Describe a pulsating X-ray source like Hercules \(\mathrm{X}-1\) or Centaurus X-3. What produces the pulsation?

Binary star systems are pairs of stars that orbit around a common center of mass. This gravitational dance is quite common in the universe; many of the stars we observe are part of binary systems or even more complex multiple star systems. In the context of pulsating X-ray sources, one of the stars in the binary system is often a compact object, such as a neutron star, which we'll explore in more detail shortly.

Understanding the dynamics of binary systems is crucial not just because they are common, but also because they can lead to a variety of interesting astrophysical phenomena. For instance, if one of the stars in a binary system is a main sequence star (a stage of stellar evolution that our Sun is currently in) and the other is a compact object like a neutron star or a black hole, the intense gravitational field of the compact object can draw in material from its companion. This siphoning of material is central to the concept of accretion disks and the X-ray pulsations we observe.

Neutron stars are one of the possible end stages of stellar evolution, particularly for massive stars. When such a star exhausts its nuclear fuel, it can undergo a supernova explosion, ejecting its outer layers into space and leaving behind an incredibly dense core. These stellar remnants have masses about 1.4 to 2 times that of the Sun but are only about 20 kilometers in diameter, resulting in densities so high that a scoopful of neutron star material would weigh as much as a mountain.

Neutron stars are not just fascinating for their extreme properties. Their strong gravitational and magnetic fields play a key role in the creation of pulsating X-ray sources. As part of binary systems, neutron stars often strip material from their companions, creating the conditions necessary for the intense emissions of X-rays—emissions that we can detect across vast interstellar distances.

Accretion disks are another compelling aspect of the astrophysics of pulsating X-ray sources. These flat, disk-like structures form when material from a companion star in a binary system is drawn toward a neutron star or black hole. The material doesn't fall directly onto the object but instead spirals in gradually, heating up due to friction and gravitational forces.

An accretion disk around a neutron star can become extremely hot, reaching temperatures of millions of degrees. It's at these temperatures that the material emits X-rays. Moreover, the combination of the neutron star's rotation and magnetic fields directs the accretion flow to its magnetic poles, producing the 'pulse' of radiation we observe as pulsating X-ray sources. Understanding accretion disks helps astronomers to study not just the behavior of matter in extreme conditions, but also the properties of the compact objects that they orbit.