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\shorttitle{Chemical Abundances in the Sgr dSph}
\shortauthors{Smecker-Hane \& McWilliam}
\begin{document}
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\title{The Complex Chemical Abundances and Evolution of the \\
Sagittarius Dwarf Spheroidal Galaxy\altaffilmark{1}}
\author{Tammy A. Smecker-Hane\altaffilmark{2}}
\affil{Department of Physics \& Astronomy,
4129 Frederick Reines Hall, \\
University of California,
Irvine, CA 92697--4575}
\email{tsmecker@uci.edu}
\and
\author{Andrew McWilliam}
\affil{The Observatories of the Carnegie Institute of Washington, \\
813 Santa Barbara St., Pasadena, CA 91101--1292}
\email{andy@ociw.edu}
\altaffiltext{1}{Data presented herein were obtained at the W.M.~Keck
Observatory, which is operated as a scientific partnership among the
California Institute of Technology, the University of California and
the National Aeronautics and Space Administration. The Observatory was
made possible by the generous financial support of the W.M.~Keck Foundation.}
\altaffiltext{2}{Visiting Astronomer, Keck Observatory}
\begin{abstract}
We report detailed chemical abundances for 14 red giant stars in the
Sagittarius dwarf spheroidal galaxy (Sgr dSph), derived from
echelle spectra obtained with the Keck I 10--meter Telescope.
The stars span a wide range of metallicities, $-1.6 \leq \feh \leq 0.0$,
with ages from $\sim 1$ to 13 Gyr. At low metallicity, $\feh < -1$,
the composition closely resembles the Galactic halo. However, for the
metal-rich Sgr stars, with $-0.6 \leq \feh \leq 0$, the relationship of
[$\alpha$/Fe] with [Fe/H] is lower than that of the Galactic disk by 0.1
dex, while the light elements [Al/Fe] and [Na/Fe] are deficient by
$\sim0.4$ dex. These ratios imply that 60 to 70\% of the iron in the
metal-rich population came from type Ia supernovae (SNe), and
that type~Ia produce some $\alpha$ elements but little or no
sodium or aluminum. The neutron-capture heavy elements, as
indicated by La and Eu, show
an increasing $s$--process component with metallicity, up to [La/Fe]
$\approx +1.0$ at [Fe/H] $\approx 0$. The high ratio of heavy to light
$s$--process elements, [La/Y] $\approx +0.5$, in the metal--rich population
shows that their $s$--process enrichments came directly from AGB stars of
the metal--poor population.
Our abundances can be understood best if the Sgr dSph formed stars over
many Gyr and lost a significant fraction of its gas during its evolution,
such that ejecta from an aging metal-poor population dominated the
metal--rich, star--forming gas. This gas was enriched with a higher
ratio of type~Ia/type~II ejecta than the solar neighborhood, implying that
either the star--formation rate in the Sgr dSph underwent a lull or
it operated with a longer e-folding time than that of the solar
neighborhood. AGB stars from the
metal-poor population produced large quantities of $s$-process elements with
[La/Y] ratios characteristic of the low metal content. The steady increase
in $s$-process elements relative to iron suggests that either iron
production decreased or $s$-process efficiency increased with time.
In addition, we discuss the insights this work gives us on whether or
not mergers of dSph-like fragments were important in the evolution of the
Galactic halo.
\end{abstract}
\keywords{stars: abundances --- galaxies: abundances --- galaxies: evolution ---
galaxies: dwarf --- galaxies: individual (Sgr dSph)}
\section{Introduction}
The Sagittarius dwarf spheroidal galaxy (Sgr dSph) is
currently being ripped apart and accreted onto the Milky Way (Ibata et al. 1997,
and references therein). Tidal debris from the Sgr dSph appears to litter the
Galactic halo tracing out Sgr's orbit (Dohm-Palmer et al.~2000, Newberg et al. 2002).
How many and how frequently have mergers
of dSphs affected the evolution of the Galaxy? When did they occur? We can
answer these questions by determining the distributions of
ages and chemical abundances in dSphs and comparing them with
those of Galactic stars (Unavane, Wyse \& Gilmore 1996, Mateo 1996,
Shetrone, C\^{o}t\'e, \& Sargent 2001, Fulbright 2002).
Abundance ratios, [X/Fe], of the intermediate--mass elements such as Na, Al,
and the $\alpha$ elements, O, Mg, Si, Ca, Ti, provide powerful constraints
on how much of the Galactic halo could have been formed in dSph--sized
fragments because halo stars have [$\alpha$/Fe] that is independent of
metallicity and approximately equal to the theoretical average yield of
type II SNe (except for Ti). (For reviews see Wheeler et al.~1989 and
McWilliam 1997.) After a instantaneous burst of star formation,
type II SNe quickly produce ejecta with high [$\alpha$/Fe] on
timescales of $\sim 10^7$ yrs, while type Ia SNe slowly produce
ejecta with low [$\alpha$/Fe] beginning at $\sim 0.1$ Gyr and
continuing for many Gyr. Thus the Galactic halo has been
inferred to have formed quickly because only ejecta from
short--lived type II SNe, and {\bf not} from long--lived
type Ia SNe, were incorporated into most halo stars.
Contrary the rapid evolution of the Galactic halo, we now know that many of the
Local Group dSphs have had surprisingly complex star--formation
histories, despite their small mass ($10^7$ to $10^8 {\rm M}_\odot$)
and current lack of gas
(see Smecker-Hane \& McWilliam 1999, and Grebel 2000 for recent reviews).
Color--magnitude diagrams show Sgr dSph stars have a wide
range in age, $\sim 1$ to 15 Gyr, and a wide range in metallicities
from $-2 \leq \feh \leq -0.7$ (Bellazzini et al. 1999,
Layden \& Sarajedini 2000). Such complex evolution should leave
obvious signatures in the abundance ratios of the stars (Gilmore \& Wyse
1991). Will Sgr dSph stars contain a mix of Type Ia and II ejecta? Yes,
if the dSph can recycle ejecta over long timescales as supported by the
observed ranges in age and metallicity. No, if the first Type II SNe disrupt
the interstellar medium in less than $0.1$ Gyr and clear the way for
subsequent SNe ejecta to escape in galactic winds, or if dSphs accrete fresh
gas that fuels star formation at later times. Therefore, determining the
abundance ratios in Sgr dSph stars also gives us unprecedented information
on its evolution. The abundance ratios of the metal--poor stars can constrain
the initial mass function of the massive stars that exploded as Type II SNe,
which is critical for estimating the energy available to power galactic winds.
By modeling the measured abundances as a function of metallicity or age, we can
constrain the rate of enrichment from Type Ia and II SNe, star--formation rate,
and the inflow/outflow of gas from the dSph.
We have obtained high--dispersion spectra of 14 red giants stars in
the Sgr dSph and derived abundances for 24 elements. In this paper we
report our results for Na, Al, $\alpha$ elements (Si, Ca, Ti), Fe
and neutron capture elements (La, Y, Eu). In addition, we
derive ages for the stars by comparing their inferred bolometric
luminosities and effective temperatures to Padova stellar
evolutionary models (Girardi et al.~2000). We conclude that star
formation and chemical enrichment occurred over many Gyr in the
Sgr dSph.
In a forthcoming paper, we will present data on the remaining elements,
which include O, Mg, Sc, V, Cr, Mn, Co, Ni, Cu, Zr, Mo, Ba, Ce, Pr, and Nd.
\section{The Sgr dSph Sample}
Program stars were selected to span the full range in color of red giant
branch stars in order to probe the full range of metallicities.
Our sample was selected from the two fields near the center of the Sgr dSph
imaged in VI--bands by Sarajedini \& Layden (1995; hereafter SL95),
and our stars were identified as members of the Sgr dSph based on radial velocities
obtained from low--dispersion spectra by Ibata et al.~(1997).
We also obtained infrared JK--band photometry for
the stars in our sample using the Cerro Tololo Inter-American Observatory
1.5--meter telescope. These data will be presented in a separate paper
(Smecker-Hane, in preparation). The combined VIJK--band photometry was used
to better quantify the effective temperatures of the stars.
Table~1 presents the star list, coordinates, and photometry.
The star ID numbers are listed as X--Y where X is the number of the
SL95 field, where 1 denotes the M54 and Sgr field and 2 denotes the second
Sgr field, and Y is the stellar ID number from SL95's photometry list.
Note that M54 is a globular cluster that is a member of the Sgr dSph.
In Figure \ref{fig-VIcmd}, we show the
dereddened color--magnitude diagram (CMD) of the Sgr dSph based on the
SL95 photometry, where we have assumed a reddening
of E(V--I)$=0.18$ and distance modulus of ${\rm (m-M)_V} = 17.65$ as
derived by SL95. The 14 stars in our spectroscopic
sample are marked by large circles.
In order to show a fairer
representation of the field star population in the Sgr dSph, we have
excluded stars that are within 2 arcmin of the center of the globular
cluster M54.
Readers should note that the sequence of stars located at
${\rm ((V-I)_0, M_V)} \approx (0.1, 0.75)$ is not the
main-sequence turnoff of a young population;
this sequence is the extended blue horizontal branch of M54. However,
more extensive photometry by Bellazzini et al.~(1999) and Layden \& Sarajedini
(2000) in which they statistically subtract out the Galactic foreground
shows that a young, metal--rich, population does exist (for example,
see Bellazzini et al.'s Figure 11). Note that the color--magnitude diagram is
heavily contaminated by Galactic foreground dwarfs because the
Sgr fields lie at low Galactic latitude, $b = -14^\circ$. The main sequence
turnoff of the Galactic disk appears as a prominent vertical feature
at ${\rm (V-I)}_0 \approx 0.7$, and lower-mass main-sequence dwarfs become
more prominent in the diagram at fainter magnitudes and redder colors.
For reference, we have overplotted isochrones based on the Padova
models (Girardi et al.~2000) for a variety of ages and metallicities.
\section{Observations}
High--dispersion spectra of 14 Sgr dSph red giant stars were acquired with the
Keck~I 10--meter telescope and the echelle spectrograph HIRES (Vogt et al.~1994)
over 6 separate observing runs from 1996 to 1998. A total of 9 nights were allocated
to this project. Bad conditions --- clouds, high humidity,
poor seeing, etc. ---
plagued our initial observing runs, and the study progressed slowly.
In our first run, we split nights with another team so that
we could maximize the amount of observing time on the Sgr dSph, a southern
hemisphere object. Our second run was lost due to bad weather. Because of
poor conditions, we obtained spectra of our initial 3 stars on our
first and third runs. These spectra were reduced and
analyzed separately, and the equivalent widths measured from the
pairs of spectra were averaged before the final abundances were calculated.
The HIRES spectra were taken with the red collimator and the C5 decker,
which has a slit width of 1.0 arcsec. The spectra have resolving power
R $\sim 34$,000, and the 22 orders that fall on the CCD cover a
wavelength range of 5210 -- 7650 \AA. Note that gaps do occur in the
wavelength coverage, because the CCD is not wide enough to capture
the width of a full order. The seeing, as measured by the full
width at half maximum of the stellar profile along the spatial direction,
was an average of 1.0 arcsec, although it varied widely from
0.8 to 2.5 arcsec depending on observing conditions. The CCD
had a pixel scale in the spatial dimension of $0.194$ arcsec/pix,
gain of 2.4 e$^-$/adu, and readnoise of $4.0$ e$^-$.
Table~2 presents the details of the observations: star IDs,
observing run, total exposure time, and the average
signal-to-noise ratio per extracted pixel (SNR)
in the combined spectrum determined by propagating the
errors in the extraction and reduction process.
The average exposure time per star was 2.5 hours, and the
average SNR $\approx 55$.
Multiple spectra (4 to 6) were taken of each star
with individual exposure times being $\simlt 30$ mins so that the
effect of cosmic rays could be mitigated in the data reduction.
HIRES is a very stable instrument, and thus exposures of the
thorium-argon arc lamp for wavelength calibration were taken
only a few times per night. During each run, spectra of rapidly
rotating B type stars were observed to identify telluric absorption
lines. Low metallicity stars with a range of effective
temperature were observed to correct for the
blaze function of the spectrograph.
\section{Data Reduction}
The usual CCD image reduction procedures of overscan fitting, overscan
subtraction, and zero subtraction were done using routines we developed
in Interactive Data Language (IDL)\footnote{IDL is commercial software sold
by Research Systems, Inc.}. Mapping and subtraction of scattered light
in 2 dimensions, flat fielding in 2 dimensions, extraction of spectra
from 2 dimensions to 1 dimension, wavelength calibration,
blaze correction, and normalizing the continuum
to unity were performed with tasks in the {\sc IMRED.ECHELLE}
package of the Image Reduction and Analysis Facility
(IRAF)\footnote{IRAF is distributed by the National Optical Astronomy
Observatories, which is operated by the Association of Universities
for Research in Astronomy, Inc., under cooperative agreement with
the National Science Foundation.} following the general outline
in the data reduction section of the HIRES users manual (Vogt 1994).
Individual spectra were combined using our own IDL routine, {\sc SCOMBINE},
which is based on IRAF's {\sc SCOMBINE} task, which uses medians
to robustly reject pixels influenced by cosmic-rays.
