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 (M2 . 0:5 2 0:7 M() and yet a large radius (R2 . 7 R() and high luminosity (L2 . 150 L(). We show that this star closely resembles a remnant of early massive Case B evolution, during which the neutron star ejected most of the , 3 M( transferred from the donor (initial mass M2i , 3:6 M() on its thermal timescale , 10 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 qi ˆ M2i=M1 in a narrow critical range near qi . 2:6. Smaller qi lead to long-period systems with the former donor near the Hayashi line, and larger qi 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. Key words: binaries: close ± stars: evolution ± stars: individual: Cygnus X-2 ± pulsars: general ± X-rays: stars. 1 I N T R O D U C T I O N Cygnus X-2 is a persistent X-ray binary with a long orbital period (P ˆ 9:84 d; Cowley, Crampton & Hutchings 1979). The observation of unambiguous type I X-ray bursts (Smale 1998) shows that the accreting component is a neutron star rather than a black hole. The precise spectroscopic information found by Casares, Charles & Kuulkers (1998), and the parameters that can be derived from it, are summarized in Table 1. The mass ratio q ˆ M2=M1 . 0:34 implies that mass transfer widens the system, and is therefore probably driven by expansion of the secondary star. Normally in long-period low-mass X-ray binaries (LMXBs) this occurs because of the nuclear evolution of a subgiant secondary along the Hayashi line, with typical effective temperatures Teff;2 . 3000±4000 K. However, Casares et al.'s observations show that this cannot be the case for Cygnus X-2. The secondary is in the Hertzsprung gap (spectral type A9 III): use of Roche geometry and the Stefan±Boltzmann law gives L2 . 150 L( with Teff;2 . 7330 K (see Table 1). Moreover, the mass ratio q . 0:34, and the assumption that the primary is a neutron star and thus obeys M1 & 2 M(; implies that the secondary has a low mass (M2 ˆ qM1 & 0:68 M(). In contrast, an isolated A9 III star would have a mass of about 4 M(. More recently, Orosz & Kuulkers (1999) have modelled the ellipsoidal variations of the secondary and thereby derived a model-dependent inclination of i ˆ 628: 5 ^ 48 which translates into component masses …M1 ˆ 1:78 ^ 0:23†M( and (M2 ˆ 0:60 ^ 0:13†M(: In this paper we consider explanations for the unusual nature of the secondary in Cygnus X-2. We find only one viable possibility, namely that this star is currently close to the end of early massive Case B mass transfer, and thus that the neutron star has somehow managed to reject most of the mass (, 3 M() transferred to it in the past. In support of this idea, we show that this type of evolution naturally explains the surprisingly large companion masses in several millisecond pulsar binaries. 2 M O D E L S F O R C Y G N U S X 2 In this section we consider four possible explanations for the unusual nature of the secondary in Cygnus X-2. We shall find that three of them are untenable, and thus concentrate on the fourth possibility. 2.1 A normal star at the onset of Case B mass transfer? The simplest explanation is that the position of the secondary in the Hertzsprung±Russell (HR) diagram is just that of a normal star crossing the Hertzsprung gap. Because such a star no longer burns hydrogen in the core, this is a massive Case B mass transfer as defined by Kippenhahn & Weigert (1967, hereafter KW). Provided that the initial mass ratio qi & 1 the binary always expands on mass transfer, which occurs on a thermal time-scale. Kolb (1998) investigated this type of evolution systematically and