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Abstract

In the fuzzy dark matter (FDM) model, gravitationally collapsed objects always consist of a solitonic core located within a virialized halo. Although various numerical simulations have confirmed that the collapsed structure can be described by a cored Navarro–Frenk–White-like density profile, there is still disagreement about the relation between the core mass and the halo mass. To fully understand this relation, we have assembled a large sample of cored haloes based on both idealized soliton mergers and cosmological simulations with various box sizes. We find that there exists a sizeable dispersion in the core–halo mass relation that increases with halo mass, indicating that the FDM model allows cores and haloes to coexist in diverse configurations. We provide a new empirical equation for a core–halo mass relation with uncertainties that can encompass all previously found relations in the dispersion, and emphasize that any observational constraints on the particle mass m using a tight one-to-one core–halo mass relation should suffer from an additional uncertainty of the order of 50  per cent for halo masses ≳10⁹[8×10⁻²³eV/(mc2)]^3/2M_⊙⁠. We suggest that tidal stripping may be one of the effects contributing to the scatter in the relation.