Jeans Instability of Dissipative Self-Gravitating Bose–Einstein Condensates with Repulsive or Attractive Self-Interaction: Application to Dark Matter

Chavanis, Pierre‐Henri

doi:10.3390/universe6120226

Cited by 20 publications

(18 citation statements)

References 338 publications

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“…This leads to DM halos presenting a central core instead of a cusp. Since the quantum Jeans length is nonzero [52,[60][61][62][63][64][65][66][67][68][69], the formation of small-scale structures is suppressed even at T = 0. Therefore, quantum mechanics may be a way to solve the small-scale problems of the CDM model such as the core-cusp problem and the missing satellite problem.…”

Section: Introductionmentioning

confidence: 99%

Predictive model of BEC dark matter halos with a solitonic core and an isothermal atmosphere

Chavanis

2019

Phys. Rev. D

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121

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We develop a model of Bose-Einstein condensate dark matter halos with a solitonic core and an isothermal atmosphere based on a generalized Gross-Pitaevskii-Poisson equation [P.H. Chavanis, Eur. Phys. J. Plus 132, 248 (2017)]. This equation provides a heuristic coarse-grained parametrization of the ordinary Gross-Pitaevskii-Poisson equation accounting for violent relaxation and gravitational cooling. It involves a cubic nonlinearity taking into account the self-interaction of the bosons, a logarithmic nonlinearity associated with an effective temperature, and a source of dissipation. It leads to superfluid dark matter halos with a core-halo structure. The quantum potential or the self-interaction of the bosons generates a solitonic core that solves the cusp problem of the cold dark matter model. The logarithmic nonlinearity generates an isothermal atmosphere accounting for the flat rotation curves of the galaxies. The dissipation ensures that the system relaxes towards an equilibrium configuration. In the Thomas-Fermi approximation, the dark matter halo is equivalent to a barotropic gas with an equation of state P = 2πas 2 ρ 2 /m 3 + ρkBT /m, where as is the scattering length of the bosons and m is their individual mass. We numerically solve the equation of hydrostatic equilibrium and determine the corresponding density profiles and rotation curves. We impose that the surface density of the halos has the universal value Σ0 = ρ0r h = 141 M /pc 2 obtained from the observations. For a boson with ratio as/m 3 = 3.28 × 10 3 fm/(eV/c 2 ) 3 , we find a minimum halo mass (M h )min = 1.86 × 10 8 M and a minimum halo radius (r h )min = 788 pc. This ultracompact halo corresponds to a pure soliton which is the ground state of the Gross-Pitaevskii-Poisson equation. For (M h )min < M h < (M h ) * = 3.30 × 10 9 M the soliton is surrounded by a tenuous isothermal atmosphere without plateau. For M h > (M h ) * we find two branches of solutions corresponding to (i) pure isothermal halos without soliton and (ii) isothermal halos harboring a central soliton and presenting a plateau. The purely isothermal halos (gaseous phase) are stable. For M h > (M h )c = 6.86 × 10 10 M , they are indistinguishable from the observational Burkert profile. For (M h ) * < M h < (M h )c, the deviation from the isothermal law (most probable state) may be explained by incomplete violent relaxation, tidal effects, or stochastic forcing. The isothermal halos harboring a central soliton (core-halo phase) are canonically unstable (having a negative specific heat) but they are microcanonically stable so they are long-lived. By extremizing the free energy (or entropy) with respect to the core mass, we find that the core mass scales as Mc/(M h )min = 0.626 (M h /(M h )min) 1/2 ln(M h /(M h )min). For a halo of mass M h = 10 12 M , similar to the mass of the halo that surrounds our Galaxy, the solitonic core has a mass Mc = 6.39×10 10 M and a radius Rc = 1 kpc. The solitonic core cannot mimic by itself a supermassive black hole at the center of the Galaxy but i...

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Section: Introductionmentioning

confidence: 99%

Predictive model of BEC dark matter halos with a solitonic core and an isothermal atmosphere

Chavanis

2019

Phys. Rev. D

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121

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“…Quantum terms are important at "small" scales implying that the soliton has a size comparable to the de Broglie length (λ dB ∼ 1 kpc). 67 Quantum mechanics stabilizes the system against gravitational collapse and solves the core-cusp problem. The halo of scalar radiation results from the quantum interferences of excited states [61].…”

Section: Validity Of the Fast Oscillation Regimementioning

confidence: 99%

A new logotropic model based on a complex scalar field with a logarithmic potential

