Comparison between observation and theory for the stand-off distance ratios of CMEs and their associated ICMEs

We examine whether the observational stand-off distance ratios of CMEs and their associated ICMEs could be explained by theoretical model or not. For this, we select 16 CME-ICME pairs from September 2009 to October 2012 with the following conditions: (1) limb CMEs by SOHO and their associated ICMEs by twin STEREO spacecraft and vice versa when both spacecraft were roughly in quadrature; (2) the faint structure ahead of a limb CME is well identified; and (3) its associated ICME clearly has a sheath structure. We determine the observational stand-off distance ratios of the CMEs by using brightness profiles from LASCO-C2 (or SECCHI-COR2) observations and those of the ICMEs by solar wind data from STEREO-IMPACT/PLASTIC (or OMNI database) observations. We also determine the theoretical stand-off distance ratios of the CME-ICME pairs using semi-empirical relationship based on the bow shock theory. We find the following results. (1) Observational CME stand-off distance ratio decreases with increasing Mach number at the Mach numbers between 2 and 6. This tendency is consistent with the results from the semi-empirical relationship. (2) The observational stand-off distance ratios of several ICMEs can be explained by the relationship.