Halo bias in Lagrangian space: estimators and theoretical predictions

Abstract

We present several methods to accurately estimate Lagrangian bias parameters and substantiate them using simulations. In particular, we focus on the quadratic terms, both the local and the non local ones, and show the first clear evidence for the latter in the simulations. Using Fourier space correlations, we also show for the first time, the scale dependence of the quadratic and non-local bias coefficients. For the linear bias, we fit for the scale dependence and demonstrate the validity of a consistency relation between linear bias parameters. Furthermore we employ real space estimators, using both cross-correlations and the Peak-Background Split argument. This is the first time the latter is used to measure anisotropic bias coefficients. We find good agreement for all the parameters among these different methods, and also good agreement for local bias with ESPτ theory predictions. We also try to exploit possible relations among the different bias parameters. Finally, we show how including higher order bias reduces the magnitude and scale dependence of stochasticity of the halo field.

Modeling biased tracers at the field level

“…The naive expectation for the large-scale amplitude of P err is that it is close to Poisson noise 1/n ≡ V /N particles , which is expected when randomly sampling the continuous density with pointlike particles. However, the amplitude of the noise measured in simulations is larger than 1/n for low-mass halos, and smaller than 1/n for high-mass halos [7,24,25,47,48]. The noise can also have a significant scale dependence, even at relatively large scales.…”

Capturing non-Gaussianity of the large-scale structure with weighted skew-spectra

“…We take p(z) = 0.84/D(z) where D(z) is the growth factor normalized to unity at z = 0 [66]. For the fiducial values of quadratic biases we assume the scaling relations of b 2 =b 2 (0.412 − 2.143b 1 + 0.929b 2 1 + 0.008b 3 1 ) and b K 2 =b K 2 (0.64 − 0.3b 1 + 0.05b 2 1 − 0.06b 3 1 ), which are fits to N -body simulations [69,70]. Based on these results, we assume that the above relation between b 2 and b K 2 with b 1 , is preserved in the redshift range we consider, and use it to set the fiducial values of the the biases in each redshift bin.…”

Bias loop corrections to the galaxy bispectrum

“…That is, the observables corresponding to the multipoint propagators are no other than the standard crosscorrelation Lagrangian bias coefficients routinely measured in N-body simulations, e.g. [52][53][54][55][56][57][58][59][60][61][62][63].…”