Expansion in higher harmonics of boson stars using a generalized RuffiniBonazzola 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 noninteracting 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 KleinGordon equation, which can be solved iteratively to ever higher precision. Our Generalized RuffiniBonazzola 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 $$\Delta \equiv \sqrt{1E_0{}^2/m^2}<1$$, 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]}
 Weizmann Inst. of Science, Rehovot (Israel)
 Univ. of Cincinnati, OH (United States)
 Publication Date:
 Report Number(s):
 FERMILABPUB17644T; arXiv:1712.04941
Journal ID: ISSN 14757516; 1643231
 Grant/Contract Number:
 AC0207CH11359
 Type:
 Accepted Manuscript
 Journal Name:
 Journal of Cosmology and Astroparticle Physics
 Additional Journal Information:
 Journal Volume: 2018; Journal Issue: 04; Journal ID: ISSN 14757516
 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) (SC25)
 Country of Publication:
 United States
 Language:
 English
 Subject:
 79 ASTRONOMY AND ASTROPHYSICS; 72 PHYSICS OF ELEMENTARY PARTICLES AND FIELDS
 OSTI Identifier:
 1431581
Eby, Joshua, Suranyi, Peter, and Wijewardhana, L. C. R.. Expansion in higher harmonics of boson stars using a generalized RuffiniBonazzola approach. Part 1. Bound states. United States: N. p.,
Web. doi:10.1088/14757516/2018/04/038.
Eby, Joshua, Suranyi, Peter, & Wijewardhana, L. C. R.. Expansion in higher harmonics of boson stars using a generalized RuffiniBonazzola approach. Part 1. Bound states. United States. doi:10.1088/14757516/2018/04/038.
Eby, Joshua, Suranyi, Peter, and Wijewardhana, L. C. R.. 2018.
"Expansion in higher harmonics of boson stars using a generalized RuffiniBonazzola approach. Part 1. Bound states". United States.
doi:10.1088/14757516/2018/04/038.
@article{osti_1431581,
title = {Expansion in higher harmonics of boson stars using a generalized RuffiniBonazzola approach. Part 1. Bound states},
author = {Eby, Joshua and Suranyi, Peter and Wijewardhana, L. C. R.},
abstractNote = {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 noninteracting 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 KleinGordon equation, which can be solved iteratively to ever higher precision. Our Generalized RuffiniBonazzola 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 $\Delta \equiv \sqrt{1E_0{}^2/m^2}<1$, 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.},
doi = {10.1088/14757516/2018/04/038},
journal = {Journal of Cosmology and Astroparticle Physics},
number = 04,
volume = 2018,
place = {United States},
year = {2018},
month = {4}
}