Evidence of galaxy cluster rotation and intrahalo gas motions in the cosmic microwave background

The gist The authors report robust evidence (3.6σ) for a dipolar rkSZ effect in CMB temperature maps centered on nearby galaxy clusters, which is attributed to the rotational kSZ effect produced by the Doppler boosting of CMB photons scattering off rotating electrons within the ICM

Evidence and Detection

The study presents the first robust observational evidence for the rkSZ effect, detecting a dipolar signature aligned with each cluster's rotation direction at 99.98% confidence (3.6σ) The detection was achieved by combining CMB intensity and polarization measurements from Planck with spectroscopic member-galaxy redshifts from the Sloan Digital Sky Survey in a sample of 25 X-ray cross-matched, low-redshift galaxy clusters The amplitude and shape of the signal are qualitatively consistent with predictions from state-of-the-art hydrodynamical simulations This measurement establishes a new tool with which to probe the dynamical state of galaxy clusters using CMB data

Theoretical Framework

The kSZ effect is sourced by the Doppler boosting of CMB photons scattering off electrons with non-zero line-of-sight bulk velocities, making it a unique probe of the momentum of the gas within clusters The rkSZ effect produces a dipolar pattern that is aligned with the angular momentum, i.e., the rotation direction, of the intracluster medium (ICM) Simulations predict rkSZ dipole amplitudes of order ∼ 10−100 µK in galaxy clusters depending on properties like cluster mass and dynamical state The kSZ-induced relative CMB temperature shift is expressed as a line-of-sight integral involving the peculiar velocity of the electrons along the line-of-sight A cluster rotating about an axis not parallel to the line-of-sight generates a dipole-like kSZ signal, as one side moves toward the observer and the other recedes

Methodology and Data Processing

To isolate the small rkSZ signal, several methodological advances were employed The internal linear combination (ILC) method, specifically Needlet ILC (NILC), was used to form a minimum-variance linear combination of single-frequency maps with unit response to the CMB blackbody SED Constrained NILC was used to “deproject,” exactly removing contributions from the non-relativistic tSZ effect The E-mode subtracted temperature map, T˜, was constructed in harmonic space by subtracting the primary CMB contribution using observed E-mode autopower and temperature-E-mode cross-power spectra This procedure reduces the variance due to primary CMB fluctuations on scales 100 ≲l≲ 1000 The final analysis involves constructing a galaxy cluster catalog with estimated rotation directions using spectroscopic redshifts of member galaxies, and then performing an oriented stack on the filtered NILC T˜ map centered on each cluster's X-ray position

Signal Extraction and Robustness Tests

The significance of the measurement is enhanced by several new methodological improvements The analysis involves constructing a weighted-average stack using a signal-to-noise weight defined as w = M500c ∆zmax dip Nmem σ2 T˜(M500c, z) The measured dipole amplitude exceeds 99.98% of the random realizations, indicating strong evidence (3.6σ) of cluster rotation Robustness tests showed that the dipole signal cannot be attributed to Doppler boosting of dust emission because repeating the stack on a component-separated map excluding the 545 GHz data or stacking on the harmonic-space-filtered 545 GHz map yields no dipole signal The results are consistent with hydrodynamical simulations, which predict a dipole amplitude (∼ 25 µK) and profile shape broadly consistent with measurements

Conclusion and Future Directions

The study concludes that the statistically significant dipole in the oriented stack is due to the kSZ effect sourced by internal gas motions within galaxy clusters In the near future, applying these techniques to larger cluster samples and higher-resolution CMB maps will enable precise characterization of the dynamical state of the gas within galaxy clusters These improvements will allow comparisons across clusters split by dynamical state, helping distinguish coherent rotation from merger-driven flows This will enable precise constraints on rotational support in the ICM, as may play a role in the hydrostatic bias in cluster mass estimates and other important aspects of ICM physics The data products and analysis pipeline will be released as part of the aardvarkSZ package

Table I Properties

Table I lists properties of the 25 X-ray cross-matched clusters used in this work, including M500c, R500c, Nmem, and the final weight assigned to each cluster in the fiducial stack Table B 1 provides detailed cluster properties such as M500c and R500c for the sample used in this work

