Issue |
A&A
Volume 507, Number 3, December I 2009
|
|
---|---|---|
Page(s) | 1393 - 1408 | |
Section | Galactic structure, stellar clusters, and populations | |
DOI | https://doi.org/10.1051/0004-6361/200912757 | |
Published online | 01 October 2009 |
A&A 507, 1393-1408 (2009)
Radial distribution of the multiple
stellar populations in
Centauri![[*]](/icons/foot_motif.png)
A. Bellini1,2 - G. Piotto1 - L. R. Bedin2 - I. R. King3 - J. Anderson2 - A. P. Milone1 - Y. Momany4
1 - Dipartimento di Astronomia, Università di Padova, Vicolo
dell'Osservatorio 3, 35122 Padua, Italy
2 - Space Telescope Science Institute, 3700 San Martin Drive,
Baltimore, MD 21218, USA
3 - Department of Astronomy, University of Washington, Seattle, WA
98195-1580, USA
4 - INAF - Osservatorio Astronomico di Padova, vicolo dell'Osservatorio
5, 35122 Padova, Italy
Received 24 June 2009 / Accepted 23 September 2009
Abstract
Aims. We present a detailed study of the radial
distribution of the multiple populations identified in the Galactic
globular cluster Cen.
Methods. We used both space-based images (ACS/WFC
and WFPC2) and ground-based images (FORS1@VLT and WFI@2.2m ESO
telescopes) to map the cluster from the inner core to the outskirts (20 arcmin).
These data sets have been used to extract high-accuracy photometry for
the construction of color-magnitude diagrams and astrometric positions
of
stars.
Results. We find that in the inner 2 core radii
the blue main sequence (bMS) stars slightly dominate the red main
sequence (rMS) in number. At greater distances from the
cluster center, the relative numbers of bMS stars with respect
to rMS drop steeply, out to
8 arcmin, and then
remain constant out to the limit of our observations. We also find that
the dispersion of the Gaussian that best fits the color distribution
within the bMS is significantly greater than the dispersion of the
Gaussian that best fits the color distribution within the rMS. In
addition, the relative number of intermediate-metallicity
red-giant-branch stars (which includes the progeny of the bMS) with
respect to the metal-poor component (the progeny of the rMS)
follows a trend similar to that of the main-sequence star-count
ratio
.
The most metal-rich component of the red-giant branch follows the same
distribution as the intermediate-metallicity component.
Conclusions. We briefly discuss the possible
implications of the observed radial distribution of the different
stellar components in Cen.
Key words: globular clusters: general -
globular clusters: individual:
Cen [NGC 5139] - stars: evolution - stars:
population II - techniques: photometric
1 Introduction
The globular cluster (GC)
Centauri is the most-studied stellar system of our Galaxy, but
nevertheless one of the most puzzling. Its stars cover a wide range in
metallicity (Cannon &
Stobie 1973;
Norris & Bessell 1975,
1977; Freeman
& Rodgers 1975;
Bessell & Norris 1976;
Butler et al. 1978;
Norris & Da Costa 1995;
Suntzeff & Kraft 1996;
Norris et al. 1996),
with a primary component at [Fe/H]
-1.7 to -1.8, and a long tail extending up to [Fe/H]
-0.6, containing three or four secondary peaks (see Johnson
et al. 2009,
for a recent update). It has been shown, both with
ground-based photometry (Lee et al. 1999; Pancino
et al. 2000;
Rey et al. 2004;
Sollima et al. 2005a;
Villanova et al. 2007)
and Hubble Space Telescope (HST) photometry
(Anderson 1997;
Bedin et al. 2004;
Ferraro et al. 2004),
that
Cen hosts different stellar populations, most of them clearly visible
in most of their evolutionary phases.
These populations have been linked to the aforementioned
metallicity peaks in photometric studies of the red-giant branch (RGB)
(Pancino et al. 2000;
Hilker & Richtler 2000;
Sollima et al. 2005a),
the subgiant branch (SGB) (Hilker et al. 2004; Sollima
et al. 2005b;
Stanford et al. 2006;
Villanova et al. 2007),
and the main sequence (MS) (Piotto et al. 2005). The most
puzzling feature in
Cen was discovered by Piotto et al. (2005), who showed
that, contrary to any expectation from stellar-structure theory, the
bluer of the two principal main sequences (bMS) is more metal-rich than
the redder one (rMS). The only possible way of reconciling the
spectroscopic observations with the photometric ones is to assume a
high overabundance of He for the bluer MS (Bedin et al. 2004; Norris 2004; Piotto
et al. 2005).
How such a high He content could have been formed is still a
subject of debate (see Renzini 2008
for a review).
One of the scenarios proposed to account for all the observed
features of
Cen is a tidal stripping of an object that was originally much more
massive (Zinnecker et al. 1988; Freeman
1993;
Dinescu et al. 1999;
Ideta & Makino 2004;
Tsuchiya et al. 2004;
Bekki & Norris 2006;
Villanova et al. 2007).
In
this scenario, the cluster was born as a dwarf elliptical galaxy, which
was subsequently tidally disrupted by the Milky Way. Since all
the populations of such a galaxy pass through the center, the nucleus
would have been left with a mixture of all of them.
It has also been suggested (Searle 1977; Makino
et al. 1991;
Ferraro et al. 2002)
that
Cen could have been formed by mergers of smaller stellar systems. In
apparent support of this scenario, Ferraro et al. (2002) claimed
that the most metal-rich RGB component of
Cen (RGB-a, following the nomenclature of Pancino et al. 2000) has a
significantly different mean proper motion from that of the other
RGB stars, and they concluded that RGB-a stars must have had
an independent origin. However, Platais et al. (2003) showed that
the proper-motion displacement seen could instead be an uncalibratable
artifact of the plate solution. More recently Bellini et al. (2009), with a new
CCD-based proper-motion analysis, were able to demonstrate that all
Cen RGB stars share the same mean motion to within
a few km s-1. Anderson
& van der Marel (2009)
also find that the lower-turnoff population (the analog of the RGB-a)
shows the same bulk motion as the rest of the cluster. Thus there is no
longer a reason to think this population to be kinematically distinct
and an indication of a recent merger. Another indication that the
cluster likely did not form by mergers can be found in the observation
in Pancino et al. (2007)
that all three RGB components share the cluster rotation,
which would not
be the case if different populations had different dynamical origins,
or at least would require an unlikely degree of fine tuning.
While
Cen was long thought to be the only cluster to exhibit a spread in
abundances, we now know that it is not alone. M 54 also
clearly exhibits multiple RGBs (Sarajedini & Layden
(1995); Siegel
et al. 2007),
SGBs (Piotto 2009),
and has hints of multiple MSs. The complexity of M 54
makes good sense, because it coincides with the nucleus of the
tidally disrupting Sagittarius dwarf-spheroidal galaxy. M 54
might be the actual nucleus or, more likely, it may represent a cluster
that migrated to the nucleus as a result of dynamical friction
(Bellazzini et al. 2008).
Cen
and M 54 are the two most massive GCs in our Galaxy,
and it is quite possible that they are the result of similar -
and peculiar - evolutionary paths (Piotto 2009). In any
case, even
Cen and M 54 are not the only clusters to exhibit non-singular
populations. Exciting new discoveries, made in the last few years,
clearly show that the GC multi-population zoo is quite
populated, inhomogeneous, and complex.
Piotto et al. (2007) published a color-magnitude diagram (CMD) of the globular cluster NGC 2808, in which they identified a well-defined triple MS (D'Antona et al. 2005, had already suspected an anomalous broadening of the MS and had associated it with the three populations proposed by D'Antona & Caloi 2004, to explain the complex horizontal branch (HB) of this cluster). Another globular cluster, NGC 1851, must have at least two distinct stellar populations. In this case, the observational evidence comes from the split of the SGB (Milone et al. 2008). There are other GCs which undoubtedly show a split in the SGB, like NGC 6388 (Moretti et al. 2009), M 22 (Piotto 2009; Marino et al. 2009), 47 Tuc (Anderson et al. 2009), which also shows a MS broadening, or in the RGB, like M4 (Marino et al. 2008). Recent investigations (Rich et al. 2004; Faria et al. 2007) suggest that also other galaxies might host GCs with more than one population of stars.
