Light curve solutions of the ultrashort-period $Kepler$ binaries

We carried out light curve solutions of the ultrashort-period binaries with MS components observed by $Kepler$. All six targets turned out almost in thermal contact with contact or slightly overcontact configurations. Two of them, KID 4921906 and KID 6309193, are not eclipsing but reveal ellipsoidal and spot variability. One of the components of KID 8108785 exhibits inherent, quasi-sinusoidal, small-amplitude variability. KID 12055255 turned out a very rare case of ultrashort-period overcontact binary consisting of two M dwarfs. Our modeling indicated that the variability of KID 9532219 is due to eclipses but not to $\delta$ Sct pulsations as it was previously supposed.