T. Bensby - S. Feltzing - I. Lundström
Lund Observatory, Box 43, 221 00 Lund, Sweden
Received 30 December 2003 / Accepted 21 March 2004
Abstract
A sample of 229 nearby thick disk stars has been
used to investigate the existence of an age-metallicity relation (AMR)
in the Galactic thick disk. The results indicate that that there is
indeed an age-metallicity relation present in the thick disk.
By dividing the stellar sample into sub-groups,
separated by 0.1 dex in metallicity, we show that the median age
decreases by about 5-7 Gyr when going
from [Fe/H]
to [Fe/H]
.
Combining
our results with our newly published
-element trends
for a local sample of thick disk stars that show
signatures from supernovae type Ia (SN Ia),
we draw the conclusion
that the time-scale for the peak of the SN Ia rate is of the order
of 3-4 Gyr in the thick disk. The tentative evidence for
a thick disk AMR that we present here also has implications for
the thick disk
formation scenario; star-formation must have been an ongoing
process for several billion years. This
appears to strengthen the hypothesis that the thick disk
originated from a merger event with a companion galaxy that puffed
up a pre-existing thin disk.
Key words: stars: Hertzsprung-Russell (HR) and C-M diagrams - stars: kinematics - Galaxy: disk - Galaxy: kinematics and dynamics - Galaxy: solar neighbourhood - Galaxy: formation
Chemical evolution of stellar populations is an important part of any model of galaxy formation and evolution. Many studies have shown how we are able to further refine and constrain models of Galactic chemical evolution by combining kinematics and elemental abundances of local dwarf stars (e.g., Chiappini et al. 2003; Matteucci 2001; Edvardsson et al. 1993; Feltzing & Gustafsson 1998; Feltzing et al. 2003a; Bensby et al. 2003; Reddy et al. 2003). As evidenced by the cited articles our understanding of chemical evolution is mainly driven by the studies in the solar neighbourhood but have far reaching impact for our interpretation of integrated light from other galaxies (e.g., Matteucci 2001).
However, it is not only the elemental abundances and kinematics of the stars that are of importance to further improve the models of galaxy formation and evolution but also the ages of the stars (see e.g. Edvardsson et al. 1993; Raiteri et al. 1996; Pilyugin & Edmunds 1996; Berczik 1999).
Many studies have found there to be a clear relation between the ages and the metallicities of the solar neighbourhood disk stars (Twarog 1980a,b; Rocha-Pinto et al. 2000; Meusinger et al. 1991). In contrast to this Edvardsson et al. (1993) found no particular evidence for an age-metallicity relation in the Galactic disk in the solar neighbourhood and Feltzing et al. (2001) confirmed this. Feltzing et al. (2001) also showed how dangerous selection effects could be and how an artificial age-metallicity relation can be created (see their Figs. 13 and 14).
Gilmore & Reid (1983) showed that our galaxy is host to two kinematically distinct disk structures. The "new'' disk was dubbed the thick disk and was found to have a mean metallicity around -0.6 dex (Wyse & Gilmore 1995) and a scale-height of 800-1300 pc (e.g., Reylé & Robin 2001; Chen 1997) while the thin disk has a mean metallicity of around -0.1 dex and a scale height of 100-300 pc (e.g., Gilmore & Reid 1983; Robin et al. 1996). Recent studies have shown that stars selected to belong to either the thin or the thick disk show different trends for the elemental abundances (e.g., Fuhrmann 1998; Feltzing et al. 2003a; Bensby et al. 2003, 2004; Reddy et al. 2003; Prochaska et al. 2000; Mashonkina & Gehren 2001).
The question then arises: could it be that the lack of a relation between ages and metallicities for stars in the solar neighbourhood is in fact a population effect? That is, are we looking at a mixture of stars from (at least) two populations that have different chemical enrichment histories?
It thus appears natural to, yet again, revisit the question of an age-metallicity relation in the solar neighbourhood. In the study presented here we will address the question of a relation between ages and metallicities for stars that are kinematically selected to resemble the thick disk closely.
The paper is organized as follows: in Sect. 2 we describe the
stellar sample and the kinematical selection criteria and
investigate if there are potential biases present in the sample.
In Sect. 3 we describe the choice of
-enhancement used in the isochrones when deriving the stellar ages.
