[Paper Review] Gravitational instability with a dark matter background: Exploring the different scenarios

Kamel Ourabah|arXiv (Cornell University)|Apr 11, 2022

Cosmology and Gravitation Theories54 references13 citations

TL;DR

This paper investigates Jeans-type gravitational instability in a two-component medium of baryonic and dark matter using a hybrid quantum-classical fluid model. Baryonic matter is treated classically, while dark matter is modeled via quantum hydrodynamics to account for quantum pressure effects from bosonic (e.g., axions) or fermionic (e.g., massive neutrinos) candidates. The model successfully reproduces Bok globule stability observations with dark matter parameters consistent with independent simulations, validating the role of quantum pressure in resolving small-scale CDM issues.

ABSTRACT

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.

Motivation & Objective

• To investigate the impact of a dark matter background on Jeans gravitational instability in self-gravitating baryonic systems.
• To explore how quantum pressure effects—arising from bosonic self-interactions or fermionic exclusion—modify the Jeans criterion in small-scale astrophysical environments.
• To test the model’s predictive power against observational data, particularly the stability of Bok globules.
• To reconcile theoretical Jeans stability thresholds with observed astrophysical structures under varying dark matter parameters.
• To demonstrate that quantum hydrodynamic modeling of dark matter provides a viable framework for resolving small-scale issues in the ΛCDM model.

Proposed method

• Uses a hybrid quantum-classical fluid approach: baryonic matter is modeled via classical hydrodynamic equations (continuity and Euler equations), while dark matter is described using the Gross-Pitaevskii equation in the mean-field approximation.
• Applies the Madelung transformation to convert the Gross-Pitaevskii equation into a set of hydrodynamic equations that include quantum pressure terms.
• Incorporates both long-range gravitational potential and short-range self-interaction (via contact potential) in the effective potential for dark matter.
• Derives the modified Jeans criterion by analyzing linear perturbations in a static, non-expanding universe, allowing for comparison with observations.
• Uses a polytropic equation of state for baryonic matter (p = Kρ^γ) to generalize pressure effects.
• Validates results by comparing predicted Jeans mass and stability thresholds with observational data from Bok globules.

Experimental results

Research questions

• RQ1 How does the inclusion of quantum pressure from dark matter affect the Jeans instability criterion in self-gravitating baryonic systems?
• RQ2 To what extent can quantum hydrodynamic models of dark matter (bosonic or fermionic) reproduce the observed stability of Bok globules?
• RQ3 What range of dark matter parameters (e.g., mass, self-interaction strength) is consistent with observed Bok globule stability?
• RQ4 How do attractive or repulsive self-interactions in bosonic dark matter (e.g., axions) alter the gravitational instability threshold?
• RQ5 Can the quantum pressure from fermionic dark matter (e.g., massive neutrinos) resolve small-scale discrepancies in the ΛCDM model?

Key findings

• The modified Jeans criterion derived from the hybrid quantum-classical model accurately predicts the stability of Bok globules when dark matter parameters are tuned to values consistent with independent numerical simulations.
• The model shows that quantum pressure from dark matter—whether from Pauli exclusion (fermionic) or Bose-Einstein condensation (bosonic)—significantly alters the Jeans length and mass, suppressing small-scale collapse.
• For axion-like bosonic dark matter with attractive self-interactions (a < 0), the model predicts enhanced stability due to additional attractive quantum pressure, consistent with observed globule structures.
• The inclusion of repulsive self-interactions (a > 0) in the BECDM model leads to a larger Jeans mass, further stabilizing dense baryonic clumps.
• The model’s predictions align quantitatively with observed Bok globule masses and densities when dark matter has a mass scale of ~10^-22 eV (axion-like) and a scattering length consistent with simulation constraints.
• The study confirms that quantum effects in dark matter can resolve the small-scale crisis of ΛCDM without requiring additional baryonic feedback or warm dark matter.