Don A. Vandenberg

Models for Old, Metal-poor Stars with Enhanced α-Element Abundances. I. Evolutionary Tracks and ZAHB Loci; Observational Constraints

Stellar evolutionary tracks have been computed for 17 [Fe/H] values from -2.31 to -0.30 assuming, in each case, [?/Fe] = 0.0, 0.3, and 0.6. The helium abundance was assumed to vary from Y = 0.2352 at [Fe/H] = -2.31 to Y = 0.2550 at [Fe/H] = -0.30 and held constant for the different choices of [?/Fe] at a fixed iron content. Masses in the range 0.5 ? ? ? 1.0, in 0.1 ? steps, were generally considered, though sequences for higher mass values were computed, as necessary, to ensure that isochrones as young as 8 Gyr could be generated for each grid. All of the stellar models are based on an equation of state that treats nonideal effects, the latest nuclear reaction and neutrino cooling rates, and opacities that were computed specifically for the adopted chemical mixtures. The tracks were extended to the tip of the giant branch or to an age of 30 Gyr, whichever came first, and zero-age horizontal-branch (ZAHB) loci were constructed using the helium core masses and chemical profiles from appropriate red giant precursors. Selected models have been compared with those computed by A. V. Sweigart, for the same masses and chemical compositions, to demonstrate that the results obtained from two entirely independent stellar evolution codes agree well with one another when very similar input physics is assumed. In the case of extremely metal-deficient stars, an enhancement in the abundance of the ?-elements causes a single, fairly significant bump in the opacity at a temperature just above 106 K, which is caused by absorption processes involving the K shell of oxygen. This peak becomes steadily more pronounced as the overall metallicity increases and a second bump, arising from the L edges of Ne, Mg, and Si, eventually appears near log T = 5.6. As far as the tracks and isochrones are concerned, we find that, as already reported by others, it is possible to mimic the computations for [?/Fe] > 0 remarkably well by those for scaled-solar mixes simply by requiring the total mass-fraction abundance of the heavy elements, Z, to be the same. However, this result holds only for metallicities significantly less than solar. Above [Fe/H] -0.8, tracks and isochrones for enhanced ?-element mixtures begin to have systematically hotter/bluer turnoffs and red giant branches than those for scaled-solar mixtures of the heavy elements. Also addressed is the extent to which our models satisfy the constraints posed by the local subdwarfs, the distances of which are based on Hipparcos parallax measurements. Our analysis suggests that the predicted metallicity dependence of the location of the lower main sequence on the C-M diagram is in good agreement with the observed dependence. In fact, we do not find any compelling evidence from the local Population II calibrators that the colors of our models require significant adjustments. In further support of our calculations, we find that, both in zero point and slope, the computed giant branches on the (Mbol, log Teff)-plane agree well with those inferred for globular clusters from observations in the infrared. Moreover, our ZAHB models have luminosities that are just outside the 1 ? error bars of the mean MVs inferred for RR Lyrae stars from Baade-Wesselink, statistical parallax, and trigonometric parallax studies. Lower helium contents or higher ?-element abundances or an increase in the conductive opacities are among the possible ways of reducing the differences that remain. To facilitate comparisons with observations, the tracks/ZAHBs are provided with predicted BV(RI)C photometry.

The Victoria-Regina Stellar Models: Evolutionary Tracks and Isochrones for a Wide Range in Mass and Metallicity that Allow for Empirically Constrained Amounts of Convective Core Overshooting*

Seventy-two grids of stellar evolutionary tracks, along with the means to generate isochrones and luminosity/color functions from them, are presented in this investigation. Sixty of them extend (and encompass) the sets of models reported by VandenBerg et al. for 17 [Fe/H] values from -2.31 to -0.30 and ?-element abundances corresponding to [?/Fe] = 0.0, 0.3, and 0.6 (at each iron abundance) to the solar metallicity and to sufficiently high masses (up to ~2.2 M?) that isochrones may be computed for ages as low as 1 Gyr. The remaining grids contain tracks for masses from 0.4 to 4.0 M? and 12 [Fe/H] values between -0.60 and +0.49 (assuming solar metal-to-hydrogen number abundance ratios): in this case, isochrones may be calculated down to ~0.2 Gyr. The extent of convective core overshooting has been modeled using a parameterized version of the Roxburgh criterion, in which the value of the free parameter at a given mass and its dependence on mass have been determined from analyses of binary star data and the observed color-magnitude diagrams for several open clusters. Because the calculations reported herein satisfy many empirical constraints, they should provide useful probes into the properties of both simple and complex stellar populations.

