Quantifying Photometric Redshift Errors in the Absence of Spectroscopic
  Redshifts
  Much of the science that is made possible by multiwavelength redshift surveys
requires the use of photometric redshifts. But as these surveys become more
ambitious, and as we seek to perform increasingly accurate measurements, it
becomes crucial to take proper account of the photometric redshift
uncertainties. Ideally the uncertainties can be directly measured using a
comparison to spectroscopic redshifts, but this may yield misleading results
since spectroscopic samples are frequently small and not representative of the
parent photometric samples. We present a simple and powerful empirical method
to constrain photometric redshift uncertainties in the absence of spectroscopic
redshifts. Close pairs of galaxies on the sky have a significant probability of
being physically associated, and therefore of lying at nearly the same
redshift. The difference in photometric redshifts in close pairs is therefore a
measure of the redshift uncertainty. Some observed close pairs will arise from
chance projections along the line of sight, but it is straightforward to
perform a statistical correction for this effect. We demonstrate the technique
using both simulated data and actual observations, and discuss how its
usefulness can be limited by the presence of systematic photometric redshift
errors. Finally, we use this technique to show how photometric redshift
accuracy can depend on galaxy type.
