Stellar Radial Velocities with SOAR

I. Science Drivers

 Stellar velocity measurements are an important tool in the study of many astrophysical problems. Along with the classical stellar mass determination in binaries which has direct implications on the mass function in HR diagram, there are the dynamical probing of open and globular clusters. Structure and population studies of the Galaxy and the Magellanic Clouds also benefit from this technique. On high energy astrophysics these measurements usually couple with line profile studies. Valid examples are X-ray novae and black holes in binary systems, low-mass X-ray binaries and LBVs.

 II. Measurement tools

 The velocity precision that is science relevant is strongly dependent on the spectral properties and the measurement technique that is applied on them. For many absorption lines in the spectra the most effective procedure is cross-correlation while for individual lines intensity weighting procedures are possibly the most common class of algorithms. Sometimes the velocity must be sampled at a particular region of the line profile, them a wide variety of masking and filtering method can be found in the literature. In binary mass function determination each radial velocity measurement are naturally time-correlated in the form of a periodic function, therefore the error of individual measurements are less relevant for the science goals since they are combined in some meaningful way. For narrow photospheric lines from cool stars the spectral resolution is a main factor for subpixel velocity precision, while for single line measurements there is a minimum S/N for windowing and numerical analysis. When stark and rotation broadening are important in our lines we are in many cases happy with intermediate resolutions.

 III Simulation

 The exploratory analysis presented here was done in the "worst case" condition, i.e. the velocity of a narrow absorption line measured by the first momentum of its intensity. These flux weighted centroids were calculated assuming a photospheric gaussian profile with a given FWHM and depth. This profile is then convoluted with the instrumental resolution. Starting from monochromatic magnitudes and typical sky background curves, the count rate is computed using the overall system efficiency and standard atmospheric extinction. The given seeing defines the slit width. The noise model contains the source photon noise, background and readout noise. The internal precision of the velocity measurements is evaluated by synthesizing statistically independent sets of spectra (for each seeing, R, magnitude triplet in a grid) and measuring the velocity scatter for each set. In addition, the velocity is randomly affected by given flexure and tracking rms errors.

 IV Results

 This exercise indicate resolution constraints for velocity measurements in the optical (figure 1). Resolutions above R>5000 are required for measuring intermediate and narrow lines with useful precision (figure 2). The velocity quality in the low resolution regime is not substantially improved by increasing exposure time or switching to brighter targets. The readout noise tend to be important at higher resolution (for R larger than the values used in this preliminary analysis). Bench or Nasmyth mounted spectrographs at a 4m class telescope have a "niche" of work at intermediate resolutions and intermediate magnitudes, where the velocity quality from competing Cassegrain mounted spectrographs is limited by flexure and tracking errors (figure 3).