We have obtained H \alpha and P \alpha emission line images covering the central 3 — 4 \arcmin of M51 using the WFPC2 and NICMOS cameras on HST to study the high-mass stellar population .
The 0.1 — 0.2 \arcsec pixels provide 4.6 — 9 pc resolution in M51 and the H \alpha /P \alpha line ratios are used to obtain extinction estimates .
A sample of 1373 H \alpha emission regions is catalogued using an automated and uniform measurement algorithm .
Their sizes are typically 10 — 100 pc .
The luminosity function for the H \alpha emission regions is obtained over the range L _ { H \alpha } = 10 ^ { 36 } to 2 \times 10 ^ { 39 } erg s ^ { -1 } .
The luminosity function is fit well by a power law with dN / dlnL \propto L ^ { -1.01 } ) .
The power law is significantly truncated and no regions were found with it observed L _ { H \alpha } above 2 \times 10 ^ { 39 } erg s ^ { -1 } ( uncorrected for extinction ) .
( The maximum seen in ground-based studies is approximately a factor of 5 higher , very likely due to blending of multiple regions . )
The extinctions derived here increase the maximum intrinsic luminosity to above 10 ^ { 40 } erg s ^ { -1 } ) .
The logarithmically binned luminosity function is also somewhat steeper ( \alpha = -1.01 ) than that found ground-based imaging ( \alpha = -0.5 \to - 0.8 ) — probably also a result of our resolving regions which were blended in the ground-based images .
The 2-point correlation function for the HII regions exhibits strong clustering on scales \leq 2 \arcsec or 96 pc .

To analyze the variations of HII region properties vis-a-vis the galactic structure , the spiral arm areas were defined independently from mm-CO and optical continuum imaging .
Although the arms constitute only 25 % of the disk surface area , the arms contain 45 % of the catalogued HII regions .
The luminosity function is somewhat flatter in spiral arm regions than in the interarm areas ( -0.72 \rightarrow -0.95 ) ; however , this is very likely the result of increased blending of individual HII regions in the arms which have higher surface density .
No significant difference is seen in the sizes and electron densities of the HII regions in spiral arm and interarm regions .
For 209 regions which had \geq 5 \sigma detections in both P \alpha and H \alpha , the observed line ratios indicate visual extinctions in the range A _ { V } = 0 to 6 mag .
The mean extinction was A _ { V } = 3.1 mag ( weighting each region equally ) , 2.4 mag ( weighting each by the observed H \alpha luminosity ) and 3.0 mag ( weighting by the extinction-corrected luminosity ) .
On average , the observed H \alpha luminosities should be increased by a factor of \sim 10 , implying comparable increases in global OB star cluster luminosities and star formation rates .
The full range of extinction-corrected H \alpha luminosities is between 10 ^ { 37 } — 2 \times 10 ^ { 40 } erg s ^ { -1 } .

The most luminous regions have sizes \geq 100 pc so it is very likely they are blends of multiple regions .
This is clear based on their sizes which are much larger than the maximum diameter ( \leq 50 pc ) to which an HII region might conceivably expand within the \sim 3 \times 10 ^ { 6 } yr lifetime of the OB stars .
It is also consistent with observed correlation ( L \propto D ^ { 2 } ) found between the measured luminosities and sizes of the HII regions .
We therefore generated a subsample of 1101 regions with sizes \leq 50 pc which constitutes those region which might conceivably be ionized by a single cluster .
Their extinction-corrected luminosities range between 2 \times 10 ^ { 37 } and 10 ^ { 39 } erg s ^ { -1 } , or between 2/3 of M42 ( the Orion Nebula ) and W49 ( the most luminous Galactic radio HII region ) .
The upper limit for individual clusters is therefore conservatively \leq 10 ^ { 39 } erg s ^ { -1 } , implying Q _ { LyC } _ { up } \simeq 7 \times 10 ^ { 50 } s ^ { -1 } ( with no corrections for dust absorption of the Lyman continuum or UV which escapes to the diffuse medium ) .
This corresponds to cluster masses \leq 5000 M _ { \odot } ( between 1 and 120 M _ { \odot } ) .

The total star formation rate in M51 is estimated from the extinction-corrected H \alpha luminosities to be \sim 4.2 M _ { \odot } yr ^ { -1 } ( assuming a Salpeter IMF between 1 and 120 M _ { \odot } ) and the cycling time from the neutral ISM into these stars is 1.2 \times 10 ^ { 9 } yr .

We develop a simple model for the UV output from OB star clusters as a function of the cluster mass and age in order to interpret constraints provided by the observed luminosity functions .
The power-law index at the high luminosity end of the luminosity function ( \alpha = -1.01 ) implies N ( M _ { cl } ) /d M _ { cl } \propto M _ { cl } ^ { -2.01 } .
The high mass clusters ( \sim 1000 M _ { \odot } ) have a mass such that the IMF is well sampled up to \sim 120 M _ { \odot } , but this cluster mass is \leq 1 % of that available in a typical GMC .
We suggest that OB star formation in a cloud core region is terminated at the point that radiation pressure on the surrounding dust exceeds the self-gravity of the core star cluster and that this is what limits the maximum mass of standard OB star clusters .
This occurs at a stellar luminosity-to-mass ratio \sim 500 – 1000 L _ { \odot } / M _ { \odot } which happens for clusters \geq 750 M _ { \odot } .
We have modelled the core collapse hydrodynamically and find that a second wave of star formation may propagate outwards in a radiatively compressed shell surrounding the core star cluster — this triggered , secondary star formation may be the mechanism for formation of super star cluster ( SSC ) seen in starburst galaxies .