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Register a new userRedshift inference from the combination of galaxy colors and clustering in a hierarchical Bayesian model $-$ Application to realistic $N$-body simulations
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Photometric galaxy surveys constitute a powerful cosmological probe but rely on the accurate characterization of their redshift distributions using only broadband imaging, and can be very sensitive to incomplete or biased priors used for redshift calibration. Sanchez & Bernstein (2019) presented a hierarchical Bayesian model which estimates those from the robust combination of prior information, photometry of single galaxies and the information contained in the galaxy clustering against a well-characterized tracer population. In this work, we extend the method so that it can be applied to real data, developing some necessary new extensions to it, especially in the treatment of galaxy clustering information, and we test it on realistic simulations. After marginalizing over the mapping between the clustering estimator and the actual density distribution of the sample galaxies, and using prior information from a small patch of the survey, we find the incorporation of clustering information with photo-$z$s to tighten the redshift posteriors, and to overcome biases in the prior that mimic those happening in spectroscopic samples. The method presented here uses all the information at hand to reduce prior biases and incompleteness. Even in cases where we artificially bias the spectroscopic sample to induce a shift in mean redshift of $Delta bar z approx 0.05,$ the final biases in the posterior are $Delta bar z lesssim0.003.$ This robustness to flaws in the redshift prior or training samples would constitute a milestone for the control of redshift systematic uncertainties in future weak lensing analyses.
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We implement a model for the two-point statistics of biased tracers that combines dark matter dynamics from $N$-body simulations with an analytic Lagrangian bias expansion. Using Aemulus, a suite of $N$-body simulations built for emulation of cosmological observables, we emulate the cosmology dependence of these nonlinear spectra from redshifts $z = 0$ to $z=2$. We quantify the accuracy of our emulation procedure, which is sub-per cent at $k=1, h {rm Mpc}^{-1}$ for the redshifts probed by upcoming surveys and improves at higher redshifts. We demonstrate its ability to describe the statistics of complex tracer samples, including those with assembly bias and baryonic effects, reliably fitting the clustering and lensing statistics of such samples at redshift $zsimeq 0.4$ to scales of $k_{rm max} approx 0.6, hmathrm{Mpc}^{-1}$. We show that the emulator can be used for unbiased cosmological parameter inference in simulated joint clustering and galaxy--galaxy lensing analyses with data drawn from an independent $N$-body simulation. These results indicate that our emulator is a promising tool that can be readily applied to the analysis of current and upcoming datasets from galaxy surveys.
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