Unit 12: Stellar Black Holes
 
 

OVERVIEW

The final stages of stellar evolution leading to a black hole are described. The three properties which can be used to specify the structure of a black hole are reviewed: mass, rotation, and electric charge. The structure of a non-rotating black hole and its properties are discussed, including its singularity, event horizon (or Schwarzschild radius) and photon sphere. The structure of a rotating black hole and its properties are discussed , including its stationary limit boundary and ergosphere. The detection of a black hole using x-rays emitted from its surrounding accretion disk is reviewed. Non-stellar black holes are also discussed.

LEARNING OBJECTIVES

At the end of this unit you should be able to:

1. Describe the stages of stellar evolution that lead to the formation of a black hole.

2. Review the finding that the basic properties of a black hole depend on its mass, rotation, and electric charge.

3. Discuss the properties of a rotating black hole, including its singularity, event horizon, photon sphere, stationary boundary limit and ergosphere.

4. Describe how a black hole might be detected.

5. Describe examples of non-stellar black holes.

 KEY WORDS stellar black hole

collapse of neutron star

black hole mass

black hole rotation

black hole angular momentum

non-rotating black hole

singularity

event horizon

Schwarzschild radius

photon sphere

rotating black hole

stationary limit boundary

ergosphere

black hole detection

accretion disk

X-ray binary candidates

non-stellar black hole

mini black hole

supermassive black hole

the Universe as a black hole

 WRITTEN NOTES

MAIN SEQUENCE STARS MORE MASSIVE THAN 8 SOLAR MASSES

The Formation of a Stellar Black Hole

During the late stages of stellar evolution when massive stars are dying and electrons and protons are pushed together to form neutrons and neutrinos, a stable stellar structure called a neutron star is formed if the force of gravity is not strong enough to push neutrons together. The technical way to state this is that there is equilibrium in a neutron star because the inward forces of gravity are balanced by the outward forces caused by neutron degeneracy.

However, neutron degeneracy will not stop a neutron star more massive than 3 solar masses from further gravitational collapse.

 [Theoretical calculations are uncertain on this point. A neutron star which has only 2 solar masses may also be too massive to stop further collapse. On the other hand, the extremely rapid rotation speeds of neutron stars inhibit collapse.] Collapse of a neutron core more massive than 3 solar masses may occur after a supernova explosion, or it may occur directly without a supernova explosion (because there is no outward explosive force caused by a rebounding neutron core).

Once the gravitational collapse of the neutron core begins, there is no force known which is strong enough to stop the collapse. The collapse will continue forever.

The General Theory of Relativity predicts that electromagnetic radiation (light) is affected by gravity. Light escaping from the surface of a white dwarf will undergo a slight gravitational redshift as it must use up some of its energy to get away. Light escaping from the surface of a neutron star will undergo a stronger gravitational redshift as it must use up even more of its energy to get away. It is possible for gravity to become so strong, that light does not have enough energy to escape its pull.

[Note that the General Theory of Relativity also predicts that mass bends light. In strong gravitational fields, light will be significantly bent back towards the mass.] Thus, in the late stages of stellar evolution, if a neutron core more massive than 3 solar masses forms, it will begin to collapse forever. At some specific distance from the center of the collapse, gravity will be strong enough that even light will not be able to escape from that point. This is a stellar black hole. The Structure of a Black Hole A black hole is a very simple object theoretically. This is because its properties can be completely described if its mass, rotation, and electric charge are specified.

From what is known about neutron stars, it is clear that a stellar black hole should be rotating very rapidly. However, the structure of a non-rotating black hole will be considered first. How rapid rotation affects the structure of a stellar black hole will then be considered.

 In the simplest terms, a non-rotating black hole has three regions of interest: 1. The Singularity. Theory predicts that no force can stop the gravitational collapse of a black hole. Mathematically, all of the mass is predicted to reside in an infinitely small point at the black hole's center. This point is called a singularity.

