Selection biases in empirical p(z) methods for weak lensing

Abstract

To measure the mass of foreground objects with weak gravitational lensing, one needs to estimate the redshift distribution of lensed background sources. This is commonly done in an empirical fashion, i.e. with a reference sample of galaxies of known spectroscopic redshift, matched to the source population. In this work, we develop a simple decision tree framework that, under the ideal conditions of a large, purely magnitudelimited reference sample, allows an unbiased recovery of the source redshift probability density function p(z), as a function of magnitude and colour. We use this framework to quantify biases in empirically estimated p(z) caused by selection effects present in realistic reference and weak lensing source catalogues, namely (1) complex selection of reference objects by the targeting strategy and success rate of existing spectroscopic surveys and (2) selection of background sources by the success of object detection and shape measurement at low signal-to-noise. For intermediate-to-high redshift clusters, and for depths and filter combinations appropriate for ongoing lensing surveys, we find that (1) spectroscopic selection can cause biases above the 10 per cent level, which can be reduced to ≈ 5 per cent by optimal lensing weighting, while (2) selection effects in the shape catalogue bias mass estimates at or below the 2 per cent level. This illustrates the importance of completeness of the reference catalogues for empirical redshift estimation.

Phenotypic redshifts with self-organizing maps: A novel method to characterize redshift distributions of source galaxies for weak lensing

“…It can bias empirical methods based on machine learning (e.g. Collister & Lahav 2004;Carrasco Kind & Brunner 2013;De Vicente et al 2016) or direct calibration from spectroscopic samples, because present spectroscopic samples are subject to selection effects at fixed broad-band observables (Bonnett et al 2016;Gruen & Brimioulle 2017). These can be both explicit (i.e.…”

The Wendelstein Weak Lensing (WWL) pathfinder: accurate weak lensing masses for Planck clusters

“…In order to get a clean background sample selection for the weak lensing analysis, we need reliable redshift estimates. This can be achieved by comparing the flux of the observed galaxies in all available filters to galaxies with known redshifts (Gruen et al 2014;Gruen & Brimioulle 2017). Those reference galaxies have to be observed with the same set of filters as has been used for the cluster fields.…”

“…Since W-EGS is comparatively small, we expect the dominant bias to arise from cosmic variance. As we only have this single reference field, we use the findings of Gruen & Brimioulle (2017) to estimate the cosmic variance in W-EGS. Gruen & Brimioulle (2017) use an approach that is quite similar to our own method.…”

“…As we only have this single reference field, we use the findings of Gruen & Brimioulle (2017) to estimate the cosmic variance in W-EGS. Gruen & Brimioulle (2017) use an approach that is quite similar to our own method. Instead of collecting all galaxies with a comparable set of magnitudes, they build a colourmagnitude decision tree based on a set of reference fields and using different sets of photometric bands.…”

“…As Gruen & Brimioulle (2017) use the full set of the CFHT Deep fields 2 , their catalogue of refer-ence galaxies is much larger than ours and contains galaxies from four different pointings. Gruen & Brimioulle (2017) test the impact of different types of biases on the lensing strengths and find cosmic variance to be the dominant bias in data sets comparable to our own. They calculate the cosmic variance σ β/B i in their catalogue as the mean of the lensing strengths in each colour-magnitude box over their four reference fields using a jackknife approach.…”