An axially-symmetric Newtonian Boson Star

A new solution to the coupled gravitational and scalar field equations for a condensed boson field is found in Newtonian approximation. The solution is axially symmetric, but not spherically symmetric. For N particles the mass of the object is given by $M = Nm - 0.02298 N^3 G_N^2 m^5$, to be compared with $M = Nm - 0.05426 N^3 G_N^2 m^5$ for the spherically symmetric case.