Bias, redshift space distortions and primordial nongaussianity of nonlinear transformations: application to Lyman alpha forest

TL;DR

This paper develops analytic expressions for biases introduced by nonlinear transformations of matter density, applies them to the Lyman-alpha forest, and explores implications for primordial nongaussianity and large-scale structure measurements.

Contribution

It derives general formulas for bias and velocity bias from nonlinear transformations, linking them to the PDF of the final field, and applies these to Lyman-alpha forest modeling.

Findings

Predicted velocity bias of -0.1 at z=2.4 matches observations.

Bias and nongaussianity bias depend on transformation parameters.

Model can match observed biases and constrain primordial nongaussianity.

Abstract

On large scales a nonlinear transformation of matter density field can be viewed as a biased tracer of the density field itself. A nonlinear transformation also modifies the redshift space distortions in the same limit, giving rise to a velocity bias. In models with primordial nongaussianity a nonlinear transformation generates a scale dependent bias on large scales. We derive analytic expressions for these for a general nonlinear transformation. These biases can be expressed entirely in terms of the one point distribution function (PDF) of the final field and the parameters of the transformation. Our analysis allows one to devise nonlinear transformations with nearly arbitrary bias properties, which can be used to increase the signal in the large scale clustering limit. We apply the results to the ionizing equilibrium model of Lyman-alpha forest, in which Lyman-alpha flux F is related to the density perturbation delta via a nonlinear transformation. Velocity bias can be expressed as an average over the Lyman-alpha flux PDF. At z=2.4 we predict the velocity bias of -0.1, compared to the observed value of -0.13 +/- 0.03. Bias and primordial nongaussianity bias depend on the parameters of the transformation. Measurements of bias can thus be used to constrain these parameters, and for reasonable values of the ionizing background intensity we can match the predictions to observations. Matching to the observed values we predict the ratio of primordial nongaussianity bias to bias to have the opposite sign and lower magnitude than the corresponding values for the highly biased galaxies, but this depends on the model parameters and can also vanish or change the sign.