730±30 km/s) are external data, not outputs of the power-spectrum model. The velocity structure function is constructed from measured velocity differences between quadrants, between the two pointings, and, under an explicit assumption, from the gas–galaxy offset; the model P(k) in eq. (2) is then fitted to these data via the standard forward-modeling relations in Appendix A (eqs. A4–A6). The Kolmogorov cross-check is legitimate: the normalization is fit to the VSF points alone, and the model then predicts σz = 475±53 km/s versus the observed ≈205 km/s, exposing a real tension. The steep-slope conclusion (α < −4.8 or ℓdis > 240 kpc) is an inference from this tension, not a restatement of an input; α and ℓdis are free parameters whose values are constrained by the data. Self-citations (XRISM Collab. 2025a,b) are limited to data-reduction, calibration, and NXB-modeling procedures and are not load-bearing for the central physics, while the cosmic-variance formalism (ZuHone et al. 2016; Clerc et al. 2019) is an independent published method. The paper explicitly flags its own limitations, including the exploratory nature of the 1 Mpc gas–galaxy VSF point ('It is possible that they are outliers, but we have to treat them as representative'), the 'cosmic variance' as the dominant uncertainty, and the restriction to a simple family of spectra. Even if the gas–galaxy/cluster-frame assumption is physically fragile and affects the conclusion, that is a correctness and robustness concern, not a circularity: the paper does not define the prediction in terms of the fitted result or import a self-citation as the justification for its central claim.

Assumptions & free parameters 5 free parameters · 7 assumptions · 0 invented entities

The central claim rests on a small number of measurement inputs and a larger set of modeling choices. The measured spectral parameters are the only direct data. The power spectrum inference adds assumptions about isotropy, Gaussianity, emissivity weighting, a two-scale functional form, the use of the galaxy mean as a large-scale gas velocity reference, and an approximate cosmic-variance distribution. The free parameters are the normalization and slope of P(k), plus the hand-fixed injection scale and the large-dissipation alternative.

free parameters (5)
  • P0 normalization of velocity power spectrum (Eq. 2) = fitted, not reported
    Normalization of P(k) is the only free parameter when fitting a Kolmogorov spectrum to the VSF, and is re-fit in the steep-slope model.
  • Spectral slope alpha of P(k) = best fit shown with alpha = -8; 68% constraint alpha < -4.8
    Steeper-than-Kolmogorov slope is selected by fitting the VSF and dispersion data; the abstract's 'much steeper' claim is this fitted value.
  • Injection scale l_inj = 1 Mpc (fixed by hand)
    Chosen as 'a logical first guess for a merger'; the steepness conclusion is not tested against other injection scales.
  • Dissipation scale l_dis = 1 kpc in Kolmogorov fit, then > 240 kpc (68%) for large-dissipation alternative
    Essentially zero is assumed for the fiducial model; a large-dissipation model with l_dis > 240 kpc is indistinguishable from the steep-slope fit.
  • Linear scale assigned to the gas-galaxy VSF point = r = 1 +/- 0.5 Mpc (chosen)
    The bulk gas-galaxy offset is placed at r ~ 35 arcmin; the exact scale is stated to be not critical, but it anchors the largest VSF bin.
assumptions (7)
  • domain assumption Velocity field is statistically isotropic, homogeneous, and Gaussian random with power spectrum P(k) as in Eq. (2).
    Appendix A sets up all VSF/dispersion predictions on this assumption; no non-Gaussian or anisotropic alternatives are modeled.
  • domain assumption Gas and galaxies fill the same potential well and share the same cluster-averaged velocity, so the galaxy mean can serve as the gas mean for the 1 Mpc VSF point.
    Section 4.3 invokes this to turn the observed -590 km/s gas-galaxy offset into a structure-function measurement.
  • domain assumption The Coma ICM is approximately isothermal, making the emission-measure weighting temperature-independent.
    Stated in Appendix A; supported by single-temperature fits but only at two pointings.
  • domain assumption Coma central ICM is a single-temperature plasma described by BAPEC with fixed solar abundance ratios.
    Section 3.1 uses one-component fits; the NW quadrant requires an additional component, so the isothermal/single-component assumption is not universal.
  • domain assumption Cosmic variance of VSF' follows an approximate power-law distribution and the sample variance formula of Clerc et al. (2019) applies.
    Appendix A uses 1500 Gaussian random field realizations and approximates the scatter as a power law; this is the dominant uncertainty.
  • domain assumption Equation (2) is a sufficient family for the velocity power spectrum.
    Section 4.3 only tests this two-scale form; the paper admits more complex spectra cannot be ruled out.
  • domain assumption The XRISM gain uncertainty is <= 0.3 eV (<= 15 km/s at 6 keV) and the L-size RMF is adequate.
    Section 2 cites calibration studies and tests RMF sizes; line shifts of 10 to 16 eV are much larger than this systematic.

