Analytical approximations to hydrostatic solutions and scaling laws of coronal loops

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 n(e)(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 s(H), and either the loop-top temperature T-max or the base heating rate E-H0. The analytical functions match the numerical solutions with a relative accuracy of less than or similar to 10(-2)-10(-3). The absolute accuracy of the scaling laws for loop base pressure p(0) (L, s(H), T-max) and base heating rate E-H0(L, s(H), T-max), previously derived for uniform heating by Rosner et al., and for nonuniform heating by Serio et al., is improved to a level of a few percent. We generalize also our analytical approximations for tilted loop planes ( equivalent to reduced surface gravity) and for loops with varying cross sections. There are many applications for such analytical approximations: ( 1) the improved scaling laws speed up the convergence of numeric hydrostatic codes as they start from better initial values, ( 2) the multitemperature structure of coronal loops can be modeled with multithread concepts, ( 3) line-of-sight integrated fluxes in the inhomogeneous corona can be modeled with proper correction of the hydrostatic weighting bias, ( 4) the coronal heating function can be determined by forward-fitting of soft X-ray and EUV fluxes, or (5) global differential emission measure distributions dEM/dT of solar and stellar coronae can be simulated for a variety of heating functions.