On the spin-up/spin-down transitions in accreting X-ray binaries

Accreting X-ray binaries display a wide range of behaviors. Some of them are observed to spin up steadily, others to alternate between spin-up and spin-down states, sometimes superimposed on a longer trend of either spin-up or spin-down. Here we interpret this rich phenomenology within a new, simple model of the disk-magnetosphere interaction. Our model, based on the simplest version of a purely material torque, accounts for the fact that when a neutron star is in the propeller regime, a fraction of the ejected material does not receive enough energy to completely unbind, and hence falls back into the disk. We show that the presence of this feedback mass component causes the occurrence of multiple states available to the system for a given, constant value of the mass accretion rate Ṁ* from the companion star. If the angle χ of the magnetic dipole axis with respect to the perpendicular to the disk is larger than a critical value χ_crit, the system eventually settles in a cycle of spin-up/spin-down transitions for a constant value of Ṁ* and independent of the initial conditions. No external perturbations are required to induce the torque reversals. The transition from spin-up to spin-down is often accompanied by a large drop in luminosity. The frequency range spanned in each cycle and the timescale for torque reversals depend on Ṁ*, the magnetic field of the star, the magnetic colatitude χ, and the degree of elasticity regulating the magnetosphere-disk interaction. The critical angle χ_crit ranges from ∼25° to 30° for a completely elastic interaction to ∼40°-45° for a totally anelastic one. For χ ≲ χ_crit, cycles are no longer possible and the long-term evolution of the system is a pure spin-up. We specifically illustrate our model in the cases of the X-ray binaries GX 1+4 and 4U 1626-67.