New spectroscopic methods for the simultaneous estimation of fundamental atmospheric parameters using the line depth Ratious

New methods are developed to estimate the effective temperature (Te), surface gravity (log g), and metallicity ([A/H]) simultaneously with the spectral line depth ratios. Using the model atmosphere grids, depth values are calculated for the wavelength range of 4000Å-5600Å for various temperatures, gravities, and metallicities. All possible different combinations of line depth ratios for different pairs of ratios are investigated. A graphical 3D figure is produced with X, Y, and Z axes corresponding to Te, log g, and [A/H], respectively. By reading a cross point of two curves plotted by a connection of three parameters obtained from spectral line depth ratio pairs on each of the three projected planes, Te, log g, and [A/H] are determined simultaneously. In addition, an analytical method is devised based on the similar algorithm developed for the graphical method. Our methods were applied to estimate the fundamental atmospheric parameters of the Sun and Arcturus.