3 Analysis of the spectra

   
3.1 Estimating the background light

Long-slit spectroscopy of extended objects notoriously suffers from difficulties in estimating the contribution of the sky and background light. Since we observe globular clusters near the Galactic Bulge, their spectra will be contaminated by an unknown fraction of the bulge light, depending on the location on the sky (see Fig. 1). In order to estimate the contribution of the background, two different approaches have been applied. The first approach was to estimate the sky and bulge contribution from separately taken sky and bulge spectra (hereafter "background modeling''). The other technique was to extract the total background spectrum from low-intensity regions at the edges of the spatial axis in the object spectrum itself (henceforth "background extraction''). While the first technique suffers from the unknown change of the background spectrum between the position of the globular clusters and the background fields, the second one suffers from lower S/N. However, tests have shown that the "background extraction'' allows a more reliable estimate of the background spectrum.

We compare both background subtraction techniques in Table B.1. We find that the "background modeling'' systematically overestimates the background light contribution as one goes to larger galactocentric radii. The index differences increase between spectra which have been cleaned using "background modeling'' and "background extraction''. This is basically due to an overestimation of the background light from single background spectra which were taken at intermediate galactocentric radii. We, therefore, drop the "background modeling'' and proceed for all subsequent analyses with the "background extraction'' technique. In summary, the crucial drawback of the "background modeling'' is that it requires a prediction of the bulge light fraction from separate spectra which is strongly model-dependent. The bulge light contains changing scale heights for different stellar populations (see Frogel 1988; Wyse et al. 1997, and references therein). The background light at the cluster position includes an unknown mix of bulge and disk stellar populations (Frogel 1988; Frogel et al. 1990; Feltzing & Gilmore 2000), an unknown contribution from the central bar (Unavane & Gilmore 1998; Unavane et al. 1998), and is subject to differential reddening on typical scales of $\sim$90 $^{\prime\prime}$ (Frogel et al. 1999) which complicates the modeling. Clearly, with presently available models (e.g. Kent et al. 1991; Freudenreich 1998) it is impossible to reliably predict a spectrum of the galactic bulge as a function of galactic coordinates. The "background extraction'' technique naturally omits model predictions and allows to obtain the total background spectrum, including sky and bulge light, from the object spectrum itself.

We selected low-luminosity outer sections in the slit's intensity profile (see Fig. 3) to derive the background spectrum for each globular cluster. Only those regions which show flat and locally lowest intensities and are located outside the half-light radius $r_{\rm h}$ (Trager et al. 1995) are selected. We sum the spectra of the background light of all available pointings to create one high-S/Nbackground spectrum for each globular cluster. All globular clusters were corrected using this background spectrum. The background-to-cluster light ratio depends on galactic coordinates, and is $\la$0.1 for NGC 6388 and $\sim$1 for NGC 6528. In order to lower this ratio, only regions inside $r_{\rm h}$ are used to create the final globular-cluster spectrum. This restriction decreases the background-to-cluster ratio by a factor of $\ga$2. In the case of NGC 6218, NGC 6553, and NGC 6626 the half-light diameter $2r_{\rm h}$ is larger or comparable to the spatial dimensions of the slit, so that no distinct background regions can be defined. For these clusters we estimate the background from flat, low-luminosity parts along the spatial axis inside $r_{\rm h}$ but avoid the central regions (see Fig. 3).

   
3.2 Contamination by bright objects

To check if bright foreground stars inside the slit contaminate the globular cluster light, we plot the intensity profile along the slit's spatial axis. The profiles of each pointing are documented in Fig. 3. Since we use the light only inside one half-light radius (indicated by the shaded region) and therefore maximize the cluster-to-background ratio, the probability for a significant contamination by bright non-member objects is very low. Even very bright foreground stars will contribute only a small fraction to the total light.

Figure 3: Intensity profiles of each pointing for all sample globular clusters. The fraction of the profile which was used to create the final globular cluster spectrum is shaded. Each cluster has at least three pointings which are shifted by a few slit widths to the north and south. Note that clusters with a sampled luminosity less than $10^4 L_\odot$ and relatively large half-light radii (i.e. see Sect. 3.4 and Table 1) have strongly fluctuating profiles.

Figure 3: continued.

However, three of our sample globular clusters (NGC 6218, NGC 6553, and NGC 6626) are extended and their half-light diameter are just or not entirely covered by the slit. The low radial velocity resolution of our spectra does not allow to distinguish between globular cluster stars and field stars inside the slit. Galactic stellar-population models (e.g. Robin et al. 1996) predict a maximum cumulative amount of 4 stars with magnitudes down to V=19.5 (all stars with V=18.5-19.5 mag) towards the Galactic center inside the equivalent of three slits. This maximum estimate applies only to the Baade's Window globular clusters NGC 6528 and NGC 6553. All other fields have effectively zero probability to be contaminated by foreground stars. Nonetheless, even in the worst-case scenario, if 4 stars of 19th magnitude would fall inside one slit, their fractional contribution to the total light would be ${\la}1.2\times 10^{-4}$. For globular clusters at larger galactocentric radii this fraction is even lower. Hence, we do not expect a large contamination by foreground disk stars.

