A method to deconvolve stellar rotational velocities II

TL;DR

This paper introduces a robust Tikhonov regularization approach to accurately recover the true distribution of stellar rotational velocities from projected measurements, validated through simulations and applied to real star data.

Contribution

It presents a simple, direct Tikhonov regularization method with a novel parameter selection procedure for deconvolving stellar rotational velocities from vsini data.

Findings

Tikhonov method is consistent and asymptotically unbiased.

Results agree with Lucy method and lie within confidence intervals.

The method is robust and straightforward, avoiding convergence issues.

Abstract

Knowing the distribution of stellar rotational velocities is essential for the understanding stellar evolution. Because we measure the projected rotational speed vsini, we need to solve an ill-posed problem given by a Fredholm integral of the first kind to recover the true rotational velocity distribution. After discretization of the Fredholm integral, we apply the Tikhonov regularization method to obtain directly the probability distribution function for stellar rotational velocities. We propose a simple and straightforward procedure to determine the Tikhonov parameter. We applied Monte Carlo simulations to prove that Tikhonov method is a consistent estimator and asymptotically unbiased. This method is applied to a sample of cluster stars. We obtain confidences intervals using bootstrap method. Our results are in good agreement with the one obtained using the Lucy method, in recovering the probability density distribution of rotational velocities. Furthermore, Lucy estimation lies inside our confidence interval. Tikhonov regularization is a very robust method that deconvolve the rotational velocity probability density function from a sample of vsini data straightforward without needing any convergence criteria.