Coronal Loops Heated by Magnetohydrodynamic Turbulence. I. A Model of Isobaric Quiet‐Sun Loops with Constant Cross Sections

Abstract

Several recent papers have presented new observational results indicating that many coronal loops in active regions are nearly isothermal. It is expected that quiet-Sun loops may have similar thermal structures, since quiet-Sun differential emission measures look similar to those in active regions. In the quiet Sun, it is well known from observations that the nonthermal velocity inferred from the excess broadening of a line over thermal broadening reaches a peak of about 30 km s-1 around 3 × 105 K and then decreases with temperature, having a value of about 20 km s-1 at 1 × 106 K. In the present work, we make the assumption that the observed nonthermal velocities are a manifestation of magnetohydrodynamic (MHD) turbulence and present a model of static, isobaric coronal loops heated by turbulence. Instead of solving the MHD equations, we adopt simple energy spectra in MHD turbulence and infer the heating rate as a function of temperature from the observed nonthermal velocities. By solving the steady state energy equation of a loop in which temperature monotonically increases with height, we obtain the following results: (1) The heating rate is predominantly near the footpoints and decreases with the loop arc length. (2) There is a critical temperature above which the loop cannot be maintained in a steady state. (3) The loop is denser and is more isothermal than uniformly heated loops, being compatible with recent observations. (4) The theoretical differential emission measures are in good agreement with the empirical values at temperatures above 105 K. Below this temperature, we still have a large discrepancy. (5) It is possible to explain the observed strong correlation between intensity and nonthermal velocity of a spectral line in the quiet Sun. Our results support the idea that quasi-statically driven MHD turbulence of the direct current (DC) type in the stratified medium (transition region and corona) is a viable mechanism for coronal heating.