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

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...

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Detalles Bibliográficos
Autor principal: Rial, Diego Fernando
Publicado: 2016
Materias:
Methods: data analysis
Methods: numerical
Methods: statistical
Stars: fundamental parameters
Stars: rotation
Distribution functions
Financial data processing
Intelligent systems
Monte Carlo methods
Numerical methods
Probability
Probability distributions
Problem solving
Stars
Statistical methods
Velocity
Velocity distribution
Methods: numericals
Methods:data analysis
Methods:statistical
Stars: Rotation
Stars:fundamental parameters
Probability density function
Acceso en línea:https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00046361_v595_n_p_Christen
http://hdl.handle.net/20.500.12110/paper_00046361_v595_n_p_Christen
Aporte de:
Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA) de Universidad de Buenos Aires
id paper:paper_00046361_v595_n_p_Christen
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spelling paper:paper_00046361_v595_n_p_Christen2023-06-08T14:28:17Z A method to deconvolve stellar rotational velocities II: The probability distribution function via Tikhonov regularization Rial, Diego Fernando Methods: data analysis Methods: numerical Methods: statistical Stars: fundamental parameters Stars: rotation Distribution functions Financial data processing Intelligent systems Monte Carlo methods Numerical methods Probability Probability distributions Problem solving Stars Statistical methods Velocity Velocity distribution Methods: numericals Methods:data analysis Methods:statistical Stars: Rotation Stars:fundamental parameters Probability density function 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. © 2016 ESO. Fil:Rial, D.F. Universidad de Buenos Aires. Facultad de Ciencias Exactas y Naturales; Argentina. 2016 https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00046361_v595_n_p_Christen http://hdl.handle.net/20.500.12110/paper_00046361_v595_n_p_Christen
institution Universidad de Buenos Aires
institution_str I-28
repository_str R-134
collection Biblioteca Digital - Facultad de Ciencias Exactas y Naturales (UBA)
topic Methods: data analysis
Methods: numerical
Methods: statistical
Stars: fundamental parameters
Stars: rotation
Distribution functions
Financial data processing
Intelligent systems
Monte Carlo methods
Numerical methods
Probability
Probability distributions
Problem solving
Stars
Statistical methods
Velocity
Velocity distribution
Methods: numericals
Methods:data analysis
Methods:statistical
Stars: Rotation
Stars:fundamental parameters
Probability density function
spellingShingle Methods: data analysis
Methods: numerical
Methods: statistical
Stars: fundamental parameters
Stars: rotation
Distribution functions
Financial data processing
Intelligent systems
Monte Carlo methods
Numerical methods
Probability
Probability distributions
Problem solving
Stars
Statistical methods
Velocity
Velocity distribution
Methods: numericals
Methods:data analysis
Methods:statistical
Stars: Rotation
Stars:fundamental parameters
Probability density function
Rial, Diego Fernando
A method to deconvolve stellar rotational velocities II: The probability distribution function via Tikhonov regularization
topic_facet Methods: data analysis
Methods: numerical
Methods: statistical
Stars: fundamental parameters
Stars: rotation
Distribution functions
Financial data processing
Intelligent systems
Monte Carlo methods
Numerical methods
Probability
Probability distributions
Problem solving
Stars
Statistical methods
Velocity
Velocity distribution
Methods: numericals
Methods:data analysis
Methods:statistical
Stars: Rotation
Stars:fundamental parameters
Probability density function
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. © 2016 ESO.
author Rial, Diego Fernando
author_facet Rial, Diego Fernando
author_sort Rial, Diego Fernando
title A method to deconvolve stellar rotational velocities II: The probability distribution function via Tikhonov regularization
title_short A method to deconvolve stellar rotational velocities II: The probability distribution function via Tikhonov regularization
title_full A method to deconvolve stellar rotational velocities II: The probability distribution function via Tikhonov regularization
title_fullStr A method to deconvolve stellar rotational velocities II: The probability distribution function via Tikhonov regularization
title_full_unstemmed A method to deconvolve stellar rotational velocities II: The probability distribution function via Tikhonov regularization
title_sort method to deconvolve stellar rotational velocities ii: the probability distribution function via tikhonov regularization
publishDate 2016
url https://bibliotecadigital.exactas.uba.ar/collection/paper/document/paper_00046361_v595_n_p_Christen
http://hdl.handle.net/20.500.12110/paper_00046361_v595_n_p_Christen
work_keys_str_mv AT rialdiegofernando amethodtodeconvolvestellarrotationalvelocitiesiitheprobabilitydistributionfunctionviatikhonovregularization
AT rialdiegofernando methodtodeconvolvestellarrotationalvelocitiesiitheprobabilitydistributionfunctionviatikhonovregularization
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