Volume 595, November 2016
|Number of page(s)||8|
|Section||Numerical methods and codes|
|Published online||28 October 2016|
A method to deconvolve stellar rotational velocities II
The probability distribution function via Tikhonov regularization
1 Instituto de Estadística, Pontificia Universidad Católica de Valparaíso, 2950 Valparaíso, Chile
2 Centro Avanzado de Ingeniería Eléctrica y Electrónica, Universidad Técnica Federico Santa María, 1680 Valparaíso, Chile
3 Large Binocular Telescope Observatory, Steward Observatory, Tucson, AZ 85546, USA
4 Instituto de Física y Astronomía, Universidad de Valparaíso, Chile
5 Departamento de Matemáticas, Facultad de Ciencias Exactas y Naturales, Universidad de Buenos Aires, 1053 Buenos Aires, Argentina
6 Universidad Nacional de General Sarmiento, Buenos Aires, 1613 Buenos Aires, Argentina
Received: 7 June 2016
Accepted: 12 September 2016
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.
Key words: stars: rotation / methods: statistical / methods: numerical / methods: data analysis / stars: fundamental parameters
© ESO, 2016
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