"Worst-Case" Micro-Lensing in the Identification and Modeling of Lensed Quasars

TL;DR

This paper investigates worst-case micro-lensing uncertainties in lensed quasars, providing bounds on flux fluctuations and identifying conditions under which these fluctuations are maximized or unbounded.

Contribution

It introduces a framework for estimating worst-case micro-lensing uncertainties for point sources in singular isothermal lens models, applicable to non-isothermal potentials via mass sheet degeneracy.

Findings

Worst-case fluctuations occur at stellar fraction κ_* = 1/|μ_macro|.

Magnification and demagnification bounds are established for macro-minima.

Demagnifications for macro-saddles can be unbounded as μ_macro approaches zero.

Abstract

Although micro-lensing of macro-lensed quasars and supernovae provides unique opportunities for several kinds of investigations, it can add unwanted and sometimes substantial noise. While micro-lensing flux anomalies may be safely ignored for some observations, they severely limit others. "Worst-case" estimates can inform the decision whether or not to undertake an extensive examination of micro-lensing scenarios. Here, we report "worst-case" micro-lensing uncertainties for point sources lensed by singular isothermal potentials, parameterized by a convergence equal to the shear and by the stellar fraction. The results can be straightforwardly applied to non-isothermal potentials utilizing the mass sheet degeneracy. We use micro-lensing maps to compute fluctuations in image micro-magnifications and estimate the stellar fraction at which the fluctuations are greatest for a given convergence. We find that the worst-case fluctuations happen at a stellar fraction $\kappa_\star=\frac{1}{|\mu_{macro}|}$. For macro-minima, fluctuations in both magnification and demagnification appear to be bounded ($1.5>\Delta m>-1.3$, where $\Delta m$ is magnitude relative to the average macro-magnification). Magnifications for macro-saddles are bounded as well ($\Delta m > -1.7$). In contrast, demagnifications for macro-saddles appear to have unbounded fluctuations as $1/\mu_{macro}\rightarrow0$ and $\kappa_\star\rightarrow0$.