5 Results

We first present our results on the abundance ratios of Mg to Fe of GCs in NGC 3115 and compare these with the Lick/IDS observations (Trager et al. 1998) of GCs in our own galaxy and M 31. In Sect. 5.2 we present our best estimates of the ages and metallicities of NGC 3115 GCs, while we compare photometric and spectroscopic metallicity estimates in Sect. 5.3.

5.1 Abundance ratios

In Fig. 7, we show a diagram of Mg b vs. $\langle$Fe$\rangle$ index. We plot our sample of GCs separated by (V-I) colour (see Fig. 5) where red and blue clusters are shown as open circles and open triangles respectively. Overplotted are the model predictions by Thomas et al. (2002a) for $\rm [Mg/Fe] = 0.0, 0.3, 0.5$, $\rm age = 3, 5, 8, 12$ Gyr and $\rm [Fe/H] = -2.25, -1.35, -0.33, 0.0, +0.35$. In this diagram the effects of age and metallicity are almost completely degenerate and the sensitivity towards abundance ratios is maximised. The models predict a significant change in line-strength for varying abundance ratios at large metallicities/ages (i.e. large Mg b & $\langle$Fe$\rangle$ line-strength) while at low metallicities the dependence is smaller. Therefore, at a given error in line-strength, abundance ratios are determined more accurately at larger metallicities/ages. We find that for GCs in NGC 3115 the abundance ratios vary from roughly solar to about ${\rm [Mg/Fe]} \simeq +0.3$ (with a maximum of ${\rm [Mg/Fe]} \simeq +0.5$, see Fig. 7a). In our small sample there is no evidence for a trend with colour. In particular, there are GCs with solar and super-solar abundance ratios in both the blue and red GC populations. There is even some weak evidence for a bimodal abundance ratio distribution with peaks at $\rm [Mg/Fe] \approx0.0$ and $\approx$0.3 (see Fig. 8). This tentative evidence needs to be confirmed with a larger sample of GCs.

The measurements for the centre of NGC 3115 itself (large filled square, data from Trager et al. 1998) and the radial gradient (small filled squares, data from Fisher et al. 1996) along the major axis up to 40 $^{\prime \prime }$ is compatible with a model of $\rm [Mg/Fe] \approx0.0$ at high metallicity/age. In Figs. 7b and c we plot the Lick/IDS observations of GCs in the Milky Way and M 31 respectively (data from Trager et al. 1998). While virtually all MW GCs are consistent with ${\rm [Mg/Fe]} \simeq +0.3$, similar to large elliptical galaxies, we find a range in [Mg/Fe] for the GCs in M 31. The overall distribution of the [Mg/Fe] ratios for GCs in M 31 is similar to the one we find in NGC 3115. The average value of $\rm [Mg/Fe] =+0.3$ we find for the MW GCs compares well with high resolution studies of individual stars in MW GCs (e.g., Lee & Carney 2002).

Figure 8: Histogram of abundance ratios [Mg/Fe] for NGC 3115 globular clusters. The abundance ratios were determined from Fig. 7a.

GCs with super-solar [Mg/Fe] ratios were previously found in other nearby galaxies but without our quantitative accuracy. For example, Forbes et al. (2001) attribute super-solar abundance ratios to 4 out of 10 GCs in NGC 1399. Using Mg and TiO features, Larsen et al. (2002) find a mean [$\alpha$/Fe] of +0.4 for both metal-poor and metal-rich GCs in the Sombrero galaxy.

   
5.2 Age and metallicity

Figure 9: Age and metallicity diagnostic diagrams using as metallicity indicator [MgFe] and as age indicator H$\beta$, H $\gamma _{\rm F}$, and H $\delta _{\rm F}$. H$\beta$ and [MgFe] are not significantly influenced by abundance ratios, for H $\gamma _{\rm F}$, and H $\delta _{\rm F}$ the behaviour is unknown. Our sample of globular clusters in NGC 3115 is shown in the left panels as open triangles (blue clusters) and open circles (red clusters). The error weighted means of the blue and red clusters are shown as filled symbols. The filled square in the left panels represents the centre of NGC 3115 Trager et al. (1998). The middle and right panels show the Lick/IDS data for Milky Way MW and M 31 globular clusters, respectively. Note, that for the MW globular cluster NGC 2158 there are no H $\gamma _{\rm F}$ and H $\delta _{\rm F}$ index measurements available. Overplotted are solar-abundance SSP models by Thomas et al. (2002a) and Maraston (2002, in preparation) for metallicities ${\rm [Fe/H]} = -2.25, -1.35, -0.33, 0.00, 0.35$ (dashed lines, left to right) and ages 3, 5, 8, and 12 Gyr (solid lines, top to bottom).

