3. The Evolution of High-Mass X-Ray Binaries

The evolution of binary systems is determined by three timescales. The time for the system to come to hydrostatic equilibrium is short compared to the other two. The thermal or Kelvin-Helmholtz timescale is

$$\left(\vphantom{{M_\odot\over M_{\rm c}}}\right. {M_\odot\over M_{\rm c}} \left.\vphantom{{M_\odot\over M_{\rm c}}}\right)^{2}_{}$$ (12)

The nuclear timescale is

$$\approx \left(\vphantom{{M_\odot\over M_{\rm c}}}\right. {M_\odot\over M_{\rm c}} \left.\vphantom{{M_\odot\over M_{\rm c}}}\right)^{5\over2}_{}$$ (13)

This is the timescale for hydrogen core burning to take place in the star at $\sim$ 10⁷ K, leading to the formation of a helium core. Figure 3 shows a possible scenario for the formation of a HMXB (1972).

Figure 6: Possible scenario for the formation of a HMXB (van den Heuvel and Heise (1972)). The center of mass of the system is represented by the vertical lines.

Conservative mass transfer will cause the orbital separation and period to decrease, causing the companion's Roche lobe to shrink (e.g. Frank et al. (1985)). In a close HMXB such as Cen X-3 tidal forces can be important. These will cause the neutron star's orbit to be circularized a few million years after the supernova that created it. Once the orbit is circularized, a tidal instability can set in if the ratio of orbital to spin angular momentum is less than 3. In this case the orbit will decay on a timescale of $\sim$ 5 x 10⁵ years and the neutron star will spiral into the companion's atmosphere. When the companion leaves the main sequence, it will overfill its Roche lobe and mass transfer will occur on the thermal timescale t_th. The primary will quickly spiral in, resulting in a LMXB comprising the primary neutron star and the He core of the companion. The companion may later undergo a supernova explosion, either disrupting the system or forming a binary pulsar system.