Luminous X-ray gas coronae in the dark matter halos of massive spiral galaxies are a fundamental prediction of structure formation models, yet only a few such coronae have been detected so far. In this paper, we study the hot X-ray coronae beyond the optical disks of two normal massive spirals, NGC1961 and NGC6753. Based on XMM-Newton X-ray observations, hot gaseous emission is detected to ~60 kpc - well beyond their optical radii. The hot gas has a best-fit temperature of kT~0.6 keV and an abundance of ~0.1 Solar, and exhibits a fairly uniform distribution, suggesting that the quasi-static gas resides in hydrostatic equilibrium in the potential well of the galaxies. The bolometric luminosity of the gas in the (0.05-0.15)r_200 region (r_200 is the virial radius) is ~6e40 erg/s for both galaxies. The baryon mass fractions of NGC1961 and NGC6753 are f_b~0.1, which fall short of the cosmic baryon fraction. The hot coronae around NGC1961 and NGC6753 offer an excellent basis to probe structure formation simulations. To this end, the observations are confronted with the moving mesh code Arepo and the smoothed particle hydrodynamics code Gadget. Although neither model gives a perfect description, the observed luminosities, gas masses, and abundances favor the Arepo code. Moreover, the shape and the normalization of the observed density profiles are better reproduced by Arepo within ~0.5r_200. However, neither model incorporates efficient feedback from supermassive black holes or supernovae, which could alter the simulated properties of the X-ray coronae. With the further advance of numerical models, the present observations will be essential in constraining the feedback effects in structure formation simulations.
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