An Analytical Model Probing the Internal State of Coronal Mass Ejections Based on Observations of Their Expansions and Propagations

In this paper, a generic self-similar flux rope model is proposed to probe the internal state of CMEs in order to understand the thermodynamic process and expansion of CMEs in interplanetary space. Using this model, three physical parameters and their variations with heliocentric distance can be inferred based on coronagraph observations of CMEs' propagation and expansion. One is the polytropic index $\Gamma$ of the CME plasma, and the other two are the average Lorentz force and the thermal pressure force inside CMEs. By applying the model to the 2007 October 8 CME observed by STEREO/SECCHI, we find that (1) the polytropic index of the CME plasma increased from initially 1.24 to more than 1.35 quickly, and then slowly decreased to about 1.34; it suggests that there be continuously heat injected/converted into the CME plasma and the value of $\Gamma$ tends to be 4/3, a critical value inferred from the model for a force-free flux rope; (2) the Lorentz force directed inward while the thermal pressure force outward, and both of them decreased rapidly as the CME moved out; the direction of the two forces reveals that the thermal pressure force is the internal driver of the CME expansion whereas the Lorentz force prevented the CME from expanding. Some limitations of the model and approximations are discussed meanwhile.