An analytic model for the sub-galactic matter power spectrum in fuzzy dark matter halos

TL;DR

This paper develops an analytic model for the sub-galactic matter power spectrum in fuzzy dark matter halos, linking quantum interference patterns to observable lensing signals, and discusses potential constraints on FDM mass from future observations.

Contribution

It introduces a novel analytic model of the sub-galactic matter power spectrum in FDM halos based on quantum clumps and compares it with strong lensing data.

Findings

Current observations do not constrain FDM mass.

Future high-resolution lensing observations can tightly constrain FDM around 10^{-22} eV.

The model links quantum interference patterns to lensing signals.

Abstract

Fuzzy dark matter (FDM), a scalar particle coupled to the gravitational field without self-interaction whose mass range is $m \sim 10^{-24} - 10^{-20}\ \rm{eV}$, 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 sub-galactic 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 averaged density follows the 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 sub-galactic 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 the mass around $10^{-22}\ \rm{eV}$.