Spectral Broadening Functions


Abstract: Many astrophysical phenomena involving velocity fields produce broadening of spectral lines. Frequently, the cross-correlation function (CCF) is used to extract information about this broadening from segments of high resolution spectra. CCF has become the standard tool for handing extraction of radial-velocity and broadening information from high resolution spectra as it permits integration of information which is common to many spectral lines into one function which is easy to calculate, visualize and interpret. However, it can be argued that this is not the best tool for applications such as determinations of metallicities ([Fe/H]), for finding locations of star spots on active stars or to study projected shapes of such distorted stars as contact binaries. For such applications, the proper broadening functions (BF) should be used. Properties of the BF's are discussed in this paper with a stress on the fact that the CCF's are not broadening functions. This note concentrates on the advantages of determining the BF's through the process of linear inversion, preferably accomplished using the Singular Value Decomposition (SVD).


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