Figure \ref{fig-spec} illustrates typical spectra of
two Sgr dSph stars, one metal--rich and one metal--poor.
Note that in the
top spectrum, the Na~I line at $\lambda$ 6154 and the Ca I line
at $\lambda$ 6256 are non-detections, and the Na I line at $\lambda$ 6161
has an equivalent width of 14 m\AA, which is roughly twice our detection
limit of $\sim 7$ m\AA.
Heliocentric radial velocities, $v_{\rm helio}$, were computed
from the observed wavelengths of a set of 15 moderately strong
absorption lines. The velocities are listed in the last column of
Table~2. The average $\rm v_{\rm helio} = 143.5$ km/s with a
standard deviation of 7.7 km/s. All stars were within 2 standard
deviations from the average. Therefore, these stars are all
bona fide radial velocity members of the Sgr dSph galaxy.
Identification and measurement of the equivalent width (EW) of atomic
lines was accomplished by use of the semi-automated routine {\sc GETJOB}
(McWilliam et al.~1995a).
Table~3 shows the measured EWs in m\AA. Values listed as ``..." in
Table~3 either represent lines that: (1) fell in gaps of wavelength
coverage, (2) were irrevocably corrupted by telluric absorption lines,
night sky emission lines, cosmic rays, or bad columns on the CCD,
(3) were not detected, or (4) were too strong to yield an accurate
abundance. Entries marked with ``:" are uncertain.
\section{Chemical Abundance Analysis}
Abundance analysis was performed using the spectrum synthesis program {\sc MOOG}
(Sneden 1973) and the Kurucz (1993) 64--layer model atmospheres.
Abundances for almost all lines were derived by matching the observed line EWs from
Table~3 with synthesis predictions. For the Y~II line at 5402.8\AA\ spectrum
synthesis profile matching was used to determine the abundance for all stars,
except 1-41 (where the line was not detected). The profile of a clean Ti~II line,
at 5418.8\AA , was matched to estimate the instrumental broadening for the Y~II line.
Line wavelengths, $gf$ values and excitation
potentials were taken from McWilliam \& Rich (1994, MR94), supplemented with extra
lines for the current work; the line list is presented in Table~4.
Our abundance analysis was restricted to lines with EW $\le$150 m\AA ,
because lines much stronger than this which are on the flat portion of the
curve of growth are quite insensitive to abundance.
For Y, La, and Eu we included the hyperfine components in our abundance
calculations. For many of our stars the barium lines were
so saturated that it was not possible to compute reliable abundances.
The La~II lines, in particular, were very strong and the inclusion
of hyperfine effects was crucial for reliable abundance analysis.
The La hyperfine splitting, $hfs$, constants were taken from Lawler et al.~(2001a).
For Y~II lines the $hfs$ A constants of W\"annstr\"om et al. (1994) were utilized.
We note that the abundance effects of $hfs$ for Y~II lines was very small,
usually within 0.01 to 0.03 dex of the single line result.
For Eu we employed the $hfs$ line list of McWilliam et al.~(1995b), which was
computed using the constants of Krebs \& Winkler (1960), Arnesen et al. (1981)
and Sen \& Childs (1987); these studies clearly resolved individual $hfs$
components so it is unlikely that there are any significant differences
with the recent Eu $hfs$ constants measured by Lawler et al. (2001b).
Through a series of spectrum synthesis experiments, using the Kurucz (1993) line
list, we identified the least blended Y~II lines in our spectra. We found that
Y~II lines at 5546.0, 6613.7, 6858.2 and 7450.3 \AA\ were severely blended in
our stars; Y~II lines at 5509.9 and 7264.2\AA\ were blended, and not used, but
might provide realively reliable Y~II abundances with spectrum synthesis profile
matching.
For abundance ratios relative to the Sun we adopted the solar abundance scale
of Grevesse \& Sauval (1998), but with a solar iron abundance of
$\epsilon ({\rm Fe}) = 7.50$\footnote{$\epsilon(M)=log_{10}N(M) - log_{10}N(H) + 12$,
where $N(M)$ is the abundance of element $M$ by number}.
Our initial effective temperature (T$_{\rm eff}$) estimates were based on
broad--band colors,
dereddened with the assumed SL95 reddening value of E(V$-$I) $=0.18$,
the reddening relations of Winkler (1997), and the
color-temperature calibrations of Alonso et al. (1999; hereafter A99).
An error in the A99 calibration formula produced spurious temperatures
for all but the (V$-$I) colors (see Alonso et al.~[2001] for the correct formula);
however, we were unaware of the error until late in the present work.
The large dispersion in computed photometric temperatures
led to some confusion and we were skeptical about their reliability,
although the (V$-$I) results appeared the most reasonable. In order to check the
photometric temperatures we computed excitation T$_{\rm eff}$ values from the
abundances of our 75 Fe~I lines.
The excitation temperatures and microturbulent velocities were computed using a program
{\sc AUTO\_AB}, written by A.McW.
The program uses {\sc MOOG} and the Kurucz (1993) 64--layer model atmosphere grid to
iteratively compute the Fe~I abundances with different model atmosphere temperatures.
When the Fe~I abundances are independent of line excitation potential
the correct temperature model has been found. This procedure requires
that the microturbulent velocity parameter is known, which is reached when the
abundances of the Fe~I lines are independent of line EW.
Thus program {\sc AUTO\_AB} consists of two loops: the inner loop iterates on
the microturbulent velocity parameter, and the outer loop iterates on the model
effective temperature. Inputs
to the program are the gravity, metallicity, EWs and the starting values for
temperature and microturbulent velocity. If spectroscopic gravities are also required
a further iterative loop is performed to bring the abundances of ionized and
neutral species into concordance. We caution, however, that when both spectroscopic
temperatures and gravities are derived together the positive covariance between these
parameters can result in a solution unexpectedly far from the true values.
In this work, our excitation temperatures were computed
using the photometric gravities.
%This temperature difference is unlikely
%to be due to under estimate in the reddening to Sgr by SL95: To resolve the two
%temperature values a reddening of E(B$-$V)$\sim0.32$ would be required, 0.19 mag higher
%than the SL95 estimate; this is completely inconsistent with the SL95 0.02 mag
%reddening uncertainty.
The adopted temperatures are particularly important for our relatively cool K--giant
atmospheres; near T$_{\rm eff}$$\sim$ 4000 $^\circ$K, Ca, Ti, and Fe go from mostly
neutral to mostly ionized in the line--forming region, and as a result the computed
abundance ratios can become particularly sensitive to the assumed T$_{\rm eff}$.
The derived excitation temperatures rest heavily on
the small number of very low excitation Fe~I lines, which we know are formed in the
upper--most layers of the atmospheres, where the models are least reliable. Furthermore,
recent investigations into the effects of granulation (e.g Steffen \& Holweger 2002),
show large differences from the classical one--dimensional LTE abundances for low
excitation lines in the Sun. Although such effects have yet to be studied for red
giant atmospheres it seems likely that similar abundance corrections for low excitation
lines might exist, which would
alter the derived excitation temperatures. The sense of the granulation corrections for the
Sun indicates that excitation temperatures would be over-estimated. However, it should
be noted than Ivans et al.~(2001) found no significant difference between their
spectroscopic and color temperatures for red giant stars in the globular cluster M5,
which has [Fe/H] $=-1.2$.
Given the above uncertainties, we decided to employ the iron ionization equilibrium
(i.e. $\epsilon$(Fe~I)=$\epsilon$(Fe~II)) to provide an additional spectroscopic
temperature indicator, T$_{\rm ion}$. Given an assumed gravity the ionization
temperature, T$_{\rm ion}$, is the temperature which forces the abundance of Fe~I
and Fe~II lines to agree. We computed gravities using the published photometry and
the following equation:
\begin{equation}
\log g = \log {\rm \left( M / M_\odot \right)} - \log \left( L/L_{\odot} \right)
+ 4 \, \log \left( {\rm T_{eff}/T_{eff,\odot}} \right) .
\end{equation}
Since the photometric gravity requires an input temperature
an iterative method was used to determine a self-consistent T$_{\rm eff}$ value
for each star: Initial values for
T$_{\rm eff}$ and $\log g$ were adopted and an abundance analysis performed, which
provided estimates of [Fe/H] and [$\alpha$/Fe]. These four atmosphere parameters were
then used to estimate the bolometric correction, B.C., by interpolation of the tables
computed by Kurucz (1993). The observed V magnitudes, reddening, and distance modulus
of SL95 permitted a calculation of the bolometric luminosity, M$_{\rm bol}$.
Padova isochrones (Girardi et al.~2000) were then employed to calculate the
age of the star and the stellar mass consistent with the assumed
temperature, luminosity and metallicity (see \S6). With the derived stellar mass,
Eqn.~1 was used to recompute the gravity. Next an abundance analysis of
Fe~I and Fe~II lines was performed with the gravity fixed (iterations on the
microturbulent velocity parameter were necessary); the temperature of
the model atmosphere was then altered until ionization equilibrium was
achieved (i.e. $\epsilon$(Fe~I)=$\epsilon$(Fe~II)). The new values of
T$_{\rm eff}$=T${\rm ion}$, $\log g$, [Fe/H], and [$\alpha$/Fe] were used as
inputs into the next loop of the iterative calculations. Convergence was
assumed when the change in $\log g$ fell below 0.10 dex.
% ANDY: Can you add a short few sentences that will calm anyone
% who thinks that the using Padova isochrones might lead us to wrong
% ages and thus wrong abundances? Because the changes from the
% initial assumptions of Teff and log g to the final weren't all that great.
% I just want to leave readers with the impression that we did a heck of a lot
% of work to make everything consistent, but that it really didn't make a
% huge difference in the abundances, or the ages, for that matter!
We note that use of ionization equilibrium inherently assumes that
non--LTE over ionization effects are insignificant. If non--LTE over
ionization of iron is important in these stars then our derived
temperatures over-estimate the true values. Calculations by Th\'evenin \&
Idiart (1999) suggest that non--LTE over ionization of Fe~I is significant
in metal--poor stars, with the abundance correction reaching 0.3 dex
at [Fe/H] $=-2.5$, while at [Fe/H] $=-0.5$ their correction is $\sim$0.05~dex.
Non-LTE calculations by Steenbock (1985) for the red giant Pollux suggested
corrections for Fe~I lines of order $\sim$0.05 dex.
The non--LTE over ionization should be relatively small for cool, metal--normal,
stars as the temperature provides very few UV photons, and line blanketing in the
blue ensures that those photons have a short path length. Empirical
evidence suggestive of non--LTE over ionization of Fe~I has been found in
metal--poor stars (e.g. Ivans et al.~2001, Fulbright 2000). However,
given that most of our sample of Sgr stars are very cool and more metal
rich than $\feh \sim -0.5$ the non--LTE corrections are unlikely to
exceed 0.05 dex, which would lead to an overestimate of $\sim$ 50 $^\circ$K
for our ionization equilibrium temperatures.
In Table~5 we compare temperatures derived from iron excitation, iron ionization
and photometric methods for our sample of Sgr stars. The mean difference
$(\rm T_{ex}-T_{ion}) = 33 \, ^\circ$K, with a 1$\sigma$
about the mean of $92 \, ^\circ$K. The $33 \, ^\circ$K mean difference
is consistent with a net zero difference between the two spectroscopic methods
at the 1.3$\sigma$ level.
If both spectroscopic methods contribute equally to the 92K dispersion, then
the 1$\sigma$ uncertainty of an individual measurement is $65 \, ^\circ$K.
However, the mean 1$\sigma$ excitation temperature uncertainty is $80 \, ^\circ$K,
computed from the scatter in Fe~I abundances; this suggests that ionization temperatures
have a 1$\sigma$ uncertainty near $45 \, ^\circ$K.
We find an unexpectedly large mean difference between temperatures based
on ionization equilibrium and those based on photometry:
$\rm (T_{ion}-T_{phot})=249 \, ^\circ$K, with a 1$\sigma$ of $112 \, ^\circ$K.
The excitation temperatures are on average $282 \, ^\circ$K hotter than the
photometric values, with a 1$\sigma$ of $100 \, ^\circ$K. The temperature
difference between photometric and spectroscopic methods could be due to
an under estimate of the reddening by SL95. However, to resolve the two
temperature scales, a reddening of E(B$-$V)$\sim0.32$ would be required, which is
0.19 mag higher than the SL95 estimate and completely inconsistent with their
estimated 0.02 mag uncertainty in E(B--V).
In order to check for systematic errors in the temperature scales
we decided to derive spectroscopic and photometric temperatures for the nearby
K2III red giant star, Arcturus. Arcturus is a useful standard star as its
temperature, metallicity, and gravity are very similar to many of our Sgr stars.
Furthermore, the atmosphere parameters for Arcturus can be constrained very
well thanks to its close proximity: the Hipparcos parallax implies a distance
of $11.25 \pm 0.09$ pc, so the reddening is insignificant. Also, the large
angular diameter, over 20 milli-arc seconds, permits an accurate estimate of the
effective temperature.
