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We present a statistical analysis of simultaneous optical and X-ray lightcurves, spanning 600 ks, for 814 pre-main-sequence (PMS) stars in the OrionNebula 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 elucidatethe origins of X-ray production in PMS stars. In a previous paper we showedthat optical and X-ray variability in PMS stars are very rarelytime-correlated. Here, using time-averaged variability indicators to examinethe joint occurrences of optical and X-ray variability, we confirm that the twoforms of variability are not directly causally related. However, a strong andhighly statistically significant correlation is found between opticalvariability and X-ray luminosity. As this correlation is found to beindependent of accretion activity, we argue that X-ray production in PMS starsmust instead be intimately connected with the presence and strength ofoptically variable, magnetically active surface regions (i.e. spots) on thesestars. Moreover, because X-ray variability and optical variability are rarelytime-correlated, we conclude that the sites of X-ray production are notexclusively 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

A Simultaneous Optical and X‐Ray Variability Study of the Orion Nebula Cluster. II. A Common Origin in Magnetic Activity