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The study of eleven contact binaries with mass ratios less than 0.1

Multi-band photometric observations of eleven totally eclipsing contact binaries were carried out. Applying the Wilson-Devinney program, photometric solutions were obtained. There are two W-subtype systems, which are CRTS J133031.1+161202 and CRTS J154254.0+324652, and the rest systems are A-subtype systems. CRTS J154254.0+324652 has the highest fill-out factor with 94.3$\%$, and the lowest object is CRTS J155009.2+493639 with only 18.9$\%$. The mass ratios of the eleven systems are all less than 0.1, which means that they are extremely low mass ratio binary systems. We performed period variation investigation and found that the orbital periods of three systems decrease slowly, which may be caused by the angular momentum loss, and of six systems increase slowly, which indicates that the materials may transfer from the secondary component to the primary component. LAMOST low$-$resolution spectra of four objects were analyzed, and using the spectral subtraction technique, H$α$ emission line was detected, which means that the four objects exhibit chromospheric activity. In order to understand their evolutionary status, the mass-luminosity and mass-radius diagrams were plotted. The two diagrams indicate that the primary component is in the main sequence evolution stage, and the secondary component is above TAMS, indicating that they are over-luminous. To determine whether the eleven systems are in stable state, the ratio of spin angular momentum to orbital angular momentum ($J_{s}/J_{o}$) and the instability parameters were calculated, and we argued that CRTS J234634.7+222824 is on the verge of a merger.