Deconvolution of high-resolution spectra as a signal-to-noise ratio enhancement method

We demonstrate the use of singular value decomposition as a method for deconvolving high-resolution spectra of rapidly rotating stars. A convolution matrix can be built from the observed template spectrum of a slowly rotating star, with the same spectral type as the target. This can then be written in terms of a set of orthogonal basis vectors which can easily be inverted. The deconvolved stellar rotation profile or broadening function is thus similarly represented as a linear combination of basis vectors. By including only the required number of vectors and rejecting higher-order terms which only describe noise, we obtain a broadening function with greatly boosted signal-to-noise ratio as compared with a mean line in the target spectrum. The high signal-to-noise ratios allow localized line distortions due to starspots to be resolved. We describe the technique and demonstrate its application to the data sets of a rapidly rotating K3 and M1 dwarf.