One critical case is the northern pointing of NGC 6637 in which a bright star falls inside the half-light radius (see upper panel of the NGC 6637 profile in Fig. 3). This star contributes $\la$10% to the total light of the sampled globular cluster and its radial velocity is indistinguishable from the one of NGC 6637. An inspection of DSS images shows that the NGC 6637 field contains more such bright stars which are concentrated around the globular cluster center and are therefore likely to be cluster members. We therefore assume that the star is a member of NGC 6637 and leave it in the spectrum.

3.3 Comparison with previous measurements

Lick indices are available in the literature for a few globular clusters in our sample, as we intentionally included these clusters for comparison. The samples of Trager et al. (1998) and Covino et al. (1995) and Cohen et al. (1998) have, respectively, three, six, and four clusters in common with our data. Note that the indices of Covino et al. (1995) and Cohen et al. (1998) were measured with the older passband definitions of Burstein et al. (1984) and are subject to potential systematic offsets. Where necessary we also converted the values of Covino et al. to the commonly used Å-scale for atomic indices and kept the magnitude scale for molecular bands. Table A.1 summarizes all measurements, including our data. Figure 4 shows the comparison of some indices between the previously mentioned data sets and ours. The mean offset in the sense $EW_{\rm data}$- $EW_{\rm lit.}$ and the dispersion are given in Table 4. Most indices agree well with the literature values and have offsets smaller than the dispersion.

Only the Fe 5270 index is $0.75~ \sigma$ higher for our data compared with the literature. This is likely to be due to imperfect smoothing of the spectra in the region of $\sim$5300 Å. Our smoothing kernel is adjusted according to the Lick resolution given by the linear relations in Worthey & Ottaviani (1997). This relations are fit to individual line resolution data which show a significant increase in scatter in the spectral range around 5300 Å (see Fig. 7 in Worthey & Ottaviani 1997). Hence even if our smoothing is correctly applied, the initial fitting of the Lick resolution data by Worthey & Ottaviani might introduce biases which cannot be accounted for a posteriori. However, the offset between the literature and our data is reduced by the use of the synthetic $\langle$Fe$\rangle$ index which is a combination of the Fe 5270 and Fe 5335 index. The $\langle$Fe$\rangle$ index partly cancels out the individual offsets of the former two indices.

 

 

Table 4: Offsets and dispersion of the residuals between our data and the literature. Dispersions are 1 $\sigma$ scatter of the residuals.

index	offset	dispersion	units
G4300	0.45	0.70	Å
H$\beta$	0.27	0.57	Å
Mg2	0.009	0.014	mag
Mgb	-0.01	0.27	Å
Fe 5270	-0.33	0.44	Å
Fe 5335	0.12	0.27	Å

Figure 4: Comparison of index measurements of Trager et al. (1998), marked by squares, Cohen et al. (1998), marked by circles (without errors for the Cohen et al. data), and Covino et al. (1995), indicated by triangles, with our data. Solid lines mark the one-to-one relation and dashed lines the mean offsets.

   
3.4 Estimating the sampled luminosity

The spectrograph slit samples only a fraction of the total light of a globular cluster's stellar population. The less light is sampled the higher the chance that a spectrum is dominated by a few bright stars. In general, globular cluster spectra of less than $10^4~L_\odot$ are prone to be dominated by statistical fluctuations in the number of high-luminosity stars (such as RGB and AGB stars, etc.). For a representative spectrum it is essential to adequately map all evolutionary states in a stellar population, such that no large statistical fluctuations for the short-living phases are expected. We therefore estimate the total sampled luminosity of the underlying stellar population 1) from spectrophotometry of the flux-calibrated spectra and 2) from the integration of globular cluster surface brightness profiles.

