Issue |
A&A
Volume 510, February 2010
|
|
---|---|---|
Article Number | L4 | |
Number of page(s) | 5 | |
Section | Letters | |
DOI | https://doi.org/10.1051/0004-6361/200913538 | |
Published online | 11 February 2010 |
LETTER TO THE EDITOR
Evidence of a thick disk rotation-metallicity correlation
A. Spagna1 - M. G. Lattanzi1 - P. Re Fiorentin2 - R. L. Smart1
1 - INAF-Osservatorio Astronomico di Torino, via Osservatorio 20, 10025
Pino Torinese, Italy
2 - University of Ljubljana, Faculty of Mathematics and Physics,
Jadranska 19, SLO-1000 Ljubljana, Slovenia
Received 23 October 2009 / Accepted 13 January 2010
Abstract
We analyze a new kinematic survey that includes accurate proper motions
derived from SDSS DR7 positions, combined with multi-epoch measurements
from the GSC-II database. By means of the SDSS spectro-photometric data
(effective temperature, surface gravity, metallicity, and radial
velocities), we estimate photometric parallaxes for a sample of
27 000 FGK (sub)dwarfs with
,
which we adopted as tracers of the seven-dimensional space distribution
(kinematic phase distribution plus chemical abundance) of the thick
disk and inner halo within a few kiloparsecs of the Sun.
We find evidence of a kinematics-metallicity correlation,
km s-1 dex-1,
amongst thick disk stars located between one and three kiloparsecs from
the plane and with abundance
,
while no significant correlation is present for
.
In addition, we estimate a shallow vertical rotation velocity gradient,
km s-1 kpc-1,
for the thick disk between 1 kpc <
kpc,
and a low prograde rotation,
km s-1
for the inner halo up to 4 kpc.
Finally, we briefly discuss the implications of these findings for the thick disk formation scenarios in the context of CDM hierarchical galaxy formation mechanisms and of secular evolutionary processes in galactic disks.
Key words: Galaxy: disk - Galaxy: kinematics and dynamics - Sun: abundances - stars: kinematics and dynamics - surveys
1 Introduction
The existence of a thick disk in our Galaxy was revealed by Gilmore & Reid (1983), who analyzed starcounts towards the South Galactic Pole. Thanks to the many studies carried out since then, the main spatial, kinematic, and chemical features of this population are well established. Thick disks have been also observed in many disk galaxies (Yoachim & Dalcanton 2006), and they represent the frozen relics of the first phases of disk galaxy formation (Freeman & Bland-Hawthorn 2002). However, in spite of the many scenarios proposed until now, the origin of this component is still unclear.
In the context of CDM hierarchical galaxy formation models, it is possible that thick disks are formed by the heating of a pre-existing thin disk through a minor merger (e.g. Villalobos & Helmi 2008), by accretion of stars from disrupted satellites (Abadi et al. 2003), or by the stars formed in situ from gas-rich chaotic mergers at high redshift (Brook et al. 2005). On the other hand, simulations suggest that thick disks could simply be produced through secular radial migration of stars induced by the spiral arms (Roskar et al. 2008; Schönrich & Binney 2009).
In any event, most astronomers agree that our thick disk is
formed of an old stellar population with an age of 8-12 Gyr
(e.g. Haywood 2008, and
references therein).
The bulk of the thick disk stars have metallicity in the range
(
,
on average) with enhanced [
/Fe]
(Reddy
et al. 2006; Bensby et al. 2005),
but note that tails with metal-poor stars down to
(Chiba & Beers 2000)
and metal-rich stars up to
(Bensby et al. 2007)
have also been revealed.
Moreover, according to Ivezic
et al. (2008), a mild vertical metallicity gradient
shifts the mean metallicity to
beyond
kpc.
The spatial distribution is usually modeled with a symmetric
exponential density distribution as a function of galactocentric
coordinates (R,z).
