Understanding radio-mode accretion and "Nature vs nurture"

The jets launched by black holes are widely believed to be a key component of the accretion process. However, despite being discovered decades ago, their physics and energetics are still poorly understood. Crucially, the semi analytical modelling of jets has advanced slowly, and simple one-zone models are still the preferred method of interpreting data, in particular for jets in Active Galactic Nuclei (AGN). These models can roughly constrain the properties of jets but they can not unambiguously couple their emission to the launching regions and internal dynamics, which are usually probed with General Relativistic Magneto-hydrodynamics (GRMHD) simulations. On the other hand, simulations are not easily comparable to observations because they cannot yet self-consistently predict spectra. This thesis focuses on developing new models and statistical methods to probe the connection between inflowing and outflowing material in accreting black holes. In chapters 2, 3 and 4 I describe the development of an advanced semi analytical model which accounts for the dynamics of the whole jet, starting from a simplified parametrisation of Relativistic Magneto-hydrodynamics in which the magnetic flux is converted into bulk kinetic energy. I apply the model to a variety of sources, from AGN to black hole X-ray binaries, using advanced modelling techniques to mitigate any degeneracies inherent to the model. Chapter 5 presents the results from a large multi-wavelength campaign following an X-ray binary outburst; I combine the same statistical techniques with a model-independent approach to probe the inflow/outflow coupling as the jet shuts down