As a basic condition of the first method we confirm that all three nights have had photometric conditions using the ESO database for atmospheric conditions at La Silla. We use the flux at 5500 Å in the co-added and background-subtracted spectra and convert it to an apparent magnitude with the relation

$$m_V = -2.5\cdot\log(F_\lambda) - (19.79\pm0.24)$$ (2)

where $F_\lambda$ is the flux in erg cm^-2 s^-1 Å^-1. The zero point was determined from five flux-standard spectra, which have been observed in every night. Its uncertainty is the 1$\sigma$standard deviation of all measurements. After correcting for the distance, the absolute magnitudes were de-reddened using the values given in Harris (1996). The reddening values are given in Table 1 along with the distance modulus (Harris 1996). Using the absolute magnitude of the combined globular cluster spectrum, we calculate the total sampled luminosity

$$L_{\rm T}=BC_V\cdot10^{-0.4\cdot\left(m_V-(m-M)_V-M_\odot-3.1\cdot{E}_{(B-V)}\right)}$$ (3)

where $M_\odot=4.82$ mag is the absolute solar magnitude in the V band (Hayes 1985; Neckel 1986a,1986b). With the bolometric correction BC_V (Renzini 1998; Maraston 1998) we obtain the total bolometric luminosity $L_{\rm T}$. The total globular cluster luminosity is compared to the sampled flux and tabulated in Table 5 as $L_{\rm slit}$.

   

Table 5: Sampled and total luminosities of observed globular clusters and bulge. All values have been determined from the co-added spectra of all available pointings. For the co-added bulge spectrum we adopted a mean metallicity of $\rm [Fe/H]\approx~ -0.33$ dex (Zoccali et al. 2002).

cluster	$F_\lambda$(@5500 Å)a	MVb	MVc	$BC_{\rm V}^{d}$	$L_{{\rm prof}}^{e}$	$L_{{\rm slit}}^{f}$	$L_{{\rm GC}}^{g}$	$\frac{L_{{\rm slit}}}{L_{{\rm GC}}}$	$N_{\rm RGB}^{h}$	$N_{\rm uRGB}^{i}$
NGC 5927	$(3.6\pm0.2)\times10^{-13}$	-5.88	-7.80	1.57	$1.7\times10^4$	$(3.0\pm0.8)\times10^4$	$1.8\times10^5$	0.171	359	9
NGC 6218	$(2.0\pm0.1)\times10^{-13}$	-2.65	-7.32	1.29	$4.0\times10^3$	$(1.3\pm0.3)\times10^3$	$9.3\times10^4$	0.014	15	0
NGC 6284	$(3.7\pm0.1)\times10^{-13}$	-6.27	-7.87	1.32	$1.9\times10^4$	$(3.6\pm0.9)\times10^4$	$1.6\times10^5$	0.230	435	11
NGC 6356	$(6.4\pm0.1)\times10^{-13}$	-6.94	-8.52	1.51	$4.8\times10^4$	$(7.6\pm1.8)\times10^4$	$3.3\times10^5$	0.233	913	23
NGC 6388	$(2.8\pm0.1)\times10^{-12}$	-8.68	-9.82	1.47	$1.6\times10^5$	$(3.7\pm1.0)\times10^5$	$1.1\times10^6$	0.351	4430	111
NGC 6441	$(2.0\pm0.1)\times10^{-12}$	-8.52	-9.47	1.49	$1.3\times10^5$	$(3.2\pm0.9)\times10^5$	$7.8\times10^5$	0.417	3894	97
NGC 6528	$(4.9\pm0.2)\times10^{-13}$	-7.28	-6.93	1.66	$2.3\times10^4$	$(1.1\pm0.3)\times10^5$	$8.3\times10^4$	1.376 $^{{\rm j}}$	1376	34
NGC 6553	$(2.0\pm0.1)\times10^{-13}$	-6.41	-7.99	1.59	$1.5\times10^4$	$(4.9\pm1.4)\times10^4$	$2.1\times10^5$	0.234	593	15
NGC 6624	$(8.0\pm0.7)\times10^{-13}$	-5.78	-7.50	1.54	$1.8\times10^4$	$(2.7\pm0.8)\times10^4$	$1.3\times10^5$	0.205	322	8
NGC 6626	$(5.6\pm0.1)\times10^{-13}$	-5.61	-8.33	1.30	$1.4\times10^4$	$(1.9\pm0.5)\times10^4$	$2.4\times10^5$	0.082	231	6
NGC 6637	$(8.0\pm1.4)\times10^{-14}$	-2.70	-7.52	1.43	$1.5\times10^4$	$(1.5\pm0.6)\times10^3$	$1.2\times10^5$	0.012	17	0
NGC 6981	$(1.2\pm0.1)\times10^{-13}$	-3.95	-7.04	1.31	$7.7\times10^3$	$(4.2\pm1.3)\times10^3$	$7.3\times10^4$	0.058	50	1
Bulge	$(4.0\pm0.3)\times10^{-13}$	-5.14	...	1.59	...	$(1.5\pm0.7)\times10^4$	...	...	180	5

^a

Sampled flux at 5500 Å in erg cm^-2 s^-1 Å^-1.

^b

Absolute magnitude of the sampled light.

^c

Absolute globular cluster magnitude (Harris 1996).

^d

V-band bolometric correction for a 12 Gyr old stellar population calculated for the according cluster metallicity (see Table 1). The values were taken from Maraston (1998,2002).

