Globular clusters (GCs) have the potential to bring light in the missing mass problem. It has been argued earlier that dark matter halos of dwarf galaxies must have central cores, to prevent their GCs to quickly settle into their galaxy nuclei: the time necessary for dynamical friction to remove their GC's energy and angular momentum would come out less than the age of the clusters if the halos were cuspy. The sunk GCs would form nuclear star clusters. It was found analytically that the problem of fast GC sinking is even more severe for MOND, a leading alternative to dark matter that otherwise well reproduces galaxy dynamics. The problem was anticipated for low-mass low-surface-brightness galaxies. We inspected the issue using high-resolution simulations. We initially investigated GCs of gas-free ultra-diffuse galaxies. We found that first GCs indeed approach the center of their host galaxy quickly, but then, once the GC moves within the central half effective radius of the galaxy, the sinking almost stops, opposing the analytic predictions. This comes from simplifying assumptions made when deriving analytically the dynamical friction effect. Actually, the phenomenon called core stalling occurs, that had previously been described in Newtonian gravity and is the reason why GCs can survive for a long time in cored dark matter halos. Next, we explored the consistency of MOND with the existence of GCs in isolated dwarf galaxies. These disky galaxies hold a large fraction of their baryons in the form of gas. We found that a GC can indeed spiral quickly into the center. However, if the supernova explosion rate is sufficient, then the GC has no problem to survive for a Hubble time, since the supernova explosions cause strong fluctuations in the gravitational potential of the galaxy, such that they give the GC random pushes.
Can the observation of globular clusters in low-mass galaxies exclude the MOND modified gravity theory?