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

Abstract

Previous studies of globular cluster (GC) systems show that there appears to be a universal specific GC formation efficiency η which relates the total mass of GCs to the virial mass of host dark matter haloes, Mvir. In this paper, the specific frequency, SN, and specific GC formation efficiency, η, are derived as functions of Mvir in Milgromian dynamics, i.e. in modified Newtonian dynamics. In Milgromian dynamics, for the galaxies with GCs, the mass of the GC system, MGC, is a two-component function of Mvir 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 η, in a Milgromian universe, for galaxies with Mvir ≤ 1012 M⊙, η decreases with the increase of Mvir, while for massive galaxies with Mvir > 1012 M⊙, η increases with the increase of Mvir.