Friedrich Wilhelm Bessel in 1832 came to the conclusion that the position of Sirius was oscillating in such a way that betrayed the presence of an unseen companion. In 1862 American astronomer and instrument maker Alvan Clark discovered this companion star visually while testing a new 18 inch refractor for Dearborn Observatory. The new star was designated Sirius B. The faintness of this star coupled with its mass (known through its effect on Sirius) indicated that Sirius B was extremely dense. So dense, in fact, that its existence could not be explained by 19th century physics. Matter of this density was thought to be impossible.
Twentieth century atomic theory provides an explanation. The basic proposition is that no two identical electrons can occupy the same space at the same time. We are familiar with the quantized orbits surrounding the nucleus of a normal atom. The lowest orbit can hold no more than two electrons (and they are not identical; they differ in a property known as spin). A third electron must go to a higher orbit. If the electrons are “free” (i.e., not attached to an atom), as in the case of an ionized gas they, too, can occupy only specified energy levels. The rule for free electrons is the same as for electrons in atoms: no two electrons can occupy the same space at the same time. Think of an egg crate. Only so many eggs, and no more, can fit into a crate, because there are only so many slots. However, under normal conditions there are many unfilled slots (energy levels) for the eggs (free electrons) to occupy. Therefore, under normal conditions, electrons can re-arrange themselves into whatever energy (temperature) and spatial configuration (density) required to satisfy the ideal gas law (Pressure = Density x Temperature). However, under the enormous gravitational pressure experienced by a collapsing star, the electrons are forced to begin filling all of the lower energy levels, and the density can not increase beyond a certain point. When all available energy levels are filled, the star cannot compress further. We have filled all available slots in the egg crate. The star is a white dwarf. The star is prevented from collapsing by degenerate electron pressure, the strength of the energy levels (or, continuing our analogy, the material of the egg crate). Matter in this state is called degenerate matter.
As strong as degenerate electron pressure is, it is not infinite. If the final mass of an evolved star (the remaining core) exceeds 1.4 times the mass of the sun, degenerate electron pressure cannot keep the star from collapsing. This figure of 1.4 solar masses is known as the Chandrasekhar limit after the Indian-American astronomer who discovered the effect in the 1930s. Current models of stellar evolution predict that the remnant core of a main sequence star 8 times the mass of the sun will exceed the Chandrasekhar limit when it is fully evolved. When the Chandrasekhar limit is exceeded, the electrons are forced into the protons, the diameter of the star shrinks from roughly the size of the earth to about 20 km (12 miles), and the star becomes a neutron star. Now all stars rotate, and as their diameters become smaller, they rotate faster to conserve angular momentum. Also, all stars have magnetic fields. As the star becomes smaller, the magnetic field lines become denser and the magnetic field intensifies. Charged particles accelerate along the magnetic field lines generating intense radiation. Thus, as the neutron star rotates, this narrow beam of radiation sweeps around the stellar axis at a very rapid rate. If the axis of the neutron star is oriented so that the beam periodically points in the direction of Earth, it can be detected as a series of pulses or “beeps” by radio and/or optical detectors. The frequency of the pulse depends on the rotation rate of the neutron star; this can be astonishingly rapid (on the order of milliseconds) for a stellar sized mass.
A young English graduate student at Cambridge University named Jocelyn Bell discovered neutron stars in 1967. She was calibrating a new radio telescope under the direction of Anthony Hewish. She found periodic noise signals occurring every 1.33 seconds – extremely rapid for an astronomical phenomena. Since they were detected as pulses, the unknown objects were originally knows as pulsars, a name still used today. Current models explain these pulses by the sweeping beam of radiation as explained above.
Like the white dwarf, the neutrons that make up a neutron star can exist only in clearly defined energy configurations that determine the maximum density of the object. This “nuclear pressure” stops the star from further collapse, but just in the case of the white dwarf, this pressure is not infinite. Physicists are not certain exactly how large a neutron star can be, but certainly the nuclear forces can not support a mass as large as four solar masses and probably not as large as three. Since main sequence stars with masses 25 times the mass of the sun will ultimately have remnant cores greater than four solar masses, they cannot end up as neutron stars. The will become black holes. These objects are among the strangest in the universe. They have only mass, charge and angular momentum. According to straightforward extrapolation of current models, they have no dimension at all – they are mathematical singularities. Whether or not this makes physical sense is a moot point for now, because long before a collapsing star reaches this stage, the escape velocity on its surface exceeds the speed of light (and, of course, all other types of radiation). Since we “see” via radiation of some sort, the star literally drops out of sight once its diameter shrinks to this point. The stellar radius for which the escape velocity exceeds the speed of light is known as the event horizon.
If you can’t see a black hole, how are they detected? What astronomers look for is a very compact source of high-energy radiation, principally x-rays. Where does this radiation come from? Consider a black hole gravitationally bound to a normal star. Remember the tidal force. For two normal stars in orbit about each other, the tidal force tends to deform the stars because one side of each star is closer to its companion than is its opposite side. Thus, there is a differential force, causing the individual stars to be stretched. Tidal forces can be much stronger for a star orbiting a black hole because it can get much closer to the black hole than to a normal star of the same mass. If it is sufficiently close, the tidal forces from the black hole can pull material away from the star, sending it into orbit around the black hole. Since this material cannot form into a solid body, it forms a disk of material known as an accretion disk. This disk also experiences tidal forces and eventually begins to fall into the black hole. As it falls into the black hole the material accelerates, and its constituent particles radiate electromagnetic energy. The faster the particles accelerate, the higher the energy (or, equivalently, the shorter the wavelength) of the radiation. A black hole has a sufficiently steep gravitational well (because of its compact size) so that accelerating particles can generate x-rays. Note that this radiation is generated before the material reaches the event horizon. Otherwise, we could not detect it.
Black holes or something very much like them were considered almost as far back as Newton’s time. In 1784 English geologist John Michell speculated about a “dark star”, collapsing onto itself because of the mutual pull of gravity from its constituent parts. This remained no more than speculation until the 20th century when Karl Schwartzschild used Einstein’s general theory of relativity to calculate the radius of the event horizon for stars of a given mass. Thus, the event horizon for a particular star is also known as its Schwartzschild Radius. In the late 1930s Robert Oppenheimer published more detailed calculations on the properties of such a star, and John Wheeler coined the term black hole in 1968.