Estimating non-gaussian bias using counts of tracers

Local-type primordial non-gaussianity generates a distinctive term in the clustering of tracers of large-scale structure, behaving as $k^{-2}$ at small wavenumbers $k$. In order to use this signal in a sample of galaxies to measure the amplitude of primordial non-gaussianity, $f_{NL}$, we need to independently determine the degenerate bias coefficient, $b_\Phi$, which quantifies the logarithmic response of the galaxy number density to a change in amplitude of the matter clustering. We study whether $b_\Phi$ may be estimated from the observed evolution of the number density of galaxies as a function of redshift. Using cosmological N-body simulations, we find that $b_\Phi$ may be estimated reasonably well for dark matter halos across the range of redshifts and halo masses used by large-scale structure surveys aimed at measuring $f_{NL}$. This includes non-gaussian secondary bias (or assembly bias) in halo concentration, which has previously been found to be quite large in amplitude. For an observed survey of galaxies, we additionally need to consider the selection function of the sample, which can introduce redshift dependence via cuts on apparent magnitude and colour. These effects of the selection function can be mitigated by further cutting the sample using k-corrected magnitudes and colours, to retain only those galaxies that would pass the targeting criteria for all redshifts within the interval considered.