# Mass Discrepancy-Acceleration Relation in Einstein Rings

## TL;DR

This study analyzes the Mass Discrepancy-Acceleration Relation in 57 elliptical galaxies using Einstein rings, finding that discrepancies decrease with higher surface mass density and that relativistic MOND explains these observations well.

## Contribution

It demonstrates that relativistic MOND can naturally account for the MDAR and mass discrepancies observed in elliptical galaxy Einstein rings, aligning lensing, dynamical, and stellar masses.

## Key findings

- Discrepancy is larger at lower accelerations.
- High-surface-density galaxies show smaller mass discrepancies.
- Relativistic MOND explains the observed relations and mass consistency.

## Abstract

We study the Mass Discrepancy-Acceleration Relation (MDAR) of 57 elliptical galaxies by their Einstein rings from the Sloan Lens ACS Survey (SLACS). The mass discrepancy between the lensing mass and the baryonic mass derived from population synthesis is larger when the acceleration of the elliptical galaxy lenses is smaller. The MDAR is also related to surface mass density discrepancy. At the Einstein ring, these lenses belong to high-surface-mass density galaxies. Similarly, we find that the discrepancy between the lensing and stellar surface mass density is small. It is consistent with the recent discovery of dynamical surface mass density discrepancy in disk galaxies where the discrepancy is smaller when surface density is larger. We also find relativistic modified Newtonian dynamics (MOND) can naturally explain the MDAR and surface mass density discrepancy in 57 Einstein rings. Moreover, the lensing mass, the dynamical mass and the stellar mass of these galaxies are consistent with each other in relativistic MOND.