4 IMF and chemical composition

To study the influence of the initial distribution of masses, we have repeated the simulations described above, this time varying the IMF power law exponent $\alpha$ over a wide range of values. Figure 9 shows synthetic colours for $\alpha~=~0$, corresponding to the extreme limit of a uniform mass distribution, $\alpha~=~1.35$, i.e. less than Salpeter's value, and $\alpha~=~3.35$, corresponding to a distribution steeper than Salpeter's one. At first glance, one would expect that decreasing the exponent the cluster becomes brighter, since a larger fraction of stars is pushed toward the more massive and, thus, more luminous stars. The upper left panel in Fig. 9 shows that is not always the case: for ages larger than, about, 1 Gyr the extreme case of a flat IMF results in fainter clusters, just because for such large ages the luminosity is produced by the now depopulated range of less massive stars.

  

Figure 9: The integrated V magnitude and colours for different assumption of the IMF exponent: solid line is $\alpha~=~2.35$,dotted line is $\alpha~=~0.0$, short dashed line is $\alpha~=~1.35$,long dashed line is $\alpha~=~3.35$

The general trends of integrated colours do not appear dramatically affected by IMF: the HST UV colours maintain their monotonic behavior and broad band colours still show a minimum around $\log t~=~8$. However, a large variation in the IMF slope can influence the absolute values of the integrated colours depending on the age and on the particular colour examined. In general, one finds that the variations are smaller than 0.2 mag and only in the case of $\alpha~=~3.35$ the colours show larger fluctuations. However, for $\log t \ge 8.5$ the colour vs. age relations do not depend on the IMF slope any more, because the colours are dominated by RGB and post RGB stars, whose distribution is fixed by evolutionary timescales only. For younger ages the influence of the IMF on the integrated colour increases since a non negligible portion of the emitted flux comes from MS stars, according to their relatively long evolutionary timescales and, thus, according to their IMF distribution. As a relevant point, one finds that HST UV colours appear affected only in the extreme case of a very steep IMF ($\alpha~=~3.35$), showing to be - in this respect - a rather robust indicator of cluster age.

  

Table 1: a) HST colours for the RF model. 1$\sigma$ error is also reported

 

Table 1: b) Broad band colours for the RF model

  

Table 2: a) HST colours for the Y=0.27, $Z=6\ 10^{-3}$ model

 

Table 2: b) Broad band colours for the Y=0.27, $Z=6\ 10^{-3}$ model

  

Table 3: a) HST colours for the Y=0.27, Z=10^-3 model

 

Table 3: b) Broad band colours for the Y=0.27, Z=10^-3 model

The influence of chemical composition has been investigated by computing selected models either keeping fixed the Helium content (Y = 0.27) while varying Z to selected values ($Z~=~2\ 10^{-2},\ 6\ 10^{-3},\ 10^{-3}$) or changing Y (Y = 0.23 and Y = 0.27) for a fixed Z (Z = 10^-3). As far as the metallicity is concerned (Fig. 10, Tables 1-3), one finds the interesting feature for which decreasing the metallicity the relation between broad band colours and age becomes more and more monotonic. For young ages, the Z = 0.001 models show much bluer colour (even 3 mag of difference in V-K colour) than the solar metallicity models. This is due to the difference in the evolution of intermediate mass stars in the phase following the exhaustion of H in the center. Solar metallicity models run to the red portion of HR diagram and set their He-burning phase at low temperature, near the Hayashi track, for at least half of their evolutionary time. On the other hand low metallicity stars ($Z\le$ 0.001) do not reach this part of the HR diagram, but stay in the blue side during all the He-burning phase. We note that such a behavior is strongly dependent on the treatment of convection in the more massive models, so that colours of young population appear sensitively model dependent (see Brocato & Castellani 1993).

  

Figure 10: The integrated V magnitude and colours for three different choice of Z: $Z~=~2\ 10^{-2}$(solid line), $Z~=~6\ 10^{-3}$ (dotted line) and Z = 10-3 (dashed line)

The behavior of HST UV colours discloses differences in their pattern according to the different metallicities. As well known, the RGB location in the HR diagram depends on metallicity, in the sense that cooler RGB are expected from stellar models of larger metallicity. For this reason the low metallicity population synthesis models have hotter RGB than RF models do. As a consequence, they are less affected by red leak and they maintain a monotonic behavior for the older ages presented here.

  

Figure 11: As in Fig. 10 but for Z = 10-3 and two different value of the original helium content Y = 0.23 (solid line) and Y = 0.27 (dashed line)

  

Table 4: a) HST colours for the Y=0.23, Z=10^-3 model

 

Table 4: b) Broad band colours for the Y=0.23, Z=10^-3 model

Finally, Fig. 11 (Tables 3-4) shows that little variations are found for different assumptions on the Y value. In particular, variations in Y do not affect the HST UV colours and most of the large band colours (a small difference can be found in V-K colour at intermediate ages) for the range of ages considered in the present work.