Its scale height spans a wide range of measurements, between hz=640 pc
and 1500 pc, while the local normalization varies
beetween 13% and 2% in anticorrelation with hz
(see Fig. 3 of Árnadóttir
et al. 2008).
The distribution above the galactic plane is supported by a vertical
velocity dispersion, km s-1,
which is associated with an asymmetric drift of
50 km s-1,
relative to the local standard of rest.
Significant asymmetries have also been detected, such as the prominent Hercules thick disk cloud (Parker et al. 2003; Juric et al. 2008), which could correspond to a merger remnant or indicate a triaxial thick disk (Larsen et al. 2008).
In this letter, we present new results regarding the vertical rotation gradient and, for the first time to our knowledge, evidence of a metallicity-rotation correlation in the thick disk stellar population.
2 The SDSS - GSC-II catalog
This study is based on a new kinematic catalog derived by assembling
the astrometric parameters extracted from the database used for the
construction of the Second Guide Star Catalog (GSC-II; Lasker et al. 2008)
with spectro-photometric data from the Seventh Data Release of the
Sloan Digital Sky Survey (SDSS DR7; e.g. Yanny et al. 2009; Abazajian
et al. 2009). The SDSS-GSC-II catalog contains
positions, proper motions, classification, and ugriz
photometry for 77 million sources down to
,
over 9000 square-degrees.
Proper motions are computed by combining multi-epoch positions
from SDSS DR7 and the GSC-II database. Typically,
5-10 observations are available for each source, spanning 50 years.
Total errors are in the range 2-3 mas yr-1
for 16<r<18.5, comparable with those
of the SDSS proper motions (Munn
et al. 2004), as confirmed by external comparisons
against QSOs. The construction and properties of this catalog are
described in detail by Smart et al. (2010, in preparation),
while a concise description can be found in Spagna
et al. (2009).
Radial velocities (
km s-1)
and astrophysical parameters (
K,
,
)
are available for 151 000 sources cross-matched with
the SDSS spectroscopic catalog. From this list, we select sources with
K
and
,
corresponding to FGK (sub)dwarfs, and apply the color thresholds from Klement et al. (2009)
in order to remove turn-off stars.
Spectro-photometric distances are computed by means of
metallicity-dependent absolute magnitude relations,
,
from Ivezic et al. (2008).
Here, the observed magnitudes are corrected for interstellar absorption
via the extinction maps of Schlegel
et al. (1998), while the spectroscopic [Fe/H] is
used, instead of the photometric metallicity applied by Ivezic et al. (2008).
The mean distance of the sample is 2 kpc, while most
(92%) of the sources are distributed between
kpc
and
kpc.
The typical accuracy of the Mr
calibration is 0.3 mag (random) and 0.1 mag
(systematic), which corresponds to distance errors of
%
and 5%, respectively. Finally, 3D velocities in the
galactocentric reference frame,
,
are derived by assuming
kpc, solar motion
from Dehnen & Binney (1998),
and local standard of rest velocity of 220 km s-1.
In order to produce an accurate sample, we select only stars
with (i) proper motion errors <10 mas yr-1
per component; (ii) errors on the velocity components
<50 km s-1; (iii) total
velocity <600 km s-1;
(iv) distance <5 kpc, and (v)
magnitude 13.5<g<20.5.
Overall, the kinematic catalog contains
46 000 stars; in the following sections a subsample
of 27 000 low metallicity dwarfs with
will be used as tracers of the inner halo and thick
disk and analyzed in details.
3 Analysis and results
3.1 Vertical rotation gradient
Figure 1
shows the
distribution of 6538 stars
with 1.0
kpc
and
.
In this sample, the contamination of thin disk stars is expected to be
negligible
, so that we fit the
distribution with only two Gaussian populations, corresponding to the
thick disk and halo.
The least-squares solution of the two-component model is good, although
the counts at
km s-1
are slightly underestimated (
-16%) and the velocity peak is
overestimated of about 7%; this explains a non-optimal
.
(If we
force a third Gaussian component corresponding to the thin disk, the
formal goodness of fit improves significantly,
,
but the solution becomes ill-conditioned with an inaccurate thin disk
normalization of
%.)
