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Register a new userTowards mapping turbulence in the intra-cluster medium -- I. Sample variance in spatially-resolved X-ray line diagnostics
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X-ray observations of galaxy clusters provide insights on the nature of gaseous turbulent motions, their physical scales and on the fundamental processes they are related to. Spatially-resolved, high-resolution spectral measurements of X-ray emission lines provide diagnostics on the nature of turbulent motions in emitting atmospheres. Since they are acting on scales comparable to the size of the objects, the uncertainty on these physical parameters is limited by the number of observational measurements, through sample variance. We propose a different and complementary approach for the computation of sample variance to repeating numerical simulations (i.e. Monte-Carlo sampling) by introducing new analytical developments for lines diagnosis. We consider the model of a turbulent gas cloud, consisting in isotropic and uniform turbulence described by a universal Kolmogorov power-spectrum with random amplitudes and phases in an optically thin medium. Following a simple prescription for the 4-term correlation of Fourier coefficients, we derive generic expressions for the sample mean and variance of line centroid shift, line broadening and projected velocity structure function. We perform a numerical validation based on Monte-Carlo simulations for two popular models of gas emissivity based on the beta-model. Generic expressions for the sample variance of line centroid shifts and broadening in arbitrary apertures are derived and match the simulations within their range of applicability. Generic expressions for the mean and variance of the structure function are provided and verified against simulations. An application to the Athena/X-IFU and XRISM/Resolve instruments forecasts the potential of sensitive, spatially-resolved spectroscopy to probe the inertial range of turbulent velocity cascades in a Coma-like galaxy cluster.
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X-ray observations of the hot gas filling the intra-cluster medium provide a wealth of information on the dynamics of clusters of galaxies. The global equilibrium of the ICM is believed to be partially ensured by non-thermal pressure support, notably the dissipation of energy through turbulent motions. Accurate mapping of turbulence using X-ray emission lines is challenging due to the lack of spatially-resolved spectroscopy. Only future instruments such as the X-ray Integral Field Unit (X-IFU) on Athena will have the spatial and spectral resolution to quantitatively investigate the ICM turbulence at all scales. Powerful diagnostics for these studies are line shift and the line broadening maps, and the second-order structure function. When estimating these quantities, instruments will be limited by uncertainties of their measurements, and by the sample variance (aka cosmic variance) of the observation. We extend here the formalism started in our companion paper I to include the effect of statistical uncertainties in the estimation of these line diagnostics, in particular for structure functions. We demonstrate that statistics contribute to the total variance through different terms, which depend on the geometry of the detector, the spatial binning and the nature of the turbulent field. These terms are important when probing the small scales of the turbulence. An application of these equations is performed for the X-IFU, using synthetic turbulent velocity maps of a Coma-like cluster of galaxies. Results are in excellent agreement with the formulas both for the structure function estimation (<3%) and its variance (<10%). The expressions derived here and in paper I are generic, and ensure an estimation of the total errors in any X-ray measurement of turbulent structure functions. They also open the way for optimisations in the upcoming instrumentation and in observational strategies.
FEARLESS (Fluid mEchanics with Adaptively Refined Large Eddy SimulationS) is a new numerical scheme arising from the combined use of subgrid scale (SGS) model for turbulence at the unresolved length scales and adaptive mesh refinement (AMR) for resolving the large scales. This tool is especially suitable for the study of turbulent flows in strongly clumped media. In this contribution, the main features of FEARLESS are briefly outlined. We then summarize the main results of FEARLESS cosmological simulations of galaxy cluster evolution. In clusters, the production of turbulence is closely correlated with merger events; for minor mergers, we find that turbulent dissipation affects the cluster energy budget only locally. The level of entropy in the cluster core is enhanced in FEARLESS simulations, in accord with a better modeling of the unresolved flow, and with its feedback on the resolved mixing in the ICM.
We present results from a joint X-ray/Sunyaev-Zeldovich modeling of the intra-cluster gas using XMM-Newton and APEX-SZ imaging data. The goal is to study the physical properties of the intra-cluster gas with a non-parametric de-projection method that is, aside from the assumption of spherical symmetry, free from modeling bias. We demonstrate a decrease of gas temperature in the cluster outskirts, and also measure the gas entropy profile, both of which are obtained for the first time independently of X-ray spectroscopy, using Sunyaev-Zeldovich and X-ray imaging data. The contribution of the APEX-SZ systematic uncertainties in measuring the gas temperature at large radii is shown to be small compared to the XMM-Newton and Chandra systematic spectroscopic errors.
Astro-H will be able for the first time to map gas velocities and detect turbulence in galaxy clusters. One of the best targets for turbulence studies is the Coma cluster, due to its proximity, absence of a cool core, and lack of a central active galactic nucleus. To determine what constraints Astro-H will be able to place on the Coma velocity field, we construct simulated maps of the projected gas velocity and compute the second-order structure function, an analog of the velocity power spectrum. We vary the injection scale, dissipation scale, slope, and normalization of the turbulent power spectrum, and apply measurement errors and finite sampling to the velocity field. We find that even with sparse coverage of the cluster, Astro-H will be able to measure the Mach number and the injection scale of the turbulent power spectrum--the quantities determining the energy flux down the turbulent cascade and the diffusion rate for everything that is advected by the gas (metals, cosmic rays, etc.). Astro-H will not be sensitive to the dissipation scale or the slope of the power spectrum in its inertial range, unless they are outside physically motivated intervals. We give the expected confidence intervals for the injection scale and the normalization of the power spectrum for a number of possible pointing configurations, combining the structure function and velocity dispersion data. Importantly, we also determine that measurement errors on the line shift will bias the velocity structure function upward, and show how to correct this bias.
In this work, we investigate the relation between the radially-resolved thermodynamic quantities of the intracluster medium in the X-COP cluster sample, aiming to assess the stratification properties of the ICM. We model the relations between radius, gas temperature, density and pressure using a combination of power-laws, also evaluating the intrinsic scatter in these relations. We show that the gas pressure is remarkably well correlated to the density, with very small scatter. Also, the temperature correlates with gas density with similar scatter. The slopes of these relations have values that show a clear transition from the inner cluster regions to the outskirts. This transition occurs at the radius $r_t = 0.19(pm0.04)R_{500}$ and electron density $n_t = (1.91pm0.21)cdot10^{-3} cm^{-3} E^2 (z)$. We find that above 0.2 $R_{500}$ the radial thermodynamic profiles are accurately reproduced by a well defined and physically motivated framework, where the dark matter follows the NFW potential and the gas is represented by a polytropic equation of state. By modeling the gas temperature dependence upon both the gas density and radius, we propose a new method to reconstruct the hydrostatic mass profile based only on the quite inexpensive measurement of the gas density profile.
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