The ASAS-SN catalogue of variable stars - VII. Contact binaries are different above and below the Kraft break

We characterize ${\sim } 71\, 200$ W Ursae Majoris (UMa) type (EW) contact binaries, including ${\sim } 12\, 600$ new discoveries, using All-Sky Automated Survey for SuperNovae (ASAN-SN)V-band all-sky light curves along with archival data from Gaia, 2MASS, AllWISE, LAMOST, GALAH, RAVE, and APOGEE. There is a clean break in the EW period-luminosity relation at $\rm \log (\it P/{\rm d})\,{\simeq }\,{\rm -0.30}$ , separating the longer period, early-type EW binaries from the shorter period, late-type systems. The two populations are even more cleanly separated in the space of period and effective temperature, by $T_{\rm eff}=6710\,{\rm K}-1760\,{\rm K}\, \log (P/0.5\,{\rm d})$ . Early-type and late-type EW binaries follow opposite trends in T_eff with orbital period. For longer periods, early-type EW binaries are cooler, while late-type systems are hotter. We derive period-luminosity relationships in the W_JK, V, Gaia DR2 G, J, H, K_s, and W₁ bands for the late-type and early-type EW binaries separated by both period and effective temperature, and by period alone. The dichotomy of contact binaries is almost certainly related to the Kraft break and the related changes in envelope structure, winds, and angular momentum loss.