Liverpool-Maidanak monitoring of the Einstein Cross in 2006$-$2019. I. Light curves in the $gVrRI$ optical bands and microlensing signatures

Quasar microlensing offers a unique opportunity to resolve tiny sources in distant active galactic nuclei and study compact object populations in lensing galaxies. We therefore searched for microlensing-induced variability of the gravitationally lensed quasar QSO 2237+0305 (Einstein Cross) using 4374 optical frames taken with the 2.0 m Liverpool Telescope and the 1.5 m Maidanak Telescope. These $gVrRI$ frames over the 2006$-$2019 period were homogeneously processed to generate accurate long-term multi-band light curves of the four quasar images A-D. Through difference light curves, we found strong microlensing signatures. We then focused on the analytical modelling of two putative caustic-crossing events in image C, finding compelling evidence that this image experienced a double caustic crossing. Additionally, our overall results indicate that a standard accretion disc accounts reasonably well for the brightness profile of UV continuum emission sources and for the growth in source radius when the emission wavelength increases: $R_{\lambda} \propto \lambda^{\alpha}$, $\alpha$ = 1.33 $\pm$ 0.09. However, we caution that numerical microlensing simulations are required before firm conclusions can be reached on the UV emission scenario because the $VRI$-band monitoring during the first caustic crossing and one of our two $\alpha$ indicators lead to a few good solutions with $\alpha \approx$ 1.