7 Conclusions

We present new, accurate measurements of absorption line-strength indices of 17 globular clusters (hereafter GCs) in the nearby S0 galaxy NGC 3115. Our objects span a range in colour so that the bimodal (V-I) colour distribution is well sampled.

A critical comparison with Lick/IDS data (Trager et al. 1998) of GCs in M 31 and the Milky Way (hereafter MW) is presented. The Lick/IDS measurements of the H $\gamma_{\rm A,F}$ and H $\delta_{\rm A,F}$ indices for MW and M 31 GCs are presented for the first time in this paper. The data are analysed with new stellar population models (Thomas et al. 2002a) which are able to predict line-strength not only as a function of age and metallicity but also as a function of abundance ratio. Specifically, abundance ratio biases in the stellar library, which is an essential ingredient to the model predictions, have been taken into account for the first time.

Our main results are listed in the following:

• The GCs in NGC 3115 show a range of abundance ratios as estimated by the strength of Mg and Fe lines. Specifically we find for both red and blue clusters solar as well as super-solar values (up to ${\rm [Mg/Fe]} \simeq +0.5$). Lick/IDS data of M 31 GCs show a similar distribution while MW GCs are consistent with a constant value of ${\rm [Mg/Fe]} \simeq 0.3$. The latter is in agreement with recent studies of the resolved stellar populations in MW GCs.
• Our analysis of H$\beta$, H $\gamma _{\rm F}$ and H $\delta _{\rm F}$ vs. [MgFe] age/metallicity diagnostic diagrams shows that the red and blue GC populations are coeval within $\approx$2 Gyr. Our best calibrated diagram (H$\beta$, [MgFe]) indicates a mean age of 11-12 Gyr. However, the higher order Balmer lines, although confirming the similar ages of blue and red clusters, indicate younger absolute ages ($\approx$6 Gyr). We ascribe these younger age estimates to inaccurate model calibrations of the higher order Balmer lines. Evidence for the existence of young (<5 Gyr) GCs in the studied galaxies is scarce. Only one cluster in NGC 3115 and perhaps $\sim$3 clusters in M 31 show a combination of Balmer and metal absorption strength which is consistent with such young ages. The strong H$\beta$ absorption can be alternatively explained if these clusters have old stellar populations with a populous extended horizontal branch.
• We present a comparison of photometric and spectroscopic metallicity determinations and find a good linear relation in the metallicity range probed by our sample of NGC 3115 clusters ( $-1.5 < {\rm [Fe/H]} < 0.0$). The photometric estimates are systematically lower ($\simeq$-0.26) in comparison with our spectroscopic measurements. We note that our observations clearly show that each colour peak has a significant spread in metallicity rather than being consistent with a narrow distribution.
• The existence of solar as well as elevated Mg-to-Fe ratios at a given metallicity for GCs in NGC 3115 indicates that a simple scenario of two distinct star-formation episodes is not sufficient to explain the formation of this galaxy. Probably a realistic model needs to incorporate more than two distinct star-formation events.
• We detect a clear signal of rotation in our sample of GCs independent of their metallicities.

Larger samples of high signal-to-noise spectra of GCs in nearby galaxies are required to increase our knowledge of how these galaxies formed. Particularly the measurement of abundance ratios in extragalactic GCs is now possible and will deliver important new constraints for galaxy formation models which are not accessible with broad-band colours alone.

Acknowledgements

Part of this work was supported by the Volkswagen Foundation (I/76 520). We thank Dr. J. Heidt (Heidelberg) and the ESO Paranal staff for the efficient observations, the resulting data of which were the basis for this Paper. We are also very grateful to D. Thomas, C. Maraston and R. Bender who provided their models prior to publication. We thank the referee B. W. Carney for a quick and helpful referee report.