Abstract
Boson stars are gravitationally bound objects that arise in ultralight dark matter models and form in the centers of galactic halos or axion miniclusters. We systematically study the excitations of a boson star, taking into account the mixing between positive and negative frequencies introduced by gravity. We show that the spectrum contains zero-energy modes in the monopole and dipole sectors resulting from spontaneous symmetry breaking by the boson star background. We analyze the general properties of the eigenmodes and derive their orthogonality and completeness conditions which have non-standard form due to the positive-negative frequency mixing. The eigenvalue problem is solved numerically for the first few energy levels in different multipole sectors and the results are compared to the solutions of the Schrödinger equation in fixed boson star gravitational potential. The two solutions differ significantly for the lowest modes, but get close for higher levels. We further confirm the normal mode spectrum in 3D wave simulations where we inject perturbations with different multipoles. As an application of the normal mode solutions, we compute the matrix element entering the evaporation rate of a boson star immersed in a hot axion gas. The computation combines the use of exact wavefunctions for the low-lying bound states and of the Schrödinger approximation for the high-energy excitations.
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Acknowledgments
We are grateful to Pierre Sikivie and Luna Zagorac for useful discussions. The research of J.H.-H.C. was made possible by the generosity of Eric and Wendy Schmidt by recommenda- tion of the Schmidt Futures program. The work of S.S. is supported by the Natural Sciences and Engineering Research Council (NSERC) of Canada. Research at Perimeter Institute is supported in part by the Government of Canada through the Department of Innovation, Science and Economic Development Canada and by the Province of Ontario through the Ministry of Colleges and Universities. W.X. is supported in part by the U.S. Department of Energy under grant DE-SC0022148 at the University of Florida.
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Chan, J.HH., Sibiryakov, S. & Xue, W. Boson star normal modes. J. High Energ. Phys. 2023, 45 (2023). https://doi.org/10.1007/JHEP08(2023)045
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DOI: https://doi.org/10.1007/JHEP08(2023)045