On Recovering the Nonlinear Bias Function from Counts‐in‐Cells Measurements

We present a simple and accurate method to constrain galaxy bias based on thedistribution of counts in cells. The most unique feature of our technique isthat it is applicable to non-linear scales, where both dark matter statisticsand the nature of galaxy bias are fairly complex. First, we estimate theunderlying continuous distribution function from precise counts-in-cellsmeasurements assuming local Poisson sampling. Then a robust, non-parametricinversion of the bias function is recovered from the comparison of thecumulative distributions in simulated dark matter and galaxy catalogs.Obtaining continuous statistics from the discrete counts is the most delicatenovel part of our recipe. It corresponds to a deconvolution of a (Poisson)kernel. For this we present two alternatives: a model independent algorithmbased on Richardson-Lucy iteration, and a solution using a parametric skewedlognormal model. We find that the latter is an excellent approximation for thedark matter distribution, but the model independent iterative procedure is moresuitable for galaxies. Tests based on high resolution dark matter simulationsand corresponding mock galaxy catalogs show that we can reconstruct thenon-linear bias function down to highly non-linear scales with high precisionin the range of $-1 \le \delta \le 5$. As far as the stochasticity of the bias,we have found a remarkably simple and accurate formula based on Poisson noise,which provides an excellent approximation for the scatter around the meannon-linear bias function. In addition we have found that redshift distortionshave a negligible effect on our bias reconstruction, therefore our recipe canbe safely applied to redshift surveys.Comment: 32 pages, 18 figures; submitted to Ap