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

We have examined correlations between coronal X-ray emission from the Yohkoh Soft X-Ray Telescope (SXT) and photospheric magnetic field measurements from the Michelson Doppler Imager (MDI) on SOHO. Our data sets span a 521 day period beginning 1996 July 25, and we have averaged the data temporally into 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 extreme latitudes. Phase shifting one data set relative to the other shows that the correlation always peaks at zero shift, indicating that coronal X-ray emission is always most strongly related to the photospheric held at the same time (essentially, the same longitude). However, higher order peaks occur for phase shifts of the order of 1 solar rotation, and a detailed analysis shows that the exact phasing of these higher order peaks is consistent with differential rotation of persistent magnetic structures in the photosphere. Cross-correlation between SXT and MDI data from different latitude bins shows that the high-latitude coronal X-ray emission is most strongly correlated with the photospheric field at -30 degrees and +30 degrees. Although this correlation is probably due to projection effects, a less likely interpretation is that the coronal magnetic field, on average, spreads from the photosphere to higher latitudes in the corona. Finally, we compute actual X-ray energy fluxes from the SXT data and show that the correlation between X-ray flux and photospheric magnetic field is in reasonable quantitative agreement with a simple model for coronal heating based on the reconnection of magnetic elements in the chromospheric network.