Sample variance in photometric redshift calibration: cosmological biases and survey requirements

TL;DR

This study investigates how sample variance in spectroscopic redshift samples affects photometric redshift calibration and cosmological parameter estimation, providing guidelines for spectroscopic follow-up to minimize biases.

Contribution

It demonstrates that sample variance impacts photo-z error calibration more than training, and offers a practical observing strategy to control cosmological biases.

Findings

Sample variance significantly affects photo-z error calibration.

Spectroscopic follow-up can be optimized to reduce biases.

Guidelines for observing proposals to ensure minimal cosmological impact.

Abstract

We use N-body/photometric galaxy simulations to examine the impact of sample variance of spectroscopic redshift samples on the accuracy of photometric redshift (photo-z) determination and calibration of photo-z errors. We estimate the biases in the cosmological parameter constraints from weak lensing and derive requirements on the spectroscopic follow-up for three different photo-z algorithms chosen to broadly span the range of algorithms available. We find that sample variance is much more relevant for the photo-z error calibration than for photo-z training, implying that follow-up requirements are similar for different algorithms. We demonstrate that the spectroscopic sample can be used for training of photo-zs and error calibration without incurring additional bias in the cosmological parameters. We provide a guide for observing proposals for the spectroscopic follow-up to ensure that redshift calibration biases do not dominate the cosmological parameter error budget. For example, assuming optimistically (pessimistically) that the weak lensing shear measurements from the Dark Energy Survey could obtain 1-sigma constraints on the dark energy equation of state w of 0.035 (0.055), implies a follow-up requirement of 150 (40) patches of sky with a telescope such as Magellan, assuming a 1/8^2 deg effective field of view and 400 galaxies per patch. Assuming (optimistically) a VVDS-like spectroscopic completeness with purely random failures, this could be accomplished with about 75 (20) nights of observation. For more realistic assumptions regarding spectroscopic completeness, or in the presence of other sources of systematics not considered here, further degradations to dark energy constraints are possible. We test several approaches for reducing the requirements. Abridged