Towards mapping turbulence in the intra-cluster medium

Abstract

Context. X-ray observations of galaxy clusters provide insights into the nature of gaseous turbulent motions, their physical scales, and the fundamental processes to which they are related. 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. Aims. We propose a different and complementary approach to repeating numerical simulations for the computation of sample variance (i.e. Monte-Carlo sampling) by introducing new analytical developments for lines diagnosis. Methods. We considered 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 four-term correlation of Fourier coefficients, we derived generic expressions for the sample mean and variance of line centroid shift, line broadening, and projected velocity structure function. We performed a numerical validation based on Monte-Carlo simulations for two popular models of gas emissivity based on the β-model. Results. 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 (Advanced Telescope for High-ENergy Astrophysics/X-ray Integral Field Unit) and XRISM/Resolve (X-ray Imaging and Spectroscopy Mission) instruments forecasts the potential of sensitive, spatially-resolved spectroscopy to probe the inertial range of turbulent velocity cascades in a Coma-like galaxy cluster. Conclusions. The formulas provided are of generic relevance and can be implemented in forecasts for upcoming or current X-ray instrumentation and observing programmes.

Dynamical properties and detectability of the magneto-thermal instability in the intracluster medium

“…So we chose the simplest model, namely the root-mean square velocity along a single line of sight (Eq. ( 5) from Clerc et al 2019, which is identical to Eq. (A.9) in Zhuravleva et al 2012), to infer the decrease in signal due to fluctuation-cancellation along the line of sight.…”

“…2. Hints about the behaviour of the root-mean square and dispersion of the emission-weighted velocity and of the second-order velocity structure function after integration along the line of sight can be gained from previous works by Churazov et al (2012), Zhuravleva et al (2012), ZuHone et al (2016, Clerc et al (2019), and Mohapatra et al (2022). Many different models have been developed, accounting for the twodimensionality of the observable fields or the variation of the A24, page 7 of 21 background thermodynamic fields over the field of view for example.…”

“…We therefore use the same toy-model Eq. ( 5) from Clerc et al (2019) to anticipate the loss of signal due to the cancellation of fluctuations along the line of sight for both the emissivity-weighted velocity field and the spectroscopic temperature fluctuations. These forecasts are shown as dotted lines in Fig.…”

The Athena space X‐ray observatory and the astrophysics of hot plasma†

“…As shown in Figure , Athena with its unprecedented collecting area and combination of high spectral and angular resolution will enable the study of how the baryonic gas accretes and evolves in the dark matter potential wells by measuring motions and turbulence in the intracluster medium (Bulbul et al ; Clerc et al ; Cucchetti et al ; Roncarelli et al ). Athena will do so by resolving the accreting region both spatially and spectroscopically, probing the physical state of the X‐ray‐emitting plasma (Ettori et al , and references therein).…”

Constraining the origin and models of chemical enrichment in galaxy clusters using theAthenaX-IFU

“…Other astrophysical questions on the ICM, specifically its level and distribution of turbulence (e.g. Roncarelli et al 2018;Clerc et al 2019;Cucchetti et al 2019), will also be explored by the X-IFU in unprecedented detail.…”