Derivation of fluid conservation relations to infer near-Sun properties of coronal mass ejections from in situ measurements

Coronal mass ejections (CMEs) are observed both near the Sun using remote solar measurements, as well as in the solar wind using in situ measurements. While many relationships have been made between these relatively disparate data sets, a number of connections remain poorly known. In this study, we use mass, momentum, and energy conservation to derive a set of conservation relations based on the observed in situ properties of CMEs and the ambient environment into which they propagate. We focus on fast CMEs that drive shocks and produce sheath regions. These relations allow us to infer the plasma and magnetic field properties of the ejecta close to the Sun based primarily on in situ observations. In this first paper, we consider the limit where both magnetic and thermal plasma pressure can be neglected and derive an equation for the initial speed of the ejecta. We apply this result to (1) a simulated fast CMEs (for which the true initial speed is known) to verify that the approach produces reasonable results and (2) an observed CME for which several other empirical techniques for inferring initial speed have been applied. Finally, using these results, we derive an estimate for the transit time of a CME from the Sun to 1 AU. Our results are promising, yet tentative. More extensive studies will be necessary to either support or refute this technique.