![]() |
Figure 1:
Histogram of the velocity distribution, |
Open with DEXTER |
Table 1: Parameters of a two-component Gaussian best fit (thick disk and halo) for six height intervals.
The same procedure is repeated for six height bins:
-1.0 kpc,
1.0-1.5 kpc, 1.5-2.0 kpc, 2.0-2.5 kpc,
2.5-3.0 kpc, and 3.0-4.0 kpc. The results are
reported in Table 1,
which lists mean height, number of stars, mean rotation velocities and
dispersions, fraction of thick disk stars, and reduced
.
The halo parameters appear quite stable: on average,
km s-1
(
kpc),
which indicates a slow prograde rotation of the inner halo, in
agreement with some authors (Chiba & Beers 2000; Kepley
et al. 2007) but different from others that favor a
non-rotating inner halo (Smith et al. 2009; Bond
et al. 2010; Vallenari et al. 2006).
The halo velocity dispersion also appears rather constant up to
kpc,
with a mean value of
km s-1
(uncorrected for the velocity errors).
Conversely, the thick disk shows a monotonic decreasing of the rotation
velocity from
km s-1
to 146 km s-1, for height from
0.5 kpc to 3 kpc. In the highest bin (3
kpc),
increases to
km s-1,
but we think this is a spurious effect of both the larger velocity
errors and the small fraction,
%, of thick disk stars that
are strongly entangled with the halo population. Similarly, in the same
z-range, the velocity dispersion increases from
km s-1
to
45 km s-1,
in part because of the tangential velocity errors that scale with
distance.
We exclude the highest bin and also the lowest, as it is
probably contaminated by thin disk stars which are difficult to
deconvolve from the thick disk population. Thus, we estimate the
gradient,
![]() |
(1) |
and the extrapolated intercept,


![$-0.8\le\rm [Fe/H]\le -0.6$](/articles/aa/full_html/2010/02/aa13538-09/img77.png)
Instead, a shallower slope was found by Majewski (1992), who derived
a gradient of km s-1 kpc-1
for
kpc,
after separating the halo population from that of the thick disk.
A low kinematical gradient was also found by Spagna
et al. (1996) and, more recently, by Allende Prieto et al.
(2006), who estimated -10 km s-1 kpc-1
and -16 km s-1 kpc-1,
respectively. The difference between these results can be explained, at
least in part, by thin disk and halo star contamination, which tends to
produce steeper velocity gradients.
![]() |
Figure 2:
Velocity-metallicity distribution of 20 251 stars with
|
Open with DEXTER |
3.2 Rotation-metallicity correlation
The disk and halo populations are apparent in the
![$-1.0<\rm [Fe/H]<-0.5$](/articles/aa/full_html/2010/02/aa13538-09/img8.png)

![$\rm [Fe/H]>-0.5$](/articles/aa/full_html/2010/02/aa13538-09/img83.png)
![$\rm [Fe/H]<-1$](/articles/aa/full_html/2010/02/aa13538-09/img84.png)
Figure 3
shows the iso-density contours of the velocity-metallicity distribution
of stars with -3.0 kpc
and
.
As in Ivezic et al. (2008)
and Bond et al. (2010),
no correlation appears in the transition region between the thin and
thick disks (
). Instead, we notice a
shallow but clear slope for
,
undetected by previous studies, which indicates that the metal-rich
stars tend to rotate faster than the metal-poor ones. In particular,
the top-density ridge increases from
km s-1
at
to
km s-1
at
.
Inspection of Fig. 3
also proves a bimodal distribution with a secondary maximum located at
[Fe/H]
-0.55,
close to the value of the mean metallicity of the thick disk, and the
peak at [Fe/H]
-0.38
due to thin disk stars.
![]() |
Figure 3:
Iso-density contours of 13 108 relatively metal-poor stars
with |
Open with DEXTER |
Table 2:
Kinematics-metallicity correlation of thick disk stars with
for three height intervals.
