Precision photometric redshift calibration for galaxy-galaxy weak lensing

TL;DR

This paper develops and applies new statistics to calibrate photometric redshifts for galaxy-galaxy lensing, demonstrating that lensing-specific calibration methods significantly improve accuracy and reduce biases in large surveys like SDSS.

Contribution

It introduces lensing-specific statistical methods to accurately calibrate photometric redshifts, accounting for non-Gaussian errors and large-scale structure effects.

Findings

Lensing calibration biases can be as low as 1% with proper methods.

Active photometric redshift algorithms show biases up to 20%.

Using independent spectroscopic samples reduces calibration errors below SDSS statistical limits.

Abstract

Accurate photometric redshifts are among the key requirements for precision weak lensing measurements. Both the large size of the Sloan Digital Sky Survey (SDSS) and the existence of large spectroscopic redshift samples that are flux-limited beyond its depth have made it the optimal data source for developing methods to properly calibrate photometric redshifts for lensing. Here, we focus on galaxy-galaxy lensing in a survey with spectroscopic lens redshifts, as in the SDSS. We develop statistics that quantify the effect of source redshift errors on the lensing calibration and on the weighting scheme, and show how they can be used in the presence of redshift failure and sampling variance. We then demonstrate their use with 2838 source galaxies with spectroscopy from DEEP2 and zCOSMOS, evaluating several public photometric redshift algorithms, in two cases including a full p(z) for each object, and find lensing calibration biases as low as 1% (due to fortuitous cancellation of two types of bias) or as high as 20% for methods in active use (despite the small mean photoz bias of these algorithms). Our work demonstrates that lensing-specific statistics must be used to reliably calibrate the lensing signal, due to asymmetric effects of (frequently non-Gaussian) photoz errors. We also demonstrate that large-scale structure (LSS) can strongly impact the photoz calibration and its error estimation, due to a correlation between the LSS and the photoz errors, and argue that at least two independent degree-scale spectroscopic samples are needed to suppress its effects. Given the size of our spectroscopic sample, we can reduce the galaxy-galaxy lensing calibration error well below current SDSS statistical errors.