We use the distant outer halo globular cluster Palomar 14 as a test case for classical vs. modified Newtonian dynamics ( MOND ) .
Previous theoretical calculations have shown that the line-of-sight velocity dispersion predicted by these theories can differ by up to a factor of three for such sparse , remote clusters like Pal 14 .
We determine the line-of-sight velocity dispersion of Palomar 14 by measuring radial velocities of 17 red giant cluster members obtained using the Very Large Telescope ( VLT ) and Keck telescope .
The systemic velocity of Palomar 14 is ( 72.28 ~ { } \pm~ { } 0.12 ) km s ^ { -1 } .
The derived velocity dispersion of ( 0.38 \pm 0.12 ) km s ^ { -1 } of the 16 definite member stars is in agreement with the theoretical prediction for the classical Newtonian case according to Baumgardt et al .
( 5 ) .
In order to exclude the possibility that a peculiar mass function might have influenced our measurements , we derived the cluster ’ s main sequence mass function down to 0.53 M _ { \odot } using archival images obtained with the Hubble Space Telescope .
We found a mass function slope of \alpha = 1.27 \pm 0.44 , which is , compared to the canonical mass function , a significantly shallower slope .
The derived lower limit on the cluster ’ s mass is higher than the theoretically predicted mass in case of MOND .
Our data are consistent with a central density of \rho _ { 0 } = 0.1 M _ { \odot } pc ^ { -3 } .
We need no dark matter in Palomar 14 .
If the cluster is on a circular orbit , our spectroscopic and photometric results argue against MOND , unless this cluster experienced significant mass loss .