THE VMC SURVEY. XVIII. RADIAL DEPENDENCE OF THE LOW-MASS, 0.55–0.82 M
e
STELLAR MASS
FUNCTION IN THE GALACTIC GLOBULAR CLUSTER 47 TUCANAE
Chaoli Zhang
1,2
, Chengyuan Li
1,3,4
, Richard de Grijs
1,3,5
, Kenji Bekki
6
, Licai Deng
7
, Simone Zaggia
8
, Stefano Rubele
8
,
Andrés E. Piatti
9,10
, Maria-Rosa L. Cioni
11,12,13
, Jim Emerson
14
, Bi-Qing For
7
, Vincenzo Ripepi
15
,
Marcella Marconi
15
, Valentin D. Ivanov
16
, and Li Chen
2
1
Kavli Institute for Astronomy & Astrophysics, Peking University, Yi He Yuan Lu 5, Hai Dian District, Beijing 100871, China;
jackzcl@outlook.com, grijs@pku.edu.cn
2
Shanghai Astronomical Observatory, Chinese Academy of Sciences, Shanghai 200030, China
3
Department of Astronomy, Peking University, Yi He Yuan Lu 5, Hai Dian District, Beijing 100871, China
4
Purple Mountain Observatory, Chinese Academy of Sciences, Beijing Xi Lu, Nanjing 210008, China
5
International Space Science Institute-Beijing, 1 Nanertiao, Zhongguancun, Hai Dian District, Beijing 100190, China
6
ICRAR M468, The University of Western Australia, 35 Stirling Highway, Crawley, WA, 6009, Australia
7
Key Laboratory for Optical Astronomy, National Astronomical Observatories, Chinese Academy of Sciences, 20A Datun Road, Chaoyang District,
Beijing 100012, China
8
INAF-Osservatorio Astronomico di Padova, vicolo dell’Osservatorio 5, I-35122 Padova, Italy
9
Observatorio Astrońomico, Universidad Nacional de Córdoba, Laprida 854, 5000, Córdoba, Argentina
10
Consejo Nacional de Investigaciones Científicas y Técnicas, Av. Rivadavia 1917, C1033AAJ, Buenos Aires, Argentina
11
Universität Potsdam, Institut für Physik und Astronomie, Karl-Liebknecht-Str. 24/25, D-14476 Potsdam, Germany
12
Leibnitz-Institut für Astrophysik Potsdam, An der Sternwarte 16, D-14482 Potsdam, Germany
13
Physics, Astronomy, and Mathematics, University of Hertfordshire, Hatfield AL10 9AB, UK
14
Astronomy Unit, School of Physics and Astronomy, Queen Mary University of London, Mile End Road, London E1 4NS, UK
15
INAF-Osservatorio Astronomico di Capodimonte, via Moiariello 16, I-80131 Naples, Italy
16
European Southern Observatory, Karl-Schwarzschild-Str. 2, Garching bei München, D-85748, Germany
Received 2015 August 25; accepted 2015 November 4; published 2015 December 14
ABSTRACT
We use near-infrared observations obtained as part of the Visible and Infrared Survey Telescope for Astronomy
(VISTA) Survey of the Magellanic Clouds (VMC), as well as two complementary Hubble Space Telescope (HST)
data sets, to study the luminosity and mass functions (MFs) as a function of clustercentric radius of the main-
sequence stars in the Galactic globular cluster 47 Tucanae. The HST observations indicate a relative deficit in the
numbers of faint stars in the central region of the cluster compared with its periphery, for
18.75m
F606W
20.9 mag (corresponding to a stellar mass range of 0.55<m
*
/M
e
<0.73). The stellar
number counts at 6
7 from the cluster core show a deficit for 17.62m
F606W
19.7 mag (i.e., 0.65<
m
*
/M
e
<0.82), which is consistent with expectations from mass segregation. The VMC-based stellar MFs
exhibit power-law shapes for masses in the range 0.55<m
*
/M
e
<0.82. These power laws are characterized by
an almost constant slope, α. The radial distribution of the power-law slopes α thus shows evidence of the
importance of both mass segregation and tidal stripping, for both the first- and second-generation stars in 47 Tuc.
