Black Holes and Quasars
by David R Lisk
This site provides an introduction to studying the formation of Black Holes and Quasars. It examines the terms used, principles involved and the main mathematics and formulas utilizied.
It also provides a guide to locating and observing Black Holes with photographs
and sky maps being availible. Using the Computer Space Observatory ©, one can view a Quasars X-ray output some 10,000 million light years away from
A Black Hole can be described as a region in space where a high degree of compression has
occured. This region of compression may have been caused by the collapse of a star or
it has been suggested in the case of smaller Black Holes as a result of the collapsing of highly
compressed regions in the primordial dense medium existing after the big bang.
These bodies have collasped catastrophically under their own gravity.
Creation of a Black Hole
During a stars lifetime nuclear reactions inside the star convert hydrogen into helium giving a
release of energy. Gradually a star runs out of its hydrogen fuel. Depending on the mass of the
star it may evolve in a number of ways. At less than twice the mass of our sun when the fuel is
finished heat will be lost, contraction will take place and a stable state into a white dwarf
Chandrasekhar in 1928 calculated the limit whereby a cold star cannot maintain its balance
in terms of a constant radius, between its gravity and the "exclusion principle" which makes the
star want to expand.
Stars exceeding the Chandrasekhar limit, those which have a mass of over twice that of our sun,
cannot settle into the stable state of a white dwarf. They may cool and swell to
become a red giant, more massive stars may become supergiants the most massive exploding
In some cases these outcomes may occur with stars exploding thus throwing off sufficient matter
to avoid gravitional collapse. Another scenario is that the star collapses under its own
With such a star exhausted of nuclear fuel nothing remains of the outward pressure
supporting the star against its own gravity. As the star shrinks the gravitional field
becomes stronger. A point is reached where the escape velocity necessary to overcome the
gravitional field cannot be exceeded even by light itself at a speed of 300,000 kilometers/second.
At this point in time light is no longer emitted from the star, a Black Hole has been formed.
Black Holes have a boundary the point at which light just fails to escape, this is called
the Event Horizon or Schwarzschild radius which can be calculated from the formula:
Where: G = Newton's Constant of gravity
M = Mass of star
c = Velocity of light
For example: for a star with a mass of 19.9 x 10^30Kg (A mass of about 10 times
that of our Sun) this calculates to give a Schwarzschild radius of about 30 kilometers.
Locating a Black Hole
There are a number of methods which have been proposed to assist in locating black holes.
One such method takes into account that a black hole whilst emitting no light will still exhert
a gravitional force.
Observations have been made in systems of two stars orbiting each other, being attracted
by their respective gravitional forces.
Other observations have been made where a star appears
to orbit an unseen partner.
A good example of this effect is Cygnus X-1. Visit X-1 by using the Virtual Space Observatory - Click here - to view.
It is not necessarly the case that the unseen object is a black hole
it could be a small, very faint, white dwarf. Some observations have shown that strong X-rays
are emitted in some cases. A plausible explaination for this is that matter is attracted from
the surface of the visible star spiralling towards the black hole. In doing so a large amount of
heat is generated emitting X-rays.
For this effect to take place the unseen object would have to be very small such as a
white dwarf, neutron star or a black hole.
Features of a Black Hole
Black Hole: A Model
It is possible to conceptulise what a black hole might be made up of in terms of mass, temperature, gravity, spin, charge, size, shape, emissions, pulsations, singularity, lifespan and external effects. These features are considered in greater detail in the next sections.
Click Here - to view a detailed Spacetime Diagram of a Black Hole
It is not possible to study black holes without coming across the term Singularity. Indeed there are different interpretations of the constituants making up a singularity for example the tidal gravity of what is known as BKL (Belinsky, Khalatnikov and Lifshitz) singularity is very different from the Oppenheimer-Snyder singularity.
What is meant by Singularity, or a singular spacetime in relation to black holes?
"A spacetime is singular if it is timelike or null geodesically incomplete but cannot be embedded in a larger spacetime."
- Stephen Hawking
Here is my own attempt at a definition based on Stephen Hawking's.
A singularity is timelike but cannot be embedded in a larger spacetime, it can be seen as a consquence of the gravity inside a black hole producing an "apparent horizon" pulling outgoing light rays back in, the gravity becoming so strong a null point in time is created.
In order to further understanding, Einstein's general relativistic laws are now seen to merge with the laws of quantum mechanics under the heading Quantum Gravity.
