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Title: Expansion in higher harmonics of boson stars using a generalized Ruffini-Bonazzola approach. Part 1. Bound states

The method pioneered by Ruffini and Bonazzola (RB) to describe boson stars involves an expansion of the boson field which is linear in creation and annihilation operators. This expansion constitutes an exact solution to a non-interacting field theory, and has been used as a reasonable ansatz for an interacting one. In this work, we show how one can go beyond the RB ansatz towards an exact solution of the interacting operator Klein-Gordon equation, which can be solved iteratively to ever higher precision. Our Generalized Ruffini-Bonazzola approach takes into account contributions from nontrivial harmonic dependence of the wavefunction, using a sum of terms with energy $$k\,E_0$$, where $$k\geq1$$ and $$E_0$$ is the chemical potential of a single bound axion. The method critically depends on an expansion in a parameter $$\Delta \equiv \sqrt{1-E_0{}^2/m^2}<1$$, where $m$ is the mass of the boson. In the case of the axion potential, we calculate corrections which are relevant for axion stars in the transition or dense branches. We find with high precision the local minimum of the mass, $$M_{min}\approx 463\,f^2/m$$, at $$\Delta\approx0.27$$, where $f$ is the axion decay constant. This point marks the crossover from transition to dense branches of solutions, and a corresponding crossover from structural instability to stability.
Authors:
 [1] ;  [2] ;  [2]
  1. Weizmann Inst. of Science, Rehovot (Israel)
  2. Univ. of Cincinnati, OH (United States)
Publication Date:
Report Number(s):
FERMILAB-PUB-17-644-T; arXiv:1712.04941
Journal ID: ISSN 1475-7516; 1643231
Grant/Contract Number:
AC02-07CH11359
Type:
Accepted Manuscript
Journal Name:
Journal of Cosmology and Astroparticle Physics
Additional Journal Information:
Journal Volume: 2018; Journal Issue: 04; Journal ID: ISSN 1475-7516
Publisher:
Institute of Physics (IOP)
Research Org:
Fermi National Accelerator Lab. (FNAL), Batavia, IL (United States)
Sponsoring Org:
USDOE Office of Science (SC), High Energy Physics (HEP) (SC-25)
Country of Publication:
United States
Language:
English
Subject:
79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
OSTI Identifier:
1431581