Carnegie Observatories Astrophysics Series, Vol. 2: "Measuring and Modeling the Universe" ed. W. L. Freedman (Cambridge: Cambridge Univ. Press)

For a PDF version of the article, click here.

Abstract. There are now 10 firm time delay measurements in gravitational lenses. The physics of time delays is well understood, and the only important variable for interpreting the time delays to determine H₀ is the mean surface mass density <> (in units of the critical density for gravitational lensing) of the lens galaxy at the radius of the lensed images. More centrally concentrated mass distributions with lower <> predict higher Hubble constants, with H₀ 1 - <> to lowest order. While we cannot determine <> directly given the available data on the current time delay lenses, we find H₀ = 48 ± 3 km s^-1 Mpc^-1 for the isothermal (flat rotation curve) models, which are our best present estimate for the mass distributions of the lens galaxies. Only if we eliminate the dark matter halo of the lenses and use a constant mass-to-light ratio (M / L) model to find H₀ = 71 ± 3 km s^-1 Mpc^-1 is the result consistent with local estimates. Measurements of time delays in better-constrained systems or observations to obtain new constraints on the current systems provide a clear path to eliminating the <> degeneracy and making estimates of H₀ with smaller uncertainties than are possible locally. Independent of the value of H₀, the time delay lenses provide a new and unique probe of the dark matter distributions of galaxies and clusters because they measure the total (light + dark) matter surface density.

Table of Contents

INTRODUCTION

TIME DELAY BASICS

UNDERSTANDING TIME DELAYS: A GENERAL THEORY

LENSES WITHIN CLUSTERS

OBSERVING TIME DELAYS AND TIME DELAY LENSES

RESULTS: THE HUBBLE CONSTANT AND DARK MATTER

SOLVING THE CENTRAL CONCENTRATION PROBLEM

CONCLUSIONS

REFERENCES