A method to deconvolve stellar rotational velocities III. The probability distribution function via maximum likelihood utilizing finite distribution mixtures
R. Orellana, P. Escárate, M. Curé, A. Christen, R. Carvajal, J. C. Agüero
Aims. The study of accurate methods to estimate the distribution of stellar rotational velocities is important for understanding many aspects of stellar evolution. From such observations we obtain the projected rotational speed (v sin i) in order to recover the true distribution of the rotational velocity. To that end, we need to solve a difficult inverse problem that can be posed as a Fredholm integral of the first kind. Methods. In this work we have used a novel approach based on maximum likelihood (ML) estimation to obtain an approximation of the true rotational velocity probability density function (PDF) expressed as a sum of known distribution families. In our proposal, the measurements have been treated as random variables drawn from the projected rotational velocity PDF. We analyzed the case of Maxwellian sum approximation, where we estimated the parameters that define the sum of distributions. Results. The performance of the proposed method is analyzed using Monte Carlo simulations considering two theoretical cases for the PDF of the true rotational stellar velocities: (i) an unimodal Maxwellian probability density distribution and (ii) a bimodal Maxwellian probability density distribution. The results show that the proposed method yielded more accurate estimates in comparison with the Tikhonov regularization method, especially for small sample length (N = 50). Our proposal was evaluated using real data from three sets of measurements, and our findings were validated using three statistical tests. Conclusions. The ML approach with Maxwellian sum approximation is a accurate method to deconvolve the rotational velocity PDF, even when the sample length is small (N = 50).
Methods: analytical
Methods: data analysis
Methods: numerical
Methods: statistical
Stars: fundamental parameters
Stars: rotation
10.1051/0004-6361/201833455
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probability distribution functions Physics & Astronomy 100%
probability density function Earth & Environmental Sciences 56%
probability density functions Physics & Astronomy 50%
distribution Earth & Environmental Sciences 29%
proposals Physics & Astronomy 21%
density distribution Physics & Astronomy 21%
approximation Physics & Astronomy 18%
method Earth & Environmental Sciences 17%
Orellana, R., Escárate, P., Curé, M., Christen, A., Carvajal, R., & Agüero, J. C. (2019). A method to deconvolve stellar rotational velocities III. The probability distribution function via maximum likelihood utilizing finite distribution mixtures. Astronomy and Astrophysics, 623, [A138]. https://doi.org/10.1051/0004-6361/201833455
Orellana, R. ; Escárate, P. ; Curé, M. et al. / A method to deconvolve stellar rotational velocities III. The probability distribution function via maximum likelihood utilizing finite distribution mixtures. In: Astronomy and Astrophysics. 2019 ; Vol. 623.
@article{5673ee3d0fd247c584d0a55e26607b43,
title = "A method to deconvolve stellar rotational velocities III. The probability distribution function via maximum likelihood utilizing finite distribution mixtures",
abstract = "Aims. The study of accurate methods to estimate the distribution of stellar rotational velocities is important for understanding many aspects of stellar evolution. From such observations we obtain the projected rotational speed (v sin i) in order to recover the true distribution of the rotational velocity. To that end, we need to solve a difficult inverse problem that can be posed as a Fredholm integral of the first kind. Methods. In this work we have used a novel approach based on maximum likelihood (ML) estimation to obtain an approximation of the true rotational velocity probability density function (PDF) expressed as a sum of known distribution families. In our proposal, the measurements have been treated as random variables drawn from the projected rotational velocity PDF. We analyzed the case of Maxwellian sum approximation, where we estimated the parameters that define the sum of distributions. Results. The performance of the proposed method is analyzed using Monte Carlo simulations considering two theoretical cases for the PDF of the true rotational stellar velocities: (i) an unimodal Maxwellian probability density distribution and (ii) a bimodal Maxwellian probability density distribution. The results show that the proposed method yielded more accurate estimates in comparison with the Tikhonov regularization method, especially for small sample length (N = 50). Our proposal was evaluated using real data from three sets of measurements, and our findings were validated using three statistical tests. Conclusions. The ML approach with Maxwellian sum approximation is a accurate method to deconvolve the rotational velocity PDF, even when the sample length is small (N = 50).",
keywords = "Methods: analytical, Methods: data analysis, Methods: numerical, Methods: statistical, Stars: fundamental parameters, Stars: rotation",
author = "R. Orellana and P. Esc{\'a}rate and M. Cur{\'e} and A. Christen and R. Carvajal and Ag{\"u}ero, {J. C.}",
note = "Funding Information: Acknowledgements. This work was partially supported by FONDECYT trough grant No 1181158, the Advanced Center for Electrical and Electronic Engineering (AC3E, Proyecto Basal FB0008), N{\'u}cleo Milenio de Formaci{\'o}n Planetaria – NPF and Programa de Iniciaci{\'o}n a la Investigaci{\'o}n Cient{\'i}fica (PIIC) de la Direcci{\'o}n de Postgrado UTFSM convenio No 015/2018. Michel Cur{\'e} thanks the support from the Centro de Astrof{\'i}sica de Valpara{\'i}so and the Centro Interdisciplinario de Estudios Atmosf{\'e}ricos y Astroestad{\'i}stica. Publisher Copyright: {\textcopyright} ESO 2019",
doi = "10.1051/0004-6361/201833455",
journal = "Astronomy and Astrophysics",
Orellana, R, Escárate, P, Curé, M, Christen, A, Carvajal, R & Agüero, JC 2019, 'A method to deconvolve stellar rotational velocities III. The probability distribution function via maximum likelihood utilizing finite distribution mixtures', Astronomy and Astrophysics, vol. 623, A138. https://doi.org/10.1051/0004-6361/201833455
A method to deconvolve stellar rotational velocities III. The probability distribution function via maximum likelihood utilizing finite distribution mixtures. / Orellana, R.; Escárate, P.; Curé, M. et al.
