XRISM constraints on the velocity power spectrum in the Coma cluster

TL;DR

This work introduces a simulation-based inference framework to recover the velocity fluctuation power spectrum of the intracluster medium from high-resolution X-ray spectroscopy data. By generating Gaussian-random-field velocity realizations from a parametric $P_{3D}(k)$ and forward-modeling emissivity weighting, projection, and PSF effects, the authors train a neural posterior estimator to infer $(M_{3D}, k_{inj}, \alpha)$ from XRISM data. Applied to Coma with two XRISM/Resolve pointings, the method prefers a large injection scale near a few Mpc and a total 3D Mach number $\mathcal{M}_{3D,tot} \approx 0.72$, with $\mathcal{M}_{3D,500} \approx 0.45$, while the slope remains weakly constrained due to limited scales and cosmic variance. The approach robustly accounts for observational effects and cosmic variance, offering a path to quantify non-thermal pressure and turbulence in clusters and motivating broader spatial coverage with current and upcoming X-ray instruments.

Abstract

The velocity field of intracluster gas in galaxy clusters contains key information on the virialization of infalling material, the dissipation of AGN energy into the surrounding medium, and the validity of the hydrostatic hypothesis. The statistical properties of the velocity field are characterized by its fluctuation power spectrum, which is usually expected to be well described by an injection scale and a turbulent cascade. Here we propose a simulation-based inference technique to retrieve the properties of the velocity power spectrum from X-ray micro-calorimeter data by generating simulations of Gaussian random fields from a parametric power spectrum model. We forward model the measured bulk velocities and velocity dispersions by including the most relevant observational effects (projection, emissivity weighting, PSF smearing). We then train a neural network to learn the mapping between the power spectrum parameters and the generated data vectors. Considering a three-parameter model describing turbulent energy injection on large scales and a power-law cascade, we found that two XRISM/Resolve pointings are sufficient to accurately determine the turbulent Mach number and set interesting constraints on the injection scale. Applying our method to the Coma cluster data, we obtain a model that is characterized by a large injection scale that rivals the size of the cluster ($\ell_{inj}=2.2_{-1.0}^{+2.0}$ Mpc). When this power spectrum model is integrated over the cluster scales ($0<\ell<R_{500}=1.4 $Mpc), the Mach number of the gas motions is $\mathcal{M}_{3D,500}=0.45_{-0.13}^{+0.18}$, which exceeds the value derived from the velocity dispersions only. Further observations covering a wider area are required to decrease the cosmic variance and constrain the slope of the turbulent cascade.

Figures (7)

• Figure 1: Example of fluctuation field generation. Left: Model 3D power spectrum described by an injection at $k_{inj}$ and a classical Kolmogorov cascade on smaller scales (Eq. \ref{['eq:classicalps']}). The vertical dashed line shows the position of $k_{inj}=({\rm 500 kpc})^{-1}$. Right: Slice of the real-space velocity fluctuation field along the $z$ axis generated from this power spectrum (Eq. \ref{['eq:realspacevel']}) for a velocity dispersion $\sigma_v=300$ km/s. The color code shows the velocity in km/s. The box size is 1.7 Mpc on a side.
• Figure 2: Coverage tests for the two-pointing configuration and the model defined in Eq. \ref{['eq:classicalps']}. All the panels show the median of the inferred posterior distribution as a function of the true input value. The panels show the recovery tests for the Mach number $\mathcal{M}_{3D}=\sigma_v/c_s$ (left), the slope of the turbulent cascade $\alpha$ (middle), and the logarithm of the injection wave number $k_{inj}$, in units of kpc$^{-1}$ (right). The gray dots show the results of individual simulations, whereas the color code indicates the point density inferred using a Gaussian kernel density estimator. The dotted black lines and the red dashed lines indicate the $1:1$ relation and the running median of the data points, respectively.
• Figure 3: Location of the XRISM/Resolve measurements superimposed on a XMM-Newton/EPIC surface brightness map of the Coma cluster. The white squares show the footprint of the two Resolve pointings split into four individual quadrants, with the number showing the bulk velocity of each region with respect to the cluster rest frame. The blue arrows show the positions of the two dominant galaxies NGC 4874 and NGC 4889 with their respective peculiar velocities. Figure reproduced with modifications from X25.
• Figure 4: Posterior distributions for the three-parameter model (Eq. \ref{['eq:classicalps']}) for the Coma cluster inferred from the XRISM/Resolve bulk velocity and velocity dispersion data.
• Figure 5: Goodness-of-fit tests applied to the Coma cluster XRISM/Resolve data. The left and middle panels show the comparison between the Resolve data (red data points) and the best fitting model for the VSF (left) and the velocity dispersion measurements in the four quadrants of the central pointings and the full southern pointing (middle). The blue curves represent the median of 1,000 simulations generated from the posterior distribution, whereas the blue shaded areas show the 16th to 84th percentiles of the generated mock datasets. The right-hand panel shows the cumulative distribution of test statistic value (Eq. \ref{['eq:teststat']}) for 1,000 simulations generated from the posterior, with the test statistic value obtained for the data indicated as the dotted vertical line. The dashed black line indicates the fraction of simulations with a better test statistic value than the one obtained for the data.