Cluster | [M/H] | (m-M)0 | E(B-V) |
NGC 6528 | -0.10 | 14.37 | 0.62 |
NGC 6553 | -0.10 | 13.46 | 0.84 |
NGC 104 | -0.57 | 13.32 | 0.05 |
NGC 6171 | -0.88 | 13.95 | 0.31 |
NGC 6121 | -1.06 | 11.68 | 0.35 |
NGC 6809 | -1.59 | 13.82 | 0.10 |
NGC 7099 | -1.84 | 14.71 | 0.01 |
NGC 4590 | -1.90 | 15.14 | 0.04 |
NGC 7078 | -1.92 | 15.15 | 0.09 |
![]() |
Figure 9: Bulge CMD resulting from the combination of the optical WFI and near-IR 2MASS data. The line represents the fiducial locus of the globular cluster NGC 6528. The distance and reddening of the bulge field adopted for this comparison are (m-M)0=14.47 and E(B-V) =0.45, respectively, while for NGC 6528 it is assumed (m-M)0=14.37 and E(B-V) =0.62 (Ferraro et al. 2000). |
From the combination of the optical (WFI) and near-IR (2MASS)
decontaminated data, a (MK,V-K) CMD was obtained including 22 000 stars with MK<0.5, and the result is shown in
Fig. 9. A comparison with the fiducial line of the globular
cluster NGC 6528 from Ferraro et al. (2000) immediately suggests that
the mean metallicity of the bulge is virtually identical to that of
this cluster, with a quite modest dispersion about this mean. This is
demonstrated by the slope of the giant branch of the cluster and of
that of the bulge field being the same. (Note that the metallicity
affects the slope, while the reddening causes a solid shift of
the RGB.) Therefore, the metallicity of NGC 6528 (and that of the
twin cluster NGC 6553) has a special importance in connection with our
attempt at determining the bulge metallicity distribution. In
Fig. 9, a distance modulus of
(m-M)0=14.47
0.08 (7.8 kpc) was adopted for the bulge, according to the most recent
determination by McNamara et al. (2000) using RR-Lyrae and
Scuti variables from the OGLE survey. The reddening of our bulge field
relative to NGC 6528 can then be estimated from Fig. 9, and
we obtain E(B-V) =0.45, needed to match the bulge and the cluster
loci given the small difference in the two distance moduli. For
NGC 6528 the corresponding quantities are given in
Table 2. The large number of stars in the upper RGB of
Fig. 9, coupled with the high sensitivity of the (V-K)
color to metallicity, and its very small sensitivity to a possible age
dispersion, allows a determination of the bulge MD via the method
described in Saviane et al. (2000).
The method is based on the construction of a family of hyperbolas in
the plane (MK,V-K) suitable to represent a grid of upper RGBs from
empirical template globular clusters, with known
metallicities. Each hyperbola is represented by the expression:
![]() |
(1) |
![]() |
(2) |
![]() |
(3) |
![]() |
(4) |
d=k10. | (5) |
![]() |
Figure 10: The V, K RGBs of the template GCs published by Ferraro et al. (2000) (open squares), together with the analytical RGBs (dotted lines). The values of [M/H] for the analytical RGBs go from solar to [M/H] = -2.0 in steps of 0.2. |
Although in principle spectroscopic determinations may be more accurate, the photometric approach has the advantage of relying on high S/N quantities (i.e., the magnitudes of the brightest stars) and on large statistics. However, it is entirely differential, i.e., it depends on the accuracy of the metallicity assigned to the templates, which ultimately relies on spectroscopic determinations. The most complete and homogeneous grid of near-IR GC RGB templates presently available in the literature (Ferraro et al. 2000; see Table 2) includes 10 low reddening, nearby GCs with metallicity [M/H] between -1.92 and -0.1. One cluster (NGC 6637) from the Ferraro et al. sample has been excluded from our calculations, for reasons explained below.