Multiple-population GCs offer observational evidence that
challenges the traditional view. For half a century,
a GC has been considered to be an assembly of stars that
(quoting Renzini & Fusi Pecci 1988): ``represent
the purest and simplest stellar populations we can find in nature, as
opposed to field populations, which result from
an admixture of ages and
compositions''. If we allow for the fact that all the GCs for
which Na and O abundances have been measured show a well
defined Na/O anti-correlation (Carretta et al. 2006,
2008),
suggesting an extended star-formation process, and that 11 of
the 16 intermediate-age Large Magellanic Cloud GCs have been
found to host multiple populations (Milone et al. 2009),
multi-populations in GCs could be more the rule than the exception. De facto,
a new era in globular-cluster research has started, and understanding
how a multiple stellar system like
Cen was born and has evolved is no longer the curious study of an
anomaly,
but rather may be a key to understanding basic star-formation
processes.
One way to understand how the multiple populations may have originated is to study the spatial distributions of the different populations, which might retain information about where they formed. In particular, theoreticians have been finding that if the second generation of stars is formed from an interstellar medium polluted and shocked by the winds of the first generation, then we would expect that the second generation would be more concentrated towards the center of the cluster than the first one (see D'Ercole et al. 2008; Decressin et al. 2008; Bekki & Mackey 2009). In the first two of these references it is shown that in such a scenario the two generations of stars would interact dynamically and would homogenize their radial distributions over time. As such, spatial gradients represent a fading fossil record of the cluster's dynamical history.
Since
Cen has such a long relaxation time (1.1 Gyr in the core and
10 Gyr at the half-mass radius, Harris 1996),
it is one of the few clusters where we might hope to infer the
star-formation history by studying the internal kinematics and spatial
distributions of the constituent populations. These measurements will
provide precious hints and constraints to allow theoreticians to
develop more reliable GC dynamical models.
In a recent paper, Sollima et al. (2007) showed that
the star-count ratio
is flat beyond
,
but that inward to
it increases to twice the envelope value. Thus the bMS stars
(i.e., the supposed ``He-enriched'' population) are more concentrated
towards the center than the rMS, which is presumed to be the first
generation. Unfortunately, Sollima et al. (2007) could not
provide information about the trend of
within
,
which corresponds roughly to 2 half-mass radii (
).
On the other hand, the radial distribution of RGB subpopulations has been analyzed by many authors (Norris et al. 1997; Hilker & Richtler 2000; Pancino et al. 2000, 2003; Rey et al. 2004; Sollima et al. 2005a; Castellani et al. 2007; Johnson et al. 2009). All these works agree that the intermediate-metallicity population (RGB-MInt) is more centrally concentrated than the more metal-poor one (RGB-MP). However, there is a disagreement about the most metal-rich population (RGB-a): Pancino et al. (2000), Norris et al. (1997), and Johnson et al. (2009) found that the most metal-rich stars (RGB-a) are as concentrated as the intermediate-metallicity ones, and consequently more concentrated than the most metal-poor stars, whereas Hilker & Richtler (2000) and Castellani et al. (2007) considered the RGB-a component to be the least-concentrated population. (Since our work in progress was already favoring the former view over the latter, we were concerned to reach the definitive truth of this matter.)
In the present paper, we trace the radial distribution of the
stars of
Cen, both on the MS and in the RGB region. Our radial density
analysis covers both the center and the outskirts of the cluster,
taking advantage of the combination of four instruments on three
different telescopes, and of our proper-motion measurements on
ground-based multi-epoch wide-field images (Bellini et al. 2009). In
Sect. 2 we describe in detail the photometric data and the
reduction procedures. Section 3 presents our analysis of the
radial distribution of the stars on the two MSs. In Sect. 4 we
perform an analogous study for the RGB stars. A brief
discussion follows in Sect. 5.
2 Observations and data reductions
To trace the radial distribution of the different stellar populations
in
Cen, we analyzed several data sets, from four different cameras.
To probe the dense inner regions of the cluster we took
advantage of the space-based high resolving power of HST,
using both the Wide Field Channel (WFC) of the Advanced Camera for
Surveys (ACS), and the Wide Field and Planetary Camera 2
(WFPC2). For the relatively sparse outskirts of the cluster, we instead
made use of deep archival ground-based observations collected with the
FORS1 camera of the ESO Very Large Telescope (VLT). In addition, to
link all the different data sets into a common astrometric and
photometric reference system, we used the Wide Field Imager (WFI) at
the focus of the ESO 2.2 m telescope (hereafter
WFI@2.2m). This shallower data set was also used to study the red-giant
branch in the outskirts of the cluster.
Figure 1
shows the footprints of the data sets, centered on the recently
determined accurate center of
Cen:
:26:47.24,
:28:46.45
(J2000.0, Anderson & van der Marel 2009). The red
footprints are those of HST observations.
The larger ones are the ACS/WFC data sets,
a 3
3 mosaic centered on the cluster center and a single field
17
SW of the center.
The smaller red field,
7
S
of the center, was observed with WFPC2. Blue rectangles show the
partially overlapping FORS1@VLT fields, extending from
6
to
25
.
The large field in magenta is the
33
field-of-view of our WFI@2.2m proper-motion catalog (Bellini
et al. 2009).
The figure also shows the major and minor axes (solid lines), taken
from van de Ven et al. (2006).
We divided the field into four quadrants, centered on the major and
minor axes. The quadrants are labeled with Roman numerals and separated
by dashed lines. We will use them to derive internal estimates of the
errors of the star-count distribution. Concentric ellipses, aligned
with the major/minor axes, have ellipticity of 0.17,
coincident with the average ellipticity of
Cen (Geyer et al. 1983).
These ellipses will be used to define radial annuli, in
Sect. 2.8. Thick black circles mark the core radius (
)
and the half-mass radius (
)
(from Harris 1996).
If we assuming a cluster distance of 4.7 kpc (van de Ven
et al. 2006;
van der Marel & Anderson 2009),
the two radii correspond to 1.9 pc and 5.7 pc,
respectively.
The details of the data sets are summarized in Table 1. In the following subsections we give brief descriptions of the reduction procedures, which have been presented in more detail in various other papers. The FORS1 data, however, were taken by Sollima et al. (2007), for a purpose similar to ours; we will give a full description of our reduction in Sect. 2.4.
![]() |
Figure 1:
The footprints of the |
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Table 1: Data sets used in this work.
2.1 HST: ACS/WFC inner 3
3 mosaic
This data set (inner nine red rectangles in Fig. 1, GO-9442,
PI Cool) consists of a mosaic of 3
3 fields obtained with the ACS/WFC through the F435W and
F625W filters. This camera has a pixel size of
50 mas
and a field of view of
.
Each of these nine fields has one short and three long exposures in
both F435W and F625W. The mosaic covers the inner
10
10
,
the most crowded region of
Cen. These images, which were used by Ferraro et al. (2004) and by
Freyhammer et al. (2005),
and which we used in both Bedin et al. (2004), and
Villanova et al. (2007),
were reduced using img2xym_WFC.09x10, which is a
publicly available FORTRAN program, described in
Anderson & King (2006).
The
program finds and measures each star in each exposure by fitting a
spatially-variable effective point-spread function. The independent
measurements of the stars were collated into a master star list that
covers the entire 3
3 mosaic field. For each star we constructed an average
magnitude in each band, and computed the rms deviation of the
multiple measurements about this average. Instrumental magnitudes were
transformed into the ACS Vega-mag flight system following the procedure
given in Bedin et al. (2005),
using the zero points of Sirianni et al. (2005). Since the
zero points are valid only for fluxes in the _drz
exposures, we computed calibrated photometry for a few isolated stars
in the _drz exposures and used this to set the
zero points for the photometry that was based on the individual _flt
images. Saturated stars in short exposures were treated as described in
Sect. 8.1 in Anderson et al. (2008).