Key words: galaxies: clusters: individual ( 47 Tucanae) – globular clusters: general – Hertzsprung–Russell and
C–M diagrams – stars: low-mass – stars: luminosity function, mass function
1. INTRODUCTION
The globular clusters (GCs) in the Milky Way are excellent
probes to study the Galaxyʼs formation history. One of the
major goals in contemporary astrophysics is to understand the
stellar mass functions (MFs) of GCs, because they are thought
to contain original information about the stellar initial mass
function (IMF). A number of physical processes can cause the
IMF to vary, including fragmentation, accretion, feedback,
stellar interactions, and magnetic-field contributions (Lar-
son 1992; Padoan & Nordlund 2002; Bonnell et al. 2007).A
detailed understanding of the IMF is required to study the
stellar populations of external galaxies, which would otherwise
be impossible to study owing to their unresolved nature.
However, it is not simple to derive the IMF from an
observed present-day MF, since the latter is affected by both
observational and theoretical limitations: observationally, it is
significantly impaired by the crowding of GCs, photometric
uncertainties, and the observational field of view, which can
lead to significant biases when attempting to determine the
underlying stellar luminosity function (LF; King 1958). The
situation is further complicated by the fact that the mass–
luminosity relation (MLR), which is required to transform the
observed stellar luminosities to the corresponding masses, is
metallicity- and age-dependent (e.g., Kroupa et al. 1990;de
Grijs et al. 2002). Theoretical MLRs for intermediate and high
stellar masses ( m
*
0.2M
e
) are relatively well constrained
observationally, but at the low-mass end (m
*
0.2M
e
)
significant uncertainties remain. In addition, the MF can also
be modified by dynamical processes over a clusterʼs lifetime.
For instance, tidal interactions with the Milky Wayʼs gravita-
tional potential affect the outskirts of clusters (Lane et al.
2012), while mass segregation affects their central regions (e.g.,
de Grijs et al. 2002).
Despite all these observational and theoretical challenges,
the MF of the Galactic GC 47 Tucanae (47 Tuc) has been
studied extensively. Paust et al. (2010) showed that the 47 Tuc
MF in the clusterʼs central region can be approximated by a
power-law distribution, i.e., dN/dM∝M
− α
, with α=0.84
for the stellar mass range of 0.2–0.8M
e
; de Marchi & Paresce
(1995) and Santiago et al. (1996) showed that the MF at a
location between 4′ and 5′ from the center ( close to the clusterʼs
The Astrophysical Journal, 815:95 (9pp), 2015 December 20 doi:10.1088/0004-637X/815/2/95
© 2015. The American Astronomical Society. All rights reserved.
1
half-mass radius) is a power law with α=1.5 for the mass
range of 0.3–0.8M
e
, but that it flattens in the range
0.14–0.3M
e
. Comparison with the most recent Monte Carlo
simulations by Giersz & Heggie (2011) showed that the stars
above the main-sequence (MS) turn-off in 47 Tuc obey a power
law with α=2.8 and follow a relatively flat IMF with an index
of about 0.4 along the lower MS. This mass distribution is
much shallower than that found based on the ground-based
observations of Hesser et al. (1987), who determined an index
of 1.2 for the mass range of 0.5–0.8M
e
. However, all stellar
MFs investigated in previous studies pertained to specific loci
in the cluster; some were located in the cluster center, some
were based on data from its periphery, and some were
determined around the half-mass radius. Here we present a
systematic analysis covering a much larger radial range using
ground-based data obtained with the 4 m Visible and Infrared
Survey Telescope for Astronomy ( VISTA) telescope as part of
the VISTA Survey of the Magellanic Clouds (VMC), combined
with HST observations at central and intermediate cluster radii,
to investigate the low-mass MS LF and MF as a function of
radius from the center of 47 Tuc.
