Linking halo mass to galaxy luminosity

In this paper we present a new, essentially empirical, model for the relation between the mass of a dark matter halo/subhalo and the luminosity of a galaxy hosted in it. To estimate this, we replace the assumption of linearity between light and mass fluctuations with the assumption of monotonicity between galaxy light and halo or subhalo mass. We are enabled to proceed with this less restrictive ansatz by the availability of new, very high resolution dark matter simulations and more detailed and comprehensive global galactic luminosity functions. We find that the relation between halo/subhalo mass and hosted galaxy luminosity is fairly well fit by a double power law, while that between halo mass and group luminosity is fairly well fit by a two branch function, with both branches double power laws. Both relations asymptote to $L\propto M^4$ at low $M$, while at high mass the former follows $L\propto M^{0.28}$ and the latter $L\propto M^{0.9}$. We also derive results for the occupation number, luminosity function of cluster galaxies, group luminosity function and multiplicity function. Then, using some additional assumptions, we further derive results for biasing between mass and light and mass and galaxy number, light distribution function and the void probability distribution. Our results for the most part seem to match well with observations and previous expectations. We feel this is a potentially powerful way of modelling this relation, since the main inputs are readily testable against dark matter simulation results and galaxy surveys. (abridged)