Study of spectroscopic binaries with TODCOR. 1: A new two-dimensional correlation algorithm to derive the radial velocities of the two components

We propose a generalization of the cross-correlation technique, to obtain simultaneously the Doppler shift of the two components of composite spectra. The technique-TODCOR-computes the correlation of an observed spectrum against combinations of the two template spectra, with all possible shifts. Thus, the correlation is a two-dimensional function whose two independent variables are the two shifts of the two components. The location of the maximum of this function corresponds to the actual shifts of the two components. The technique is made feasible through the use of an Fast Fourier Transform (FFT) algorithm. TODCOR improves the analysis of binary spectra with small velocity differences, which are difficult to analyze with the original cross correlation. The new algorithm was tested with numerous simulated spectra. We were able to derive the correct velocities of the two components in all cases, one of which is presented.