Determination of coronal temperatures from electron density profiles

The most popular method for determining coronal temperatures is the scale-height-method (shm). It is based on electron density profiles inferred from White Light (WL) brightness measurements of the corona during solar eclipses. This method has been applied to several published coronal electron density models. The calculated temperature distributions reach a maximum at r > 1.3 RS, and therefore do not satisfy one of the conditions for applying the shm method. Another method is the hydrostatic equilibrium method (hst), which enables coronal temperature distributions to be determined, providing solutions to the hydrostatic equilibrium equation. The temperature maximas using the hst method are almost equal to those obtained using the shm method, but the temperature peak is always at significantly lower altitude when the hst-method is used than when the shm-method is used. A third and more recently developed method, dyn, can be used for the same published electron density profiles. The temperature distributions obtained using the dyn method are regular solutions of the hydrodynamic equations. They depend on the expansion velocity of the coronal plasma considered as a free input parameter in the calculations. At the base of the solar corona, where the coronal bulk velocity is small (subsonic), the dyn and hst methods give similar temperature values. Larger differences are found at higher altitudes where the expansion velocity approaches and exceeds the velocity of sound. This paper shows also the effects of the flow tube geometry and ion temperatures on the electron temperature distributions. The dyn method is a generalization of the hst method, where the electron temperature distribution tends to zero at infinite radial distances. It is a new diagnostic tool for determining from WL coronal observations the range of radial distances where the coronal heating rate is at its maximum.