Core-halo scaling relations in self-interacting scalar field dark matter

TL;DR

The paper investigates how self-interactions in scalar field dark matter modify the core–halo structure of halos by performing 3D soliton-merger simulations within the non-relativistic Gross-Pitaevskii-Poisson framework. By exploring repulsive, attractive, and no-SI cases across a range of scattering lengths, it derives core–halo scaling relations that extend beyond the standard FDM paradigm, revealing non-universal behavior tied to SI strength and evolutionary stage. The results show repulsive SI tends to produce more massive, extended cores with lower central densities, while attractive SI enhances central densities and can lead to core collapse, thereby affecting SMBH-seed formation and inner galactic signatures. These findings highlight SI as a natural regulator of core properties and provide a framework to connect microphysical SFDM parameters to observable galactic core features.

Abstract

We study the impact of self-interactions on the structure and evolution of scalar field dark matter (SFDM) halos. Using three-dimensional Gross-Pitaevskii-Poisson simulations of multiple soliton mergers, we explore both repulsive and attractive regimes across a wide range of scattering lengths. Our results show that repulsive self-interactions lead to more massive and extended cores with lower central densities compared to the free (non-interacting) fuzzy dark matter case, while attractive interactions enhance central densities and can drive cores toward collapse, once a critical mass is exceeded. We confirm that the mass-radius relation of solitonic cores is well described by analytical predictions, even in the presence of self-interactions, and we extend the core-halo mass relation to scenarios beyond fuzzy dark matter. We find that the scaling relations between core mass, size, and total energy are not universal but depend sensitively on the strength and sign of the self-interaction, as well as on the evolutionary stage of the halo. These results demonstrate that self-interactions provide a natural mechanism to regulate core properties, with important implications for the formation of supermassive black holes and for potential astrophysical signatures in galactic cores.

Figures (13)

• Figure 1: Evolution of the density profiles for repulsive (top panels) and attractive (bottom panels) interactions. Some representative values of $a_s$ were selected from Table \ref{['tab: table_params']}. The profiles are displayed up to the final snapshot in time which corresponds to $10\tau_{\text{dyn}}$ for all simulations. Spikes at large radii trace non-virialized, infalling solitons and interference-dominated streams; they are transient outer-envelope features that damp away as the system relaxes.
• Figure 2: Comparison of the density profile at $2\tau_{\text{dyn}}$ (left panel) and 10$\tau_{\text{dyn}}$ (right panel) for all the values in Table \ref{['tab: table_params']}. The blue (red) lines show models with repulsive (attractive) SI, while the black dashed curve represents the FDM case ($a_s=0$). In the beginning, the profiles show strong oscillations, particularly at the outskirts which fade as the halo evolves. The central density increases for the attractive case as the system evolves. The opposite happens for the repulsive scenario, whose central density goes below the FDM regime ($a_s=0$); stronger repulsive SI (i.e. higher positive $a_s$) leads to lower central densities and larger core size.
• Figure 3: Evolution of the normalized central density given by $\lambda=\left(\frac{\rho(r=0,t)}{\rho(0,0)}\right)^{1/4}$ as a function of time for a subset of representative values in Table \ref{['tab: table_params']}. The star indicates the moment when $M_{\text{max}}$, according to eq. (\ref{['eq: mmax']}) is reached.
• Figure 4: Mass–size relation for SFDM halo cores for the highest values of $a_s$ considered in Table \ref{['tab: table_params']}, with only a subset shown for clarity. Simulation results are compared with the analytical prediction from eq. (\ref{['eq: mc_rc_analytical']}), shown as solid curves. More transparent dots correspond to early times, while darker ones represent later times, up to $10\tau_{\text{dyn}}$. The dashed lines represent $M_{\text{max}}$ for the attractive cases.
• Figure 5: Normalized soliton core mass ($M_c/M$) versus the invariant quantity $\Xi$ for the repulsive (upper panel) and the attractive (lower panel) cases. We can observe a correlation for the virialized halos and a slight change in the slope in all cases.