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In hierarchical models of structure formation, the first galaxies form in low-mass dark matter potential wells, probing the behavior of dark matter on kiloparsec scales. Even though these objects are below the detection threshold of current telescopes, future missions will open an observational window into this emergent world. In this Letter, we investigate how the first galaxies are assembled in a "fuzzy" dark matter (FDM) cosmology where dark matter is an ultralight ∼10^{-22}  eV boson and the primordial stars are expected to form along dense dark matter filaments. Using a first-of-its-kind cosmological hydrodynamical simulation, we explore the interplay between baryonic physics and unique wavelike features inherent to FDM. In our simulation, the dark matter filaments show coherent interference patterns on the boson de Broglie scale and develop cylindrical solitonlike cores, which are unstable under gravity and collapse into kiloparsec-scale spherical solitons. Features of the dark matter distribution are largely unaffected by the baryonic feedback. On the contrary, the distributions of gas and stars, which do form along the entire filament, exhibit central cores imprinted by dark matter-a smoking gun signature of FDM.

We derive a model that describes the dynamics of a Brownian particle, such as a massive black hole, in a stellar system dominated by gravitational forces, and examine whether it achieves a state of equipartition of kinetic energy with the stars. This problem has been considered before only for stellar systems with an isothermal Maxwellian distribution of velocities; here we study other examples and confirm our calculations with N-body simulations. We show that in certain cases the black hole's steady state kinetic energy can be very far from equipartition.