This paper is organized as follows. In Section 2, we present
the observational data and our analysis method. Our results are
presented in Section 3. In Section 4, we discuss our results in
the context of mass segregation and tidal stripping processes
affecting 47 Tuc. Our conclusions are provided in Section 5.
2. DATA SELECTION AND ANALYSIS
2.1. VISTA Data
The near-infrared Y, J , and K
s
observations used in this study
were obtained as part of the VMC survey (Cioni et al. 2011).
47 Tuc is projected onto the Small Magellanic Cloud (SMC)
and is located on VMC tile SMC 5_2. The SMCʼs main body is
partially located on the adjacent, southern tile SMC 4_2. The
VMC data were processed with the VISTA Data Flow System
pipeline (VDFS) and calibrated to match the VISTA photo-
metric system, which is close to the Vegamag system (Irwin
et al. 2004). We extracted the paw-print VMC images for all
three filters from the VISTA Science Archive and used the
IRAF/DAOPHOT package to derive the point-spread functions
(PSFs; Stetson 1987). The data selected for this study,
composed of two epochs in the Y and J bands and nine in
K
s
, were PSF-homogenized and stacked to obtain a final, deep
tile image.
17
We performed PSF photometry on the homo-
genized, deep VMC SMC 5_2 and 4_2 tiles image using the
PSF
and ALLSTAR tasks. The photometry was calibrated using the
method described in Rubele et al. (2015). Subsequently, we
correlated the three-band photometry to produce a multi-band
catalog. Figure 1 shows the spatial distribution of the MS stars
in 47 Tuc. The observations cover an area of almost 2 ×5 deg
2
(one VISTA InfraRed Camera—VIRCam—tile consists of six
offset paw-print exposures covering a ∼1.6 deg
2
field of view),
which contains more than 190,000 stars with Yä [16.8,
19.6] mag. A detailed overview of our observations of
47 Tuc as well as of our analysis procedures, was given by
Li et al. (2014).
The cluster is located toward the southwest in the SMC 5_2
tile image, while the southeastern corner of the field is
dominated by SMC field stars. Therefore, the area occupied by
47 Tuc could contain significant numbers of field stars
associated with both the SMC and the Milky Way. SMC tile
5_2 cannot be used for the field-star decontamination, since the
clusterʼs tidal radius can reach r
t
=2500″ (Harris 1996; Lane
et al. 2012), which essentially covers the entire tile. For
background star decontamination, it is crucial to find a region
that is representative both in terms of the star counts from the
Milky Way and their counterparts from the variable SMC
background. The bottom right-hand corner of the field, shown
in cyan in Figure 1 and contained in SMC tile 4_2, is ideal for
our decontamination of the clusterʼs color–magnitude diagram
(CMD) from background stars, for two reasons. First, it is
located at the same Galactic latitude as 47 Tuc so that Galactic
field contamination should be similar to that affecting our
47 Tuc observations; second, this region is located at a suitable
distance from both 47 Tuc and the SMC, thus minimizing the
number of possible residual 47 Tuc and SMC stars.
We therefore adopted a region dominated by the 47 Tuc
member stars centered at α
J2000
=00
h
24
m
04 80(6°.020),
δ
J2000
=−72°04′48″ (−72°.080) and within a radius of
1100″ (Li et al. 2014). A second region, shown in cyan in
Figure 1, centered on α
J2000
=00
h
18
m
48 00 (4°.70),
δ
J2000
=−73°09′02″(−73°.15) with a radius of 600″, was
adopted to calculate the background stellar density.
Figure 1. Spatial distribution of the stars in 47 Tuc (coordinates are given for
the J2000 epoch), combining SMC tiles 5_2 (top half) and 4_2 (bottom half).
The background stars were drawn from the VISTA data; the red annulus
indicates the VMC data used for this study, which is further radially binned into
five subsets. The blue region corresponds to the HST catalog of Sarajedini et al.
