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We present new BVRIbroadband photometry for the old open cluster NGC 188, based on an analysis of 299 CCD images either obtained by us, donated by colleagues, or retrieved from public archives. We compare our results on a star-by-star basis with data from 11 previous photometric data sets for the cluster. We homogenize and merge the data from all the photometric studies, and also merge membership probabilities from four previous proper-motion studies of the cluster field. Fiducial cluster sequences in the BV(Johnson) RI(Cousins) photometric system of Landolt (1993, AJ, 104, 340) represent the principal result of this paper. These are compared to reference samples defined by (1) Landolt's standard stars, (2) the old open clusters M67 and NGC 6791, and (3) stars within 25 pc having modern photometry and precise Hipparcosparallaxes. In a companion paper, we show that our derived cluster results agree well with the predictions of modern stellar interior and evolution theory, given reasonable estimates of the cluster chemical abundances and foreground reddening. The individual and combined data sets for NGC 188 have been made available through our Web site.

Evolutionary models taking into account radiative accelerations, thermal diffusion, and gravitational settling for 28 elements, including all those contributing to OPAL stellar opacities, have been calculated for solar metallicity stars of 0.5-1.4 M. The Sun has been used to calibrate the models. Isochrones are fitted to the observed color-magnitude diagrams (CMDs) of M67 and NGC 188, and ages of 3.7 and 6.4 Gyr are respectively determined. Convective core overshooting is not required to match the turnoff morphology of either cluster, including the luminosity of the gap in M67, because central convective cores are larger when diffusive processes are treated. This is due mainly to the enhanced helium and metal abundances in the central regions of such models. The observation of solar metallicity open clusters with ages in the range of 4.8-5.7 Gyr would further test the calculations of atomic diffusion in central stellar regions: according to nondiffusive isochrones, clusters should not have gaps near their main-sequence turnoffs if they are older than [?]4.8 Gyr, whereas diffusive isochrones predict that gaps should persist up to ages of [?]5.7 Gyr. Surface abundance isochrones are also calculated. In the case of M67 and NGC 188, surface abundance variations are expected to be small. Abundance differences between stars of very similar Teff are expected close to the turnoff, especially for elements between P and Ca. Moreover, in comparison to the results obtained for giants, small generalized underabundances are expected in main-sequence stars. The Li/Be ratio is discussed briefly and compared with observations. The inclusion of a turbulent transport parameterization that reduces surface abundance variations does not significantly modify the computed isochrones.

We review the history of the discovery of field subgiant stars, the role that they played in the development of the early understanding of stellar evolution, and their importance in the age dating of the Galactic disk. We use the cataloged data from the Hipparcossatellite in this latter capacity.

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.

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 [a/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 Galaxy's 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.

Stellar evolutionary tracks have been computed for 17 [Fe/H] values from -2.31 to -0.30 assuming, in each case, [a/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 [a/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 a-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 [a/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 a-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 s error bars of the mean MV's inferred for RR Lyrae stars from Baade-Wesselink, statistical parallax, and trigonometric parallax studies. Lower helium contents or higher a-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.