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The multi-messenger universe is one of the most fruitful areas of research in astronomy. The last fifteen years have seen in particular i) the unveiling of the gamma-ray sky at GeV energies in space and at TeV energies from the ground; ii) the discovery of neutrinos of astrophysical origin up to PeV energies; iii) the direct observation of gravitational waves; iv) the discovery of the anisotropy in the arrival directions of cosmic rays beyond EeV energies. These discoveries marked the rise of the multi-messenger field.

A particular class of astrophysical sources of interest to multi-messenger studies are active galactic nuclei (AGNs). Jetted AGNs account for 80% of the ~1,600 sources detected in gamma rays above 10 GeV by Fermi-LAT over the full sky. These non-thermal sources emit across the entire electromagnetic spectrum with high bolometric luminosity, linked to the relativistic motion of the radiative region along the jets. With jets almost aligned with the line of sight, blazars that host a supermassive black hole of millions to billions of solar masses can persistently or transiently outshine the billions of stars in the host galaxy. Blazars display a variable flux on timescales ranging from several years to a few minutes. The rapid variability of these sources provides constraints on the size of the emission region and on its overall speed of approach to the observer. Their flux distributions are often heavy-tailed and relatively well modelled by log-normal distributions, with debated conclusions on the origin of flux variation: cascade propagation of fluctuations in the accretion disk or variations in the acceleration rate within the jet. While theoretical work is being actively developed to predict these variations, an unbiased census of blazar variability remains out of reach. This lack of knowledge prevents us from drawing firm conclusions about the association of blazars with messengers such as TeV-PeV neutrinos and EeV cosmic rays.

Blazars observed in the gamma-ray range by Fermi-LAT are also observed in optical surveys. Their optical and gamma-ray emissions share common properties, as expected from broadband emission models. With the advent of time-domain astronomy, optical surveys will soon make it possible to map the variability of most of the transient sky. For example, the ZTF survey currently generates ~10⁵ optical alerts per night, and the upcoming Vera C. Rubin Observatory with its deep and wide survey of the sky will revolutionise the time domain astronomy reaching dozens of millions alerts per night between 2025 and 2035. These data are sorted by alert managers (brokers) such as Fink, which, in addition to a high-frequency processing capabilities, can ingest and redistribute alerts openly, cross-reference them with those from other observatories and correlate them with catalogues of known sources. We have already configured Fink to ingest real-time data streams from Fermi-LAT blazars. This gamma-ray data stream is the best path-finder for alerts to be sent and received by the Cherenkov Telescope Array (CTA), the next-generation gamma-ray observatory.

This PhD project takes advantage of the latest developments in time-domain astronomy, with a combination of optical and gamma-ray surveys to tackle the challenge of blazar variability. In particular, the first year of the PhD work will see the start of operations at Rubin/LSST and CTA-North, to which the PhD supervisors are actively contributing. The aim is to establish a coherent mathematical framework to characterise altogether the optical and gamma-ray properties of blazars. The PhD work will focus on constructing a four-dimensional (direction, distance, time) mapping of blazars which will serve as the basis to deduce the duty cycle of blazars and automate the detection of transient events from these sources. Such an approach will continuously benefit from new information obtained (automatic and/or human learning), eventually leading to the discovery of new transient events from blazars, and ultimately opening a new window on the transient sky.