We present a 2.5D MHD simulation of a magnetic flux rope (FR) propagating in the heliosphere and investigate the cause of the observed sharp plasma beta transition. Specifically, we consider a strong internal magnetic field and an explosive fast star
t, such that the plasma beta is significantly lower in the FR than the sheath region that is formed ahead. This leads to an unusual FR morphology in the first stage of propagation, while the more traditional view (e.g. from space weather simulations like Enlil) of a `pancake shaped FR is observed as it approaches 1 AU. We investigate how an equipartition line, defined by a magnetic Weber number, surrounding a core region of a propagating FR can demarcate a boundary layer where there is a sharp transition in the plasma beta. The substructure affects the distribution of toroidal flux, with the majority of the flux remaining in a small core region which maintains a quasi-cylindrical structure. Quantitatively, we investigate a locus of points where the kinetic energy density of the relative inflow field is equal to the energy density of the transverse magnetic field (i.e. effective tension force). The simulation provides compelling evidence that at all heliocentric distances the distribution of toroidal magnetic flux away from the FR axis is not linear; with 80% of the toroidal flux occurring within 40% of the distance from the FR axis. Thus our simulation displays evidence that the competing ideas of a pancaking structure observed remotely can coexist with a quasi-cylindrical magnetic structure seen in situ.
We perform four numerical magnetohydrodynamic simulations in 2.5 dimensions (2.5D) of fast Coronal Mass Ejections (CMEs) and their associated shock fronts between 10Rs and 300Rs. We investigate the relative change in the shock standoff distance, Sd,
as a fraction of the CME radial half-width, Dob (i.e. Sd/Dob). Previous hydrodynamic studies have related the shock standoff distance for Earths magnetosphere to the density compression ratio (DR,Ru/Rd) measured across the bow shock (Spreiter, Summers and Alksne 1966). The DR coefficient, kdr, which is the proportionality constant between the relative standoff distance (Sd/Dob) and the compression ratio, was semi-empirically estimated as 1.1. For CMEs, we show that this value varies linearly as a function of heliocentric distance and changes significantly for different radii of curvature of the CMEs leading edge. We find that a value of 0.8+-0.1 is more appropriate for small heliocentric distances (<30Rs) which corresponds to the spherical geometry of a magnetosphere presented by Seiff (1962). As the CME propagates its cross section becomes more oblate and the kdr value increases linearly with heliocentric distance, such that kdr= 1.1 is most appropriate at a heliocentric distance of about 80Rs. For terrestrial distances (215Rs) we estimate kdr= 1.8+-0.3, which also indicates that the CME cross-sectional structure is generally more oblate than that of Earths magnetosphere. These alterations to the proportionality coefficients may serve to improve investigations into the estimates of the magnetic field in the corona upstream of a CME as well as the aspect ratio of CMEs as measured in situ.
