Using the MIKE spectrograph, mounted on the 6.5-m Magellan/Clay telescope at the Las Campanas observatory in Chile, we have obtained highresolution spectra for 60 F and G dwarf stars, all likely members of a density enhancement in the local velocity distribution, referred to as the Hercules stream. By comparing with an existing sample of 102 thin- and thick-disk stars we have used space velocities, detailed elemental abundances, and stellar ages to trace the origin of the Hercules stream. We find that the Hercules-stream stars exhibit a wide spread in stellar ages, metallicities, and element abundances. However, the spreads are not random but separate the Hercules stream into the abundance and age trends outlined by either the thin disk or the thick disk. We hence claim that the major constituents of the Hercules stream actually are thin- and thick-disk stars. These diverse properties of the Hercules stream indicate a dynamical origin, probably caused by the Galactic bar. However, we can at the moment not entirely rule out the possibility that the Hercules stream could be the remnants of a relatively recent merger event.

We study the effect of assuming different formation timescales for the thick and thin disks on the variation of the abundance ratios of several elements with metallicity. We show that, if the thin disk was formed on a onger timescale (≃7 Gyr) than the thick disk (≃0.8 Gyr), the abundance ratio shifts between the thick and thin disk, as a function of the metallicity, can be well explained. Moreover, these observations offer a powerful constraint on stellar yields in general (massive stars, low- and intermediate-mass stars, and SN Ia) and their dependence on metallicity.

Results of several investigations of FGK stars in the Solar neighborhood have suggested that thin-disk stars with an iron abundance similar to that of the Sun appear to have higher abundances of other elements, such as silicon, titanium, and nickel. Offsets could arise if the samples contain stars with ages, mean Galactocentric distances, or kinematics that differ on average from the Solar values. They could also arise due to systematic errors in the abundance determinations, if the samples contain stars that are different from the Sun regarding their atmospheric parameters. We re-examine this issue by studying a sample of 80 nearby stars with Solarlike colors and luminosities. Among these Solar analogs, the objects with Solar iron abundances exhibit Solar abundances of carbon, silicon, calcium, titanium, and nickel.

Chemical abundances of metal-rich H II regions: why?

Ionized nebulae (H II regions) trace the sites of massive-star formation in spiral and irregular galaxies. The rapid evolution of these stars, ending in supernova explosions, and the subsequent recycling of nucleosynthesis products into the interstellar medium, make H II regions essential probes of the present-day chemical composition of star-forming galaxies across the Universe. The study of nebular abundances is therefore crucial for understanding the chemical evolution of galaxies. In the following pages I will provide an optical astronomer's perspective on some of the issues concerning the measurement of abundances in metal-rich H II regions, by focusing on the observational difficulties that are peculiar to the high-metallicity regime, discussing some of the most recent abundance determinations from H II regions in the metal-rich zones of spiral galaxies, and indicating some possibilities for further progress. Throughout this paper I will use the oxygen abundance as a proxy for the metallicity (oxygen makes up roughly half of the metal content of the interstellar medium), and assume the Solar value from Asplund et al. (2004), 12 + log(O/H)⊙ = 8.66. Elements besides oxygen will not be discussed in great detail.

Motivations

Why measure abundances of metal-rich H II regions? After all, as we will see in Section 2, metal-rich H II regions pose difficulties to the observer that are not present at lower metallicities, i.e. roughly below half the Solar O/H value. However, high abundances are encountered in a variety of astrophysical contexts, and the study of ionized nebulae often provides the only way to measure these abundances.

Although damped Lyman-alpha (DLA) systems are usually considered metal-poor, it has been suggested that this could be due to observational bias against metal-enriched absorbers. I review recent surveys to quantify the particular issue of dust obscuration bias and demonstrate that there is currently no compelling observational evidence to support the hypothesis of a widespread effect due to extinction. On the other hand, a small subset of DLAs may be metal-rich and I review some recent observations of these metal-rich absorbers and the detection of diffuse interstellar bands in one DLA at z ∼ 0.5.

I present a review of chemical-evolution models of the Solar neighborhood. I pay special attention to the ingredients necessary to reproduce the observed [Xi/Fe] ratios in nearby metal- and super-metal-rich stars, and to the chemical properties of the Solar vicinity, focusing on [Fe/H]≥–0.1. I suggest that the observed abundance trends are due to material synthesized and ejected by intermediate-mass stars with Solar metallicity in the AGB stage, and also by massive stars with (super)solar metallicity in the stellar wind and supernovae stages. The required tool to build chemicalevolution models that reach supersolar metallicities is the computation of stellar yields for stellar metallicities higher than the initial Solar value. With these models it might be possible to estimate the importance of merger events in the recent history of the Galactic disk as well as the relevance of radial stellar migration from the inner to the outer regions of the Galaxy. I also present a short review of the photospheric Solar abundances and their relation to the initial Solar abundances.

