Testing one-loop galaxy bias: Power spectrum

Abstract

We test the regime of validity of one-loop galaxy bias for a wide variety of biased tracers. Our most stringent test asks the bias model to simultaneously match the galaxy-galaxy and galaxy-mass spectrum, using the measured nonlinear matter spectrum from the simulations to test one-loop effects from the bias expansion alone. In addition, we investigate the relevance of short-range nonlocality and halo exclusion through higher-derivative and scale-dependent noise terms, as well as the impact of using co-evolution relations to reduce the number of free fitting parameters. From comparing validity and merit of these assumptions we find that a four-parameter model (linear, quadratic, cubic nonlocal bias, and constant shot noise) with fixed quadratic tidal bias provides a robust modeling choice for the auto power spectrum of the less massive halos in our set of samples and their galaxy populations (up to kmax = 0.35 h/Mpc for a sample volume of 6 (Gpc/h) 3 ). For the more biased tracers it is most beneficial to include scale-dependent noise. This is also the preferred option when considering combinations of the auto and cross power spectrum, which might be relevant in joint studies of galaxy clustering and weak lensing. We also test the use of perturbation theory to account for matter loops through gRPT, EFT and the hybrid approach RESPRESSO. While all these have similar performance, we find the latter to be the best in terms of validity and recovered mean posterior values, in accordance with it being based partially on simulations.

Testing one-loop galaxy bias: Power spectrum

“…In the limit k → ∞ we expect the shot noise to approach the Poisson limit and so lim k→∞ C gg (k) = 0 [90], which suggests an anti-correlation between N P,0 and the scale-dependent noise parameter N P,2 . This was empirically confirmed in [62], which presented the first detailed measurements of N P,2 , and showed further that its contribution is important for making consistent predictions of the galaxy auto power spectrum and the galaxymatter cross spectrum.…”

“…This has already been invalidated by detailed measurements in [53,54], which have found that γ 2,L < 0 and thus demonstrated an impact of at least the tidal field at initial time, although in practice Eq. ( 17) with γ 2,L = 0 can still be a reasonable assumption, depending on how sensitive a given observable is to effects from the tidal field [62]. Given that all terms deriving from the nonlocality of gravity (our NLE operators) are inherently linked to nonlinear evolution, a potential simplification is to assume that these operators are not needed for characterizing the distribution of proto-halos -a property that is also manifest in peak bias models [e.g.…”

“…These studies have shown that the coevolution relations generally provide a good description of the measurements, although deviations have been reported in particular for the tidal bias parameter. Due to parameter space degeneracies this is likely not a concern for analyses of the power spectrum alone [62], but in combination with the bispectrum, which is affected by tidal bias even on large scales, application of the coevolution relation can lead to significant errors.…”

“…Our strategy for tackling these questions closely follows the approach presented in the other two installments of this series of papers [62,63]. We perform full likelihood fits to the measured power spectra and bispectra from a diverse pool of tracers, including samples that mimic the SDSS Main, as well as the BOSS LOWZ and CMASS galaxies, in addition to four halo catalogs with different mass cuts and redshifts.…”

Perturbation theory models for LSST-era galaxy clustering: tests with sub-percent mock catalog measurements in Fourier and configuration space

“…This study complements various recent studies aiming to study galaxy bias models with high resolution simulations [24,44,[63][64][65][66][67][68][69]. Unlike previous studies which focus either on Fourier or configuration space, in this study we perform the analysis using the two point functions in both spaces.…”