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We study the X-ray emission of baryon fluid in the universe using the WIGEONcosmological hydrodynamic simulations. It has been revealed that cosmic baryonfluid in the nonlinear regime behaves like Burgers turbulence, i.e. the fluidfield consists of shocks. Like turbulence in incompressible fluid, the Burgersturbulence plays an important role in converting the kinetic energy of thefluid to thermal energy and heats the gas. We show that the simulation sampleof the $\Lambda$CDM model without adding extra heating sources can fit well theobserved distributions of X-ray luminosity versus temperature ($L_{\rm x}$ vs.$T$) of galaxy groups and is also consistent with the distributions of X-rayluminosity versus velocity dispersion ($L_{\rm x}$ vs. $\sigma$). Because thebaryonic gas is multiphase, the $L_{\rm x}-T$ and $L_{\rm x}-\sigma$distributions are significantly scattered. If we describe the relationships bypower laws $L_{\rm x}\propto T^{\alpha_{LT}}$ and $L_{\rm x}\propto\sigma^{\alpha_{LV}}$, we find $\alpha_{LT}>2.5$ and $\alpha_{LV}>2.1$. TheX-ray background in the soft $0.5-2$ keV band emitted by the baryonic gas inthe temperature range $10^5<T<10^7$ K has also been calculated. We show that ofthe total background, (1) no more than 2% comes from the region withtemperature less than $10^{6.5}$ K, and (2) no more than 7% is from the regionof dark matter with mass density $\rho_{\rm dm}<50 \bar{\rho}_{\rm dm}$. Theregion of $\rho_{\rm dm}>50\bar{\rho}_{\rm dm}$ is generally clustered anddiscretely distributed. Therefore, almost all of the soft X-ray backgroundcomes from clustered sources, and the contribution from truly diffuse gas isprobably negligible. This point agrees with current X-ray observations.Comment: 32 pages including 14 figures and 2 tables. Final version for  publication in Ap

X‐Ray Emission of Baryonic Gas in the Universe: Luminosity‐Temperature Relationship and Soft‐Band Background