Clusters in the inner spiral arms of M51: the cluster IMF and the formation history

We present the results of an analysis of the HST-WFPC2 observations of the interacting galaxy M 51. From the observations in 5 broadband filters (UBVRI) and two narrowband filters (H$\alpha $ and [OIII]) we study the cluster population in a region of 3.2 $\times 3.2$ kpc2 in the inner spiral arms of M 51, at a distance of about 1 to 3 kpc from the nucleus. We found 877 cluster candidates and we derived their ages, initial masses and extinctions by means of a comparison between the observed spectral energy distribution and the predictions from cluster synthesis models for instantaneous star formation and solar metallicity. The lack of [OIII] emission in even the youngest clusters with strong H$\alpha $ emission, indicates the absence of the most massive stars and suggests a mass upper limit of about 25 to 30 $M_{\odot }$. The mass versus age distribution of the clusters shows a drastic decrease in the number of clusters with age, much more severe than can be expected on the basis of evolutionary fading of the clusters. This indicates that cluster dispersion is occurring on a timescale of 10 Myr or longer. The cluster initial mass function has been derived from clusters younger than 10 Myr by a linear regression fit of the cumulative mass distribution. This results in an exponent $\alpha = -{\rm d} \log~ N(M) /{\rm d} \log~(M) =
2.1 \pm 0.3 $ in the range of $2.5\times 10^3 < M < 5\times 10^4~\mbox{$M_{\odot}$ }$ but with an overabundance of clusters with $M > 2\times 10^4$ $M_{\odot }$. In the restricted range of $2.5\times 10^3 < M < 2\times 10^4$ $M_{\odot }$ we find $\alpha = 2.0 \pm 0.05$. This exponent is very similar to the value derived for clusters in the interacting Antennae galaxies, and to the exponent of the mass distribution of the giant molecular clouds in our Galaxy. To study the possible effects of the interaction of M 51 with its companion NGC 5195 about 400 Myr ago, which triggered a huge starburst in the nucleus, we determined the cluster formation rate as a function of time for clusters with an initial mass larger than 104 $M_{\odot }$. There is no evidence for a peak in the cluster formation rate at around 200 to 400 Myr ago within 2 $\sigma$ accuracy, i.e. within a factor two. The formation rate of the detected clusters decreases strongly with age by about a factor 102 between 10 Myr and 1 Gyr. For clusters older than about 150 Myr this is due to the evolutionary fading of the clusters below the detection limit. For clusters younger than 100 Myr this is due to the dispersion of the clusters, unless one assumes that the cluster formation rate has been steadily increasing with time from 1 Gyr ago to the present time.