On the link between nuclear star cluster and globular cluster system mass, nucleation fraction, and environment

We present a simple model for the host mass dependence of galaxy nucleation fraction ($f_{nuc}$), galaxy's nuclear star cluster (NSC) and in its surviving globular clusters ($M_{GC,obs}$). Considering orbital evolution GC potential, we define critical limit ($M_{GC,lim}$) above which can simultaneously in-spiral to centre due dynamical friction survive tidal dissolution, build up NSC. The analytic expression this threshold allows us populations galaxies. find that slope curvature initial size-mass relation is most important factor (with shape function secondary effect) setting galaxies are nucleated at given mass. well defined skew-normal $f_{nuc} - M_{gal}$ observations naturally reproduced these models, provided there an inflection {initial} $M_{gal} \sim 10^{9.5} {\rm M_{\odot}}$. Our also predicts limits M_{GC,tot}$ M_{NSC}$ relations bound scatter observational data. Moreoever, illustrate how scaling $f_{nuc}$ vary if formation efficiency, function, environment or altered. Two key predictions our are: 1) with NSC masses greater than their system more compact fixed stellar mass, 2) higher denser environments. That single framework reproduce both provides strong evidence mechanism formation.