Cosmological Structure Formation in Scalar Field Dark Matter with Repulsive Self-Interaction: The Incredible Shrinking Jeans Mass*

Scalar Field Dark Matter (SFDM) comprised of ultralight (> 10^-22 eV) bosons is an alternative to standard, collisionless Cold Dark Matter (CDM) that is CDM-like on large scales but inhibits small-scale structure formation. The free-field ("fuzzy") limit (FDM) suppresses structure below the de Broglie wavelength, λ_deB, but with a strong enough repulsive self-interaction (SI), structure is inhibited, instead, below the Thomas-Fermi (TF) radius, R_TF (the size of an SI-pressure supported (n=1)-polytrope), when R_TF > λ_deB. We developed tools to describe SFDM dynamics on scales above λ_deB, and showed that SFDM-TF halos formed by spherical collapse have R_TF-sized cores, surrounded by CDM-like envelopes. We also derived the SFDM-TF transfer function from linear perturbation theory to predict statistical measures of structure formation, such as the HMF. Since FDM and SFDM-TF transfer functions both have small-scale cut-offs, we can let constraints on FDM proxy for SFDM-TF, finding FDM with particle masses 1 < m/(10^-22 eV) < 30 corresponds to SFDM-TF with 10 > R_TF/(1 pc) > 1, favoring sub-galactic core-size. The SFDM-TF HMF cuts off gradually, however, leaving more small-mass halos: its Jeans mass shrinks so fast, scales filtered early can still recover and grow!