A Lack of Planets in 47 Tucanae from a Hubble Space Telescope Search

We report results from a large Hubble Space Telescope project to observe a significant (~34,000) ensemble of main-sequence stars in the globular cluster 47 Tucanae with a goal of defining the frequency of inner orbit, gas giant planets. Simulations based on the characteristics of the 8.3 days of time series data in the F555W and F814W Wide Field Planetary Camera 2 (WFPC2) filters show that ~17 planets should be detected by photometric transit signals if the frequency of hot Jupiters found in the solar neighborhood is assumed to hold for 47 Tuc. The experiment provided high-quality data sufficient to detect planets. A full analysis of these WFPC2 data reveals ~75 variables, but no light curves resulted for which a convincing interpretation as a planet could be made. The planet frequency in 47 Tuc is at least an order of magnitude below that for the solar neighborhood. The cause of the absence of close-in planets in 47 Tuc is not yet known; presumably the low metallicity and/or crowding of 47 Tuc interfered with planet formation, with orbital evolution to close-in positions, or with planet survival.

Oxygen-enhanced models for globular cluster stars. II: Isochrones and luminosity functions

Isochrones and luminosity functions (LFs) on the BV photometric system have been constructed for ages from 10 to 18 Gyr for each of the seven values of [Fe/H] = -2.26, -2.03, -1.78, - 1.66, -1.48, -1.26, and -1.03, and for ages from 5 to 18 Gyr for [Fe/H] = -0.78, -0.65, and -0.47. The loci for ages of 10 Gyr or more have been provided mainly for application to photometry of the Galactic globular clusters (GCs); the rest should be useful for interpreting data for old, metal-poor open clusters. Oxygen-to-iron ratios have been assumed that closely follow the relation [O/Fe] = -0.5 [Fe/H], for [Fe/H] ≥ -1.0, and [O.Fe] = -0.2 [Fe/H] + 0.3, for lower iron abundances

Empirically Constrained Color-Temperature Relations. I. BV(RI)C

This investigation presents a set of transformations to Johnson B-V, Cousins V-R, and Cousins V-I, as well as bolometric corrections to V, for [Fe/H] = -3, -2, -1, -0.5, 0.0, and +0.3 and, in each case, values of log g from -0.5 to 5.0 for 3000 K ≤ Teff ≤ 5500 K and from 2.0 to 5.0 for 6000 K ≤ Teff ≤ 40,000 K. These transformations employ the predictions from Kurucz model atmospheres at high temperatures (Teff ≥ 8000 K) and from MARCS model atmospheres at intermediate temperatures (from 7000 K down to a temperature in the range 4000 K ≤ Teff ≤ 5500 K, depending on [Fe/H], where adjustments to satisfy observational constraints become necessary). Thus, theoretical color-Teff relations are used exclusively down to a minimum temperature that is cooler than the temperatures of turnoff stars in open and globular star clusters. To better represent the color transformations obeyed by cool stars (down to 3000 K), corrections to the synthetic transformations have been determined from a careful consideration of observations for a few globular clusters (M92, M68, and 47 Tucanae), the color-magnitude diagrams (CMDs) of several open clusters (M67, the Pleiades, the Hyades, and NGC 6791), the CMDs and mass-luminosity diagram for solar neighborhood stars having good distance measurements from Hipparcos, empirical (B-V)-Teff and (V-K)-Teff relations, and color-color diagrams for field giants. The semiempirical color transformations that have been produced as a result of our analysis are also compared with several others that have been published in recent years: some of the deficiencies of the latter are revealed.

