Modeling of coronal EUV loops observed with TRACE. I. Hydrostatic solutions with nonuniform heating

Recent observations of coronal loops in EUV wavelengths with the Transition Region and Coronal Explorer (TRACE) and the Extreme-Ultraviolet Imaging Te lescope (EIT) on the Solar and Heliospheric Observatory (SOHO) demonstrated three new results that cannot be explained by most of the existing loop mo dels: (1) EUV loops are near-isothermal along their coronal segments, (2) t hey show an overpressure or overdensity compared with the requirements of s teady state loops with uniform heating, and (3) the brightest EUV loops exh ibit extended scale heights up to 4 times the hydrostatic scale height. The se observations cannot be reconciled with the classical RTV (Rosner, Tucker , & Vaiana) model, they do not support models with uniform heating, and the y even partially violate the requirements of hydrostatic equilibrium. In th is study we are fitting for the first time steady state solutions of the hy drodynamic equations to observed intensity profiles, permitting a detailed consistency test of the observed temperature T(s) and density profiles n(e) (s) with steady state models, which was not possible in previous studies ba sed on scaling laws. We calculate some 500 hydrostatic solutions, which cov er a large parameter space of loop lengths (L approximate to 4-300 Mm), of nonuniform heating functions (with heating scale heights in the range of la mbda (H) approximate to 1-300 Mm), approaching also the limit of uniform he ating (lambda (H) much greater than L). The parameter space can be subdivid ed into three regimes, which contain (1) solutions of stably stratified loo ps, (2) solutions of unstably stratified loops (in the case of short heatin g scale heights, lambda (H, Mm) approximate to rootL(Mm)), and (3) a regime in which we find no numerical solutions (when lambda (H), (Mm) less than o r similar to rootL(Mm)). Fitting the hydrostatic solutions to 41 EUV loops observed with TRACE (selected by the criterion of detectability over their entire length), we find that only 30% of the loops are consistent with hydr ostatic steady state solutions. None of the observed EUV loops is consisten t with a uniform heating function while in quasi-steady state. Those loops compatible with a steady state are found to be heated near the footpoints, with a heating scale height of lambda (H) = 12 +/- 5 Mm, covering a fractio n lambda (H)/L = 0.2 +/- 0.1 of the loop length. These results support coro nal heating mechanisms operating in or near the chromosphere and transition region.