On November 27 1783, two days after the last of the British troops evacuated New York City to conclude the Revolutionary War, the rector of St. Michael’s Church near Leeds postulated the existence of stars so massive light could not escape its gravitational field. The rector, John Michell, was also a scientist and the first to conceptualize what we now call a black hole. Michell was using Newton’s theory of light consisting of corpuscles that had mass and were affected by gravity in the same manner any other body of mass would be. This didn’t quite turn out the case and would take Einstein’s new theory of gravity described by relativity in 1915 to formalize the concept of a black hole.
Before we get into all that, we need to familiarize ourselves with the concept of escape velocity. This is the velocity required to escape the gravity of a body of mass and is defined as follows:
Vescape = √(2GM/r) where:
G is the gravitation constant = 6.67408 × 10-11 m3 kg-1 s-2
M = mass of the body
r = radius of the body
To calculate the escape velocity of Earth:
Vescape = √[2(6.67408 × 10-11 m3 kg-1 s-2)(5.972 x 1024 kg)/6,371 km]
= 11.2 km/s or 7 miles/second
What would have to happen for Earth to become a black hole? Earth’s radius would have to be reduced to the point where the escape velocity is equal to the speed of light at 3.0 x 108 m/s or 186,282 miles per second. For this to occur, Earth’s radius has to be reduced to 9 mm or about a third of an inch. For the Sun to become a black hole, its radius would have to be reduced to 3 km or 1.9 miles. As you probably now have surmised, black holes have to be very dense and/or very small. This is where Einstein comes in.
By the time the 20th Century rolled around, it was thought that light consisted only of electromagnetic waves. As such, gravity would not affect light and thus, Michell’s idea of a dark star had been forgotten. In 1905, Einstein discovered the photoelectric effect. Light striking a metal ejected electrons from the surface meaning light had to consist of particles as well as waves. In 1915, Einstein’s general relativity theory viewed gravity as a bending of space-time rather than a force between two objects. Light would be affected by gravity as it would travel along the bend on space-time around a body of mass. The next step in formalizing a theory of black holes would come from the Eastern Front in Russia during World War I raging at the time general relativity theory was published.
Karl Schwarzschild was a German astrophysicist who had volunteered for military duty in World War I. While calculating artillery trajectories, Schwarzschild somehow found the time to solve Einstein’s field equation for a gravitational field around a non-rotating object. If a mass was smaller than a certain radius, space-time would curve into itself in a manner that would not allow light to escape. This is in some sense, the Michell solution but using Einstein’s relativity theory to describe gravity instead of Newton’s theory. This radius, now called the Schwarzschild radius, is defined as:
rs = 2GM/c2
c = speed of light
Using the Sun as an example:
rs = 2(6.67408 × 10-11 m3 kg-1 s-2)(1.989 x 1030 kg)/(3.0 x 108 m/s)2
rs = 2944 m or 2.94 km
This is to say any mass the size of the Sun with a radius less than 2.94 km will form a black hole. Any light or matter within the 2.94 km radius will not be able to escape the gravitational field of the black hole. The radius defined by this equation is the event horizon surrounding a black hole. The more mass in a black hole, the larger the event horizon. Once an object or light passes the horizon, it can never get back out. However, outside the radius, the effect of gravity is the same. If the Sun’s radius was reduced to the point of being a black hole, Earth’s orbit would remain the same as the Sun’s mass is the same.
Unlike Michell’s concept, rather than a dark star smaller than this radius, a singularity would form. A singularity is an object of only one dimension and of infinite density and is infinitely small (volume = 0). Admittedly, this is a mathematically abstract concept that is difficult to imagine. Think of a gravity well in the image above that has an infinite depth, the proverbial bottomless pit. Time also stands still in a black hole from the perspective of an outside observer. The nature of a singularity seemed so bizarre that Einstein himself doubted there was a physical process that could create such an object. It would be the father of the atomic bomb, Robert Oppenheimer, who would confirm that theoretically black holes could exist.
As a star the mass of the Sun nears the end of its life, it runs out of hydrogen to fuse into helium atoms. What’s left are helium atoms to fuse into carbon, and this type of nuclear fusion burns hotter. This pushes the outer layers outward to form a red giant, a star so large it will swallow up the Earth. Eventually, the helium runs out and the outward expansion ceases. The red giant sheds its outer layers and what’s left over is a planetary nebula surrounding a shrinking core. The core is shrinking as the inner force of gravity is now greater than the outward force of heat produced by fusion. The remaining core is compressed to a white dwarf the size of Earth. That’s pretty dense, in fact one teaspoon weighs 15 tons, but not quite small enough to be a black hole. The radius of a white dwarf is on the scale of a few thousand kilometers and the Sun, as noted above, would have to collapse to smaller than 3 kilometers to be a black hole.
What keeps a sun-like star from collapsing into a black hole are the nuclear forces that bind atoms together. This force is strong enough to keep atoms intact and prevents a gravitational collapse beyond the white dwarf stage. When a star is 8-20 times the mass of the Sun, it ends its life in a supernova explosion. These stars fuse elements up to iron at which point fusion can no longer occur. The resultant supernova leaves an iron core that becomes a neutron star. Here, the gravitational force is strong enough to compress electrons and protons to form neutrons. The density becomes higher than in a white dwarf, one teaspoon of a neutron star weights about 10 million tons. The gravity here is pretty intense but still not quite enough to form a black hole. More mass is required, and this is where Robert Oppenheimer comes in.
