Three‐dimensional Stereoscopic Analysis of Solar Active Region Loops. I.SOHO/EIT Observations at Temperatures of (1.0–1.5) x 106K

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Abstract
The three-dimensional structure of solar active region NOAA 7986 observed on 1996 August 30 with the Extreme-Ultraviolet Imaging Telescope (EIT) on board the Solar and Heliospheric Observatory (SOHO) is analyzed. We develop a new method of dynamic stereoscopy to reconstruct the three-dimensional geometry of dynamically changing loops, which allows us to determine the orientation of the mean loop plane with respect to the line of sight, a prerequisite to correct properly for projection effects in three-dimensional loop models. With this method and the filter-ratio technique applied to EIT 171 and 195 Å images we determine the three-dimensional coordinates [x(s), y(s), z(s)], the loop width w(s), the electron density ne(s), and the electron temperature Te(s) as a function of the loop length s for 30 loop segments. Fitting the loop densities with an exponential density model ne(h) we find that the mean of inferred scale height temperatures, Tλe=1.22 ± 0.23 MK, matches closely that of EIT filter-ratio temperatures, TEITe=1.21 ± 0.06 MK. We conclude that these cool and rather large-scale loops (with heights of h≈30-225 Mm) are in hydrostatic equilibrium. Most of the loops show no significant thickness variation w(s), but we measure for most of them a positive temperature gradient (dT/ds>0) across the first scale height above the footpoint. Based on these temperature gradients we find that the conductive loss rate is about 2 orders of magnitude smaller than the radiative loss rate, which is in strong contrast to hot active region loops seen in soft X-rays. We infer a mean radiative loss time of τrad≈40 minutes at the loop base. Because thermal conduction is negligible in these cool EUV loops, they are not in steady state, and radiative loss has entirely to be balanced by the heating function. A statistical heating model with recurrent heating events distributed along the entire loop can explain the observed temperature gradients if the mean recurrence time is 10 minutes. We computed also a potential field model (from SOHO/MDI magnetograms) and found a reasonable match with the traced EIT loops. With the magnetic field model we determined also the height dependence of the magnetic field B(h), the plasma parameter β(h), and the Alfvén velocity vA(h). No correlation was found between the heating rate requirement EH0 and the magnetic field Bfoot at the loop footpoints.