Three-dimensional stereoscopic analysis of solar active region loops. I. SOHO EIT observations at temperatures of (1.0-1.5) x 10(6) K

The three-dimensional structure of solar active region NOAA 7986 observed o n 1996 August 30 with the Extreme-Ultraviolet Imaging Telescope (EIT) on bo ard the Solar and Heliospheric Observatory (SOHO) is analyzed. We develop a new method of dynamic stereoscopy to reconstruct the three-dimensional geo metry of dynamically changing loops, which allows us to determine the orien tation of the mean loop plane with respect to the line of sight, a prerequi site to correct properly for projection effects in three-dimensional loop m odels. With this method and the filter-ratio technique applied to EIT 171 a nd 195 Angstrom images we determine the three-dimensional coordinates [x(s) , y(s), z(s)], the loop width w(s), the electron density n(e)(s), and the e lectron temperature T-e(s) as a function of the loop length s for 30 loop s egments. Fitting the loop densities with an exponential density model n(e)( h) we iind that the mean of inferred scale height temperatures, T-e(lambda) = 1.22 +/- 0.23 MK, matches closely that of EIT filter-ratio temperatures, T-e(EIT) = 1.21 +/- 0.06 MK. We conclude that these cool and rather large- scale loops (with heights of h approximate to 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 tempe rature gradients we find that the conductive loss rate is about 2 orders of magnitude smaller than the radiative loss rate, which is in strong contras t to hot active region loops seen in soft X-rays. We infer a mean radiative loss time of tau(rad) approximate to 40 minutes at the loop base. Because thermal conduction is negligible in these cool EUV loops, they are nor in s teady state, and radiative loss has entirely to be balanced by the heating function. A statistical heating model with recurrent heating events distrib uted along the entire loop can explain the observed temperature gradients i f the mean recurrence time is less than or similar to 10 minutes. We comput ed also a potential field model (from SOHO/MDI magnetograms) and found a re asonable match with the traced EIT loops. With the magnetic field model we determined also the height dependence of the magnetic field B(h), the plasm a parameter beta(h), and the Alfven velocity v(A)(h). No correlation was fo und between the heating rate requirement E-HO and the magnetic field B-foot at the loop footpoints.