An Analytic Model for the Subgalactic Matter Power Spectrum in Fuzzy Dark Matter Halos

Fuzzy dark matter (FDM), a scalar particle coupled to the gravitational field without self-interaction, whose mass range is m ∼ 10 −24 –10 −20 eV, is one of the promising alternative dark matter candidates to cold dark matter. The quantum interference pattern, which is a unique structure of FDM, can be seen in halos in cosmological FDM simulations. In this paper, we first provide an analytic model of the subgalactic matter power spectrum originating from quantum clumps in FDM halos, in which the density distribution of the FDM is expressed by a superposition of quantum clumps whose size corresponds to the de Broglie wavelength of the FDM. These clumps are assumed to be distributed randomly, such that the ensemble average density follows a halo profile such as the Navarro–Frenk–White profile. We then compare the convergence power spectrum projected along the line of sight around the Einstein radius, which is converted from the subgalactic matter power spectrum, to that measured in the strong lens system SDSS J0252 + 0039. While we find that the current observation provides no useful constraint on the FDM mass, we show that future deep, high spatial resolution observations of strong lens systems can tightly constrain FDM with a mass around 10 −22 eV.