Abstract
The projected rotational velocity v sin i is a fundamental observable quantity. In order to obtain the rotational velocity distribution of a sample of v sin i, Chandrasekhar & Münch (1950) developed a formalism to obtain this distribution under the assumption that rotational axes are uniformly distributed, but this method is not usually applied due to an intrinsic numerical problem associated to the derivative of an Abel's integral. An alternative iterative method was developed by Lucy (1974) to disentangle the distribution function of this kind of inverse problem, but this method has no convergence criteria. Here we present a new method to disentangle the distribution of rotational velocities, based on Chandrasekhar & Münch (1950) formalism. We obtain the cumulative distribution function (CDF) of the rotational velocities from projected velocities (v sin i) under the standard assumption of uniform distributed rotational axes. Through simulations the method is tested using a) theoretical Maxwellian distribution functions for the rotational velocity distribution and b) with a sample of about 12.500 main-sequence field stars. Our main results are: The method is robust and in just one step gives the cumulative distribution function of rotational velocities. When applied to theoretical distributions it recovers the CDF with very high confidence. When applied to real data, we recover the results from Carvalho et al. (2009) proving that the velocity distribution function of main-sequence field stars is non-Maxwellian and are better described by Tsallis or Kaniadakis distribution functions.
