A Discussion on the physics of the solar atmosphere - The structure and energy balance of solar active regions

Abstract

The interpretation of the emission measures calculated from e.u.v. and X-ray line intensities is discussed. A general method for deriving the temperature and density structure and energy balance in either the quiet Sun or active regions is given. In particular simple relations are found between the coronal temperature, the pressure in the chromosphere—corona transition region, P 0 , the conductive flux at P 0 , the mechanical energy dissipated above P 0 and the radiation losses above P 0 . A range of models for quiet and active regions is given. The rate of change of the mechanical energy deposition as a function of height is used to find empirical damping lengths which are compared with those expected from either the conduction damping of sound waves or the viscous damping of Alfven waves. The wave frequencies and peak amplitude velocities required to satisfy both the empirical and theoretical damping lengths and energy deposition rates are discussed.

Thermal Diagnostics With the Atmospheric Imaging Assembly on Board the Solar Dynamics Observatory: A Validated Method for Differential Emission Measure Inversions

“…to enforce positive definite functional forms of solutions and then to perform χ 2 -minimization to find the optimal set of parameters. Commonly used functional forms of the DEM function include Gaussians (Aschwanden & Boerner 2011;Guennou et al 2012a,b), power laws (Jordan 1976) or a combination of the two (Guennou et al 2013). Discretized splines have also been used (Monsignori-Fossi & Landini 1992;Parenti et al 2000, , see also the xrt iterative2 inversion code by Weber, available in the Hinode/XRT package in Solarsoft).…”

Understanding Heating in Active Region Cores through Machine Learning. I. Numerical Modeling and Predicted Observables

“…Many observational and theoretical studies have suggested that the "cool" portion of the EM(T ) (i.e. leftward of the peak, 10 5.5 T 10 6.5 K), can be described by EM(T ) ∼ T a (Jordan 1976;Cargill 1994;Cargill & Klimchuk 2004). The so-called emission measure slope, a, is an important diagnostic for assessing how often a single strand may be reheated and has been used by several researchers to interpret active region core observations in terms of both high-and low-frequency heating (see Table 3 of Bradshaw et al 2012, and references therein).…”

Pointing Chandra toward the Extreme Ultraviolet Fluxes of Very Low Mass Stars

“…Those studies found values close to α LC = 3/2 (e.g. Athay 1966;Jordan 1975Jordan , 1976, a result that can be understood in terms of the energy balance in spherically-symmetric hydrostatic equilibrium and constant cross-section loop models considering the dissipation of heating within the corona and cooling through radiation and conduction back to the chromosphere. Extensive discussions have been provided by, e.g., Jordan 6.8 6.7 6.6 6.5 Log T(EM max ) 6.9 6.8 6.7 6.6 6.5 Log T(EM max ) 6.9 6.8 6.7 6.6 6.5 Log T(EM max ) 6.9 6.8 6.7 6.6 (1976); Craig et al (1978); ?…”

“…Since the advent of high resolution EUV and X-ray spectroscopy of, first, the solar corona corona and, subsequently, stellar coronae, many studies have examined the form of the plasma DEM. The reader is referred to the following work as a starting point for deeper exploration of the extant literature: Pottasch (1963); Withbroe (1975); Jordan (1976); Craig & Brown (1976); Bruner & McWhirter (1988); Kashyap & Drake (1998) The body of existing work demonstrates some universal aspects of the coronal DEM: from chromospheric temperatures of a few 10 4 K the DEM decreases by approximately an order of magnitude to a minimum at temperatures of approximately 1-4 × 10 5 K; the DEM then rises by a approximately order of magnitude, or more, to a maximum at temperatures between 10 6 -10 7 K, beyond which it extends to higher temperatures over either a plateau or a shallow downward slope, before a precipitate decline by several orders of magnitude. It is possible there is further fine structure in the shape of the DEM in some cases, although assessing the veracity of such structure is far from trivial owing to the nature of the ill-constrained integral inversion problem of inferring the DEM from observed spectra (see, e.g., Craig & Brown 1976;Kashyap & Drake 1998).…”