Abstract
According to the statistical law of large numbers, the expected mean of
identically distributed random variables of a sample tends toward the
actual mean as the sample increases. Under this law, it is possible to test the Chandrasekhar's relation (CR), < V > = (pi/4)(-1) < Vsin i >,
using a large amount of Vsin i and V data from different samples of
similar stars. In this context, we conducted a statistical test to check
the consistency of the CR in the Kepler field. In order to achieve this,
we use three large samples of V obtained from Kepler rotation periods
and a homogeneous control sample of Vsin i to overcome the scarcity of
Vsin i data for stars in the Kepler field. We used the
bootstrap-resampling method to estimate the mean rotations (< V > and <
V sin i >) and their corresponding confidence intervals for the stars
segregated by effective temperature. Then, we compared the estimated
means to check the consistency of CR, and analyzed the influence of the
uncertainties in radii measurements, and possible selection effects. We found that the CR with < sin i > = pi/4 is consistent with the behavior
of the < V > as a function of Vsin i for stars from the Kepler field as
there is a very good agreement between such a relation and the data.
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