(2007), and the orange region represents the ultra-deep HST catalog of Kalirai
et al. (2012). The cyan region is adopted to compute the background field-star
density, which is in turn used to decontaminate the cluster CMD.
17
We found that the VMC observations of 47 Tuc are significantly affected by
PSF and sensitivity inhomogeneities for some epochs. For this reason, we
selected only epochs characterized by minimal seeing variations and the
highest sensitivity for analysis in the present paper, resulting in two epochs in
the Y band, two and one concatenation in J (corresponding to two and a half
epochs), and nine in K
s
.
2
The Astrophysical Journal, 815:95 (9pp), 2015 December 20 Zhang et al.
Li et al. (2014) showed, for the same VMC data, that the
observational completeness levels drop off rapidly in the
clusterʼs inner region. This is caused by a combination of the
increased blending probability and the enhanced background
brightness. They performed a large number of artificial-star
tests to study the effects of crowding on the uncertainties in the
resulting PSF photometry. For details of the artificial-star tests,
please refer to Rubele et al. (2012). The latter authors generated
∼10
6
artificial stars in the image and repeated their PSF
photometry in the same manner as for our sample of real stars.
This resulted in an artificial-star catalog that contained the input
and output magnitudes, as well as the photometric errors,
computed as “output minus input” magnitudes. Our observa-
tions’ completeness reaches a level of 50% at Y=19.6 mag
within a radius of 500″ from the cluster center. We therefore
restricted our study to MS stars in an annulus defined by
rä[500, 1100]″ and Yä [16.8, 19.6] mag.
2.2. Hubble Space Telescope (HST) Data
We also made use of two different HST data sets of 47 Tuc to
study the clusterʼs central regions, rä[0, 500]″, which are not
resolved by the VMC data. Both data sets were obtained with
HSTʼs Advanced Camera for Surveys (ACS) . One of the data
sets was taken as part of the Globular Cluster Treasury program
(PI: A. Sarajedini; Sarajedini et al. 2007, hereafter SA07),
which aimed at obtaining accurate photometry for stars well
below the MS turn-off in the F606W and F814W filters. We
directly use the Anderson et al. (2008) catalog: see the blue
data points in Figure 1.
Second, we used observations obtained by (Kalirai et al.
2012, hereafter KA12), who collected photometry for white
dwarfs in 47 Tuc based on 121 orbits of Cycle 17 HST
observations. Their main goal was to obtain photometry in the
ACS F606W and F814W filters with extremely long exposure
times to reach very faint magnitudes ( approaching 29 mag in
F606W) to study the entirety of the white dwarf cooling
sequence in the cluster. The advantages of using the KA12 data
are, first, that their field is located 6
7 (8.8 pc) west of the
cluster center. This region is neither too sparse nor too crowded
for our analysis. It allows us to resolve large numbers of MS
stars down to very low luminosities. Second, the authors’
completeness tests demonstrate that their photometry is very
precise and place the 50% completeness limit for the F606W
filter at 29.75 mag. A detailed discussion of the observations
and the corresponding data reduction can be found in KA12.
The KA12 catalog data points are colored orange in Figure 1.
In the context of the study presented here, we emphasize that
for both HST data sets, we restricted our study to magnitudes of
m
F606W
ä[17.53,20.9] mag for comparison with the VMC
data. The HST data was decontaminated by proper-motion
selection. This thus enabled us to construct highly robust
local LFs.
2.3. Isochrone Fitting and MS Selection
A number of studies have demonstrated that 47 Tuc displays
multiple stellar populations across its entire CMD (e.g.,
Anderson et al. 2009; Milone et al. 2012; Li et al. 2014).We
therefore adopted slightly different isochrones to fit the CMDs
corresponding to the different data sets used in this paper.
