We present a statistical analysis of simultaneous optical and X-ray light
curves, spanning 600 ks, for 814 pre-main-sequence (PMS) stars in the Orion
Nebula Cluster. The aim of this study is to establish the relationship, if any,
between the sites of optical and X-ray variability, and thereby to elucidate
the origins of X-ray production in PMS stars. In a previous paper we showed
that optical and X-ray variability in PMS stars are very rarely
time-correlated. Here, using time-averaged variability indicators to examine
the joint occurrences of optical and X-ray variability, we confirm that the two
forms of variability are not directly causally related. However, a strong and
highly statistically significant correlation is found between optical
variability and X-ray luminosity. As this correlation is found to be
independent of accretion activity, we argue that X-ray production in PMS stars
must instead be intimately connected with the presence and strength of
optically variable, magnetically active surface regions (i.e. spots) on these
stars. Moreover, because X-ray variability and optical variability are rarely
time-correlated, we conclude that the sites of X-ray production are not
exclusively co-spatial with these regions. We argue that solar-analog coronae,
heated by topologically complex fields, can explain these findings.Comment: To appear in the Astrophysical Journal. 33 pages, 3 figure