Intergalactic Magnetic Field constraints from detected very high-energy Gamma-Ray Bursts using the Cherenkov Telescope Array Observatory

Defined as the magnetic field permeating cosmic voids, the Intergalactic Magnetic Field (IGMF) is thought to be a relic of the Big Bang, tracing a primordial magnetic seed at the origin of all astrophysical fields. Yet, it has thus far escaped detection. Lower limits on the IGMF strength can be established by observing very high-energy (VHE) photons from extragalactic sources. Specifically, this can be achieved by characterising the time-delayed secondary emission induced by highly energetic transient sources, such as gamma-ray bursts (GRBs). Most studies exclude values of the IGMF below $10^{-17}\;\mathrm{G}$ by comparing the expected effect to the sensitivity curves of various instruments in the $\mathrm{GeV}$ range or above. In this work, we simulate CTAO observation data under realistic observation conditions and perform spectral-temporal fits to estimate the constraints CTAO will bring on the IGMF once fully deployed. We apply the methodology to simulated sources with properties comparable to the few GRBs detected at VHE. In particular, we show that CTAO will probe strengths up to $\sim 10^{-15}\;\mathrm{G}$ when detecting sources similar to GRBs 221009A and 190114C. We also show that existing observations of GRB 221009A by the first CTAO Large Sized Telescope LST-1 favour a strength of $3\times 10^{-17}\;\mathrm{G}$.