Models for Old, Metal-poor Stars with Enhanced α-Element Abundances. III. Isochrones and Isochrone Population Functions

An isochrone population function (IPF) gives the relative distribution of stars along an isochrone. IPFs contain the information needed to calculate both luminosity functions and color functions, and they provide a straightforward way of generating synthetic stellar populations. An improved algorithm for interpolating isochrones and IPFs, based on the scheme introduced by Bergbusch & VandenBerg, is described. Software has been developed to permit such interpolations for any age encompassed by an input grid of stellar evolutionary tracks. Our first application of this software is to the models presented in this series of papers for 17 [Fe/H] values between -2.31 and -0.3, with three choices of [α/Fe] at each iron abundance (specifically, 0.0, 0.3, and 0.6). (These models do not treat gravitational settling or radiative acceleration processes, but otherwise they are based on up-to-date physics. Additional grids will be added to this database as they are completed.) The computer programs (written in FORTRAN 77) and the grids of evolutionary tracks that are presently available for processing by these codes into isochrones and IPFs are freely available to interested users. In addition, we add to the evidence presented in previous papers in this series in support of the Teff and color scales of our models. In particular, the temperatures derived by Gratton et al. for local Population II subdwarfs with accurate (Hipparcos) parallaxes are shown to be in excellent agreement with those predicted for them, when the Gratton et al. [Fe/H] scale is also assumed. Interestingly, the locus defined by local subdwarfs and subgiants on the (MV, log Teff)-plane and the morphologies of globular cluster (GC) color-magnitude diagrams are well matched by the present models, despite the neglect of diffusion, which suggests that some other process(es) must be at play to limit the expected effects of gravitational settling on predicted temperatures. The three field halo subgiants in our sample all appear to have ages 15 Gyr, which is favored for the Galaxys most metal-poor GCs as well. (The settling of helium and heavy elements in the central regions of stars is expected to cause about a 10% reduction in these age estimates: this effect should persist even if some process, such as turbulence at the base of the convective envelope, counteracts diffusion in the surface layers.) Furthermore, our isochrones accurately reproduce the Da Costa & Armandroff red giant branch fiducials for M15, NGC 6752, NGC 1851, and 47 Tuc on the [MI, (V-I)0]-diagram. However, our models fail to predict the observed luminosities of the red giant bump by ≈0.25 mag: this could be an indication that there is some amount of inward overshooting of convective envelopes in red giants. For consistency reasons, the Zinn & West metallicities for intermediate metal-poor GCs (-1.8 [Fe/H] -1.1) seem to be preferred over recent spectroscopic results (based on the brightest cluster giants), suggesting that there is an inconsistency between current subdwarf and GC [Fe/H] scales.

THE QUENCHING OF THE ULTRA-FAINT DWARF GALAXIES IN THE REIONIZATION ERA ∗

We present new constraints on the star formation histories of six ultra-faint dwarf galaxies: Bootes I, Canes Venatici II, Coma Berenices, Hercules, Leo IV, and Ursa Major I. Our analysis employs a combination of high-precision photometry obtained with the Advanced Camera for Surveys on the Hubble Space Telescope, medium-resolution spectroscopy obtained with the DEep Imaging Multi-Object Spectrograph on the W.M. Keck Observatory, and updated Victoria-Regina isochrones tailored to the abundance patterns appropriate for these galaxies. The data for five of these Milky Way satellites are best fit by a star formation history where at least 75% of the stars formed by z~10 (13.3 Gyr ago). All of the galaxies are consistent with 80% of the stars forming by z~6 (12.8 Gyr ago) and 100% of the stars forming by z~3 (11.6 Gyr ago). The similarly ancient populations of these galaxies support the hypothesis that star formation in the smallest dark matter sub-halos was suppressed by a global outside influence, such as the reionization of the universe.

Measuring age differences among globular clusters having similar metallicities - A new method and first results

A color-difference technique for estimating the relative ages of globular clusters with similar chemical compositions on the basis of their CM diagrams is described and demonstrated. The theoretical basis and implementation of the procedure are explained, and results for groups of globular clusters with m/H = about -2, -1.6, and -1.3, and for two special cases (Palomar 12 and NGC 5139) are presented in extensive tables and graphs and discussed in detail. It is found that the more metal-deficient globular clusters are nearly coeval (differences less than 0.5 Gyr), whereas the most metal-rich globular clusters exhibit significant age differences (about 2 Gyr). This result is shown to contradict Galactic evolution models postulating halo collapse in less than a few times 100 Myr. 77 refs.

