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Knowing the distribution of stellar rotational velocities is essential forthe understanding stellar evolution. Because we measure the projectedrotational speed vsini, we need to solve an ill-posed problem given by aFredholm integral of the first kind to recover the true rotational velocitydistribution. After discretization of the Fredholm integral, we apply theTikhonov regularization method to obtain directly the probability distributionfunction for stellar rotational velocities. We propose a simple andstraightforward procedure to determine the Tikhonov parameter. We applied MonteCarlo simulations to prove that Tikhonov method is a consistent estimator andasymptotically unbiased. This method is applied to a sample of cluster stars.We obtain confidences intervals using bootstrap method. Our results are in goodagreement with the one obtained using the Lucy method, in recovering theprobability density distribution of rotational velocities. Furthermore, Lucyestimation lies inside our confidence interval. Tikhonov regularization is avery robust method that deconvolve the rotational velocity probability densityfunction from a sample of vsini data straightforward without needing anyconvergence criteria.

A method to deconvolve stellar rotational velocities II