  X-ray emitting gaseous coronae around massive galaxies are a basic prediction
of galaxy formation models. Although the coronae around spiral galaxies offer a
fundamental test of these models, observational constraints on their
characteristics are still scarce. While the presence of extended hot coronae
has been established around a handful of massive spiral galaxies, the short
X-ray observations only allowed for measurements of the basic characteristics
of the coronae. In this work, we utilize deep XMM-Newton observations of NGC
6753 to explore its extended X-ray corona in unprecedented detail.
Specifically, we establish the isotropic morphology of the hot gas, suggesting
that it resides in hydrostatic equilibrium. The temperature profile of the gas
shows a decrease with increasing radius: it drops from $kT\approx0.7$ keV in
the innermost parts to $kT\approx0.4$ keV at 50 kpc radius. The temperature map
reveals the complex temperature structure of the gas. We study the metallicity
distribution of the gas, which is uniform at $Z\approx0.1$ Solar. This value is
about an order of magnitude lower than that obtained for elliptical galaxies
with similar dark matter halo mass, hinting that the hot gas in spiral galaxies
predominantly originates from external gas inflows rather than from internal
sources. By extrapolating the density profile of the hot gas out to the virial
radius, we estimate the total gas mass and derive the total baryon mass of NGC
6753. We conclude that the baryon mass fraction is $f_{\rm b} \approx 0.06$,
implying that about half of the baryons are missing.
