Variability in Supermassive Black-Hole Accretion Rates in Fuzzy Dark Matter Cores due to Black-Hole Wandering

Soliton cores in fuzzy dark matter (FDM) deepen nuclear potentials and have been proposed to strongly boost Bondi accretion, potentially aiding rapid black-hole growth at high redshift. We test this in live Schrodinger-Poisson FDM cores coupled to isothermal gas, evolving a moving black hole that grows via a strictly mass-conserving sink. We measure boosts relative to the initial mean-density Bondi rate. Low-mass seeds, with initial black-hole masses less than about 10^6 solar masses, do not sustain large boosts: black-hole wandering and soliton sloshing drive bursty accretion, with dense gas only intermittently present near the black hole. Intermediate seeds, with initial black-hole masses around 10^7 solar masses, produce the most durable enhancement, reaching boosts of order 100 for sound speed cs = 60 km/s, while hotter gas approaches near-background Bondi rates. High-mass seeds, with initial black-hole masses around 10^8 solar masses, quickly exhaust the sink-scale reservoir and become supply-limited, suppressing long-lived growth despite the deepened potential. In general, central-potential deepening, for example by a soliton halo, does not guarantee long-lived fueling: sustained boosts emerge only when the black hole remains dynamically confined within the dense nuclear gas region. Our results suggest that SMBH formation channels relying on soliton-enhanced accretion alone are unlikely to provide sufficient early growth.