Microlensing of Lensed Supernovae

Given the number of recently discovered galaxy-galaxy lens systems, we anticipate that a gravitationally lensed supernova will be observed within the next few years. We explore the possibility that stars in the lens galaxy will produce observable microlensing fluctuations in lensed supernova light curves. For typical parameters, we predict that ~70% of lensed SNe will show microlensing fluctuations > 0.5 mag, while ~25% will have fluctuations > 1 mag. Thus microlensing of lensed supernova will be both ubiquitous and observable. Additionally, we show that microlensing fluctuations will complicate measurements of time delays from multiply imaged supernovae: time delays accurate to better than a few days will be difficult to obtain. We also consider prospects for extracting the lens galaxy's stellar mass fraction and mass function from microlensing fluctuations via a new statistical measure, the time-weighted light curve derivative.Comment: 13 pages, emulateapj format; accepted in ApJ; expanded discussion of time delay uncertaintie

Lensing by Kerr Black Holes. I: General Lens Equation and Magnification Formula

We develop a unified, analytic framework for gravitational lensing by Kerr black holes. In this first paper we present a new, general lens equation and magnification formula governing lensing by a compact object. Our lens equation assumes that the source and observer are in the asymptotically flat region and does not require a small angle approximation. Furthermore, it takes into account the displacement that occurs when the light ray's tangent lines at the source and observer do not meet on the lens plane. We then explore our lens equation in the case when the compact object is a Kerr black hole. Specifically, we give an explicit expression for the displacement when the observer is in the equatorial plane of the Kerr black hole as well as for the case of spherical symmetry.Comment: 11 pages; final published versio

A New Hybrid Framework to Efficiently Model Lines of Sight to Gravitational Lenses

In strong gravitational lens systems, the light bending is usually dominated by one main galaxy, but may be affected by other mass along the line of sight (LOS). Shear and convergence can be used to approximate the contributions from less significant perturbers (e.g. those that are projected far from the lens or have a small mass), but higher order effects need to be included for objects that are closer or more massive. We develop a framework for multiplane lensing that can handle an arbitrary combination of tidal planes treated with shear and convergence and planes treated exactly (i.e., including higher order terms). This framework addresses all of the traditional lensing observables including image positions, fluxes, and time delays to facilitate lens modelling that includes the non-linear effects due to mass along the LOS. It balances accuracy (accounting for higher-order terms when necessary) with efficiency (compressing all other LOS effects into a set of matrices that can be calculated up front and cached for lens modelling). We identify a generalized multiplane mass sheet degeneracy, in which the effective shear and convergence are sums over the lensing planes with specific, redshift-dependent weighting factors.Comment: 13 pages, 2 figure