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

Authors
Christen, Alejandra; Escarate, Pedro; Cure, Michel; Rial, Diego Fernando; Cassetti, Julia Analía
Publication Year
2016
Language
English
Format
article
Status
Published version
Description
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.
Fil: Christen, Alejandra. Pontificia Universidad Católica de Valparaíso; Chile
Fil: Escarate, Pedro. University of Arizona; Estados Unidos. Universidad Técnica Federico Santa María; Chile
Fil: Cure, Michel. Universidad de Valparaiso; Chile
Fil: Rial, Diego Fernando. Consejo Nacional de Investigaciones Científicas y Técnicas. Oficina de Coordinación Administrativa Ciudad Universitaria. Instituto de Investigaciones Matemáticas "Luis A. Santaló". Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales. Instituto de Investigaciones Matemáticas "Luis A. Santaló"; Argentina
Fil: Cassetti, Julia Analía. Universidad Nacional de General Sarmiento; Argentina
Subject
METHODS: DATA ANALYSIS
METHODS: NUMERICAL
METHODS: STATISTICAL
STARS: FUNDAMENTAL PARAMETERS
STARS: ROTATION
Astronomía
Ciencias Físicas
CIENCIAS NATURALES Y EXACTAS
Access level
Open access
License
https://creativecommons.org/licenses/by-nc-sa/2.5/ar/
Repository
CONICET Digital (CONICET)
Institution
Consejo Nacional de Investigaciones Científicas y Técnicas
OAI Identifier
oai:ri.conicet.gov.ar:11336/55514