Mass decomposition of SLACS lens galaxies in Weyl conformal gravity

TL;DR

This paper uses Weyl conformal gravity to analyze mass decomposition in SLACS lens galaxies, revealing that luminous mass closely accounts for total lens mass and resolving previous light bending discrepancies.

Contribution

It introduces a novel analytic method for separating luminous and dark matter in lens galaxies within Weyl conformal gravity, addressing longstanding issues in light bending calculations.

Findings

Luminous mass estimates closely match total lens masses within error margins.

The solution adds a positive contribution to light bending, resolving previous inconsistencies.

The approach provides a new, purely analytic mass decomposition scheme.

Abstract

We study here, using the Mannheim-Kazanas solution of Weyl conformal theory, the mass decomposition in the representative subsample of $57$ early-type elliptical lens galaxies of the SLACS on board the HST. We begin by showing that the solution need not be an exclusive solution of conformal gravity but can also be viewed as a solution of a class of $f(R)$ gravity theories coupled to non-linear electrodynamics thereby rendering the ensuing results more universal. Since lensing involves light bending, we shall first show that the solution adds to Schwarzschild light bending caused by the luminous mass ($M_{\ast }$) a positive contribution $+\gamma R$ contrary to the previous results in the literature, thereby resolving a long standing problem. The cause of the error is critically examined. Applying the expressions for light bending together with an input equating Einstein and Weyl angles, we develop a novel algorithm for separating the luminous component from the total lens mass (luminous+dark) within the Einstein radius. Our results indicate that the luminous mass estimates differ from the observed total lens masses by a linear proportionality factor. In quantitative detail, we observe that the ratios of luminous over total lens mass ($f^{\ast }$) within the Einstein radius of individual galaxies take on values near unity, many of which remarkably fall inside or just marginally outside the specified error bars obtained from a simulation based on the Bruzual-Charlot stellar population synthesis model together with the Salpeter IMF favored on the ground of metallicity [Grillo,2009]. We shall also calculate the average dark matter density of individual galaxies within their respective Einstein spheres. The present approach, being truly analytic, seems to be the first of its kind attempting to provide a new decomposition scheme distinct from the simulational ones.