Collecting photoelectrons along the bleeding columns allowed us to
measure magnitudes of saturated stars up to 3.5 mag above
saturation (i.e., up to
12 mag), with errors of only a few percent (Gilliland 2004). We used
the final catalog, which contains more than
760 000 stars, to trace the radial distribution of
RGB and MS stars in this most crowded region of
the cluster.
2.2 HST: ACS/WFC outer field
The outer ACS field (17
SW
of the cluster center, see Fig. 1) comes from
proposals GO-9444 and GO-10101 (both with PI King), using the
F606W and F814W filters. The photometry from the first-epoch
observations was published in Bedin et al. (2004). The
photometry presented in the present paper comes from the full two-epoch
data set for this field; the two epochs also allow us to derive proper
motions and perform a critical cluster/field separation.
A detailed description of the data reduction, the
proper-motion measurement, and the resulting CMDs will be presented in
a forthcoming paper. The reduction and calibration of these data sets
use procedures similar to those used for the central mosaic, and
provided photometry for
3500 stars.
2.3 HST: WFPC2 field
We also make use of one WFPC2 field, 7
south of the cluster
center (see Fig. 1).
This data set consists of 2
300+600 s exposures in F606W, and 2
400+1000 s in F814W (GO-5370, PI Griffiths), and
contains 9214 stars. These images have been reduced with the
algorithms described in Anderson & King (2000). The field
was calibrated to the photometric Vega-mag flight system of WFPC2
according to the prescriptions of Holtzman et al. (1995). This
WFPC2 field is
particularly important in tracing the distribution of stars in the MS
of
Cen, because it is at a radial distance from the center of the cluster
where there are no suitable ACS/WFC observations and where ground-based
observations are almost useless because of crowding.
![]() |
Figure 2:
Selection criteria used to isolate FORS1@VLT stars for our
MS subpopulation analysis. Panel (a)
shows sharp values versus B magnitude,
and panel (b) |
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2.4 VLT: eight FORS1 fields
The VLT data set consists of eight partially overlapping FORS1 fields,
each with a pixel size of 200 mas and a field of view of
.
These fields (the blue rectangles in
Fig. 1)
probe the regions between
and
from the center of
Cen. The set of images consists of 20
1100 s exposures in B, and
20
395 s in R, and are the same
images used by Sollima et al. (2007). There are
four images in each field (two per filter), except that the third and
fourth fields have four images per filter (see Fig. 1 for field
numbers). This is the only data set that we reduced specifically for
the present work. For this reason we give a more detailed description
of our reduction procedure.
We retrieved the data sets from the ESO archive; master-bias
and flat-field frames were constructed using standard IRAF routines.
Photometric reduction of the images was performed using Stetson's
DAOPHOT-ALLSTAR-ALLFRAME packages (Stetson 1987, 1994). For each
exposure we constructed a quadratic spatially variable point-spread
function (PSF) by using a Penny
function, and for each individual
exposure we chose - by visual inspection - the
best 100 (at least) isolated, bright, unsaturated stars that
were
suitable for mapping the PSF variations all over the image. We
used ALLFRAME on each individual field, keeping only stars measured in
at least four images. The photometric zero points of each field were
registered to the instrumental magnitudes of the fourth field
(the less crowded of the two that have more exposures).
Finally, photometric and astrometric calibration was performed using
the WFI@2.2m astrometric-photometric catalog by Bellini et al.
(2009) as a
reference. As a result, we brought the FORS1 R magnitudes
to the Cousins-
photometric
system used by WFI@2.2m. Our final FORS1 catalog contains
133 000 objects.
Since the innermost FORS1 field is seriously affected by
crowding, we did not use it in the present analysis. Figure 2 plots the sharp,
,
and
and
calculated by ALLFRAME, as functions of stellar magnitude, for the
stars in the
FORS1 catalog. To choose the well-measured stars, we drew by
eye the cut-off boundaries in the quality parameters that retained
objects that were most likely to be well-measured stars.
Panel (a) shows sharp values versus B magnitude.
Stars that passed the selection criterion are shown in black.
Panel (b), which includes only stars that passed the sharp
cut, shows
values
versus B. Stars that also passed the
criterion
are in black. In panel (c) we plot the
values
versus B, for the stars that survived these
two selections. Again, the stars with good photometry are shown in
black. Finally, in the last panel we plot
values
versus
,
for all the survivors, and we highlight in black those that survived
this selection too. At the end of these selection procedures,
we are left with a catalog of
66 500 stars.
We note that while these selection criteria affect stars at different
magnitudes differently, they should not affect the ratio of stars on
the bMS and rMS, since at a given magnitude the two populations should
both have about the same photometric error, and the same probability of
making it into our catalog.
2.5 WFI@2.2m
This data set was collected at the 2.2 m ESO Telescope, with
the WFI camera, between 1999 and 2003. The WFI@2.2m camera is made up
of a mosaic of 4
2 chips, 2048
4096 pixels each, with a pixel scale of
238 mas/pixel). Thus, each WFI exposure covers
34
.
The
Cen astrometric, photometric, and proper-motion catalog based
on this data set and presented in Bellini et al. (2009) is public,
and contains several wide-band (
) filters
plus a narrow-band filter (658 nm), and covers an area of
33
centered on the cluster center. We refer the reader to Bellini
et al. (2009)
for a detailed discussion of the data-reduction and
calibration procedures.
Briefly, photometry and astrometry were extracted with the
procedures and codes described in Anderson et al. (2006).
Photometric measurements were corrected for ``sky concentration''
effects and for differential
reddening, as described in Manfroid & Selman (2001) and
Bellini et al. (2009).
Global star positions are measured to better than
45 mas
in each coordinate. Photometric calibration in the
bands
is based on a set of
3000 secondary
standard stars in
Cen, available on-line (Stetson 2000,
2005). Color
equations were derived to transform our instrumental photometry into
the photometrically calibrated system using an iterative least-squares
linear fit. Thanks to the four-year time-baseline, we were able to
successfully separate cluster members from field stars by means of the
local-transformation approach (Anderson et al. 2006), giving
us proper motions more precise than
4
down to B
20 mag, for
54 000 stars.
![]() |
Figure 3:
(Top left:) selected stars in common between the
ACS/WFC 3 |
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2.6 The astrometric and photometric reference frame
The large field of view of the WFI@2.2m camera makes our WFI catalog an
ideal photometric and astrometric reference frame to which to refer all
the other observations, from different telescope-camera-filter
combinations. For each catalog we made the tie-in by means of stars
that were in common with the reference catalog. For positions we
derived a general six-parameter linear transformation to the
astrometric system of the WFI catalog. For photometry we used
as a
reference standard the B and Cousins- magnitudes
of the WFI@2.2m catalog, and transformed the magnitudes of each other
catalog to this standard. For the
and
magnitudes of the
central mosaic of 3
3 ACS/WFC fields, we used
3300 stars that had
been observed in common, located outside
from the cluster center to avoid the most crowded regions in the
WFI data set (top-left panel of Fig. 3). We excluded
from this sample saturated stars in the WFI data set, keeping
only the brighter (
14.9<B<16.5)
and well measured (
mag)
ones (top-right panel in
Fig. 3).
The adopted calibration fits are shown in the bottom panels of
Fig. 3.
We did similarly for the FORS1 B and R magnitudes.
Calamida et al. (2005) measured a
differential reddening of up to E(B-V)
0.14 in a region of
14
14
centered on
Cen. This result has been questioned by Villanova et al. (2007); in their
Figs. 1-6, the
sharpness of the SGB sequences suggests that the existence of
any serious differential reddening is very unlikely. But in any case, a
proper radial-distribution analysis needs correction even for a
differential reddening that is of the order of few hundredths of a
magnitude. Our corrections for differential reddening followed the
method outlined by Sarajedini et al. (2007), which
uses the displacements of individual stars from a fiducial sequence to
derive a reddening map.
