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 without 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.

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• Dark matter