Coronal X-ray brightness and photospheric magnetic field: A study in correlations

We have examined correlations between coronal X-ray emission from the Yohko h Soft X-Ray Telescope (SXT) and photospheric magnetic field measurements f rom the Michelson Doppler Imager (MDI) on SOHO. Our data sets span a 521 da y period beginning 1996 July 25, and we have averaged the data temporally i nto one bin per day and spatially into nine latitude bins, each spanning 15 degrees. We find strong correlations between SXT and MDI data at all but e xtreme latitudes. Phase shifting one data set relative to the other shows t hat the correlation always peaks at zero shift, indicating that coronal X-r ay emission is always most strongly related to the photospheric held at the same time (essentially, the same longitude). However, higher order peaks o ccur for phase shifts of the order of 1 solar rotation, and a detailed anal ysis shows that the exact phasing of these higher order peaks is consistent with differential rotation of persistent magnetic structures in the photos phere. Cross-correlation between SXT and MDI data from different latitude b ins shows that the high-latitude coronal X-ray emission is most strongly co rrelated with the photospheric field at -30 degrees and +30 degrees. Althou gh this correlation is probably due to projection effects, a less likely in terpretation is that the coronal magnetic field, on average, spreads from t he photosphere to higher latitudes in the corona. Finally, we compute actua l X-ray energy fluxes from the SXT data and show that the correlation betwe en X-ray flux and photospheric magnetic held is in reasonable quantitative agreement with a simple model for coronal heating based on the reconnection of magnetic elements in the chromospheric network.