ner_tags: O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-CelestialObject O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Mission O B-Mission O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation O B-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation I-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O B-Citation I-Citation I-Citation O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O O
tokens: how the fitted magnetic field inside MEs and the radial size of MEs vary with distance and discussed the implications of their study for the self-similar expansion of MEs. They concluded that, for individual cases, reconnection between the ME and the solar wind and/or pancaking of the ME cross section is necessary to understand the evolution of the ME size as compared to the evolution of the magnetic field. In a previous work, Leitner et al. ( 2007 ) noted that the expected difference in the decrease rate with the distance of the axial and azimuthal components of the magnetic field may create differences in the trend found for the inner and outer heliosphere. Good et al. ( 2019 ) discussed the change in orientation of the 18 CMEs measured in conjunction that they studied, finding a tendency toward lower-inclined MEs at the outer spacecraft compared to the first spacecraft. This implies a (small) difference in the way different magnetic-field components change with distance. We note that for a force-free field with self-similar expansion, the axial magnetic field is expected to vary with distance as r −1 , whereas the poloidal field should vary as r −2 . In Lugaz et al. ( 2020 ) for the 2013 July 10–13 CME, we found that a uniform decrease of the magnetic-field components as r −1.6 was a better fit to the data than a separate fit for the y (axial) or z (poloidal) components of the magnetic field. Here, we continue this analysis for the 42 CMEs measured in conjunction between two spacecraft. Because MESSENGER and VEX were planetary missions, there are significant “data gaps” in the interplanetary magnetic field measurements corresponding to the time when the spacecraft were in the planetary magnetospheres. In addition, the magnetic fields inside MEs have been reported to significantly rotate in the inner heliosphere in some cases (e.g., see Nieves-Chinchilla et al. 2012 ; Winslow et al. 2016 ) and it is unclear how this should be considered when comparing the axial or poloidal fields measured by these spacecraft with those measured near 1 au. As such, we compare the tangential and normal components of the magnetic field measured at the two spacecraft in the RTN coordinate system. We focus on the extrema of the variation of the magnetic-field components. For an ME that has a clear low (respectively high) inclination, the B T (respectively B N ) component typically keeps the same sign throughout the ME interval. In addition, the expansion of the front and back half of the ejecta may occur at different rates. For example, in event 21-2013, discussed in Lugaz et al. ( 2020 ), B T is always positive, while B N varies from positive to negative (North–West–South ME following the classification of Bothmer Schwenn 1998 ). For this event, as shown in Table 1 , the B N positive component (at the front) decreases with an index of −1.4, whereas the B N negative (at the back) decreases with an index of −1.1. We therefore calculate the average of the indices