The outer ACS/WFC field at 17
from the cluster center and the WFPC2 field at
7
provide stellar photometry in the F606W and F814W bands. For
the ACS field we have overlap with the WFI catalog,
which allows us to calibrate the photometry, but the stars available
are all on the main sequence above
,
so they have a very narrow range in color, and we cannot empirically
determine the color term in the calibration. For
the WFPC2 field, in addition to the problem of the limited
color baseline, the WFI photometry in this inner field is of
low quality on account of ground-based crowding. For these reasons, we
decided to not transform the photometry of these two fields into the
photometric reference system of WFI@2.2m, but dealt with them in the HST Vega-mag
flight system.
![]() |
Figure 4:
B vs. |
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2.7 The deep color-magnitude diagrams
Our proper-motion-selected WFI@2.2m B vs. CMD
is shown in Fig. 4.
All the main features of the cluster are clearly visible, except for
the split MS, since the WFI data go down only a
magnitude or so below the turnoff. The CMDs of the other data sets that
we analyzed are presented in Fig. 5, where
the top-left panel refers to the eight FORS1@VLT fields, the
middle-left panel to the proper-motion-selected CMD of the external
ACS/WFC, the bottom-left panel to the CMD from
the WFPC2 field, and the right panel of Fig. 5 to the
CMD of the inner 3
3 ACS/WFC mosaic. It is clear that the
MS population can be
studied in all but the WFI CMD, and the RGB population can be
studied in the WFI and inner ACS data sets.
Now that we have a comprehensive sample of
Cen stars, both for the bright stars and for the faint ones,
covering the central region all the way out to
25
,
we can define robust selection criteria for the subpopulations to track
how the population fractions vary with radius.
2.8 The angular radial distance: r*
Since
Cen is elongated in the plane of the sky, it does not make
sense to analyze its radial profile via circular annuli. We therefore
decided to extract radial bins in the following way. We adopted the
position angle (PA) of
for the major-axis (van de Ven et al. 2006), and an average
ellipticity of 0.17 (Geyer et al. 1983).
To define the bins of the radial distribution we adopted
elliptical annuli, whose major axes are aligned with the
Cenmajor axis, and stars were extracted accordingly (see Fig. 1). To indicate the
angular radial distance from the cluster center, we used the equivalent
radius r*, defined as
the radius of the circle with the same area as the corresponding
ellipse (i.e., the geometrical mean of the semi-major and semi-minor
axes). Each of the small fields (the outer ACS field and the
WFPC2 field), we considered as a single radial bin.
![]() |
Figure 5:
(Top left): CMD from the eight FORS1@VLT fields. We
can measure stars from the bottom of the RGB down to B |
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3 MS subpopulations
Our goal in putting together these varied catalogs is to quantify the
differences in the radial profiles of the various subpopulations of Cen.
One way to do this would be to measure the surface density profile for
each group and compare them directly, but this would require accurate
completeness corrections and careful attention to magnitude bins. Since
our interest, however, is simply to determine how the populations vary
with respect to each other, we need only to measure the ratio
of the populations as a function of radius. This ratio should be
independent of completeness corrections and the details of the
magnitude bins used, since the bMS and rMS differ only slightly in
color and are observed over the same magnitude range.
Our analysis of the
ratio is based mostly on the data sets from the inner ACS/WFC
3
3 mosaic and FORS1@VLT, which allow us to map the ratio of
bMS/rMS from the cluster center out to
25
,
once the photometry and astrometry have been brought into the same
reference
system. The other two fields, each of which covers only a small region,
provide only one point each in our analysis of
versus
radius. Moreover, since we were not able to bring
and
photometry of the
outer ACS and the WFPC2 field into the WFI B
and
photometric
system, we kept the WFPC2 and the outer ACS/WFC data sets in
their native photometric system, and used them only for a further
(though important) confirmation of the radial
gradient found with the FORS1 and inner ACS/WFC data sets.
3.1 Straightened main sequences
![]() |
Figure 6:
The left panel shows a randomly
selected 8% of the stars in
the CMD of the inner |
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![]() |
Figure 7: Same as Fig. 6, but after subtraction, from the color of each star, of the color of the fiducial line at the same luminosity. In the left panel we show a randomly selected 20% of the stars from the ACS/WFC central-mosaic data (rather than the previous 8%, since the color-scale is now less compressed). |
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In order to analyze the color distribution of the stars along the MS in
a more convenient coordinate system, we adopted a technique previously
used with success in
Cen (Anderson 1997,
2002), and
in other works (Sollima et al. 2007; Villanova
et al. 2007;
Piotto et al. 2007;
Milone et al. 2008;
Anderson et al. 2009).
We defined fiducial lines in the CMDs (drawn by hand), such as
to be equidistant from the ridge lines of the bMS and
rMS stars. We avoided choosing the ridge line of either
sequence as our fiducial line, because we wanted a system in which both
the sequences are as parallel and as rectified as possible. We used
different fiducial lines for the B, CMDs
of the inner ACS/WFC and the FORS1 data sets and for the
,
CMDs of the WFPC2 and outer ACS/WFC data sets. In this way, we
were sure to straighten the MSs in the same consistent way for the two
different sets of filters. Then we subtracted from the color of each
star the color of the fiducial line at the same luminosity as
the star.
In Fig. 6
we show the CMDs in the
Cen MS region for the central mosaic of
ACS/WFC data (left panel), the FORS1@VLT (middle panel), and
the WFPC2
7
field
and the ACS/WFC field at
17
(right panels). In the case of the central ACS/WFC data, we
plotted only a randomly chosen 8% of the stars, in order to show the
two sequences clearly. In all the CMDs the MS splitting is clearly
visible. For the inner ACS/WFC and FORS1 data sets we
restricted our MS analysis to the magnitude range
(dashed lines in Fig. 6), the
interval in which the two MSs are most separated in color and are
parallel. For the same reasons we analyzed stars in the magnitude range
for
the WFPC2 and the outer ACS/WFC data sets. The bright limit
also avoids the saturated stars in the deep WFC exposures. The
adopted fiducial lines are again plotted (in red in the color
version of the paper).
In Fig. 7
we show straightened CMDs for the same data sets shown in Fig. 6, with the
only difference being that we now plot a 20% randomly
generated sample of stars for the inner ACS/WFC data set,
since the expanded color baseline allows
more points to be seen. It is worth noting that even a simple
inspection shows the
ratio clearly decreasing as we go from the central cluster regions to
the outer ones. It is also clear that the spread in the bMS is
somewhat greater than that of the rMS.
Finally, note that we call the color deviation of a star from
the fiducial line .
We shall use this notation frequently in what follows.
Our aim in selecting the best-measured stars in the previous sections was so that we would be able to assign the stars to the different populations as accurately as possible. Similarly, as much as possible we transformed our photometry into the same system, so that our population selections throughout the cluster would be as consistent as possible.
Even with these careful steps, however, it is still difficult to ensure that we are selecting stars of the same population in the inner parts of the cluster as in the outer parts. Even if we had observations with the same detector at all radii, the greater crowding at the center would increase the errors there. On the other hand, our use of ground-based images for the outer fields actually makes those fields even more vulnerable to crowding effects.
Another complication comes from main-sequence binaries, which at the distance of a globular cluster are unresolved. Relaxation, causing mass segregation, will concentrate them to the cluster center and cause a redward distortion of the main sequence there.
Moreover, in the lower-density outer regions of the cluster we
can get the same statistical significance only by using larger areas,
with an increased vulnerability to inclusion of field stars. Finally,
the red side of the main sequence is contaminated by the anomalous
metal-rich
population (hereafter MS-a), which is clearly connected with RGB-a.
Even if these stars include only 5% of the total cluster
members (Lee et al. 1999;
Pancino et al. 2000;
Sollima et al. 2005a;
Villanova et al. 2007),
they are an additional source of pollution for
rMS stars - against which we now take specific
precautions.
