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

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 n e ( s ), and the electron temperature T e ( s ) as a function of the loop length s for 30 loop segments. Fitting the loop densities with an exponential density model n e ( h ) we find that the mean of inferred scale height temperatures, T λ e =1.22 ± 0.23 MK, matches closely that of EIT filter-ratio temperatures, T EIT e =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 τ rad ≈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 v A( h ). No correlation was found between the heating rate requirement E H 0 and the magnetic field B foot at the loop footpoints.