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 c
osmological 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
In Lima et al. 2008 we presented a new method for estimating the redshift distribution, N(z), of a photometric galaxy sample, using photometric observables and weighted sampling from a spectroscopic subsample of the data. In this paper, we extend thi
s method and explore various applications of it, using both simulations of and real data from the SDSS. In addition to estimating the redshift distribution for an entire sample, the weighting method enables accurate estimates of the redshift probability distribution, p(z), for each galaxy in a photometric sample. Use of p(z) in cosmological analyses can substantially reduce biases associated with traditional photometric redshifts, in which a single redshift estimate is associated with each galaxy. The weighting procedure also naturally indicates which galaxies in the photometric sample are expected to have accurate redshift estimates, namely those that lie in regions of photometric-observable space that are well sampled by the spectroscopic subsample. In addition to providing a method that has some advantages over standard photo-z estimates, the weights method can also be used in conjunction with photo-z estimates, e.g., by providing improved estimation of N(z) via deconvolution of N(photo-z) and improved estimates of photo-z scatter and bias. We present a publicly available p(z) catalog for ~78 million SDSS DR7 galaxies.
We present an empirical method for estimating the underlying redshift distribution N(z) of galaxy photometric samples from photometric observables. The method does not rely on photometric redshift (photo-z) estimates for individual galaxies, which ty
pically suffer from biases. Instead, it assigns weights to galaxies in a spectroscopic subsample such that the weighted distributions of photometric observables (e.g., multi-band magnitudes) match the corresponding distributions for the photometric sample. The weights are estimated using a nearest-neighbor technique that ensures stability in sparsely populated regions of color-magnitude space. The derived weights are then summed in redshift bins to create the redshift distribution. We apply this weighting technique to data from the Sloan Digital Sky Survey as well as to mock catalogs for the Dark Energy Survey, and compare the results to those from the estimation of photo-zs derived by a neural network algorithm. We find that the weighting method accurately recovers the underlying redshift distribution, typically better than the photo-z reconstruction, provided the spectroscopic subsample spans the range of photometric observables covered by the photometric sample.
We present and describe a catalog of galaxy photometric redshifts (photo-zs) for the Sloan Digital Sky Survey (SDSS) Data Release 6 (DR6). We use the Artificial Neural Network (ANN) technique to calculate photo-zs and the Nearest Neighbor Error (NNE)
method to estimate photo-z errors for ~ 77 million objects classified as galaxies in DR6 with r < 22. The photo-z and photo-z error estimators are trained and validated on a sample of ~ 640,000 galaxies that have SDSS photometry and spectroscopic redshifts measured by SDSS, 2SLAQ, CFRS, CNOC2, TKRS, DEEP, and DEEP2. For the two best ANN methods we have tried, we find that 68% of the galaxies in the validation set have a photo-z error smaller than sigma_{68} =0.021 or $0.024. After presenting our results and quality tests, we provide a short guide for users accessing the public data.