In: Astronomy and Astrophysics, Vol. 623, A138, 2019.
T1 - A method to deconvolve stellar rotational velocities III. The probability distribution function via maximum likelihood utilizing finite distribution mixtures
AU - Orellana, R.
AU - Escárate, P.
AU - Curé, M.
AU - Christen, A.
AU - Carvajal, R.
AU - Agüero, J. C.
N1 - Funding Information: Acknowledgements. This work was partially supported by FONDECYT trough grant No 1181158, the Advanced Center for Electrical and Electronic Engineering (AC3E, Proyecto Basal FB0008), Núcleo Milenio de Formación Planetaria – NPF and Programa de Iniciación a la Investigación Científica (PIIC) de la Dirección de Postgrado UTFSM convenio No 015/2018. Michel Curé thanks the support from the Centro de Astrofísica de Valparaíso and the Centro Interdisciplinario de Estudios Atmosféricos y Astroestadística. Publisher Copyright: © ESO 2019
N2 - Aims. The study of accurate methods to estimate the distribution of stellar rotational velocities is important for understanding many aspects of stellar evolution. From such observations we obtain the projected rotational speed (v sin i) in order to recover the true distribution of the rotational velocity. To that end, we need to solve a difficult inverse problem that can be posed as a Fredholm integral of the first kind. Methods. In this work we have used a novel approach based on maximum likelihood (ML) estimation to obtain an approximation of the true rotational velocity probability density function (PDF) expressed as a sum of known distribution families. In our proposal, the measurements have been treated as random variables drawn from the projected rotational velocity PDF. We analyzed the case of Maxwellian sum approximation, where we estimated the parameters that define the sum of distributions. Results. The performance of the proposed method is analyzed using Monte Carlo simulations considering two theoretical cases for the PDF of the true rotational stellar velocities: (i) an unimodal Maxwellian probability density distribution and (ii) a bimodal Maxwellian probability density distribution. The results show that the proposed method yielded more accurate estimates in comparison with the Tikhonov regularization method, especially for small sample length (N = 50). Our proposal was evaluated using real data from three sets of measurements, and our findings were validated using three statistical tests. Conclusions. The ML approach with Maxwellian sum approximation is a accurate method to deconvolve the rotational velocity PDF, even when the sample length is small (N = 50).
AB - Aims. The study of accurate methods to estimate the distribution of stellar rotational velocities is important for understanding many aspects of stellar evolution. From such observations we obtain the projected rotational speed (v sin i) in order to recover the true distribution of the rotational velocity. To that end, we need to solve a difficult inverse problem that can be posed as a Fredholm integral of the first kind. Methods. In this work we have used a novel approach based on maximum likelihood (ML) estimation to obtain an approximation of the true rotational velocity probability density function (PDF) expressed as a sum of known distribution families. In our proposal, the measurements have been treated as random variables drawn from the projected rotational velocity PDF. We analyzed the case of Maxwellian sum approximation, where we estimated the parameters that define the sum of distributions. Results. The performance of the proposed method is analyzed using Monte Carlo simulations considering two theoretical cases for the PDF of the true rotational stellar velocities: (i) an unimodal Maxwellian probability density distribution and (ii) a bimodal Maxwellian probability density distribution. The results show that the proposed method yielded more accurate estimates in comparison with the Tikhonov regularization method, especially for small sample length (N = 50). Our proposal was evaluated using real data from three sets of measurements, and our findings were validated using three statistical tests. Conclusions. The ML approach with Maxwellian sum approximation is a accurate method to deconvolve the rotational velocity PDF, even when the sample length is small (N = 50).
KW - Methods: analytical
KW - Methods: data analysis
KW - Methods: numerical
KW - Methods: statistical
KW - Stars: fundamental parameters
KW - Stars: rotation
U2 - 10.1051/0004-6361/201833455
DO - 10.1051/0004-6361/201833455
JO - Astronomy and Astrophysics
JF - Astronomy and Astrophysics
M1 - A138
Orellana R, Escárate P, Curé M, Christen A, Carvajal R, Agüero JC. A method to deconvolve stellar rotational velocities III. The probability distribution function via maximum likelihood utilizing finite distribution mixtures. Astronomy and Astrophysics. 2019;623:A138. doi: 10.1051/0004-6361/201833455