In the previous section we were able to determine the abundance ratios of GCs without knowing the age and metallicity since the latter parameters are almost completely degenerate in a Mg b vs. $\langle$Fe$\rangle$ diagnostic diagram. However, our earlier discussion of the model systematics shows that we need to take the abundance ratios into account in order to estimate the age and metallicity of the GCs (see also e.g., Trager et al. 2000; Kuntschner et al. 2001).

Principle age sensitive lines within our observed wavelength range are the Balmer lines H$\beta$, H$\gamma$, and H$\delta$. For H$\gamma$ and H$\delta$, the dependence on $\alpha$-element to Fe ratio is yet unknown. H$\beta$ is only marginally sensitive to abundance ratio variations, at least in comparison to our average observational error. To further minimise the influence of abundance ratios, we employ as metallicity indicator [MgFe], that also shows no significant [Mg/Fe] dependence (see Fig. 6). Within the accuracy of our data sample, an H$\beta$ vs. [MgFe] diagram can therefore be used to estimate the ages and metallicities of our NGC 3115 GCs without being significantly affected by abundance ratios.

In Fig. 9 we show diagrams of [MgFe] versus the three Balmer lines for our sample of NGC 3115 GCs (left panels) and the respective data for GCs in the Milky Way and M 31 from the Lick/IDS observations (middle and right panels; the index values for H$\beta$, Mg b and $\langle$Fe$\rangle$ were taken from Trager et al. (1998); the higher order Balmer lines of the Lick/IDS observations are presented in Tables A.2 and A.3 in the Appendix). Overplotted in Fig. 9 are solar-abundance ratio models by Thomas et al. (2002a) and Maraston (2002, in preparation) for metallicities ${\rm [Fe/H]} = -2.25, -1.35, -0.33, 0.00, 0.35$ (dashed lines, left to right) and ages 3, 5, 8 and 12 Gyr (solid lines, top to bottom).

We first caution that a direct comparison between models and our data to derive absolute ages and metallicities can be dangerous due to possible systematic calibration errors. However, we estimate that systematic observational errors are smaller than 0.1 Å for the indices shown here and emphasize that relative comparisons within one sample will be significant.

The observed H$\beta$ values for NGC 3115 GCs show a large spread with respect to the model predictions. However, the data points which are well below the model predictions are the ones with the largest errors. Most of the well determined data points are close to the region of a 12 Gyr SSP model. Our [MgFe] measurements show that there is a clear distinction in metallicity between blue (open triangles) and red clusters (open circles), with the red clusters being more metal rich (a more detailed analysis of the metallicity distribution is presented in Sect. 5.3).

Since only about half of our data points have small enough error bars to be useful for an individual age/metallicity evaluation we also calculate the error weighted mean of the blue and red clusters, respectively. These average values (filled symbols in Fig. 9, left panels) give for the metal poor (blue) population an age of 12.0( ^+1.5_-2.0) Gyr and ${\rm [Fe/H]} = -1.05(\pm0.09)$, while the metal rich (red) population has an estimated age of 10.8( ^+1.7_-1.8) Gyr and  ${\rm [Fe/H]} = -0.26(\pm0.05)$. The errors on the age and metallicity are quoted as 1$\sigma$ errors on the mean values.

We note in Sect. 4 that for metallicities ${\rm [Fe/H]} \le -1.35$ and an age larger than 8 Gyr the strength of the H$\beta$ and [MgFe] indices is not uniquely connected to one age anymore. In fact there is a "crossing'' of iso-age curves. For clarity we do not plot iso-age lines for ages greater than 12 Gyr in Fig. 9, but this effect has been taken into account when deriving the errors on our best age and metallicity estimates.