The median of 6 literature estimates (Blackwell et al 1975, Augason et al. 1980,
Blackwell et al. 1986, Bell \& Gustafsson 1989, Blackwell et al. 1990, Alonso et al. 1999)
for the total flux from Arcturus was
found to be 4.95$\times$10$^{-12}$ W/cm$^2$; with this value and the
limb--darkened angular diameter of Perrin (1998) we computed an effective
temperature of 4290 $^\circ$K, with an uncertainty of $\pm$10 $^\circ$K.
We note that Alonso et al.~(1999) adopted a lower total flux for
Arcturus than any other study, at 4.83$\times$10$^{-12}$ W/cm$^2$, which
indicates an effective temperature of $4268 \pm 55 \, ^\circ$K.
Alonso et al.~(1999) adopted a temperature for Arcturus of $4233 \pm 55 \, ^\circ$K,
based on the infrared flux method, which is consistent with our result.
However, the average Arcturus effective temperature
computed from the Alonso et al.~(1999, 2001) color-temperature
calibrations and literature (B$-$V) and (V$-$K) colors in the $SIMBAD$
database is $4300 \, ^\circ$K ($17 \,^\circ$K $rms$ scatter), and agrees
well with T$_{\rm eff}$=4280 $^\circ$K from McWilliam (1990) based
on 10 broad--band colors. The adopted T$_{\rm eff}$, with extant
photometry and the {\it Revised Yale Isochrones} (Green et al. 1987)
indicate that Arcturus has a mass of $\sim 1.1 \pm 0.1 \rm M_{\odot}$,
and a gravity of $\log \, g=1.64$ dex with an uncertainty of order $\pm$0.05.
For our spectroscopic analysis of Arcturus the EWs were measured
from the high quality spectrum of Hinkle et al.~(2000), characterized
by R=150,000 and S/N=1000 per pixel. Our initial analysis indicated an
excitation temperature for Arcturus of 4400 $^\circ$K with 1$\sigma$ of
40 $^\circ$K. However, upon inspecting the plot of abundance versus excitation
potential, we noticed a clump of 8 high--excitation lines well above the main group of
abundance values, and we suspected that these lines may be affected by blends.
The lines are at the following wavelengths: 6173.34, 6380.75, 6481.88, 6820.37,
7007.98, 7090.39, 7130.93, and 7142.52 \AA . When we eliminated these lines from
the analysis the excitation temperature for Arcturus was reduced to
$4330 \pm 34 \, ^\circ$K, entirely consistent with our value for the photometric
effective temperature. The ionization temperature derived for Arcturus was
$4294 \, ^\circ$K without the 8 suspect lines and $4280 \, ^\circ$K using all lines.
Thus we conclude that the color temperature, excitation temperature, ionization
temperature, and physical effective temperature of Arcturus are all consistent,
with T$_{\rm eff}$=4290 $^\circ$K. The temperature based on ionization
equilibrium of iron is more robust than the excitation temperature, probably
because a few pathological lines can affect the slope of the abundance versus
excitation potential regression more easily than they can change
average abundances. However, it should be remembered that
ionization temperatures are sensitive to the accuracy of the adopted gravity,
which in turn depends upon the reliability of the distance estimate.
When the 8 suspect lines were excluded from the spectroscopic analysis
of the Sgr stars the average effect was to reduce the excitation temperatures
by $54 \, ^\circ$K, while the ionization temperatures changed by less than
$5 \, ^\circ$K; resulting in a mean difference $\rm (T_{ex}-T_{ion})=-25 \, ^\circ$K.
Thus, agreement between the two spectroscopic temperatures actually improved
slightly for the Sgr stars.
Given the self-consistency of the Arcturus temperature estimates and the agreement
between ionization and excitation temperatures we decided to adopt a spectroscopic
temperature scale for the Sgr stars. We prefer the ionization temperatures
because of their insensitivity to small numbers of pathological lines. We
must conclude that for some unknown reason the Sgr color--temperature relations
are much redder than normal. This could occur because non-standard blanketing
makes the stars appear too red, or because of an unusual reddening law in the
direction of Sagittarius. In this regard it is interesting that the Galactic
bulge red giants seem to be afflicted by a similar problem (e.g. Kubiak et al.~2002);
since these two objects share a similar direction we favor
the idea that the answer lies with a non-standard reddening law.
The final adopted stellar parameters are shown in Table~6, which lists
star name, bolometric correction (B.C.), bolometric luminosity ($M_{\rm bol}$)
computed from the photometry, the adopted effective temperature
($T_{\rm eff}$), gravity ($\log g$), the total metallicity of the model
[A/H], the microturbulence ($\xi$).
The assumed typical 1--$\sigma$ errors in the adopted stellar parameters are
$\sigma_{M_{\rm bol}} = 0.15$~mag, $\sigma_{\rm T_{\rm eff}} = 70\,^\circ$K,
$\sigma_{\log g} = 0.15$ dex, and $\sigma_{\xi} = 0.05$ km/s.
Table~6 lists the derived metallicities, [Fe/H], and abundance
ratios, [X/Fe]. Note that here we adopt the average of
[Ca/Fe], [Si/Fe], and [Ti/Fe] for the [$\alpha$/Fe] ratio, because
the abundances of these elements are much better defined than O or Mg due
to the availability of many more lines. As is typically the case,
systematic errors rather than random errors are
the dominant source of error in our abundances.
Propagating the errors in the adopted stellar parameters yields
typical 1--$\sigma$ errors of $\sigma_\feh = 0.07$ dex and
$\sigma_\alphafe = 0.07$ dex. Typical errors for other
element ratios are listed in the last row of Table~6 as well as
average abundances and standard deviations for the metal--poor
and metal-rich groups.
\section{Ages}
Ages were derived for each star by comparing the star's bolometric luminosity
and effective temperature listed in Table 6 with isochrones
interpolated for the star's derived metallicity using the
Padova models (Girardi et al.~2000).
We chose to do the interpolation of the age in the
$M_{\rm bol} - T_{\rm eff}$ plane in order to avoid additional uncertainties
introduced by adopting a specific color--temperature transformation.
Padova models from Girardi et al.~(2000) were used to
generate isochrones at given metallicities; these were kindly provided
to us by our collaborator Andrew Cole.
The Padova models were calculated assuming a scaled-solar mix of elements.
Because some Sgr red giants show significant departures from
solar element ratios (primarily the three metal--poor stars),
as we show below, we must take this into account when
deriving their ages. The $\alpha$ elements and Fe are the main sources of
opacity. Salaris, Chieffi \& Straniero (1993) show that an isochrone for
a model of a given [Fe/H] and [$\alpha$/Fe] is nearly identical to
that of a scaled solar model with an effective metallicity equal to
\begin{equation}
\feh_{\rm eff} = \feh + \log(0.638 \times 10^{[\alpha/{\rm Fe}]} + 0.362).
\end{equation}
\noindent Therefore, we interpolate the age of a star using a Padova
model with the derived $\feh_{\rm eff}$. Effective metallicities are
listed in Table~6. The derived ages ($t$) and age errors ($\sigma_t$)
are listed in Table 5.
Errors in the derived age of each star were calculated
by propagating the 1--$\sigma$ errors in $M_{\rm bol}$, $\rm T_{eff}$
and [Fe/H]$_{\rm eff}$ assuming all three variables were uncorrelated.
This should be an innocuous assumption, whose effect might be to somewhat
inflate the calculated error relative to the true error. The age error is
assumed to be
\begin{eqnarray}
\sigma_{\rm t}^2 & = & \left( \left. \frac{\delta t}{\delta \rm [Fe/H]}
\right| ^{\rm [Fe/H]_2} _{\rm [Fe/H]_1} \right)^2_{\rm M_{bol},T_{eff}} \times
\; \sigma_{\rm [Fe/H]}^2 \; + \; \\
& & \rm \left( \left. \frac{\delta t}{\delta M_{bol}} \right| ^{M_{bol,2}} _{M_{bol,1}}
\right) ^2 _{\rm T_{eff},[Fe/H]} \times \; \sigma_{M_{bol}}^2 \; + \;
\left( \left. \frac{\delta t}{\delta \rm T_{eff}}
\right| ^{\rm T_{eff,2}} _{T_{eff,1}} \right) ^2 _{\rm [Fe/H],M_{bol}} \times
\; \sigma_{\rm T_{eff}}^2 \nonumber
\end{eqnarray}
\noindent where we evaluated the partial derivative with respect to variable $x$
from $x_1 = x - \sigma_x$ to $x_2 = x + \sigma_x$ while holding the other
two variables fixed. Note that these errors do not take into account
uncertainties in the theoretical models themselves. In short,
there are serious limitations in our current understanding and
parameterization of the relevant physics in red giant stars
(opacities, convection theory, etc.) that could produce errors in
the derived shape of theoretical giant branches, and thus produce additional
systematic errors in our derived ages. For two recent reviews of
the status of theoretical modeling of red giant stars, we refer readers to
D'Antona (2001) and Salaris, Cassisi \& Weiss (2002).
\section{Results and Discussion}
Below we discuss the distribution of metallicities, element ratios and ages
in Sgr dSph stars, and how these constrain the amount of enrichment from
type~Ia SNe, type~II SNe, and long--lived, low--mass AGB stars, and
the initial mass function. We conclude that the
Sgr dSph formed stars and chemically enriched itself over a timescale
of many Gyr; its star--formation rate was either slow or episodic,
and outflow of chemically--enriched gas was important to
its evolution. We also discuss how the complex evolution of the
Sgr dSph gives us interesting insight into the hierarchical merging
history of our Galaxy.
\subsection{[Fe/H] and Age Distribution}
In Figure \ref{fig-VIcmd2}, we show the dereddened CMD for the Sgr dSph
stars with stars in the spectroscopic sample shown with color--coded
symbols that reflect their derived effective metallicities. Note that the
large spread in color for stars in the narrow metallicity range of
$-0.39 \leq \feh \leq -0.31$ suggests a significant range in age for
the stars. The populous red giant branch sequence at the reddest side
of the CMD, which is very narrow in color, contains stars with a mix of
metallicities, $-0.30 \leq \feh \leq 0.$ Again, this suggests a range in
ages because of the degeneracy of age and metallicity (red giants
become redder if they are more metal--rich, but bluer if they are younger).
It can be seen from Figure \ref{fig-VIcmd2} that our selection of objects
was slightly biased towards the old/metal-rich Sgr stars.
Figure \ref{fig-agefeh} shows the age--[Fe/H] relationship for
our Sgr dSph stars. The metallicities range from $-1.6 \leq \feh \leq
0.0$. The stars in our sample are all radial velocity members;
furthermore, the unusual chemical compositions (as discussed below)
indicates that they are not Galactic halo, bulge, or disk interlopers.
Our high-dispersion abundances confirm the existence of a solar
metallicity component as suggested by the strengths of the Ca II
near-infrared triplet lines in low--dispersion spectra obtained by
Ibata and collaborators (1996, private communication to TSH).
The metallicity spread in the Sgr dSph was inferred to be large,
$-2.0 \simlt \feh \simlt -0.7$, based on the wide distribution in
colors of its red giant stars (Bellazzini et al.~1999).
Bellazzini et al.~performed a VI--band photometric survey over a wide area
in 3 different Sgr fields. For $\sim100$ stars on the upper
red giant branch, they derived metallicities
by interpolating fiducial sequences of Galactic globular
clusters. This provided the best way of separating Sgr stars
from Galactic foreground dwarfs and the estimating the metallicity
distribution from photometry alone. They concluded that
80--90\% of Sgr stars were metal--poor, $\feh < -1$.
However our spectroscopic metallicities for most Sgr stars
are significantly higher than this. This discrepancy is understandable
because of the degeneracy of age and metallicity in color--magnitude diagrams.
The derived ages of our stars vary from $\sim 1.0$ to 15 Gyr, hence many
Sgr stars are significantly younger than globular clusters.
Significantly decreasing the age of these stars would have yielded
a much higher metallicity in the Bellazzini et al.~analysis, reaching
solar, as we find from our spectroscopy.
The age sensitivity of the red giant branch is small for ages $\simgt 3$ Gyr,
and thus our derived ages for the stars older than this have large uncertainties.
To compliment the field star data, we also show in Figure~\ref{fig-agefeh}
data from 4 globular clusters that are members of the Sgr dSph (M54, Ter8, Arp2, Ter7).
Cluster ages, derived from the V magnitude of the cluster subgiant branch,
were taken from Layden \& Sarajedini (2000) and placed on the
age scale of the Bertelli et al.~(1994) isochrones. The Bertelli et al.~models
were the precursors of the Padova models that we use to derive the
ages of our Sgr field stars, and their absolute age scales are roughly
similar. In order to compare with our field star metallicities derived
from high-dispersion spectra, we adopt [Fe/H] $=-1.55$ for M54 as
derived by Brown, Wallerstein \& Gonzalez (1999) from high-dispersion
spectra of five M54 red giants; although a recalibration of the Zinn \& West (1984)
scale by Kraft \& Ivans (2003) suggests that [Fe/H]=$-$1.41.
For the other clusters without
high-dispersion spectroscopy, we use metallicities from
the catalog of Rutledge et al.~(1997) that are derived from
the strengths of the Ca II infrared triplet lines in low-dispersion spectra
of red giants, but calibrated to the Carretta \& Gratton [Fe/H] scale,
which is based on high-dispersion spectroscopic abundances.