3.2 Dual-Gaussian fitting
There is no way of dealing with the above issues perfectly, but we did our best to make our measurements as insensitive to them as possible. To this end, we measured the bMS and rMS fractions by simultaneously fitting the straightened color distributions with two Gaussians, and taking the area under each Gaussian as our estimate of the number of stars in each population. By keeping the width of each Gaussian an adjustable parameter, we allowed in a natural way for the fact that the photometric scatter differs from one radius and data set to another.
While the dual Gaussians provide a natural way of measuring the two populations in data sets that have different color baselines and different photometric errors, there is one serious complication. As we have indicated, there is an unresolved, broad population of stars redward of the rMS that consists of blends, binaries, and members of the MS-a branch. Since it is unclear what relation this mixed population has with the two populations that we are studying, we wanted to exclude it from the analysis as much as possible. We did so by cutting off the reddest part of the color range, and confining our fitting to the color range that is least disturbed by the contaminated red tail.
In order to choose the red cutoff as well as possible, we
gathered together all of the stars in each data set. Below we will
describe for simplicity only the case of the central 3
3 mosaic of ACS images in B and
.
The procedure followed is, however, the same for the other data sets.
Within this data set we chose the MS stars that were in the
magnitude range
(within which the two MSs are almost parallel and are maximally
separated in color) and in the color range
mag.
We emphasize that this ensemble of the data set, within which we will
later see a considerable gradient in the relative numbers of bMS and
rMS stars, will not be used to derive population results in
the case of the inner ACS/WFC data set, but only to choose the
red cutoff. We divided these stars into five magnitude intervals,
because the observational errors, which increase the spread of the
sequences, depend on magnitude. Next, we plotted histograms of the
distribution
within each magnitude interval, using a bin size of 0.006 mag.
This size is
1/4
of the typical photometric error in color; it makes a good compromise
between a fine enough color resolution, on the one hand, and adequate
statistics, on the other hand.
The actual choice of the red cutoff is a two-tiered procedure.
We must first develop a procedure for the fitting of dual Gaussians to
a set of bins that has a red cutoff; then we must decide on a value
of
,
the number of bins that we include on the redder side of the red
Gaussian.
Although from a mere inspection of the histograms it is clear
where, approximately, the peak of the red Gaussian should lie, the
narrowness of the bins leaves it uncertain in which particular bin the
peak of the red Gaussian will actually fall. Since the red cutoff, ,
is defined as being counted from that bin, we had to resort to an
iterative procedure to locate the cutoff for a given value of
.
We began by choosing a cutoff safely to the red of where we guessed
that the cutoff would actually fall, and then using that cutoff in a
first try at fitting the dual Gaussians. The iteration then consisted
of placing the cutoff just beyond
bins
on the red side of the peak of the red Gaussian and fitting again; this
new fit might cause the red peak to move to a different bin.
When the red peak stays in the same bin, the iteration has converged;
this happened after very few iterations.
We assumed trial values of
from 2 to 5, and for each of those values we iteratively
computed the Gaussian parameters for each of the five magnitude
intervals. We chose as the best value for
the one for which the five values of
were the most consistent. This value turned out to be
.
With this choice made, we then moved on to fit dual Gaussians to each
of our detailed data sets.
![]() |
Figure 8:
(Left panel): B versus |
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![]() |
Figure 9: Dual-Gaussians fits. As in Fig. 8, the Gaussian fits to the bMS and rMS are in blue and red respectively, and their sum in black. The vertical dashed lines mark the centers of the individual Gaussians. The individual panels are arranged in order of effective radius. (Note that all our fields are shown here, in radial order, so that the WFPC2 field follows the inner ACS fields, and the outer ACS field falls between two of the FORS1 fields.) |
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Figure 8
shows the results of this procedure. In the left panel we show our
selected stars in the B versus diagram -
all of the stars this time, rather than a
random selection of a fraction of them. The horizontal lines delineate
our five magnitude intervals. On the right we show the final
histogram
for each magnitude interval, and the dual-Gaussian fit to it.
The individual Gaussians are shown in blue
and red, respectively, and the black curve is their sum. The vertical
blue and red lines are the centers of the respective Gaussians, and the
vertical black line shows the red cutoff. Note that we do not show the
vertical boundaries between the bins of a histogram, because on this
scale they would be too close to each other. Nor do we show the Poisson
errors of the counts in the bins, because they are small and would
obscure the bin values themselves; the size of the errors is
amply clear from the smoothness of the values in neighboring bins. The
counts in the histograms are normalized so as to make the height of the
red Gaussian equal to unity.
![]() |
Figure 10:
|
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Table 2: Dual-Gaussian fitting results.
3.3 The radial gradient of NbMS/NrMS
Having chosen the position of the red cutoff, we were able to perform dual-Gaussian fitting on each of our data sets. Figure 9 shows our fits. We divided the inner ACS/WFC mosaic and the outer FORS1@VLT data sets into five radial intervals for each. The intervals were chosen in such a way as to have the same number of selected stars in each of them, so that the statistical sampling errors will be uniform. (The reader should note that Fig. 9 shows all of our fields, in radial order, so that the WFPC2 field follows the inner ACS fields, and the outermost ACS field falls between two of the FORS1 fields.)
Figure 10 shows our results for the radial variation of the bMS to rMS ratio, for the five radial parts of the inner ACS mosaic, the five radial intervals of our FORS1 fields, the WFPC2 field, and the outer ACS field. Symbols of a different shape distinguish the various types of field. The outermost radial interval of the ACS/WFC mosaic is a special case, however, since it consists largely of the four corners of the mosaic, and it spans a larger radial extension. To better map the bMS/rMS distribution in this radial interval, we decided to further split it into four sub-annuli. In this way we increase the radial resolution, but pay the price of larger sampling errors. We have therefore plotted the outermost radial interval of the inner ACS/WFC mosaic twice, once as a whole annulus, and once as four sub-annuli (marked as crossed open circles in Fig. 10).
Our choice of using ellipses with fixed ellipticity and
position angle to extract radial bins could have introduced some
systematics in our derived
ratios. To address this issue, we recalculated the
ratios
by extracting radial bins using simple circles, and we found no
significant differences between the two radial binning methods.
Estimating the errors of our points required special
attention. First we took the Poisson errors of the numbers of stars,
and used them to generate Poisson errors for the values of
.
These, however, are only a lower bound for the true error, which has
additional contributions that are impossible to estimate directly; they
come from blends, binaries, etc. To estimate the true errors
empirically, for each value of
we subdivided the sample of stars that had been used. In the inner
ACS/WFC mosaic the subsamples were the quadrants shown in
Fig. 1,
while for each of the outer fields, where we do not have symmetric
azimuthal coverage, we divided the sample into magnitude intervals,
four for each FORS1@VLT field and three each for the
WFPC2 field and the outer ACS/WFC field.
We treated each set of subsamples as follows: Within each
subsample we performed a dual-Gaussian fit, and derived from it the
value of .
We weighted each subsample according to the number of stars in it, and
took a weighted mean of the four (or three) values of
,
to verify that this mean was equal, within acceptable round-off errors,
to the value that we had found for the whole sample. (It was,
within a per cent or two in nearly every case.) Finally we derived an
error for
the sample, from the residuals of the individual
values
from their mean, using the same weights as we had used for the mean.
These are the error bars that are shown in Fig. 10. These
errors are indeed larger than the Poisson errors, but only by
about 10%. We must note, however, that in addition to the
random error represented by the error bars, it is likely that there is
still some systematic error in our values of
,
due to the effects of blends and binaries. On the one hand, blends have
the same photometric effect as true binaries; they tend to move
bMS stars into the rMS region, while many of the
rMS stars that are similarly affected are eliminated by our
red cut-off. This effect tends to reduce our observed value
of
.
