Bose-Einstein Condensate Dark Matter Halos Research Articles

Maximum mass of relativistic self-gravitating Bose-Einstein condensates with repulsive or attractive |φ|4 self-interaction

We derive an approximate analytical expression of the maximum mass of relativistic self-gravitating Bose-Einstein condensates with repulsive or attractive $|\ensuremath{\varphi}{|}^{4}$ self-interaction. This expression interpolates between the general relativistic maximum mass of noninteracting bosons stars, the general relativistic maximum mass of bosons stars with a repulsive self-interaction in the Thomas-Fermi limit, and the Newtonian maximum mass of dilute axion stars with an attractive self-interaction [P. H. Chavanis, Phys. Rev. D 84, 043531 (2011)]. We obtain the general structure of our formula from simple considerations and determine the numerical coefficients in order to recover the exact asymptotic expressions of the maximum mass in particular limits. As a result, our formula should provide a relevant approximation of the maximum mass of relativistic boson stars for any value (positive and negative) of the self-interaction parameter. We discuss the evolution of the system above the maximum mass and consider application of our results to dark matter halos and inflaton clusters. We also make a short review of boson stars and Bose-Einstein condensate dark matter halos and point out analogies with models of extended elementary particles.

Jeans mass-radius relation of self-gravitating Bose-Einstein condensates and typical parameters of the dark matter particle

We study the Jeans mass-radius relation of Bose-Einstein condensate dark matter in Newtonian gravity. We show at a general level that it is similar to the mass-radius relation of Bose-Einstein condensate dark matter halos [P.H. Chavanis, Phys. Rev. D {\bf 84}, 043531 (2011)]. Bosons with a repulsive self-interaction generically evolve from the Thomas-Fermi regime to the noninteracting regime as the Universe expands. In the Thomas-Fermi regime, the Jeans radius remains approximately constant while the Jeans mass decreases. In the noninteracting regime, the Jeans radius increases while the Jeans mass decreases. Bosons with an attractive self-interaction generically evolve from the nongravitational regime to the noninteracting regime as the Universe expands. In the nongravitational regime, the Jeans radius and the Jeans mass increase. In the noninteracting regime, the Jeans radius increases while the Jeans mass decreases. The transition occurs at a maximum Jeans mass which is similar to the maximum mass of Bose-Einstein condensate dark matter halos with an attractive self-interaction. We use the mass-radius relation of dark matter halos and the observational evidence of a ``minimum halo'' (with typical radius $R\sim 1\, {\rm kpc}$ and typical mass $M\sim 10^8\, M_{\odot}$) to constrain the mass $m$ and the scattering length $a_s$ of the dark matter particle.

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

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 $P=2\pi a_s\hbar^2\rho^2/m^3+\rho k_B T/m$, where $a_s$ 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. Our model has no free parameter so it is completely predictive. Extension of this model to noninteracting bosons and fermions will be presented in forthcoming papers.

Bose-Einstein Condensate Dark Matter Halos Confronted with Galactic Rotation Curves

We present a comparative confrontation of both the Bose-Einstein Condensate (BEC) and the Navarro-Frenk-White (NFW) dark halo models with galactic rotation curves. We employ 6 High Surface Brightness (HSB), 6 Low Surface Brightness (LSB), and 7 dwarf galaxies with rotation curves falling into two classes. In the first class rotational velocities increase with radius over the observed range. The BEC and NFW models give comparable fits for HSB and LSB galaxies of this type, while for dwarf galaxies the fit is significantly better with the BEC model. In the second class the rotational velocity of HSB and LSB galaxies exhibits long flat plateaus, resulting in better fit with the NFW model for HSB galaxies and comparable fits for LSB galaxies. We conclude that due to its central density cusp avoidance the BEC model fits better dwarf galaxy dark matter distribution. Nevertheless it suffers from sharp cutoff in larger galaxies, where the NFW model performs better. The investigated galaxy sample obeys the Tully-Fisher relation, including the particular characteristics exhibited by dwarf galaxies. In both models the fitting enforces a relation between dark matter parameters: the characteristic density and the corresponding characteristic distance scale with an inverse power.

