Expressions to determine temperatures and emission measures for solar X-ray events from GOES measurements

Expressions which give the effective color temperatures and corresponding emission measures for solar X-ray events observed with instruments onboard any of the GOES satellites are developed. Theoretical spectra were used to simulate the solar X-ray input at a variety of plasma temperatures. These spectra were folded through the wavelength dependent transfer functions for the two GOES detectors. The resulting detector responses and their ratio as a function of plasma temperature were then fit with simple analytic curves. Over the entire range between 5 and 30 million degrees, these fits reproduce the calculated color temperatures within 2 percent and the calculated emission measures within 5 percent. With the theoretical spectra, similar expressions for any pair of broadband X-ray detectors whose sensitivities are limited to wavelengths between 0.2 and 100 A are calculable.