Combining spectroscopic and photometric surveys using angular cross-correlations I: Algorithm and modelling

Abstract

Weak lensing (WL) clustering is studied using 2D (angular) coordinates, while redshift space distortions (RSD) and baryon acoustic oscillations (BAO) use 3D coordinates, which requires a model dependent conversion of angles and redshifts into comoving distances. This is the first paper of a series, which explore modelling multi-tracer galaxy clustering (of WL, BAO and RSD), using only angular (2D) cross-correlations in thin redshift bins. This involves evaluating many thousands cross-correlations, each a multidimensional integral, which is computationally demanding. We present a new algorithm that performs these calculations as matrix operations. Nearby narrow redshift bins are intrinsically correlated, which can be used to recover the full (radial) 3D information. We show that the Limber approximation does not work well for this task. In the exact calculation, both the clustering amplitude and the RSD effect increase when decreasing the redshift bin width. For narrow bins, the cross-correlations has a larger BAO peak than the auto-correlation because smaller scales are filtered out by the radial redshift separation. Moreover, the BAO peak shows a second (ghost) peak, shifted to smaller angles. We explore how WL, RSD and BAO contribute to the cross-correlations as a function of the redshift bin width and present a first exploration of non-linear effects and signal-to-noise ratio on these quantities. This illustrates that the new approach to clustering analysis provides new insights and is potentially viable in practice.

References in corpus (3)

• Extended Limber Approximation
• The onion universe: all sky lightcone simulations in spherical shells
• Combining spectroscopic and photometric surveys using angular cross-correlations II: Parameter constraints from different physical effects

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• The clustering of galaxies in the completed SDSS-III Baryon Oscillation Spectroscopic Survey: Angular clustering tomography and its cosmological implications
• 3D galaxy clustering with future wide-field surveys: Advantages of a spherical Fourier-Bessel analysis
• Impact of astrophysics on cosmology forecasts for 21 cm surveys
• RCSLenS: A new estimator for large-scale galaxy-matter correlations
• Combining spectroscopic and photometric surveys using angular cross-correlations III: Galaxy bias and stochastisity
• Cosmological constraints from multiple tracers in spectroscopic surveys
• Blending and obscuration in weak lensing magnification