A method to deconvolve stellar rotational velocities

Rotational speed is an important physical parameter of stars and knowing the distribution of stellar rotational velocities is essential for the understanding stellar evolution. However, it cannot be measured directly but the convolution of the rotational speed and the sine of the inclination angle, $v \sin i$. We developed a method to deconvolve this inverse problem and obtain the cumulative distribution function (CDF) for stellar rotational velocities extending the work of Chandrasekhar & M\"unch (1950). This method is applied a) to theoretical synthetic data recovering the original velocity distribution with very small error; b) to a sample of about 12.000 field main--sequence stars, corroborating that the velocity distribution function is non--Maxwellian, but is better described by distributions based on the concept of maximum entropy, such as Tsallis or Kaniadakis distribution functions. This is a very robust and novel method that deconvolve the rotational velocity cumulative distribution function from a sample of $v \sin i$ data in just one single step without needing any convergence criteria.Comment: Accepted in A&

Wavelets Analysis for Time Series

Wavelet analysis has been widely used to analyze time series and has countless applications in astronomy. Because of its characteristics it is a method that is well suited to approximate functions, eliminate noise, detect points of change, discontinuities and periodicities. In this article an introduction to the wavelet theory and its use in time series is presented. Numerical simulations and some real examples are developed in the software R.Facultad de Ciencias Astronómicas y Geofísica

Estudio de curvas de luz sintéticas multiperiódicas aplicando análisis wavelet

Las características de las funciones wavelet las hacen adecuadas para analizar datos que presentan variaciones o discontinuidades abruptas; por esta razón son particularmente útiles para estudiar curvas de luz de estrellas supergigantes y binarias. Sin embargo, al analizar una señal pueden surgir efectos no deseados tales como la detección de períodos espurios y períodos alias que resultan del nivel de ruido de la señal o como resultado de un muestreo no-equidistante. Para estudiar cómo estos efectos interfieren en la detección de períodos, se ha generado un diseño de simulación de curvas de luz de estrellas binarias eclipsantes que presentan fenómenos de pulsación. Se utilizaron funciones sinusoidales para emular pulsaciones radiales y no radiales. Las curvas resultantes se analizaron con la transformada de Fourier y con la función wavelet de Morlet, usando el programa Periodo4 y el paquete WaveletComp de R, respectivamente.The characteristics of wavelet functions make them suitable for analyzing data that present abrupt variations or discontinuities, which is why they are particularly useful for studying light curves of supergiant and binary stars. However, when analyzing a signal, undesired effects can arise such as the detection of spurious periods resulting from the noise level of the signal or as a result of non-equidistant sampling. To study how these effects interfere with period detection we generated a simulation design of light curves of eclipsing binary stars exhibiting pulsation phenomena. Sinusoidal functions were used to emulate radial and non-radial pulsations. The resulting curves were analyzed with the Fourier transform and with the Morlet wavelet function, using the Period04 software and the WaveletComp R-package, respectively.Facultad de Ciencias Astronómicas y GeofísicasInstituto de Astrofísica de La Plat

A method to deconvolve stellar rotational velocities II

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

Simulaciones y análisis temporal de curvas de luz de estrellas binarias pulsantes

La detección y el estudio de estrellas pulsantes en sistemas binarios es fundamental para explorar la estructura interna de las estrellas y verificar los modelos de evolución estelar. Sin embargo, al analizar una señal pueden surgir efectos no deseados como la detección de períodos espurios y alias que resultan del nivel de ruido de la señal o como resultado de un muestreo no-equidistante. Para estudiar cómo estos efectos interfieren en la detección de períodos se ha generado un diseño de simulación de curvas de luz de estrellas binarias eclipsantes que presentan fenómenos de pulsación. Se utilizaron funciones sinusoidales para emular pulsaciones no radiales con diferentes escalas de períodos y de amplitud, considerando un ruido tipo ARMA (1,1) para la señal. Las curvas resultantes se analizaron con la transformada de Fourier y con la función wavelet de Morlet, usando el software Period04 y los paquetes spectral y WaveletComp de R.The detection and study of pulsating stars in binary systems is essential to explore the internal structure of stars and verify stellar evolution models. However, undesired effects can arise when analyzing a signal, such as the detection of spurious periods resulting from the noise level of the signal or as a result of non-equidistant sampling. To study how these effects interfere with period detection, we generated a simulation design of light curves of eclipsing binary stars exhibiting pulsation phenomena. Sinusoidal functions were used to emulate non-radial pulsations with different period and amplitude scales, considering an ARMA (1,1) type noise for the signal. The resulting curves were analyzed with the Fourier transform and the Morlet wavelet function, using the Period04 software and the spectral and WaveletComp packages of R.Asociación Argentina de AstronomíaInstituto de Astrofísica de La Plat

Total variation estimates for the TCP process

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Synthetic Light Curve Design for Pulsating Binary Stars to Compare the Efficiency in the Detection of Periodicities

B supergiant stars pulsate in regular and quasi-regular oscillations resulting in intricate light variations that might conceal their binary nature. To discuss possible observational bias in a light curve, we performed a simulation design of a binary star affected by sinusoidal functions emulating pulsation phenomena. The Period04 tool and the WaveletComp package of R were used for this purpose. Thirty-two models were analysed based on a combination of two values on each of the k = 6 variables, such as multiple pulsations, the amplitude of the pulsation, the pulsation frequency, the beating phenomenon, the light-time effect, and regular or quasi-regular periods. These synthetic models, unlike others, consider an ARMA (1, 1) statistical noise, irregular sampling, and a gap of about 4 days. Comparing Morlet wavelet with Fourier methods, we observed that the orbital period and its harmonics were well detected in most cases. Although the Fourier method provided more accurate period detection, the wavelet analysis found it more times. Periods seen with the wavelet method have a shift due to the slightly irregular time scale used. The pulsation period hitting rate depends on the wave amplitude and frequency with respect to eclipse depth and orbital period. None of the methods was able to distinguish accurate periods leading to a beating phenomenon when they were longer than the orbital period, resulting, in both cases, in an intermediate value. When the beating period was shorter, the Fourier analysis found it in all cases except for unsolved quasi-regular periods. Overall, the Morlet wavelet analysis performance was lower than the Fourier analysis. Considering the strengths and disadvantages found in these methods, we recommend using at least two diagnosis tools for a detailed time series data analysis to obtain confident results. Moreover, a fine-tuning of trial periods by applying phase diagrams would be helpful for recovering accurate values. The combined analysis could reduce observational bias in searching binaries using photometric techniques