TYC 1337-1137-1 and TYC 3836-0854-1: Two Low-mass Ratio, Deep Overcontact Systems Near the End Evolutionary Stage of Contact Binaries

New high-precision CCD photometric light curves of two contact binary stars, TYC 1337-1137-1 and TYC 3836-0854- 1, are displayed and analyzed by using the Wilson-Devinney(W-D) program. The light curve solutions show that both of them are low-mass ratio, deep overcontact binary systems with a mass ratio of q = 0.1716. +/- 0.0010 and a high fillout factor of f. = 76.0. +/- 2.9% for TYC 1337-1137-1, and q = 0.1900. +/- 0.0032 and f = 79.4. +/- 7.9% for TYC 3836-0854-1, respectively. These results indicate that they are near the end evolutionary stage of contact binaries. The absolute parameters were calculated by using the new method of mass-radius relationship (0.238 +/- 0.009 M-circle dot and 1.386 +/- 0.050 M-circle dot for TYC 1337-1137-1, 0.228 +/- 0.014 M-circle dot and 1.20 +/- 0.07 M-circle dot for TYC 3836-0854-1, respectively). The preliminary orbital period analysis suggests that long-term period increases exist for both of them, which may be interpreted in two possible ways. A first possibility is mass transfer conservation from the less massive component to the more massive one leading to an orbital period increase. In this case, when their orbital angular momentum is less than three times the total spin angular momentum, they may evolve into a rapidly rotating single star. A second possibility is that the parabolic variation in the (O- C) diagram is only a part of a long-period cyclic change caused by a potential third body. In future, more high-precision observations of these two binaries are needed to confirm the form of orbital period changes.