Boson Stars: Gravitational Equilibria of Self-Interacting Scalar Fields

Spherically symmetric gravitational equilibria of self-interacting scalar fields $\phi$ with interaction potential $V\left(\phi \right)=\frac{1}{4}\lambda {\left|\phi \right|}^4$ are determined. Surprisingly, the resulting configuration may differ markedly from the noninteracting case even when $\lambda \ll 1$. Contrary to generally accepted astrophysical folklore, it is found that the maximum masses of such boson stars may be comparable to the Chandrasekhar mass for fermions of mass $m_{\mathrm{fermion}}\sim {\lambda }^{-\frac{1}{4}}{m}_{\mathrm{boson}}$.