XRISM ICM Velocity Measurements

• The paper presents XRISM's precise measurement of ICM velocities using spectral line shifts and broadening to constrain gas dynamics in galaxy clusters.
• It details methodologies that leverage high-resolution microcalorimeters to distinguish bulk and turbulent motions, achieving velocity uncertainties of tens of km/s.
• The results have significant implications for correcting hydrostatic mass bias and refining feedback models in cluster plasma physics.

The measurement of intracluster medium (ICM) velocities using XRISM—an X-ray observatory with high-spectral-resolution microcalorimeters—constitutes a cornerstone in the current effort to directly probe the dynamical and thermodynamic state of galaxy clusters. Such measurements enable precise determination of both bulk and turbulent gas motions, essential for constraining non-thermal pressure, hydrostatic mass bias, merger and accretion history, feedback mechanisms, and the microphysics of the hot plasma. This article reviews key theoretical frameworks, simulation predictions, measurement approaches, early XRISM results, and their cosmological and astrophysical significance, following the progression from measurement methodology through feedback, thermal support, dynamical state, and implications for cosmology.

1. Measurement Techniques and Instrumental Approaches

ICM velocity diagnostics, as implemented with XRISM, utilize the instrument’s capability to resolve X-ray emission lines—most notably, the Fe XXV Heα and Fe XXVI Lyα complexes—around 6.7–6.9 keV. The methodologies include:

• X-ray Spectral Line Shifts and Broadening: XRISM’s Resolve instrument measures Doppler shifts (bulk velocities) and line broadening (velocity dispersion) with an energy resolution of ~5–7 eV. The observed shift ΔE of a line centroid is linked to the line-of-sight velocity $v_{bulk}$ through

$\Delta E = E_{line} \frac{v_{bulk}}{c}$

while the measured line width (after deconvolution of the instrumental response) is

$W_{obs}^2 = W_{therm}^2 + W_{turb}^2 + W_{inst}^2$

where

$W_{turb} = \frac{\nu_0}{c} \sigma_{v,\parallel}$

and $W_{therm}$ is the thermal component, dependent on plasma temperature and ionic mass.

• Energy Scale Calibration: For XMM-Newton/EPIC-pn or Chandra data, energy calibration techniques using instrumental fluorescent lines (notably Cu Kα) have reduced systematic velocity uncertainties to $\sim$100–150 km/s (Sanders et al., 2019, Gatuzz et al., 2023, Gatuzz et al., 2022). XRISM leverages sub-eV energy resolution to routinely reach velocity uncertainties of tens of km/s, limited primarily by photon statistics and gain calibration.
• Kinematic Sunyaev–Zel’dovich (kSZ) Effect (Complementary): The CMB temperature decrement induced by gas bulk motion probes the mass-weighted line-of-sight velocity via

$$\Delta T_{CMB}/T_{CMB} = -\frac{\sigma_T}{c}\int n_e v_{pec,r} dr$$

while X-ray spectroscopy, by targeting high-density central regions, is more sensitive to local and turbulent velocities (Dolag et al., 2012).

• Indirect Probes:
  • Resonant scattering suppression of optically thick lines (e.g., Fe XXV Heα) (Simionescu et al., 2019).
  • Surface brightness fluctuation power spectra related to turbulence amplitude via $(\delta\rho/\rho)_k \approx \eta (v_k/c_s)$ (Heinrich et al., 26 Jan 2024, Simionescu et al., 2019).
  • Velocity structure functions (VSF) to probe spatial scaling of turbulence, typically of the form

  $$\mathrm{VSF}(r) = \langle |v(\mathbf{x}+r) - v(\mathbf{x})| \rangle$$

  driving constraints on driving and dissipation scales (Gatuzz et al., 2023, Sotira et al., 9 Oct 2024).

2. Simulation Predictions and Model Comparisons

Simulation work, performed both in large cosmological volumes and in high-resolution idealized cluster setups, underpins the interpretation and predicted range of ICM velocities:

• Velocity Distributions: In relaxed clusters, typical ICM 1D velocity dispersions are predicted at $\sim$150–250 km/s (cores), with $\sim$220–300 km/s in merging/unrelaxed systems (Dolag et al., 2012, Truong et al., 2023, Heinrich et al., 26 Jan 2024). The Maxwellian form

$$P(v_{pec}) = A_0 v_{pec}^2 \exp\left(-\frac{v_{pec}^2}{2\sigma_v^2}\right)$$

describes the peculiar motions, with $\sigma_v$ environment-dependent,

$$\sigma_v(\delta_{20\,\mathrm{Mpc}}) = 185\,\mathrm{km/s}\cdot\exp(\delta_{20\,\mathrm{Mpc}}/10)$$

• Turbulent Pressure Support: For clusters’ inner regions, simulations predict a kinetic-to-total pressure fraction of $4-10\%$ in relaxed systems and upward of $10–30\%$ at large radii or in mergers (Truong et al., 2023, Dolag et al., 2012, Heinrich et al., 26 Jan 2024). However, state-of-the-art cosmological simulations (TNG-Cluster, Three Hundred/Gadget-X, GIZMO-SIMBA) systematically overpredict cool-core velocity dispersions and kinetic pressure (by factors of $1.5–1.7$ and $2–3$ respectively) relative to XRISM and Hitomi (Collaboration et al., 7 Oct 2025).