2. The Event Horizon. Gravity is infinitely strong at the singularity. Gravity becomes weaker at distances further from the singularity. If a 3 solar mass black hole is considered, light has no chance of escaping unless it is more than 9 km from the singularity. This location in the black hole is known as the event horizon. Karl Schwarzschild first calculated the size of the event horizon in 1916 using the General Theory of Relativity; therefore, the event horizon is also known as the Schwarzschild radius. Schwarzschild calculated that the size of the event horizon is directly proportional to the mass of the black hole.

3. The Photon Sphere. At some point outside of the event horizon is the photon sphere. The photon sphere corresponds to a distance at which light would orbit about the center of the black hole. The photon sphere is 1.5 times larger than the event horizon.

 Because relativistic effects are so strong in the vicinity of a black hole, phenomena like length contraction and time dilation, which go against common sense, take place.

Pay close attention to the explanations in the text as to what you would observe if you were standing near a black hole and watched as someone approached the black hole's event horizon and fell into it. They cover this in good detail (more than I can put here), and it will be on the exam.  You will  especially need to know what you see happening to time and light as he approaches the horizon.  (To summarize briefly...) You observe his time to run slower the closer he gets, and it would come to a complete stop as he crossed the horizon, so you can never see him crossing the event horizon.  He would simply seem stuck just outside it.  Also as he approached, the light coming from him to you would be more and more redshifted the closer he got to the horizon.  When he crossed the horizon, it would be redshifted to an infinite wavelength.  However, the man approaching the horizon himself does not see these effects on him.  His watch runs at normal speed, from what he sees, and he doesn't see his own color redshifting, because the light does not have to move against the strong gravity to reach his eyes.

 A Rotating Black Hole As a black hole begins to rotate, its event horizon becomes smaller because the inward force of gravity is diminished to some extent by the outward force cause by the spinning.

It is helpful to consider another boundary around a rotating black hole called the stationary limit. At the poles of a rotating black hole, the stationary limit boundary touches the new (smaller) event horizon. At the equator of a rotating black hole, the stationary limit boundary is the size of the (bigger) event horizon of a non-rotating black hole.

The region between the stationary limit and the event horizon of a rotating black hole is called the ergosphere. Whether or not light can escape from the ergosphere depends on the direction in which it is traveling. Theoretically, it is possible to extract energy from a black hole's ergosphere.

Some theorists have proposed that the warped or curved spaces in rotating black holes form bridges to other parts of the Universe or other Universes.

 The Detection of a Black Hole If we were to watch an entire star collapse into a black hole, we would simply see all of its electromagnetic radiation become infinitely redshifted, and then disappear, in a fraction of a second. There is little chance of observing such an event.

At the present time the only methods used to investigate the idea of a black hole are to search for matter which may be orbiting around one and to identify binary systems which contain invisible companion stars which have masses greater than 3 solar masses.

Extremely hot matter is expected to orbit around a black hole. The idea is that some of the matter attracted (accreted) by a black hole will not fall in but will go into orbit around it. This orbiting matter is called an accretion disk. The orbital motions will be so energetic that friction between the various parts of the disk will cause it to heat to high enough temperatures so that observable X-rays are emitted.

The best stellar black hole candidates are in X-ray binaries where the invisible companion star has a mass greater than 3 solar masses. Cygnus X-1 is one of the best candidates.

 Non-Stellar Black Holes So far, the formation of black holes during the late stages of evolution of massive stars has been considered. Black holes may also form in other ways, some of which will be considered later. For example: 1. Mini black holes may have formed as a result of great compressive forces present in the Early Universe near the time of the Big Bang. [A black hole with the mass of an asteroid would be the size of a pin head.] 2. Supermassive black holes (with masses of 1 million to 1 billion solar masses) are likely to exist at the centers of quasars and some galaxies.  Yes, "Supermassive" is the technical term.    Now we believe that probably every galaxy has a supermassive black hole at its center, including the Milky Way.  We will discuss quasars later in the course, including whether the Milky Way was ever once a quasar.

3. The Universe itself could be thought of as the interior of a black hole since light cannot escape its boundaries and one day it may collapse back in on itself to form a singularity.

 READING ASSIGNMENT

Chapter 17.4

HOMEWORK

Ch. 17, Review Question 17