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arxiv: 2607.00610 · v1 · pith:NJR3RAD3new · submitted 2026-07-01 · 🌌 astro-ph.CO

Correcting the hydrostatic mass for non-thermal gas motions: a comparison of two approaches

Th\'eo Lebeau , Nabila Aghanim , Jenny Sorce , Stefano Ettori This is my paper

Pith reviewed 2026-07-02 07:21 UTC · model grok-4.3

classification 🌌 astro-ph.CO
keywords hydrostatic massnon-thermal pressuregalaxy cluster mass biasintracluster mediummomentum equationprojection effectsvirial radius
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The pith

Two methods for correcting hydrostatic mass estimates for non-thermal gas motions produce different radial profiles in three-dimensional cluster data.

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

The paper compares two proposed fixes for the bias in hydrostatic mass estimates of galaxy clusters caused by non-thermal pressure support from gas motions. One fix replaces the thermal pressure with the sum of thermal and non-thermal pressures in the equilibrium equation. The other adds effective mass terms obtained from the full gas momentum equation. When both are applied to three-dimensional radial profiles from a cluster simulation, the total-pressure method produces a correction that grows outward, reaching roughly 40 percent at the virial radius, while the effective-mass method yields a correction that changes little with radius. In line-of-sight projections the two methods agree to within a few percent, yet both recover only about half the true non-thermal pressure fraction present in the three-dimensional data.

Core claim

The non-thermal pressure correction increases the mass by a growing amount with radius from a few per cent in the core to ∼40% at the virial radius, whereas the effective mass terms provide a correction that varies less with radius. When estimated from projections, the two methods agree to within a few per cent for a given sightline, but the non-thermal pressure fraction is underestimated by about a factor of 2 compared to the 3D case. Projection effects can change the inferred non-thermal pressure fraction by up to a factor of 2, particularly when the sightline is aligned with cosmic filaments.

What carries the argument

Application of the gas momentum equation to simulated intracluster gas to obtain either total pressure or effective mass correction terms for the hydrostatic equilibrium equation.

If this is right

  • The total-pressure method produces a mass bias that increases steadily outward while the effective-mass method produces a roughly constant bias.
  • Projected data cause both methods to underestimate the non-thermal pressure fraction by a factor of approximately two.
  • Alignment of the line of sight with filaments can shift the recovered non-thermal pressure fraction by up to a factor of two.
  • The choice between the two corrections therefore changes the inferred radial dependence of the hydrostatic mass bias.

Where Pith is reading between the lines

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

  • The differing radial behaviors imply that cosmological parameter constraints derived from cluster abundance could shift depending on which correction is adopted at large radii.
  • Line-of-sight velocity measurements will require explicit modeling of projection geometry to avoid systematic underestimation of non-thermal support.
  • Repeating the comparison across multiple independent cluster simulations would test whether the discrepancy between the two methods is a general feature.

Load-bearing premise

The distribution of non-thermal gas motions in one simulated galaxy cluster is representative of their distribution in real clusters.

What would settle it

Independent weak-lensing mass profiles for a sample of clusters whose three-dimensional velocity fields have been measured, compared against the radial correction curves predicted by each method.

Figures

Figures reproduced from arXiv: 2607.00610 by Jenny Sorce, Nabila Aghanim, Stefano Ettori, Th\'eo Lebeau.

