6 Constraining the upper end of the IMF

As shown above, and in contrast to previous studies considering WR populations in objects with sub-solar metallicities, the quantitative modeling of the WR features in metal-rich H  II regions is not straightforward. The reliability of constraints on the IMF obtained from modeling of the WR features appears thus unclear at present and other constraints are therefore desirable.

Figure 13: Maximum predicted ${\rm H}\beta$ equivalent width at the beginning of the WR phase as a function of $M_{\rm up}$ for solar metallicity (Z=0.02)burst models with a Salpeter IMF (upper three curves) and a steeper IMF ( $\alpha =3.3$, lower two curves). The dotted curves show models for Z=0.04. The short dashed line corresponds to an extended burst of duration $\Delta t= 4$ Myr (Salpeter IMF, Z=0.02.) The observations are plotted at arbitrary $M_{\rm up}$ using the same symbols as in Fig. 8. The observed maximum ( $\log W({\rm H}\beta)\sim 2.2$-2.4) indicates $M_{\rm up}\sim 80$-90 $M_{\odot }$ for a Salpeter slope, and $\protect\ga$120 $M_{\odot }$ for $\alpha =3.3$, or somewhat lower values for extended bursts.

The maximum observed equivalent width of hydrogen recombination lines (e.g. $W({\rm H}\beta )$) of a large sample of star forming regions provide in principal a constraint on the upper mass cut-off of the IMF (e.g. Kennicutt 1983; Leitherer et al. 1999). In practice, however, as well known but not understood to date, there is a notable absence of regions with $W({\rm H}\beta )$ as large as predicted for very young bursts with ages between $\sim$0 to 1.5-2 Myr. As the onset of the WR phase is expected after $\sim$2-3 Myr quite independently of the exact adopted stellar tracks (e.g. different mass loss scenarios) this sets a new clock, and therefore the ${\rm H}\beta$ equivalent width of the youngest observed WR region also contains information on the value of $M_{\rm up}$.

In Fig. 13 we show the dependence of the predicted $W({\rm H}\beta )$ at the beginning of the WR phase (i.e. the maximum of $W({\rm H}\beta )$ during this phase) on the upper mass cut-off for different IMF slopes in instantaneous bursts. The maximum $W({\rm H}\beta )$ depends little on metallicity (see the dotted lines) and on the choice of stellar tracks (not shown here). Overplotted are the observed $W({\rm H}\beta )$ in our WR region sample (triangles) and the sample of BK02 (squares) drawn at arbitrary $M_{\rm up}$. The observed max( $W({\rm H}\beta )$) ( $\log W({\rm H}\beta)\sim 2.2$-2.4) indicates an upper mass cut-off of $\sim$80-90 $M_{\odot }$ for a Salpeter IMF or $M_{\rm up} \ga 120$ $M_{\odot }$ for a steeper IMF with $\alpha =3.3$. From all the above considerations (Sect. 5) flatter slopes seem excluded. If the bulk of the regions were forming stars in extended bursts the deduced value of $M_{\rm up}$ has to be lower; for the example illustrated here (burst duration $\Delta t= 4$ Myr) this would correspond to $M_{\rm up} \sim 60~M_{\odot}$for the Salpeter IMF.

It is important to note that the value of $M_{\rm up}$ derived in this way represents a lower limit. This is the case since all observational effects known to affect potentially the ${\rm H}\beta$ equivalent width (loss of photons in slit or leakage, dust inside H  II regions, differential extinction, underlying population) can only reduce the observed $W({\rm H}\beta )$. The observed $W({\rm H}\beta )$ represent therefore lower limits when compared to evolutionary synthesis models. We thus conclude that the available $W({\rm H}\beta )$ measurements in metal-rich H  II regions with WR stars yield a lower limit of $M_{\rm up} \ga 60$-90 $M_{\odot }$ for the upper mass-cut off of the IMF. Larger values of $M_{\rm up}$ are not excluded. This result is also compatible with our favoured models presented in Sect. 5 (see Fig. 10). Our new estimate of $M_{\rm up}$, based only on a sample of WR regions, provides a more stringent limit than previous studies (SGIT00, BK02).