Appendix C Profile Theory

The theoretical model for the beam-convolved rotational kSZ signal is derived using a solid-body rotation model, resulting in the expression TˆrkSZ(R) which depends on the projected electron number density profile Fe(R) and Bessel functions The marginalized posterior for the amplitude of this profile is ArkSZ = 1.05 ± 0.32 at the 68% two-tailed confidence limit, corresponding to a 3.3σ preference for a non-zero amplitude This result is not interpreted as a constraint on the physical rkSZ amplitude because the rotational velocity is fixed to produce a dipole of order 25 µK The solid-body rotation model fits the azimuthally-averaged profile well, with a probability-to-exceed (PTE) of 0.51

Figure Analysis

Figure 1 shows the oriented and weighted stack of filtered Planck CMB temperature data on 25 galaxy clusters, where a dipole signal is clearly visible along the expected rotation direction Figure 2 shows the azimuthally-averaged rkSZ profile derived from the weighted stack of 25 clusters, finding significant evidence for a non-zero amplitude, ArkSZ = 1.05 ± 0.32 Figure 6 compares the estimated dipole for different blackbody temperature maps, demonstrating that the significance increases after applying physically motivated procedures designed to extract the rkSZ signal Figure 12 shows the impact of varying weights in the oriented stack, indicating that weighting by M500c∆zmax dip leads to significant (3.7σ) evidence of a dipole Figure 13 shows that the dipolar signal presented in the Letter is not an artifact of the pixel-space filter

Figure 10 Rotation Estimate

Figure 10 shows the difference in the average redshift between left and right hemispheres as a function of trial rotation angle, with a significant dipole aligned with the estimated rotation axis The Pearson correlation coefficient r between the sinusoidal template and the measured ∆zdip(∆θ) is used to estimate fidelity, discarding clusters where r ≤ 0.

1. The AI system can now perform robust detection of rotational kinematic Sunyaev-Zel’dovich (rkSZ) effects by implementing a robust observational evidence pipeline, as reported by the authors: We detect a dipolar rkSZ signature aligned with the estimated rotation direction of each cluster, ruling out a chance fluctuation at 99.98% confidence (3.6σ).

2. The system can accurately characterize the dynamical state of galaxy clusters using CMB data by utilizing advanced component separation techniques, specifically internal linear combination (ILC) method and needlet ILC (NILC) to isolate the signal from primary CMB fluctuations and noise.

3. The AI system can perform parameter estimation for cluster dynamics by fitting the azimuthally-averaged rkSZ profile using a theoretical model, yielding a marginalized posterior of ArkSZ = 1.05 ± 0.32 at the 68% two-tailed confidence limit.

4. The system can quantify the impact of different analytical techniques on detection significance by comparing results from various stacking procedures: Stack on E modes reduces the significance from 3.6σ to 3.0σ, and demonstrates that the dipole in our stack is not an artifact of the pixel-space filter.

5. The system can assess the robustness of its measurements against common foregrounds by performing null tests, showing that the dipole signal cannot be attributed to Doppler boosting of dust emission by repeating the stack on maps excluding 545 GHz data.

We report the first robust evidence for the rotational kinematic Sunyaev-Zel'dovich (rkSZ) effect: the dipolar signal produced by the Thomson scattering of cosmic microwave background (CMB) photons off intracluster gas in dynamically active systems (including rotations and mergers). By combining CMB intensity and polarization measurements from the Planck satellite with spectroscopic member-galaxy redshifts from the Sloan Digital Sky Survey in a sample of 25 X-ray cross-matched, low-redshift (0.02< z< 0.09), massive (10 13.9 M 500c/M 10 14.6) galaxy clusters, we detect a dipolar rkSZ signature aligned with the estimated angular momentum of each cluster, ruling out a chance fluctuation at 99.98% confidence (3.6 σ). The significance of this measurement is enhanced by several new methodological improvements for isolating the rkSZ signal from primary CMB fluctuations and noise. The amplitude and shape of the signal are qualitatively consistent with predictions from state-of-the-art hydrodynamical simulations. These results establish a new tool with which to probe the dynamical state of galaxy clusters using CMB data.