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Radial oscillations of boson stars made of ultralight repulsive dark matter. (English) Zbl 1475.85009

Summary: We compute the lowest frequency radial oscillation modes of boson stars. It is assumed that the object is made of pseudo-Goldstone bosons subjected to a scalar potential that leads to a repulsive self-interaction force, and which is characterized by two unknown mass scales \(m\) (mass of the particle) and \(F\) (decay constant). First we integrate the Tolman-Oppenheimer-Volkoff equations for the hydrostatic equilibrium of the star, and then we solve the Sturm-Liouville boundary value problem for the perturbations using the shooting method. The effective potential that enters into the Schrödinger-like equation as well as several associated eigenfunctions are shown as well. Moreover, we found that the large frequency separation, i.e. the difference between consecutive modes, is proportional to the square root of the mass of the star and the cube of the mass scale defined by \(\Lambda \equiv \sqrt{mF} \).

MSC:

85A15 Galactic and stellar structure
81V25 Other elementary particle theory in quantum theory
81V73 Bosonic systems in quantum theory
83C56 Dark matter and dark energy
81T12 Effective quantum field theories
76E20 Stability and instability of geophysical and astrophysical flows
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