Table 1 summarizes their basic parameters. The metallicity
([Fe/H]) adopted in the table decreases slightly (from [Fe/
H]=−0.66 dex to [Fe/H]=−0.82 dex) with increasing
radius, which is consistent with the results of Li et al. (2014),
who found that stars in the cluster core are more metal-rich than
their counterparts in the clusterʼs periphery. The theoretical
isochrones we used to fit our CMDs were taken from the
Dartmouth Stellar Evolution Program (DSEP; Dotter
et al. 2008) for the HST data sets, since the DSEP models
are highly commensurate with other models (e.g., Pietrinferni
et al. 2006) and thus provide a robust and reliable MLR.
However, the DSEP suite does not provide models in the
VISTA Y, J, and K
s
photometric system. Therefore, we adopted
the Princeton–Goddard–Pontificia Universidad Católica
(PGPUC
18
) stellar evolutionary code (Valcarce et al. 2012) to
obtain best fits to the VMC data. The red curves in Figure 2
shows the CMDs and their corresponding best-fitting iso-
chrones; the vertical purple lines in all panels show the
magnitude ranges adopted for selecting the corresponding MS
regime.
In order to select all MS stars in 47 Tuc with minimal
contamination owing to photometric uncertainties, we char-
acterized the photometric errors in each passband and each data
set as follows. We first divided the magnitude range in each
band into 100 bins and subsequently determined the mean
photometric uncertainty in each bin. Subsequently, we
interpolated the bin-averaged values. Figure 3 shows an
example for the VISTA Y filter: the bin-averaged photometric
uncertainties are plotted as the red curve, while the green curve
represents the 5σ range. We also determined the fiducial ridge
line of the MS stars in the CMDs, using bin sizes of 0.3 mag for
Yä[16.8, 19.6] mag and m
F606W
ä[17.53, 20.9] mag. The
fiducial ridge lines for all three data sets were then used to
normalize the CMDs: see Figure 4. In this figure, the red curves
indicate all stars selected within pre-determined photometric
uncertainty ranges, i.e., 5σ,4σ, and 5σ for SA07, KA12, and
VMC data, respectively. This selection is required to limit
unmodeled effects owing to the presence of a population of
unresolved binary systems.
Table 1
Basic Representative 47 Tuc CMD Fit Parameters
Parameter HST SA07 HST KA12 VISTA VMC
Model DSEP
a
DSEP PGPUC
b
t (Gyr) 12.5 12.5 12.5
Y 0.251 0.252 0.26
[Fe/H] (dex) −0.66 −0.74 −0.83
[α/Fe] (dex) 0.0 0.4 0.3
E(B−V)(mag)
c
0.04 0.04 0.04
(m−M)
0
(mag) 13.3 13.3 13.35
α
J2000
00
h
24
m
04 80 00
h
22
m
39 00 L
δ
J2000
−72°04′48″ −72°04′04″ L
MS range (mag) [17.53, 20.9][17.62, 20.9][16.8, 19.6]
Completeness (%) [99, 85][100, 99.8][86, 65]
d
Note
a
DSEP: Dotter et al. (2008).
b
PGPUC: Valcarce et al. (2012).
c
Harris (1996).
d
For stars in an annulus with radii of 500″ and 1100″.
18
http://www2.astro.puc.cl/pgpuc/iso.php
3
The Astrophysical Journal, 815:95 (9pp), 2015 December 20 Zhang et al.
3. RESULTS
3.1. Luminosity Functions
The completeness-corrected local LFs based on the two HST
data sets are shown in the top panel of Figure 5. The stars in
both CMDs were divided into 15 bins. The error bars represent
Poissonian counting statistics. The LFs extend over the
magnitude range 17.53m
F606W
20.9 mag. However, we
note that the SA07 LF declines toward the low-mass end, for
18.75m
F606W
20.9 mag, while the KA12 LF exhibits a
deficit at the high-mass end, 17.62m
F606W
19.7 mag. The
vertical dashed lines in both panels indicate the decline on the
left of the dashed line for SA07 and the deficit on the right for
the KA12 data.
