# Probability of magnification in the $\textit{Hubble Frontier Fields}$ clusters

## TL;DR

This paper models gravitational lensing in six Hubble Frontier Fields clusters, analyzing magnification probabilities, cluster efficiencies, and effects on high-redshift galaxy luminosity functions, with implications for dark matter models.

## Contribution

It provides free-form lensing models and magnification maps for six clusters, comparing lensing efficiencies and exploring implications for high-redshift galaxy observations and dark matter theories.

## Key findings

- MACS 0717 has the most complex structure and highest lensing efficiency.
- Lensing efficiency increased by a factor of 1.4 to 2.3 compared to previous data.
- Good correlation between lensing efficiency and Einstein radius across redshifts.

## Abstract

We present free-form gravitational lensing models derived with the WSLAP+ code for the six $\textit{Hubble Frontier Fields}$ clusters using the latest data available from the $\textit{Frontier Fields Lensing Models v.4}$ collaboration. We present magnifications maps in the lens plane and caustic maps in the source plane. From these maps, we derive the probability of magnification using two different, but related, methods. We confirm MACS 0717 as the cluster with the most complex structure, and having the largest lensing efficiency and Einstein radius. When comparing these results with the ones obtained by previous observations of these clusters, we obtain an increase in the lensing efficiency between 1.4 and 2.3. We also find a good correlation with a relatively small dispersion between the lensing efficiency and Einstein radius as a function of the source redshift ($z_s$). Finally, we estimate the lensing effects produced by the six $\textit{Hubble Frontier Fields}$ clusters on the luminosity function of galaxies at high redshift ($z=9$) for standard luminosity functions and an alternative luminosity function based on predictions from wave dark matter ($\psi$DM) models.