In Sect. 4 we derive ages from
stellar isochrone fitting and find that there is a possible
age-metallicity relation present in the thick disk. In
Sect. 6 we discuss the implications this tentative
age-metallicity relation has on the star-formation history of the thick disk,
on the time-scale of SN Ia rate in the thick disk, and on our understanding
of the origin and evolution of the thick disk.
Finally, in Sect. 7 we give a short summary.
The stellar sample has been selected on purely kinematical grounds
(see also Bensby et al. 2003; Bensby et al. submitted). We have
assumed that the Galactic space velocities (
,
,
and
)
for the stellar populations in the solar neighbourhood
all can be described by Gaussian
distributions. For each star (with its specific combination of
,
,
and
)
it is then possible to calculate the
probabilities that it belongs to either the thin disk (D), thick disk (
),
or the halo (H). These can then be used to, for each star, calculate the
"relative probabilities"
and
.
When doing this, the fraction
(normalization) of the
three components in the solar neighbourhood must be taken into
account. The final relationship is (see Bensby et al. 2003):
![]() |
(2) |
Table 1:
Characteristic velocity dispersions
(
,
,
and
)
in the thin
disk, thick disk, and stellar halo, used in
Eq. (1). X is the observed fraction of stars for
the populations in the solar neighbourhood and
is the
asymmetric drift (values taken from Bensby et al. 2003 and
Bensby et al. submitted).
A
ratio of 10 means that the star
is ten times more likely to be a thick disk star than a thin disk star.
For our previous studies of elemental abundances in the thick
and thin disks we selected stars with
as thick disk
stars and
as thin disk stars. In Bensby et al. (2003) we
also analyzed spectra of a few stars with
between 10 and 2 and
it turns out that these stars show the typical thick disk trends
for the elemental abundances that the stars with
showed.
Thus it appears likely that we could use a somewhat lower
than 10 to increase our sample of
thick disk stars without compromising the results, but see discussion in
Sect. 5.
The most uncertain parameter in the calculation of the
ratios
is the normalization of the number density of thick disk stars in the
solar neighbourhood.
Different authors quote different values:
2% was found by Gilmore & Reid (1983) and
Chen (1997),
6% was found by
Robin et al. (1996) and Buser et al. (1999) and
15% by Chen et al. (2001) and
Soubiran et al. (2003).
As there is no simple way to determine which is the correct value we inspected
colour-magnitude diagrams (CMD) of the thin and thick disks, respectively,
derived using different normalizations for the solar neighbourhood thick
disk contribution (see Bensby et al. submitted). From this inspection it is
clear that a very low normalization (2%) must be ruled out since then the
thin disk CMD showed a population that was identical in age
and turn-off properties to that of the thick disk CMD.
The other values of the normalization are, however, not as easily
distinguished. As a compromise we will use a normalization of 10% and
a
and
as our selection criteria for thick disk
stars.
The other parameters, such as the velocity dispersions, of course
also influence the
ratios. They are however better known.
That the resulting samples are well defined regardless of the normalization
can be understood through the following argument.
All stars with
,
using a 10% normalization,
will for all normalizations lower than 10% still have
.
This means that if we select stars with
(10% normalization) as our thick disk stars they would also be selected
as thick disk stars using any of the normalizations listed in the literature.
In the same way stars with
(10% normalization)
would always be selected as thin disk irrespective of the value of the
thick disk normalization.
![]() |
Figure 1:
Boxplots showing the distribution in (B-V), ![]() ![]() ![]() ![]() |
Open with DEXTER |
We will restrict
the selection of the stellar sample to a certain area in
the
plane.
The limits have been marked in
Fig. 3 by the dotted lines.
This area has been selected on the grounds
that we do not want to include stars for which
age determinations are nearly impossible,
which is the case for the lower part of the main sequence
where the isochrones are very crowded (i.e.
). We also exclude
stars that lie on the giant branch, since the metallicity calibrations
are not valid for such stars (see Feltzing et al. 2001).
In this region the colour of the stellar isochrones are also uncertain
(see e.g. Yi et al. 2001, their Fig. 2).
We have also excluded stars that fall outside the following
boundaries: (B-V)<0, (B-V)>1 and
(see Fig. 3).
