Minute-cadence Observations of the LAMOST Fields with the TMTS: I. Methodology of Detecting Short-period Variables and Results from the first-year Survey

Tsinghua University-Ma Huateng Telescopes for Survey (TMTS), located at Xinglong Station of NAOC, has a field of view upto 18 deg^2. The TMTS has started to monitor the LAMOST sky areas since 2020, with the uninterrupted observations lasting for about 6 hours on average for each sky area and a cadence of about 1 minute. Here we introduce the data analysis and preliminary scientific results for the first-year observations, which covered 188 LAMOST plates ( about 1970 deg^2). These observations have generated over 4.9 million uninterrupted light curves, with at least 100 epochs for each of them. These light curves correspond to 4.26 million Gaia-DR2 sources, among which 285 thousand sources are found to have multi-epoch spectra from the LAMOST. By analysing these light curves with the Lomb-Scargle periodograms, we identify more than 3700 periodic variable star candidates with periods below 7.5 hours, primarily consisting of eclipsing binaries and Delta Scuti stars. Those short-period binaries will provide important constraints on theories of binary evolution and possible sources for space gravitational wave experiments in the future. Moreover, we also identified 42 flare stars by searching rapidly-evolving signals in the light curves. The densely-sampled light curves from the TMTS allow us to better quantify the shapes and durations for these flares.