Propagating data-driven galaxy redshift distribution uncertainties in 3 × 2-pt analyses

Monthly Notices of the Royal Astronomical Society, vol. 550

Abstract

ABSTRACT Uncertainties in the radial distribution of galaxies, $\boldsymbol{n}(\boldsymbol{z})$, are one of the major contributions to the error budget of early Stage-IV galaxy survey analyses of weak gravitational lensing, galaxy clustering, and galaxy–galaxy lensing (3$\times$2-pt). Based on ensembles of simulated $\boldsymbol{n}(\boldsymbol{z})$ including stochastic and systematic variations, we study the impact of four different $\boldsymbol{n}(\boldsymbol{z})$ uncertainty models: shifts, shifts and stretches, Gaussian processes, and principal component analysis (PCA). Due to the high dimensionality of the latter models, we make use of state-of-the-art gradient-based inference methods as well as approximate analytical marginalization schemes. Our results show that Stage-IV 3$\times$2-pt analyses must go beyond simple shift and stretch models. In particular, we advocate for the adoption of PCA models even in early Stage-IV surveys. Our results show that considering a five-parameter PCA model only degrades the constraint on the $S_{\rm 8}$ parameter by 5 per cent with respect to the case when only a shift and a stretch parameter are included, while incurring half the bias in its constituents parameters, $\Omega _{\rm m}$ and $\sigma _{\rm 8}$. We demonstrate that all models considered can be safely marginalized analytically, with speed-ups of up to a factor of 25 depending on the dimensionality of the model. This will allow Stage-IV analyses to safely include higher-dimensional $\boldsymbol{n}(\boldsymbol{z})$ uncertainty models in their analysis at negligible additional computational cost.

Authors 9

1. Jaime Ruiz-Zapatero corresponding

   University College London

   Affiliation as printed

   Advanced Research Computing Centre, University College London , 90 High Holborn, London WC1V 6LJ ,

   Department of Physics and Astronomy, University College London , Gower Street, London WC1E 6BT ,

2. Qianjun Hang

   University College London

   Affiliation as printed

   Department of Physics and Astronomy, University College London , Gower Street, London WC1E 6BT ,

3. Yun-Hao Zhang Aachen Leiden Observatory

   Leiden University · Royal Observatory · Leiden Observatory · University of Edinburgh

   Affiliation as printed

   Institute for Astronomy, University of Edinburgh, Royal Observatory , Blackford Hill, Edinburgh EH9 3HJ ,

   Leiden Observatory, Leiden University , Einsteinweg 55, NL-2333 CC Leiden ,

4. Benjamin Joachimi

   University College London

   Affiliation as printed

   Department of Physics and Astronomy, University College London , Gower Street, London WC1E 6BT ,

5. Joe Zuntz

   Royal Observatory · University of Edinburgh

   Affiliation as printed

   Institute for Astronomy, University of Edinburgh, Royal Observatory , Blackford Hill, Edinburgh EH9 3HJ ,

6. I. Harrison

   Cardiff University

   Affiliation as printed

   School of Physics and Astronomy, Cardiff University , The Parade, Cardiff, CF24 3AA ,

7. Carlos García-García

   University of Waterloo

   Affiliation as printed

   Department of Physics and Astronomy, University of Waterloo , Waterloo, ON N2L 3G1 ,

   Waterloo Centre for Astrophysics, University of Waterloo , Waterloo, ON N2L 3G1 ,

8. Alex I. Malz

   Space Telescope Science Institute

   Affiliation as printed

   Space Telescope Science Institute , Baltimore, MD 21218 ,

9. Benjamin Stölzner

   Ruhr University Bochum

   Affiliation as printed

   Ruhr University Bochum, Faculty of Physics and Astronomy, Astronomical Institute (AIRUB), German Centre for Cosmological Lensing , D-44780 Bochum ,