On the Drag parameter of ICME propagation models

ICME (Interplanetary Coronal Mass Ejection) are violent phenomena of solar activity that affect the whole heliosphere and the prediction of their impact on different solar system bodies is one of the primary goals of the planetary space weather forecasting. The travel time of an ICME from the Sun to the Earth can be computed through the Drag-Based Model (DBM), which is based on a simple equation of motion for the ICME defining its acceleration as a=-Γ(v-w)v-w, where a and v are the CME acceleration and speed, w is the ambient solar-wind speed and Γ is the so-called drag parameter (Vršnak et al., 2013).
In this framework, Γ depends on the ICME mass and cross-section, on the solar-wind density and, to a lesser degree, on other parameters. The typical working hypothesis for DBM implies that both Γ and w are constant far from the Sun. To run the codes, forecasters use empirical
input values for Γ and w, derived by pre-existent knowledge of solar-wind condition and by solving the “inverted problem” (where the ICME travel time is known and the unknowns are Γ and/or w). In
the 'Ensemble' approaches (Dumbovich et al., 2018; Napoletano et al. 2018), the uncertainty about the actual values of such inputs are rendered by Probability Distribution Functions (PDFs), accounting for the values variability and our lack of knowledge. Among those PDFs, that of Γ is poorly defined due to the relatively scarce statistics of recorded values. 

Employing a list of past ICME events, for which initial conditions when leaving the Sun and arrival conditions at the Earth are known, we employ a statistical approach to the Drag-Based Model to determine a measure of Γ and w for each case. This allows to obtain distributions for the model parameters on experimental basis and, more importantly, to test whether different conditions of relative velocity to the solar wind influence the value of the drag efficiency, as it must be expected for solid objects moving into an external fluid. In addition, we perform numerical simulations of a solid ICME-shaped structure moving into the solar-wind modelled as an external fluid. Outcomes from these simulations are compared with our experimental results, and thus employed to interpret them on physical basis.