Misc,
Harnessing Unresolved Lensed Quasars: The Mathematical Foundation of the Fluctuation Curves
(2022)cite arxiv:2209.11078Comment: 20 pages, 8 figures, 1 table.
Abstract
Strong gravitational lensed quasars (QSOs) have emerged as powerful and novel
cosmic probes as they can deliver crucial cosmological information, such as a
measurement of the Hubble constant, independent of other probes. Although the
upcoming LSST survey is expected to discover $10^3-10^4$ lensed QSOs, a large
fraction will remain unresolved due to seeing. The stochastic nature of the
quasar intrinsic flux makes it challenging to identify lensed ones and measure
the time delays using unresolved light curve data only. In this regard, Bag et
al (2022) introduced a data-driven technique based on the minimization of the
fluctuation in the reconstructed image light curves. In this article, we delve
deeper into the mathematical foundation of this approach. We show that the
lensing signal in the fluctuation curve is dominated by the auto-correlation
function (ACF) of the derivative of the joint light curve. This explains why
the fluctuation curve enables the detection of the lensed QSOs only using the
joint light curve, without making assumptions about QSO flux variability, nor
requiring any additional information. We show that the ACF of the derivative of
the joint light curve is more reliable than the ACF of the joint light curve
itself because intrinsic quasar flux variability shows significant
auto-correlation up to a few hundred days (as they follow a red power
spectrum). In addition, we show that the minimization of fluctuation approach
provides even better precision and recall as compared to the ACF of the
derivative of the joint light curve when the data have significant
observational noise.
