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Be stars are found to rotate close to their critical rotation and therefore they are considered an important laboratory for the study of stellar rotation. In this context, we obtain the projected rotational velocity of a sample of classical Be southern stars in the BeSOS database via Fourier transforms in an automated way for several absorption lines at different epochs. A Gaussian profile is fitted to eight observed photospheric He i  lines in order to select automatically from the profile the spectral signal given by areas under the curve of 95.45, 98.75, and 99.83 per cent, to obtain v sin  i  via the Fourier transform technique. The values obtained are in global agreement with the literature. Analysing only one line is not enough to set the v sin  i  value: depending on the line, the value in most cases is underestimated with respect to λ 4471. When gravity-darkening effects are included, apparent values increase by ∼10 per cent. The resolution of the instrument Pontificia Universidad Catolica High Echelle Resolution Optical Spectrograph (PUCHEROS) used for BeSOS spectra (⁠|$R \sim 17\, 000$|⁠) constrains the theoretical lower bound possible to v sin  i  ∼ 100  km s−1. The procedure has limitations, using a linear limb-darkening function with ε = 0.6 for classical Be stars rotating close to the break-up velocity without gravity-darkening corrections, which cannot be negligible. Previous works measure v sin  i  values using just one spectral line and here we demonstrate that with more lines the results can vary. This could be due to the photospheric distribution of atomic transitions in classical Be stars. [ABSTRACT FROM AUTHOR]

Aims. It is important to know the binary mass-ratio distribution to better understand the evolution of stars in binary systems and to constrain their formation. However, in most cases, that is, for single-lined spectroscopic binaries, the mass ratio cannot be measured directly, but can only be derived as the convolution of a function that depends on the mass ratio and on the unknown inclination angle of the orbit on the plane of the sky. Methods. We extend our previous method for deconvolving this inverse problem by obtaining the cumulative distribution function (CDF) for the mass-ratio distribution as an integral. Results. After a suitable transformation of variables, this problem becomes the same as the problem of rotational velocities v sin i, allowing a close analytic formulation for the CDF.We here apply our method to two real datasets: a sample of Am star binary systems, and a sample of massive spectroscopic binaries in the Cyg OB2 association. Conclusions. We are able to reproduce previous results for the sample of Am stars. In addition, the mass-ratio distribution of massive stars shows an excess of systems with a low mass ratio, in contrast to what was claimed elsewhere. Our method proves to be very reliable and deconvolves the distribution from a sample in one single step. [ABSTRACT FROM AUTHOR]

Aims. Rotational speed is an important physical parameter of stars, and knowing the distribution of stellar rotational velocities is essential for understanding stellar evolution. However, rotational speed cannot be measured directly and is instead the convolution between the rotational speed and the sine of the inclination angle v sin i. Methods. We developed a method to deconvolve this inverse problem and obtain the cumulative distribution function for stellar rotational velocities extending the work of Chandrasekhar & Münch (1950, ApJ, 111, 142) Results. This method is applied: a) to theoretical synthetic data recovering the original velocity distribution with a very small error; and 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. Conclusions. This is a very robust and novel method that deconvolves the rotational velocity cumulative distribution function from a sample of v sin i data in a single step without needing any convergence criteria. [ABSTRACT FROM AUTHOR]

Rotational speed is an important physical parameter of stars: knowing the distribution of stellar rotational velocities is essential for understanding stellar evolution. However, rotational speed cannot be measured directly and is instead the convolution between the rotational speed and the sine of the inclination angle vsin(i). The problem itself can be described via a Fredhoml integral of the first kind. A new method (Curé et al. 2014) to deconvolve this inverse problem and obtain the cumulative distribution function for stellar rotational velocities is based on the work of Chandrasekhar & Münch (1950). Another method to obtain the probability distribution function is Tikhonov regularization method (Christen et al. 2016). The proposed methods can be also applied to the mass ratio distribution of extrasolar planets and brown dwarfs (in binary systems, Curé et al. 2015). For stars in a cluster, where all members are gravitationally bounded, the standard assumption that rotational axes are uniform distributed over the sphere is questionable. On the basis of the proposed techniques a simple approach to model this anisotropy of rotational axes has been developed with the possibility to “disentangling” simultaneously both the rotational speed distribution and the orientation of rotational axes. [ABSTRACT FROM AUTHOR]