A&A 415, 571-576 (2004)
DOI: 10.1051/0004-6361:20034638
Ch. Bonatto1 - E. Bica1 - L. Girardi2
1 - Universidade Federal do Rio Grande do Sul, Instituto de Física, CP 15051,
Porto Alegre
CEP 91501-970, RS, Brazil
2 -
Osservatorio Astronomico di Trieste, Via Tiepolo 11, Trieste, Italia
Received 27 August 2003 / Accepted 14 November 2003
Abstract
We study classical disk clusters at nearly solar metallicity with ages in the
range 200 Myr - 6 Gyr using 2MASS photometry and theoretical isochrones.
As a first step we employ J, H and K Johnson's Padova isochrones which, on a
large scale, result in a good fit of the observed data. However, we find some
significant deviations, especially in the red giant branch for intermediate age
clusters and the low-mass main-sequence end in general. Subsequently, isochrones
involving the 2MASS J, H and
transmission curves were generated which
account for differences of
0.02 of the above deviations, in the sense
required by the 2MASS observations. However, these corrections are not enough to
fully account for the observed differences. We suggest that the remaining deviations
should be accounted for by model atmosphere limitations, particularly the lack of
molecular opacity data in low-temperature giants. Future models will
incorporate these updated data in order to produce isochrones suitable for
the whole range of stellar masses.
Key words: Galaxy: open clusters and associations: general - stars: Hertzsprung-Russell (HR) and C-M diagrams
Understanding stellar evolution from very low to high mass stars represents one of the most important - and complex - efforts of modern Astronomy, with major consequences to vastly different research fields such as galaxy formation and cosmology. Nuclear reaction rates, radiative and conductive opacities, as well as equations of state for the whole range of physical conditions prevailing in the main classes of stars are necessary to build consistent theoretical models of stellar interiors and atmospheres. Additional simplifying approximations, such as the mixing-length theory and gray atmospheres, are also necessary and widely used in this stage. The resulting model quantities, such as luminosities, effective temperatures, and surface gravities may be converted to a given photometric system by using libraries of synthetic spectra derived from more detailed atmosphere models (e.g. Kurucz 1993; Castelli et al. 1997; see Girardi et al. 2002 for a discussion). However, crucial data on molecular opacities, particularly on the atmospheres of low-temperature giants are scarce and/or poorly determined (see, e.g. Plez 1999; Alvarez & Plez 1998; Alvarez et al. 2000; and Houdashelt et al. 2000a,b), which in turn may affect the conversion tables, in particular for infrared bands. Isochrones, the end-product of this task, are excellent theoretical tools to derive parameters such as age, metal content, mass function slope and distance to star systems.
Recently the Two Micron All Sky Survey (hereafter 2MASS, Skrutskie et al.
1997 - available at http://www.ipac.caltech.edu/2mass/releases/allsky/),
including the Point-Source Catalogue and Atlas, has produced huge amounts
of data to be explored in the coming years. The photometric system comprises
Johnson's J (
)
and H (
)
bands with the addition of
(
), slightly bluer than Johnson's K. The 2MASS sky coverage,
homogeneity and depth will certainly make this set of filters a photometric
standard reference for the future.
Table 1: WEBDA parameters on well-studied open clusters.
In the present state of the art it is fundamental to compare existing isochrones
in the Johnson system with 2MASS data, followed by the generation of isochrones
built with the J, H and
2MASS transmission curves themselves.
Among the available isochrone sets in Johnson's system are those built by the Padova
group (e.g. Bertelli et al. 1994; Girardi et al. 2000),
which are based on the J, H and K Johnson system as specified in Bessell & Brett
(1988). The Padova isochrone sets were computed with updated opacities
and equations of state, and a moderate amount of convective overshoot. The basic
isochrone set presented in Girardi et al. (2002) - available at http://pleiadi.pd.astro.it/~lgirardi/isoc_photsys.00/ - covers a very wide
range of initial masses (from 0.15 to
), metallicities, and photometric
systems, being well suited for studies of clusters of all ages. As a first step in this
work we test these isochrones on 2MASS observations of classical open clusters around the
solar metallicity level with known parameters derived mainly from the optical domain.
