A heuristic wave equation parameterizing BEC dark matter halos with a quantum core and an isothermal atmosphere

Abstract

The Gross-Pitaevskii-Poisson equations that govern the evolution of self-gravitating Bose-Einstein condensates, possibly representing dark matter halos, experience a process of gravitational cooling and violent relaxation. We propose a heuristic parametrization of this complicated process in the spirit of Lynden-Bell's theory of violent relaxation for collisionless stellar systems. We derive a generalized wave equation (that was introduced phenomenologically in [P.H. Chavanis, Eur. Phys. J. Plus {\bf 132}, 248 (2017)]) involving a logarithmic nonlinearity associated with an effective temperature $T_{\mathrm{eff}}$ and a damping term associated with a friction $\xi$. These terms can be obtained from a maximum entropy production principle and are linked by a form of Einstein relation expressing the fluctuation-dissipation theorem. The wave equation satisfies an $H$-theorem for the Lynden-Bell entropy and relaxes towards a stable equilibrium state which is a maximum of entropy at fixed mass and energy. This equilibrium state represents the most probable state of a Bose-Einstein condensate dark matter halo. It generically has a core-halo structure. The quantum core prevents gravitational collapse and may solve the core-cusp problem. The isothermal halo leads to flat rotation curves in agreement with the observations. These results are consistent with the phenomenology of dark matter halos. Furthermore, as shown in a previous paper [P.H. Chavanis, Phys. Rev. D {\bf 100}, 123506 (2019)], the maximization of entropy with respect to the core mass at fixed total mass and total energy determines a core mass--halo mass relation which agrees with the relation obtained in direct numerical simulations. We stress the importance of using a microcanonical description instead of a canonical one. We also explain how our formalism can be applied to the case of fermionic dark matter halos.

References in corpus (12)

• Ultralight scalars as cosmological dark matter
• Too big to fail? The puzzling darkness of massive Milky Way subhaloes
• Cosmic Structure as the Quantum Interference of a Coherent Dark Wave
• Constraints on the Self-Interaction Cross-Section of Dark Matter from Numerical Simulations of the Merging Galaxy Cluster 1E 0657-5
• Understanding the Core-Halo Relation of Quantum Wave Dark Matter, $\psi$DM, from 3D Simulations
• Bose-Einstein Condensation of Dark Matter Axions
• Axion dark matter, solitons, and the cusp-core problem
• Erasing Dark Matter Cusps in Cosmological Galactic Halos with Baryons
• First star-forming structures in fuzzy cosmic filaments
• Nonlinear mean field Fokker-Planck equations. Application to the chemotaxis of biological populations
• MOA-II Galactic Microlensing Constraints: The Inner Milky Way has a Low Dark Matter Fraction and a Near Maximal Disk
• Gravitational instability via the Schrodinger equation

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• The Effect of Boundary Conditions on Structure Formation in Fuzzy Dark Matter
• Dynamical galactic effects induced by stable vortex structure in bosonic dark matter
• A new logotropic model based on a complex scalar field with a logarithmic potential
• Cosmological models based on a complex scalar field with a power-law potential associated with a polytropic equation of state
• Vortex Lines in Ultralight Bosonic Dark Matter around Rotating Supermassive Black Holes
• Thermodynamics of self-gravitating fermions as a robust theory for dark matter halos: Stability analysis applied to the Milky Way