Chavanis

2022

Preprint

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We introduce a new logotropic model based on a complex scalar field with a logarithmic potential that unifies dark matter and dark energy. The scalar field satisfies a nonlinear wave equation generalizing the Klein-Gordon equation in the relativistic regime and the Schrödinger equation in the nonrelativistic regime. This model has an intrinsically quantum nature and returns the ΛCDM model in the classical limit → 0. It involves a new fundamental constant of physics A/c 2 = 2.10 × 10 −26 g m −3 responsible for the late accelerating expansion of the Universe and superseding the Einstein cosmological constant Λ. The logotropic model is almost indistinguishable from the ΛCDM model at large (cosmological) scales but solves the CDM crisis at small (galactic) scales. It also solves the problems of the fuzzy dark matter model. Indeed, it leads to cored dark matter halos with a universal surface density Σ th 0 = 5.85 (A/4πG) 1/2 = 133 M /pc 2 . This universal surface density is predicted from the logotropic model without adjustable parameter and turns out to be close to the observed value Σ obs 0 = 141 +83 −52 M /pc 2 . We also argue that the quantities Ω dm,0 and Ω de,0 , which are usually interpreted as the present proportion of dark matter and dark energy in the ΛCDM model, are equal to Ω th dm,0 = 1 1+e (1 − Ω b,0 ) = 0.2559 and Ω th de,0 = e 1+e (1 − Ω b,0 ) = 0.6955 in very good agreement with the measured values Ω obs dm,0 = 0.2589 and Ω obs de,0 = 0.6911 (their ratio 2.669 is close to the pure number e = 2.71828...). We point out, however, important difficulties with the logotropic model, similar to those encountered by the generalized Chaplygin gas model. These problems are related to the difficulty of forming large-scale structures due to an increasing speed of sound as the Universe expands. We discuss potential solutions to these problems, stressing in particular the importance to perform a nonlinear study of structure formation.

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“…Besides, in the limit → 0 (for a vanishing quantum potential Q d ), the model corresponds to classical dark matter (warm dark matter for K d = 0 or pressureless CDM for K d = 0). The limit → 0 also corresponds to BECDM in the Thomas-Fermi approximation [18] (where the quantum potential can be neglected).…”

Section: The Modelmentioning

confidence: 99%

“…In this case, one retains only the effect of quantum pressure for dark matter. This limit corresponds to BECDM without short-range self-interaction (see for instance [17,18]). In this case, the stability of dark matter is assured solely by the quantum pressure acting against gravity, and the critical wave number (24) becomes…”

Section: Jeans Instability Analysismentioning

confidence: 99%

“…One may cite for example its extension to general relativity [2] and to an expanding universe background [2][3][4], its formulation in the language of kinetic theory [5][6][7], its generalization to alternative gravity theories [8][9][10][11], where it regularly serves as a possible phenomenon to constraint their parameters [12,13]. The Jeans mechanism has also been extensively studied in various dark matter models [14][15][16][17][18] and for mixtures of baryonic and dark matter particles [7,19].…”

Section: Introductionmentioning

confidence: 99%

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Gravitational instability with a dark matter background: Exploring the different scenarios

Ourabah

2022

Preprint

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We study the Jeans-type gravitational instability for a self-gravitating medium composed of two species, baryonic (bright) and dark matter particles, using a hybrid quantum-classical fluid approach. Baryonic matter is treated classically, which is appropriate for most astrophysical environments, e.g., Bok globules, while dark matter is treated through a quantum hydrodynamic approach allowing for possible nonlinearities. These nonlinearities may arise in bosonic dark matter due to attractive or repulsive short-range self-interaction (attractive interaction being more relevant for axions) or from the Pauli exclusion principle for fermionic dark matter, e.g., massive neutrinos. This allows us to explore, in a very broad context, the impact of a dark matter background on the Jeans process for different scenarios discussed in the literature. In the simplest case, it is shown that the effect of a dark matter background on the Jeans mass depends only on the ratio of densities and velocity dispersions of baryonic and dark matter particles. Taking advantage of that, we confront the established stability criterion with Bok globule stability observations and show that the model adequately accounts for the data with dark matter parameters close to those predicted independently from numerical simulations.

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Jeans Instability of Dissipative Self-Gravitating Bose–Einstein Condensates with Repulsive or Attractive Self-Interaction: Application to Dark Matter

Cited by 20 publications

References 338 publications

Predictive model of BEC dark matter halos with a solitonic core and an isothermal atmosphere

Predictive model of BEC dark matter halos with a solitonic core and an isothermal atmosphere

A new logotropic model based on a complex scalar field with a logarithmic potential

Gravitational instability with a dark matter background: Exploring the different scenarios

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