F. Fusi Pecci
, O. Bendinelli
, C. Cacciari
, C.E. Corsi
,
G.S. Djorgovsky
, L. Federici
, F.R. Ferraro
, I.R. King
,
G. Parmeggiani
, F. Zavatti
Osservatorio Astronomico, Bologna, Italy
Università di Bologna, Italy
Osservatorio Astronomico, Roma, Italy
California Institute of Technology, Pasadena, CA, USA
University of California at Berkeley, Berkeley, CA, USA
---with varying [Fe/H] :
where the associated errors result from the formal errors in the measuring and best fitting procedures. Important implications on the ages of Galactic globular clusters are schematically discussed.
Keywords: globular clusters,M31,photometry,HST
The general aims of this program are: a) comparison with the Milky Way
counterparts providing information on galaxy formation scenarios;
b) straightforward (in principle) determination of the slope of the
M
vs. [Fe/H] relation, which is presently difficult to derive in the
Milky Way.
Specifically, we want to derive CMDs as faint and accurate as possible
(down to the HB and fainter) in order to study:
vs. [Fe/H] relation, which has implications on the
definition of the distance scale, age determination, models of galaxy
formation.
The full description of the detailed photometric treatments and the data is postponed to a forthcoming paper where also the surface profiles and the structural cluster parameters will be measured and discussed.
The data for the M31 GCs K351 and K280 were obtained by us (GO 5420)
using the 
pixel
imaging mode of the f/96 camera of
the COSTAR-FOC (4
sec F480LP + (1500+2300)sec F430W).
The data for the other 5 clusters (K1, 58, 105, 108, 219) were
retrieved from the HST archive. In particular, we have reduced all the
PC frames taken from GTO program 5112 (P.I.: Westphal)
(2
1000s with F555W (V) + 2
1000s with F814W (I))
and the PC frames taken with the same filters from GO 5464
(P.I. M. Rich) (1600s with F555W (V) + 1200s with F814W (I), in total).
The results obtained from this material have been published by
Ajhar et al. (1995) and Rich et al. (1995), respectively.
Concerning the pre-processing and calibrating procedures we have strictly adopted the pipeline applied at the STScI.
The photometry of individual stars on the co-added frames was performed using ROMAFOT (Buonanno et al. 1983), purposely adapted to handle HST data. In particular, the HST point spread function (PSF) has been modelled by a Moffat (1969) function (in the central part of the profile) plus a numerical experimental map of the residuals in the wings. The optimal PSF has been determined from the analysis of the brightest uncrowded stars independently in both frames in each color.
The standard searching procedure available in ROMAFOT (see Ferraro et al. 1991) was then applied to each frame, excluding a small central area in order to avoid regions which are severely crowded even with HST .
The instrumental magnitudes resulting from the fitting procedure have been transformed to the HST photometric system by using a sample of selected isolated stars whose magnitudes have been computed using both the fitting procedure and the classic aperture photometry.
Ajhar et al. (1995) and Rich et al. (1995) have widely discussed the problem of estimating the global (i.e., internal + systematic) errors in the HST photometry of the M31 GCs, also using simulations and artificial star experiments.
A detailed discussion of our photometric errors and a complete comparison with the previous photometries will be presented in the forthcoming full paper.
The internal errors are mostly due to noise from the sky, imperfections of the PSF fitting, and blending effects. The method adopted with ROMAFOT to describe the PSF is particularly effective in reducing the size of the internal errors essentially because of the combination of a ``known'' Moffat-function and a map of the local residual plus a multicomponent fitting procedure.
A straightforward way of estimating our internal errors can be the direct comparison of the observed widths of the various branches in the final CMDs for the clusters in common with previous studies based on the same original HST data. Figure 1a,b compares the CMDs of K105 as obtained here and as reported in Figure 9 of Ajhar et al. (1995). As one can see, both the location and the spread of the data points around the main ridge lines are comparable, and even the substructures along the branches are very similar. This ensures that the photometric quality of the reductions are comparable, and we conclude that our internal photometric errors are at most as high as those quoted by Ajahr et al. (1995), which they claim to be fully consistent with those expected on the basis of their simulations.
Figure: CMD of the globular cluster K105 in M31.
Concerning the systematic errors, there are many reasons for uncertainty and most of them can hardly be quantified safely. In particular, there are problems related, for instance, to charge transfer efficiency (CTE) with WFPC2. Then, there are uncertainties in the conversion to Standard System for both cameras. Eventually, there is additional concern about the exact zero-points.
In conclusion, we believe that while the internal errors are surely small enough to guarantee that they are close to the minimum limit achievable, the residual systematic errors, especially in the zero-points, can still be quite large (up to 0.05 mag). This may have a strong impact on the following discussion as we are forced to collect data taken from different cameras, operated at different temperature conditions. Since the whole problem of absolute calibrations (both with FOC and WFPC2) is under investigation, it is natural to conclude that any differential variation of the zero-points for one of the used configurations will affect the final results.