To quantify the correlation, we first select the stars within [Fe/H] = 0.05
bins in the range
and located at the different height intervals:
-1.5 kpc,
1.5-2.0 kpc, and 2.0-3.0 kpc. Then, the stars with
velocities
outside 3
from the thick disk velocity ellipsoid, corresponding to a confidence
level of 97.1%, were rejected to minimize the contamination
from the halo stars. We adopted
as a function of z derived from
Table 1
and assumed constant dispersions:
km s-1
and
km s-1.
Finally, mean velocities were computed for the bona fide thick
disk stars and the slope,
[Fe/H], is
estimated by means of a linear fit for the height intervals
-1.5 kpc,
1.5-2.0 kpc, and 2.0-3.0 kpc. For each bin, mean
height, total number of stars, number of stars used (after 3
and 2
rejection), slope, and Spearman's rank correlation coefficient are
listed in Table 2,
while the observed distributions are shown in Fig. 4.
Overall, a kinematic-metallicity correlation of about
50 km s-1 dex-1
is detected up to
kpc,
while a shallower slope (
35 km s-1 dex-1)
is present between
kpc.
It is possible that these values are affected by a residual
contamination of halo stars, whose presence can be inferred by the
number of rejected high velocity stars shown in Table 2 being greater
than the 3% expected in the case of a pure Gaussian
distribution. Nevertheless, even if we apply a conservative 2
selection (73.8% confidence level), we still find a correlation at the
level of
km s-1 dex-1,
as reported in the last column of Table 2.
This conclusion is consistent with the systematic slowing down
of the thick disk rotation, which results from fitting a two
Gaussian-component model, representing the thick disk and halo
populations, as more metal-poor thresholds are applied: [Fe/H]
...
<-1.0 (see Table 3).
This effect is
depicted in Fig. 5,
which shows how the thick disk component both decreases and
shifts towards lower
values, when different subsamples of metal poor stars are selected.
Table 3:
Fitted parameters, as in Table 1, for different
metallicity intervals,
,
where
.
![]() |
Figure 4:
|
Open with DEXTER |
![]() |
Figure 5:
|
Open with DEXTER |
![]() |
Figure 6:
Mean |
Open with DEXTER |
In addition, we estimate the rotation-metallicity correlation by
fitting the thick disk
values from Table 3
through the following integral linear model:
where
![$\langle {\rm [Fe/H]}\rangle$](/articles/aa/full_html/2010/02/aa13538-09/img117.png)
![$-3<\rm [Fe/H]\le [Fe/H]_{\rm max}$](/articles/aa/full_html/2010/02/aa13538-09/img118.png)
![$a=\partial \langle V_\phi\rangle/\partial{\rm [Fe/H]}$](/articles/aa/full_html/2010/02/aa13538-09/img119.png)



We also considered the hypothesis that a false trend
vs. [Fe/H] might derive from the tangential velocity estimated through
the metallicity-dependent photometric parallaxes. Actually, the
correlation would still be significant even if the Mr-calibration
were subjected to a systematic error up to 0.4 mag per dex.
Moreover, no kinematics-metallicity correlation is expected to arise
because of the color-selection criteria of the SDSS spectroscopic
targets, which although they produce a bias towards metal poor stars,
cannot affect the conditional
probability distribution at a given metallicity, Pr(
[Fe/H]),
and no further kinematical selection is applied.
Thus, we conclude that the observed correlation is an intrinsic signature of our sample.
4 Discussion and conclusions
The existence of a vertical velocity gradient and a
rotation-metallicity correlation sets important constraints on the
origin of the thick disk. The estimated gradient of km s-1 kpc-1
is consistent with Nbody simulations of disks thickened by a single
minor merger with a low/intermediate orbital inclination (e.g. Villalobos & Helmi 2008),
as well as by the interaction with numerous dark subhalos, as discussed
by Hayashi & Chiba (2006)
and Kazantzidis
et al. (2008), whose simulations show kinematic
gradients of
km s-1 kpc-1
and of -20 km s-1 kpc-1,
respectively, for 1
kpc.