Figure 1
Figure 1. Figure 1: Top: 3D radial profiles of the temperature. Bottom: ratios of MHE over Mtot = MDM + Mgas, which is the sum of the mass of all the DM particles and the gas cells in the simulation. named afterwards Outflow, Collapse, Collimated filament, and Multistream filament. These regions are shown in Fig. A.1, and are displayed in red, purple, green, and blue, respectively, also in the following figures. In addition, … view at source ↗
Figure 3
Figure 3. Figure 3: 3D radial profiles of the radial velocity (top row), its dispersion (second row), the tangential velocity (third row), its dispersion (fourth row), and the anisotropy parameter β = 1 − σ 2 t /2σ 2 r (bottom row). the two correction methods do not yield the same results across all radii and regions, which we discuss further in Sect. 6. 5. Masses from projected quantities After computing the corrected masses… view at source ↗
Figure 4
Figure 4. Figure 4: Ratios of Mdisp (top), Mrot (middle) over Meff = MHE + Mdisp + Mrot, and Meff over MHE (bottom). We thus cannot estimate the log-derivative of σ 2 r in Eq. 10, this term is thus set to zero. Moreover, we make the usual assump￾tion that the ICM gas motion is isotropic since we only have ac￾cess to 1D information through spectroscopy, even though the anisotropy parameter β (Eq. 11, see bottom panel of [PITH… view at source ↗
Figure 6
Figure 6. Figure 6: Values of the α parameter (top) and the Mα/MHE ratio estimated within R500 and Rvir from projections. 0.4 0.2 0.0 0.2 M dis p / M eff xew yew zew cenew 3D, entire cluster xmw ymw zmw cenmw 0.00 0.05 0.10 0.15 0.20 Mrot/ M eff 10 3 2 × 10 3 R[kpc] 0.8 1.0 1.2 1.4 M eff/ M H E R 5 0 0 R vir [PITH_FULL_IMAGE:figures/full_fig_p007_6.png] view at source ↗
Figure 7
Figure 7. Figure 7: Ratios of Mdisp (top), Mrot (middle) over Meff = MHE + Mdisp + Mrot, and Meff over MHE (bottom) estimated from projections. Then, the relative contributions of Mdisp and Mrot to Meff, and the Meff/MHE ratio, are shown in the top, middle and bottom pan￾els of [PITH_FULL_IMAGE:figures/full_fig_p007_7.png] view at source ↗
Figure 9
Figure 9. Figure 9: Ratio of Mα over Meff. The large fluctuations of the filament regions beyond Rvir are due to the steep gradients of the velocity disper￾sion entering the numerical derivatives in these regions. ∼1.13 at R500 and ∼1.3 at Rvir. The difference is even more pro￾nounced in the Collimated filament regions, where the ratio rises higher than ∼1.45 around Rvir, whereas it stays around ∼1.1 in the Outflow region. Th… view at source ↗
read the original abstract

An accurate estimation of the mass of galaxy clusters is key to precisely and unbiasedly constraining cosmological parameters through their number count. The hydrostatic mass, estimated from the properties of the intracluster medium (ICM) assuming hydrostatic equilibrium, sphericity, and thermal-only pressure, is known to be biased by 10 to 20%, most likely due to non-thermal pressure support from gas motions. Two corrections have been proposed: i) replacing the thermal pressure by the total pressure $P_\mathrm{tot}=P_\mathrm{th}+P_\mathrm{nth}$, or ii) adding effective mass terms derived from the gas momentum equation. We compare these approaches using a numerical replica of the Virgo cluster as a case study, estimating corrected masses from 3D radial profiles in different cluster regions and from projected sightline velocities mimicking XRISM observations. We find that the two methods do not yield the same results in 3D: the non-thermal pressure correction increases the mass by a growing amount with radius (from a few per cent in the core to $\sim$40% at the virial radius), whereas the effective mass terms provide a correction that varies less with radius. When estimated from projections, the two methods agree to within a few per cent for a given sightline, but the non-thermal pressure fraction is underestimated by about a factor of 2 compared to the 3D case. Furthermore, projection effects can change the inferred non-thermal pressure fraction by up to a factor of 2, particularly when the sightline is aligned with cosmic filaments.

Editorial analysis

A structured set of objections, weighed in public.

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

Referee Report

2 major / 2 minor

Summary. The manuscript compares two methods for correcting hydrostatic mass estimates of galaxy clusters for non-thermal gas motions: (i) replacing thermal pressure with total pressure P_tot = P_th + P_nth, and (ii) adding effective mass terms derived from the gas momentum equation. Using 3D radial profiles and projected sightline velocities from a numerical replica of the Virgo cluster, the authors report that the methods differ in 3D (non-thermal pressure correction grows from a few percent in the core to ~40% at R_vir, while effective-mass terms vary less radially), but agree to within a few percent in projections; projections underestimate the non-thermal fraction by a factor of ~2 relative to 3D, and sightline alignment with filaments can change the inferred fraction by up to a factor of 2.

Significance. If the reported differences hold, the work is significant for cluster cosmology because it quantifies how the choice of non-thermal correction affects mass bias estimates that enter number-count constraints. The direct comparison against the known true mass in a controlled simulation provides a clear benchmark, and the projection analysis is timely for interpreting XRISM data. The use of a high-resolution numerical replica as an external benchmark is a methodological strength.

