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We perform four numerical magnetohydrodynamic simulations in 2.5 dimensions(2.5D) of fast Coronal Mass Ejections (CMEs) and their associated shock frontsbetween 10Rs and 300Rs. We investigate the relative change in the shockstandoff distance, Sd, as a fraction of the CME radial half-width, Dob (i.e.Sd/Dob). Previous hydrodynamic studies have related the shock standoff distancefor Earths magnetosphere to the density compression ratio (DR,Ru/Rd) measuredacross the bow shock (Spreiter, Summers and Alksne 1966). The DR coefficient,kdr, which is the proportionality constant between the relative standoffdistance (Sd/Dob) and the compression ratio, was semi-empirically estimated as1.1. For CMEs, we show that this value varies linearly as a function ofheliocentric distance and changes significantly for different radii ofcurvature of the CMEs leading edge. We find that a value of 0.8+-0.1 is moreappropriate for small heliocentric distances (<30Rs) which corresponds to thespherical geometry of a magnetosphere presented by Seiff (1962). As the CMEpropagates its cross section becomes more oblate and the kdr value increaseslinearly with heliocentric distance, such that kdr= 1.1 is most appropriate ata heliocentric distance of about 80Rs. For terrestrial distances (215Rs) weestimate kdr= 1.8+-0.3, which also indicates that the CME cross-sectionalstructure is generally more oblate than that of Earths magnetosphere. Thesealterations to the proportionality coefficients may serve to improveinvestigations into the estimates of the magnetic field in the corona upstreamof a CME as well as the aspect ratio of CMEs as measured in situ.

A study of the Heliocentric dependence of Shock Standoff Distance and Geometry using 2.5D MHD Simulations of CME-driven shocks