# Revealing the nonlinear behaviour of the lensed quasar Q0957+561

## TL;DR

This study investigates the nonlinear multifractal behavior of the lensed quasar Q0957+561's optical signals, revealing intrinsic and extrinsic variability influences and their relation to microlensing activity and the broad-line region.

## Contribution

It applies a wavelet-based multifractality analysis to quasar light curves, uncovering the nonlinear signatures and their temporal variations related to microlensing effects.

## Key findings

- Strong multifractal signatures detected in quasar light curves.
- Degree of multifractality varies over time and between images.
- Stronger multifractality in the r band during quiescent microlensing periods.

## Abstract

Knowledge about how the nonlinear behaviour of the intrinsic signal from lensed background sources changes on its path to the observer provides much information, particularly about the matter distribution in lensing galaxies and the physical properties of the current universe, in general. Here, we analyse the multifractal (nonlinear) behaviour of the optical observations of A and B images of Q0957+561 in the $r$ and $g$ bands. AIMS: To verify the presence, or absence, of extrinsic variations in the observed signals of the quasar images and investigate whether extrinsic variations affect the multifractal behaviour of their intrinsic signals. METHOD: We apply a wavelet transform modulus maxima-based multifractality analysis approach. RESULTS: We detect strong multifractal (nonlinear) signatures in the light curves of the quasar images. The degree of multifractality for both images in the $r$ band changes over time in a non-monotonic way, possibly indicating the presence of extrinsic variabilities in the light curves of the images, i.e., the signals of the quasar images are a combination of both intrinsic and extrinsic signals. Additionally, in the r band, in periods of quiescent microlensing activity, we find that the degree of multifractality (nonlinearity) of image A is stronger than that of B, while B has a larger multifractal strength in recent epochs (from day 5564 to day 7527) when it appears to be affected by microlensing. Finally, comparing the optical bands in a period of quiescent microlensing activity, we find that the degree of multifractality is stronger in the $r$ band for both quasar images. In the absence of microlensing, the observed excesses of nonlinearity are most likely generated when the broad-line region (BLR) reprocesses the radiation from the compact sources.