Even though metals constitute only a few per cent of the total mass fraction of stars, they have a huge impact on the way stars and galaxies evolve. In that respect, metallicity in the Universe is, like the salt in a dish, a small amount that can completely change its flavour!

The metal-rich stars have never attracted as much attention as the metal-poor halo stars, which tell us about the first supernovae and the early chemical evolution of our Galaxy. However, metal-rich stars are of interest in their own right and can shed new lights on very topical subjects. For instance, it is now well established that stars rich in metals are more likely to harbour giant planets. This awareness has elicited careful and detailed abundance studies of ever more metal-rich stars. As a byproduct, trends of the abundances of many elements at high metallicity are now available and await an interpretation in terms of stellar nucleosynthesis and chemical-evolution models. The extent to which these observed trends are in line with what is expected from the current stellar and chemical-evolution models largely remains to be checked and this is one of the main topics of these proceedings.

Putting the subject into a larger context, let us recall that the attainment of adequate models of the high-metallicity regime is of great interest for the study of the central regions of galaxies, which are thought to have higher-than-solar metallicity. Also, it appears that many quasar environments are metal-rich out to redshifts of at least 5.

We present long-slit spectra for 11 early-type galaxies observed with the Keck telescope. We measure rotation-velocity and velocity-dispersion profiles together with 20 Lick line-strength gradients. Gradients of indices are transformed into ages, metallicities and [α/Fe] using stellar-population models that take into account variations in chemical-abundance ratios. We find that the line-strength gradients are mainly due to radial variations of metallicity, although small gradients of [α/Fe] and age are also present. Contrary to what is expected in simple collapse models, galaxies in our sample have both positive and negative [α/Fe] profiles. This rules out a solely inside-out or outside-in formation mechanism for all early-type galaxies. Metallicity gradients correlate with the shape of the isophotes and the rotational velocity but do not correlate with the mass of the galaxies. Galaxies with younger populations in their centres have steeper metallicity gradients. Our results suggest a scenario whereby galaxies form through the merger of smaller structures and the degree of dissipation during those mergers increases when the masses of the progenitor galaxies decrease.

Thick disks are common in spiral and S0 galaxies and seem to be an inherent part of galaxy formation and evolution. Our own Milky Way is host to an old thick disk. The stars associated with this disk are enhanced in the α-elements relative to similar stars present in the thin disk. The Milky Way thin disk also appears to be younger than the thick disk. Elementalabundance trends in stellar samples associated with the thin and thick disks in the Milky Way are reviewed. Special attention is paid to how such samples are selected. Our current understanding of the elemental abundances and ages in the Milky Way thick and thin disks is summarized and discussed. The need for differential studies is stressed. Finally, formation scenarios for the thick disk are briefly discussed in the light of the current observational picture.

I review current models of star formation and discuss potential effects of high metallicity. Our current paradigm for star formation is that it is a dynamical process in which molecular clouds and regions of star formation form on their local dynamical times. Molecular clouds are characterised by turbulent motions, which, together with gravity, lead to their fragmentation and the formation of individual stars. The resulting distribution of stellar masses can be most easily understood as a combination of fragmentation, continued accretion to form higher-mass stars and dynamical interactions. Regions of high metallicity are likely to differ in terms of their star formation in three main areas: the formation of molecular gas on grains; the cooling processes which determine the characteristic stellar mass; and the higher opacity of dust grains, which increases the effects of radiation pressure in limiting the growth of massive stars by accretion. Characterising star formation in regions of high metallicity will allow accurate determinations of these effects.

We present the results of our recent abundance survey of the Galactic thick disk. We selected from the Hipparcos catalog 176 sample stars satisfying the following criteria: they are nearby (d ≤ 150 pc) subgiants and dwarfs, of spectral types F and G, and with thick-disk kinematics (VLSR ≤ −40 kms−1, │WLSR│ ≤ 30 kms−1). Assuming that the velocity distribution of each stellar population is Gaussian, we assigned stars with a probability P ≤ 70% to one of the three components. This resulted in 95 thick-disk stars, 17 thin-disk stars, and 24 halo stars. The remaining 40 objects cannot be unambiguously assigned to one of the three components.

