Testing quasi-linear modified Newtonian dynamics theory with Galactic globular clusters in a weak external field

We developed self-consistent dynamical models of stellar systems in the framework of quasi-linear modified Newtonian dynamics (QUMOND). The models are constructed from the anisotropic distribution function of Gunn and Griffin, combined with the modified Poisson equation defining this gravitation theory and take into account the external field effect. We have used these models, and their Newtonian analogues, to fit the projected density and the velocity dispersion profiles of a sample of 18 Galactic globular clusters, using the most updated data sets of radial velocities and Gaia proper motions. We have thus obtained, for each cluster, estimates of the dynamical mass-to-light ratio (M/L) for each theory of gravity. The selected clusters have accurate proper motions and a well-sampled mass function down to the very low-mass regime. This allows us to constrain the degree of anisotropy and to provide, from comparison with stellar evolution isochrones, a dynamics-independent estimate of the minimum mass-to-light ratio (M/L)(min). Comparing the best-fitting dynamical M/L with (M/L)(min), we find that for none of the analysed clusters the two gravity theories are significantly incompatible with the observational data, although for one of them (NGC 5024) the dynamical M/L predicted by QUMOND lies at 2.8 & sigma; below (M/L)(min). Though the proposed approach suffers from some limitations (in particular the lack of a treatment of mass segregation), the obtained results suggest that the kinematics of globular clusters in a relatively weak external field can be a powerful tool to prove alternative theories of gravitation.

Automated summary

We developed self-consistent dynamical models of stellar systems using quasi-linear modified Newtonian dynamics (QUMOND). These models were constructed by combining the anisotropic distribution function of Gunn and Griffin with the modified Poisson equation defining this theory of gravitation, taking into account the external field effect. By fitting the density and velocity dispersion profiles of 18 Galactic globular clusters, we obtained estimates of the dynamical mass-to-light ratio (M/L) for each gravity theory. Comparison with stellar evolution isochrones provided a dynamics-independent estimate of the minimum mass-to-light ratio (M/L)(min). The results suggest that the kinematics of globular clusters in a weak external field can be a powerful tool to test alternative theories of gravitation.