Cygnus X-2, super-Eddington mass transfer, and pulsar binaries

We consider the unusual evolutionary state of the secondary star in Cygnus X-2. Spectroscopic data give a low mass (M_2 \simeq 0.5 - 0.7\msun) and yet a large radius (R_2 \simeq 7\rsun) and high luminosity (L_2 \simeq 150\lsun). We show that this star closely resembles a remnant of early massive Case B evolution, during which the neutron star ejected most of the \sim 3\msun transferred from the donor (initial mass M_{\rm 2i}\sim 3.6\msun) on its thermal time-scale $\sim 10^6$ yr. As the system is far too wide to result from common-envelope evolution, this strongly supports the idea that a neutron star efficiently ejects the excess inflow during super--Eddington mass transfer. Cygnus X-2 is unusual in having had an initial mass ratio $q_{\rm i} = M_{\rm 2i}/M_1$ in a narrow critical range near $q_{\rm i}\simeq 2.6$. Smaller $q_{\rm i}$ lead to long-period systems with the former donor near the Hayashi line, and larger $q_{\rm i}$ to pulsar binaries with shorter periods and relatively massive white dwarf companions. The latter naturally explain the surprisingly large companion masses in several millisecond pulsar binaries. Systems like Cygnus X-2 may thus be an important channel for forming pulsar binaries.Comment: 9 pages, 4 encapsulated figures, LaTeX, revised version with a few typos corrected and an appendix added, accepted by MNRA

About the Linear Complexity of Ding-Hellesth Generalized Cyclotomic Binary Sequences of Any Period

We defined sufficient conditions for designing Ding-Helleseth sequences with arbitrary period and high linear complexity for generalized cyclotomies. Also we discuss the method of computing the linear complexity of Ding-Helleseth sequences in the general case