Selecting all stars in the Hipparcos catalogue that have relative errors in
their parallaxes less than 25% (and not flagged as binaries or probable
binaries) and that have radial velocities
published in the compilation by Barbier-Brossat et al. (1994) we get
a sample of 12 600 stars. Adding our thick disk criteria (
and
)
and the restrictions in (B-V) and
given above,
we get a sample of 295 stars that are likely to belong to the Galactic thick
disk.
Estimates of [Fe/H] for the stars can be derived using calibrations of Strömgren photometry (compare Feltzing et al. 2001). However, not all the stars in the Hipparcos catalogue have published Strömgren photometry. 229 out of the 295 thick disk stars have Strömgren photometry from the compilation by Hauck & Mermilliod (1998).
![]() |
Figure 2:
The [Mg/Fe] trend for a sample of thick disk stars from
Bensby et al. (2003) (circles) and
Bensby et al. (submitted) (triangles).
The stars were selected according to
the same kinematical criteria as discussed in Sect. 2.
The solid line indicates the degree of ![]() |
Open with DEXTER |
At a quick glance, the distributions of the MV, (B-V) and the
,
,
velocities do not seem to be
appreciably affected when the stars without
Strömgren photometry are rejected. We verify this by performing two-sample
Kolmogorov-Smirnov (KS) tests. The probability that the distributions are
identical is 99.4% for MV, 89.7% for (B-V) and >99.9%
for all three velocities. This means that for all but (B-V) the distributions
are essentially the same. For (B-V) we have inspected the CMDs before
and after adding the Strömgren photometry. This inspection showed that
there is no appreciable deterioration in the sampling of red, old stars.
This makes us comfortable in believing that we do not introduce any
of the biases discussed in Feltzing et al. (2001).
In summary we do not introduce any bias to our thick disk sample by only selecting those stars with published Strömgren photometry.
Stars more metal-poor than the Sun have long been known to show enhanced levels
of -elements (see e.g. Edvardsson et al. 1993).
In Bensby et al. (2003) and Bensby et al. (submitted) we
use the same kinematic definitions of thick disk stars as we do here
and we derive stellar abundances for a large number of thin and thick disk
stars spanning a range of metallicities. In Fig. 2 we show
the resulting [Mg/Fe] vs. [Fe/H] trend for the thick disk stars in those
two papers.
As can be seen from Fig. 2 the enhancement of
[Mg/Fe] varies with [Fe/H] for the thick disk. At
the enhancement is
0.3 dex while at [Fe/H] = 0 it has decreased to almost solar
values.
The thick disk stars in Mashonkina et al. (2003)
show the same degree of Mg enhancement, i.e. [Mg/Fe]
-0.4
for metallicities below [Fe/H] =-0.4.
(Note that the
-element abundance often is defined
as the average of the Mg, Si, Ca, and Ti abundances, while
in Fig. 2 we show Mg).
It is important to know how enhanced the stars are in
the -elements as
-enhancement has a strong
effect on stellar evolutionary tracks, and hence on the stellar
isochrones that we want to use to determine the ages.
A set of isochrones with an
-enhancement of [
/Fe] = 0.3
is compared to a set of solar-scaled isochrones in Fig. 3.
The effect of taking
-enhancement into account is that ages
will be lower than otherwise.
![]() |
Figure 3:
Example of how ![]() ![]() |
Open with DEXTER |
In the determination of stellar ages from isochrones with different [Fe/H]
we will use -enhancements that are in concordance with the the
trend that has been outlined in Fig. 2 and is also
listed in Table 2. The Yonsei-Yale (Y2) set of isochrones
(Yi et al. 2001; Kim et al. 2002)
provides a versatile tool since they not only have published calculated
sets of isochrones but also an interpolator that enables the user to calculate
a set of isochrones with a specific [Fe/H] and [
/Fe].
Table 2:
Median ages and spreads for the sub-samples.
The first column gives the central
metallicity, and the second column the -enhancement.
Columns 3-6 give the following for the samples
selected with
:
the number of stars in the sub-sample,
the lower quartile for the age distribution, the median age,
and the upper quartile for the age distribution.
Columns 7-10 give the same information but for the samples
selected with
.
