Non-isotropic distributions of stellar rotational velocities
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2021-03
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Universidad de Valparaíso
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Instituto de Fisica y Astronomia
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Stellar rotation is defined from the angular motion of a star about its own rotational axis and study this phenomenon is useful to constrain models of stellar formation and evolution. The equatorial velocity v is defined as the surface angular speed at latitude 0o , however, the projected rotational velocity v sin i value is one of the most straightforward and cheapest (from an observational point of view) ways to obtain the rotational velocity of a star, where i is the inclination angle between the axis of rotation with respect to the observer. This research is separated in two parts; obtain this v sin i value via Fourier Transform in an automated procedure and apply a non- isotropic distribution model for the axes on the unit sphere of observation:
1)Obtaining v sin i: There are several methods to infer v sin i data, in the case of Fourier Transform, this method consists in obtain the first zero of the Fourier Trans- form domain from a rotational kernel for the observed absorption line profile. First, an automated procedure to obtain v sin i via Fourier Transform is constructed, for multi- ple absorption lines at different epochs. The method consists in fit a Gaussian profile to the respective line and select the signal from the curve. Monte Carlo simulations are performed where theoretical lines are constructed for specific rotational velocities. Then, the noise is added and multiple repetitions are computed to analyze the consis- tence of the method. Later, our automatized Fourier Transform method is used in the BeSOS database to obtain their v sin i values. Results are in global agreement with the literature.
2) How is distributed v sin i: An integral equation that governs the two distribu- tions v and v sin i (true and apparent rotational speed distributions respectively) is given by a Fredholm integral in which an α parameter is added into the kernel of the equation to model a non-isotropic distribution, where α < 0 yields inclination angles close to the polar axis, α > 0 a non-isotropic near to the equator and α = 0 is the typical isotropic axes distribution. The true distribution is calculated via Tikhonov regularization method from the observed distribution which is estimated by a kernel density estimator. As α parameter is unknown, we made a grid of α to compute the Fredholm integral. To obtain the best α value, we minimized the mean square error of the projected kernel density estimator distribution with respect to the new grid of solutions for the Fredholm integral equation. The Monte Carlo random sampling repetitions ensures that the method, in general terms, is reliable until α ∼ 1. Theprocedure is applied to several open stellar clusters and field stars to see the behav- ior of the non-isotropy finding effectively that the different databases of stars are not isotropic rotating with respect to Earth.
In summary, we have developed two novel methods; measures the v sin i values from any stellar spectrum for multiple absorption lines at different epochs where the line is broadening mainly by rotation (high rotators); the second, obtains the non-isotropy from a sample of v sin i data without any convergence criteria. As fu- ture works we want to implement this last method to binary systems (star-star or exoplanet-star) discovered by transit and also an extra parameter β can be introduced into the Fredholm integral to compute more complex distribution of axes.
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ROTACION DE ESTRELLAS, VELOCIDAD, ANALISIS DE FOURIER, METODO DE MONTE CARLO