Abstract
Aims. Inspired by the statistical mechanics of an ensemble of interacting particles (BBGKY hierarchy), we propose to account for small-scale inhomogeneities in self-gravitating astrophysical fluids by deriving a nonideal virial theorem and nonideal Navier-Stokes equations. These equations involve the pair radial distribution function (similar to the two-point correlation function used to characterize the large-scale structures of the Universe), similarly to the interaction energy and equation of state in liquids. Within this framework, small-scale correlations lead to a nonideal amplification of the gravitational interaction energy, whose omission leads to a missing mass problem, for instance, in galaxies and galaxy clusters. Methods. We propose to use a decomposition of the gravitational potential into a near- and far-field component in order to account for the gravitational force and correlations in the thermodynamics properties of the fluid. Based on the nonideal virial theorem, we also propose an extension of the Friedmann equations in the nonideal regime and use numerical simulations to constrain the contribution of these correlations to the expansion and acceleration of the Universe. Results. We estimate that the nonideal amplification factor of the gravitational interaction energy of the baryons lies between 5 and 20, potentially explaining the observed value of the Hubble parameter (since the uncorrelated energy accounts for ∼5%). Within this framework, the acceleration of the expansion emerges naturally because the number of substructures induced by gravitational collapse increases, which in turn increases their contribution to the total gravitational energy. A simple estimate predicts a nonideal deceleration parameter qni ≃ −1; this is potentially the first determination of the observed value based on an intuitively physical argument. We also suggest that small-scale gravitational interactions in bound structures (spiral arms or local clustering) could yield a transition to a viscous regime that can lead to flat rotation curves. This transition could also explain the dichotomy between (Keplerian) low surface brightness elliptical galaxy and (nonkeplerian) spiral galaxy rotation profiles. Overall, our results demonstrate that nonideal effects induced by inhomogeneities must be taken into account, potentially with our formalism, in order to properly determine the gravitational dynamics of galaxies and the large-scale Universe.
Highlights
Astrophysical flows are by nature multi-scale systems exhibiting a large range of dynamical regimes whose understanding remains quite challenging
Inspired by the statistical mechanics of an ensemble of interacting particles (BBGKY hierarchy), we propose to account for small-scale inhomogeneities in self-gravitating astrophysical fluids by deriving a non-ideal Virial theorem and non-ideal NavierStokes equations
Based on the non-ideal Virial theorem, we propose an extension of the Friedmann equations in the non-ideal regime and use numerical simulations to constrain the contribution of these correlations to the expansion and acceleration of the Universe
Summary
Astrophysical flows are by nature multi-scale systems exhibiting a large range of dynamical regimes whose understanding remains quite challenging. A noticeable exception is the case of Coulombic fluids, which interact throughout the Coulomb potential (∝ 1/r); large-scale convergence in that case is insured by the neutralizing electron background This (screening) property is not met by a self-gravitating fluid since the gravitational force is long-range and always attractive: the interaction energy is a priori non-extensive and requires possibly a new extension of statistical mechanics to include non-extensive hierarchical systems (see, e.g. de Vega & Sánchez 2002; Pfenniger 2006). This prevents astrophysicists from benefiting from the insight found from developments of statistical mechanics in the presence of interactions For this reason, at large scales such as galaxies or the large-scale structures of the Universe, the gravitational interactions of unresolved structures in the simulations are usually ignored or neglected, resulting from the use of an ideal gas approximation when calculating the thermodynamic properties of the fluid.
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