  Understanding how the hot circum-galactic medium (CGM) properties relate to
the galaxy's properties can constrain galaxy evolution models. We aim to
measure the scaling relations between the X-ray luminosity of the hot CGM and
the fundamental properties of a galaxy, i.e., its stellar mass and halo mass.
We calculate the X-ray luminosity of the hot CGM based on the surface
brightness profiles of central galaxy samples measured in Zhang et al. (2024a,
submitted) from Spectrum Roentgen Gamma (SRG)/eROSITA all-sky survey data. We
relate the X-ray luminosity to the galaxies' stellar and halo mass. We compare
the observed relations to the TNG, EAGLE, and SIMBA simulations. The hot CGM
X-ray luminosity correlates with the galaxy's stellar mass ($M_*$). It
increases from $2.1 \pm 1.3\times10^{39} \rm erg/s$ to $2.0 \pm
0.1\times10^{41} \rm erg/s$, when $\log(M_*)$ increases from 10.0 to 11.5. A
double power law describes the correlation, with a break at $\log(M_*)=11.28\pm
0.03$ and a power-law index or $1.9\pm 0.2$ ($4.2\pm0.1$) below (above) the
break. The hot CGM X-ray luminosity as a function of halo mass is measured
within $\log(M_{\rm 500c})=11.3-13.7$, extending our knowledge of the scaling
relation by more than two orders of magnitude. $L_{\rm X,CGM}$ increases with
$M_{\rm 500c}$ from $2.7 \pm 0.9\times10^{39}\ \rm erg/s$ at $\log(M_{\rm
500c})=11.3$ to $9.2 \pm 0.4\times10^{41}\ \rm erg/s$ at $\log(M_{\rm
500c})=13.7$. The relation follows a power law of $\log(L_{\rm X,CGM})=
(1.35\pm 0.04)\times \log(M_{\rm 500c})+(23.8\pm0.5)$. We find a general
agreement between simulations and observation. We explore, at the low mass end,
the average scaling relations between the CGM X-ray luminosity and the galaxy's
stellar mass or halo mass, which constitutes a new benchmark for galaxy
evolution models and feedback processes.