Wheeler has argued that because there is no such thing as time in the singularity, when BKL tidal gravity forces peak, space gives way to "Quantum foam".
Black Holes and Particle Emission
A Black Hole radiates with a temperature proportional to its surface gravity. Its entropy and the area of its horizon are proportional to its mass squared.
As it turns out the laws thermodynamics and the laws of black hole mechanics fit neatly together when looking at radiation from a black hole.
Black hole Thermal Radiation
Temperature T = k
Entropy S = 1 x A
Temperature and surface gravity are proportional to its mass divided by its area. When a black hole emits radiation its mass is converted into energy. As its mass is reduced its entropy
and area also reduce, in consquence its temperature and surface gravity increase.
First law of Thermodynamics
§E = T§S + P§V
First law of Black Hole Mechanics
§E = K §A + n§J + ¢§Q
Vacuum fluctuations are random and unpredictable oscillations in small regions of space.
Where vacuum fluctions give rise to an instantainously high value, energy being momentarily stolen from adjacent space and then returned, virtual particles and virtual antiparticles, are formed. As energy cannot be created out of nothing one is positive and one is negative. Normally as the field fluctuates the positive and negative particles seek out and annihilate each other.
Electromagnetic vacuum fluctions give rise to virtual photons and gravitional vacuum fluctuations give rise to virtual gravitons.
A black holes tidal gravity can pull a pair of newly formed virtual photons apart and in doing so will feed energy into them, if sufficient energy is aquired they can materialize into real photons. At the same time excess energy is returned to the neighboring negative regions of space. In the presence of a black hole a particle with negative energy can fall into the hole no longer annihilating its partner. Its partner now free may also fall into the black hole or escape carrying away the energy (mass) given to it by the holes tidal gravity.
As well as a particle escaping the black hole, now with a reduced mass, shrinks.
Using Einstein's most famous equation;
E=mc² where: E = Energy, m = Mass, c = Velocity of light,
it has been shown that the positive flow of energy should be balanced by the negative flow of energy particles into the black hole. The negative energy flowing into the hole causes the black hole to lose mass, with the area of the event horizon getting smaller. Further, as the mass of a black hole reduces its surface gravity and temperature increases.
"Hairless" Black Holes
Hairless Black Holes
A black holes final properties are dependant only on its mass, spin and charge. This gave rise to the term: a black hole has no hair. During the formation of a black hole the star from which it collapses will not be perfectically spherical, it may have buldges. Price's Theorem shows that the buldge or protrusion will be converted into gravitational radiation carring the protrusion away leaving the hole "hairless".
This means that apart from:
mass M, spin(angular momentum J) and electric charge Q,
no information is left to determine any other details about the star which formed the hole.
Following from this it can be concluded that the types of black hole which might be found are limited, this simplifies the necessary calculations when describing a black hole.
Hawking argues from this that when a star collapses to form a black hole a very large amount of information is lost putting forward the view that this loss of information introduces further levels of uncertainty within quantum physics.
Spinning and Pulsating Black Holes
Spinning Black Holes
The effect of a black hole spinning is to create a swirl in space. The spinning action also has an effect on the horizon shape of the hole. Black Holes which do not spin are spherical, a spinning hole bulges at its horizon. There is a limitation as to the speed at which a black hole can spin.
For a black hole of one solar mass, with a circumference of 18.5 kilometers the maximum spin rate is calculated as 0.000062 of a second per revolution. This gives a spin speed of about 299,800 kilometers/second, close to the speed of light.
Electric field lines emerging from the horizon of a spinning black hole produces a swirl of space. This swirl also has an effect on the motion of particles which fall into the hole. Particles approaching from different directions and at different rates will be dragged by the swirl of space into "lockstep" rotation on nearing the holes horizon.
By a manulipation of Kerr's solution to Einstein's field equation Penrose was able to show that spinning black holes store rotational energy around themselves in the swirl of space outside the holes horizon. It is this energy which can be used to power a Quasars jets.
Pulasating Black Holes
When a black hole is viewed from outside its horizon it can be seen as a space-time curvature, with ripples of space time-time bouncing about. This give rise to the view that it is the spinning black hole itself which pulsates. Subsequent calculations by Teukolsky developed a set of equations to analyse black hole pulsations.
The following findings were concluded:
Pulsations extract rotational energy from the hole, at the same time radiating energy away as gravitional waves at a greater rate than it is extracted.
