The three phases of self-gravitating scalar field ground states

TL;DR

The paper addresses how two interacting ULDM scalar fields can form ground states when interspecies couplings are repulsive, challenging the single-soliton core paradigm. It combines analytic energy arguments (via a Gaussian ansatz) with numerical imaginary-time evolution (nSPIRal) to map phase transitions and identify three ground-state phases: nested solid, nested hollow, and separate, with a critical coupling $\\lambda_{12}^*$ around $0.1\Lambda_{12}$ for equal masses. This reveals that inner halo cores in multifield ULDM can be more diverse than previously thought, with symmetry-breaking in the immiscible phase and potential observational consequences. The work lays a framework for extending to 3D, more species, and connecting to axiverse-inspired constraints and cosmological structure formation.$

Abstract

It is generally assumed that scalar field dark matter halos would contain solitonic cores -- spherically symmetric ground state configurations -- at their centers. This is especially interesting in the case of ultralight dark matter (ULDM), where the solitons sizes are on the order of galaxies. In this work, we show that the paradigm of a spherically symmetric soliton embedded in the center of each halo is not universally valid in a scenario with multiple interacting scalar fields. In particular, sufficiently strong repulsive interspecies interactions make the fields immiscible. In such models, the ground state configuration can fall into a number of different phases that depend on the fields' relative densities, masses, and interaction strengths. This raises the possibility that the inner regions of ULDM halos are more complex and diverse than previously assumed.

Figures (5)

• Figure 1: Illustrations of the three classes of ground state configurations discussed in this paper. Each panel shows a slice through the center of a 3D numerical box. Each case has the same ratio of the two species' axion masses ($m_1$ and $m_2$, where $m_2 = 10^{-22} \, \mathrm{eV}$), but the inter-species interaction strength ($\Lambda_{ij}$, presented in code units described in Appendix A) increases from left to right. Upper panels show the densities of the individual fields; lower panels show the corresponding total density. For comparison, single-field solitons of equivalent total and particle masses are shown in light gray. The existence of three distinct classes of ground states and the resulting diversity in halo density shapes is the main result of this work.
• Figure 2: Scalar fields appear in many areas of cosmology, including as answers to the open questions of inflation, dark matter, and dark energy. We will particularly concern ourselves with their role as dark matter consisting of two ultralight axion-like particles (ULAs), though our results easily generalize to other applications. Considering how various scalar fields' phenomenologies impact astrophysical observables could help narrow down the parameter space of theories of quantum gravity.
• Figure 3: Density profiles of numerically calculated spherically symmetric ground states. The solid lines are densities of $\psi_1$ and the dashed lines are densities of $\psi_2$. The color scale indicates the interaction strength $\lambda_{12}$; large positive values are repulsive. In each case, $M_1 = M_2 = 50 \mathcal{M}$, $m_1 = m_0$ and $m_2 = 10^{-0.1} m_0$. When the interaction strength is small, solutions are nested, similar to those presented in \ref{['fig:profile_nested']} and discussed elsewhere in the literature. The less massive field $\psi_2$ has a larger characteristic radius, as expected from \ref{['eq:soliton_profile']}. When interactions are strongly repulsive, we find hollow solutions, in which $\psi_2$ has a local minimum at $r=0$.
• Figure 4: Classification of spherically symmetric solutions found by relaxation in imaginary time, as a function of interaction strength $\Lambda_{12}$ and particle mass ratio $m_2/m_1$ (top) and total mass ratio $M_2/M_1$ (bottom). Points are classified as "solid" if both fields have a local maximum at $r = r_{\text{min}}$, or "hollow 1" ("hollow 2") if $\psi_1$ ($\psi_2$) has local minimum at $r = r_{\text{min}}$. The dotted line shows the analytic prediction $\Lambda_{12} = 0.09$ for the transition from solid to hollow states. The dashed line shows the expected separation between "hollow 1" and "hollow 2" states at $r_{s, 1} = r_{s, 2}$. In the top panel, all points have $M_1 = M_2 = 50 \mathcal{M}$ and $m_1 = m_0$; in the bottom, $M_1 = 50 \mathcal{M}$ and $m_1 = m_2 = m_0$.
• Figure 5: Density profiles of nested solitons, computed by imaginary time relaxation in nSPIRal The solid lines denote $\rho_1$ and the dashed lines denote $\rho_2$. The color scale denotes the ratio $m_2/m_1$ of the particle masses. In each case the total masses are $M_1 = M_2 = 50 \mathcal{M}$ and $\Lambda = 0$.