Stationary scalar hairy configurations supported by Neumann compact stars

We study stationary scalar field hairy configurations supported by asymptotically flat horizonless compact stars. At the star surface, we impose Neumann boundary conditions for the scalar field. With analytical methods, we obtain bounds on the frequency of scalar fields. For certain discrete frequency satisfying the bounds, we numerically get solutions of scalar hairy stars. We also disclose effects of model parameters on the discrete frequency of scalar fields.