The hot gas distribution, X-ray luminosity and baryon budget in the L-Galaxies semi-analytic model of galaxy formation

Hot ionized gas is important in the baryon cycle of galaxies and contributes the majority of their ``missing baryons''. Until now, most semi-analytic models of galaxy formation have paid little attention to hot gaseous haloes and their X-ray emission. In this paper, we adopt the one-dimensional model from Sharma et al. instead of the isothermal sphere to describe the radial distribution of hot gas in the L-Galaxies semi-analytic model. The hot gas halo can be divided into two parts according to the ratio of the local thermal instability time-scale and the free-fall time-scale: a cool core with $t_{\rm TI}/t_{\rm ff}=10$ and a stable outer halo with $t_{\rm TI}/t_{\rm ff}>10$. We update the prescriptions of cooling, feedback and stripping based on the new hot gas profiles, and then reproduce several X-ray observational results, like the radial profiles of hot gas density, and the scaling relations of X-ray luminosity and temperature. We find: (1) Consistent with observations, flatter density profiles in halo centers produce lower X-ray emission than an isothermal sphere; (2) Cool core regions prone to precipitation have higher gas temperature than the virial temperature, and a larger $T_{\rm X}/T_{\rm 200}$ ratio in smaller haloes leads to a steeper slope in the $L_{\rm X}-T_{\rm X}$ relation; (3) The ionized gas in the unbounded reservoir and low temperature intergalactic gas in low mass haloes could be the main components of the halo ``missing baryons''. Our model outputs can predict the observations of hot gas in the nearby universe and produce mock surveys of baryons probed by future X-ray telescopes.