The Long-Term Evolution of AR 7978: The Scalings of the Coronal Plasma Parameters with the Mean Photospheric Magnetic Field

We analyze the evolution of the fluxes observed in X-rays and correlate them with the magnetic flux density in active region (AR) NOAA 7978 from its birth throughout its decay, for five solar rotations. We use Solar and Heliospheric Observatory Michelson Doppler Imager (MDI) data, together with Yohkoh Soft X-Ray Telescope (SXT) and Yohkoh Bragg Crystal Spectrometer (BCS) data, to determine the global evolution of the temperature and the emission measure of the coronal plasma at times when no significant brightenings were observed. We show that the mean X-ray flux and derived parameters, temperature and emission measure (together with other quantities deduced from them, such as the density and the pressure), of the plasma in the AR follow power-law relationships with the mean magnetic flux density (B). The exponents (b) of these power-law functions (aBb) are derived using two different statistical methods, a classical least-squares method in log-log plots and a nonparametric method, which takes into account the fact that errors in the data may not be normally distributed. Both methods give similar exponents, within error bars, for the mean temperature and for both instruments (SXT and BCS); in particular, b stays in the range [0.27, 0.31] and [0.24, 0.57] for full-resolution SXT images and BCS data, respectively. For the emission measure, the exponent b lies in the range [0.85, 1.35] and [0.45, 1.96] for SXT and BCS, respectively. The determination of such powerlaw relations, when combined with the results from coronal heating models, can provide us with powerful tools for determining the mechanism responsible for the existence of the high-temperature corona.