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.
Highlights
Galaxy clusters form by accretion of matter along filaments of the cosmic web, either continuously or episodically through major and minor merger events
The most promising and efficient diagnostics are issued from spectroscopic observations of the hot intra-cluster gas, which permeates the entire volume of massive halos and emits copious amounts of X-ray light
Using numerically simulated clusters instead, Roncarelli et al (2018) performed end-to-end simulations to derive expected values of the indicators of turbulence issued from emission line measurements, postponing the calculation of sample variance to a later stage by means of multiple realisations
Summary
Galaxy clusters form by accretion of matter along filaments of the cosmic web, either continuously or episodically through major and minor merger events. Focusing mainly on X-ray emission lines extracted along a single line of sight, Inogamov & Sunyaev (2003) demonstrated that departures from Gaussian line shapes carry important indications on the nature of large-scale turbulence in the intra-cluster medium The authors extended their formula to two-dimensional diagnostics by introducing the correlation function of the projected velocity field and calculating its scaling relative to fundamental parameters such as the turbulent injection and dissipation scales. Instrumental characteristics and signal-to-noise considerations, related for example to the exposure time or the energy resolution, are deliberately excluded and addressed in a separate work (Cucchetti et al 2019, hereafter Paper II) The results of the present work are instrument-independent to some extent Amongst these indicators, the structure function appears as a very promising diagnostic of turbulence since it takes advantage of spatially-resolved spectroscopic observations, as enabled by integral field units. One- and three-dimensional Fourier transforms are indicated with a tilde (e.g. ρ ), two-dimensional transforms with a hat (e.g. W)
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