The presence of hot gaseous coronae around present-day massive spiral galaxies is a fundamental prediction of galaxy formation models .
However , our observational knowledge remains scarce , since to date only four gaseous coronae were detected around spirals with massive stellar bodies ( \gtrsim 2 \times 10 ^ { 11 } { M _ { \odot } } ) .
To explore the hot coronae around lower mass spiral galaxies , we utilized Chandra X-ray observations of a sample of eight normal spiral galaxies with stellar masses of ( 0.7 - 2.0 ) \times 10 ^ { 11 } { M _ { \odot } } .
Although statistically significant diffuse X-ray emission is not detected beyond the optical radii ( \sim 20 kpc ) of the galaxies , we derive 3 \sigma limits on the characteristics of the coronae .
These limits , complemented with previous detections of NGCÂ 1961 and NGCÂ 6753 , are used to probe the Illustris Simulation .
The observed 3 \sigma upper limits on the X-ray luminosities and gas masses exceed or are at the upper end of the model predictions .
For NGCÂ 1961 and NGCÂ 6753 the observed gas temperatures , metal abundances , and electron density profiles broadly agree with those predicted by Illustris .
These results hint that the physics modules of Illustris are broadly consistent with the observed properties of hot coronae around spiral galaxies .
However , a shortcoming of Illustris is that massive black holes , mostly residing in giant ellipticals , give rise to powerful radio-mode AGN feedback , which results in under luminous coronae for ellipticals .