# The case for two-dimensional galaxy-galaxy lensing

## TL;DR

This paper demonstrates that the two-dimensional galaxy-galaxy lensing method provides significantly tighter constraints on halo parameters than traditional one-dimensional methods, especially in high-density galaxy regions, with unbiased results shown in simulations.

## Contribution

The paper evaluates the performance and biases of the two-dimensional lensing approach, highlighting its advantages over traditional methods and validating its unbiased nature using hydrodynamical simulations.

## Key findings

- Two-dimensional analysis yields over three times tighter confidence regions under ideal conditions.
- Higher galaxy densities improve the method's constraint power.
- The method produces unbiased halo mass estimates in the EAGLE simulation.

## Abstract

We revisit the performance and biases of the two-dimensional approach to galaxy-galaxy lensing. This method exploits the information for the actual positions and ellipticities of source galaxies, rather than using only the ensemble properties of statistically equivalent samples. We compare the performance of this method with the traditionally used one-dimensional tangential shear signal on a set of mock data that resemble the current state-of-the-art weak lensing surveys. We find that under idealised circumstances the confidence regions of joint constraints for the amplitude and scale parameters of the NFW model in the two-dimensional analysis can be more than three times tighter than the one-dimensional results. Moreover, this improvement depends on the lens number density and it is larger for higher densities. We compare the method against the results from the hydrodynamical EAGLE simulation in order to test for possible biases that might arise due to lens galaxies being missed, and find that the method is able to return unbiased estimates of halo masses when compared to the true properties of the EAGLE galaxies. Because of its advantage in high galaxy density areas, the method is especially suitable for studying the properties of satellite galaxies in clusters of galaxies.