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 (HIRES) 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
HST/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 (LRIS) at the Keck II telescope. We find a mean cluster velocity
of 72.55+/-0.22 km/s and a velocity dispersion of 0.87+/-0.18 km/s. The global
mass function of the cluster, in the mass range 0.55<=M<=0.85 M_solar, is
shallower than a Kroupa mass function and the cluster is significantly depleted
in low-mass stars in its center 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 29800 M_solar. 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.
