The velocity dispersion and mass function of the outer halo globular cluster Palomar 4

We obtained precise line-of-sight radial velocities of 23 member stars of the remote halo globular cluster Palomar 4 (Pal 4) using the High Resolution Echelle Spectrograph at the Keck I telescope. We also measured the mass function of the cluster down to a limiting magnitude of V similar to 28 mag using archival Hubble Space Telescope/Wide Field Planetary Camera 2 (WFPC2) imaging. We derived the clusters surface brightness profile based on the WFPC2 data and on broad-band imaging with the Low Resolution Imaging Spectrometer at the Keck II telescope. We find a mean cluster velocity of 72.55 +/- 0.22 km s-1 and a velocity dispersion of 0.87 +/- 0.18 km s-1. The global mass function of the cluster, in the mass range 0.55 =M= 0.85 M?, is shallower than a Kroupa mass function and the cluster is significantly depleted in low-mass stars in its centre compared to its outskirts. Since the relaxation time of Pal 4 is of the order of a Hubble time, this points to primordial mass segregation in this cluster. Extrapolating the measured mass function towards lower mass stars and including the contribution of compact remnants, we derive a total cluster mass of 29 800 M?. For this mass, the measured velocity dispersion is consistent with the expectations of Newtonian dynamics and below the prediction of modified Newtonian dynamics (MOND). Pal 4 adds to the growing body of evidence that the dynamics of star clusters in the outer Galactic halo can hardly be explained by MOND.