Astrophysical plasma modeling of the hot Universe : advances and challenges in high-resolution X-ray spectroscopy

Hot astrophysical plasma is ubiquitous in the Universe, from comets in our Solar system to the largest scale structures -- the cosmic web filaments. These hot plasmas, with the temperature of a few millions of degrees, are often observed in the X-ray wavelength range. Spectroscopic diagnostics enable us to probe physical properties like temperature, density, abundance, microscopic turbulence, the line of sight velocity, etc. High resolving power is essential to overcome the confusion caused by unresolved spectral features. Thanks to the grating spectrometers aboard XMM-Newton and Chandra, our knowledge of the hot and energetic Universe are advanced. Meanwhile, high-quality spectra from current and future generations of X-ray spectrometers also challenge plasma models that are widely used in the community. More complete and accurate atomic data are required to improve plasma models. Suitable management of the ever-growing atomic data is also important. This thesis starts with the updates of radiative recombination data in the spectral analysis package SPEX, where various plasma models built on the atomic database are available. The updated plasma models are then used to better understand the physics of circumnuclear media in NGC 5548 and NGC 3783, as well as the nitrogen enrichment in the intracluster media.