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 ∼ 28 mag using archival Hubble Space Telescope/Wide Field Planetary Camera 2 (WFPC2) imaging. We derived the cluster’s 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.