Spectrophotometry with Hectospec, the MMT's Fiber-Fed Spectrograph

The spectrophotometric calibration of surveys is a significant, but often neglected, issue when measuring the history of star formation by combining spectroscopic surveys conducted with different instruments. We describe techniques for photometric calibration of optical spectra obtained with the MMT's fiber-fed spectrograph, Hectospec. The atmospheric dispersion compensation prisms built into the MMT's f/5 wide-field corrector effectively eliminate errors due to differential refraction and simplify the calibration procedure. The procedures that we describe here are applicable to all 220,000+ spectra obtained to date with Hectospec because the instrument response is stable. We estimate the internal error in the Hectospec measurements by comparing duplicate measurements of ~1500 galaxies. For a sample of 400 galaxies in the Smithsonian Hectospec Lensing Survey (SHELS) with a median z = 0.10, we compare line and continuum fluxes measured by Hectospec through a 1.5'' diameter optical fiber with those measured by the Sloan Digital Sky Survey (SDSS) through a 3'' diameter optical fiber. Agreement of the [O II] and Hα SHELS and SDSS line fluxes, after scaling by the R-band flux in the different apertures, suggests that the spatial variation in star-formation rates over a 1.5 to 3 kpc radial scale is small. The median ratio of the Hectospec and SDSS spectra, smoothed over 100 A scales, is remarkably constant to ~5% over the range of 3850 to 8000 A. Offsets in the ratio of the median [O II] and Hα fluxes, the equivalent width of Hδ and the continuum index d4000 are a few percent, small compared with other sources of scatter. We also explore the impact of atmospheric absorption. Observing redward of 6500 A, it is impossible to remove the effects of atmospheric absorption perfectly because the variation of absorption with wavelength is not resolved by a moderate dispersion spectrograph. Thus measurements of spectral line fluxes including Hα, and derived physical quantities including star-formation rates, may have sizable systematic errors where the redshifted spectral features land on strong atmospheric absorption troughs.