Abstract
Scalar Field Dark Matter (SFDM) comprised of ultralight bosons has attracted
great interest as an alternative to standard, collisionless Cold Dark Matter
(CDM) because of its novel structure-formation dynamics, described by the
coupled Schrödinger-Poisson equations. In the free-field ("fuzzy") limit of
SFDM (FDM), structure is inhibited below the de Broglie wavelength, but
resembles CDM on larger scales. Virialized haloes have "solitonic" cores of
radius $\simłambda_deB$, surrounded by CDM-like envelopes. When a
strong enough repulsive self-interaction (SI) is also present, structure can be
inhibited below a second length scale, $łambda_SI$, with
$łambda_SI> łambda_deB$ -- called the Thomas-Fermi (TF) regime.
FDM dynamics differs from CDM because of quantum pressure, and SFDM-TF differs
further by adding SI pressure. In the small-$łambda_deB$ limit,
however, we can model all three by fluid conservation equations for a
compressible, $\gamma=5/3$ ideal gas, with ideal gas pressure sourced by
internal velocity dispersion and, for the TF regime, an added SI pressure,
$P_SI\rho^2$. We use these fluid equations to simulate halo
formation from gravitational collapse in 1D, spherical symmetry, demonstrating
for the first time that SFDM-TF haloes form with cores the size of
$R_TF$, the radius of an SI-pressure-supported $(n=1)$-polytrope,
surrounded by CDM-like envelopes. In comparison with rotation curves of dwarf
galaxies in the local Universe, SFDM-TF haloes pass the "too-big-to-fail" +
"core-cusp"-test if $R_TF1$ kpc.
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