The spread in [Fe/H] and age of Sgr dSph stars indicates that star
formation and chemical enrichment was prolonged, with a possible gap
between metal--rich and metal--poor populations.
It would be interesting to obtain high-dispersion spectra of stars in
Ter 7, the cluster inferred to be $\sim 4$ Gyr younger than the other
globular clusters, as well as additional intermediate-aged and older
field stars in the Sgr dSph to flesh out the age-metallicity relationship.
In Figure \ref{fig-agefeh}, the solid line shows the prediction from
a simple chemical evolution model that assumes instantaneous recycling,
a closed box, star formation that has gone to completion at the present time
(i.e., the mass of gas at 15 Gyr is zero) and a star formation rate
that is constant in time. Layden \& Sarajedini (2000) suggested such a model
was a good fit to the age-[Fe/H] relationship they derived from
color--magnitude diagram analysis. (Note that they derived [Fe/H] from
photometric methods rather than spectroscopy.) A model with a yield of
$p = 0.0033=0.17 \, {\rm Z}_\odot$ is implied by our data although
this model does not fit the data very well. Note that this
yield is much lower than the yield inferred from stellar nucleosynthesis.
For comparison, the yield in the Galactic bulge, which is reasonably well
fit by a simple closed box model, is $p=0.7 \, {\rm Z}_\odot$ (Rich 1990)
and that implied by the the metallicity distribution function of the Galactic
disk indicates the yield is $p = 0.50 \, {\rm Z}_\odot$ (Pagel \&
Patchett 1975). Such a low yield in Sgr implies that the closed box
assumption is probably not valid. In a simple outflow model, where the
outflow rate is assumed to be proportional to the star formation
rate ($\dot{M}_{gas} = \nu \psi$, where $\psi$ is the star--formation
rate and $\nu$ is the dimensionless proportionality constant), the
age-metallicity relationship is identical to that predicted by the
closed box model but with the effective yield being $p_{\rm eff} = p/\nu$.
{\bf Therefore, our Sgr results would imply $\nu \approx 0.28$ if the
true yield is the same as that in the Galaxy, and thus mass loss
has been a significant factor in the evolution of the Sgr dSph.}
\subsection{Alpha Elements}
In this paper, we discuss the element ratio [$\alpha$/Fe] where $\alpha$ is
taken to be the average of the Si, Ca, and Ti abundances; O and Mg abundances
were not used in the present paper because of the uncertainty associated with
their paucity of lines.
In the following plots of element ratios, our data on Sgr dSph
stars will be shown as filled circles. For comparison, we plot
as open circles the abundances for 2 field stars in the Sgr
dSph derived from high-dispersion spectroscopy by Bonifacio
et al.~(2000). In addition, we plot as an open star symbol
the average abundance of 4 stars in the globular cluster M54,
which is member of the Sgr dSph, obtained from high-dispersion
spectra by Brown, Wallerstein \& Gonzalez (1999). We discuss these
studies in detail in \S7.5.
Figure \ref{fig-alphafe} shows that the most metal--poor Sgr dSph stars
exhibit an enhanced [$\alpha$/Fe] ratio, similar to Galactic halo stars,
which have an average [$\alpha$/Fe] $= +0.35$ (McWilliam 1997);
however, for stars with [Fe/H]$>-1$, it is clear that the $\alpha$ elements
are deficient by $\sim$0.1 dex relative to the solar neighborhood trend.
The metal-rich Sgr stars also appear to have a fixed [$\alpha$/Fe] ratio.
The standard interpretation of such an observation (e.g. Wheeler et
al.~1989, McWilliam 1997) is that the ratio of type~Ia/type~II
SNe ejecta incorporated into the metal-rich Sgr stars is larger than in
solar neighborhood stars of similar metallicity.
This could be due to episodic star--formation,
meaning that the star--formation rate went to
zero for an appreciable length of time
between the formation of the metal--poor
and metal--rich stars, allowing type Ia SNe to continue to explode and
enrich the interstellar medium in Fe when no accompanying type II SNe
produced additional $\alpha$ elements. Alternatively, if the star--formation rate
was continuous with time then it must have had a shorter e-folding
timescale than that of the solar neighborhood. For reference,
Scalo (1986) finds that the average star--formation rate, $\psi(t)$,
in the solar neighborhood was 2 to 3 times its current star--formation
rate, $\psi(T)$. If we assume a simple star--formation rate of the
form $\psi \propto e^{-t/\tau}$ for the Galactic disk in the
solar neighborhood, then $\tau = 0.62 T \sim 7$ Gyr if the
current age of the disk is 12 Gyr. Deficiencies in the
$\alpha$ elements have long been predicted for low-mass galaxies
(e.g. Matteucci \& Brocato 1990, Gilmore \& Wyse 1991).
A similar result was found for disk stars with large Galactocentric
radii in the study by Edvardsson et al.~(1993), where it was
concluded that star formation proceeded at a slower pace
in the outer disk than in the inner disk.
An interesting feature of Figure \ref{fig-alphafe} is the apparent
constant value of the [$\alpha$/Fe] ratios above [Fe/H]$\sim$$-$0.6 dex.
If this is correct, then the ratio of type~Ia to type~II SNe must have
been roughly constant over this metallicity range.
How much type~Ia ejecta does the observed [$\alpha$/Fe] imply for the
Sgr stellar populations? The theoretical yields of type~II SNe are
fairly uncertain because the mass cut and explosion energy are imposed
parameters rather than derived from the models themselves (e.g., Woosley \&
Weaver 1995; hereafter WW95).
Therefore, to estimate the relative amount of type~Ia
verses type~II SNe enrichment, we assume the average yield of
type~II SNe integrated over the initial mass function (IMF)
is equal to the average observed for Galactic halo stars,
[$\alpha$/Fe]$_{\rm II} = +0.35$ (McWilliam 1997). Models of type~Ia SNe
are uncertain because we do not yet know the exact progenitors. Are
these double CO white dwarfs whose merger is induced by gravitational
wave radiation, or a CO white dwarf accreting material from a
Roche-lobe filling red giant companion? However the inherent mechanism
is believed to the explosion of a CO white dwarf because it produces enough
radioactive Ni and Co to power the observed light curve. We adopt the
theoretical yields of the popular W7 model of type~Ia SNe from
Thielemann, Nomoto \& Yokoi (1986, hereafter TNY86), but we note that the yields are
uncertain particularly for the intermediate-mass elements which are not
constrained well by direct observations. We note that in both the type~Ia
and type~II SNe models, the predictions for Ti are not well correlated with Si
and Ca, despite the fact that Ti correlates well with them in Galactic and
Sgr dSph stars. Therefore, we will adopt the averages of
the Si and Ca ratios for the theoretical [$\alpha$/Fe] yields of SNe;
for the W7 model, [$\alpha$/Fe]$_{\rm Ia} = -0.36$.
It is difficult, if not impossible, to place reliable uncertainties on the
theoretical yields for type~Ia SN, because the errors are dominated
by unknown systematic effects; neither TNY86, nor Thielemann et al. (1984)
quantify the uncertainties, although comparison with the solar
abundance distribution is made at the level of 0.3 dex.
The 7 type~Ia SN models investigated by Iwamoto et al.~(1999) show
a dispersion in the predicted Si/Fe yield ratio of 0.16 dex, which are
particularly sensitive to the deflagration to detonation transition; the
highest Si/Fe yeilds, near $-$0.8 dex, occurs when the density ahead of the flame
is artificially decreased from 2.2 to $1.7\times 10^7 g cm^{-3}$.
For a stellar population with a given $\alpha$-element ratio, [$\alpha$/Fe],
the fraction, $f$, of Fe that came from type~Ia SNe in that population
is given by Equation~4; note that this assumes zero contribution of $\alpha$
elements by other sources, such as novae.
\begin{equation}
f = \frac{ {\rm \left( 10^{[\alpha /Fe]} -
10^{[\alpha /Fe]_{II}} \right) } }
{ {\rm \left( 10^{[\alpha /Fe]_{Ia}} -
10^{[\alpha /Fe]_{II}} \right) } } \, .
\end{equation}
For the metal-poor Sgr stars [$\alpha$/Fe] $ = +0.27$, from which we infer
$f = 0.21$ if the IMF in the Sgr dSph was the same as that in the
Galactic halo. Note that [$\alpha$/Fe] declines with metallicity
even among the metal-poor group; although this is not highly
significant given the errors and the numbers of stars observed, it
suggests that the metal-poor population could be enriched
by type~Ia ejecta. In regard to the question of whether or not the
IMFs in dSphs and the Galaxy are similar, we note that the
low-mass end of the IMF in the Ursa Minor dSph has been shown to be
indistinguishable from low-metallicity Galactic globular clusters over
the mass range of 0.3 -- 0.85 $\rm M_\odot$ (Wyse, et al.~2002).
In addition, the bulk of the present evidence suggests that little
variation occurs in the IMF at different metallicities or in different
environments; see the recent review by Kroupa (2002).
The median $\alpha$-element ratio in the metal-rich Sgr population, at
[$\alpha$/Fe] $ = 0.0$, implies a fraction, $f = 0.68$, of iron from
type~Ia SNe; under the assumption that the Sgr dSph IMF was the same as
in the Galactic halo. The standard deviation in the [$\alpha$/Fe] ratio
of 0.05 dex, implies that the acceptable range on the fraction is $0.62 \leq f \leq 0.75$.
For comparison, the $\alpha$-element ratio of solar neighborhood stars,
with metallicities equal to the mean metallicity of the metal-rich Sgr stars, is
[$\alpha$/Fe] $ = +0.10$, for which $f = 0.54$.
The lowest metallicity star in the Sgr dSph
has [$\alpha$/Fe] $=+0.32 \pm 0.07$, which is similar to those of
Galactic halo stars. What constraints can this place on the upper-mass
end of the IMF in the Sgr dSph? Unfortunately, no definitive answer
can be made because of the uncertainties in the type II SNe models
(e.g., Gibson 1998, WW95), but a comparison is certainly worthwhile.
WW95 published type~II SNe yields for a range of initial stellar metallicities,
and their low metallicity models are relevant for
comparing with this Sgr star, which has [Fe/H] $=-1.6$.
We have calculated the yields weighted over a given IMF, where
\begin{equation}
\Phi(m) \propto m^{-(1+x)}
\end{equation}
\noindent is the number of stars formed with initial mass in the range
$m$ to $m+dm$, and
the slope of the IMF is $x$. Note that $x=1.35$ is the slope derived by
Salpeter (1955), and $x=2.3$ is the slope derived by Miller \& Scalo
(1979) for $m> 10$ M$_\odot$ in the solar neighborhood.
We assume the initial mass range for type~II progenitors is
$10 \leq ({\rm m/M}_\odot) \leq 50$. We use the ejected masses
calculated for the WW95 models as tabulated by F. Timmes
(2002, private communication to TSH) and the
solar abundances of Grevesse \& Sauval (1998).
The WW95 models predict that Ti should behave more like an Fe-peak
element than an $\alpha$-element, contrary to what is observed in the
Galaxy and the Sgr dSph. Therefore, we adopt
the average of Si and Ca for [$\alpha$/Fe].
The WW95 models with initial stellar metallicities
$Z=10^{-4} Z_\odot$ have [$\alpha$/Fe] yields that are nearly constant
as a function of stellar mass; $+0.36 \leq$ [$\alpha$/Fe] $\leq 0.35$
for $0 \leq x \leq 3$. This element ratio is encompassed by the 1--$\sigma$
upper limit for the Sgr star, but we can place no constraint on the
IMF slope. Note
that altering the progenitor mass range will not
change appreciably the predicted [$\alpha$/Fe]. The $Z=10^{-2}$ models
are probably more relevant to our [Fe/H] $=-1.5$ Sgr star, because we expect
many more stars of this metallicity contributed to its enrichment.
The predicted yields of the $Z=10^{-2}$ models are sensitive
to the IMF slope, but the models imply a surprisingly low [$\alpha$/Fe]
yield; [$\alpha$/Fe] $=+0.32$ for $x=-0.9$, and [$\alpha$/Fe] $ =
+0.26, +0.11$, and 0 for $x = 0, 1.35,$ and 2.3, respectively.
A proper prediction of the element ratios would necessitate a full
chemical evolution model, but that is not worthwhile given
the uncertainties on the present yields and the poorly--constrained
star--formation rate.
Thus, for the time being, all we can say about the upper-mass end of the
IMF in the Sgr dSph is that it greatly resembled that of the
Galactic halo. When the yields of Type II SNe are on
firmer footing, we may be able to place firmer constraints on the
upper-mass end of the IMF, which is a crucial piece of information to
determine because this sets the amount of energy available to
power galactic winds.
An issue of interest is whether there is a trend of [$\alpha$/Fe] with
[Fe/H] for the metal-rich Sgr stars. Figure \ref{fig-alphafe} shows
a hint of a downward trend, but the slope isn't significantly different
from zero. A zero slope
would imply a constant ratio of type~II to type~Ia SNe that might
arise from a steady star-formation rate, whereas declining [$\alpha$/Fe]
ratios are expected in the aftermath of a star formation burst.
\subsection{Aluminum and Sodium}
In Figure \ref{fig-naal} we show comparisons of [Al/Fe] and [Na/Fe] in the
Sgr dSph with the results for solar neighborhood stars from Chen et al.~(2000).
