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

Pierre-Henri Chavanis ()
Additional contact information
Pierre-Henri Chavanis: Université de Toulouse, CNRS, UPS

The European Physical Journal B: Condensed Matter and Complex Systems, 2022, vol. 95, issue 3, 1-43

Abstract: 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 Chavanis (Eur Phys J Plus 132:248, 2017) involving a logarithmic nonlinearity associated with an effective temperature $$T_\mathrm{eff}$$ T eff and a damping term associated with a friction $$\xi $$ ξ . 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 (Chavanis in Phys Rev D 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. Graphic abstract

Date: 2022
References: View complete reference list from CitEc
Citations:

Downloads: (external link)
http://link.springer.com/10.1140/epjb/s10051-022-00299-9 Abstract (text/html)
Access to the full text of the articles in this series is restricted.

Related works:
This item may be available elsewhere in EconPapers: Search for items with the same title.

Export reference: BibTeX RIS (EndNote, ProCite, RefMan) HTML/Text

Persistent link: https://EconPapers.repec.org/RePEc:spr:eurphb:v:95:y:2022:i:3:d:10.1140_epjb_s10051-022-00299-9

Ordering information: This journal article can be ordered from
http://www.springer.com/economics/journal/10051

DOI: 10.1140/epjb/s10051-022-00299-9

Access Statistics for this article

The European Physical Journal B: Condensed Matter and Complex Systems is currently edited by P. Hänggi and Angel Rubio

More articles in The European Physical Journal B: Condensed Matter and Complex Systems from Springer, EDP Sciences
Bibliographic data for series maintained by Sonal Shukla () and Springer Nature Abstracting and Indexing ().