A visual inspection of these CMDs directly shows that the turn-off for the CMD centered at -0.1 dex is significantly younger than the turn-off in the CMD centered at -0.7 dex (see Figs. 4a and 4c, respectively).
We now proceed to quantify this visual impression.
The stars are divided into 10 sub-samples according to their metallicities.
Each sub-sample has a central metallicity and all stars 0.15 dex
around this value are included in the sub-sample. The central metallicity
changes by 0.1 dex between each sub-sample. In this way we create a sliding
metallicity binning for the age determinations, i.e. the sub-samples are not
independent.
Ages for each sub-sample were simply estimated in the following way:
![]() |
Figure 4: CMDs for the thick disk which show how the age distribution increases to older ages as we move to lower [Fe/H]. The isochrones are as indicated. We show ages from 20 to 1 Gyr with a step of 1 Gyr. The isochrones for 5, 10, 15, and 20 Gyrs are indicated by solid lines. |
Open with DEXTER |
We believe that the change in age with [Fe/H] is significant as we are using a set of isochrones and a sample of stars that have had their parameters determined in the same way. Thus we should not expect systematic errors between bins. Furthermore the decline is up to 5 billion years from the most metal-poor to the most metal-rich bin. Such a large, and systematic, change would be hard to achieve through an erroneous analysis.
![]() |
Figure 5:
Age-metallicity diagram for the age estimates and central
metallicities listed in Table 2 for the samples
selected with
![]() |
Open with DEXTER |
![]() |
Figure 6:
Histograms showing the distributions of the
![]() ![]() |
Open with DEXTER |
In Fig. 5 we see a strong decrease in the mean age for the highest metallicities. Given that the thin disk dominates more and more as we go to higher metallicities the question arises: are we simply adding more and more of the younger thin disk stars into our sample?
There is in fact some hint in our data that we are picking up thin
disk stars in our most metal-rich bins. Figure 6
shows the distributions of
for the three CMDs in Fig. 4.
As can be seen we detect more and more stars
with low
ratios as we go to higher metallicities.
The stars with
could be intervening thin disk stars.
Ideally, if the metallicity distribution functions for the two disks were well known we could weight the probabilities we use to select the stars accordingly.
The metallicity distributions of
the thin and thick disks peak at different metallicities
(Wyse & Gilmore 1995).
The thick disk appears to peak in the interval
and the thin disk around -0.2 dex.
However, the two distributions are not well constrained. The
distribution for the thick disk truncates at
in Wyse & Gilmore (1995). We find that due to the shortcomings
in our knowledge about the metallicity distribution functions
of the two disk populations it is not possible to use them to further
deconvolve the two populations.
![]() |
Figure 7:
Same as Fig. 4 but using
![]() |
Open with DEXTER |
We will here try to address the issue of intervening thin disk stars in a
different way. In Fig. 7 we show the same CMDs as in Fig. 4 but with a stronger constraint
on
,
i.e.
,
and compare Fig. 6.
In this figure we see the same trend (albeit with fewer stars)
as in the original CMDs, strengthening
our earlier conclusion that there is an AMR present in the thick disk.
In Fig. 8 we show the resulting AMR constructed in the
same way as in Fig. 5. Note, however, in this new case we have
as a furher precaution excluded all stars with MV>5.4to make sure that we have as accurate ages as possible. Furthermore,
very few stars are on the sub-giant branch, where
the evolutionary timescale is short and hence age determinations can
be erroneous (see Pont & Eyer 2004). As a further extreme test
we have
inspected the CMDs where all stars with
km s-1have been excluded. These CMDs clearly show that the stars centered
on
form on average a younger population that the
stars centered around
.
Thus we again find an AMR to be present in the thick disk.
![]() |
Figure 8:
Same as Fig. 5 but using
![]() |
Open with DEXTER |
From a spectroscopist's point of view there is now mounting evidence that the stars that today have kinematics that we associate with the thick disk show elemental abundance trends that are distinct from those seen in stars on solar-type orbits (thin disk). A recent review can be found in Nissen (2003). Our own results have been published in Feltzing et al (2003a,b) and Bensby et al. (2003, 2004), see also Fig. 9. These observations appear to point to some homogeneity in the chemical enrichment process that proceeded the formation of the stars that we today associate with the thick disk.
