Abstract Contact binaries consist of two strongly interacting component stars where they are filling their critical Roche lobes and sharing a common envelope. Most of them are main-sequence stars, but some of them are post main-sequence systems. They are good astrophysical laboratories for studying several problems such as the merging of binary stars, evolution of the common envelope, the origin of luminous red nova outbursts and the formation of rapidly rotating single stars with possible planetary systems. A large number of contact binary candidates were detected by several photometric surveys around the world and many of them were observed by the LAMOST spectroscopic survey. Based on follow-up observations, the evolutionary states and geometrical structures of some systems were understood well. In this review, we will introduce and catalog new stellar atmospheric parameters (i.e., the effective temperature (Teff), the gravitational acceleration (log(g)), metallicity ([Fe/H]) and radial velocity (Vr)) for 9149 EW-type contact binaries that were obtained based on low- and medium-resolution spectroscopic surveys of LAMOST. Then we will focus on several groups of contact binary stars, i.e., marginal contact binary systems, deep and low-mass ratio contact binary stars, binary systems below the short-period limit of contact binaries and evolved contact binaries. Marginal contact binaries are at the beginning of the contact stage, while deep and low-mass ratio contact binary stars are at the final evolutionary stage of tidally locked binaries. Several statistical relations including the period-temperature relation are determined well by applying LAMOST data and their formation and evolutionary states are reviewed. The period-color relation of M-type binaries reveals that there are contact binaries below the short-period limit. Searching for and investigating contact binaries near and below this limit will help us to understand the formation of contact binary systems and a new prediction for the short-period limit is about 0.15 d. Some evolved contact binaries were detected by the LAMOST survey where both components are sub-giants or giants. They provide a good opportunity to investigate evolution of the common envelope and are the progenitors of luminous red novae like V1309 Sco.
Keywords binaries: eclipsing — stars: late-type — stars: low-mass — stars: formation — stars: evolution
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