A vertical rotation gradient of about -20 km s-1 kpc-1
can also be inferred from Fig. 5 of Abadi
et al. (2003), who investigated thick disks formed
by accretion of both the stars of a pre-existing thin disk and the
debris from disrupted satellites.
Unfortunately, we have not found any explicit kinematic prediction in
the scenario of the chaotic gas-rich mergers described by Brook et al. (2005),
although Hayashi & Chiba
(2006) state that a velocity shear ``may have difficulties in
this regard''.
Finally, to the best of our knowledge, explicit predictions of
kinematics-metallicity correlations are missing in the current CDM
scenarios of satellite accretion or minor mergers. Hopefully, our
results will motivate theoreticians to investigate this issue in their
future models.
In the context of models based on disk secular processes of
stellar migration driven by interactions with spiral arms, a vertical
gradient of -15
km s-1 kpc-1
is reported by Loebman
et al. (2008), who, conversely, did not detected any
vs. [Fe/H]
correlation. The simulations carried out by Schönrich
& Binney (2009)
indicate a mild trend (
10 km s-1 dex-1)
at
kpc, which decreases
with height and disappears for
kpc.
Possibly, by adopting appropriate parameters, their inside-out disk
formation model could reproduce the observed downtrend (Schönrich 2009,
private communication). Thus, more attention should be devoted to this
scenario as a possible theoretical framework to explain the
rotation-metallicity relation in the thick disk of the Milky Way.
We are grateful to the anonymous referee for all the valuable comments. A.S. thanks Beatrice Bucciarelli and Ralph Schönrich for helpful discussions. We acknowledge B. McLean and the GSC-II team for supporting the data mining of the GSC-II database. The authors acknowledge the financial support of INAF through the PRIN 2007 grant n. CRA 1.06.10.04 ``The local route to galaxy formation''. Support through the Marie Curie Research Training Network ELSA under contract MRTN-CT-2006-033481 to P.R.F. is also thankfully acknowledged. Funding for the SDSS and SDSS-II has been provided by the Alfred P. Sloan Foundation, the Participating Institutions, the National Science Foundation, the U.S. Department of Energy, the National Aeronautics and Space Administration, the Japanese Monbukagakusho, the Max Planck Society, and the Higher Education Funding Council for England. The Guide Star Catalogue II is a joint project of the Space Telescope Science Institute and the Osservatorio Astronomico di Torino.
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Footnotes
- ... negligible
- Assuming a standard model with a thin disk and a thick disk
having scale-heights of 300 pc and 900 pc,
respectively, and a thick disk normalization of 10% at z
= 0 pc, about half of the stars belongs to the thin disk for
kpc, but only a few percent of them with
(cf. e.g. Aumer & Binney 2009). Also, we estimate the contamination of metal poor thin disk stars does not exceed 10%, even if we adopt a thick disk with a shorter hz=580 pc and a local normalization of 13% (Chen et al. 2001).
All Tables
Table 1: Parameters of a two-component Gaussian best fit (thick disk and halo) for six height intervals.
Table 2:
Kinematics-metallicity correlation of thick disk stars with
for three height intervals.
Table 3:
Fitted parameters, as in Table 1, for different
metallicity intervals,
,
where
.
All Figures
![]() |
Figure 1:
Histogram of the velocity distribution, |
Open with DEXTER | |
In the text |
![]() |
Figure 2:
Velocity-metallicity distribution of 20 251 stars with
|
Open with DEXTER | |
In the text |
![]() |
Figure 3:
Iso-density contours of 13 108 relatively metal-poor stars
with |
Open with DEXTER | |
In the text |
![]() |
Figure 4:
|
Open with DEXTER | |
In the text |
![]() |
Figure 5:
|
Open with DEXTER | |
In the text |
![]() |
Figure 6:
Mean |
Open with DEXTER | |
In the text |
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