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 \sim 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 \pm 0.22 { km s ^ { -1 } } and a velocity dispersion of 0.87 \pm 0.18 { km s ^ { -1 } } .
The global mass function of the cluster , in the mass range 0.55 \leq \mathrm { M } \leq 0.85 M _ { \odot } , 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 29,800 M _ { \odot } .
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 .