Optimal Measurements of Redshifts using the Weighted CrossCorrelation (Kelson et al 2003)
realcc.pdf — PDF document, 2.29 MB (2400978 bytes)

Optimal Measurements of Redshifts using the Weighted CrossCorrelation (Kelson et al 2003)
A large component of astronomy involves the measurement of redshifts using
absorption line spectroscopy. Typically such data have nonuniform sources
of noise and other systematic defects not easily dealt with when one
employs Fourierbased techniques because such methods explicitly weight the
data uniformly. Here we develop a method for the measurement of redshifts
using the crosscorrelation in the Real domain, in which one is free to
employ nonuniform weighting. The implementation we describe in this paper
allows for the arbitrary exclusion of bad data, and weights each remaining
pixel by the inverse of the variance. This prescription for weighting the
pixels has the advantage that the units of the crosscorrelation are
exactly half that of $\chi^2$. Thus, the topology of the peak of the
weighted crosscorrelation is directly related to the confidence limits on
the measured redshifts. The validity of the redshifts and formal errors
derived with this method are tested using simulations of galaxy spectra
with a broad range of signaltonoise ratios. These simulations also
include tests of the effects of template mismatch. Overall, template
mismatch is only significant when the data have high signaltonoise
ratios, and in such cases the systematic error due to mismatch is minimized
when one chooses the template that minimizes the error in the redshift.
While the weighted
crosscorrelation is here discussed in the context of extragalactic
redshift surveys, this method is also useful for measuring the radial
velocity of stars and other astronomical objects.
realcc.pdf — PDF document, 2.29 MB (2400978 bytes) 