Polarized solitons in higher-spin wave dark matter

We first show that the effective non-relativistic theory of gravitationally interacting, massive integer-spin fields (spin-$0$, $1$, and $2$ in particular) is described by a $2s+1$ component Schr\"{o}dinger-Poisson action, where $s$ is the spin of the field. We then construct $s+1$ distinct, gravitationally supported solitons in this non-relativistic theory from identically polarized plane waves. Such solitons are extremally polarized, with macroscopically large spin, but no orbital angular momentum. These $s+1$ solitons form a basis set, out of which partially polarized solitons can be constructed. All such solitons are ground states, have a spherically symmetric energy density but not field configurations. We discuss how solitons in higher-spin fields can be distinguished from scalar solitons, and potential gravitational and non-gravitational probes of them.