Spectroscopic failures in photometric redshift calibration: cosmological biases and survey requirements

We use N-body-spectrophotometric simulations to investigate the impact of incompleteness and incorrect redshifts in spectroscopic surveys on photometric redshift training and calibration and the resulting effects on cosmological parameter estimation from weak lensing shear-shear correlations. The photometry of the simulations is modelled after the upcoming Dark Energy Survey and the spectroscopy is based on a low/intermediate-resolution spectrograph with wavelength coverage of 5500 < lambda < 9500 angstrom. Spectroscopic follow-up surveys suffer from both incompleteness ( inability to obtain spectroscopic redshifts for certain galaxies) and wrong redshifts. Encouragingly, we find that a neural network-based approach can effectively describe the spectroscopic incompleteness in terms of the galaxies' colours, so that the spectroscopic selection can be applied to the photometric sample. Hence, we find that spectroscopic incompleteness yields no appreciable biases to cosmology, although the statistical constraints degrade somewhat because the photometric survey has to be culled to match the spectroscopic selection. Unfortunately, wrong redshifts have a more severe impact: the cosmological biases are intolerable if more than a per cent of the spectroscopic redshifts are incorrect. Moreover, we find that incorrect redshifts can substantially degrade the perceived accuracy of training set based photo-z estimators, though the actual accuracy is virtually unaffected. The main problem is the difficulty of obtaining redshifts, either spectroscopically or photometrically, for objects at z > 1.3. We discuss several approaches for reducing the cosmological biases, in particular finding that photo-z error estimators can reduce biases appreciably when the photo-z errors are correlated with the spectroscopic failures, but not otherwise.