From the H$\beta$ vs. [MgFe] diagram we conclude that within our observational errors the two populations of GCs in NGC 3115 have the same age of 11-12 Gyr (assuming the calibration of models and data is accurate). The observed indices for the integrated light in the centre of NGC 3115 (taken from and shown as filled square in Fig. 9 Trager et al. 1998) are consistent with a luminosity weighted age of $\approx$12 Gyr.

The Lick/IDS observations of MW GCs also show a significant number of objects below the model predictions. We note that there are no systematic observational offsets to be expected since the data was taken with the original Lick/IDS system. We speculate that observations of these GCs may be contaminated by fore/back-ground stars. New spectroscopic observations of MW GCs (Puzia et al. 2002a) support this hypothesis since the new observations do not show such low H$\beta$ values. Consistent with recent age estimates from the resolved stellar populations of MW GCs (e.g., Rosenberg et al. 1999; Salaris & Weiss 2002) we do not find evidence for clusters younger than $\approx$8 Gyr.

The Lick/IDS observations for M 31 GCs show a relatively small scatter close to a 12 Gyr model prediction, with only three, metal-rich clusters showing evidence of a younger age. We note however, that for metallicities ${\rm [Fe/H]} < -1.35$ the models seem to systematically over-estimate the H$\beta$ absorption strength (or alternatively over-estimate the [MgFe] absorption strength).

In the next paragraphs we will present our measurements of the higher order Balmer lines H $\gamma _{\rm F}$ and H $\delta _{\rm F}$. We emphasize here that while these indices can be measured with a higher precision than H$\beta$, it is currently unknown how these indices depend on abundance ratios. Furthermore the absolute calibration of these indices has not yet been investigated in as much detail as the H$\beta$ index.

The distributions of H $\gamma _{\rm F}$ and H $\delta _{\rm F}$ vs [MgFe] are narrower compared to H$\beta$ vs. [MgFe] and mostly encompassed by the model grid. The error weighted means for NGC 3115 GCs indicate an age of $\approx$7 and $\approx$5 Gyr for the blue and red clusters, respectively. These average ages are substantially lower than what we inferred from the H$\beta$ vs. [MgFe] diagram. We note that our observations of H $\gamma _{\rm F}$ and H $\delta _{\rm F}$ for GCs in NGC 3115 agree well with the Lick/IDS observations of M 31 and therefore we conclude that the calibration of the models is not consistent between H$\beta$ and the higher order Balmer lines. Despite this absolute calibration problem we find a good agreement in a relative sense between H$\beta$, H $\gamma _{\rm F}$ and H $\delta _{\rm F}$. Therefore, at least to first order, we can say that the higher Balmer indices are not significantly affected by abundance ratios in the metallicity range probed by our data.

Comparing the distributions for MW and M 31 GCs, we find that the MW one is broader and offset towards smaller H $\gamma _{\rm F}$ and H $\delta _{\rm F}$ absorption consistent with the H$\beta$ measurements. We ascribe this to contaminated observations for MW GCs (see above). The Lick/IDS data (particularly the H$\beta$ vs. [MgFe] diagram), suggest that perhaps $\sim$3 metal rich M 31 GCs have younger ages (3-5 Gyr). Alternatively, one could account for the strong H$\beta$ absorption in these metal rich clusters if the H$\beta$ index is significantly influenced by an extended blue horizontal branch in an otherwise old, metal rich stellar population. Maraston & Thomas (2000) show that this effect can play a role in metal poor stellar populations, however, to date there is scarce observational evidence for the existence of a populous extended blue horizontal branch in metal rich clusters. Rich et al. (1997) detected a blue horizontal branch in two metal rich MW GCs and Ferraro et al. (2001) detected UV-excess stars in the core of 47 Tuc (see also Moehler et al. 2000).

Few spectroscopic observations of GCs in early-type galaxies with sufficient S/N to investigate these effects have been published. Forbes et al. (2001) find that most of their 10 GCs in the giant elliptical NGC 1399 are old and compatible with a model age of 11 Gyr (using models by Maraston 2002, in preparation). Only two GCs display such large H$\beta$ values that these have either a very young age of $\sim$2 Gyr or are "contaminated'' by a significant blue horizontal branch population which causes large H$\beta$ absorption. The authors prefer the first interpretation. Larsen et al. (2002) present spectra of 14 GCs in the Sombrero Galaxy (NGC 4594). Their analysis of the co-added spectra of metal-poor and metal-rich GCs leads to age estimates between 10-15 Gyr. The majority (11 out of 14 GCs) of the spectroscopic sample of Schroder et al. (2002) of M 81 GCs is compatible with old ages (using models by Worthey 1994). There is only one outlier with a very high H$\beta$ line strength.

