Development of a formalism for computing transits of Earth-directed CMEs, plasma sheaths, and shocks. Towards a forecasting tool

Interplanetary Coronal mass ejections (ICMEs) (super-magnetosonically) faster than the ambient solar wind are preceded by shock waves. Earth-directed shock waves, plasma sheaths and ICMEs are precursors of the major geomagnetic storms. The plasma sheath between the shock and the ICME leading edge plays a very important role to determine the geoeffectiveness of the events. There are multiple efforts (empirical, analytical and numerical) to forecast ICME-shock transit times and arrival speeds to 1 AU. We present a formalism (combining analytical and empirical solutions) to compute trajectories of fast halo Earth directed ICMEs, plasma sheaths, and shocks. This formalism combines the 'piston-shock' semi-empirical model (Corona-Romero et al., 2013), and the MHD polytropic jump relations (Petrinec and Russell, 1997) to approximate the 1 AU plasma sheath and ICME properties. Nine Earth directed ICME-shock cases, including the “Bastille” and “Halloween” events were analyzed. The model obtained compares well with in situ data. Finally, we found a possible empiric relation for the free parameter of our formalism. If this empiric relationship is confirmed, it could turn this formalism into a space weather forecasting tool.