We present the first study of high-precision internal proper motions (PMs) in a large sample of globular clusters, based on Hubble Space Telescope (HST) data obtained over the past decade with the ACS/WFC, ACS/HRC, and WFC3/UVIS instruments. We determine PMs for over 1.3 million stars in the central regions of 22 clusters, with a median number of ∼60,000 stars per cluster. These PMs have the potential to significantly advance our understanding of the internal kinematics of globular clusters by extending past line-of-sight (LOS) velocity measurements to two-or three-dimensional velocities, lower stellar masses, and larger sample sizes. We describe the reduction pipeline that we developed to derive homogeneous PMs from the very heterogeneous archival data. We demonstrate the quality of the measurements through extensive Monte-Carlo simulations. We also discuss the PM errors introduced by various systematic effects, and the techniques that we have developed to correct or remove them to the extent possible. We provide in electronic form the catalog for NGC 7078 (M 15), which consists of 77,837 stars in the central 2. ′ 4. We validate the catalog by comparison with existing PM measurements and LOS velocities, and use it to study the dependence of the velocity dispersion on radius, stellar magnitude (or mass) along the main sequence, and direction in the plane of the sky (radial/tangential). Subsequent papers in this series will explore a range of applications in globular-cluster science, and will also present the PM catalogs for the other sample clusters.

We exploit the large number of archival HST images of 47 Tuc to examine its subgiant branch (SGB) and main sequence (MS) for signs of multiple populations. In the cluster core, we find that the cluster's SGB exhibits a clear spread in luminosity, with at least two distinct components: a brighter one with a spread that is real but not bimodal, and a second one about 0.05 mag fainter, containing about 10% of the stars. In a less crowded field 6 ′ from the center, we find that the MS is broadened much more than can be accounted for by photometric errors, and that this broadening increases at fainter magnitudes.

We use 14 orbits of ACS observations to reach the end of the white-dwarf cooling sequence in the globular cluster M4. Our photometry and completeness tests show that the end is located at magnitude m F606W = 28.5 ± 0.1, which implies an age of 11.6 ± 0.6 Gyr (internal errors only). This is consistent with the age from fits to the main sequence turn-off (12.0 ± 1.4 Gyr).

Aims. We present a detailed study of the radial distribution of the multiple populations identified in the Galactic globular cluster ω Cen. Methods. We used both space-based images (ACS/WFC and WFPC2) and ground-based images (FORS1@VLT and WFI@2.2m ESO telescopes) to map the cluster from the inner core to the outskirts (∼20 arcmin). These data sets have been used to extract high-accuracy photometry for the construction of color−magnitude diagrams and astrometric positions of ∼900 000 stars. Results. We find that in the inner ∼2 core radii the blue main sequence (bMS) stars slightly dominate the red main sequence (rMS) in number. At greater distances from the cluster center, the relative numbers of bMS stars with respect to rMS drop steeply, out to ∼8 arcmin, and then remain constant out to the limit of our observations. We also find that the dispersion of the Gaussian that best fits the color distribution within the bMS is significantly greater than the dispersion of the Gaussian that best fits the color distribution within the rMS. In addition, the relative number of intermediate-metallicity red-giant-branch stars (which includes the progeny of the bMS) with respect to the metal-poor component (the progeny of the rMS) follows a trend similar to that of the main-sequence star-count ratio N bMS /N rMS . The most metal-rich component of the red-giant branch follows the same distribution as the intermediatemetallicity component. Conclusions. We briefly discuss the possible implications of the observed radial distribution of the different stellar components in ω Cen.

We use 10 orbits of Advanced Camera for Surveys observations to reach the end of the white dwarf cooling sequence in the solar-metallicity open cluster NGC 2158. Our photometry and completeness tests show that the end falls at magnitude m F606W = 27.5 ± 0.15, which implies an age between ∼1.8 and ∼2.0 Gyr, consistent with the age of 1.9 ± 0.2 Gyr obtained from fits to the main-sequence turn-off. The faintest white dwarfs show a clear turn toward bluer colors, as predicted by theoretical isochrones.Subject headings: open clusters and associations: individual (NGC 2158) -Hertzsprung-Russell diagram -white dwarfs