Our new result, that there is a possible age-metallicity relation in the thick disk, adds a further dimension. The results indicate that star formation continued up to 5 billion years in the population we identify as the thick disk.
The observational properties and a standard interpretation for the chemical
evolution of the thick disk is the following:
the abundance trends for the thick disk are well-defined and show large
-enhancements at a constant value for metallicities below
[Fe/H]
-0.4. This is normally interpreted as that the star
formation was intense and that massive stars were the main contributors to the
chemical enrichment. At higher [Fe/H] the
-enhancement starts to
decline toward solar values. This is typical for what happens when long-lived
low-mass stars start to contribute to the chemical enrichment through the
explosion of SN Ia. The SN Ia mainly produce iron peak elements and none
or only little of the
-elements which results in a lowering of the
[
/Fe] ratio (compare e.g. Fig. 8.6 in Pagel 1997).
The time at which the decline starts is not only a function of the lifetime
of SN Ia but also of the SN Ia rate. The exact model, and hence lifetime
for SN Ia, is still debated. The two most probable scenarios are a double
or a single degenerate system consisting of either two white dwarfs or a
white dwarf and a red giant. In the latter case the life time is set by the
main sequence lifetime of the star that becomes the red giant, while in the
first case the lifetime for the system prior to becoming
supernova is set by the
time it takes the two white dwarfs to spiral in and coalesce,
and hence it depends on the
initial separation and could be longer than the Hubble time. For a recent,
in-depth discussion of these issues see Livio (2001). Furthermore,
the population synthesis of the SN Ia progenitors does, in general, not agree
too well with the observed frequencies of possible progenitor systems
(see Livio 2001, and references therein). This means that any
interpretation of our -abundance trends in terms of a minimum
timescale for the star formation period in the thick disk will be
rather complex (see also Fig. 5.7 in Matteucci 2001).
However, our investigation of the relation between ages, metallicities,
and elemental abundances for stars with typical thick disk kinematics points
to a conclusion that the SN Ia rate peaked after a few
(3-4) billion years.
We also note that the observed abundance trends are tight
(compare the oxygen trends in Fig. 9) which should
indicate that the gas must have been rather well mixed throughout.
This seems to indicate that the gas that the thick disk stars formed out
of must have been confined to a reasonably "small" physical volume
for the mixing to work efficiently.
![]() |
Figure 9: Abundance trends for oxygen in the thin and thick disks (Bensby et al. 2004). Thin and thick disk stars are marked by open and filled symbols, respectively. Triangles are data points that have been gathered from Nissen et al. (2002). |
Open with DEXTER |
Simulations of galaxy formation indicate that we should expect all or a large part of our galaxy to have been assembled from smaller parts (e.g., Murali et al. 2002). The question then arises - did these smaller building blocks form stars before they merged into today's thick disk? If they did and if they were of different sizes, as one may imagine, then they would each form their own unique set of elemental abundance trends which would depend on the initial mass function and the star formation rate in each individual building block. Then clearly we would not see any homogeneous elemental abundance trends as has been found by several authors (Fuhrmann 1998; Mashonkina & Gehren 2001; Prochaska et al. 2000; Feltzing et al. 2003a). Of course, if these building blocks were collected before they formed stars it might be possible to find abundance trends in today's thick disk. Another, and perhaps more likely possibility, is that what we today observe as a thick disk originally was a thin disk that, after having produced its stars, was puffed up (see e.g. Robin et al. 1996; Quinn et al. 1993). Such a scenario would allow the gas to be more well mixed at the time of star formation and abundance trends would be possible.
Another possible scenario is a close encounter between the Milky Way and another galaxy. This scenario has been modelled by Kroupa (2002) who shows that such an event would result in a kinematical heating of a pre-existing gaseous disk and an increased star formation in this gas.
Using a sample of 229 kinematically-selected thick disk stars
we have been able to probe the existence of an age-metallicity relation in
Galactic thick disk. Ages have been determined in a consistent way,
using isochrones with the appropriate levels of -enhancement at
different metallicities as indicated by recent studies that
use detailed abundance analysis.
Although the stellar sample is rather small we believe
it to be free from severe biases that could affect the results. From
the investigation we are able to draw three main conclusions:
Acknowledgements
We would like to thank Poul Erik Nissen and the anonymous referee for valuable comments on the first version of the paper.