  By using high-resolution observations of nearly co-temporal and co-spatial
Solar Optical Telescope spectropolarimeter and X-Ray Telescope coronal X-ray
data onboard Hinode, we revisit the problematic relationship between global
magnetic quantities and coronal X-ray brightness. Co-aligned vector magnetogram
and X-ray data were used for this study. The total X-ray brightness over active
regions is well correlated with integrated magnetic quantities such as the
total unsigned magnetic flux, the total unsigned vertical current, and the
area-integrated square of the vertical and horizontal magnetic fields. On
accounting for the inter-dependence of the magnetic quantities, we inferred
that the total magnetic flux is the primary determinant of the observed
integrated X-ray brightness. Our observations indicate that a stronger coronal
X-ray flux is not related to a higher non-potentiality of active-region
magnetic fields. The data even suggest a slightly negative correlation between
X-ray brightness and a proxy of active-region non-potentiality. Although there
are small numerical differences in the established correlations, the main
conclusions are qualitatively consistent over two different X-ray filters, the
Al-poly and Ti-poly filters, which confirms the strength of our conclusions and
validate and extend earlier studies that used low-resolution data. We discuss
the implications of our results and the constraints they set on theories of
solar coronal heating.
