Analytical Approximations to Hydrostatic Solutions and Scaling Laws of Coronal Loops

Abstract

We derive accurate analytical approximations to hydrostatic solutions of coronal loop atmospheres, applicable to uniform and nonuniform heating in a large parameter space. The hydrostatic solutions of the temperature T(s), density ne(s), and pressure profile p(s) as a function of the loop coordinate s are explicitly expressed in terms of three independent parameters: the loop half-length L, the heating scale length sH, and either the loop-top temperature Tmax or the base heating rate EH0. The analytical functions match the numerical solutions with a relative accuracy of