In Sect. 2 we compare the Johnson isochrones with 2MASS open cluster data. In Sect. 3 we discuss discrepancies between the Johnson isochrones and the observational data. In Sect. 4 we introduce isochrones specifically calculated with the 2MASS transmission filters. In Sect. 5 we discuss remaining residuals and suggest corrections to the isochrones in terms of atmospheric opacities.
We selected the following well-studied open clusters for the present analysis: M 41 (NGC 2287), Praesepe (M 44, NGC 2632), M 67 (NGC 2682), Pleiades (M 45) and NGC 6791. Parameters for these clusters, obtained from the open cluster WEBDA database (Mermilliod 1996 - http://obswww.unige.ch/webda), are compiled in Table 1. The clusters have metallicities around the solar value and are located in regions not heavily contaminated by field stars.
We used in this study photometry from the 2MASS all-sky data release.
Star extractions have been performed using the VizieR tool at
http://vizier.u-strasbg.fr/viz-bin/VizieR?-source=2MASS, using the circular
mode with an extraction radius comparable to the angular dimension of each cluster,
as given in Col. 5 of Table 1. The center of each extraction was as follows:
M 41 at J2000
(
,
);
Praesepe at
(
,
);
M 67 at
(
,
);
Pleiades at
(
,
);
and NGC 6791 at
(
,
).
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Figure 1:
2MASS CMDs for the Pleiades (M 45) built with WEBDA parameters and Padova
isochrones. Left panel:
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Figure 2: Same as Fig. 1 for M 41 (NGC 2287). |
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Figure 3: Same as Fig. 1 for Praesepe (NGC 2632). |
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Figure 4: Same as Fig. 1 for M 67 (NGC 2682). |
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Figure 5:
Same as Fig. 1 for NGC 6791. With respect to the WEBDA distance
modulus, we needed to apply an additional correction of
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In the present study we will employ intrinsic diagrams (absolute magnitudes and
dereddened colours according to Table 1 parameters).
We present in Figs. 1 to 5 the
and
2MASS colour-magnitude diagrams (CMDs) for the clusters studied in this work. The
isochrone fit in each panel has been obtained by shifting the positions of the stars
in each cluster according to the corresponding WEBDA parameters - observed distance modulus,
reddening and absorption (Table 1). Dereddening transformations employed the ratios
and
,
which were
derived from absorption ratios in Schlegel et al. (1998) and the ratio
from Dutra et al. (2002).
The parameters of the selected Padova
Johnson's isochrones are those closest available to the WEBDA age and metallicity.
We remind that the Padova isochrones are built with Johnson's K band, whereas the
clusters have been observed and calibrated with the 2MASS
filter. For comparison
purposes,
we also include in Figs. 1 to 5 the standard loci (Johnson photometry)
of solar vicinity main-sequence (MS) and giant stars adapted from Binney & Merrifield
(1998). We recall that the Hipparcos data (Robinchon et al.
1999) give a distance to the Pleiades of about 118 pc, which corresponds
to a distance modulus nearly 0.3 mags smaller than that used in the present isochrone
superposition to the 2MASS data (Fig. 1). Applying the Hipparcos modulus would degrade
the solution, particularly for the
.
Despite field contamination, the low MS can be studied in the Pleiades (Fig. 1) and Praesepe (Fig. 3), since they are nearby clusters. Massive giants can be studied in the 250 Myr M 41 (Fig. 2); the giant branch and clump can be assessed for the intermediate-age clusters M 67 (Fig. 4) and NGC 6791 (Fig. 5). The MS can be studied in all clusters except NGC 6791, which is too far from the Sun. Inferences on the turnoff can be made for M 41, Praesepe and M 67.
