Effects of Self-Interaction and of an Ideal Gas in Binary Mergers of Bosonic Dark Matter Cores

Abstract

We study binary mergers of dark matter cores in the Bose-Einstein condensate (BECDM) model. We include two scenarios: scalar self-interaction and the presence of a gravitationally coupled ideal gas. Using 3D simulations of the Gross-Pitaevskii-Poisson and Schrödinger-Poisson-Euler systems, we analyze the properties of the resulting remnants. We find that the final core-mass ratio reaches a stable average value after the merger. Repulsive self-interaction increases the mass of the final solitonic core, while attractive interaction enhances mass loss. In mergers involving an ideal gas, namely of fermion-boson stars, a stable solitonic core always forms in the bosonic component, even when the gas dominates, whereas the gas itself does not form a compact core. We explain these results using energy scalings and find that self-interaction, equilibrium cores follow $E \propto -M^3$, which leads to an almost universal merger fraction. Self-interaction changes this scaling, because repulsive $g$ moves the system toward a milder $E \propto -M^2$ scaling and increases mass retention, while attractive $g$ strengthens binding and favors mass ejection. In the case of interaction with an ideal gas, this component only modifies the gravitational background and does not change the intrinsic scaling of the bosonic part. These results show that the merger outcome is not universal but controlled by the interaction strength, while solitonic BECDM cores remain robust across diverse environments including gas.

Figures (7)

• Figure 1: Illustration of the initial setup for the binary merger of soliton cores.
• Figure 2: Snapshots of the density evolution on the plane $z = 0$ at various times. Each row corresponds to a different value of the self-interaction $g = -0.1$, 0, 0.1, 0.2, and 0.3. The parameters for this simulations are $\lambda = \sqrt{2.0}$, $y_1 = 10$, and $v_{x_1} = 0.2$.
• Figure 3: Angle-averaged density profile (\ref{['eq:average_density']}) shown with points, at three different times along with the empirical fit (\ref{['eq:soliton_density']}) with solid line. Each panel corresponds to a different value of $g = -0.1$, 0, 0.1, 0.2, and 0.3. Here we use the parameters $\lambda = \sqrt{2.0}$, $y_1 = 10$, and $v_{x_1} = 0.2$.
• Figure 4: Time evolution of the core mass ratio $R_{M_c}$ for $g = -0.1$, 0.0, 0.1, 0.2, and 0.3, from top to bottom. Each panel shows results from 20 simulations for each given $g$. The thick dotted line in each case indicates the average value of $R_{M_c}$ during the evoilution, and the gray band its standard deviation.
• Figure 5: Snapshots of the density evolution on the plane $z = 0$ at various times ($t = 0$, $25$, $50$, and $112$). Each row corresponds to a different value of the mass ratio $MR = 0.1$, 1.0 and 10.0. The bosonic and polytropic gas components are represented by isocontours and a color map, respectively. The merger leads to the formation of a new BEC soliton core at the center. The parameters used in these cases are $\lambda = \sqrt{1.5}$, $y_1 = 5$ and $v_{x_1} = 0.2$.