Estimating Redshifts for Long Gamma-Ray Bursts
  We are constructing a program to estimate the redshifts for GRBs from the
original Swift light curves and spectra, aiming to get redshifts for the Swift
bursts \textit{without} spectroscopic or photometric redshifts. We derive the
luminosity indicators from the light curves and spectra of each burst,
including the lag time between low and high photon energy light curves, the
variability of the light curve, the peak energy of the spectrum, the number of
peaks in the light curve, and the minimum rise time of the peaks. These
luminosity indicators can each be related directly to the luminosity, and we
combine their independent luminosities into one weighted average. Then with our
combined luminosity value, the observed burst peak brightness, and the
concordance redshift-distance relation, we can derive the redshift for each
burst. In this paper, we test the accuracy of our method on 107 bursts with
known spectroscopic redshift. The reduced $\chi^2$ of our best redshifts
($z_{best}$) compared with known spectroscopic redshifts ($z_{spec}$) is 0.86,
and the average value of $log_{10}(z_{best}/z_{spec})$ is 0.01, with this
indicating that our error bars are good and our estimates are not biased. The
RMS scatter of $log_{10}(z_{best}/z_{spec})$ is 0.26. For Swift bursts measured
over a relatively narrow energy band, the uncertainty in determining the peak
energy is one of the main restrictions on our accuracy. Although the accuracy
of our $z_{best}$ values are not as good as that of spectroscopic redshifts, it
is very useful for demographic studies, as our sample is nearly complete and
the redshifts do not have the severe selection effects associated with optical
spectroscopy.