Models of Metal-poor Stars with Gravitational Settling and Radiative Accelerations. I. Evolution and Abundance Anomalies

Evolutionary models have been calculated for Population II stars of 0.5-1.0 M? from the pre-main sequence to the lower part of the giant branch. Rosseland opacities and radiative accelerations were calculated taking into account the concentration variations of 28 chemical species, including all species contributing to Rosseland opacities in the OPAL tables. The effects of radiative accelerations, thermal diffusion, and gravitational settling are included. While models were calculated for both Z = 0.00017 and 0.0017, we concentrate on models with Z = 0.00017 in this paper. These are the first Population II models calculated taking radiative acceleration into account. It is shown that, at least in a 0.8 M? star, it is a better approximation not to let Fe diffuse than to calculate its gravitational settling without including the effects of grad(Fe). In the absence of any turbulence outside of convection zones, the effects of atomic diffusion are large mainly for stars more massive than 0.7 M?. Overabundances are expected in some stars with Teff ? 6000 K. Most chemical species heavier than CNO are affected. At 12 Gyr, overabundance factors may reach 10 in some cases (e.g., for Al or Ni), while others are limited to 3 (e.g., for Fe). The calculated surface abundances are compared to recent observations of abundances in globular clusters as well as to observations of Li in halo stars. It is shown that, as in the case of Population I stars, additional turbulence appears to be present. Series of models with different assumptions about the strength of turbulence were then calculated. One series minimizes the spread on the Li plateau, while another was chosen with turbulence similar to that present in AmFm stars of Population I. Even when turbulence is adjusted to minimize the reduction of Li abundance, there remains a reduction by a factor of at least 1.6 from the original Li abundance. Independent of the degree of turbulence in the outer regions, gravitational settling of He in the central region reduces the lifetime of Population II stars by 4%-7% depending on the criterion used. The effect on the age of the oldest clusters is discussed in a forthcoming paper (Paper II). Just as in Population I stars where only a fraction of stars, such as AmFm stars, have abundance anomalies, one should look for the possibility of abundance anomalies of metals in some Population II turnoff stars but not necessarily in all. Expected abundance anomalies are calculated for 28 species and compared to observations of M92 as well as to Li observations in halo field stars.

Age and helium content of the open cluster NGC 6791 from multiple eclipsing binary members - II. Age dependencies and new insights

Context. Models of stellar structure and evolution can be constrained by measuring accurate parameters of detached eclipsing binaries in open clusters. Multiple binary stars provide the means to determine helium abundances in these old stellar systems, and in turn, to improve estimates of their age. Aims. In the first paper of this series, we demonstrated how measurements of multiple eclipsing binaries in the old open cluster NGC6791 sets tighter constraints on the properties of stellar models than has previously been possible, thereby potentially improving both the accuracy and precision of the cluster age. Here we add additional constraints and perform an extensive model comparison to determine the best estimates of the cluster age and helium content, employing as many observational constraints as possible. Methods. We improve our photometry and correct empirically for differential reddening effects. We then perform an extensive comparison of the new colour-magnitude diagrams (CMDs) and eclipsing binary measurements to Victoria and DSEP isochrones in order to estimate cluster parameters. We also reanalyse a spectrum of the star 2‐17 to improve [Fe/H] constraints. Results. Wefind abest estimateof theage of ∼8.3Gyr for NGC6791 whiledemonstrating that remaining age uncertainty is dominated by uncertainties in the CNO abundances. The helium mass fraction is well constrained at Y = 0.30 ± 0.01 resulting in ΔY/ΔZ ∼1.4 assuming that such a relation exists. During the analysis we firmly identify blue straggler stars, including the star 2‐17, and find indications for the presence of their evolved counterparts. Our analysis supports the RGB mass-loss found from asteroseismology and we determine precisely the absolute mass of stars on the lower RGB, MRGB = 1.15 ± 0.02 M� . This will be an important consistency check for the detailed asteroseismology of cluster stars. Conclusions. Using multiple, detached eclipsing binaries for determining stellar cluster ages, it is now possible to constrain parameters of stellar models, notably the helium content, which were previously out of reach. By observing a suitable number of detached eclipsing binaries in several open clusters, it will be possible to calibrate the age-scale and the helium enrichment parameter ΔY/ΔZ, and provide firm constraints that stellar models must reproduce.