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An open cluster is an ideal region to study the evolution of stars. In this work, we use Gaia Early Data Release 3 (Gaia EDR3) to derive the fundamental parameters of 30 faint open clusters listed in the catalogue given by Cantat-Gaudin et al. (2018, A&A, 618, A93), but the G magnitude of all of the member stars of that catalogue is brighter than ∼18 mag. This catalogue does not provide isochrone fitting parameters and spatial structure parameters. We acquired the member stars of 30 open clusters using the Density-Based Spatial Clustering of Applications with Noise algorithm in Gaia EDR3. The G magnitude of the member stars using our method can be found down to ∼21 mag. The G-band, GBP-band, and GRP-band data of the member stars construct a good color–magnitude diagram, which can further ensure the precision of isochrone fitting. We also calculated the spatial structure parameters, which are the core radius and the limiting radius, using Markov chain Monte Carlo algorithm.

Contact binary stars are important research objects in astrophysics. The calculation speed of deriving the parameters of contact binaries with the Wilson–Devinney program and the Phoebe with Markov chain Monte Carlo (MCMC) program is relatively slow. It is unrealistic to derive the parameters in batches with the program for sky survey data. We obtain a neural network model of supervised learning with the training of synthetic light curves with Phoebe. We calculate the parameters of eight special targets from the simulated data and the Kepler data. Then, we generate the new light curve to fit the light curve of the special target base on these parameters. The correlation index R2 of the fitting result is more than 0.98. The method can be used to fit the target which has orbital inclinations greater than 50°. By fitting the Kepler data and the observed data on the ground, the method has a good generalization ability to these targets, which have some noise and some starspots. The calculation speed of one light curve with this method is less than seconds. We can derive the parameters quickly in batches to undertake some statistical work for sky survey data with the method.

The first B-, V-, Rc-, and Ic-band light curves of CSS J022914.4+044340 are presented and analyzed. It is found that CSS J022914.4+044340 is a low mass ratio (0.198 +- 0.005) deep (63.7 +- 7.9%) contact binary, indicating that it has been already at the end evolutionary stage of tidally-locked evolution via magnetized wind. Because of the totally eclipsing character, the photometric solutions are reliable. The temperature and the metallicity are determined from the spectroscopic data as T = 5855 +- 15 K, and [Fe/H] = -0.842 +- 0.031, respectively. Based on the parallax of Gaia EDR3, the physical parameters of CSS J022914.4+044340 are estimated as M1 = 1.44 (+0.25,-0.22) solar mass, M2 = 0.29 (+0.05,-0.05) solar mass, R1 = 1.26 (+0.08,-0.06) solar radius, R2 = 0.65 (+0.03,-0.04) solar radius, L1 = 1.718 (+0.186,-0.191) solar luminosity, L2 = 0.416 (+0.039,-0.050) solar luminosity. Combined the fraction in light of the third body via the photometric solution (54%), the luminosity of the third body is estimated as 2.705 solar luminosity. The third body may be inferred as a subgiant. Thus, it is explained that why the primary component of CSS J022914.4+044340 has higher mass among the similar systems, and why its metallicity is so poor., Comment: Accepted

Contact binary systems are very important for studying physical processes such as strong interactions between stars, mass transfer, and stellar merger. Further, the members of an open cluster have the same age, metal abundance, and interstellar extinction conditions. Therefore, we can conduct a comparative study on the different binary systems of the same open cluster. NGC 6811 is an observed intermediate-aged, slightly reddened open cluster in the Kepler field of view; we conducted a corresponding study on the contact binary systems in this cluster. We analyzed six suspected targets and found a total of five EW-type binary systems within a field of 40′ radius of the NGC 6811 cluster center. These targets were analyzed base on the Kepler data, and the corresponding system parameters were obtained by using the latest version of the Wilson–Devinney code. Further, we also used Gaia DR2 data and the cluster distance data to estimate the absolute parameters of these targets to determine whether they are members of the cluster. Finally, we determined that two targets (KIC 9470175 and KIC 9533706) are most likely cluster members; KIC 9957411 and KIC 9776718 are definitely not members of the cluster, just background stars.

KIC 4762887 is a variable star with a very small amplitude discovered by K e p l e r and show the EW-type light curve. We analyzed the light curve of KIC 4762887 by using the 2015 version of the Wilson-Devinney code. The results indicated that it is not a contact binary, maybe not even an eclipsing binary. We also modelled the light curve by the Fourier analysis. The results indicated that the main effect in the light variations of KIC 4762887 is the ellipsoidal effect. Finally, we confirmed that KIC 4762887 is not an eclipsing binary, but rather an ellipsoidal variable star.

A lot of data in time domain were obtained by the Kepler mission, including many contact binaries. Long-term observation lets us obtain more information about the short time scale variation in their light curves or in their orbital periods. Unfortunately, the exposure time is too long (most of them are 30 minutes). Hence, many variations in light curves are smoothed. To avoid this problem, we analyzed some Kepler contact systems with both long-cadence mode and short-cadence mode data. Using the latest version of the Wilson-Devinney code, we obtained the physical parameters of a batch of contact binaries and find out four targets(KIC 5123176, KIC 5296877, KIC 8496820, KIC 9776718) have low mass ratios (q