Photometric study of three ultrashort-period contact binaries

We carried out high-precision photometric observations of three eclipsing ultrashort-period contact binaries (USPCBs). Theoretical models were fitted to the light curves by means of the Wilson-Devinney code. The solutions suggest that the three targets have evolved to a contact phase. The photometric results are as follows: (a) 1SWASP J030749.87‑365201.7, q=0.439±0.003, f=0.0±3.6%; (b) 1SWASP J213252.93‑441822.6, q=0.560±0.003, f=14.2±1.9%; (c) 1SWASP J200059.78+054408.9, q=0.436±0.008, f=58.4±1.8%. The light curves show O'Connell effects, which can be modeled by the assumed cool spots. The cool spots models are strongly supported by the night-to-night variations in the I-band light curves of 1SWASP J030749.87‑365201.7. For a comparative study, we collected the whole set of 28 well-studied USPCBs with P<0.24 day. Thus, we found that most of them (17 of 28) are in shallow contact (i.e. fill-out factors f<20%). Only four USPCBs have deep fill-out factors (i.e. f>50%). Generally, contact binaries with deep fill-out factors are going to merge, but it is believed that USPCBs have just evolved to a contact phase. Hence, the deep USPCB 1SWASP J200059.78+054408.9 seems to be a contradiction, making it very interesting. Particularly, 1SWASP J030749.87‑365201.7 is a zero contact binary in thermal equilibrium, implying that it should be a turn-off sample as predicted by the thermal relaxation oscillation (TRO) theory.