Lensing and Dynamics in Two Simple Steps

TL;DR

This paper introduces a simple, practical method to determine the density profiles of early-type galaxy lenses using surface brightness and kinematic data, avoiding complex deprojection.

Contribution

The authors develop a straightforward approach combining the virial theorem and lens equation to constrain the density slope without needing orbital anisotropy assumptions.

Findings

Method accurately estimates density slopes in tested systems.

Approximates broken power-law profiles with mild bias.

Applicable to existing lens systems with minimal data.

Abstract

We present a ready-to-use method to constrain the density distribution in early-type galaxy lenses. Assuming a power-law density profile, then joint use of the virial theorem and the lens equation yields simple formulae for the power-law index (or logarithmic density gradient). Any dependence on orbital anisotropy can be tightly constrained or even erased completely. Our results rely just on surface brightnesses and line-of-sight kinematics, making deprojection unnecessary. We revisit three systems that have already been examined in the literature (the Cosmic Horseshoe, the Jackpot and B1608+656) and provide our estimates. Finally, we show that the method yields a good approximation for the density profile even when the true profile is a broken power-law, albeit with a mild bias towards isothermality.