We present a study of the star cluster formation in M51 based on the image data taken with Advanced Camera for Surveys ( ACS ) and Wide Field Planetary Camera 2 ( WFPC2 ) of Hubble Space Telescope ( HST ) .
We have derived the star cluster formation rate using the ages and masses of about 2,000 star clusters estimated by comparing photometric data ( F 336 W , F 435 W , F 555 W , and F 814 W ) with theoretical population synthesis models .
The star cluster formation rate increased significantly during the period of 100 \sim 250 Myr ago .
This period roughly coincides with the epoch of dynamical encounters of two galaxies , NGC 5194 and NGC 5195 , expected by theoretical models .
The age distribution of the star clusters also shows two peaks at about 100 Myr and 250 Myr ago .
The star cluster mass ranges from 10 ^ { 3 } to 10 ^ { 6 } M _ { \odot } and the mass function can be represented by a power law with an index ranging from \alpha = -2.23 \pm 0.34 for t < 10 Myr to \alpha = -1.37 \pm 0.11 for t > 100 Myr .
The mass function of star clusters older than 10 Myr also appears to display the steepest distribution with \alpha \approx - 1.50 at around 200 Myr ago , near the expected epoch of the galaxy interaction .
We also confirm the correlations of cluster size increasing with cluster mass ( with a best fit slope of 0.16 \pm 0.02 ) , and with cluster age ( 0.14 \pm 0.03 ) .