We consequently truncated the LF based on the SA07 data at
the luminosity where the linear regime (indicated in green) is
fitted adequately by a power law, i.e., dN(L)/dL∝L
− α
, where
N(L) corresponds to the number of stars per unit luminosity L.
To determine α statistically robustly, we ran Monte Carlo
simulations, assuming that the stellar number counts in each
bin are well-represented by Gaussian distributions. We then
randomly drew stellar number counts from each bin to
construct our sample LFs and fitted the results using a power
law to obtain α. This random sampling based on Gaussian
distributions in each bin was repeated ∼15,000 times. The
resulting α distributions are shown in the right-hand panels of
Figure 5, leading to (mean) μ
α
=0.104 for the SA07 data and
μ
α
=0.175 for the KA12 catalog.
The VMC-based LF of 47 Tuc is shown at the bottom of
Figure 5, also corrected for the effects of sampling incomplete-
ness and field-star contamination. We divided the annulus
rä[500, 1100]″ further into five radial subsets, i.e., rä[500,
600], rä[ 600, 700]″, rä[700, 800]″, rä[800, 900]″, and
rä[900, 1100]″. Applying the same routines as for the HST
data, for each annulus we fitted the observed LFs with a power
law and ran Monte Carlo simulations to obtain the distribution
of α. The results showed that the LFs at different radii are all
closely approximated by power laws, and that the α index
increases toward the outer regions of the cluster.
3.2. Mass–luminosity Relation and MFs
To determine the stellar MF the observed LF is commonly
divided by the derivative of the MLR. However, the shape of
the MLR depends sensitively on the stellar model used.
Figure 6 includes the three most-up-to-date stellar evolution
models—DSEP (Dotter et al. 2008), PGPUC (Valcarce
et al. 2012)
, and the Padova models (Marigo et al. 2008;
Girardi et al. 2010)—in both the VISTA photometric system
and for the HST/ACS photometric passbands used by SA07
and KA12. The stellar mass range we study here is 0.55
m
*
/M
e
0.82, a range where the input physics is relatively
better constrained than at the low-mass end, and therefore all
Figure 2. 47 Tuc CMDs. The red curves are the model isochrones defined in Table 1. The vertical purple lines indicate the magnitude ranges adopted for selecting MS
stars.
Figure 3. Photometric uncertainties as a function of magnitude for the VMC
data set in the Y filter. The red solid curve represents the bin-averaged
photometric uncertainties, while the green curve represents the 5σ range.
4
The Astrophysical Journal, 815:95 (9pp), 2015 December 20 Zhang et al.
models are characterized by smooth MLRs. We adopted
PGPUC and DSEP as our reference models.
The left-hand panels of Figure 7 show the 47 Tuc MF for our
two HST data sets and for the VMC data. The Monte Carlo
simulation results for the α distribution of power-law fits are
indicated in the right-hand panels. As already shown for the
LFs, the SA07 MF shows a decline toward the low-mass end,
for a mass range of 0.55<m
*
/M
e
<0.73, whereas a deficit
is again observed in the KA12 data for the high-mass end, at
0.65<m
*
/M
e
<0.82 (see the red dashed lines). Similarly to
our approach pertaining to the LFs, we truncated the SA07 MF
where it starts to deviate from a power-law distribution and
fitted a power law to this part of the MF. The resulting α
distribution increases from α=2.31 (SA07; center) to
α=3.37 (KA12;6
7 from the center), this result is in line
with the expectations from mass segregation.
The local MFs based on our VMC data are shown at the
bottom of Figure 7 for different clustercentric radii. The MFs are
all power laws and exhibit almost constant α indices. The mean
value of the five indices is
3.1
3
a
á
ñ=
, with a standard derivation
of σ
α
=0.07. We will discuss this flat trend in α index in the
next section in the context of the effects of mass segregation and
tidal stripping. For comparison, Bochanski et al. (2010) found
α=2.38 for the MF of low-mass dwarfs in the field over the
mass range 0.32M
e
<m
*
<0.8M
e
, while Kalirai et al. (2013)
determined that the field MF in the outer regions of the SMC for
the stellar mass range m
*
ä[0.37, 0.93]M
e
is well presented by
a power-law with α=1.9. Except for the innermost annulus, our
47 Tuc MFs are thus steeper than expected for field stars, which
reflects the effects of dynamical processing.