We derived abundances for 23 elements from C to Eu. The thick-disk abundance patterns are compared with earlier results from the thin-disk survey of Reddy et al. (2003). The levels of α-elements (O, Mg, Si, Ca, and Ti), thought to be produced dominantly in Type-ii supernovae, are enhanced in thick-disk stars relative to the values found for thin-disk members in the range −0.3 > [Fe/H] > −1.2. The scatter in the abundance ratios [X/Fe] at a given [Fe/H] for thick-disk stars is consistent with the predicted dispersion due to measurement errors, as is the case for the thin disk, suggesting a lack of “cosmic” scatter. The observed compositions seem consistent with a model of galaxy formation by mergers in a ∧ CDM universe.

The Bologna Open Cluster Chemical Evolution (BOCCE) project is intended to study the disk of our Galaxy using open clusters as tracers of its properties. We are building a large sample of clusters, deriving homogeneously their distance, age, reddening, and detailed chemical composition. Among our sample we have several objects more metal-rich than the Sun and we present here first results of the analysis for NGC 6819, IC 4651, NGC 6134, NGC 6791, and NGC 6253, the last two being the most metal-rich open clusters known.

In this appendix we provide some basic definitions and relations for functions that play an important role in Section 2.3.

We shall not provide the related mathematical theory nor discuss theta functions in generality here. Starting from the (usual) theta functions, which were introduced by Jacobi, we follow the path taken by Rosenhain and define hyperelliptic theta functions of two variables, sometimes called ‘ultra-elliptic theta functions’ (Rosenhain 1850). Moreover, we list some useful relations between theta functions of each type. Besides the definition of the well-known elliptic integrals of the first and second kinds and the Jacobian elliptic functions, we include two less well-known functions, which can be constructed from elliptic integrals, namely Heuman's lambda function and Jacobi's zeta function. Furthermore, the relations between the Jacobian theta functions and the Jacobian elliptic functions that are important for our purpose in Subsection 2.3.3 are given. Finally, we list derivatives for some of the above functions that were used in Subsection 2.3.4.

Note that the notation in the literature (especially concerning theta functions) is not standardized. Throughout this book we comply strictly with the definitions presented here.

In general, a relativistic figure of equilibrium as calculated in the previous chapters is to be expected to exist in nature only if it is in stable equilibrium. Therefore, in addition to other aspects, like realistic equations of state, magnetic fields and initial conditions, the investigation of stability properties is very important for identifying configurations that might be astrophysically relevant. Acomplete stability analysis of relativistic figures of equilibrium is extremely difficult. Moreover, the stability depends on matter properties like viscosity and thermal conductivity, which are unimportant for the equilibrium state itself and therefore do not need to be specified in this book. Our intention, as expressed in the preface, is to ‘place emphasis on the rigorous treatment of simple models instead of trying to describe real objects with their many complex facets’ and, consequently, an extensive treatment of stability questions is beyond the scope of this book. Nevertheless, in the following we will discuss some aspects of stability of rotating fluid configurations in general relativity.

Stability with respect to axisymmetric perturbations

Friedman et al. (1988) have shown that a version of the turning-point method going back to Poincaré (1885), who investigated the stability of Newtonian equilibrium configurations (cf. Subsection 3.3.1), can be used to locate points along sequences of relativistic figures of equilibrium at which secular instability with respect to axisymmetric perturbations sets in, see also Thorne (1967).

The theory of figures of equilibrium of rotating, self-gravitating fluids was developed in the context of questions concerning the shape of the Earth and celestial bodies. Many famous physicists and mathematicians such as Newton, Maclaurin, Jacobi, Liouville, Dirichlet, Dedekind, Riemann, Roche, Poincaré, H. Cartan, Lichtenstein and Chandrasekhar made important contributions. Within Newton's theory of gravitation, the shape of the body can be inferred from the requirement that the force arising from pressure, the gravitational force and the centrifugal force (in the corotating frame) be in equilibrium. Basic references are the books by Lichtenstein (1933) and Chandrasekhar (1969).

Our intention with the present book is to treat the general relativistic theory of equilibrium configurations of rotating fluids. This field of research is also motivated by astrophysics: neutron stars are so compact that Einstein's theory of gravitation must be used for calculating the shapes and other physical properties of these objects. However, as in the books mentioned above, which inspired this book to a large extent, we want to present the basic theoretical framework and will not go into astrophysical detail. We place emphasis on the rigorous treatment of simple models instead of trying to describe real objects with their many complex facets, which by necessity would lead to ephemeral and inaccurate models.

The basic equations and properties of equilibrium configurations of rotating fluids within general relativity are described in Chapter 1.