A Large Dark Matter Core in the Fornax Dwarf Spheroidal Galaxy?

TL;DR

This study uses the Fornax dwarf spheroidal galaxy to constrain its dark matter halo by fitting the stellar velocity-dispersion profile with Jeans modelling for a cored/cusped halo. It reveals a strong degeneracy between the halo maximum circular velocity $V_{\rm max}$ and the core radius $r_{\rm core}$, showing that large cores ($r_{\rm core}\sim$1 kpc) require unusually large $V_{\rm max}$ (and hence massive halos), while modest $V_{\rm max}$ values imply small cores. By translating the dynamical solutions into central phase-space density $Q$, the paper derives stringent limits from warm dark matter and Ly$\alpha$ forest constraints, giving $r_{\rm core}\lesssim 85$ pc for canonical WDM and $\lesssim 10$ pc under strong WDM bounds, and $\lesssim 300$ pc for a broader class of DM models. Independent, phase-space-independent arguments further cap $r_{\rm core}$ at about 700 pc for $V_{\rm max}\lesssim 100$ km/s; a 1.5 kpc core would imply an implausibly massive halo and is inconsistent with standard DM scenarios and the observed globular cluster distribution, pushing toward alternative explanations such as tidal heating or merger-driven processes. Overall, the work links kinematic data to phase-space considerations to place robust bounds on the core size of Fornax and tests the viability of giant DM cores in dwarf galaxies.

Abstract

We use measurements of the stellar velocity dispersion profile of the Fornax dwarf spheroidal galaxy to derive constraints on its dark matter distribution. Though the data are unable to distinguish between models with small cores and those with cusps, we show that a large > 1 kpc dark matter core in Fornax is highly implausible. Irrespective of the origin of the core, reasonable dynamical limits on the mass of the Fornax halo constrain its core radius to be no larger than 700 pc. We derive an upper limit core radius of 300 pc by demanding that the central phase space density of Fornax not exceed that directly inferred from the rotation curves of low-mass spiral galaxies. Further, if the halo is composed of warm dark matter then phase-space constraints force the core to be quite small in order to avoid conservative limits from the Ly alpha forest power spectrum, implying a core radius < 85 pc. We discuss our results in the context of the idea that the extended globular cluster distribution in Fornax can be explained by the presence of a large 1.5 kpc core. A self-consistent core of this size would be drastically inconsistent with the expectations of standard warm or cold dark matter models, and would also require an unreasonably massive dark matter halo, with a maximum circular velocity of 200 km/s.

Figures (2)

• Figure 1: Measurements of the Fornax velocity dispersion profile compared to models for the dark matter halo. Left panel: Predictions for the case of a fixed $r_{\rm core} = 1$ kpc; the solid curve shows a large $V_{\rm max}$ = 140 km/s, and the dashed curve shows a small $V_{\rm max}$ = 30 km/s. Right panel: The best-fitting cases for two distinct density profiles: the solid curve shows the fit for the $=1.5$ profile described in the text with $V_{\rm max} = 28$ km/s, and the long-dashed curve shows the best-fitting cuspy NFW profile with $V_{\rm max} = 50$ km/s.
• Figure 2: Constraints on the core radius of Fornax as a function of central phase-space density (left) and maximum circular velocity (right) derived from the velocity dispersion profile. We define $r_{\rm core}$ as the radius where the log-slope of the density profile is $= -0.1$ in equation \ref{['eqt:rho']} with $= 1.5$, $r_{\rm core} \simeq 0.1 r_0$. The long-dashed, solid, and short-dashed lines use $=0.5$, $0.0$, and $-0.5$ respectively. Values of $r_{\rm core}$ with $Q \gtrsim 3 \times 10^{-5}$ M$_{\odot}$ pc$^{-3}$$(\rm{km/s})^{-3}$ are ruled out by Ly$$ forest constraints in the case of WDM with g = 2 ($r_{\rm core} \lesssim 85$ pc). In a more general class of dark matter models, directly observed phase-space limits from low-mass spiral rotation curves, $Q \gtrsim 10^{-6}$ M$_{\odot}$ pc$^{-3}$$(\rm{km/s})^{-3}$, demand $r_{\rm core} \lesssim 300$ pc. Most generally and irrespective of the cause of the core, a Fornax halo with $V_{\rm max} \gtrsim 100~{\rm km}\,{\rm s}^{-1}$ is disfavored from dynamical considerations. This implies $r_{\rm core} \lesssim 700$ pc.