^e

Sampled bolometric luminosity $L_{\rm T}$ in $L_\odot$ from the integration of King surface brightness profiles of Trager et al. (1995).

^f

Sampled bolometric luminosity $L_{\rm T}$ in $L_\odot$ calculated from the total light sampled by all slit pointings.

^g

Globular cluster's total bolometric luminosity $L_{\rm T}$ in $L_\odot$.

^h

Expected number of RGB stars contributing to the sampled luminosity.

ⁱ

Expected number of upper RGB stars ( $\Delta M_{\rm Bol}\leq 2.5$ mag down from the tip of the RGB) contributing to the sampled luminosity.

^j

See Sect. 3.4.

For the integration of the surface brightness profiles we use the data from Trager et al. (1995) who provide the parameters of single-mass, non-rotating, isotropic King profiles (King 1966) for all sample globular clusters. The integrated total V-band luminosities have been transformed to $L_{\rm T}$ and are included in Table 5 as $L_{\rm prof}$. Note that for most globular clusters the results from both techniques agree well. However, for some globular clusters the integration of the surface brightness profile gives systematically larger values. This is due to the fact that the profiles were calculated from the flux of all stars in a given radial interval whereas the slits sample a small fraction of the flux at a given radius. Hence, the likelihood to sample bright stars which dominate the surface brightness profile falls rapidly with radius. Since bright stars are point sources the slit will most likely sample a smaller total flux than predicted by the surface brightness profile. This effect is most prominent for globular clusters with relatively large half-light radii and waggly intensity profiles (cf. Fig. 3).

Among the values reported in Table 5, the case of NGC 6528 is somewhat awkward, as the estimated luminosity sampled by the slit is apparently higher than the total luminosity of the cluster, which obviously cannot be. This cluster projects on a very dense bulge field, and therefore the inconsistency probably arises from either an underestimate of the field contribution that we have subtracted from the cluster+field co-added spectrum, or to an underestimate of the total luminosity of the cluster as reported in Harris (1996), or from a combination of these two effects.

From the sampled flux $L_{\rm slit}$ we estimate the number of red giant stars contributing to the total light. Renzini (1998) gives the expected number of stars for each stellar evolutionary phase of a $\sim$15 Gyr old, solar-metallicity simple stellar population. In general, in this stellar population the brightest stars which contribute a major fraction of the flux to the integrated light are found on the red giant branch (RGB) which contributes $\sim$40% (Renzini & Fusi Pecci 1988) to the total light. The last two columns of Table 5 give the expected number of RGB and upper RGB stars in the sampled light. Upper RGB stars are defined here as those within 2.5 bolometric magnitudes from the RGB tip. The RGB and upper RGB lifetimes are ${\sim}6\times 10^8$ and ${\sim}1.5\times 10^7$ years, respectively.

Due to the small expected number of RGB and upper RGB stars contributing to the spectra of NGC 6218 and NGC 6637, both spectra are prone to be dominated by a few bright stars. In fact, for both clusters the intensity profiles (see Fig. 3) show single bright stars. However, the contribution of the brightest single object is $\la$10% (see Sect. 3.2) for all spectra. All other spectra contain enough RGB stars to be unaffected by statistical fluctuations in the number of bright stars.

The sampled luminosity of the bulge fields is more difficult to estimate. Uncertain sky subtraction (see problems with "background modeling'' in Sect. 3.1), and patchy extinction in combination with the bulge's spatial extension along the line of sight make the estimate of the sampled luminosity quite uncertain. Here we simply give upper and lower limits including all available uncertainties. The average extinction in Baade's Window is $\langle A_V\rangle\approx1.7$ mag and varies between 1.3 and 2.8 mag (Stanek 1996). The more recent reddening maps of Schlegel et al. (1998) confirm the previous measurements and give for our three Bulge fields the extinction in the range $1.6\la A_{V}\la 2.1$ mag. We adopt a distance of 8-9 kpc to the Galactic center and use the faintest and brightest sky spectrum to estimate the flux at 5500 Å. The total sampled luminosity $L_{\rm T}$ of the final co-added Bulge spectrum is $(1.3{-}2.6)\times 10^4~ L_\odot$. Our value is in good agreement with the sampled luminosity derived from surface brightness estimates in Baade's Window and several fields at higher galactic latitudes by Terndrup (1988). According to his V-band surface brightness estimates for Baade's Window and a field at the galactic coordinates $l=0.1^{\circ}$ and $b=-6^{\circ}$, the sampled luminosity in an area equivalent to all our bulge-field pointings in one of the two fields is $(2.6\pm0.5)\times 10^4~ L_\odot$ and $(1.2\pm0.3)\times10^4~L_\odot$, respectively.