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The light curve of an eclipsing system shows anomalies whenever the eclipsingbody passes in front of active regions on the eclipsed star. In some cases, thepattern of anomalies can be used to determine the obliquity $\Psi$ of theeclipsed star. Here we present a method for detecting and analyzing thesepatterns, based on a statistical test for correlations between the anomaliesobserved in a sequence of eclipses. Compared to previous methods, ours makesfewer assumptions and is easier to automate. We apply it to a sample of 64stars with transiting planets and 24 eclipsing binaries for which precisespace-based data are available, and for which there was either some indicationof flux anomalies or a previously reported obliquity measurement. We were ableto determine obliquities for ten stars with hot Jupiters. In particular wefound $\Psi \lesssim$10$^\circ$ for Kepler-45, which is only the second M dwarfwith a measured obliquity. The other 8 cases are G and K stars with lowobliquities. Among the eclipsing binaries, we were able to determineobliquities in 8 cases, all of which are consistent with zero. Our results alsoreveal some common patterns of stellar activity for magnetically active G and Kstars, including persistently active longitudes.

Stellar obliquities and magnetic activities of Planet-Hosting Stars and Eclipsing Binaries based on Transit Chord Correlation