In 1939, Oppenheimer, along with his student, George Volkoff, published a paper demonstrating that a collapsing star, with sufficient mass, could overcome nuclear forces and form a singularity. As World War II was about to commence, Oppenheimer found himself busy with the Manhattan Project and the paper generally went forgotten. At the time, general relativity and singularities were considered fallow ground for experimental research. Black holes were still considered an odd offshoot of relativity theory. The problem is, how to observe an object that by definition, does not emit light. The solution could be found in Michell’s 1783 paper and some 20th Century technological advancements.
Michell noted in his paper that a black hole would have to be detected by observing the impact on the mass around it. By the 1960’s, interest had been revived in the topic, especially by John Wheeler. It was Wheeler, in fact, who popularized the term black hole in 1967 (The Star Trek episode Tomorrow is Yesterday, aired in January 1967, refers to a black star). Just three years prior, the first black hole candidate was detected as an x-ray source dubbed Cygnus X-1. Why would the presence of x-ray emissions possibly be a sign of a black hole? The answer lies in the surrounding accretion disk of matter falling into the black hole.
Matter falling in the surrounding accretion disk can be heated up to several million degrees. At this temperature, matter will begin to emit high energy, short wavelength x-rays. We are not able to observe x-rays from the Earth’s surface as they are absorbed in the upper atmosphere. That’s a good thing as x-rays are harmful to life, but it does require observations above the surface. The first observations of Cygnus X-1 in the 1960’s were made by sounding rockets and high-altitude aircraft. The launch of the Chandra X-Ray Observatory in 1999 gave astronomers an opportunity to take a good look at Cygnus X-1 from space.
The hot gas is siphoned off from an orbiting blue giant that is visible. This star orbits Cygnus X-1 every 5.6 days and from that, it can be deduced that Cygnus X-1 is 15 solar masses. There is nothing known that can be that large and not be visible besides a black hole. In 1975, Stephen Hawking bet Kip Thorne that Cygnus X-1 was not a black hole. Since then, Hawking has conceded that he lost the gamble. The age of orbiting telescopes would also reveal a different kind of black hole, one much larger in mass than the remnants of supernova explosions.
M87 is a very large elliptical galaxy containing several trillion stars and is 54 million light years from Earth. Back in the 1950’s, there were hints of something unusual in M87 when a large radio source was detected. When charged particles are accelerated, they emit radio waves. This is the principle behind radio towers as electrons are accelerated up and down the tower producing a radio broadcast. Sounding rockets during the 1960’s detected x-ray sources from the galaxy as with Cygnus X-1. In 1998, the Hubble Space Telescope imaged a jet of electrons and sub-atomic particles protruding from M87. Originally discovered in 1919 at the Lick Observatory, Hubble’s high resolution capabilities determined this 5,000 light year jet was caused by a black hole with a mass 2 billion times that of the Sun.
How does a jet of matter become ejected from a region with a black hole? Astronomers are not quite sure but it appears so much mass is trying to enter the black hole that it results in a traffic jam of sorts. Think of it as shooting a fire hose into a bathtub drain. The rejected material gets shot out along the intense magnetic field surrounding the black hole as charged particles will travel along the path of magnetic field lines. M87 is not the only galaxy with a central black hole, in fact, most galaxies have been discovered to have these including the Milky Way.
During the summer months, the constellation Sagittarius is visible. Located in this constellation is the center of the Milky Way. We cannot see the center as it is shrouded by dust. However, infrared observations allow us to peer behind the dust. The UCLA Galactic Center Group has been using the 10-m Keck Telescope to observe the galactic center since 1995 to track the motions of stars in the region. Just like using the orbit of the blue giant around Cygnus X-1 to determine the properties of the black hole, the UCLA team has been able to determine that the Milky Way’s central black hole is 4 million times the mass of the Sun and has a Schwarzschild radius 17 times the Sun’s radius. Below are the observations from the UCLA team.
What does the future hold for black hole research? One intriguing prospect is the possible existence and detection of atomic sized black holes. Speculation is these would have formed during the Big Bang and pass routinely through our bodies. The CERN supercollider may be able to produce such black holes. No need to worry, it would not present a danger to Earth. Most importantly, black holes represent where quantum mechanics and general relativity theory intersect. Quantum mechanics provides the physics for atomic sized particles, relativity provides the physics for gravity and large objects. Relativity breaks down once you reach the singularity. As the universe was a singularity at the beginning of time, understanding the physics of gravity at this scale is required to understand the universe when it originated. Black holes, once considered an abstract oddity of relativity theory, may be able to provide the key to the answer of how the universe came to exist.
* Image atop post is a computer simulation of a galactic black hole. The edge of the black region is the Schwarzschild radius. The light from stars passing near, but not inside, the Schwarzschild radius is smeared by the curvature in space-time caused by the black hole. Credit: NASA, ESA, and D. Coe, J. Anderson, and R. van der Marel (STScI)