Tully-Fisher relation, galactic rotation curves and dissipative mirror dark matter

TL;DR

This paper demonstrates that a dissipative mirror dark matter model naturally explains galactic rotation curves and the Tully-Fisher relation by deriving a specific dark matter density profile linked to galaxy size.

Contribution

It introduces a dynamical halo model within mirror dark matter that predicts a quasi-isothermal density profile and explains key galactic scaling relations.

Findings

Dark matter density profile is quasi-isothermal with a core radius scaling with disk size.

The model reproduces the Tully-Fisher relation between luminosity and rotational velocity.

Rotation curve examples support the model's predictions.

Abstract

If dark matter is dissipative then the distribution of dark matter within galactic halos can be governed by dissipation, heating and hydrostatic equilibrium. Previous work has shown that a specific model, in the framework of mirror dark matter, can explain several empirical galactic scaling relations. It is shown here that this dynamical halo model implies a quasi-isothermal dark matter density, $\rho (r) = \rho_0 r_0^2/(r^2 + r_0^2)$, where the core radius, $r_0$, scales with disk scale length, $r_D$, via $r_0/{\rm kpc} = 1.4\left(r_D/{\rm kpc}\right)$. Additionally, the product $\rho_0 r_0$ is roughly $constant$, i.e. independent of galaxy size (the $constant$ is set by the parameters of the model). The derived dark matter density profile implies that the galactic rotation velocity satisfies the Tully-Fisher relation, $L_B \propto v^{3}_{max}$, where $v_{max}$ is the maximal rotational velocity. Examples of rotation curves resulting from this dynamics are given.