In summary we conclude from our best calibrated diagram of H$\beta$ vs. [MgFe] that the majority of our sample of GCs in NGC 3115, regardless of their metallicity, are consistent with an age of $\approx$12 Gyr. Only one, metal rich cluster (Slitlet ID: 7) shows a combination of H$\beta$ and [MgFe] absorption strength which indicates an age lower than 8 Gyr. The higher order Balmer lines indicate a narrow distribution in age, with a hint of the metal rich clusters being younger by $\approx$2 Gyr. The unknown dependence of the higher order Balmer lines on abundance ratios makes this age difference highly speculative. The absolute ages indicated by the higher order Balmer lines are lower compared to the H$\beta$ index. We ascribe this age difference to an inaccurate calibration of the higher order Balmer lines in the current stellar population models. The Lick/IDS samples of MW and M 31 GCs also show old stellar populations; only $\sim$3 GCs in M 31 show tentative evidence of younger stars.

   
5.3 Photometric versus spectroscopic metallicity estimates

In this section we compare our spectroscopic metallicity estimates with photometric methods and also investigate the general distribution of metallicities. For this purpose we assume an average age of the GCs in NGC 3115 of 12 Gyr which is consistent with our findings in the previous section.

Figure 10a shows the purely empirical relation between (V-I) colour and our mean metallicity indicator [MgFe]. There is a tight relation over the observed parameter space. Overplotted as solid line are model predictions by Maraston (2002, in preparation) and Thomas et al. (2002a) for a constant age of 12 Gyr, which is in excellent agreement with our data. We note that the model predictions for colours do not include the effects of non-solar abundance ratios.

In order to convert the colours into metallicity estimates several authors have derived linear conversion formulae based on observations for MW GCs. For example, Kundu & Whitmore (1998) conclude that ${\rm [Fe/H]} = -5.89 + 4.72 (V-I)$ is a good linear approximation. One can also use the predictions of stellar population models (Maraston 2002, in preparation) to predict the relation between (V-I) colour and metallicity [Fe/H]. A comparison of the empirical and synthetic calibration (12 Gyr model) is shown in Fig. 10b.

Overall, the agreement is acceptable, although there are significant differences. Specifically at the low metalicity end the models predict a shallower trend than the empirical relation. In order to stay consistent with the Kundu & Whitmore (1998) paper we use their relation to convert (V-I) colour to metallicity (see also Table 1). Furthermore we determine metallicity estimates from our spectra by using the [MgFe] index in conjunction with the model predictions by Thomas et al. (2002a) and assuming a constant age of 12 Gyr. The comparison between photometric and spectroscopic metallicity estimates is shown in Fig. 10c.

We find a good linear relation between both methods. The best fitting linear relation including the observational errors is ${\rm [Fe/H]}_{{\rm phot}} = -0.26(\pm0.05) + 0.95(\pm0.08) \times {\rm [Fe/H]}_{{\rm spec}}$ with a $\chi^2$ probability of 0.30. The systematic offset of approximately ${\rm [Fe/H]} = -0.26$in the sense that the spectroscopic metallicity measurements are larger is consistent with the difference between model predictions and empirical calibration of the conversion formulae between colour and [Fe/H] as shown in Fig. 10b. The predicted non-linearity of (V-I) colour as function of metallicity below $\rm [Fe/H] =-1.5$cannot be tested since our data do not really cover this range.

In summary we confirm with our accurate spectroscopic observations that the bimodal colour distribution seen in NGC 3115 GCs is dominated by a metallicity effect rather than by an age difference. Furthermore, both (V-I) colour peaks do show a substantial spread in metallicity. We conclude that in the metallicity range $-1.5 \le {\rm [Fe/H]} \le 0.0$ and in absence of young GCs, the (V-I) colour is indeed a good indicator for metallicity. We note that for metallicities below $\rm [Fe/H] =-1.5$ this may not be the case anymore.