Cosmological structure formation in scalar field dark matter with repulsive self-interaction: The Incredible Shrinking Jeans Mass

TL;DR

This paper explores how scalar field dark matter with repulsive self-interaction influences cosmic structure formation, revealing a shrinking Jeans mass that allows small-scale structures to form despite initial suppression.

Contribution

It introduces a cosmological model of scalar field dark matter with self-interaction, deriving its transfer function and predicting structure formation, including a novel shrinking Jeans mass effect.

Findings

SFDM-TF haloes have cores of size R_TF surrounded by CDM-like envelopes.

The transfer function aligns SFDM-TF with fuzzy dark matter constraints.

The Jeans mass shrinks rapidly, enabling small-scale structures to form over time.

Abstract

Scalar Field Dark Matter (SFDM) comprised of ultralight ($\gtrsim 10^{-22}$ 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. As a Bose-Einstein condensate, its free-field ("fuzzy") limit (FDM) suppresses structure below the de Broglie wavelength, $\lambda_\text{deB}$, creating virialized haloes with central cores of radius $\sim\lambda_\text{deB}$, surrounded by CDM-like envelopes, and a halo mass function (HMF) with a sharp cut-off on small scales. With a strong enough repulsive self-interaction (SI), structure is inhibited, instead, below the Thomas-Fermi (TF) radius, $R_\text{TF}$ (the size of an SI-pressure-supported ($n=1$)-polytrope), when $R_\text{TF} > \lambda_\text{deB}$. Previously, we developed tools to describe SFDM dynamics on scales above $\lambda_\text{deB}$ and showed that SFDM-TF haloes formed by Jeans-unstable collapse from non-cosmological initial conditions have $R_\text{TF}$-sized cores, surrounded by CDM-like envelopes. Revisiting SFDM-TF in the cosmological context, we simulate halo formation by cosmological infall and collapse, and derive its transfer function from linear perturbation theory to produce cosmological initial conditions and 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 align them to let observational constraints on FDM proxy for SFDM-TF, finding FDM with particle masses $1 \lesssim m/(10^{-22} \text{ eV}/c^2) \lesssim 30$ corresponds to SFDM-TF with $10 \gtrsim R_\text{TF}/(1 \text{ pc}) \gtrsim 1$, favoring sub-galactic (sub-kpc) core-size. The SFDM-TF HMF cuts off gradually, however, leaving more small-mass haloes: its Jeans mass shrinks so fast, scales filtered early can still recover and grow!