Cusp vs core: the observational problem

The sharpest structural difference between cold and fuzzy dark matter is what happens at a halo's very centre — a diverging cusp, or a flat core. This has been a live observational controversy for decades, and fuzzy dark matter produces cores for free.

Two behaviours at r→0

A cusp means the density keeps climbing to the centre (CDM/NFW, $\rho\propto r^{-1}$). A core means it levels off to a finite central value. The distinction is sharp and, in principle, observable in the inner rotation curves and stellar kinematics of galaxies (figure).

Same halo mass, two theories: $\Lambda$CDM (NFW, solid) rises to a central cusp, while FDM (dashed) flattens into a solitonic core inside $r_c$ before rejoining the NFW envelope. The centre is where they differ.

Why CDM cusps

Collisionless cold particles have nothing to halt their infall; hierarchical merging drives the central density up without limit. Every pure-CDM halo, at every mass, is cuspy — a robust prediction of dissipationless simulations.

Why FDM cores

Fuzzy dark matter's quantum pressure resists compression. At the centre it balances gravity and settles into a smooth, flat-topped soliton (Topic 3.3, 5): inside the core radius the density is essentially constant, and only outside a few $r_c$ does it rejoin the NFW envelope. Cores are automatic, not tuned.

The observational stakes

Many dwarf galaxies show rotation curves and stellar kinematics that prefer cored inner profiles — the long-running core–cusp problem. FDM produces cores naturally, which is part of its appeal.

Worked example — is it FDM, or just baryons?

The catch: supernova feedback in baryon-rich galaxies can also flatten a CDM cusp into a core, so a cored dwarf is not by itself proof of FDM. The cleanest discriminant is a dark-matter-dominated dwarf (little gas to provide feedback) that is still cored — there, only new physics like FDM's quantum pressure can explain the core. This is why the faintest dwarfs are the key battleground (Topic 10.1).

Inner rotation curves: a cusp rises steeply, a core rises slowly — the observable discriminant.

In our research

This is the headline of Task 2: FDM halos are cored, CDM halos are cusped, and the two profiles are identical only outside a few core radii. Our GAMER runs resolve the cored FDM profile directly (GM-F12), and the core–cusp discriminant motivates the whole dwarf-galaxy side of the mass tension (Topic 10).

Key references

de Blok (2010), The core–cusp problem, Adv. Astron. 2010, 789293 (arXiv:0910.3538).
Oh et al. (2015), High-resolution rotation curves (THINGS), AJ 149, 180.
Hui, Ostriker, Tremaine & Witten (2017), Phys. Rev. D 95, 043541.

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