It is less easy to predict,
however, how such effects increase toward the cluster center. Blends,
on the one hand, increase because of the greater crowding. Binaries, on
the other hand, increase because their greater mass gives them a
greater central concentration. To repeat, the result has been
that our values of
are somewhat depressed toward the cluster center, so that the
gradient of
that we report is probably a little lower than the real one.
Table 3: Results of the two artificial-star tests.
Figure 10
clearly shows a strong radial trend in the ratio of bMS to
rMS stars, with the bMS stars more centrally
concentrated than the rMS stars. The most metal-rich
population, MS-a, is too sparse, and also too hopelessly mixed with the
red edge of the rMS, to allow any reliable measurement of its radial
distribution, but in the next section we will examine the distribution
of its progeny, RGB-a. Table 2 summarizes our
results. The first column identifies the data set. Columns 2-4
give, for the inner ACS/WFC 3
3 mosaic and the FORS1 data sets, the minimum, median, and
maximum radius of the central circle or the annulus, while for the
other fields these columns give the inner, median, and maximum radius
that the field covers. The sigmas of the Gaussians that best fit the
bMS and rMS color distributions, with their uncertainties, are
in Cols. 5-8. Columns 9 and 10 give the
ratio
and its error. Column 11 gives the difference
(in straightened color) between the peaks of the Gaussians
that best fit the bMS and rMS. The last column gives the
color baseline of each data set. By
we mean a color difference or width, in the straightened CMD (either (B,
)
or (
,
),
whichever applies).
Our results are qualitatively consistent with those of Sollima
et al. (2007),
within the common region of radial coverage. We confirm the flat radial
distribution of
outside
8-10 arcmin,
and a clear increase of
toward the cluster center. For the first time, and as a complement to
the Sollima et al. (2007)
investigation, our ACS/WFC 3
3 mosaic data set has enabled us to study the distribution of
Cen MS stars in the innermost region of the cluster.
Inside of
1.5
(i.e., inward of
2
),
the
ratio
is almost flat and close to unity, with a slight overabundance of
bMS stars. At larger distances from the cluster
center, the
ratio
starts decreasing. Between
3
and
8
(the latter corresponding to
2 half-mass radii)
the ratio rapidly decreases to
0.4, and
remains constant in the cluster envelope. Better azimuthal and radial
coverage of the region where the maximum gradient is observed would be
of great value. In the radial interval between 1 and
2 half-mass radii, we can use only the corners of the ACS/WFC
3
3 mosaic, and the FORS1 photometry, which inside
of
is seriously affected by crowding and saturated stars. In any case, the
star counts and even visual inspection of the histograms in
Fig. 9
leave no doubt about the overall gradient.
Note that in the two innermost bins there are more bMS than rMS stars, even though the heights of the two peaks would suggest the opposite. The apparent contradiction disappears, however, when we note the much greater width of the bMS Gaussian, which more than makes up for the difference in heights. This seems to be consistent with a greater spread in chemical composition for metal-intermediate than for metal-poor stars, as first seen by Norris et al. (1997). Our approach, using a dual-Gaussian fit, has been optimized to estimate the value of the number ratio of bMS to rMS stars, avoiding as much as possible any contamination by blends, binaries, and MS-a stars.
We must also address the fact that the values
found by Sollima et al. (2007)
are consistently lower than our values. The difference is largely due
to their use, on the red side, of a wide color range (see
their Fig. 5)
that includes nearly all of the contamination by blends, binaries, and
MS-a stars that our method has so studiously avoided. This makes their
numbers of rMS stars much too high - easily enough to
account for their finding a value of
0.16 in the cluster envelope,
rather than our
0.4,
which is certainly much closer to the truth. Note also that we have
concentrated exclusively on the ratio of numbers of
bMS and rMS stars, making no attempt to derive absolute
numbers for each component. We felt that absolute numbers would be
subject to different incompleteness corrections in our different data
sets, whereas the incompleteness in each data set should be the same
for each component and should therefore not affect their ratio.
Finally, the robustness of our method is shown by the close agreement of our - proper-motion selected - outer ACS field (magenta open circle in Fig. 10), which has almost no crowding problems, with the outer ground-based FORS1 fields (last two red squares in Fig. 10), which are certainly affected somewhat by crowding.
3.4 Artificial star tests
![]() |
Figure 11:
TEST1 artificial star analysis for the central ACS/WFC 3 |
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Figure 12: Same as Fig. 11, but now for TEST2. See text for details. |
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Even with the technique that we have used to exclude the effects of
photometric blends and binaries, which lie above and to the red of any
MS, there is a concern that some bMS stars would be shifted
into the rMS region (and some rMS stars lost on the
red side of the MS), and that these shifts would distort the ratio.
As a check against this possibility we have made two tests using
artificial stars (AS). In each test we introduced the same AS
into both the F435W and the F625W images,
as follows.
For each test, we first created 45 000 artificial stars, with random F435W instrumental magnitudes between -11.1 and -9.9 (corresponding to 20.9<B<21.1), and random positions. We then took each of these 45 000 AS, assigned it a color that placed it on the bMS, and inserted it in the F625W images, at the same position but with the F625W magnitude that corresponds to this color. We then repeated this procedure for 45 000 new AS, but this time we gave them colors that put them on the rMS. (What we mean by ``on'' (bMS or rMS) differs between the two tests; see below for an explanation of the difference.) Each artificial star in turn was added, measured, and then removed, so as not to interfere with the other AS that were to be added after it; this procedure is that of Anderson et al. (2008), where it is explained in detail.
In order to test the effects of crowding, each of the two
tests used two fields from the central 3
3 mosaic: the central field where crowding effects are
maximal, and one of the corner
fields, about 5 arcmin (
)
southeast of the center (see Fig. 1 for a map of the
3
3 mosaic of fields).
The first of the tests (TEST1) was aimed at checking the photometric errors in the colors. To do this, we chose the color of each AS so as to put it exactly on the ridge line of the bMS or rMS; the color spread of the recovered AS would then serve as a lower-limit estimate of our photometric error.
The aim of TEST2 is to verify our ability to insert AS with = 1
and then recover that value, when the two MSs have intrinsic
dispersions in color. To do this, we first derived the
intrinsic
spreads of the two sequences by taking from the fifth and seventh
columns of Table 2
the simple unweighted mean of the entries in lines 1
and 2 for the central field, and in lines 4
and 5 for the corner one. (The more fastidious procedure,
weighting the entry in each of the two lines according to the number of
stars contributed by that annulus, would have been quite laborious and
would have made no significant change in the results.) These are the
observed total color
spreads (intrinsic spread plus measuring error) of the bMS and rMS,
respectively, in the two fields that we are using here. From these
total spreads we quadratically subtracted the corresponding
measuring-error spreads that we had found in TEST1, so as to get
estimates of the intrinsic color spreads of the two sequences. We
created AS in the same manner as in TEST1, but this time instead of
placing the AS on the center lines of bMS and rMS, we adjusted the
F625W magnitudes so as to give the AS a Gaussian
spread in color around each sequence, using the intrinsic sigmas that
we had just found. After the measuring process, these AS should
duplicate the observed total spreads,
and can be used to estimate the amount of contamination between the two
main sequences. To repeat, each test was performed both on
both the central and the corner field.
The results of these AS tests are summarized in brief
numerical form in Table 3
and in graphical form in Figs. 11 and 12. In each figure
the left and right
halves refer to the central and corner fields, respectively, while each
half figure is divided into three panels that show, from left to right,
the CMD, the straightened CMD, and the decomposition of the number
densities of the latter into best-fitting Gaussians. Each panel showing
the Gaussian fits is subdivided into five magnitude intervals (very
similarly to what is done in Fig. 8).
Columns 2-4 of Table 3 give, for each
field and AS test, the ratio
of the inserted AS and the dispersions of the MSs. The recovered values
(weighted mean of the five magnitude bins and its error, as explained
in detail for real stars in Sect. 3.3) are shown
in Cols. 5-8.