The Sgr stars with [Fe/H] $<-1$ possess Galactic halo--like abundances
of Al and Na, as we see for the $\alpha$ elements.
In the Fulbright (2000, 2002) sample of metal-poor stars in the solar
neighborhood, the averages for halo stars with Galactic rest frame
velocities $v_{\rm GRF} < 300$ km/s and $-2 < \feh < -1$ are
[Na/Fe] $=-0.09$ and [Al/Fe] $=+0.23$, similar to
the metal-poor Sgr stars. Note that Fulbright
finds a population of halo stars with unusual chemical abundance ratios
in his sample, but these exclusively have $v_{\rm GRF} > 300$ km/s, and
hence we omit them from the calculation of the halo average. The
halo stars with unusual chemical abundances are on orbits that take
them far into the Galactic halo (maximum Galactocentric radii
$\simgt 20$ kpc). The relevance of these stars to the question
of whether dSph--like fragments merged to form the Milky Way halo
will be discussed in \S7.7.
One metal-poor Sgr star stands out with Na and Al ratios very
different from the Galactic halo. This is star 1$-$73 with
$\feh = -1.09$ which shows a
large enhancement of Al, [Al/Fe] $ = +1.1$ dex (so large that it is
not plotted in Figure \ref{fig-naal}), a small enhancement in Na,
[Na/Fe] $=+0.2$, and a large deficit of O, the upper-limit being
[O/Fe] $\simlt -0.8$ dex.
This appears to be the same phenomenon seen in some Galactic globular cluster
red giants, which are probably due to self-polllution with proton-burning
products in the stellar atmosphere, with depleted O and enhanced Na and Al
(e.g. Kraft et al.~1997); although primordial abundance variations may
play a role (e.g. Ivans et al.~1999, Sneden et al.~1997).
At [Fe/H]=$-$1.09 the metallicity of 1$-$73 is significantly different from
the mean metallicity of M54 stars, $\feh = -1.55$ (Brown,
Wallerstein \& Gonzalez 1999). Thus we believe this star
is a field star and not a cluster member, although its position on the sky
and radial velocity are similar to M54 stars.
Unfortunately, with only one Al-rich object we cannot estimate a lower limit
to the frequency among Sgr field giants; in this study we find 7\%$\pm$7\%.
In the Galaxy, envelope proton burning appears to be a phenomenon
limited to some (but not all) Galactic globular cluster stars.
Among the field red giants in the Galactic halo Fulbright (2000, 2002) found no stars
with evidence of envelope nucleosynthesis of Al, from 168 stars investigated.
Clearly, if future studies establish that $\sim$7\% of Sgr giants possess
enhanced Al, produced by proton burning, then very few Sgr--like dwarfs
could have been incorporated into the Galactic halo field.
Additional searches for Sgr field stars with similar signs of proton-burning would
be very interesting.
For the stars with $\feh > -1$ in the Sgr dSph, both Al and Na are deficient
relative to the solar neighborhood trend by $\sim 0.4$ dex.
Although such low [Na/Fe] and [Al/Fe] ratios are very rare, they are not unheard-of
in the Galaxy: Nissen \& Schuster (1997) found four halo field stars
([Fe/H] $\sim -1.0$) with low [$\alpha$/Fe] $\sim +0.05$, and [Na/Fe] $\sim -0.3$ dex.
Brown et al. (1997) found that the young globular clusters Rup~106 and Pal~12
([Fe/H]=$-$1.45 and $-$1.0, respectively) possess
near-solar [$\alpha$/Fe] with [Na/Fe] $= -0.50$
and $-$0.26 dex respectively; for aluminum there was an upper limit only
for Pal~12, at [Al/Fe] $\le -0.37$. King (1997) found a common proper-motion
pair in the halo ([Fe/H] $= -1.50$) with solar [$\alpha$/Fe] and [Na/Fe]=$-$0.4 dex.
Fulbright (2000, 2002) finds $\sim 25$\% of his sample has $-0.3 \simlt
{\rm [Na/Fe]} \simlt -0.7$ and $-2.6 \simlt {\rm [Fe/H]} \simlt -1.4$, and
these are the outer halo stars with unusual chemical abundances as noted above.
Notable among Fulbright's stars is BD$+$80~245 (originally identified as having
low [$\alpha$/Fe] by Carney et al. 1997), with [$\alpha$/Fe]=$-$0.13 and
[Na/Fe]=$-$0.50 dex.
The metal-rich Sgr stars are similar to the Al and Na deficient Galactic halo
stars in that they also exhibit low [$\alpha$/Fe] ratios; however,
we are unaware of {\it any} Galactic stars with [Na/Fe]$\sim$$-$0.4 dex at
metallicities as high as the metal-rich Sgr stars, $-0.6 \simlt \feh \simlt 0$.
The majority of sodium and aluminum synthesis occurs during
carbon and oxygen burning in massive stars, which ultimately end as type~II SNe.
(Na synthesis is also sensitive to the neutron excess, which
makes the [Na/Fe] yield metallicity-dependent, e.g. Pardo et al.~1974).
We conclude that the Al and Na deficiencies seen in
Sgr dSph stars are due to a paucity of nucleosynthesis products from massive stars
relative to type~Ia ejecta. This is in qualitative,
and quantitative, agreement with the observed deficiency in
[$\alpha$/Fe] ratios. The Al and Na deficiencies are larger than the
$\alpha$--element deficiences, which can be understood if type~Ia SNe
produce small amounts of $\alpha$ elements and very little Na or Al.
This is exactly what the predictions are for type Ia;
the yields from Thielemann, Nomoto \& Yokoi (1986)
are [Na/Fe]$_{\rm Ia} = -4.00$ and [Al/Fe]$_{\rm Ia} = -1.83$.
Using Eqn.~1, with the yields for type II SNe again taken to be the
averages of Fulbright's halo
stars, [Na/Fe]$_{\rm II} =-0.09$ and [Al/Fe]$_{\rm II}=+0.23$,
we derive the fraction of Fe created in type Ia SNe in the Sgr
metal-rich stars. From [Na/Fe], we find $f = 0.49$ with the $\pm 1\sigma$
limits giving $0.29 \leq f \leq 0.63$. From [Al/Fe], we find $f=0.73$
with $\pm 1 \sigma$ limits giving $0.63 \leq f \leq 0.81$. Thus the
fraction of iron from Type Ia SNe in the metal-rich Sgr population
implies $f \approx 61$\%.
Note that we would get essentially the same values of $f$ if we
assumed that type~Ia SNe make {\it no} significant amount of Na or Al,
because the theoretical yields of [Na/Fe] and [Al/Fe] for Type Ia
are so much smaller than that inferred for Type II SNe.
If type~Ia SNe make {\it any} Na or Al, or if the Galactic halo composition
contains iron from some type~Ia SNe (which seems likely considering that
some 9 to 10 M$_{\odot}$ stars end as type~Ia SNe ) then the value of $f$ must be
increased further.
If we assume Type Ia make no $\alpha$ elements then the fact that our
metal-rich Sgr stars have an average of [$\alpha$/Fe] = 0.0 implies
$f = 0.50$ or 0.55 depending on whether one assumes the average for
Galactic halo stars is [$\alpha$/Fe] $= 0.30$ or 0.35 dex, respectively
(see McWilliam 1997). For the [$\alpha$/Fe] ratios to give a value of
$f =61$\%, as implied by the Na and Al ratios, then
type~Ia SNe must produce some $\alpha$ elements with a yield
in the range of [$\alpha$/Fe]$_{\rm Ia} = -0.44$ to $-0.68$ dex.
{\bf Therefore, we get a very consistent
picture when we consider the observed Na, Al, Si, Ca and Ti abundances
relative to Fe, from which we conclude that each of these element ratios can be
explained if $\approx 60$ to 70\% of the Fe in the metal-rich Sgr population
was synthesized by type Ia SNe and the remainder by type II SNe.}
\subsection{Neutron-Capture Elements}
In Figure~\ref{fig-lafe} we present the trend of [La/Fe] with [Fe/H].
While the metal--poor stars, with [Fe/H]=$-$1.1 to $-$1.6 appear quite similar
to the Galactic halo in the figure, the more
metal--rich stars show a steady increase in La enhancement with
increasing [Fe/H], up to [La/Fe]$\sim+1.0$ dex. The [La/Fe] trend
suggests that there was a rough progression of metallicity with time, and
that either the production of neutron-capture elements increased, or the efficiency of
iron production decreased steadily. Iron from type~Ia SNe might explain a
reduced iron production rate, due to the decreasing probability that mass
transfer to a white dwarf will exceed the Chandrasekhar limit for
a population of older, and hence less massive, secondaries.
In contrast, the trend of [Y/Fe] with [Fe/H], seen in Figure~\ref{fig-yfe} is
close to the solar ratio for all but the most metal-rich stars. We note that
our Y abundances are significantly higher than the values found by
Bonifacio et al. (2000).
Except in the most
metal--poor stars ([Fe/H]$\le$$-$2.5) La is thought to be produced mostly by
the $s$--process; the solar $s$--process fraction for La is estimated at 75\%
(Burris et al.~2000). To investigate the neutron source for La in
the Sgr dSph stars we show the [La/Eu] ratios in Figure~\ref{fig-laeu};
it is clear that [La/Eu] is increasingly dominated by the $s$--process at
higher [Fe/H]. The average of the three highest [Fe/H] stars have super-solar
[La/Eu]$\sim +0.15$ dex; although this is dominated by one star. However, the
Bonifacio et al (2000) [La/Eu] points support the value of the highest star, near
$+$0.3 dex.
We note that because of the particularly small neutron-capture cross sections of
the barium isotopes [Ba/Eu] is especially sensitive to the ratio of
$s$ to $r$--process elements; thus, we normally favor the use of [Ba/Eu]
as a neutron-capture diagnostic. However, because the Ba lines in our spectra
are very strong (150 to 400m\AA ) they lie on the flat portion of the curve of
growth, and are not very sensitive to abundance.
For this reason [La/Eu] is probably a more reliable neutron-capture diagnostic in
our sample of Sgr dSph stars than [Ba/Eu], despite the less favorable neutron-capture
cross sections of La relative to Ba.
Since AGB stars are the dominant source of heavy $s$--process elements
at Galactic disk metallicities (see Travaglio et al.~1999), the Sgr dSph
heavy element abundance enhancements indicate a significant contribution
from AGB nucleosynthesis, which increases relative to iron at higher [Fe/H].
Figure~\ref{fig-laeulah} shows a plot of [La/Eu] versus [La/H]:
The horizontal dotted lines represent [La/Eu] for $s-$ and $r$-process
composition; it is clear that at low [La/H] the Sgr stars were near the pure
$r$-process value, similar to the Galactic Halo. The solid line shows the
locus of [La/Eu] resulting from an addition of pure $s$-process material to
the halo ratio with [La/H]=$-$0.8 dex, and the dashed line shows the locus
arising from addition of pure $s$-process material
starting with halo composition at [La/H]=$-$0.3 dex. Note that addition of
pure $s$-process material gives the steepest possible slope; shallower slopes result
with the addition of $r$-process material: the dot-dashed line shows the locus of
halo composition plus 95\% $s$-process and 5\% $r$-process La. The available data are
best fit with the addition of 97\% $s$-process plus 3$\pm$3\% $r$-process La composition,
starting [La/H]=$-$0.3 dex; a point corresponding to the most metal-poor star in the
metal-rich Sgr population, at [Fe/H]=$-$0.61 dex. This suggests that the halo-like
[La/Eu] ratios, characteristic of a dominantly $r$-process origin, persisted in the Sgr
gas up until [Fe/H]$\sim$$-$0.6 dex. More data are required to accurately
determine the extent of the $r$-process contribution to the metal-rich Sgr stars,
particularly for the more metal-poor Sgr stars.
Figure~\ref{fig-laeulah} indicates that the halo $s$/$r$ mix of neutron-capture elements
persisted until [Fe/H]$\simeq$$-$0.6 dex, despite the [La/Fe] enhancement of $\sim$0.3 to
0.4 dex at this metallicity (see Figure~\ref{fig-lafe}). This enhancement in [La/Fe]
suggests that either the rate of iron production decreased, or the rate of production of
predominantly $r$-process, halo-like, neutron-capture composition increased.
Our [Eu/Fe] abundance ratios, in Figure~\ref{fig-eufe}, demonstrate that it is dangerous
to draw conclusions about the neutron-capture process responsible for europium by
comparison with iron. Figure~\ref{fig-eufe} shows [Eu/Fe] enhanced in metal-rich
Sgr dSph stars, as compared to the trend seen in the solar neighborhood. Although
the solar system Eu is 97\% $r$-process it would be incorrect to assume that
the observed enhancement is due to extra $r$-process material; as shown in
Figure~\ref{fig-laeulah} the Eu abundances for the most metal-rich Sgr stars are
consistent with a halo composition plus large $s$-process enhancement.
In Figure~\ref{fig-lay} we present a plot
of [La/Y], showing that the heavy $s$--process element lanthanum is
enhanced more than the light $s$--process element yttrium in the
metal--rich Sgr dSph stars ([Fe/H]$geq$$-$0.6), with [La/Y] = $+$0.45$\pm$0.02 dex,
roughly independent of metallicity. We note that the Bonifacio et al. (2000)
results do not agree with the present work.