major comments (2)
  1. [Section 3 and Results (3D profiles)] The central claim that the two correction methods produce different radial behaviors in 3D (non-thermal pressure term reaching ~40% at R_vir versus less radial variation for effective-mass terms) rests on a single numerical replica of the Virgo cluster (Section 3, simulation setup). Both the definition of P_nth and the momentum-equation derivation of the effective-mass terms depend on the specific velocity field (bulk flows plus dispersion) realized in that run; if the turbulence spectrum, radial decline, or filamentary structure differs from the ensemble of real clusters, the reported mismatch need not be general.
  2. [Projection results section] In the projection analysis, the manuscript states that the non-thermal pressure fraction is underestimated by a factor of ~2 and can vary by up to a factor of 2 across sightlines, yet no error bars, number of independent sightlines sampled, or multiple simulation realizations are reported (abstract and projection results). This leaves the robustness of the agreement between methods (to within a few percent) and the factor-of-2 offset uncertain when extrapolated beyond the specific geometry of this replica.
minor comments (2)
  1. [Abstract and Section 2] The abstract and main text would benefit from explicit statements of the radial range over which the ~40% correction is measured (e.g., in units of R_vir) and the precise definition of the effective-mass terms (reference to the relevant equation in the momentum-equation derivation).
  2. [Methods] Notation for P_nth and the effective-mass terms should be introduced consistently in the methods section before being used in the results; a short table summarizing the two correction formulae side-by-side would improve clarity.

Simulated Author's Rebuttal

2 responses · 0 unresolved

We thank the referee for the constructive comments, which help clarify the scope and robustness of our results. We respond point-by-point to the major comments below.

read point-by-point responses

  1. Referee: [Section 3 and Results (3D profiles)] The central claim that the two correction methods produce different radial behaviors in 3D (non-thermal pressure term reaching ~40% at R_vir versus less radial variation for effective-mass terms) rests on a single numerical replica of the Virgo cluster (Section 3, simulation setup). Both the definition of P_nth and the momentum-equation derivation of the effective-mass terms depend on the specific velocity field (bulk flows plus dispersion) realized in that run; if the turbulence spectrum, radial decline, or filamentary structure differs from the ensemble of real clusters, the reported mismatch need not be general.

    Authors: We agree that the analysis uses a single high-resolution replica and that the quantitative radial trends are tied to the specific velocity field realized in that run. The manuscript presents the work explicitly as a case study chosen for its fidelity to a well-observed cluster and the availability of the true mass. The methodological difference (local P_nth versus integrated momentum terms) produces the reported radial divergence even when applied to identical velocity data; this comparison remains valid for the chosen setup. We will revise the text to state more explicitly that the results are specific to this replica and to note that ensemble simulations would be required to assess generality across different turbulence realizations. revision: partial

  2. Referee: [Projection results section] In the projection analysis, the manuscript states that the non-thermal pressure fraction is underestimated by a factor of ~2 and can vary by up to a factor of 2 across sightlines, yet no error bars, number of independent sightlines sampled, or multiple simulation realizations are reported (abstract and projection results). This leaves the robustness of the agreement between methods (to within a few percent) and the factor-of-2 offset uncertain when extrapolated beyond the specific geometry of this replica.

    Authors: The projection results are derived from multiple sightlines through the single replica, chosen to sample a range of orientations including filament alignments. To address the concern we will add the precise number of sightlines, report the variation across them (including a measure of spread), and include error bars on the projected quantities where appropriate. The agreement between methods to within a few percent and the factor-of-2 offset relative to 3D are observed consistently across the sampled sightlines; we will make these details explicit in the revised manuscript. Multiple independent cluster realizations are not available in the present study. revision: yes

Circularity Check

0 steps flagged

No circularity: results obtained from direct comparison against external simulation benchmark

full rationale

The paper's central comparison between non-thermal pressure correction and effective-mass terms is performed by applying both methods to 3D radial profiles and projected sightlines extracted from a numerical Virgo replica. These outputs serve as an independent external benchmark; the reported radial growth (few percent to ~40%) and projection effects are measured quantities rather than quantities fitted or defined in terms of the target result. No self-citations, ansatzes, or uniqueness theorems are invoked in the provided text to justify the methods or the difference between them. The derivation chain therefore remains self-contained against the simulation data.

Axiom & Free-Parameter Ledger

0 free parameters · 2 axioms · 0 invented entities

The paper's conclusions rest on the validity of the numerical simulation as a proxy for real clusters and the applicability of the two correction formalisms without additional assumptions about sphericity or other effects.

axioms (2)
  • domain assumption Hydrostatic equilibrium holds in the simulated cluster except for the non-thermal motions being corrected.
    The corrections are applied on top of the standard hydrostatic assumption.
  • domain assumption The simulation provides accurate 3D profiles of thermal and non-thermal pressures and velocities.
    Used to compute the corrections in 3D and projections.

pith-pipeline@v0.9.1-grok · 5829 in / 1427 out tokens · 51565 ms · 2026-07-02T07:21:13.045533+00:00 · methodology

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Reference graph

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