A heuristic wave equation parameterizing BEC dark matter halos with a quantum core and an isothermal atmosphere
In: Eur.Phys.J.B ; https://hal.science/hal-03217622 ; Eur.Phys.J.B, 2022, 95 (3), pp.48. ⟨10.1140/epjb/s10051-022-00299-9⟩, 2022
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International audience ; 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 $T_\mathrm{eff}$ 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 (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 not available: see fulltext][graphic not available: see fulltext]
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A heuristic wave equation parameterizing BEC dark matter halos with a quantum core and an isothermal atmosphere
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Autor/in / Beteiligte Person: | Chavanis, Pierre-Henri ; Laboratoire de Physique Théorique (LPT) ; Université Toulouse III - Paul Sabatier (UT3) ; Université de Toulouse (UT)-Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Fédération de recherche « Matière et interactions » (FeRMI) ; Institut National des Sciences Appliquées - Toulouse (INSA Toulouse) ; Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Université Toulouse III - Paul Sabatier (UT3) ; Université de Toulouse (UT)-Centre National de la Recherche Scientifique (CNRS)-Institut National des Sciences Appliquées - Toulouse (INSA Toulouse) ; Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS) ; Physique Statistique des Systèmes Complexes (LPT) (PhyStat) ; Institut National des Sciences Appliquées (INSA)-Université de Toulouse (UT)-Institut National des Sciences Appliquées (INSA)-Centre National de la Recherche Scientifique (CNRS)-Université Toulouse III - Paul Sabatier (UT3) |
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Zeitschrift: | Eur.Phys.J.B ; https://hal.science/hal-03217622 ; Eur.Phys.J.B, 2022, 95 (3), pp.48. ⟨10.1140/epjb/s10051-022-00299-9⟩, 2022 |
Veröffentlichung: | HAL CCSD, 2022 |
Medientyp: | academicJournal |
DOI: | 10.1140/epjb/s10051-022-00299-9 |
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