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 Telescope (EIT) on the Solar and Heliospheric Observatory (SOHO) demonstrated three new results that cannot be explained by most of the existing loop models: (1) EUV loops are near-isothermal along their coronal segments, (2) they show an overpressure or overdensity compared with the requirements of steady state loops with uniform heating, and (3) the brightest EUV loops exhibit extended scale heights up to 4 times the hydrostatic scale height. These observations cannot be reconciled with the classical RTV (Rosner, Tucker, & Vaiana) model, they do not support models with uniform heating, and they even partially violate the requirements of hydrostatic equilibrium. In this study we are fitting for the first time steady state solutions of the hydrodynamic 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 based on scaling laws. We calculate some 500 hydrostatic solutions, which cover a large parameter space of loop lengths (L ≈ 4-300 Mm), of nonuniform heating functions (with heating scale heights in the range of λ_H ≈ 1-300 Mm), approaching also the limit of uniform heating (λ_H ≫ L). The parameter space can be subdivided into three regimes, which contain (1) solutions of stably stratified loops, (2) solutions of unstably stratified loops (in the case of short heating scale heights, λ_H,Mm ≈ ), and (3) a regime in which we find no numerical solutions (when λ_H,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 hydrostatic steady state solutions. None of the observed EUV loops is consistent 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 λ_H = 12 ± 5 Mm, covering a fraction λ_H/L = 0.2 ± 0.1 of the loop length. These results support coronal heating mechanisms operating in or near the chromosphere and transition region.