Note that for m1 being much greater than m2 this approaches m1/2, meaning the massive star would have to lose half its mass. Note that, by the discussion in Section 5.4, this result doesn't change for elliptical orbits, since the equation for the energy is the same, with R replaced by the semi-major axis.
Therefore, the explosion should break up the binary system. This scenario explains the existence of "runaway stars". These are individual stars moving through space with much higher than average speeds.
X-ray observations have been made of systems in which it appears that a neutron star is still in orbit with a normal star. This means that there must be some way of forming such a system, and eventually theoreticians have come up with a number of plausible scenarios. Different scenarios might work in different types of systems that are found. (1) Theoretical simulations have shown that, while most systems in which the more massive star goes supernova first will become unbound, there are some combinations of initial conditions that will lead to bound systems after the supernova explosion. (2) Before the supernova explosion, the more massive star might have filled its Roche lobe and transferred mass to the less massive star. If enough mass is transferred before an explosion, the system can stay bound. (3) An alternative explanation is that the compact star may have originally been a white dwarf, not a neutron star. However, mass transfer from the companion may have pushed the mass of the white dwarf beyond the 1.44 M0 limit. The electron degeneracy pressure could no longer support the star and it would collapse until it became a neutron star. So, the neutron star would have formed without a supernova explosion. (It is interesting to note that a 1.44 M0 white dwarf that suddenly collapsed to form a neutron star would, according to general relativity, appear to exert the gravitational force of a 1.3 M0 star. Thus, there may be stars we think are white dwarfs, but which are really neutron stars.)
We now suppose that we have a binary system with a neutron star and a normal star, with mass being transferred from the normal star to the neutron star. The mass falling in is heated and gives off irregular bursts of X-ray emission. To see how this works, we look at the case of a well studied X-ray source, Her X-1 (Fig. 12.7a). (The name implies the brightest X-ray source in the constellation Hercules.) It is also coincident with a variable star HZ Her. The star is a binary with a period of 1.7 days. The mass of the unseen companion is estimated to be in the range 0.4 to 2.2 M0. The X-rays are observed to pulse with a period of 1.24 s.
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