AbstractThe cross-correlation function (CCF) has become the standard tool for extraction of radial-velocity and broadening information from high resolution spectra. It permits integration of information which is common to many spectral lines into one function which is easy to calculate, visualize and interpret. However, the CCF is not the best tool for many applications where it should be replaced by the proper broadening function (BF). Typical applications requiring use of BFs rather than CCFs involve finding locations of star spots, studies of projected shapes of highly distorted stars such as contact binaries (as no assumptions can be made about BF symmetry or even continuity) and [Fe/H] metallicity determinations (good baselines and avoidance of negative lobes are essential). It is stressed that the CCFs are not broadening functions. This note concentrates on the advantages of determining BFs through the process of linear inversion, preferably accomplished using the singular value decomposition (SVD). Some basic examples of numerical operations are given in the IDL programming language.
Regularized Linear Inversion with Randomized Singular Value Decomposition
