3 Selection of the clusters

The U-band images were taken in 1994, 8 months earlier than the images in the other passbands. The orientation of HST-WFPC2 was not the same at the two epochs. In the 1995 BVRI-images the nucleus of M 51 was in the center of the PC-image. The U-image was centered on SN1994I (that was 15'' off from the nucleus) so that the nucleus was near the edge of the PC-image. The orientation of the WFPC2-images is shown in Fig. 1.

Figure 1: The location of the WFPC2 camera when the BVRI images were taken, superimposed on an optical image of M 51. Right: the orientation of the WFPC2 camera when the BVRI and the U images were taken. The grey area indicates the location of the WF2 chip, covering an area of $3.25 \times 3.25$ kpc (for an adopted distance of 8.4 Mpc), that was used in this analysis. Its exact location and orientation are given in Fig. 2. The dark grey region shows the overlap of the BVRI and U images.

For our analysis only the part of WF4-chip of the U image that overlap with the WF2-chip of the BVRI images is used (see Fig. 1). To identify the various sources, we obtained a position of the sources in U and transformed these positions to the coordinate frame of the BVRI images. The orientation of the [OIII] and H$\alpha$ images is very similar to those of the BVRI images. We transformed these narrow band images to the same orientation as the BVRI images. We applied our analysis of the cluster energy distributions to the sources that were detected in the images of at least three of the BVRI broad-band filters with a magnitude uncertainty smaller than 0.2 in each band. To this purpose we compared the positions of all detected sources in the BVRI images. If objects occur in at least three images within a position tolerance of 2 pixels they are selected for our study. This tolerance was chosen on the basis of tests with clearly identifiable sources that were observed in most bands. For the sources detected in at least three images we then checked for the presence of a source in the U image, in the region where the U image and the BVRI images do overlap (the dark grey region in Fig. 1). If a source was not detected in a particular band, we adopted a conservative lower limit for the magnitude in that band (see below). This was not always possible for the U-magnitude, because many of the sources detected in the BVRI bands are located in an area that was not covered by the U-image. As a consequence, we have no information on the U-magnitude for many of the sources. The location of the sources in the WF2-chip is shown in Fig. 2. The overlay of the sources on the V band image clearly shows that the clusters are concentrated in or near the spiral arms at a distance of about 1.5 kpc from the nucleus of M 51. The number of sources, detected in the various bands, is listed in Table 1. The sample contains a total of 877 sources for which we have reliable photometry ( $\sigma < 0.20$ mag) in at least three bands.

Figure 3 shows the magnitude distribution of the sources in the various bands. All distributions show a slow increase in numbers towards fainter objects, a maximum and a steep decrease towards even fainter sources. The slow increase to fainter sources reflects their luminosity function. The steep decrease to high magnitudes is due to the detection limit. This detection limit is not a single value for each band, because of the variable background in the WF2 field due to the spiral arms. The maximum of the distributions are near $U \simeq 20.0$, $B \simeq 22.0$, $V\simeq 22.0$, $R \simeq 21.5$ and $I \simeq 21.0$. These values will be adopted as conservative lower limits for the magnitudes of sources that were not detected in any given band.

All the objects fall in the visual magnitude range of 16.5 <V < 23.6. For distance modulus of 29.62 this corresponds to an absolute magnitude range of -12.1 < M_V <-6.0 in the case of zero extinction and -12.6 < M_V<-6.5 in case of moderate extinction with $E(B-V) \simeq 0.17$. This means that the faintest objects could be either very bright stars or small clusters. The vast majority of the selected point sources are so bright that they must be clusters. (See Sect. 5.6.)

 

 

Table 1: Numbers of point sources detected in the different WFPC2-HST-images.

F336W	F439W	F555W	F675W	F814W	number
(U)	(B)	(V)	(R)	(I)	objects
d	d	d	d	d	76
l	d	d	d	d	366
n	d	d	d	d	109
d	l	d	d	d	30
l	l	d	d	d	144
n	l	d	d	d	39
d	d	d	d	l	21
l	d	d	d	l	78
n	d	d	d	l	14
					877

d means "detected", l means "lower magnitude limit" (i.e. the object is fainter than the detection limit) and n means "not observed".

