We have studied the X-ray source population of the face-on spiral galaxy M101 ( NGC 5457 ) .
Within a field of radius 17 ^ { \prime } ( 36 kpc at the distance of 7.2 Mpc ) , covered by an ultradeep ( 229 ks ) ROSAT HRI image , 51 X-ray sources are detected with signal-to-noise ratios greater than 3.5 .
About half of these sources are associated with the galaxy .
The luminosity of these galactic sources individually ranges from \sim 4 \times 10 ^ { 37 } to 2 \times 10 ^ { 39 } { ~ { } ergs~ { } s ^ { -1 } } in the 0.5-2 keV band .
The average luminosity distribution of the sources can be characterized by a power law function : dN / dL _ { x } = 9.5 L _ { x } ^ { -1.9 } sources per 10 ^ { 38 } { ~ { } ergs~ { } s ^ { -1 } } .

Combined with archival data from the ROSAT PSPC , the Einstein IPC , and the ASCA GIS , we have examined spatial , spectral , and timing properties of the X-ray sources .
In particular , we have explored the nature of various superluminous X-ray sources with luminosities significantly greater than the Eddington limit ( \sim 2 \times 10 ^ { 38 } { ~ { } ergs~ { } s ^ { -1 } } ) for a \sim 1.6 M _ { \odot } object ( neutron star ) .
These X-ray sources , detected in various ROSAT HRI and PSPC observations , are not transients and appear to result from recent massive star formation in outer spiral arms .
3 superluminous PSPC sources are associated with giant H II complexes and are clearly resolved .
2 other superluminous RHRI sources are likely associated with shell-like supernova ( or more likely hypernova ) remnants , which are known to be abnormally luminous in optical and/or radio .
We further identify 2 superluminous sources , which all show highly-absorbed X-ray spectra and time variability during and/or between the observations , as candidates for X-ray binary systems that contain black holes .

A comparison of 7 nearby spirals shows that their X-ray source luminosity distributions , normalized by total \ion H1 masses , are very similar .
But both the number of superluminous X-ray sources and the total X-ray luminosity appear to be correlated with the star forming rate of a galaxy .