From the results of TEST1 we conclude that in each field the
color spread introduced by measuring error is the same for
bMS stars as for the rMS, and that it is about
40% higher in the central field than in the less-crowded
corner field. TEST1 has served two purposes: (1) it gave us a
clear, effective measure of the effect of crowding on the color spread.
(2) It evaluated the color spreads due to measuring error
alone, which we used in setting up TEST2. (Its results for
are given, pro forma, but they have no real significance, since the
color spreads used in TEST1 are so narrow that our color bin-width does
not sample them adequately.) It is TEST2 which directly tests
our previous conclusions about the size of
.
We conclude from it that the AS tests recover our input values
of
,
within the uncertainties of the measurement.
In this section we have demonstrated, on two extreme fields of the ACS inner mosaic, that our dual-Gaussian fitting method is fully effective in overcoming the effects of crowding on the distribution of colors, and that it reliably estimates the relative star numbers in the two sequences. (Note that we use this same method for all of our other data sets too.) As we noted at the end of Sect. 3.3, the excellent agreement between the results from our completely uncrowded outer ACS field and those from our outer FORS1 fields establishes the validity of the latter, without recourse to any additional AS texts for them.
4 Radial gradients in the RGB subpopulations
It has been known since the end of the sixties that the RGB of
Cen is broader than would be expected from photometric errors
(Woolley & Dickens 1967),
but it was only in 1999 that Lee et al. (1999) clearly
detected at least two distinct RGBs. Later on, Pancino et al. (2000)
demonstrated that there is a correlation between the photometric peaks
across the RGB and three peaks in the metallicity distribution. On this
basis, they defined the three RGB groups: RGB-MP, RGB-MInt,
and RGB-a, characterized by an increasing metallicity. In this section
we will present a detailed study of the radial distributions of these
components.
4.1 Defining the RGB-MP, RGB-MInt, and RGB-a subsamples
Unfortunately the WFPC2, FORS1, and outer ACS/WFC data sets we used to analyze the main-sequence population in the previous section are saturated even at the MS turn-off level, and are therefore unusable for the study of the RGB radial distributions.
Our WFI@2.2m photometric and proper-motion catalog (Bellini
et al. 2009),
however, is an excellent data base for this study, particularly in view
of the fact that we can safely remove field
objects in the foreground and background, thanks to our accurate proper
motions. This proper-motion cleaning is of fundamental importance in
the outer envelope of the cluster, where there can be
more field stars than cluster giants. In the central regions of the
cluster, the WFI@2.2m data are less accurate due to the poorer
photometry caused by the crowded conditions, so there we take advantage
of our high-resolution inner ACS/WFC 3
3 mosaic, which included short exposures to measure the bright
stars. Below we describe how we extracted the
Cen RGB subsamples from these two data sets.
Because of the complex distribution of the stars along the RGB we were forced to use bounding boxes to select the different RGBs. This selection procedure is less accurate than what we were able to do for the bMS and the rMS; nevertheless it is still accurate enough to study the general trend of the radial distribution of the relative numbers of RGB-MP, RGB-Mint, and RGB-a stars. The Poisson error from the smaller number of RGB stars makes the more precise procedure less critical.
For the ACS data, we defined bounding boxes for the
RGB subpopulations of
Cen in the CMD obtained from the data set of the ACS/WFC 3
3 mosaic, for which the large-number statistics make the
separation among the different RGBs easier to see. We extracted three
RGB subpopulations, in a way very similar to that used by
Ferraro et al. (2002).
(Note that other authors, e.g. Rey et al. 2004; Sollima
et al. 2005a;
Johnson et al. 2009,
have defined four or even five RGB subpopulations.) The left
panel of Fig. 13
shows the three RGB bounding-box regions drawn in the CMD from
the ACS/WFC 3
3 mosaic, to identify the three subgroups RGB-MP, RGB-MInt,
and RGB-a. Our RGB selections are limited to magnitudes
brighter than B=17.9, and contain
5184 RGB-MP stars, 4379 RGB-MInt stars, and
383 RGB-a stars.
In extracting the RGB subpopulations from our
WFI@2.2m data set we chose to define the subpopulations in the
B, B-V CMD.
Even though we cannot adopt exactly the same selection boxes in the B,
CMD as for the
ACS/WFC 3
3 mosaic. This choice might appear awkward, not only because
the color baseline B-V
is shorter than the
baseline,
but also because the WFI
filter is very
similar to the ACS/WFC F625W filter. There are other
good reasons for adopting the B-V color
baseline, however. The most important one is that the
WFI photometry obtained with the V filter
has ten times as much integration time, and more dithered images than
those available for the
filter.
Therefore our V photometry is considerably
more
precise, and more accurate, than our
magnitudes.
Moreover, our empirical sky-concentration correction (very important
for such studies) is better defined in V
than in
(see Bellini et al. 2009).
In this WFI@2.2m B vs. B-V CMD,
we tried to define the bounding boxes in a way that was as consistent
as possible with what we did for the data set from ACS/WFC 3
3 mosaic. We cross-identified the stars that are in common
between the sample that we had selected from the RGB CMD of
the ACS/WFC 3
3 mosaic, on the one hand, and the WFI@2.2m B-V
data set on the other hand, and we carefully drew by hand, in the (B,B-V) CMD,
bounding boxes that would include the same stars as in the sample from
the ACS/WFC 3
3 mosaic.
In addition, we selected from the WFI@2.2m data set the stars
that were measured best (both photometrically and astrometrically), and
were most likely to be members of
Cen. To make the selection we used the error quantities in
Cols. 7, 9, 13, and 15 of Table 6 of Bellini
et al. (2009).
These are the errors of the two components of proper motion and of the B
and V magnitudes. Our selection consisted
of choosing, at the bright end of the RGB, stars whose
proper-motion error has a magnitude less than 1.8
,
and whose photometric error is less than 0.02 mag in each
band; we also required that the proper motion of a star differs from
the mean motion of cluster stars by no more than 2.1
.
At the faint end of the RGB we allowed these three tolerances
to rise to: 2.1
,
0.03 mag and 3.8
,
respectively. This high-quality data set comprised
4993 RGB-MP stars, 3057 RGB-MInt, and
292 RGB-a stars.
The right-hand panel of Fig. 13 shows the WFI@2.2m RGB subpopulations that were selected in this way. We note that whereas the RGB-a sample is well separated from the other two RGB components, the RGB-MP and RGB-MInt components are separated only by an arbitrary dividing line, so that small differences in defining the bounding boxes might result in some cross-contamination in those two samples.
4.2 Relative radial distributions of RGB stars
![]() |
Figure 13:
CMDs of the |
Open with DEXTER |
![]() |
Figure 14:
(a) Radial distribution of the ratio
RGB-a/RGB-MInt for the WFI@2.2m data set (red triangles) and
for the ACS/WFC 3 |
Open with DEXTER |
We divided our WFI@2.2m data set into ten radial bins, each containing
approximately the same number of RGB-MInt stars, and the ACS/WFC
3
3 data set into five radial bins, again with the same
equal-number criterion. For each of these bins we counted the number of
RGB stars in each subpopulation.
In Fig. 14
we show the derived radial gradients. As it has not been
possible to perform the same error analysis as was done for the
MS stars (because of the much smaller number of stars), the
error bars in Fig. 14
represent only Poisson errors, and should be considered a lower limit
to the real errors. In panel (a) we show the radial
distribution of the ratio RGB-a/RGB-MInt. Blue full circles refer to
the ACS/WFC 3
3 data set, and red
triangles to the WFI@2.2m data. Vertical dashed lines mark the
core radius
and the half-mass radius
.
We found that, within the errors, the RGB-a and the RGB-MInt stars
share the same radial distribution, since their ratio is constant over
the entire radial range covered by our two data sets. In
panel (b), we plot the ratio RGB-MInt/RGB-MP for the two data
sets. The RGB-MInt stars are more centrally concentrated than the
RGB-MP stars, with a flatter trend within
1
,
a rapid decline out to
,
and again a flat relative distribution outside. There is a hint, also,
that the RGB-MInt/RGB-MP ratio could be nearly constant within the
half-mass radius. We find that the general radial trend of the
RGB-MInt/RGB-MP star-count ratio is consistent with that of
.
