# Impact of kinetic and potential self-interactions on scalar dark matter

## TL;DR

This paper explores how scalar dark matter models with self-interactions and non-canonical kinetic terms influence structure formation, revealing the existence of stable solitonic cores and their size limitations in various halos.

## Contribution

It introduces a comprehensive analysis of scalar dark matter with generic potentials and kinetic terms, deriving effective equations and identifying conditions for stable solitonic cores.

## Key findings

- Stable solitonic cores can form with sizes up to 60 kpc.
- Self-interactions induce a density-dependent speed of sound in dark matter.
- Solitonic cores are absent in massive halos with high density contrasts.

## Abstract

We consider models of scalar dark matter with a generic interaction potential and non-canonical kinetic terms of the K-essence type that are subleading with respect to the canonical term. We analyze the low-energy regime and derive, in the nonrelativistic limit, the effective equations of motions. In the fluid approximation they reduce to the conservation of matter and to the Euler equation for the velocity field. We focus on the case where the scalar field mass $10^{-21} \ll m \lesssim 10^{-4} \, {\rm eV}$ is much larger than for fuzzy dark matter, so that the quantum pressure is negligible on cosmological and galactic scales, while the self-interaction potential and non-canonical kinetic terms generate a significant repulsive pressure. At the level of cosmological perturbations, this provides a dark-matter density-dependent speed of sound. At the nonlinear level, the hydrostatic equilibrium obtained by balancing the gravitational and scalar interactions imply that virialized structures have a solitonic core of finite size depending on the speed of sound of the dark matter fluid. For the most relevant potential in $\lambda_4 \phi^4/4$ or K-essence with a $(\partial \phi)^4$ interaction, the size of such stable cores cannot exceed 60 kpc. Structures with a density contrast larger than $10^6$ can be accommodated with a speed of sound $c_s\lesssim 10^{-6}$. We also consider the case of a cosine self-interaction, as an example of bounded nonpolynomial self-interaction. This gives similar results in low-mass and low-density halos whereas solitonic cores are shown to be absent in massive halos.