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 --- v sin(alpha).
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.
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