We point out that the distance modulus for NGC 6791 given by WEBDA was too small by an
amount of 0.8 to fit the data. Consequently, we needed to apply a correction of
to stars for both magnitude axes in order to reconcile observation and isochrone.
The WEBDA parameters for M 67 give a non-satisfactory fit of the turnoff region
(Fig. 4). In this age range, the turnoff shape strongly depends on age. Indeed,
with isochrones in the range 2.8-3.2 Gyr, somewhat older than WEBDA's
2.5 Gyr, a better solution to the turnoff is obtained. We show this new
fit in Fig. 6, which will be that subsequently used in the analyses. A more
detailed analysis of M 67 using 2MASS photometry is presented in Bonatto & Bica
(2003), in which we derive an age of
Gyr, null
reddening and a distance to the Sun of
kpc.
A qualitative analysis of Figs. 1 to 6 shows that the overall isochrone
fits are to first order representative of the observations.
Particularly worthy of notice is that the isochrones give a good general description
of the main sequence of the Pleiades (Fig. 1) and Praesepe (Fig. 3),
over a large range of absolute magnitudes (from
to
).
They clearly predict the most prominent changes in the main sequence slope,
occurring at about
,
,
and
,
.
This description of the main sequence by the models is
better than the empirical curve given by Binney & Merrifield (1998).
However, the isochrones do not
reproduce some details of the observed CMDs, particularly with respect to the
lower MS and, to a lesser extent, the giant branch. This effect does not systematically
depend on age and metallicity. For example, the isochrone fit with the WEBDA parameters for
the Pleiades, the youngest cluster of this sample with age 135 Myr (Fig. 1),
is considerably redder than the observed lower-MS stars in the (J-H)0 colour (by
0.10 mag), at magnitudes
.
On the other hand, this part of the main sequence is well described by the solar
vicinity stars (the Binney & Merrifield 1998 relation in the left panel of Fig. 1).
In (
(right panel), both sequences
are compatible with the observed stars. For Praesepe (Fig. 3), the Padova
isochrone is also redder in (J-H)0 (by
0.07 mag) than the observed
lower MS, while the agreement is good in (
.
Although there occur only a few massive giants in the CMDs of M 41 (Fig. 2),
they appear to be well described by the Padova isochrones both in (J-H)0 and
.
Intermediate-age giants are well adjusted in both colours for M 67 (Fig. 4) and for NGC 6791 (Fig. 5).
The isochrones for M 67 and NGC 6791 are too red in (J-H)0 by 0.07with respect to the sub-giant branches (Figs. 6 and 5, respectively).
The giant clump is well described for M 67 (Fig. 6). For NGC 6791,
the
fit is good, but the corresponding isochrone locus is
too red by
0.07 in (J-H)0.
Considering uncertainties in the parameters, the turnoff region is well
described for the Praesepe and M 67. For M 41, the (
)0 solution
is suitable, while there are deviations in the (J- H) 0 solution (Fig. 2).
For clusters younger than 1 Gyr, the MS fits are suitable except
for the
solution for the Pleiades, in which the isochrone is
too faint by about 0.25 mag. The solar vicinity sequence also describes well
the observed MSs, except those of the Praesepe (Fig. 3) where it is too
faint by about 0.25 mag. In
)0, the solar
vicinity MS is also too faint (Fig. 1).
At intermediate ages (M 67), the isochrones turned out bluer than the observed
stars, by about 0.04 in (J-H)0 and 0.08 in (
)0. In this
case we suspect that most of the discrepancy is not due to the models, since
M 67 is known to have at least a fraction of
of binaries (Montgomery
et al. 1993). However, the behaviour is not exactly the same
in the (J-H)0 and (
diagrams (Fig. 6), which might
be accounted for by the models.
The above series of differences between theory and observation cannot be fully ascribed to simple observational in the uncertainties parameter, instead they appear in most cases to reflect some systematic effects in the theory which should be properly taken into account.
