[Paper Review] Chance and Chandra (and repulsive dark matter)

Jeremy Goodman, Zachary Slepian|arXiv (Cornell University)|Apr 13, 2011

Cosmology and Gravitation Theories29 references3 citations

TL;DR

This paper explores a hypothetical form of repulsive dark matter (RDM) composed of bosons with nontrivial statistical mechanics, proposing that such particles could produce observable dynamical friction effects and core-like density profiles in galactic halos. The model predicts a conflict between astrophysical constraints on scattering cross-section and core radius, leading to the conclusion that RDM of this type is likely ruled out by current data.

ABSTRACT

A few examples are given of Chandra's work on statistical and stochastic problems that relate to open questions in astrophysics, in particular his theory of dynamical relaxation in systems with inverse-square interparticle forces. The roles of chaos and integrability in this theory require clarification, especially for systems having a dominant central mass. After this prelude, a hypothetical form of repulsive bosonic dark matter is discussed. The repulsion leads to nontrivial thermodynamic behavior, including superfluidity, and would tend to suppress dynamical friction, greatly reducing the drag exerted on rotating galactic bars. However, this form of dark matter can probably be ruled out, at least for parameters that allow halos to reach thermal equilibria within a Hubble time. One combination of the particle mass and interparticle repulsion determines the minimum core radius of dark halos. Bounds on dark-matter collisionality inferred from the Bullet Cluster constrain a second combination. It is possible to satisfy both constraints only for parameters that predict unacceptable rotation curves outside the halo core.

Motivation & Objective

• To investigate the implications of a hypothetical bosonic dark matter model with repulsive interactions for galactic dynamics.
• To assess whether such a model can produce observable dynamical friction effects and consistent halo structure.
• To derive constraints on the particle mass and scattering cross-section using astrophysical observations.
• To test the viability of the model against constraints from the Bullet Cluster and isothermal halo assumptions.

Proposed method

• Uses the Fokker-Planck equation and statistical mechanics to model velocity diffusion and dynamical friction in self-gravitating systems.
• Applies the Holtzmark distribution to describe the gravitational force field from a Poisson-distributed mass distribution.
• Derives the core radius and scattering cross-section in terms of the interaction strength $U_0$ and particle mass $m$.
• Combines constraints from the Bullet Cluster ($\sigma/m \approx 1.25\,\text{cm}^2\text{g}^{-1}$) and isothermal halo behavior ($\theta \geq 10^{-4}$) to bound the particle mass.
• Evaluates timescales for collisional relaxation and thermal conduction to assess the validity of local thermodynamic equilibrium.
• Uses the de Broglie wavelength $\lambda_{\rm dB} \approx h/mv_{\rm c}$ to estimate quantum effects and scattering mean free path.

Experimental results

Research questions

• RQ1 Can a repulsive dark matter model with nontrivial statistical mechanics produce observable dynamical friction effects?
• RQ2 What constraints does the Bullet Cluster place on the scattering cross-section and mass of such a dark matter particle?
• RQ3 Is the assumption of global isothermality in galactic halos consistent with the derived particle parameters?
• RQ4 How do the core radius and particle mass relate through the interaction potential and quantum statistics?
• RQ5 Can the model produce a stable, observationally viable halo profile with a core and flat rotation curve?

Key findings

• The model predicts a lower bound on the dark matter particle mass of $ m > 9 \times (10^4\theta)^{1/4} \left(\frac{v_{\rm c}}{100\,\text{km s}^{-1}}\right)^{-1/4} \left(\frac{r_{\rm c}}{1\,\text{kpc}}\right)^{-1/2} \,\text{eV}/c^2 $, with $ \theta \geq 10^{-4} $ from isothermal halo constraints.
• An upper bound on the mass is derived as $ m < 7 \times 10^{-4} \left(\frac{\sigma/m}{1.25\,\text{cm}^2\text{g}^{-1}}\right)^{1/5} \left(\frac{r_{\rm c}}{1\,\text{kpc}}\right)^{-4/5} \,\text{eV}/c^2 $ from Bullet Cluster data.
• The two bounds are incompatible for standard astrophysical values of core radius and circular velocity, suggesting the RDM model is ruled out.
• The core radius $ r_{\rm c} \sim \sqrt{\pi U_0 / 4Gm^2} $ depends on the interaction strength and mass, allowing a finite core even with weak scattering.
• Thermalization timescales suggest that while local equilibrium may be reached, global isothermality is questionable unless the mean free path is comparable to galactic scales.
• The model predicts a sharp drop in density at the core edge for low $ \theta $, with a rotation curve drop of up to a factor of 2 for $ \theta = 10^{-4} $, inconsistent with observed halo profiles.