• Baryonic Physics and Feedback:

  • Baryonic processes (cooling, star formation, AGN, etc.) cause the core ICM to “slosh” and drive additional scatter (up to $\sim$50\% for small apertures) in measured velocities, especially in massive systems (Dolag et al., 2012).
  • AGN feedback is a dominant source of turbulent and bulk heating in cores, but the predicted velocity dispersion and kinetic support are higher in simulations than observed, suggesting that feedback models may be excessively “ejective” in their impact (Collaboration et al., 7 Oct 2025).
  • SMBH feedback in simulations produces local, anisotropic high-velocity outflows up to several $\times 10^3$ km/s, although these deeply affect only a small fraction of the gas and are hard to detect in integrated spectra (Truong et al., 2023).
• Rotation: Axisymmetric and composite-polytropic models permit non-negligible rotational support in the ICM, with peak speeds $300-600$ km/s predicted. XRISM will be able to recover $55–70\%$ of the hydrostatic mass bias due to rotation via direct velocity measurements (Bartalesi et al., 2023, Bartalesi et al., 17 Mar 2025).

3. Empirical Findings from XRISM and Precursor Observations

Early XRISM results, supported by calibration advances in XMM-Newton and Chandra, establish several robust patterns:

• Low Bulk Motions and Velocity Dispersion: XRISM measurements in cluster cores (e.g., Abell 2029, Perseus, Virgo, Centaurus, Ophiuchus) consistently yield:
  • LOS bulk velocities close to zero relative to BCGs, e.g., $|v_{bulk}| < 100$ km/s (Abell 2029) (Collaboration, 9 Jan 2025).
  • Turbulent velocity dispersions $\sim$150–200 km/s in relaxed cores and up to $230–250$ km/s in mildly disturbed or sloshing systems (Coma, A2319, A1914, and mergers) (Collaboration, 9 Jan 2025, Collaboration et al., 29 Apr 2025, Collaboration et al., 7 Aug 2025, Heinrich et al., 23 Sep 2025).
• Nonthermal Pressure Fractions: Subsonic turbulence is universal, with kinetic-to-total pressure ratios of $2–4\%$ at $r\lesssim180$ kpc (cool cores), e.g.,

$P_{NT}/P_{tot} = M_{3D}^2/(M_{3D}^2+3/\gamma)$

with $M_{3D} \simeq 0.21$ for $c_s \sim 1350$ km/s and $\sigma_v \sim 170$ km/s (Abell 2029) (Collaboration, 9 Jan 2025, Collaboration et al., 29 Apr 2025, Collaboration et al., 7 Oct 2025).

• Merger Dynamics and Outflows:
  • XRISM Resolve can directly identify distinct components in merging clusters, e.g., in Abell 1914, two ICM components are offset by $\sim$1000 km/s with individual $\sigma_v \sim 200$ km/s, creating a “yin-yang” spatial velocity pattern (Heinrich et al., 23 Sep 2025).
  • Bulk velocity differences between cluster gas and galaxies can reach several hundred km/s (e.g., Coma: $\Delta v \sim 450–730$ km/s), with line profiles often requiring multiple kinematic components for adequate modeling (Collaboration et al., 29 Apr 2025).
• Turbulence, Sloshing, and Feedback:
  • In merging or sloshing clusters (A2319, Coma, A1914), regions affected by cold fronts or sloshing often display enhanced velocity dispersion (up to $400$ km/s), with spatially resolved maps revealing local velocity gradients of order $200–400$ km/s (Collaboration et al., 7 Aug 2025, Heinrich et al., 23 Sep 2025).
  • XRISM is sensitive to local turbulence driven by AGN, mergers, or sloshing, but small-scale turbulence often remains limited—even in “stormy” clusters, most turbulent energy is at large scales and total pressure support from random motions remains modest (few percent) (Collaboration et al., 29 Apr 2025, Sotira et al., 9 Oct 2024).

4. Implications for Cluster Physics, Plasma Microphysics, and Mass Estimates

The direct measurement of ICM velocities with XRISM has broad ramifications:

