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 prole based on the WFPC2 data and on broad-band imaging with the Low-Resolution Imaging Spectrometer (LRIS) at the Keck II telescope. We nd 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 6 M 6 0:85 M , is shallower than a Kroupa mass function and the cluster is signicantly 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 29,800 M . For this mass, the measured velocity dispersion is consistent with the expectations of Newtonian dynamics and below the prediction of 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.