Figure 2: Left: the location of all the detected point sources in the WF2 chip superimposed on the V-band image. This image is rotated 90 degrees clockwise compared to Fig. 1. The coordinates of the lower-left and upper-right corners of the image are: pixel (1, 1): $\rm RA(2000)=13^h29^m55\hbox{$.\!\!^{\rm s}$ }90$, $\rm Dec(2000)=47^011'27\hbox{$.\!\!^{\prime\prime}$ }2.$ and pixel 800, 800: $\rm RA(2000)=13^h29^m57\hbox{$.\!\!^{\rm s}$ }94$, $\rm Dec(2000)=47^013'16\hbox{$.\!\!^{\prime\prime}$ }6$.

Figure 3: The histogram of the magnitudes in the different bands. The slow increase at bright magnitudes is due to the luminosity function and the steep decrease at fainter magnitudes is due to the detection limit.

   
3.1 The $\mathsfsl{H{\alpha}}$ and [OIII] magnitudes

The magnitudes in the narrow-band images of filters F656N ( $m({\rm H}\alpha )$) and F502N ( $m{\rm [OIII]}$) can be compared with those of the wide-band filters F675W (R) and F555W (V) respectively to derive a measure of the equivalent width of the H$\alpha$ and [OIII] lines. When the magnitudes are expressed in the HST-system, the magnitude differences $R-\mbox{$m({\rm H}\alpha)$ }$ and $V-\mbox{$m{\rm [OIII]}$ }$ are by definition equal to 0.0 if the spectrum of a source is a featureless, flat continuum (i.e. the spectrum of the source is a continuum $F_\lambda=\rm const.$ without a photospheric H$\alpha$ absorption, and there is no HII region around the star). The differences $R-\mbox{$m({\rm H}\alpha)$ }$ and $V-\mbox{$m{\rm [OIII]}$ }$ are either positive or negative if the source spectrum has an emission or an absorption line, respectively, falling in the narrow band filter, independently of the interstellar extinction. With the Vega-system magnitudes one has to fold in both the non-zero spectral slope and the discrete features present in $\alpha$ Lyrae's spectrum. Therefore, a featureless flat continuum would correspond to $R-\mbox{$m({\rm H}\alpha)$ }\simeq +0.08$ and $V-\mbox{$m{\rm [OIII]}$ }\simeq -0.26$ colors in the Vega-system.

Figure 4a shows the $m({\rm H}\alpha )$ versus R and Fig. 4b shows $m{\rm [OIII]}$ versus V for the subset of sources for which we could measure these magnitudes with an accuracy better than 0.2. The figure shows that many sources have H$\alpha$ emission ( $\mbox{$m({\rm H}\alpha)$ } < R$) but none (!) of the sources has [OIII] emission (note that $m{\rm [OIII]}$ is slightly fainter than the V magnitude as appropriate for complete absence of an emission line). The lack of [OIII] emission indicates that the far-UV flux, at $\lambda < 350$ Å  i.e. at energies higher than the second ionization potential of oxygen, is quite low. For main sequence stars with $L>2.5 \times 10^5~ \mbox{$L_{\odot}$ }$ (i.e. with $M > 30~\mbox{$M_{\odot}$ }$ and $\mbox{$T_{\rm eff}$ }> 33~000$ K), surrounded by an HII region with approximately solar abundances, we would expect $V - \mbox{$m{\rm [OIII]}$ }> R - \mbox{$m({\rm H}\alpha)$ }$. We will show later, on the basis of the study of the energy distributions, that many of the objects are very young clusters with ages less than a 10 Myr. The lack of [OIII] emission shows that these clusters do not contain stars with $T_{\rm eff}$ above about 30 000 K, which corresponds to about 25 to 30 $M_{\odot }$ (e.g. Chiosi & Maeder 1986). We can exclude the possibility that the lack of [OIII] emission be due to just a high metallicity, which could reduce the electron temperature in an HII region and weaken optical forbidden lines considerably, without requiring a lower effective temperature, or, equivalently, a low upper mass cutoff. This is because in many HII regions in M 51 and in other metal-rich spiral galaxies not only are the [OIII] lines faint or absent but also the HeI lines are unusually faint relative to Balmer lines (Panagia 2000; Lenzuni & Panagia, in preparation). This result indicates that He is only partially ionized and, therefore, that the ionizing radiation field is indeed produced exclusively by stars with effective temperatures much lower than 33 000 K . So we conclude that the upper mass limit for clusters in the inner spiral arms of M 51 is about 25 to 30 $M_{\odot }$.

Figure 4: The top figure shows $m({\rm H}\alpha )$ versus R and the lower figure shows $m{\rm [OIII]}$ versus V for objects were these magnitudes could be determined with an accuracy better than 0.2 mag. Notice that many objects have H$\alpha$ emission, but no object has detectable [OIII] emission.