• Hydrostatic Mass Bias: Nonthermal pressure from turbulence, if unaccounted for, leads to systematic mass underestimates in hydrostatic equilibrium calculations. XRISM enables correction for the fraction due to rotation or turbulence—residual bias can be brought below $3\%$ in some models after measuring the LOS rotational speed (Bartalesi et al., 2023, Bartalesi et al., 17 Mar 2025).
• Turbulent Heating and Mixing: Measured velocity dispersions ($\sim$170 km/s) in relaxed clusters are insufficient to offset radiative cooling by turbulent dissipation alone (Collaboration, 9 Jan 2025, Soker, 29 Jan 2025), but may drive efficient mixing of AGN-shocked gas, which delivers heat over $\sim$10 kpc during the local cooling time, thus indirectly mitigating rapid cooling (Soker, 29 Jan 2025).
• Turbulence and Heating Mechanisms: Velocity structure functions (VSF) and power spectrum analyses show turbulence is injected on $10–20$ kpc scales in Virgo, for instance, and persists on dissipation timescales longer than the AGN jet cycle, pointing to the need for additional heating mechanisms in cluster cores (Gatuzz et al., 2023, Sotira et al., 9 Oct 2024).
• Plasma Microphysics: Constraints on ICM viscosity—from comparison of observed density fluctuation spectra and simulations—show ICM viscosity is suppressed by at least a factor of $8$ compared to Spitzer values, affirming the collisionless, high-$\beta$ plasma regime (Heinrich et al., 26 Jan 2024).

5. Current Challenges and Theoretical Implications

A number of theoretical issues are raised by XRISM measurements:

• Discrepant Turbulent Levels: In cool cores, velocity dispersions and kinetic support are systematically below simulation medians (by a factor $1.5-1.7$, or $2.2\%$ observed kinetic fraction vs $5-6.5\%$ predicted), suggesting current feedback models (SMBH, AGN) are too “ejective”—injecting excessive turbulence and bulk motion in simulated cluster cores (Collaboration et al., 7 Oct 2025).
• Suppression/Interruption of Small-Scale Turbulence: In some merging clusters (Coma), the combination of high bulk velocity differences and narrow line widths cannot be reconciled with a Kolmogorov cascade, instead requiring a steeper velocity power spectrum, interpreted as large dissipation scales ($\gtrsim 240$ kpc) or a transient post-merger state prior to cascade completion (Collaboration et al., 29 Apr 2025).
• Multi-Component and Non-Gaussian Line Profiles: Mergers with significant line-of-sight projection (A1914) or internal substructure yield spectra requiring two-component fits, each with modest $\sigma_v$ but offset by $\sim$1000 km/s—highlighting the necessity of high spectral resolution for disentangling complex kinematics (Heinrich et al., 23 Sep 2025, Biffi et al., 2022).

6. Future Prospects, Observational Needs, and Model Refinement

• Expanded Cluster Samples and Radial Profiles: Systematic XRISM surveys, especially targeting non-cool-core and dynamically disturbed systems, will be critical for clarifying if current discrepancies in the gravity-dominated ICM regime are systematic and for tightly constraining the evolution of turbulence and feedback at various radii (Collaboration et al., 7 Oct 2025).
• Spatially Resolved Measurements: Mapping velocity dispersion and VSF profiles as a function of clustercentric radius, and distinguishing between gas phases, will directly inform the interplay of AGN feedback, sloshing, and merger-driven turbulence (Collaboration et al., 7 Aug 2025, Sotira et al., 9 Oct 2024).
• Model Improvements: Simulations must incorporate or better constrain the roles of less “ejective” feedback, plasma microinstabilities, cosmic ray pressure, and anisotropic transport, to match the observed low turbulence and nonthermal support in cluster cores (Collaboration et al., 7 Oct 2025, Bartalesi et al., 2023).
• Synergies With SZ and Multiwavelength Probes: Joint X-ray and kSZ, radio (halo/relic), and optical redshift mapping will provide a comprehensive view of bulk flows, turbulent cascade, and mode coupling in the ICM (Heinrich et al., 26 Jan 2024, Simionescu et al., 2019). Future high-resolution SZ observations (e.g., AtLAST) are required to spatially resolve kSZ signals comparable to X-ray constraints.

7. Summary Table: Empirical XRISM Velocity Results and Selected Simulation Predictions

Cluster/State	XRISM/Hitomi σ_v (km/s)	Kinetic Fraction (%)	Note
Abell 2029 (core)	169 ± 10	2.6	Relaxed, low turbulence
Perseus (core)	164 ± 10 (Hitomi)	4–6	Mild sloshing, AGN feedback
Coma (central)	208 ± 12	3.1	Merging, high bulk flows
Abell 2319 (core)	230–250 (local 400)	up to ∼10 (est.)	Sloshing/turbulence, cold front
Virgo (core)	~100–200	1	Very relaxed
Simulations (cool core)	250–350 (predicted)	5–7 (median)	Feedback possibly too strong
Simulations (merger)	250–400	4–10 (core), up to 30 outer	Range depends on dynamics

This compilation draws on (Collaboration, 9 Jan 2025, Collaboration et al., 29 Apr 2025, Collaboration et al., 7 Oct 2025, Truong et al., 2023, Collaboration et al., 7 Aug 2025, Heinrich et al., 23 Sep 2025, Dolag et al., 2012) and associated simulation/empirical literature.

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Overall, XRISM measurements have established a new empirical regime for ICM velocity structure, revealing that core turbulence and nonthermal pressure are lower and more spatially/temporally variable than most contemporary feedback models predict. This directly advances mass calibration, cluster physics, and plasma microphysics and is expected to trigger further refinement of feedback prescriptions and models of energy transport and cascade in the hot cosmic baryonic medium.