Gravitational, lensing, and stability properties of Bose-Einstein condensate dark matter halos

The possibility that dark matter, whose existence is inferred from the study of the galactic rotation curves, and from the mass deficit in galaxy clusters, can be in a form of a Bose-Einstein Condensate, has been extensively investigated lately. In the present work, we consider a detailed analysis of the astrophysical properties of the Bose-Einstein Condensate dark matter halos that could provide clear observational signatures that help discriminate between different dark matter models. In the Bose-Einstein condensation model dark matter can be described as a non-relativistic, gravitationally confined Newtonian gas, whose density and pressure are related by a polytropic equation of state with index $n=1$. The mass and gravitational properties of the condensate halos are obtained in a systematic form, including the mean logarithmic slopes of the density and of the tangential velocity. The lensing properties of the condensate dark matter are investigated in detail. In particular, a general analytical formula for the surface density, an important quantity that defines the lensing properties of a dark matter halos, is obtained in the form of series expansions. This enables arbitrary-precision calculations of the surface mass density, deflection angle, deflection potential, and of the magnification factor, thus giving the possibility of the comparison of the predicted lensing properties of the condensate dark matter halos with observations. The stability properties of the condensate halos are also investigated by using the scalar and the tensor virial theorems, respectively, and the virial perturbation equation for condensate dark matter halos is derived.

Gravitational collapse of Bose-Einstein condensate dark matter halos

We study the mechanisms of the gravitational collapse of the Bose-Einstein condensate dark matter halos, described by the zero temperature time-dependent nonlinear Schr\"odinger equation (the Gross-Pitaevskii equation), with repulsive interparticle interactions. By using a variational approach, and by choosing an appropriate trial wave function, we reformulate the Gross-Pitaevskii equation with spherical symmetry as Newton's equation of motion for a particle in an effective potential, which is determined by the zero-point kinetic energy, the gravitational energy, and the particles interaction energy, respectively. The velocity of the condensate is proportional to the radial distance, with a time-dependent proportionality function. The equation of motion of the collapsing dark matter condensate is studied by using both analytical and numerical methods. The collapse of the condensate ends with the formation of a stable configuration, corresponding to the minimum of the effective potential. The radius and the mass of the resulting dark matter object are obtained, as well as the collapse time of the condensate. The numerical values of these global astrophysical quantities, characterizing condensed dark matter systems, strongly depend on the two parameters describing the condensate, the mass of the dark matter particle, and of the scattering length, respectively. The stability of the condensate under small perturbations is also studied, and the oscillations frequency of the halo is obtained. Hence these results show that the gravitational collapse of the condensed dark matter halos can lead to the formation of stable astrophysical systems with both galactic and stellar sizes.

Can dark matter be a Bose–Einstein condensate?

We consider the possibility that the dark matter which is required to explain the dynamicsof the neutral hydrogen clouds at large distances from the galactic centre could be in theform of a Bose–Einstein condensate. To study the condensate we use the non-relativisticGross–Pitaevskii equation. By introducing the Madelung representation of thewavefunction, we formulate the dynamics of the system in terms of the continuity equationand of the hydrodynamic Euler equations. Hence dark matter can be described as anon-relativistic, Newtonian Bose–Einstein gravitational condensate gas, whosedensity and pressure are related by a barotropic equation of state. In the case of acondensate with quartic non-linearity, the equation of state is polytropic with indexn = 1. In the framework of the Thomas–Fermi approximation the structure of the Newtoniangravitational condensate is described by the Lane–Emden equation, which can be exactlysolved. General relativistic configurations with quartic non-linearity are studied, bynumerically integrating the structure equations. The basic parameters (mass and radius) ofthe Bose–Einstein condensate dark matter halos sensitively depend on the mass of thecondensed particle and of the scattering length. To test the validity of the model we fit theNewtonian tangential velocity equation of the model with a sample of rotation curves oflow surface brightness and dwarf galaxies, respectively. We find a very good agreementbetween the theoretical rotation curves and the observational data for the low surfacebrightness galaxies. The deflection of photons passing through the dark matter halos isalso analysed, and the bending angle of light is computed. The bending angleobtained for the Bose–Einstein condensate is larger than that predicted by standardgeneral relativistic and dark matter models. The angular radii of the Einstein ringsare obtained in the small angle approximation. Therefore the study of the lightdeflection by galaxies and the gravitational lensing could discriminate between theBose–Einstein condensate dark matter model and other dark matter models.