4. DISCUSSION
The observed MF α index increases from 2.31 in the central
region (SA07) to 3.37 at intermediate radii (at r≈6
7; KA12).
This shows that mass segregation significantly affects the
resulting stellar MF as a cluster undergoes dynamical relaxation
(Anderson & King 1996). Dynamical mass segregation causes
the high-mass stars to attain lower velocities, and they will thus
gradually sink toward the cluster center and boost the lower-
mass stars to the clusterʼs periphery. This will, in turn, lead to a
flatter MF in the inner regions and a gradually steeper MF
when moving toward the outskirts. This is evident for 47 Tuc,
given the observed declining MF trend for low-mass stars in
the central region, and the clear drop in stellar numbers starting
from a mass of m
*
=0.65M
e
or log(m
*
/M
e
)=−0.18 dex.
This drop cannot have been caused by incompleteness effects
nor by field-star contamination, since the KA12 catalog is
proper-motion cleaned and is 100% complete at the brightness
levels of interest here. The radial diffusion of low-mass stars
was recently observed for the first time by Heyl et al. (2015),
based on a sample of young white dwarfs.
This dynamical evolution can be further complicated by the
recent discovery that 47 Tuc hosts multiple stellar populations
(Milone et al. 2012; Li et al. 2014).D’Ercole et al. (2010) and
Bekki (2011) predicted that (i) the first-generation (FG) stars in
a GC can be at least 5–10 times more massive that the second-
generation (SG) stars at the epoch of GC formation and (ii) the
SG population is much more centrally concentrated than their
FG counterparts. This consequently leads to different two-body
relaxation timescales (t
relax
) for the two populations, because
t
relax
depends on the GC mass and size for a given typical
stellar mass. We emphasize that even though the observations
indicate that approximately two-thirds of present-day cluster
stars are SG descendants, with a substantial majority of FG
stars having been stripped from their host clusters, it is still
reasonable to discuss the effects of two-body relaxation on the
dynamical evolution of a young 47 Tuc dominated by FG stars,
because the stripping of FG stars takes hundreds of Myr.
(Bekki 2011). We therefore investigated the half-mass relaxa-
tion timescales
19
t
relax
separately for FG and SG stars to argue
Figure 4. 47 Tuc CMD, “normalized” by removing the trend defined by the MS ridge line. The red lines are the 5σ,4σ, and 5σ selections used to correct for the
presence of background field stars. The green line is the zero-color reference.
19
Here we use the median relaxation timescales (e.g., Spitzer & Hart 1971)
just for convenience in the discussion.
5
The Astrophysical Journal, 815:95 (9pp), 2015 December 20 Zhang et al.
![Figure 5. 47 Tuc MS LFs. LFs based on (top) the SA07 catalog for stars in the cluster center and (second panel) the KA12 catalog, containing stars located 6 7 west of the cluster center. The bottom five panels are local LFs for radial annuli covered by our VMC observations. The full annulus, rä[500, 1100]″, is divided into five radial subsets, i.e., rä[500, 600]″, rä[600, 700]″, rä[700, 800]″, rä[800, 900]″, and rä[900, 1100]″. The numbers of MS stars per unit magnitude vs. apparent magnitude F606W are plotted; the error bars were estimated based on Poissonian counting statistics. The green line is the power-law fit to the LF, and the two arrows in top two panels are an indication of a possible LF break magnitude. The Gaussian distributions on the right are the results of our Monte Carlo simulations to determine the best-fitting power-law index α.](/figures/figure-5-47-tuc-ms-lfs-lfs-based-on-top-the-sa07-catalog-for-21icl9lb.webp)