2. Independantly of how fast the hole spins its pulsations are stable.
Black Hole lifespans
With a black hole equaliavent to two solar masses,emitting particles, increasing its temperature and gravity and reducing in mass, a calculated lifespan of:
that is1.2x10^67 years could be expected. Initially such a black hole would have a very low temperature, 3x10^-8 kelvin. In the early stages of a holes formation any particle radiation would be very slow. Over a period of time as the hole shrinks and its temperature rises it will radiate more strongly.
Given the universe has only been in existance for about 16,000,000,000 years (1.6x10^10 years )it will be a very long time before the outcome at the end of a black holes life could be observed.
Holes with a larger mass will have an even longer lifespan as the larger the hole the lower its temperature and surface gravity and therefore the more weakly it emits particles.
When the black holes mass reduces to a figure of below 100 million tons, with its event horizon now smaller than an atomic nucleus, the hole will be then be at a temperature in the order of a trillion to 100,000 trillion kelvin. Reasonable speculation suggests that it is now so hot that it will finally explode in a final burst of energy.
A Quasi-stellar object or Quasar is a class of active galaxy amongst the most distant and luminous astromical objects observed from 2000 million light years to 10,000 million light years from earth.
Quasar 3C273 is a good example. Visit 3C273 by using the Virtual Space Observatory - Click here - to view.
Quasars have a very large redshift indicating that they are moving away from us at an enormous rate. The implications of these findings, in particular the luminousity, would suggest that Quasars are enormously powerful. Typical energy requirements for a quasar would be in the region of 1,000,000,000 solar masses (10^9) of nuclear fuel at 100% efficiency.
The Quasar Engine
To fuel the incredible energy requirements of a quasar current research would suggest that the implosion of a massive star, in the order of 100 million times the mass of the sun, could form a massive black hole sufficent to power a Quasar.
Structure of a Quasar
Theoretical models of quasars have been developed serving to explain their features.
The currently accepted model of a quasar places a spinning Black Hole at its center. This spinning action produces a "swirl of space" pulling gas streams in a spiral motion towards the hole. These gas streams collide as a result of the enormous gravitional energy, thereby creating intense friction and heating the disk. This is what gives a quasar its high luminosity.
This spinning action of the black hole, capturing the gases, creates a gyroscopic effect.
The effect of this is to hold the accredition disk in the same equitorial orientation near the center of the hole.
From the center of a quasar two oppositely pointed Jets emerge in the form of hot magnitised gas. These jets of gas eminating from the quasars central engine feed the radio lobes which can be picked up on earth by interferometers.
These jets form as fast thin streams of gas projecting outward in opposite directions for distances up to 1 million light years. The jets remain straight, due to the gyroscopic effect of the spinning black hole and accredition disk, indicating that their direction has remained constant over a considerable period of time.
A number of explainations have been put forward to explain the formation of two oppositely pointed jets eminating from the black hole/accretion disk of a quasar.
1. The hot gas punching through the orifice formed by a bubble in a spinning gas cloud.
2. The funneling effect provided by the pressure of the accretion disks internal heat.
3. The effect of whirling magnetic field lines anchored in the disk being forced out wards in opposite directions.
4. A whirling magnetic effect where the field lines thread through the black hole itself.
Model of a Quasar
Features of a quasar include:
Enormously high luminosity,
Emission of X-rays,
Gas streams in the form of an accretion disk.
Click Here - to view a detailed 3D Computer Model of a Quasars structure
Given the number of processes taking place Quasars send out quite a unique signature of X-rays, radio jets and and intense light output at various wavelenghts. At the center of the accredition disk where the heat is most intense with temperatures in excess of 100,000 Kelvin X-rays are emitted. Slightly further out around 50,000 Kelvin ultraviolet radiation is emitted. On further, the temperature drops below 10,000 Kelvin and visible radiation (light) is given off. Beyond this at with typical temperaturers of 1000 Kelvin dropping to under 100 Kelvin towards the edge of the accredition disk, near and far infrared radiation is emitted.
Dimensions of a Quasar
Typically the light emitting region of a quasar is about a light-year in diameter although it can be as much as 12 times smaller than this as in the case of 3C273. At the edge of this light emitting region a ring of gas clouds, giving rise to broad spectural lines, surround the central area of the quasar. Beyond this a warm dusty matter spreads out up to 100 light years from the center. Interspersed with dust clouds the outer region of the quasar eventually merges with the galaxy hosting the active nucleus.
Virtual: Space Observatory Computer
Probable locations of Black Holes and Quasars
Use the Space Observatory to view these
Click Here for - Virtual: Space Observatory Computer ©
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