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 haloes, M-vir. 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. 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) M-circle dot, eta decreases with the increase of M-vir, while for massive galaxies with M-vir > 10(12) M-circle dot, eta increases with the increase of M-vir.