A soliton inside a halo: core + granular envelope

Two regions, one wavefunction

The full halo is a single wavefunction $\psi$ with two regimes. In the centre it settles into the coherent, stationary soliton core. Outside, the same field is a superposition of many modes whose interference produces a fluctuating, granular density — the halo envelope. There is no seam: the two are limits of one continuous $\psi$.

The core–envelope profile

The spherically-averaged density follows the flat Schive soliton inside a transition radius of a few $r_c$, then matches onto an NFW-like envelope ($\rho\propto r^{-3}$ in the outskirts) — the same profile a cold-dark-matter halo would have (figure). The soliton replaces the CDM cusp; beyond a few core radii the two theories agree, because gravity dominates and quantum pressure is negligible there.

Granules and the de Broglie texture

The envelope is not smooth: interference produces order-unity density granules of size $\sim\lambda_{\rm dB}$, forming and dissolving on the dispersion timescale (Topic 3.2). These granules gravitationally scatter orbits (dynamical heating) and are a distinctive, if subtle, FDM signature. Their coherence length is a direct probe of the de Broglie wavelength.

The core mass is set by the halo

How big is the central soliton? Not free — it is tied to the host halo by the core–halo relation $M_c\propto M_h^{1/3}$ (Topic 8.5). A more massive halo grows a more massive (hence smaller, denser) core. This link between the halo's global mass and its inner soliton is the campaign's headline measurement.