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We study stationary scalar field hairy configurations supported byasymptotically flat horizonless compact stars. At the star surface, we imposeNeumann boundary conditions for the scalar field. With analytical methods, weobtain bounds on the frequency of scalar fields. For certain discrete frequencysatisfying the bounds, we numerically get solutions of scalar hairy stars. Wealso disclose effects of model parameters on the discrete frequency of scalarfields.

Stationary scalar hairy configurations supported by Neumann compact stars