The CMDs eventually obtained from all the measured stars in the 7 clusters are reported in Figure 2a-g. The clusters have been ordered with increasing metallicity to put into evidence the regular variation of the CMD morphology with [Fe/H] . This overall behavior makes the CMDs of the observed M31 GCs essentially identical to those of Galactic globulars having the same [Fe/H] .
Since our specific aim here is to determine the M
vs. [Fe/H] relation,
we postpone any further quantitative analysis and discussion of the CMDs,
and simply report the procedure followed to derive the quantities
involved in this calibration.
We report in Table 1 the values of [Fe/H] obtained by Huchra et al. (1991) from a small set of spectroscopic indices and those estimated by Bonoli et al. (1987) from V-K integrated colors calibrated in terms of [Fe/H] . As one can see, the two estimates are in sufficiently good agreement for most clusters, although more information seems to be essential in some cases.
The availability of new, sufficiently reliable ridge lines for the giant branches can allow, in principle, some improvement also in the estimate of metallicity if one compares the morphology and slope of the RGB of each individual M31 GC with a reference grid of Galactic GCs with known metallicities in the same observational plane (see, for instance, Da Costa & Armandroff 1990). Unfortunately, this procedure is complicated by the lack of independent estimates of reddening, and it may actually be more rewarding to use it in the opposite sense, i.e., to adopt a value for the metallicity and, by imposing a best fit to the underlying grid of Galactic clusters of known metallicity, deduce a value for the reddening.
This is actually the basic method followed by Ajhar et al. (1995) and we did essentially the same. Table 1 reports the figures we eventually adopted for each cluster.
We have plotted radial CMDs over various (4--6) annuli centered
on each cluster and selected the best interval to trace the ridge lines
of the various branches. Due to shortage of space, we omit the several
Figures. We note, however, that, in general, the ridge line of
the more internal annuli yields slightly bluer colors (by
mag) at fixed luminosity. This may be due to residual
effects on the background local estimate or may reflect a bluer color
of the ridge line. Moreover, due to statistical reasons, it is quite
difficult to firmly trace the brightest portion of the giant branch
as just a few very bright stars actually dominate the different annuli.
Concerning specifically the measure of V
, we have adopted various
approaches to take into account the intrinsic differences in the
HB-morphologies, as already done by Ajhar et al. (1995).
Table 1 lists the adopted dereddened and corrected V
values.
The errors listed include the estimated contributions from aperture photometry
correction, uncertainties in the reddening, in the adopted
reddening law, and in the adopted measure of V
.
Adjustments made to the HB magnitudes of the metal rich clusters
are discussed in the full paper.
Because HB magnitudes for metal-rich clusters as determined above are
actually contaminated by red RGB stars and, moreover, the ridge
point so adopted can hardly be taken to represent the luminosity
level of the HB at the instability strip (a part from the problems
of evolution within the strip which should be somehow taken into
account), we adopted a procedure a priori to correct
the observed V
for this problem (Ajhar et al. 1995).
Having determined corrected V
we can now consider the calibration
of the standard candle. For simplicity we adopt (m-M)
= 24.43
(Freedman & Madore 1990).
While this choice has no effect on the following discussion concerning
the slope of the relation, it is crucial for the comparison of
the zero-points and, in turn, for the problem of absolute
ages.
Figure: CMDs of the 7 globular clusters observed in M31 with HST.
Table 1: Relevant data for the 7 globular clusters observed in M31
with HST.
Using the data listed in Table 1 (and plotted in Figure 3, 1
error-bar), we
have computed the best fitting solution to the available points
taking into account the size of the errors in both axes.
In Figure 3 we report the best fit and the two solutions compatible
within 
of the errors in the slope coefficient.
The final M
vs. [Fe/H] relation adopted is:
Figure: V
vs. [Fe/H] calibration.
This result is of course strongly dependent on various assumptions (more or less explicitly) made during the procedure and must be checked in detail.
The slope of the derived relation is fully consistent with that predicted
by the standard and canonical models (
) and obtained by various
ground-based observations, while it is marginally compatible
with higher values (
), repeatedly obtained in the past.
The zero-point, crucial to absolute age determinations, is also
affected by an additional error due to the residual uncertainties in the
HST photometric zero-points (
mag, at least).
If confirmed, such a calibration of the M
vs. [Fe/H] relationship
would imply old absolute ages (> 16Gyr) for the oldest Galactic
globulars and fairly small age spread among those having a
constant magnitude difference between the Main-Sequence Turnoff and
the HB.
It is a pleasure to thank P. Battistini, F. Bònoli, R. Buonanno for their early efforts in this project. This research was supported by the Consiglio delle Ricerche Astronomiche (CRA) of the Ministero delle Università e della Ricerca Scientifica e Tecnologica (MURST), Italy, by the Agenzia Spaziale Italiana (ASI), and by the National Aeronautics and Space Administration, and the National Science Foundation, USA.
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