1D Modeling for Temperature-Dependent Upflow in the Dimming Region Observed by Hinode/EIS

We have previously found a temperature-dependent upflow in the dimming region following a coronal mass ejection (CME) observed by the {\it Hinode} EUV Imaging Spectrometer (EIS). In this paper, we reanalyzed the observations along with previous work on this event, and provided boundary conditions for modeling. We found that the intensity in the dimming region dramatically drops within 30 minutes from the flare onset, and the dimming region reaches the equilibrium stage after $\sim$1 hour later. The temperature-dependent upflows were observed during the equilibrium stage by EIS. The cross sectional area of the fluxtube in the dimming region does not appear to expand significantly. From the observational constraints, we reconstructed the temperature-dependent upflow by using a new method which considers the mass and momentum conservation law, and demonstrated the height variation of plasma conditions in the dimming region. We found that a super radial expansion of the cross sectional area is required to satisfy the mass conservation and momentum equations. There is a steep temperature and velocity gradient of around 7 Mm from the solar surface. This result may suggest that the strong heating occurred above 7 Mm from the solar surface in the dimming region. We also showed that the ionization equilibrium assumption in the dimming region is violated especially in the higher temperature range.