A method to deconvolve stellar rotational velocities II

Christen, Alejandra; Escárate, Pedro; Curé, M.; Rial, Diego; Cassetti, Julia

doi:10.1051/0004-6361/201629070

Cited by 5 publications

(22 citation statements)

References 15 publications

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“…This particular problem is of great importance, since it allows astronomers to describe and model the stars formation, their internal structure and evolution, as well as how they interact with other stars, see e.g. [19, 41, 42].…”

Section: A Systematic Approach To Construct Surrogate Functions Formentioning

confidence: 99%

A data augmentation approach for a class of statistical inference problems

et al. 2018

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We present an algorithm for a class of statistical inference problems. The main idea is to reformulate the inference problem as an optimization procedure, based on the generation of surrogate (auxiliary) functions. This approach is motivated by the MM algorithm, combined with the systematic and iterative structure of the Expectation-Maximization algorithm. The resulting algorithm can deal with hidden variables in Maximum Likelihood and Maximum a Posteriori estimation problems, Instrumental Variables, Regularized Optimization and Constrained Optimization problems. The advantage of the proposed algorithm is to provide a systematic procedure to build surrogate functions for a class of problems where hidden variables are usually involved. Numerical examples show the benefits of the proposed approach.

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Section: A Systematic Approach To Construct Surrogate Functions Formentioning

confidence: 99%

A data augmentation approach for a class of statistical inference problems

et al. 2018

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“…On the other hand, in Christen et al (2016) a method to estimate the PDF from the Fredholm integral (Eq. (1)) by means of the Tikhonov regularization method (TRM) was obtained.…”

Section: Introductionmentioning

confidence: 99%

“…The main departure from Christen et al (2016) and the standard solutions for the integral equation is that in our approach, the measurements are treated as realizations of the PDF that defines the projected rotational velocity instead of evaluations of the PDF. Thus, the observed samples are used as realizations of a known parametric random variable (y), belonging to a known parametric family that is a mixture (see Eq.…”

Section: Introductionmentioning

confidence: 99%

“…We use the ML method (estimators with good statistical properties) to estimate the parameters, which are calculated without directly estimating f Y (y). Other methods need to perform an approximation in order to use a Kernel density estimator (KDE) to estimate the projected rotational speed density (see e.g., Curé et al 2014or Christen et al 2016. This implies that, since we obtain the ML estimates of the parameters that define the unknown PDF, our solution is, in general, well-conditioned (more data points than unknown parameters).…”

Section: Introductionmentioning

confidence: 99%

“…In Sect. 4, Monte Carlo simulations are presented to show the benefits of this method, comparing the results with TRM algorithm proposed by Christen et al (2016). In Sect.…”

Section: Introductionmentioning

confidence: 99%

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A method to deconvolve stellar rotational velocities

Orellana

Escárate

Curé

et al. 2019

A&A

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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).

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A method to deconvolve stellar profiles

Escárate,

Curé,

Araya

et al. 2023

A&A

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Context. Currently, one of the standard procedures used to determine stellar and wind parameters of massive stars involves to comparing the observed spectral lines with a grid of synthetic lines. These synthetic lines are calculated using non-local thermodynamic equilibrium radiative transfer codes. In this standard procedure, after estimating the stellar-projected rotational speed (v sin i), all synthetic models need to be convolved using this value in order to perform the comparison with the observed line and estimate the stellar parameters. Aims. In this work, we propose a methodology to deconvolve the observed line profile to one from a non-rotating star. Thus, to perform a comparison, we will not need to convolve all the synthetic profiles, saving significant time and resources. Methods. The proposed deconvolution method is based on transforming this inverse problem into an optimization of a direct problem. We propose using a Gaussian sum approximation (GSA) to obtain the line profile without the broadening effect due to stellar rotation. After selecting the most adequate model to derive the fundamental GSA parameters, we convolved it with the known v sin i in order to obtain the profile considering the v sin i. Finally, we compared this approximated line profile directly with the observed spectrum. Results. The performance of the proposed method is analyzed using synthetic and observed lines. The results show that the proposed deconvolution method yields accurate non-rotating profiles. Conclusions. The proposed approach utilizing GSA is an accurate method to deconvolve spectral lines.

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A method to deconvolve stellar rotational velocities II

Cited by 5 publications

References 15 publications

A data augmentation approach for a class of statistical inference problems

A data augmentation approach for a class of statistical inference problems

A method to deconvolve stellar rotational velocities

A method to deconvolve stellar profiles

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