Newtonian boson spheres

Abstract

The Newtonian limit of a boson star is analyzed as a function of the number of its component particles ($N$). For moderate $N$, the sphere is in the collisionless regime and its radius ($R$) satisfies the law $R\ensuremath{\propto}{N}^{\ensuremath{-}1}{m}^{\ensuremath{-}3}$, $m$ being the elementary boson mass. For increasing $N$, this dependence stops when the interparticle repulsion takes over in the equation of state and the cluster turns into an $n=1$ polytrope: Thus $R$ becomes constant, independent of $N$. The physical scales involved and some phenomenological implications are briefly discussed.