A method to deconvolve stellar rotational velocities II: The probability distribution function via Tikhonov regularization

Alejandra Christen, Pedro Escarate, Michel Curé, Diego F. Rial, Julia Cassetti

Research output: Contribution to journalArticlepeer-review

1 Scopus citations

Abstract

Aims. Knowing the distribution of stellar rotational velocities is essential for understanding stellar evolution. Because we measure the projected rotational speed v sin i, we need to solve an ill-posed problem given by a Fredholm integral of the first kind to recover the "true" rotational velocity distribution. Methods. 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 the Tikhonov method is a consistent estimator and asymptotically unbiased. Results. This method is applied to a sample of cluster stars. We obtain confidence intervals using a bootstrap method. Our results are in close agreement with those obtained using the Lucy method for recovering the probability density distribution of rotational velocities. Furthermore, Lucy estimation lies inside our confidence interval. Conclusions. Tikhonov regularization is a highly robust method that deconvolves the rotational velocity probability density function from a sample of v sin i data directly without the need for any convergence criteria.

Original languageEnglish
Article numberA50
JournalAstronomy and Astrophysics
Volume595
DOIs
StatePublished - 1 Nov 2016
Externally publishedYes

Keywords

  • Methods: data analysis
  • Methods: numerical
  • Methods: statistical
  • Stars: fundamental parameters
  • Stars: rotation

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