Empirical Optical k-Corrections for Redshifts

The Smithsonian Hectospec Lensing Survey (SHELS) is a magnitude-limited spectroscopically complete survey for R <= 21: 0 covering 4 deg(2). 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 bands from z = 0 to similar 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: D(n)4000 and redshift, z. We use D(n)4000 rather than the standard observed galaxy color, because D(n)4000 is a redshift-independent tracer of the stellar population of the galaxy. Our approximations for the k-corrections using D(n)4000 are as good as those based on observed galaxy color (g - r) (sigma of the scatter is similar to 0.08 mag). The approximations for the k-corrections are available in an online calculator. Our results agree with previously determined analytical approximations from single stellar population (SSP) models fitted to multiband optical and near-infrared photometry for galaxies with a known redshift. Galaxies with the smallest D(n)4000-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 (REWs) less than or similar to 100 angstrom, 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 D(n)4000 for ugriz and UBVRI (sigma of the scatter is typically similar to 0: 10 mag, and the rms is typically similar to 0.15 mag). Again, the approximations using D(n)4000 are as good as those based on a suitably chosen observed galaxy color. We provide all analytical approximations in an online calculator.