Empirical optical k-Corrections for redshifts <= 0.7
  The Smithsonian Hectospec Lensing Survey (SHELS) is a magnitude limited
spectroscopically complete survey for R<=21.0 covering 4 square degrees. SHELS
provides a large sample (15,513) of flux calibrated spectra. The wavelength
range covered by the spectra allows empirical determination of k-corrections
for the g- and r-band from z=0 to ~0.68 and 0.33, respectively, based on large
samples of spectra. We approximate the k-corrections using only two parameters
in a standard way: Dn4000 and redshift. We use Dn4000 rather than the standard
observed galaxy color because Dn4000 is a redshift independent tracer of the
stellar population of the galaxy. Our approximations for the k-corrections
using Dn4000 are as good as (or better than) those based on observed galaxy
color (g-r) (sigma of the scatter is ~0.08 mag). The approximations for the
k-corrections are available in an on-line calculator. Our results agree with
previously determined analytical approximations from single stellar population
(SSP) models fitted to multi-band optical and near-infrared photometry for
galaxies with a known redshift. Galaxies with the smallest Dn4000-the galaxies
with the youngest stellar populations-are always attenuated and/or contain
contributions from older stellar populations. We use simple single SSP fits to
the SHELS spectra to study the influence of emission lines on the k-correction.
The effects of emission lines can be ignored for rest-frame equivalent widths
<~ 100 A depending on required photometric accuracy. We also provide analytic
approximations to the k-corrections determined from our model fits for z<=0.7
as a function of redshift and Dn4000 for ugriz and UBVRI (sigma of the scatter
is typically ~0.10 mag). Again, the approximations using Dn4000 are as good (or
better than) those based on a suitably chosen observed galaxy color. We provide
all analytical approximations in an on-line calculator.
