Multi-color and TESS photometric investigation of four lo mass-ratio contact binary systems

We present the TESS and BVRcIc light curves solution of four low mass-ratio contact binary systems TIC 159102550), V1068 Her, MW Pav and TIC 321576458. Except MW Pav, all three systems have been studied for the first time. The period analysis of TIC 159102550 show anti-correlation between primary and secondary minima and no long term variation is reported. The systems V1068 Her and MW Pav show increasing orbital period trends. Data for TIC 321576458 is too few to determine any periodic variations. The light curve analysis using Wilson-Divinney model shows that systems are low mass-ratio contact binaries. Out of four targets, two systems TIC 159102550 and V1068 Her, are shallow contact binary systems with fill-out factor of 20% and 14%, respectively. The two contact binaries MW Pav and TIC 321576458 are in deep contact state with fill-out factor 63% and 61%, respectively. V1068 Her shows EB-type light curve, however the temperature difference between the primary secondary component is only 17K, which indicates that system is in thermal contact. To understand the evolutionary status of these systems, the components are plotted on the mass-luminosity diagram. The primary companions are in the ZAMS zone while the secondary components of all the systems are away from TAMS which indicates that secondary is more evolved than the primary components. V1068 Her and MW Pav are expected to evolve into a single rapidly rotating star provided that they meet the well-know Hut's criterion. Through statistical investigation of more than hundred low mass-ratio contact binary systems including our targets, we have found that all of the low mass-ratio contact binaries have undergone the mass-ratio inversion process. Based on our sample, the relationship between mass ratio and spin and orbital angular momentum ratio has been updated and proposed a new value of qmin = 0.0388 for Darwin's stability.