Accurate Internal Proper Motions of Globular Clusters

We have undertaken a long term program to measure high precision proper motions of nearby Galactic globular cluster (GC) stars using multi-epoch observations with the WFPC2 and the ACS cameras on-board the Hubble Space Telescope. The proper motions are used to study the internal cluster kinematics, and to obtain accurate cluster distances. In this paper, we also show how the proper motions of the field stars projected in the direction of the studied clusters can be used to set constraints on the Galaxy kinematics. 1. Proper Motions in the Field of M4 Some of us have recently developed a method (Anderson and King, 2000, 2003), based on multi-epoch HST images, which allows us to derive very accurate proper motions. The key to our success is the removal of systematic errors of many types from our astrometry. Presently, we are able to measure the position of a well exposed star in a single image with a precision of 0.02 pixel, i.e. 2 mas in the WFs, 1 mas in the PC. Multiple observations allow to reduce this uncertainty of a factor √ N , where N is the number of frames. 1.1. The Internal Proper Motion of M4 and its Distance The internal proper motions of M4 is ∼0.50 mas/yr. This means that with our 8 frames in each of two epochs, and with a time baseline of ∼5 yrs, we can reach a precision of ∼0.2 mas/yr. We can then subtract, in quadrature, the distribution of the errors to the observed distribution, and have a precise measure of the internal dipersion of proper motions. Figure 1 shows some preliminary results. We plan to furtherly improve the proper motions of M4 stars by the reducing the third epoch WF@ACS images which overlap with our fields. We have recently undertaken a program aimed at obtaining radial velocities for stars located in the same radial interval and in the same magnitude