In addition, two of the three metal-poor stars in the plot show evidence
for slightly enhanced [La/Y] ratios; although this might be explained by noise
enhancement of the apparent equivalent widths of the weak Y~II lines.
The unusual [La/Y] ratios seen in the Sgr stars might be understood by either
rapid, or slow, neutron capture nucleosynthesis.
With regard to rapid neutron capture,
Wasserburg et al.~(1996) showed that there exist at least two $r$-process sites
in the Galaxy, with very different rates; the low-frequency and high-frequency events
dominate the synthesis of $r$-process elements below and above A$=$130, respectively.
Therefore, unusual heavy (e.g. Ba, La, Nd) relative to light (e.g. Sr, Y, Zr)
neutron-capture element ratios, [hs/ls], may be obtained from abnormal mixtures of material
from the two $r$-process sites: our observed high [hs/ls] ratios in the metal-rich Sgr
stars would require relatively more production from the high-frequency $r$-process
events. Although the site of the $r$-process has not yet been confirmed, if it
is assumed to occur during type~II SNe events, a niave interpretation would suggest
that the SGr dSph contained more $r$-process material from low-mass type~II SNe.
SCS01 suggested that the unusual [Ba/Y] ratios in their sample of stars from three Local
Group dSph galaxies were due to an unusual mix of high and low $r$-process events. We
note that the SCS01 stars were much more metal-poor (at [Fe/H]$leq$$-$1.4) than our
sample of Sgr stars with enhanced [La/Y].
Given the strong $s$-process signature, indicated by the [La/Eu] ratio, in the most
metal-rich Sgr stars, it seems very unlikely that the high-frequency $r$-process sites of
Wasserburg et al.~(1996) could be responsible for the observed high [La/Y] ratios. However,
the enhanced [La/Y] ratio in the most metal-poor star of the metal-rich Sgr population, I-150,
is not consistent with this picture, because it's halo-like [La/Eu] ratio suggests
predominantly $r$-process material. The apparent contradiction my be solved by appealing to
measurement errors, somewhat $s$-process enhanced [La/Y] for the metal-poor Sgr stars, or
by an initial $r$-process enhanced [La/Y] ratio near [Fe/H]$\sim$$-$0.6 replaced by an $s$-process
enhanced ratio at [Fe/H]$\sim$$-$0.1.
The $s$-process [hs/ls] ratios in AGB stars is predicted to depend on the
metallicity of the s-process site (Busso, et al.~1999, Busso, et al.~2001).
AGB $s$-process nucleosynthesis in low mass stars begins with protons ingested from
the envelope into the helium inter-shell region, most likely during the ``third-dredge-up''
(TDU) after He shell flash. These protons are
consumed in the $\rm ^{12}C(p,\gamma)^{13}C$ reaction, resulting in copious
amounts of $\rm ^{13}C$, subsequently burned radiatively during the AGB inter-pulse phase by
$\rm ^{13}$C($\alpha$, n)$^{16}$O. The neutrons released from this reaction drive the $s$-process.
At low metallicity TDU is more efficient and there are many fewer iron-peak seed nuclei
than at high metallicity. Consequently, the seed nuclei in the inter-shell region
capture many neutrons at low metallicity, which enhances the production of heavy $s$-process
nuclei relative to the lighter nuclei.
%This follows the Busso et al.~(1999, 2001) predictions for $s$--process nucleosynthesis
%in metal--poor stars.
From Figure~3a of Busso et al.~(2001), we estimate that the
metallicity of the AGB stars responsible for the $s$--process enhancement in
the metal--rich Sgr population was either $\feh \le -1.6$, or
at a single, higher, metallicity, $\feh \approx -0.8$
(due to the bi-valued nature of the heavy/light yield function),
assuming the initial mass of the AGB stars is $\approx 1.5 \rm M_\odot$ and
the prescription for the mass of the $^{13}$C pocket is the
``standard value" divided by 1.5, which Busso et al.~(2001) found best fits
the observed composition of $s$-process enhanced stars.
%Figure~\ref{fig-lay} also shows that the group of metal--poor ($\feh \le -1$) Sgr dSph
%stars do not exhibit the enhanced [La/Y] ratios, and have ratios more like those
%seen in the Galactic halo. This does not invalidate the above arguments: we suggest that,
%like the halo, this is due to the dominance of an $r$--process abundance pattern from
%massive star nucleosynthesis.
It is significant that metal--rich, $\feh \sim -0.1$, stars are expected to
produce [La/Y] $\approx -0.25 \pm 0.25$ (Busso et al.~2001);
much lower than the observed value of [La/Y] $= +0.5$ dex.
Therefore, the $s$--process enrichments in the metal--rich stars could not
have been generated by the stars themselves, or produced by evolved companions.
This observation also invalidates the instantaneous recycling assumption for
the chemical evolution of the Sgr dSph.
Supporting evidence that these stars are not the products of self pollution
comes from the fact that none of the metal--rich Sgr dSph stars are luminous
enough to be on the thermally-pulsing AGB (TP-AGB). Our metal-rich Sgr sample
have $\rm 2.5 \leq \log L/L_{\odot}
\leq 2.9$, compared to the lowest TP-AGB onset luminosity of
$\rm \log L/L_{\odot}=3.1$ from the calculations of Boothroyd \& Sackmann (1988).
Additional evidence against mass--transfer from an evolved companion comes
from the frequency of such $s$--process enriched stars in the Galactic disk,
at only 1 to 2\% (MacConnell \& Frye 1972). Thus it is extremely unlikely that
all the metal--rich Sgr dSph stars could have come from such a rare population.
{\bf The observation that all the metal--rich Sgr dSph stars show a similar
enhancement in the ratio of heavy to light $s$--process elements,
[La/Y] $\approx +0.45$, suggests that the progenitor AGB stars
responsible for the $s$--process elements had $\feh \simlt -1.6$.
Therefore, material from the metal--poor population must have been retained and
recycled over timescales of many Gyr.}
Our ages for the metal--rich Sgr dSph stars ($\feh \simgt -0.7$) range from
$\sim 0.5$ to 3 Gyr, while the metal--poor stars range from
$\sim 3$ to 12.5 Gyr; this is consistent with the expectation that metallicity
smoothly increased with time (i.e., there were no accretion events
mixing in large amounts of pristine gas on short timescales, which
would have lowered the metallicity
of the gas while leaving the element ratios unchanged) and that
the most metal--poor population in the Sgr dSph are very
similar to typical Galactic halo stars. The derived ages for
the Sgr stars are in qualitative agreement with a period of extended star formation
as indicated by the abundances of neutron-capture elements.
A sophisticated chemical evolution model -- incorporating inflow, outflow,
non-instantaneous recycling, etc. -- would be needed to fully test the
qualitative agreement. Until we have better constraints on the star--formation
history of the Sgr dSph, this will be left for future work; an unbiased metallicity
function would be especially useful.
If our interpretation is correct, then these stars will show overabundances
of lead and other heavy $s$-process elements. In addition the metal-rich Sgr
stars should show no evidence of the short-lived element technitium if
the $s$-process enhancements came from previous generations of AGB stars.
It is clear that detailed chemical composition of the Sgr dSph stars,
when combined with an accurate star--formation history for this galaxy, will
provide useful constraints on $s$-process nucleosynthesis. In this regard,
abundances of the diagnostic species rubidium and $\rm ^{96}Zr$ will be
useful, as these are sensitive to details of the $s$-process conditions,
which ultimately can constrain mass of the AGB progenitor and implicate
an enrichment timescale.
We note that similar $s$--process enhancements have been seen in stars
of the globular cluster Omega Centauri (e.g. Smith et al.~2000), but at lower
metallicity; those enhancements were attributed to AGB nucleosynthesis by
M $< 3 \, {\rm M_\odot}$ stars, whose lifetimes are $\sim 0.3$ Gyr (Girardi
et al.~2000).
Similar $s$--process enhancements, accompanied by low $\alpha$--element abundances
have also been seen for stars in the Magellanic Clouds (e.g. Hill 1997).
It seems that the Magellanic Clouds may have experienced a chemical
evolution history similar to Sgr.
Our model for the evolution of the Sgr dSph is curiously opposite,
in a sense, to the situation in the solar neighborhood.
Near the Sun, the G--dwarf problem (van den Bergh 1962, Schmidt 1963;
see Pagel 1997 for a thorough review of proposed solutions)
is the observation that there are too few metal-poor
stars to account for the high numbers of metal-rich stars
under the assumption of simple, closed box, chemical evolution.
Continuous inflow of lower or zero metallicity gas is the most favored
way of solving the G-dwarf problem.
Our model for the Sgr dSph requires a significant amount of
outflow to explain the abundance patterns and the
age--metallicity relationship. At the same time, we find
that recycling of newly-synthesized elements operated over
timescales of many Gyr because we believe the metal-poor
population generated the elements that enriched the
younger, more metal-rich, stars.
%To explain all our data would require the high [La/Y] ratio at [Fe/H]$\sim$-0.6 set by an
%excess of high-frequency $r$-process events, but by [Fe/H]$\sim$$-$0.1 the [La/Y] ratio
%was set by $s$-process ejecta from metal-poor AGB stars. The complexity of this model,
%and the fortuitous similarity of [La/Y] enhancements from the two processes, make it difficult to
%accept. Certainly, more data would be required for a more complete understanding of the origin
%of the neutron-capture elements in Sgr dSph.
\subsection{Comparison with Other Abundance Studies of Sgr dSph Stars}
Including the chemical abundances found for M54 red giants
(Brown, Wallerstein \& Gonzales 1999; hereafter BWG99)
and those of 2 Sgr dSph stars (Bonifacio et al. 2000;
hereafter B00) strengthens the abundance trends we find in Sgr stars.
BWG99 derived chemical abundances for 5 red giant stars
in the globular cluster M54, a member of the Sgr dSph,
derived from CTIO 4m echelle spectra ($R \sim 24,000$; SNR $\approx 60$).
The stars were similar in color and magnitude
to our three most metal--poor stars. BWG99 derived initial
effective temperatures using (V--I) colors and the color--temperature
relationships of Buser \& Kurucz (1992). The
reddening was assumed to be E(B--V) $=0.20$ (higher than our assumed
value of 0.13), in order to make their spectroscopic abundances
derived from the Fe~I and Fe~II lines consistent.
Gravities were computed assuming a mass of 0.7 M$_\odot$, and a short
distance, at ${\rm (m-M)_V} = 17.49$.
An older set of model atmospheres from Bell
et al.~(1976) was used, but like us they assumed LTE analysis and
used a version of MOOG for the abundance analysis. The line
list was similar in size to our own, although the lines used differ.
The abundance ratios of the M54 stars are similar to our
three most metal--poor stars. BWG99 note that the average
abundance ratio [Ti/Fe] $=+0.30$ was somewhat higher than the average
of their other $\alpha$ elements (Mg, Si, and Ca), at $+$0.16 dex. We do
not find such a correlation for our metal-poor Sgr field stars. BWG99 detected
Al in only one star, Ibata 1, and that star had such strong Al,
[Al/Fe] $=+0.78$, accompanied by depleted O, [O/Fe] $=-0.23$,
that they concluded its primordial abundance had been altered
by proton-burning, similar to our star 1--73 as discussed in \S7.3.
We excluded Ibata 1 from the calculation of the average
[Na/Fe] for M54 stars that is plotted in Figure \ref{fig-naal}, because
the Na abundance also appears enhanced over primordial.
BWG00 did not determine the abundance of Y, but the abundance
ratios of the other neutron-capture elements follow the
trends defined by our stars.
B00 derived chemical abundances for 2 field red giants
in the Sgr dSph from high-dispersion spectra
($R \sim 43,000$; SNR $\approx 30$) obtained with UVES on an
ESO 8.2-meter telescope. The stars are somewhat hotter
((V--I)$_0 \approx 0.95$, T$_{\rm eff} \approx 4900$ $^\circ$K)
and fainter (V $= 18.2$) than our sample.
Effective temperatures were based on (V--I) colors and
Alonso et al.~(1999) color--temperature relationship, and
gravities were assumed to be $\log g = 2.5$, consistent with the stars'
positions in the color--magnitude diagram. Kurucz (1993) model atmospheres and
LTE were assumed to derive abundances. The line list was different than used in
the present work.
The B00 spectra extend farther to the blue than ours,
and cover some gaps in our spectra. However, our line list
contains roughly double the number of lines for most of elements
studied by B00. For example, for Ca and Fe we use 18 and 76 lines,
respectively, while B00 use 6 and 16. However even though we
use different line lists, we find very similar abundance results.
The derived metallicities of the B00 stars are
[Fe/H] $= -0.28$ and $-0.21$, similar to our dominant group at
high metallicity. The abundance ratios B00 derive fit very well
onto the trends defined by our data, except that
their [Fe/H] $= -0.21$ star has [$\alpha$/Fe] $=-0.16$
which is lower by $\sim 0.15$ dex than the average value of
our metal--rich stars, and their [Y/Fe] abundances are lower
by $\sim 0.3$ dex than the average value of our metal--rich stars.
