Evolution of binaries with ultra-short periods: Systematic study

A detailed investigation of the evolution of low-mass binaries is performed for the case when the secondary fills its Roche lobe at the stage of core hydrogen exhaustion. The obtained results are compared with observational data for ultra-short periodic X-ray systems MXB 1820-30 and MXB 1916-05. In the frame of the proposed evolutionary scenario it is possible to obtain for MXB 1820-30 its periodP=11.4 min twice (see Figure 2). In the first case the parameters of the system are:M ₂ 0.13–0.15M ,X0.05–0.13, |P/P| (3.6–6.2) } 10^–7 yr^–1, M₂ (4.1–9.6) } 10^–9 M yr^–1, for the second:M ₂ 0.08–0.09M ,X= 0, |P/P| (1.3–1.5) } 10^–7 yr^–1, M₂ (1.4–1.8) } 10^–8 M yr^–1. It is suggested that MXB 1916-05 is the progenitor of the system MXB 1820-30 (M ₂ = 0.1M,X 0.221,M ₂ 1.8 × 10^–10 M yr^–1).