Schrödinger-Poisson Solitons: Perturbation Theory

Abstract

Self-gravitating quantum matter may exist in a wide range of cosmological and astrophysical settings from the very early universe through to present-day boson stars. Such quantum matter arises in a number of different theories, including the Peccei-Quinn axion and UltraLight (ULDM) or Fuzzy (FDM) dark matter scenarios. We consider the dynamical evolution of perturbations to the spherically symmetric soliton, the ground state solution to the Schrödinger-Poisson system common to all these scenarios. We construct the eigenstates of the Schrödinger equation, holding the gravitational potential fixed to its ground state value. We see that the eigenstates qualitatively capture the properties seen in full ULDM simulations, including the soliton "breathing" mode, the random walk of the soliton center, and quadrupolar distortions of the soliton. We then show that the time-evolution of the gravitational potential and its impact on the perturbations can be well described within the framework of time-dependent perturbation theory. Applying our formalism to a synthetic ULDM halo reveals considerable mixing of eigenstates, even though the overall density profile is relatively stable. Our results provide a new analytic approach to understanding the evolution of these systems as well as possibilities for faster approximate simulations.

12 pages, 11 figures; accepted to PRD The content and conclusions of Sec IV changed in the review process. Fig 9 was changed and Fig 10 added to illustrate our averaging procedure. Fig 11 changed significantly due to a tweak in the analysis pipeline. We added more discussion on the utility of our approach, more information on our numerical solver, and made small editorial changes

References in corpus (10)

• Ultralight scalars as cosmological dark matter
• Cosmic Structure as the Quantum Interference of a Coherent Dark Wave
• Understanding the Core-Halo Relation of Quantum Wave Dark Matter, $\psi$DM, from 3D Simulations
• Wave Dark Matter
• Oscillations and Random Walk of the Soliton Core in a Fuzzy Dark Matter Halo
• Lighting the Dark: The Evolution of the Post-Inflationary Universe
• Instability of rotating Bose stars
• On the Random Motion of Nuclear Objects in a Fuzzy Dark Matter Halo
• Don't cross the streams: caustics from Fuzzy Dark Matter
• Formation of inflaton halos after inflation

Cited by in corpus (6)

• Small-scale structure in vector dark matter
• Soliton Formation and the Core-Halo Mass Relation: An Eigenstate Perspective
• Coherent and incoherent structures in fuzzy dark matter halos
• Scalar dark matter vortex stabilization with black holes
• Theory and phenomenology of stressed wave-dark-matter soliton
• Gravitational soliton solutions to self-coupled Klein-Gordon and Schrödinger equations