Unfortunately, the four Y lines they used are all bluer
than the limit of our spectral coverage so we
cannot make a line-by-line comparison.
Since B00 detected 2 metal--rich stars in a dSph thought to be
predominantly a metal-poor galaxy (recall Bellazzini et al.'s [1999]
assertion that $\sim 85$\% of the red giants were metal--poor
based on their position in the color magnitude diagram, and an assumed age
of $\sim$ 15 Gyr) with unusual heavy element abundances, they were
understandably confused about how to interpret their results.
The stars had very similar atmospheric parameters and abundances,
but their positions in the color--magnitude diagram were significantly
different. In order to explain this, they discussed 5 hypotheses.
They rejected photometric errors and differential reddening as the
possible causes. Although they noted that an age difference of
$\sim 1$ Gyr would explain the difference in photometry, they chose
as the ``most likely explanation" different distances for the stars
and suggested the Sgr dSph had a non-negligible depth along
the line of sight.
With many more stars in our sample, we find that a range in
ages is the better explanation. An age range of $\sim 1$ to 13 Gyr,
as inferred from our derived abundances and ages, is exactly
what is needed to explain the trend in element ratios we see as a
function of metallicity. B00 rejected the idea that the element ratios
of the neutron capture were contaminated by the $s$--process in AGB stars
because: (1) the stars were not luminous enough to have gone through
thermal pulses that would contaminate their atmospheres, and (2)
they rejected the idea that there was significant range in age of
the stellar population of the Sgr dSph. B00 reached a different
conclusion than we do simply because they had too small a sample to
see the evolution of the element ratios with metallicity.
B00 noted that the unusual abundances found for the
Sgr stars are very much like those seen in young supergiants
in the Large and Small Magellanic Cloud (c.f., Hill 1997 and references
therein). Therefore, our explanation of Sgr's unusual abundance
variations -- namely, slow evolution of the star--formation rate accompanied
by mass loss and chemical enrichment of the young, metal--rich population by the old,
metal--poor population -- is probably applicable to the Magellanic Clouds.
It is curious that the youngest stars in the Sgr dSph have approximately the
same metallicities, as measured by [Fe/H], as the young stars in the
LMC despite the fact that the total absolute magnitude, M$_{\rm V}$, for the
LMC is more than 5 magnitudes brighter than the Sgr dSph. Is this an artifact
of star formation running to completion in Sgr dSph, or is it that
much of Sgr's luminosity has already been stripped by tidal interactions
with the Galaxy?
\subsection{The Complex Evolution of the Sgr dSph}
% A detailed modeling of the age and metallicity relationship is outside
% the scope of the present data. Ideally, one would want to obtain spectroscopy
% for a much large number of stars and simultaneously analyze the
% derived abundances and a well--populated color--magnitude diagram.
We can glean more information about the evolution of the
Sgr dSph by comparing our data to some simple models. In Figure
\ref{fig-agealphah}, we plot the age and [$\alpha$/H] abundance,
which is more likely to be a good candidate for the instantaneous
recycling approximation than [Fe/H] because of the delayed
explosion of type Ia SNe which generate significant amounts of Fe but little
$\alpha$ elements. For each of the globular clusters, we have assumed
[$\alpha$/Fe] = +0.21, which is the value found by BWG99 for M54, but the
true value could be lower if its age is indeed 6 Gyr younger than
the other clusters.
Figure \ref{fig-agealphah} illustrates the results of simple outflow chemical
evolution models with instantaneous recycling. For comparison, the models
have all been normalized to pass through the same point. Each model
assumes that star formation goes to completion at the present
time of $T=15$ Gyr, but adopts different
prescriptions for the star--formation rate, $\psi(t)$.
The black line shows the prediction assuming $\psi$ is constant in time. Results
for an exponentially decreasing star formation rate of the form
$\psi(t) \propto e^{-t/\tau}$ are illustrated by the blue
line for $\tau = 5$ Gyr and the green line for $\tau = 1$ Gyr.
A model with an increasing star formation rate
of the form $\psi \propto t$ is illustrated by the red line.
Note that none of these simple outflow models accurately reproduces the
observed age-metallicity relationship, but the sharp increase in
[$\alpha$/H] for ages $\simlt 5$ Gyr would imply an increasing,
as opposed to decreasing, star
formation rate. The most plausible model might well involve a discontinuous
star--formation rate. Episodic star formation events have been found for a
number of dSphs in the Local Group with the most stunning example being
the Carina dSph (c.f., Hurley-Keller et al.~1998, Smecker-Hane \&
McWilliam 1999).
% Further work on the Sgr dSph will benefit greatly from
% new generations of spectrographs, such as the MIKE fiber--fed echelle
% spectrograph being developed for the 6.5-meter Magellan Telescopes,
% which will allow one to obtain high-dispersion spectra for $\sim 100$
% stars simultaneously. Modeling of the color--magnitude diagrams,
% [Fe/H], and chemical abundance ratios promises to yield powerful
% constraints on the physical processes that regulated the complex
% evolution of dSphs.
\subsection{Relevance to the Merger History of the Galaxy}
In \S7.3 we introduced Fulbright's high-dispersion chemical abundance
survey of 168 field stars in the solar neighborhood (Fulbright 2000).
A detailed analysis of the kinematics of $\sim 45$\% of
these stars has been performed by Fulbright (2002). From such an extensive,
homogeneous,
database, strong constraints can be place on the merger history of the
Galaxy by comparing the abundance ratios as a function of metallicity
and kinematics to stars in dSph galaxies. In addition to our new data
on 14 Sgr dSph stars, Shetrone, C\^{o}t\'{e} \& Sargent (2001;
hereafter SCS01) have surveyed a total of 17 stars among the
Ursa Minor, Draco and Sextans dSphs, also using HIRES. The philosophies of our
programs are significantly different: we prefer to study many stars in
one dSph to provide a detailed picture of the evolution of one galaxy, and
we choose higher S/N data in order to analyze a larger set of chemical
elements and always determine same set of elements in each star.
SCS01 have obtained lower S/N data for a few stars in numerous dSphs
with the primary goal of comparing the sum of the distribution to
Galactic halo stars in order to constrain the merging history of the
Galaxy. Even though the specifics of our two studies differ, they
are extremely complimentary. Below we compare the composition of
dSph stars with Fulbright's Galactic stars.
As mentioned in \S7.3, Fulbright (2000) found a population of stars that have
chemical peculiarities, [Na/Fe] $< -0.2$ as opposed to the average of
[Na/Fe] $\approx 0$ for the majority of Galactic stars. In
Figure~\ref{fig-sgr_halo_dsphs5}
we show [Na/Fe] as a function of [Fe/H] for these stars as well as
the dSph stars; Fulbright's ``chemically--peculiar'' stars are defined as
those with [Na/Fe] $< -0.2$.
% and we plot them as the
% filled squared in all our subsequent plots. The remainder of his sample is
% plotted as open squares. Sgr dSph stars are plotted as red squares, and
% dSph stars from SCS01 are plotted as blue stars.
In the Fulbright
sample, stars with [Na/Fe] deficits are also deficient in
[$\alpha$/Fe], although by a smaller amount. This is exactly
analogous to what we see in the metal--rich Sgr dSph stars. We have
shown that the smaller [$\alpha$/Fe] deficits simply come from the fact
that type Ia do produce some $\alpha$--elements but very little Na.
We suggest the {\it same} is true in Fulbright's chemically--peculiar
stars. The proto-galactic fragments in which these stars formed apparently
retained their individuality long enough for type Ia to explode in them
and long enough for their nucleosynthetic products to cool and be
recycled into new stars. Hence their star--formation activity must
have lasted $\simgt 1$ Gyr, maybe more. The dSph stars show a mix
of [Na/Fe] ratios. Some have [Na/Fe] roughly similar to normal Galactic
halo stars while the majority show the same deficits in Na that the
the chemically--peculiar halo stars and the metal--rich Sgr stars share.
Therefore, we have evidence that even the lowest mass dSphs, Ursa Minor
and Draco, underwent star formation on timescales $\simgt 1$ Gyr.
Fulbright (2002) shows that the majority of the
chemically peculiar stars have very high Galactic rest frame
velocities, $> 300$ km/s, and they are on very elliptical orbits,
thus their kinematics suggest they could be the remnants of an
outer halo, proto--galactic fragment(s).
We can actually place an upper-limit on the duration of their
star formation by looking at the ratio of $r$ and $s$--process elements.
Again, the $r$--process is thought to primarily operate in massive
stars that explode as type II SNe, so their enrichment happens quickly
as opposed to the $s$--process enrichments, which may take on the order
of a few Gyr or more. In Figure~\ref{fig-sgr_halo_dsphs2.eps}, we plot the
ratio of $s$--process to
$r$--process elements as a function of metallicity. For the Fulbright and
SCS01 stars, we plot the ratio [Ba/Eu], and for our Sgr dSph stars, we
plot [La/Eu]. We do this because La was not measured in the Fulbright or
SCS01 spectra, because at the lower metallicities, these
lines can be very weak (e.g., Table 3).
However, in our Sgr
dSph spectra, the Ba lines for most stars are too strong for accurate abundance
analysis, being on the flat portion of the curve of growth.
Examination of Figure~\ref{fig-sgr_halo_dsphs2.eps} shows that only one of the
Fulbright stars and one of the Ursa Minor dSph stars show much evidence for
significant amounts of $s$--process material. Note that the Ursa Minor
star is located right at the tip of the red giant branch and one wonders if it
potentially has enriched itself or been enriched by mass transfer from
a companion. CMDs of the Ursa Minor dSph show that most of its stars
are very old, $\simgt 10$ Gyr (Hernandez, Gilmore, \& Valls--Gabaud 2000,
Dolphin 2002), and thus the timescale is such that self--pollution
could be an issue. A point to note is that only a
small subset of the Fulbright and SCS01 stars have measurements
of La, Eu because the lines are weak in such metal-poor stars.
Because of this, we caution that careful thought must be put
into interpreting these diagrams. Selection effects could bias
one's interpretation.
In Figure~\ref{fig-sgr_halo_dsphs4.eps}, we show the same $s$ to $r$--process ratios
but as a function of the [Na/Fe] ratio. Stars enriched by Type Ia
SNe will have [Na/Fe] below that of the normal yield of Type II SNe,
[Na/Fe] $\approx 0$. This diagram shows that there is no evidence for
large amounts of $s$--process material in Fulbright's chemically--peculiar
stars or in SCS01 stars, but again we really need more data
on which to firmly base our conclusions because very few of these stars
have measurements in La, Eu, Na and Fe. Therefore, we tentatively conclude
that the SCS01 dSphs and the proto-galactic fragments that
gave rise to the chemically--peculiar stars stopped forming their stars
before the onset of significant enrichment from the $s$--process.
Determining exactly what time that corresponds to
will require additional input from theoretical models, but we can
compare to the Sgr dSph abundances and ages to get a hint.
The [$s$/$r$] ratios of the Fulbright stars are certainly lower than
the metal-rich Sgr stars, the youngest of which is $\sim 3$ Gyr
old, and thus formed $\sim 12$ Gyr after the initial epoch of
star formation. Therefore, this is only a weak constraint in
that the proto-galactic fragments and dSphs must have stopped forming
stars $> 3$ Gyr ago.
%
% TAMMY: I think that this whole paragraph, referring to Figure 15, should
% be removed, because the issue has already been mentioned in SCS01; I think
% it also means that we should remove Figure 15. I have a replacement
% paragraph in case you insist on mentioning Figure 15, but would be
% embarassed to include it.
%
%---------------------------------------------------------------------------
% My replacement paragraph
%
%In Figure~15, we show the ratio of heavy to light $s$--process elements,
%[$hs$/$ls$] = [Ba/Y] for the Fulbright stars and SCS01 stars, and
%[$hs$/$ls$] = [La/Y] for the Sgr dSph stars.
%It is unlikely that the high [Ba/Y] ratios of SCS01 can be explained by
%a low-metallicity AGB s-process, because the [Ba/Eu] ratios (see Figure~13)
%are consistent with dominantly r-process material. If the SCS01 [Ba/Y]
%and [Ba/Eu] measurements are correct this suggests an unusual r-process
%with high [$hs$/$ls$]. In this case we expect that the SCS01 Ba/Y ratios are
%most consistent with r-process from the high-frequency, H, events of
%Wasserburg et al. (1996). This has already been discussed by SCS01.
%
% ----------------------------------------------------------------------------
% Your original paragraph
%
%In Figure~15, we show the ratio of heavy to light $s$--process elements,
%[$hs$/$ls$] = [Ba/Y] for the Fulbright stars and SCS01 stars, and
%[$hs$/$ls$] = [La/Y] for the Sgr dSph stars.
%We find a puzzle! Most of the chemically--peculiar
%Galactic stars, the normal Galactic stars, and the low metallicity
%Sgr stars have [hs/ls] $\approx 0$, as we would expect based on
%[La/Eu] $\approx -0.6$, the expected yield of the $r$--process.
%We have suggested that the Sgr metal-rich stars have such high values,
%[La/Y] $= +0.5$ because this is the yield of the $s$--process in
%low metallicity, [Fe/H] $\leq -1.5$, AGB stars and more of the La and
%Y was made in the $s$--process than the $r$--process in these
%metal-rich stars. If that is the case, then why do {\it most} the
%dSph stars of SCS01 also have [Ba/Y] $= +0.5$?