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Cite this review

Pith. "Pith review of XRISM forecast for the Coma cluster: stormy, with a steep power spectrum." pith.science (2026). https://pith.science/paper/4QGIDNZO

@misc{pith2026250420928,
  author       = {Pith},
  title        = {Pith review of: XRISM forecast for the Coma cluster: stormy, with a steep power spectrum},
  year         = {2026},
  howpublished = {\url{https://pith.science/paper/4QGIDNZO}},
  note         = {Machine review of arXiv:2504.20928}
}
read the original abstract

The XRISM Resolve microcalorimeter array measured the velocities of hot intracluster gas at two positions in the Coma galaxy cluster: 3'x3' squares at the center and at 6' (170 kpc) to the south. We find the line-of-sight velocity dispersions in those regions to be sigma_z=208+-12 km/s and 202+-24 km/s, respectively. The central value corresponds to a 3D Mach number of M=0.24+-0.015 and the ratio of the kinetic pressure of small-scale motions to thermal pressure in the intracluster plasma of only 3.1+-0.4%, at the lower end of predictions from cosmological simulations for merging clusters like Coma, and similar to that observed in the cool core of the relaxed cluster A2029. Meanwhile, the gas in both regions exhibits high line-of-sight velocity differences from the mean velocity of the cluster galaxies, Delta v_z=450+-15 km/s and 730+-30 km/s, respectively. A small contribution from an additional gas velocity component, consistent with the cluster optical mean, is detected along a sightline near the cluster center. The combination of the observed velocity dispersions and bulk velocities is not described by a Kolmogorov velocity power spectrum of steady-state turbulence; instead, the data imply a much steeper effective slope (i.e., relatively more power at larger linear scales). This may indicate either a very large dissipation scale resulting in the suppression of small-scale motions, or a transient dynamic state of the cluster, where large-scale gas flows generated by an ongoing merger have not yet cascaded down to small scales.

Figures

Figures reproduced from arXiv: 2504.20928 by the authors.

Figure 1
Figure 1. XRISM Resolve fields of view and exposure times over￾laid on the XMM-Newton image of the Coma cluster (Sanders et al. 2020). The two brightest cluster galaxies are marked. galaxies with bent and contorted tails, believed to trace the ICM winds (e.g., Burns 1998; Botteon et al. 2020). The recently launched X-ray microcalorimeter array Re￾solve onboard the XRISM observatory (Tashiro et al. 2020; Ishisaki et al. 2022) … view at source ↗
Figure 2
Figure 2. XRISM Resolve spectra for (a) Center and (b) South pointings in the He-like and H-like Fe line region, binned by 4 eV and 8 eV, respectively. Red lines show the best-fit models ( [PITH_FULL_IMAGE:figures/full_fig_p004_2.png] view at source ↗
Figure 3
Figure 3. XRISM Resolve measurements of (a) the LOS velocities relative to the mean velocity of cluster member galaxies and (b) LOS velocity dispersion, overlaid on the XMM-Newton image. Uncertainties are statistical 1σ. The values to the left of the fields represent the entire 3 ′ ×3 ′ field, while the values inside the FOV pertain to the 1.5′ quadrants, for which the relatively small PSF smearing effect is not included. The… view at source ↗
Figures from the paper (4 more)
Figure 4
Figure 4. Figure 4: The spectrum for the NW quadrant of the Center field (the one with the highest velocity dispersion, see Fig. 3b). Only the Fe-Heα line complex is displayed, binned by 4 eV. Two velocity components are needed to model the line profile. The main com￾ponent (blue) is blue…
Figure 6
Figure 6. Figure 6: compares this kinetic pressure in the Coma Center to predictions from several cosmological simulations, select￾ing sightlines through the cluster center and estimating pkin based on the LOS velocity dispersions, as done for Coma, while choosing Coma-like disturbed clus…
Figure 7
Figure 7. Figure 7: A histogram of velocities of cluster member galaxies within r < 20′ from the Coma X-ray center, retrieved from SDSS, DESI, and NED (2019) archival data. The gas velocities measured with XRISM for the Center and South fields (marked C and S, re￾spectively) are offset fr…
Figure 8
Figure 8. Figure 8: Turbulence power spectrum inferred from the observed gas velocity differences and dispersions. (a) The velocity structure function is shown by blue crosses. The two velocity dispersions are shown in the inset by blue symbols. The gas-galaxy offset (see text) is include…

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Forward citations

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