Constraints on the Effects of Locally Biased Galaxy Formation

While it is well known that {open_quotes}biased galaxy formation{close_quotes} can increase the strength of galaxy clustering, it is less clear whether straightforward biasing schemes can change the {ital shape} of the galaxy correlation function on large scales. Here we consider {open_quotes}local{close_quotes} biasing models, in which the galaxy density field {delta}{sub {ital g}} at a point {ital x} is a function of the matter-density field {delta} at that point: {delta}{sub {ital g}} = {ital f}({delta}). We consider both deterministic biasing, where {ital f} is simply a function, and stochastic biasing, in which the galaxy-density {delta}{sub {ital g}} is a random variable whose distribution depends on the matter density: {delta}{sub {ital g}} = {ital X}({delta}). We show that even when this mapping is performed on a highly nonlinear density field with a hierarchical correlation structure, the correlation function {xi} is simply scaled up by a constant, as long as {xi} {lt} 1. In stochastic biasing models, the galaxy autocorrelation function behaves exactly as in deterministic models, with {ovr X}({delta}) (the mean value of {ital X} for a given value of {delta}) taking the role of the deterministic bias function. We extend our results to the power spectrum {ital P}({ital k}), showing that for sufficiently small {ital k} the effect of local biasing is equivalent to the multiplication of {ital P}({ital k}) by a constant, with the addition of a constant term. If a cosmological model predicts a large-scale mass correlation function in conflict with the shape of the observed galaxy correlation function, then the model cannot be rescued by appealing to a complicated but local relation between galaxies and mass. {copyright} {ital {copyright} 1998.} {ital The American Astronomical Society}