%We have inferred from their [Ba/Eu] ratios that these stars have little
%$s$--process enrichment. We do not know the answer;
%if the problem is not due to measurement
%errors perhaps the solution lies in variance within the $r$-process,
%or the alternative site for light neutron capture elements
%proposed by McWilliam (1998). The paradox of the low metallicity dSph
%stars from SCS01 having the deficient [$hs$/$ls$] ratios, similar to
%the metal-rich Sgr stars, is intriguing and deserves closer study. Lurking
%behind it could be an important lesson about the physics of
%neutron capture nucleosynthesis.
% ----------------------------------------------------------------------------
%
\section{Summary}
Our observations of the Sgr dSph are consistent with prolonged star formation
and chemical enrichment with significant mass loss. The radial velocities
and chemical compositions firmly establish the 14 stars in our
sample as bona fide Sgr dSph members with metallicities of
$-1.6 \leq \feh \leq 0.0$ and an corresponding age range of
$\sim$ 13 to 1 Gyr.
While the composition of the metal--poor, $\feh < -1$, Sgr dSph stars
closely resembles Galactic halo stars, the metal--rich component with
$-0.6 \simlt \feh \simlt 0$ shows a very unusual chemical composition:
[Na/Fe] and [Al/Fe] ratios are on average 0.4 dex below those
of stars with the same metallicity in the solar neighborhood while
the [$\alpha$/Fe] ratios are only 0.1 dex below the solar
neighborhood stars. From this we conclude
the ratio of number of type~II to type~Ia SNe that enriched the
metal-rich stars in the Sgr dSph was lower than that of
stars in the solar neighborhood. These abundance ratios are consistent
with $\approx 60$ to 70\% of the Fe in the metal-rich Sgr population
synthesized in type Ia SNe and the remainder in type II SNe.
Such abundance ratios could arise if the Sgr dSph experienced an episodic
star-formation rate (meaning that star formation activity went through
a lull between the formation of the Sgr metal-poor and Sgr metal-rich
populations) or if the star--formation rate of the Sgr dSph proceeded
at a steady pace but the pace was slower than that of the Galactic
disk in the solar neighborhood.
Enhancements of neutron-capture heavy elements, which increase with [Fe/H]
(up to [La/Fe]$\sim$1 dex at [Fe/H]$\sim$0),
and the $s$--process signature seen in the [La/Eu] ratios,
indicate the importance of AGB nucleosynthesis in the metal--rich Sgr dSph
population. However, the [La/Y] ratios suggest a nucleosynthetic origin
from sites of much lower metallicity than the stars themselves. These
observations may be understood if heavy elements in the metal--rich population
were dominated by input from low-mass, long-lived, AGB stars belonging to
the old, metal--poor population. The relatively long-lived AGB progenitors
require that star formation in Sgr dSph took place over an extended
period of time, $\simgt 0.3$ to 2 Gyr if the initial mass of the
AGB stars are $\sim$ 3 to 1.5 M$_\odot$, respectively.
Finally, the increasing trend in [La/Fe] ratios to higher [Fe/H]
indicates that either the efficiency of $s$-process production increased,
or the production of iron decreased with time. The latter alternative
strikes us as more likely, because the probability that mass transfer to a
white dwarf will exceed the Chandrasekhar limit must be lower for
a population of older, and hence less massive, secondaries.
These assertions are supported by age estimates for our sample of
Sgr dSph stars, based on Padova isochrones, which span the range
from 0.5 to 12.5 Gyr. The age-metallicity relationship for these Sgr field
stars and the Sgr globular clusters suggest that the loss of gas in
a galactic wind was very important in the evolution of this dSph.
Thus we conclude that the Sgr dSph has had a surprisingly complex
history of star formation and chemical enrichment.
\vspace{5ex}
\acknowledgments
We gratefully acknowledge financial support from the NSF through grants
AST-9619460 and AST-0070895 to TSH, and AST-9618623 and AST-0098612 to
AM. TSH also thanks the American Astronomical Society for
a Small Research Grant that supported travel to Keck Observatory.
We thank Rodrigo Ibata for sharing his radial velocities with us prior
to their publication, and Inese Ivans for useful comments on the manuscript.
We thank the staff at Keck Observatory for their
excellent observing support, and Steve Vogt and collaborators for creating
HIRES, an extremely reliable and efficient spectrograph. We thank Graeme Smith and
Robert Kraft for agreeing to share nights in (what was then)
an innovate scheduling arrangement. In addition,
we want to extend special thanks to the people of Hawai`ian ancestry on
whose sacred mountain, Mauna Kea, we were privileged to be guests.
Our research was expedited by the wide range of data made available at
Canadian Astronomy Data Center, which is part of the Herzberg Institute of
Astrophysics, a facility of the National Research Council of Canada,
the Digitized Sky Survey, which was produced at the
Space Telescope Science Institute under US Government grant
NAG W-2166, and the NASA Astrophysics Data System Abstract
Service.
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\clearpage
\begin{figure}
\plotone{f1.eps}
%\plotfiddle{FILE}{VSIZ}{ROT}{HSF}{VSF}{HTRANS}{VTRANS}
%\plotfiddle{f1.eps}{8.5cm}{0.}{80.}{80.}{0}{0}
\caption{The color--magnitude diagram for the Sgr dSph (see text for details)
with our spectroscopic targets shown as large circles. Our sample
spans the full spread in color of red giant stars in order to probe
the full range of metallicity. Isochrones based on the Padova models
(Girardi et al.~2000) are shown as solid lines for a variety of age
and metallicity combinations: black shows $\feh = -1.4$ and age $= 13$ Gyr,
blue shows $\feh = -1.0$ and age $= 5$ Gyr, green shows $\feh = -0.4$
and ages $= 1$ and 3.5 Gyr, and red shows $\feh = 0$ and age $=1$ and 1.4 Gyr.
For the sake of clarity, evolutionary stages past the tip of the red giant
branch are shown only for the two youngest models.}
\label{fig-VIcmd}
\end{figure}
\begin{figure}
\plotone{f2.eps}
\caption{Spectra of a metal--poor (top) and metal--rich (bottom) Sgr dSph
star. Spectra are shown redshifted to rest wavelengths, measured lines
are labeled, and the derived metallicities are shown. Bad columns on
the CCD are designated with the $\oplus$ symbol.}
\label{fig-spec}
\end{figure}
\begin{figure}
\plotone{f3.eps}
\caption{The color--magnitude diagram for the Sgr dSph (SL95)
with stars in the spectroscopic sample circled in colors that
reflect their derived effective metallicities (Eqn.~2).}
\label{fig-VIcmd2}
\end{figure}
\begin{figure}
\plotone{f4.eps}
\caption{The age--[Fe/H] relationship for the Sgr dSph. Data for our
red giant stars are shown as filled circles. Open circles show
data for 4 globular clusters that belong to the Sgr dSph (see section 7.1
of the text for details). The solid line shows the prediction from
a simple chemical evolution model that assumes instantaneous recycling,
a closed box, star formation that has gone to completion at the present time.}
\label{fig-agefeh}
\end{figure}
\begin{figure}
\vspace{1.2truein}
\plotone{f5.eps}
\vspace{-2.0truein}
\caption{Chemical abundances for red giants in the Sgr dSph (filled circles),
where [$\alpha$/Fe] is the average of [Si/Fe], [Ca/Fe], and [Ti/Fe].
A typical error bar shown on the lower left. The average abundance of
red giants in M54, a globular cluster in the Sgr dSph,
from Brown, Wallerstein \& Gonzalez (1999) is shown as the open
star symbol. Sgr dSph stars for which Bonifacio, et al.~(2000) derived
abundances are shown as open circles.
The dashed line represents the mean trend in [$\alpha$/Fe] for
stars in the solar neighborhood from Edvardsson et al.~(1993).
\label{fig-alphafe} }
\end{figure}
\begin{figure}
\plotone{f6.eps}
\caption{{\bf a: }A plot of [Al/Fe] versus [Fe/H].
{\bf b: }A plot of [Na/Fe] versus [Fe/H].
Symbols are the same as in Fig.~\ref{fig-alphafe}. Crosses
represent abundances from Chen et al.~(2000) for
solar neighborhood F stars.
\label{fig-naal}}
\end{figure}
\begin{figure}
\plotone{f7.eps}
\caption{{\bf a:} A plot of [La/Fe] versus [Fe/H].
Symbols are the same as in Fig.~\ref{fig-alphafe}.
Open squares represent chemical abundances
of Galactic stars from Gratton \& Sneden (1994).
\label{fig-lafe} }
\end{figure}
\begin{figure}
\plotone{yfe.eps}
\caption{{\bf a:} A plot of [Y/Fe] versus [Fe/H].
Symbols are the same as in Fig.~\ref{fig-alphafe}.
Open squares represent chemical abundances
of Galactic stars from Gratton \& Sneden (1994).
\label{fig-yfe} }
\end{figure}
\begin{figure}
\plotone{f8.eps}
\caption{
A plot of [La/Eu] versus [Fe/H]. Dotted lines indicate the
solar $r$--process ratio, and a pure $s$--process ratio from Malaney (1987).
Symbols are the same as in Fig.~\ref{fig-alphafe}.
Open squares represent chemical abundances
of Galactic stars from Gratton \& Sneden (1994).
\label{fig-laeu} }
\end{figure}
\begin{figure}
\plotone{laeulah.eps}
\caption{
A plot of [La/Eu] versus [La/H]. Dotted lines indicate the
solar $r$--process ratio, and a pure $s$--process ratio from Malaney (1987).
Symbols are the same as in Fig.~\ref{fig-alphafe}. The solid curve shows the
composition locus of when pure $s$-process material is added to halo composition
at [La/H]=$-$0.8, the dashed line shows the locus for pure $s$-process added
to halo composition at [La/H]=$-$0.3, and the dot-dashed line shows the result
of adding 95\% $s$-process and 5\% $r$-process La composition to the halo mixture.
\label{fig-laeulah} }
\end{figure}
\begin{figure}
\plotone{eufe.eps}
\caption{
A plot of [Eu/Fe] versus [Fe/H] for the Sgr dSph stars (filled circles),
compared with Galactic stars: crosses from Woolf et al. (1995); open squares from
Gratton \& Sneden (1994); open stars are Globular cluster mean values from Shetrone
(1996); filled triangles are field halo stars from Shetrone (1996).
\label{fig-eufe} }
\end{figure}
\begin{figure}
\plotone{lay3.eps}
\caption{
A plot of [La/Y] versus [Fe/H].
Symbols are the same as in Fig.~\ref{fig-alphafe}.
Open squares represent chemical abundances
of Galactic stars from Gratton \& Sneden (1994).
\label{fig-lay} }
\end{figure}
\begin{figure}
\plotone{f10.eps}
\caption{The age--metallicity relationship for the Sgr dSph. Filled circles show
the data for our 14 red giant stars. Open circles show data for 4 globular
clusters that are members of the Sgr dSph. Simple chemical evolution models
that assume instantaneous recycling are shown as solid lines. See text in section 7.6
for details.
\label{fig-agealphah} }
\end{figure}
\begin{figure}
\plotone{sgr_halo_dsphs5.eps}
\caption{The ratio of [Na/Fe] as a function of [Fe/H] in dSph and Galactic
stars. Sgr dSph stars from this paper are plotted as red squares. Stars in the
Ursa Minor, Draco and Sextans dSphs from Shetone, C\^{o}t\'{e} \& Sargent (2001)
are plotted as blue stars. Galactic stars in the Fulbright (2000) sample
that have [Na/Fe] $< -0.2$ are plotted as black squares while those with
[Na/Fe] $\geq -0.2$ are plotted as open squares.}
\label{fig-sgr_halo_dsphs5}
\end{figure}
\begin{figure}
\plotone{sgr_halo_dsphs2.eps}
\caption{The ratio of $s$--process to $r$--process elements, [La/Eu] for Sgr
stars or [Ba/Eu] for other dSph or Galactic stars, as a function of metallicity.
Symbols are the same as Figure~\ref{fig-sgr_halo_dsphs5}.}
\label{fig-sgr_halo_dsphs2}
\end{figure}
\begin{figure}
\plotone{sgr_halo_dsphs4.eps}
\caption{The ratio of $s$--process to $r$--process elements,
[La/Eu] for Sgr stars or [Ba/Eu] for other dSph or Galactic stars,
as a function of [Na/Fe]. Same symbols as
Figure~\ref{fig-sgr_halo_dsphs5}.}
\label{fig-sgr_halo_dsphs4}
\end{figure}
\begin{figure}
\plotone{sgr_halo_dsphs1.eps}
\caption{The ratio of heavy to light $s$--process elements,
[La/Y] for Sgr stars or [Ba/Y] for other dSph or Galactic stars,
as a function of metallicity. Same symbols as
Figure~\ref{fig-sgr_halo_dsphs5}.}
\label{fig-sgr_halo_dsphs1}
\end{figure}
\clearpage
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\input{table2}
\input{table3}
\input{table4}
\input{table5}
\input{table6}
\input{table7}
\end{document}