Attaining Doppler precision of 3 m s(-1)

Current spectroscopic techniques yield Doppler-shift errors of 10 to 50 m s(-1), barely adequate to detect reflex velocities caused by Jupiter-like and lower-mass planets. We describe a technique which yields relative radial-velocity errors of 3 m s(-1). This technique makes use of a fast echelle spectrograph at resolution of R=62,000 and a large-format CCD which acquires the entire visible and near-IR spectrum in each exposure. Starlight is sent through an iodine absorption cell placed at the spectrometer entrance slit. The resulting superimposed iodine lines provide a fiducial wavelength scale against which to measure radial-velocity shifts, The shapes of iodine lines convey the PSF of the spectrometer to account for changes in spectrometer optics and illumination on all time scales. We construct a model of each observed spectrum by multiplying a stellar spectrum with an iodine spectrum and convolving the result with the spectrometer PSF. The free parameters of the model include the wavelength scale, spectrometer PSF, and stellar Doppler shift. All model parameters are derived anew for each exposure and the synthesis is done on a grid of CCD sub-pixels, using spline functions as interpolation predictors. We present Doppler rests of the Sun, tau Ceti, and 107 Psc, observed with the Lick and Keck echelles. All exhibit apparent errors of about 3 m s(-1), maintained on time scales of minutes to a year. This precision agrees with the theoretically predicted errors that stem primarily from photon statistics.