Black holes

7.13 Black holes

If one projected a ball vertically from the equator of the Earth with increasing speed, there comes a point, when the speed reaches 11.2 km s ⫺1 , when the ball would not fall back to Earth but would escape the Earth’s gravitational pull. This is the Earth’s escape velocity. If either the density of the Earth was greater or its radius smaller (or both) then the escape velocity would increase as Newton’s for- mula for escape velocity shows:

0 ⫽ 冑 苴苴苴 r 2GM 0

where v 0 is the escape velocity, M the mass of the object, r 0 its radius and G the universal constant of gravitation.

If one naively used this formula in realms where relativistic formula would

be needed, one could predict the mass and/or size of an object where the escape velocity would exceed the speed of light and thus nothing, not even light, could escape. The object would then be what is termed a black hole .

Black holes have no specifi cally defi ned size or mass, but so far we have only found evidence for black holes in two circumstances. The fi rst, with masses of up to a billion or more times that of our Sun, are found the heart of galaxies and will

Introduction to Astronomy and Cosmology

a stellar core whose mass exceeds ∼3 solar masses – the point at which neutron degeneracy pressure can no longer prevent gravitational collapse.

The surface surrounding the remnant within which nothing can escape is called the event horizon . In the simplest case when the black hole is not rotating, the

event horizon is the surface of a sphere and has a radius, called the Schwarzschild

radius , given by:

R S ⫽ 2GM/c 2

The interior of an event horizon is forever hidden from us, but Einstein’s theories predict that at the centre of a non-rotating black hole is a singularity, a point of zero volume and infi nite density where all of the black hole’s mass is located and where space–time is infi nitely curved. This author does not like singularities; in his view they are where the laws of physics are inadequate to describe what is actually the case. We know that somehow, Einstein’s classical theory of gravity must be combined with quantum theory and so, almost certainly, relativity cannot predict what happens at the heart a black hole.

As will be covered in more detail in the description of the Big Bang in Chapter 9, nucleons are thought to be composed of up quarks and down quarks. It is possible that at densities greater than those that can be supported by neutron degeneracy pressure, quark matter could occur – a degenerate gas of quarks. Quark- degenerate matter may occur in the cores of neutron stars and may also occur in hypotheti- cal quark stars. Whether quark-degenerate matter can exist in these situations depends on the, poorly known, equations of state of both neutron-degenerate matter and quark-degenerate matter.

Some theoreticians even believe that quarks might themselves be composed of more fundamental particles called preons and if so, preon-degenerate mat- ter might occur at densities greater than that which can be supported by quark- degenerate matter. Could it be that the matter at the heart of a black hole is of one of these forms?

The more massive a black hole, the greater the size of the Schwarzschild radius: a black hole with a mass 10 times greater than another will have a radius

10 times as large. A black hole of 1 solar mass would have a radius of 3 km, so a typical 10 solar mass stellar black hole would have a radius of 30 km.

7.13.1 The detection of stellar mass black holes

If a stellar black hole, formed when a massive star ends its life in a supernova explosion, existed in isolation, it would be very diffi cult to detect: gravitational

Stellar Evolution – The Life and Death of Stars

Figure 7.17 Material accreting on to a black hole from a companion star. Image: Thierry Lombry.

able to do so. However, many stars exist in binary systems. In a binary system in which one of the components is a black hole, it appears that its gravity can pull matter off the companion star forming an accretion disc of gas swirling into the black hole (Figure 7.17). As gas spins up as it nears the black hole due to conservation of angular momentum, the differential rotation speeds give rise to friction and the matter in the accretion disc reaches temperatures of more than 1 million K. It thus emits radiation, mostly in the X-ray part of the spectrum.

X-ray telescopes have now detected many such X-ray binary systems, some of which are thought to contain a black hole. Observations of the orbital size and velocity of the normal star in the system enable one to estimate the mass of its companion. If this is both invisible and exceeds a calculated mass of ∼3 solar masses, then it is likely to be a black hole. An excellent candidate in our own Gal- axy is Cygnus X-1 – so-called because it was the fi rst X-ray source to be discovered in the constellation Cygnus and is the brightest persistent source of high energy X-rays in the sky. Usually called Cyg X-1, it is a binary star system that contains

a super-giant star with a surface temperature of 31 000 K (with its spectral type lying on the O and B boundary) together with a compact object. The mass of the super-giant is from 20 to 40 solar masses and observations of its orbital param- eters imply a companion of 8.7 solar masses. This is well above the 3 solar mass limit of a neutron star, so it is thought to be a black hole.

Introduction to Astronomy and Cosmology

7.13.2 Black holes are not entirely black

In the 1970s, Stephen Hawking showed that due to quantum-mechanical effects, black holes actually emit radiation – they are not entirely black! The energy that produces the radiation in the way described below comes from the mass of the black hole. Consequently, the black hole gradually loses mass and, perhaps sur- prisingly, the rate of radiation increases as the mass decreases, so the black hole continues to radiate with increasing intensity losing mass as it does so until it fi nally evaporates.

The theory describing why this happens is highly complex and results from the quantum mechanical concept of virtual particles – mass and energy can arise spontaneously provided they disappear again very quickly and so do not violate the Heisenberg Uncertainty Principle. In what are called vacuum fl uctuations ,

a particle and an antiparticle can appear out of nowhere, exist for a very short time, and then annihilate each other. Should this happen very close to the event of a black hole, it can sometimes happen that one particle falls across the horizon, while the other escapes. The particle that escapes carries energy away from the black hole and can, in principle, be detected so that it appears as if the black hole was emitting particles.

Black holes can be said to have an effective temperature, and unless this is less than the temperature of the universe the black hole cannot evaporate. This tem- perature is now ∼2.7 K – the remnant of the radiation left over from the Big Bang which will be discussed in Chapter 9 – and is vastly higher than the effective tem- peratures of even solar mass black holes. Eventually, in aeons, when the tempera- ture of this relict radiation has fallen suffi ciently and assuming Hawking’s theory is correct, stellar mass black holes may fi nally begin to evaporate – on a timescale of 10 100 years!