With the exception of the two most metal rich clusters (NGC 6528 and
NGC 6553), for the GCs in Table 2 we adopted the iron
abundance [Fe/H] from Harris (1996), and corrected it to [M/H]
adopting an -element enhancement [
/Fe] = 0.3 for
clusters with [Fe/H] <-1.0, and [
/Fe] = 0.20 for more
metal-rich clusters (Carney 1996; Salaris & Cassisi 1996). As emphasized earlier, the case of NGC 6528 and NGC 6553 is particularly
important. A few stars in each of the two clusters have been observed
at intermediate and high spectral resolution, but different groups
have obtained quite discrepant results. For NGC 6528, Carretta et al. (2001) and Coelho et al. (2001) report respectively [Fe/H] = +0.07
and -0.5 (the latter value coming from low-resolution spectra). For
[M/H] the same authors derive +0.17 and -0.25, respectively. For NGC 6553 Barbuy et al. (1999) give [Fe/H] = -0.55 and [M/H] = -0.08, while
Cohen et al. (1999) report [Fe/H] = -0.16, and Origlia et al. (2002) give [Fe/H] = -0.3, with [
/Fe] = +0.3. These
discrepancies are uncomfortably large, and may hopefully disappear as
soon as more high-resolution data are gathered at 8-10 m class
telescopes. For both clusters we finally adopt [M/H]=-0.1 (the value
reported in Table 2) with the uncertainty of the resulting MD being
dominated by the uncertainty of the metallicity of these two clusters.
Figure 10 shows the resulting grid of RGB loci: open squares represent the fiducial points extracted from the empirical templates, while the RGBs from the analytical interpolation are shown as dotted lines. The coefficients of the Eqs. (4)-(7) are listed inside the figure. The analytical RGBs are shown for metallicities ranging from [M/H] = 0 to [M/H] =-2.0, in steps of 0.2. All the empirical templates, with the exception of NGC 104 (third cluster from the right) follow very well the RGB shape trend of the analytical solution. We could find no obvious explanation for the apparent discrepancy of NGC 104: its CMD is quite populated in this region, and, being one of the best studied clusters, the adopted parameters (metallicity, reddening and distance) are rather robust. The near-IR observations of this cluster were done with the ESO/MPG 2.2 m telescope mounting IRAC-2, an early IR array detector (Ferraro et al. 2000); perhaps the use of a more modern instrument may clarify the issue.
As evident from Fig. 10, the sensitivity to metallicity is a strong function of the position in the CMD, hence of metallicity itself. The leverage increases with both luminosity and color, being favored at high metallicities by the increasing TiO blanketing in the V band causing redder and redder V-K colors.
In order to investigate the effect of distance and reddening
dispersion on the MD derived using the adopted method we simulated
such effects on the (MK,V-K) CMD of the bulge cluster NGC 6553
(Guarnieri et al. 1998). To each star of NGC 6553 we associated a
distance modulus randomly extracted according to a bulge space density
distribution of the form
(Sellwood
& Sanders 1988; Terndrup 1988), where r is the spatial distance
from the Galactic center. The line of sight integration at the field
position (
(l,b)=(0,-6)) gives a 1-
dispersion of 0.13 mag in
the distance modulus, the distribution being close to Gaussian in the
core, but with somewhat broader wings. A top hat reddening
distribution of
0.15 was also adopted. The latter is believed to
be an upper limit to the observed bulge reddening variation across our
field, but has been chosen as a conservative assumption, in order to
have an upper limit on the possible biases in the derived MD. Random
extractions of both distance modulus and reddening were repeated 6
times for each star in the original CMD by Guarnieri et al. (1998) in
order to obtain a more populated CMD. Figure 11 shows the
resulting simulated CMD including distance and reddening dispersion
effects (upper panel). The lower panel shows the MD obtained in the same way as that
to be applied to the bulge, and reveals two interesting effects. First,
if all the stars brighter than MK=-3 are considered, the resulting
MD (dashed histogram) is extremely broad with a long metal-poor
tail. This is entirely due to the fact mentioned above: the
separation between the RGBs corresponding to different metallicities
becomes very small towards faint magnitudes, much smaller than the
magnitude/color dispersion due to distance and reddening
dispersions. However, if the analysis is restricted to stars brighter
than MK=-4.5 then the derived MD shows a fairly sharp peak at
[M/H] = -0.1 (i.e., centered on the adopted metallicity for
this cluster), well fitted by a Gaussian distribution with
(FWHM= 0.24). This exercise demonstrates that, as long as the analysis
is confined to the stars brighter than MK=-4.5: (i) one should
not expect systematic biases; (ii) the spread introduced by the
distance and reddening dispersions is of the order of
0.1 dex
in [M/H]; and (iii) contamination by AGB stars (which would
introduce a bias artificially skewing the distribution towards the
metal-poor side) is negligible at these magnitudes due to the
exclusion of the more populated (and bluer) AGB "clump'', located at
.
