The specific frequency and the globular cluster formation efficiency in Milgromian dynamics

Previous studies of globular cluster (GC) systems show that there appears to be a universal specific GC formation efficiency $\eta$ which relates the total mass of GCs to the virial mass of host dark matter halos, $M_{vir}$ (Georgiev et al 2010, Spitler & Forbes2009). In this paper, the specific frequency, $S_N$, and specific GC formation efficiency, $\eta$, are derived as functions of $M_{vir}$ in Milgromian dynamics, i.e., in modified Newtonian dynamics (MOND). In Milgromian dynamics, for the galaxies with GCs, the mass of the GC system, $M_{GC}$, is a two-component function of $M_{vir}$ instead of a simple linear relation. An observer in a Milgromian universe, who interprets this universe as being Newtonian/Einsteinian, will incorrectly infer a universal constant fraction between the mass of the GC system and a (false) dark matter halo of the baryonic galaxy. In contrast to a universal constant of $\eta$, in a Milgromian universe, for galaxies with $M_{vir}<={10}^{12}\text{msun}$, $\eta$ decreases with the increase of $M_{vir}$, while for massive galaxies with $M_{vir}>{10}^{12}\text{msun}$, $\eta$ increases with the increase of $M_{vir}$.