Improved Determination of the Location of the Temperature Maximum in the Corona

The most used method to calculate the coronal electron temperature [ $T_{\mathrm{e}} (r)$ ] from a coronal density distribution [ $n_{\mathrm{e}} (r)$ ] is the scale-height method (SHM). We introduce a novel method that is a generalization of a method introduced by Alfven (Ark. Mat. Astron. Fys. 27, 1, 1941) to calculate $T_{\mathrm{e}}(r)$ for a corona in hydrostatic equilibrium: the “HST” method. All of the methods discussed here require given electron-density distributions [ $n_{\mathrm{e}} (r)$ ] which can be derived from white-light (WL) eclipse observations. The new “DYN” method determines the unique solution of $T_{\mathrm{e}}(r)$ for which $T_{\mathrm{e}}(r \rightarrow \infty) \rightarrow 0$ when the solar corona expands radially as realized in hydrodynamical solar-wind models. The applications of the SHM method and DYN method give comparable distributions for $T_{\mathrm{e}}(r)$ . Both have a maximum [ $T_{\max}$ ] whose value ranges between 1 – 3 MK. However, the peak of temperature is located at a different altitude in both cases. Close to the Sun where the expansion velocity is subsonic ( $r < 1.3\,\mathrm{R}_{\odot}$ ) the DYN method gives the same results as the HST method. The effects of the other free parameters on the DYN temperature distribution are presented in the last part of this study. Our DYN method is a new tool to evaluate the range of altitudes where the heating rate is maximum in the solar corona when the electron-density distribution is obtained from WL coronal observations.