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Context. Inferring spectral parameters from X-ray data is one of the cornerstones of high-energy astrophysics, and is achieved using software stacks that have been developed over the last 20 years and more. However, as models get more complex and spectra are obtained with higher resolutions, these established software solutions become more feature-heavy, difficult to maintain and less efficient. Aims. We present jaxspec, a Python package for performing this task quickly and robustly in a fully Bayesian framework. Based on the JAX ecosystem, jaxspec allows the generation of differentiable likelihood functions compilable on core or graphical process units (GPUs), enabling the use of robust algorithms for Bayesian inference. Methods. We demonstrate the effectiveness of jaxspec samplers, in particular the no U-turn sampler, using a composite model and comparing what we obtain with the existing frameworks. We also demonstrate its ability to process high-resolution spectroscopy data using original methods by reproducing the results of the Hitomi collaboration on the Perseus cluster, while solving the inference problem using variational inference on a GPU. Results. We obtain identical results when compared to other software and approaches, meaning that jaxspec provides reliable results while being ~10 times faster than existing alternatives. In addition, we show that variational inference can produce convincing results even on high-resolution data in less than 10 minutes on a GPU. Conclusions. With this package, we aim to pursue the goal of opening up X-ray spectroscopy to the existing ecosystem of machine learning and Bayesian inference, enabling researchers to apply new methods to solve increasingly complex problems in the best possible way. Our long-term ambition is the scientific exploitation of the data from the newAthena X-ray Integral Field Unit (X-IFU). [ABSTRACT FROM AUTHOR]

The intra-cluster medium is prone to turbulent motion that will contribute to the non-thermal heating of the gas, complicating the use of galaxy clusters as cosmological probes. Indirect approaches can estimate the intensity and structure of turbulent motions by studying the associated fluctuations in gas density and X-ray surface brightness. In this work, we aim to constrain the gas density fluctuations occurring in the CHEX-MATE sample to obtain a detailed view of their properties in a large population of clusters. To do so, we use a simulation-based approach to constrain the parameters of the power spectrum of density fluctuations, assuming a Kolmogorov-like spectrum and including the stochastic nature of the fluctuation-related observables in the error budget. Using a machine-learning approach, we learn an approximate likelihood for each cluster. This method requires clusters not to be too disturbed, as fluctuations can originate from dynamic processes such as merging. Accordingly, we removed the less relaxed clusters (centroid shift w > 0.02) from our sample, resulting in a sample of 64 clusters. We defined different subsets of CHEX-MATE to determine properties of density fluctuations as a function of dynamical state, mass, and redshift, and we investigated the correlation with the presence or not of a radio halo. We found a positive correlation between the dynamical state and density fluctuation variance, a non-trivial behaviour with mass, and no specific trend with redshift or the presence of a radio halo. The injection scale is mostly constrained by the core region. The slope in the inertial range is consistent with the Kolmogorov theory. When interpreted as originating from turbulent motion, the density fluctuations in R500 yield an average Mach number of ℳ3D ≃ 0.4 ± 0.2, an associated non-thermal pressure support of Pturb/Ptot ≃ (9 ± 6)%, or a hydrostatic mass bias bturb ≃ 0.09 ± 0.06. These findings align with expectations from existing literature. [ABSTRACT FROM AUTHOR]