Definition and significance of average temperatures in time-dependent solar chromosphere models

¹ Kiepenheuer-Institut für Sonnenphysik, Schöneckstr. 6, 79104 Freiburg, Germany e-mail: wrammacher@kis.uni-freiburg.de
² Department of Physics, Science Hall, University of Texas at Arlington (UTA), Arlington, TX 76019-0059, USA e-mail: cuntz@uta.edu
³ Institut für Theoretische Astrophysik, Universität Heidelberg, Albert Überle Str. 2, 69120 Heidelberg, Germany

Received: 19 October 2004
Accepted: 22 March 2005

Abstract

We assess different types of average temperatures in time-dependent solar chromosphere models. They include the conventional definition of mean and median temperature, and a formal definition related to the model-dependent hydrogen ionization degree, referred to as ionization temperature. It is found that the latter is always higher than the mean and median temperatures, except in the photosphere, and that the mean temperatures are always higher than the median temperatures, especially in models with frequency spectra. The most dramatic differences are attained in the topmost portion of one of our models with the ionization temperatures up to a factor 150 higher than the mean and median temperatures. The differences between the mean, median, and ionization temperatures are a direct consequence of nonlinearities (“spikyness”) of the temperatures in the models mostly due to strong shocks. The main results hold for both acoustic and magnetic models despite significant differences in the initial wave energy fluxes, densities, and geometrical settings.