Simultaneous radio, optical and X-ray monitoring of hard X-ray selected AGN: a variability study

AGN emission is intrinsically variable across the electromagnetic spectrum. Mapping the coupling between the accretion disk, the X-ray corona, and ejection flows is key to understanding the energy flow within the central engine. We characterize the multi-wavelength variability of 14 hard X-ray selected AGN from the INTEGRAL/IBIS catalog in the radio, optical, and X-ray bands, to determine the coupling between these frequencies and how variability relates to the physical properties of the central engine, with emphasis on the radio band. We analyzed multi-epoch observations from AMI-LA at 15 GHz, ZTF in the g and r bands, and Swift/XRT over 2018--2020. Variability was quantified using the normalized excess variance, the fractional variability amplitude, and the Mexican Hat filter at 70- and 200-day timescales. We also characterized the radio-loudness of the sample and evaluated the impact of variability on the Fundamental Plane of black hole activity by comparing time-averaged with strictly simultaneous data. Significant variability is detected in 86% of the sample, with a clear amplitude stratification: the fractional rms amplitude is highest in X-rays, with a median of 30% (11-67%), followed by the optical g and r bands at 19% (2-33%) and 8.5% (0.2-24%), and the radio band at 10% (4-23%). The Mexican Hat analysis reveals a red-noise power spectrum dominated by long-term fluctuations. The sample follows the expected Fundamental Plane scaling; although individual sources shift within the relation due to stochastic fluctuations, this dispersion accounts for only 3% of the total scatter. Our findings support a core-dominated origin for the 15 GHz emission, likely a compact jet base or a magnetized corona, while differences in variability patterns, radio-loudness, and Fundamental Plane location point toward distinct accretion/ejection processes and degrees of corona-jet coupling.