  In this work, we compute multi-field core and halo properties in wave Dark
Matter models. We focus on the case where Dark Matter consists of two light
(real) scalars, interacting gravitationally. As in the single-field Ultra Light
Dark Matter (ULDM) case, the scalar field behaves as a coherent BEC with a
definite ground state (at fixed total mass), often referred to in the
literature as a gravitational soliton. We establish an efficient algorithm to
find the ground and excited states of such two-field systems. We then use
simulations to investigate the gravitational collapse and virialization,
starting from different initial conditions, into solitons and surrounding halo.
As in the single-field case, a virialized halo forms with a gravitational
soliton (ground state) at the center. We find some evidence for an empirical
relation between the soliton mass and energy and those of the host halo. We use
this to then find a numerical relation between the properties of the two.
Finally, we use this to address the issue of alleviating some of the tensions
that single-field ULDM has with observational data, in particular, the issue of
how a galaxy's core and radius are related. We find that if galaxies of
different masses have similar percentages of the two species, then the
core-radius scaling tension is not addressed. However, if the lighter species
is more abundant in lighter galaxies, then the tension can be alleviated.

Cosmology and Nongalactic Astrophysics;High Energy Physics - Phenomenology;High Energy Physics - Theory