TY - JOUR
T1 - A method to deconvolve stellar rotational velocities II
T2 - The probability distribution function via Tikhonov regularization
AU - Christen, Alejandra
AU - Escarate, Pedro
AU - Curé, Michel
AU - Rial, Diego F.
AU - Cassetti, Julia
N1 - Publisher Copyright:
© 2016 ESO.
PY - 2016/11/1
Y1 - 2016/11/1
N2 - 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.
AB - 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.
KW - Methods: data analysis
KW - Methods: numerical
KW - Methods: statistical
KW - Stars: fundamental parameters
KW - Stars: rotation
UR - http://www.scopus.com/inward/record.url?scp=84993993230&partnerID=8YFLogxK
U2 - 10.1051/0004-6361/201629070
DO - 10.1051/0004-6361/201629070
M3 - Article
AN - SCOPUS:84993993230
VL - 595
JO - Astronomy and Astrophysics
JF - Astronomy and Astrophysics
SN - 0004-6361
M1 - A50
ER -