Time Delay Anomalies of Fuzzy Gravitational Lenses

TL;DR

This paper investigates how fuzzy dark matter causes perturbations in gravitational lensing time delays, providing theoretical relationships and simulations, and highlights the potential of precise measurements to study fuzzy dark matter properties.

Contribution

It extends previous work by analyzing the impact of fuzzy dark matter fluctuations on time delay anomalies in strong lensing systems, with theoretical and simulation-based insights.

Findings

Time delay perturbation scales as λ_dB^{1.5}.

Strong fuzzy dark matter fluctuations can alter lens system topology.

Precise time delay measurements can probe fuzzy dark matter properties.

Abstract

Fuzzy dark matter is a promising alternative to the standard cold dark matter. It has quite recently been noticed, that they can not only successfully explain the large-scale structure in the Universe, but can also solve problems of position and flux anomalies in galaxy strong lensing systems. In this paper we focus on the perturbation of time delays in strong lensing systems caused by fuzzy dark matter, thus making an important extension of previous works. We select a specific system HS 0810+2554 for the study of time delay anomalies. Then, based on the nature of the fuzzy dark matter fluctuations, we obtain theoretical relationship between the magnitude of the perturbation caused by fuzzy dark matter, its content in the galaxy, and its de Broglie wavelength $\lambda _{\mathrm{dB}}$. It turns out that, the perturbation of strong lensing time delays due to fuzzy dark matter quantified as standard deviation is $\sigma_{\Delta t} \propto \lambda _{\mathrm{dB}}^{1.5}$. We also verify our results through simulations. Relatively strong fuzzy dark matter fluctuations in a lensing galaxy make it possible to to destroy the topological structure of the lens system and change the arrival order between the saddle point and the minimum point in the time delays surface. Finally, we stress the unique opportunity for studying properties of fuzzy dark matter created by possible precise time delay measurements from strongly lensed transients like fast radio bursts, supernovae or gravitational wave signals.