Gas rotation and turbulence in the galaxy cluster Abell 2029

TL;DR

The paper presents an axisymmetric, equilibrium model for Abell 2029 that jointly fits XRISM/Resolve high-resolution spectra with XMM-Planck SZ data to quantify rotation and turbulent pressure in the ICM. By adopting a composite-polytropic gas distribution in a spherically symmetric NFW halo and forward-modeling PSF and metallicity weighting, the authors derive robust constraints on the rotation profile, turbulence level, and the hydrostatic mass bias, finding a turbulence-to-total-pressure ratio around $2\%$ and a rotation-to-dispersion ratio peaking near $0.15$ at intermediate radii. The joint X-ray/SZ analysis yields a hydrostatic-to-total mass ratio of $\approx 0.97$ at $r_{2500}$, indicating near-hydrostatic support in the inner regions, while Monte Carlo XRISM-like spectral simulations validate the forward-modeling approach and the inferred dynamical state. Overall, the findings support a scenario where non-thermal pressure support in A2029 is modest and consistent with expectations from cosmological simulations, highlighting the importance of accurate PSF handling in high-resolution cluster kinematics.

Abstract

We constrain the rotation and turbulent support of the intracluster medium (ICM) in Abell 2029 (A2029), using dynamical equilibrium models and a combination of state-of-the-art X-ray datasets. We reduce and conduct the spectral analysis of the XRISM/Resolve data. The rotating, turbulent ICM in the model has a composite polytropic distribution in equilibrium in a spherically-symmetric, cosmologically motivated dark halo. The profile of rotation velocity and the distribution of turbulent velocity dispersion are described with flexible functional forms, consistent with the properties of synthetic clusters formed in cosmological simulations. Adopting realistic profiles for the metallicity distribution of the ICM and for the point spread function of XRISM and XMM-Newton, we tune via a Markov chain Monte Carlo algorithm the observables of the intrinsic quantities of the plasma in our model to reproduce the radial profiles of the thermodynamic quantities as derived from the spectral analysis of the XMM-Newton and Planck maps and the measurements of the line-of-sight (LOS) non-thermal velocity dispersion and redshift (probing the LOS velocity) in the XRISM pointings. Our model accurately reproduces the measurements of redshift and LOS non-thermal velocity dispersion, as further demonstrated by simulating and analyzing synthetic counterparts of the XRISM spectra, in accordance with the posterior distribution of our model. We find turbulence-to-total pressure ratio $\approx$ 2% across the (0 - 650) kpc radial range, and a rotation-to-dispersion velocity ratio peaking at 0.15 between 200 - 600 kpc. The hydrostatic-to-total mass ratio is $\approx$ 0.97 at r2500, the radius enclosing an overdensity of 2500 times the average value.

Figures (5)

• Figure 1: Profiles (upper panel) and residuals (lower panel) of the brightness ($\mathcal{N}$; left-top panel), temperature ($T$; right-top panel), redshift ($z_{\rm{u}}$; left-middle panel), LOS non-thermal velocity dispersion ($\sigma_\mathrm{v}$; right-middle panel) and of SZ-derived thermal pressure ($P_\mathrm{SZ}$; bottom panel). The observational measurements are the black dots with the horizontal and vertical error bars indicating the bin extents and the $1\sigma$ statistical errors, $\sigma_{\rm{stat}}$, respectively. The cyan vertical error bars indicate the total errors, $\sqrt{1 + \epsilon^2} \sigma_{\rm{stat}}$ (see Sect. \ref{['sec:stat']}, for details). The corresponding median values computed from the model and the corresponding median measurements from the mock spectra (see Sect. \ref{['sec:simulation']}, for details) are the blue and red dashed lines, respectively, while the shaded rectangles span vertically the 16th -- 84th percentile intervals of the mock measurements. Both the uncertainty in the parameter values from the posterior and the Poisson noise in the mock spectra contribute to the error of the mock measurements, which is estimated as follows. We start with 100 measurements of the quantity $W_m$, extracted from each mock spectrum. We randomly generate 100 values for each mock measurement according to the corresponding error. From the distribution consisting of all the values generated for every mock datum at a given bin, we measure the 16th -- 84th percentile interval.
• Figure 2: Squared rotation-velocity-to-velocity-dispersion ratio, turbulent-to-total pressure ratio (left panel), rotation velocity and turbulent velocity dispersion (right panel) as a function of the cylindrical radius. We overplot the median and average profiles of turbulence and rotation measured in simulated clusters by angelinelli20 and BALDI17 (dark red and dark blue regions; see text, for details), respectively. The dashed lines indicate the median profiles; the shaded regions represent the 16th -- 84th percentile interval profiles. The angelinelli20 and BALDI17 profiles are obtained as in Figs. 2 of Bartalesi25 and 3 of Bartalesi24, respectively. The 16th -- 84th percentile interval of BALDI17 profile refers to the uncertainty in the posterior distribution of our model parameters.
• Figure 3:
• Figure 4: Profile of the metallicity (blue line) as a function of the projected radius $\hat{R}$ (the profile in the extrapolation range is dashed). The Ghirardini19 measurements are the black dots, with vertical and horizonthal error bars corresponding to the statistical uncertainties in the spectral analyses and to the extent of the radial bins. The XRISM/Resolve pointings extend from the center out to the vertical line.
• Figure 5: Marginal (diagonal panels) and two-parameters joint (off-diagonal panels) distributions of all the free parameters in the MCMC run ($\gamma'_{\rm{IN}}$, $\gamma'_{\rm{OUT}}$, $\nu$, $T_{\rm{equiv,\star}}$, $R_{\star}$, $M_{200}$, $\ln c_{200}$, $u_{\rm{peak}}$, $R_{\rm{peak}}$, $\log \xi$, $\alpha_{\rm{inf}}$, $\alpha_0$, $R_{\rm{CEN}}$, $\gamma'_{\rm{CEN}}$, $\eta$, $\log \epsilon_{\rm{N}}$, $\log \epsilon_{\rm{T}}$ and $\log \epsilon_{\rm{SZ}}$; see Sect. \ref{['sec:stat']}, for details). In each diagonal panel, the black curve and the orange histogram are the marginal prior and posterior, respectively; the light-orange vertical band is the 16th-84th percentile interval of the marginal posterior. In each off-diagonal panel, the dark-orange and light-orange regions, enclosed by the blue lines, define the 68% and 90% credible regions of the joint posteriors, respectively.