FLARE HEATING AND IONIZATION OF THE LOW SOLAR CHROMOSPHERE .1. INVERSION METHODS FOR MG-I LAMBDA,LAMBDA-4571 AND 5173

We examine various methods of inverting solar Mg I λλ4571 and 5173 spectral line observations to find the best method of using these lines to calculate the vertical temperature and electron density structure around the temperature minimum region. Following a perturbation analysis by Mein, we obtain a Fredholm integral equation of the first kind which can be inverted to yield these temperature and density structures as a function of time. We have tested several inversion methods and compared the accuracy, stability, and mathematical foundation of each. We have applied each of these methods to test data as well as to a subset of observations of these absorption lines taken on 1986 February 3 before and during a solar flare. We have found a small but significant increase in the temperature and a relatively large increase in the electron density during this flare. The observations are inconsistent with heating and ionization by an intense beam of electrons and with ionization by UV photoionization of Si I.