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Wave dark matter ($\psi$DM), which satisfies the Schr\"odinger-Poissonequation, has recently attracted substantial attention as a possible darkmatter candidate. Numerical simulations have in the past provided a powerfultool to explore this new territory of possibility. Despite their successes toreveal several key features of $\psi$DM, further progress in simulations islimited, in that cosmological simulations so far can only address formation ofhalos below $\sim 2\times 10^{11} M_\odot$ and substantially more massive haloshave become computationally very challenging to obtain. For this reason, thepresent work adopts a different approach in assessing massive halos byconstructing wave-halo solutions directly from the wave distribution function.This approach bears certain similarity with the analytical construction ofparticle-halo (cold dark matter model). Instead of many collisionlessparticles, one deals with one single wave that has many non-interactingeigenstates. The key ingredient in the wave-halo construction is thedistribution function of the wave power, and we use several halos produced bystructure formation simulations as templates to determine the wave distributionfunction. Among different models, we find the fermionic King model presents thebest fits and we use it for our wave-halo construction. We have devised aniteration method for constructing the nonlinear halo, and demonstrate itsstability by three-dimensional simulations. A Milky-Way-sized halo has alsobeen constructed, and the inner halo is found flatter than the NFW profile.These wave-halos have small-scale interferences both in space and timeproducing time-dependent granules. While the spatial scale of granules varieslittle, the correlation time is found to increase with radius by one order ofmagnitude across the halo.

Self-consistent construction of virialized wave dark matter halos