Kinematic Properties of Slow ICMEs and an Interpretation of a Modified Drag Equation for Fast and Moderate ICMEs

We report kinematic properties of slow interplanetary coronal mass ejections (ICMEs) identified by SOHO/LASCO, interplanetary scintillation, and in situ observations and propose a modified equation for the ICME motion. We identified seven ICMEs between 2010 and 2011 and compared them with 39 events reported in our previous work. We examined 15 fast (VSOHO−Vbg>500 km s−1), 25 moderate (0 km s−1≤VSOHO−Vbg≤500 km s−1), and 6 slow (VSOHO−Vbg<0 km s−1) ICMEs, where VSOHO and Vbg are the initial speed of ICMEs and the speed of the background solar wind. For slow ICMEs, we found the following results: i) They accelerate toward the speed of the background solar wind during their propagation and reach their final speed by 0.34±0.03 AU. ii) The acceleration ends when they reach 479±126 km s−1; this is close to the typical speed of the solar wind during the period of this study. iii) When γ1 and γ2 are assumed to be constants, a quadratic equation for the acceleration a=−γ2(V−Vbg)|V−Vbg| is more appropriate than a linear one a=−γ1(V−Vbg), where V is the propagation speed of ICMEs, while the latter gives a smaller χ2 value than the former. For the motion of the fast and moderate ICMEs, we found a modified drag equation a=−2.07×10−12(V−Vbg)|V−Vbg|−4.84×10−6(V−Vbg). From the viewpoint of fluid dynamics, we interpret this equation as indicating that ICMEs with 0 km s−1≤V−Vbg≤2300 km s−1 are controlled mainly by the hydrodynamic Stokes drag force, while the aerodynamic drag force is a predominant factor for the propagation of ICME with V−Vbg>2300 km s−1.