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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.