Mapping cluster angular momentum with the rotational kinetic Sunyaev-Zel'dovich effect
Jack Y. L. Kwok, Bernardita Ried Guachalla, William R. Coulton, Selim C. Hotinli, Emmanuel Schaan
Solid, practical optimal-estimator and forecast framework for a niche but growing observable, with a useful mass-dependent filtering insight, but forecast-only and dependent on idealized proxies.
Abstract
Galaxy clusters carry angular momentum. If the intracluster gas rotates coherently, the kinetic Sunyaev-Zel'dovich (kSZ) effect imprints a dipole on the microwave sky centered on the cluster. We show that microwave maps alone can be used to reconstruct a noisy vector field tracing the projected angular momentum of the ionized gas. We present an optimal multifrequency matched filter (MMF) that isolates the rotational kSZ (rkSZ) signal from the much larger miscentered thermal Sunyaev-Zel'dovich (tSZ) effect, cosmic microwave, and infrared background contributions, improving on both real-space oriented stacking and matched filtering of maps cleaned with full-sky multifrequency weights. For the rkSZ profile, we introduce a simple model for coherent intracluster gas rotation and validate it against TNG-Cluster and TNG300-1. The model consists of differentially rotating concentric shells with constant equatorial tangential velocity, characterized by a mass- and redshift-indepedent tangential-to-circular velocity ratio of . Using this model, we forecast single-cluster signal-to-noise (SNR) as a function of mass and redshift for Simons Observatory; cross-correlation with an external catalog of rotation proxies yields a cumulative detection SNR. For an idealized mass-limited catalog with perfectly known spin directions, the cumulative SNR of our optimal MMF reaches , , and when including all clusters above , 14.5, and 15, respectively. This work provides a practical framework for CMB measurements of intracluster gas rotation, with applications to the rotational contribution to non-thermal pressure in cluster mass calibration, as well as spin alignments and clustering biases.
AI Impact Assessments
(1 model)Core Contribution
The paper builds a practical framework for measuring coherent rotation of intracluster gas through the rotational kinetic SZ (rkSZ) dipole, using CMB maps alone. It has three parts.
1. A minimal, simulation-validated rkSZ template. Concentric solid-body shells have constant equatorial tangential velocity, with v_tan ≈ 4λ_gas·V_c,200c = 0.18 V_c. A shell–cluster spin-misalignment taper β̄(x) is calibrated on TNG-Cluster and TNG300-1, and a Battaglia gNFW electron profile is assumed. The model reproduces the integrated rkSZ statistic S within ~10% at R200c across mass bins. It also gives an analytic M^{4/3} scaling.
2. A harmonic-space vector matched filter that turns each cluster cutout into a 2D estimate of the dipole vector, i.e. a noisy projected angular-momentum field. The filter works on the imaginary part of the Fourier modes. This nulls the even-parity tSZ monopole and bulk kSZ, so only miscentering and asphericity leak in. It is extended to a mass- and redshift-dependent multifrequency matched filter (MMF) with an analytic miscentered-tSZ covariance, and to a tensor (axis-only) variant.
3. A Simons Observatory forecast using WebSky foregrounds and SO-goal noise. The main finding is a two-regime structure. The most massive clusters (≳10^14.7 Msun) are tSZ-dominated, and MMF converges to tSZ-deprojected cILC there. Most of the cumulative SNR comes from the abundant 10^13.7–10^14.7 Msun, noise-dominated population, where deprojecting the tSZ wastes about half the SNR. The idealized cumulative SNR is ≈53 (>10^14 Msun), 25 (>10^14.5) and 6 (>10^15), assuming perfect spin-direction knowledge. The tensor estimator has essentially no power.
Methodological Rigor
The estimator derivation is clean: a Lagrange-multiplier minimum-variance unbiased filter, with explicit treatment of covariance mismodeling (which does not bias the result) and a Monte-Carlo null from randomized directions that agrees with the analytic SNR. The signal model is checked against two simulation sets, with a careful extraction pipeline (appendix C) and averaging over lines of sight. The paper compares honestly with Baldi et al. and Altamura et al. It admits it cannot reconcile Altamura's quoted spin parameter. It also admits that the flat v_tan(r) misses the concave-down radial shape observed in the simulations.
Weaknesses:
Overall the design is sound, with moderate gaps in realism.
Potential Impact
For a first detection, the paper gives a ready-to-use recipe: a template, an optimal filter, and a quantitative strategy. The practical value of the mass-dependent filter insight is clear. The observation that cumulative information is dominated by modest-mass clusters, and that the bottleneck is the spin-proxy catalog rather than map noise, redirects attention toward building large spin-orientation catalogs. Examples are IFU surveys, member-galaxy kinematics and constrained-realization reconstructions. The framework could also be reused for other cluster-centered dipoles, such as the moving-lens and lensing dipoles.
Downstream science includes the rotational contribution to non-thermal pressure and the hydrostatic mass bias, spin–filament and spin–shape alignments, and halo spin bias. The impact is mostly prospective, because no detection exists and the realistic SNR is much lower than the idealized one.
Timeliness & Relevance
The paper is timely. SO is coming online, ACT and SPT data exist, and recent oriented-stacking efforts (Baxter+19, Goldstein & Hill) are limited by noise and small proxy catalogs. XRISM is probing ICM motions, and non-thermal pressure is a live issue for cluster cosmology. An optimal-filter treatment that supersedes the left-minus-right statistics addresses a real methodological gap.
Strengths
Limitations
Overall
This is a solid, well-executed methodological and forecasting paper for CMB cluster astrophysics. It is likely to be cited and used by the rkSZ detection efforts with SO, ACT and SPT. It is unlikely to be transformative beyond that niche.
Generated Oct 30, 2026
Comparison History (0)
Solid, practical optimal-estimator and forecast framework for a niche but growing observable, with a useful mass-dependent filtering insight, but forecast-only and dependent on idealized proxies.