Low Magnetic-Field Neutron Stars in X-ray Binaries

In this chapter we give an overview of the properties of X-ray binary systems containing a weakly magnetized neutron star. These are old (Giga-years life-time) semi-detached binary systems containing a neutron star with a relatively weak magnetic field (less than $\sim 10^{10}$ Gauss) and a low-mass (less than $1 M_\odot$) companion star orbiting around the common center of mass in a tight system, with orbital period usually less than 1 day. The companion star usually fills its Roche lobe and transfers mass to the neutron star through an accretion disk, where most of the initial potential energy of the in-falling matter is released, reaching temperatures of tens of million Kelvin degrees, and therefore emitting most of the energy in the X-ray band. Their emission is characterized by a fast-time variability, possibly related to the short timescales in the innermost part of the system. Because of the weak magnetic field, the accretion flow can approach the neutron star until it is accreted onto its surface sometimes producing spectacular explosions known as type-I X-ray bursts. In some sources, the weak magnetic field of the neutron star ($\sim 10^8-10^9$ Gauss) is strong enough to channel the accretion flow onto the polar caps, modulating the X-ray emission and revealing the fast rotation of the neutron star at millisecond periods. These systems are important for studies of fundamental physics, and in particular for test of Relativity and alternative theories of Gravity and for studies of the equation of state of ultra-dense matter, which are among the most important goals of modern physics and astrophysics.