Jeans-type instability of a complex self-interacting scalar field in general relativity

Suárez, Abril; Chavanis, Pierre‐Henri

doi:10.1103/physrevd.98.083529

Cited by 34 publications

(19 citation statements)

References 246 publications

(400 reference statements)

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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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“…We first study how the Jeans length λ J and the Jeans mass M J of the logotropic gas depend on the density of the Universe ρ. In the nonrelativistic regime (DM-like era) the density evolves with time as [63]…”

Section: A the Jeans Scalesmentioning

confidence: 99%

“…) 62 Here V (ϕ) denotes the total potential of the SF including the rest-mass term. In addition, the time variable stands here for ct. 63 We assume a non-phantom Universe w > −1.…”

Section: Sfmentioning

confidence: 99%

“…We can also obtain an estimate of the minimum halo mass and minimum halo radius as a function of m and a s from the Jeans instability theory (see, e.g., Refs. [63,68] and Appendices H an I of [102]) but this method is less accurate. We note that the fermionic or bosonic models of DM halos are not fully predictive since (i) we have to assume the value of Σ 0 from the observations [see Eq.…”

Section: Appendix B: Logotropic Models Of Type I Ii and Iiimentioning

confidence: 99%

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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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“…Self-interaction pressure introduces a characteristic length scale, analogous to the standard Jeans length, below which gravitational instability is suppressed (cf. Suárez & Chavanis 2018). Consider the QHD equations, equations ( 10) and ( 11), derived from the Madelung transformation, and assume the quantum potential term in equation ( 11) is everywhere subdominant and can be neglected in favor of the self-interaction term.…”

Section: Gravitational Instability In the Tf Regime: The Self-interac...mentioning

confidence: 99%

Core-Envelope Haloes in Scalar Field Dark Matter with Repulsive Self-Interaction: Fluid Dynamics Beyond the de Broglie Wavelength

Dawoodbhoy,

Shapiro,

Rindler-Daller

2021

Preprint

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Scalar Field Dark Matter (SFDM) comprised of ultralight bosons has attracted great interest as an alternative to standard, collisionless Cold Dark Matter (CDM) because of its novel structure-formation dynamics, described by the coupled Schrödinger-Poisson equations. In the free-field ("fuzzy") limit of SFDM (FDM), structure is inhibited below the de Broglie wavelength, but resembles CDM on larger scales. Virialized haloes have "solitonic" cores of radius ∼ 𝜆 deB , surrounded by CDM-like envelopes. When a strong enough repulsive self-interaction (SI) is also present, structure can be inhibited below a second length scale, 𝜆 SI , with 𝜆 SI > 𝜆 deB -called the Thomas-Fermi (TF) regime. FDM dynamics differs from CDM because of quantum pressure, and SFDM-TF differs further by adding SI pressure. In the small-𝜆 deB limit, however, we can model all three by fluid conservation equations for a compressible, 𝛾 = 5/3 ideal gas, with ideal gas pressure sourced by internal velocity dispersion and, for the TF regime, an added SI pressure, 𝑃 SI ∝ 𝜌 2 . We use these fluid equations to simulate halo formation from gravitational collapse in 1D, spherical symmetry, demonstrating for the first time that SFDM-TF haloes form with cores the size of 𝑅 TF , the radius of an SI-pressure-supported (𝑛 = 1)-polytrope, surrounded by CDM-like envelopes. In comparison with rotation curves of dwarf galaxies in the local Universe, SFDM-TF haloes pass the ["too-big-to-fail" + "core-cusp"]-test if 𝑅 TF 1 kpc.

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Jeans-type instability of a complex self-interacting scalar field in general relativity

Cited by 34 publications

References 246 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

Core-Envelope Haloes in Scalar Field Dark Matter with Repulsive Self-Interaction: Fluid Dynamics Beyond the de Broglie Wavelength

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