This result provides additional evidence (in agreement with
the metallicity measurements by Piotto et al. 2005) that the bMS
and the RGB-MInt population must be part of the same group of stars,
with the same metal content and the
same radial distribution within the cluster. Panel (c) shows
that the ratio RGB-a/RGB-MP resembles, within the errors, the
RGB-MInt/RGB-MP trend. We were unable to examine this trend for the
MS part of the RGB-a population, since the MS-a
sequence cannot be followed below B
20.
Our analysis confirms the results by Norris et al. (1997), Hilker
& Richtler (2000),
Pancino et al. (2000),
Rey et al. (2004),
and Johnson et al. (2009),
who found that the most metal-poor RGB stars are less
concentrated than the RGB-MInt ones. Moreover, we can also confirm that
the RGB-a and the RGB-MInt share the same radial distribution within Cen,
as found by Norris et al. (1997), Pancino
et al. (2000),
and Pancino et al. (2003)
for RGB-a only.
It is important to note that because we were able to use proper motions to construct a pure cluster sample, our results are not affected by field-star contamination, which would tend to enhance the RGB-a star counts in the cluster outskirts with respect to the more populous RGB-MP sample (which also covers a smaller region in the CMD). Field-star contamination is likely the reason that Hilker & Richtler (2000) and Castellani et al. (2007) found the RGB-a/RGB-MP ratio to increase with distance from the cluster center - the opposite trend from what is seen here. Moreover, it is interesting to note that the different RGB-Mint subgroups (as highlighted, e.g., by Sollima et al. 2005a) might well have a different radial behavior, but necessarily - since we cannot distinguish them in the CMD - we have to treat them together and study only their average gradient.
5 Discussion
In this paper we have analyzed the radial distribution of the different
MS and RGB components in the globular cluster Centauri.
We used high-resolution ACS/WFC images to study the inner
regions of the cluster, and ACS/WFC, WFPC2 and FORS1@VLT images, as
well as WFI@2.2m images, for the cluster envelope. We found that there
are slightly more bMS stars than rMS stars in the
inner 2 core radii. At larger distances from the
cluster center, out to
8 arcmin,
the relative number of
stars
drops sharply, and then remains constant at
0.4,
out to half the tidal radius of the cluster.
Our most precise photometry comes from the outer ACS field
at 17
(12
),
where we find that the color dispersion (
)
of the bMS is about 50% larger than that of the rMS. The
other observations are consistent with this, though they are unable to
measure
so precisely, on account of crowding (in the inner
ACS field) and other errors (in the ground-based fields).
The RGB-MInt population (associated with the bMS by Piotto
et al. 2005)
and the RGB-MP sample (which includes the progeny of
the rMS) follow a trend similar to that of
.
The most metal-rich component of the RGB, RGB-a, also follows the same
distribution as the
RGB-MInt component.
On the hypothesis that the bMS, the presumably helium-rich population, is a second generation of stars formed by the low-velocity material ejected by a primordial population (which we assume to be the more metal-poor rMS population), the bMS must have formed from matter that collected in the cluster center via some kind of cooling flow. This is in qualitative agreement with the recent models by Bekki & Norris (2006) and D'Ercole et al. (2008). The very long relaxation time (half-mass relaxation time longer than 10 Gyr, according to the Harris 1996 compilation) has preserved some information about the original kinematic and spatial distribution of the material from which the younger component took form. Interestingly enough, the third, most-metal-rich population is also more concentrated than the most metal-poor component, and has a radial distribution that is rather similar to that of the intermediate-metallicity sample. It is also noteworthy that the bMS component has a broader color distribution than the rMS one. This fact may reflect, at least in part, the large dispersion in iron abundance of the intermediate-metallicity component (e.g. Norris & Da Costa 1995). Alternatively, this bMS spread could be an indication of the dispersion of other chemical elements, including He. Only a detailed analysis of the metal content of the two MSs can solve this issue, but for this we might need to wait for the next generation of 30+ m telescopes, on account of the faintness of these stars.
AcknowledgementsA.B. acknowledges support by the CA.RI.PA.RO. foundation, and by STScI under the 2008 graduate research assistantship program. I.R.K. and J.A. acknowledge support by STScI under grants GO-9442, GO-9444, and GO-10101. G.P. and A.P.M. acknowledge partial support by MIUR under the program PRIN2007 (prot. 20075TP5K9) and by ASI under the program ASI-INAF I/016/07/0.
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Footnotes
- ... Centauri
- Based on observations with the NASA/ESA Hubble Space Telescope, obtained at the Space Telescope Science Institute, which is operated by AURA, Inc., under NASA contract NAS 5-26555, and on observations made with ESO telescopes at La Silla and Paranal Observatories.
- ...
function
- A Penny function is the sum of a Gaussian and a Lorentz function. In this case we used five free parameters: half-width at half-maximum of the Penny function, in the x and in the y coordinate; the fractional amplitude of the Gaussian function at the peak of the stellar profile; the position angle of the tilted elliptical Gaussian; and a tilt of the Lorentz function in a different direction from the Gaussian. The Lorentz function may be elongated too, but its long axis is parallel to the x or y direction.
- ... effects
- Light contamination caused by internal reflections of light in theoptics, causing a redistribution of light in the focal plane.
All Tables
Table 1: Data sets used in this work.
Table 2: Dual-Gaussian fitting results.
Table 3: Results of the two artificial-star tests.
All Figures
![]() |
Figure 1:
The footprints of the |
Open with DEXTER | |
In the text |
![]() |
Figure 2:
Selection criteria used to isolate FORS1@VLT stars for our
MS subpopulation analysis. Panel (a)
shows sharp values versus B magnitude,
and panel (b) |
Open with DEXTER | |
In the text |
![]() |
Figure 3:
(Top left:) selected stars in common between the
ACS/WFC 3 |
Open with DEXTER | |
In the text |
![]() |
Figure 4:
B vs. |
Open with DEXTER | |
In the text |
![]() |
Figure 5:
(Top left): CMD from the eight FORS1@VLT fields. We
can measure stars from the bottom of the RGB down to B |
Open with DEXTER | |
In the text |
![]() |
Figure 6:
The left panel shows a randomly
selected 8% of the stars in
the CMD of the inner |
Open with DEXTER | |
In the text |
![]() |
Figure 7: Same as Fig. 6, but after subtraction, from the color of each star, of the color of the fiducial line at the same luminosity. In the left panel we show a randomly selected 20% of the stars from the ACS/WFC central-mosaic data (rather than the previous 8%, since the color-scale is now less compressed). |
Open with DEXTER | |
In the text |
![]() |
Figure 8:
(Left panel): B versus |
Open with DEXTER | |
In the text |
![]() |
Figure 9: Dual-Gaussians fits. As in Fig. 8, the Gaussian fits to the bMS and rMS are in blue and red respectively, and their sum in black. The vertical dashed lines mark the centers of the individual Gaussians. The individual panels are arranged in order of effective radius. (Note that all our fields are shown here, in radial order, so that the WFPC2 field follows the inner ACS fields, and the outer ACS field falls between two of the FORS1 fields.) |
Open with DEXTER | |
In the text |
![]() |
Figure 10:
|
Open with DEXTER | |
In the text |
![]() |
Figure 11:
TEST1 artificial star analysis for the central ACS/WFC 3 |
Open with DEXTER | |
In the text |
![]() |
Figure 12: Same as Fig. 11, but now for TEST2. See text for details. |
Open with DEXTER | |
In the text |
![]() |
Figure 13:
CMDs of the |
Open with DEXTER | |
In the text |
![]() |
Figure 14:
(a) Radial distribution of the ratio
RGB-a/RGB-MInt for the WFI@2.2m data set (red triangles) and
for the ACS/WFC 3 |
Open with DEXTER | |
In the text |
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