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Figure 6:
A best-fit for M 67 is obtained with somewhat older isochrones
(with respect to WEBDA's data) which, however, do not fix the MS and giant
branch deviations. Left panel:
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It is fundamental for 2MASS data analysis consistency that a new set of isochrones be built taking into account specifically the transmission filters employed by 2MASS.
The 2MASS transmission curves have been downloaded from the site
http://www.ipac.caltech.edu/2mass/releases/second/doc/sec3_1b1.html).
Figure 7 compares them with Johnson filters (cf. Bessell & Brett 1988),
and a few representative stellar spectra. A new set of 2MASS
isochrones
was generated in the same
way as in Girardi et al. (2002)
. In Fig. 8 we compare the present
new J, H and
set with that of Johnson's (Girardi et al. 2002) in a
)
CMD for solar metallicity isochrones with ages 63 Myr,
250 Myr, 2 Gyr and 10 Gyr.
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Figure 7:
2MASS J, H and ![]() |
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Figure 8:
Comparison of Johnson K with 2MASS ![]() ![]() ![]() ![]() |
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The 2MASS transmission filters produced isochrones very similar to the
Johnson ones, with small (
)
differences which are slightly dependent
on age. For intermediate-to-old ages, (
for the lower+upper
main sequences and turnoff, while for young ages (
for the lower
main sequence and (
for the upper main sequence and turnoff.
in the giant branch for all ages.
In the insets of Fig. 8 we show blowups of the turnoff and giant branch
regions, where K and
differ significantly. In the turnoff region of the
10 Gyr isochrones the difference is (
while at the
giant branch (
.
For the low-mass end, the differences found
are (
for all ages.
With respect to the J and H filters, the present 2MASS set produced isochrones which differ at most 0.01 in (J-H)0 (Fig. 9).
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Figure 9: Same as Fig. 8 for the J and H filters. Differences in (J-H)0 colour are at most 0.01 throughout. |
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A comparison of the 2MASS observations (Sect. 2) and the new J, H
and
isochrones shows that the corrections of
+0.02 are in general
in the required sense, however, significant deviations still remain which
probably arise in the theory.
In this work we have compared J, H and
2MASS observations of reference disk
open clusters at nearly solar metallicity, with previously available J, H and K
Padova isochrones. On a large scale, the Johnson isochrones produce a reasonable
representation of the main features observed on the CMDs of the clusters. However,
some significant differences between the isochrones and observations arise which
cannot be ascribed to observational parameters such as reddening, distance, age and
metallicity uncertainties.
As a second step, we generated new isochrones specifically built with the 2MASS filter
transmission curves. Empirical corrections were applied to the original models, thus
producing a new J, H and
set of isochrones which, in principle, shouldbe more
appropriate to study open clusters of nearly solar metallicity observed with 2MASS.
Although some small improvements with respect to the Johnson's
JHK isochrones have been obtained, this new set of isochrones (presented in
Sect. 4) does not appreciably change the description of the 2MASS observations.
In short, most of the discrepancies pointed out in Sect. 3 still remain, and
new ones appeared, which could be related to data deficiency on atmospheric opacities in
the models.
Further improvements in the J, H and
isochrones with respect to the observations
certainly involve a few small changes on the transformation tables from stellar model
parameters to observational quantities, since the lack of molecular opacity data in
Kurucz's (1993) models may account for some (or even most) of the remaining
deviations.
Acknowledgements
This publication makes use of data products from the Two Micron All Sky Survey, which is a joint project of the University of Massachusetts and the Infrared Processing and Analysis Center/California Institute of Technology, funded by the National Aeronautics and Space Administration and the National Science Foundation. We employed data from CDS/Simbad/VizieR (Strasbourg) and also made use of the WEBDA open cluster database. We acknowledge support from the Brazilian Institution CNPq. We thank Dr. D. Soderblom for useful comments.