We therefore restrict to MK<-4.5 the derivation of the
bulge MD.
Figure 12 shows the analytical RGBs overplotted on the bulge
upper RGB. The dotted part of each RGB is the extrapolation above the
theoretical location of the RGB tip (cf. Sect. 7), hence only AGB
stars are expected in this region. The
metallicities of the analytical RGBs range from [M/H] = +0.2 to -1.8,
in steps of 0.2. Note that the most metal-rich templates have
metallicity of [M/H] =-0.1, therefore the shape of the analytical
RGBs for higher metallicity is the result of a small extrapolation. Stars
bluer than V-K=2.8 (vertical dashed line) were not considered, in
order to exclude a few bluer objects that are most likely a disk
residue due to imperfect statistical decontamination. Stars fainter
than MK=-4.5 (horizontal dashed line) were excluded as well, for
the reasons explained above. After these cuts, a sample of 503 stars
has been used to derive the bulge MD. It is already clear from this
figure that most of the bulge stars are located between the [M/H]
and [M/H] =-0.6 templates, with a peak at [M/H] =-0.1 and very few
stars more metal-poor than
-1. Formally, super-solar
metallicity stars ([M/H] >0) represent 29
of the sample. This
should be regarded as an upper limit, due to the diffusion to
higher [M/H] values caused by the dispersion in distance, reddening,
etc. (see Fig. 11).
Before proceeding to derive the bulge MD a few biases must be quantitatively evaluated and compensated for: 1) the rate at which stars leave the main sequence (called evolutionary flux in Renzini & Buzzoni 1986) has a slight metallicity dependence, 2) the rate of evolution along the RGB scales as Z-0.04 (Rood 1972), and 3) by adopting the MK=-4.5 cut one samples (bolometrically) deeper on the RGB the higher the metallicities.
![]() |
Figure 14: Comparison between the bulge MD derived from Fig. 12 (shaded histogram) and those derived with spectroscopic surveys. |
The amplitude of these factors is shown in Fig. 13. The upper
panel shows how the evolutionary flux changes as a function on
metallicity, relative to its value at .
The
middle panel shows the combination of effect 2) and 3) mentioned
above: the time spent on the RGB, from MK=-4.5 to the tip,
normalized at solar value, slowly increases as a function of metallicity.
Finally the lower panel shows the combination of the two factors
above, which is the correction to apply to each metallicity
bin of the MD to take into account the evolutionary effects.
Since the evolutionary flux and the RGB lifetime have opposite
behaviour with metallicity, the final correction factor is never
larger than few percent, well within the intrinsic precision of
our measurement.
The resulting bulge MD for the 503 stars in Fig. 12 is
finally shown in the three panels of Fig. 14 as a shaded
histogram. Also shown in Fig. 14, as thick "open''
histograms, are the bulge MDs determined from various spectroscopic
studies, normalized to the total number of stars in our sample. Note
that all these spectroscopic determinations of the bulge MD refer to
[Fe/H] abundance. Since the template RGBs are on the [M/H] scale, we
subtracted from the bulge [M/H] distribution the same -element
enhancement (i.e., 0.2 for [Fe/H] >-1 and 0.3 for [Fe/H] <-1) that
had been applied to the template GCs, in order to obtain a [Fe/H]
distribution. Although the bulge high resolution studies do not
permit to draw strong conclusions on the
-element enhancement,
the similarity of the bulge CMD with that of bulge GCs would favor a
similar chemical enrichment history. Certainly the new generation
multi-object spectrographs will allow us to improve our knowledge in
this field.
The comparisons shown in Fig. 14 shows that the present,
"photometric'' MD is broadly consistent with the spectroscopic ones
by McWilliam & Rich (1994) and Ramirez et al. (2000), with just a
somewhat less pronounced supersolar [Fe/H] tail in the photometric
MD. (This characteristic is exacerbated in the comparison with the MD
of Sadler et al. 1996, based on low resolution data.) We caution,
however, that the position of the high [Fe/H] cutoff is entirely
dependent on the metallicity assigned to the two template clusters
NGC 6528 and NGC 6553. For instance, the apparent discrepancy with,
e.g., McWilliam & Rich (1994) at high metallicity would disappear if
we would have assigned to NGC 6528 and NGC 6553 a metallicity 0.2 dex higher. Indeed this would bring to coincidence with M&R the
high metallicity cutoff, while stretching the distribution and
reducing the excess at [Fe/H]
.
We believe that the
homogeneous high-resolution studies of cluster and bulge field
stars that will soon become available, e.g., with the forthcoming
FLAMES multifibre spectrograph on VLT (Pasquini et al. 2000), will
clarify this problem.
On the other hand, we tend to consider as quite reliable the sharpness of the cutoff at high [M/H]. Due to the TiO blanketing in the V band, the V-K color of RGB stars has a strong, rapidly increasing sensitivity to [M/H], and any high metallicity tail would have resulted in a dramatic broadening of the upper RGB, which instead is clearly absent in the CMD of the bulge shown in Fig. 9. Moreover, the high [Fe/H] cutoff would be even sharper, had we underestimated the effect of the distance and reddening dispersions.
The most straightforward approach is now to compare this empirical MD
with the Simple (or one-zone, closed-box) Model of chemical evolution
(Searle & Sargent 1972). Rich (1990) first made this comparison for
the bulge and found the Simple Model to be a good fit to the abundance
distribution from Rich (1988). The Simple Model assumes that no
infall or outflow of metals has occurred during the star-forming phase
of the system. The distribution follows the relation
,
where the single parameter y, the yield, is given by
.
Hence, the yield is the average metallicity of
the stars in a one-zone system following the exhaustion of the gas
(Hartwick 1976; Mould 1984). If metals are lost from the system by
outflow, the functional form of the distribution is unchanged, but the
mean abundance
is the yield (as would be calculated
from supernova models) reduced by the appropriate outflow parameter.
Figure 15 shows a plot of the Simple Model distribution (for
)
overlaying the data. Note that both
panels show the same model and the same data, once using [M/H] and
once using
as abscissa. As the Simple Model satisfies the
requirements of a probability distribution, the function is scaled by
the area under the data histogram, so that the area covered by data
and fit are identical.
From the plots, the general shape of the abundance distribution is in
fairly good agreement with the Simple Model. However, there are
noticeable deviations: in the subsolar regime (
)
less stars are observed than predicted, while with respect to the
model there is an excess of near-solar metallicity objects. This excess
can be traced back to the fairly sharp clustering of the bulge stars
around the RGB template at such metallicity (see again Figs. 7 and 10). This feature is most likely real, as many factors conjure to
broaden the derived distribution (dispersion along the line of sight,
differential reddening, incomplete disk decontamination, etc.). For
the same reasons, most likely real is the sharp cutoff at high
metallicity, that may even be sharper given the mentioned effects that
tend to smooth out any sharp feature in the MD. The moderate shortage
of metal-poor stars compared to the Simple Model may flag the presence
of a G-dwarf problem, a point on which we return in Sect. 8.
The sharp high-metallicity cutoff of the MD suggests that star formation did not proceed to complete gas consumption. If the bulge formed in a rapid and intense starburst, one can imagine that much of the metals would have been produced in situ in core-collapse supernovae, eventually driving strong, metal-rich galactic winds. There are at least two independent arguments favoring this scenario, one direct and one indirect: a) high redshift galaxies thought to be proto-bulges are observed to have strong metal enriched winds (Steidel et al. 1996), and b) in clusters of galaxies at least as much metal mass is out of galaxies in the intracluster medium, as there is locked into stars inside galaxies, which is taken as evidence for early metal-enriched galactic winds (Renzini 1997, 2002). Therefore, a relatively sharp cutoff at the metal rich end, such as we observe, would result if the star formation was sufficiently violent as to eventually evacuate the gas from the proto-bulge before it was exhausted by star formation.
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