1. Supernovas Neutron Stars and Black Holes
General properties
Calculation of the radius of the event horizon for a black hole
Schwarzschild radius

2. Supernovas
We have seen previously how supernovas are produced by stars with greater than 8 solar masses.
There are two possible outcomes for the core remnant:
With stars of mass greater than 8 solar masses but less than 40 solar masses the result is a neutron star (pulsar)
With stars greater than 40 solar masses the result is a black hole
The crab supernova remnant.
At the heart of the debris is a pulsar.

3. Escape Velocity
The escape velocity that an object would have to be projected upward with to escape from a large mass is known as the escape velocity of the body
G= 6.67 x 10-11Nm2kg
Mass of Earth
= 6.06 x 1024kg
Radius of Earth
=6.4 x 106m
1. Calculate the escape velocity of Earth
2. Calculate the escape velocity of a typical neutron star
(Diameter 20km Density 4 x1017kgm-3)

4. Pulsars Composition; Mainly neutrons Density 4 x1017kgm-3
Diameter c20km
dipole magnetic field strength c109 Tesla

5. The field strength of a pulsar at the poles is such that e. m
The field strength of a pulsar at the poles is such that e.m. radiation is directed by the field in arrow beams from the magnetic poles.
The pulsar is spinning rapidly. If we are within the circle swept out by the beam we receive the pulse once every rotation

6. Pulsar Cassiopeia/Persius 0.715s

7. Pulsars The vela pulsar 86.3 ms
The Vela Pulsar is a radio, optical, X-ray and gamma-emitting pulsar
associated with Vela Supernova Remnant, in the constellation of Vela.
The association of the Vela pulsar with the Vela Supernova Remnant,
made by astronomers at the University of Sydney in 1968,
was direct observational proof that supernovae form neutron stars

8. Pulsar in vulpecular 1.56ms

9. Period (s)
0.865
3.25
0.167
0.375
0.402
3.44
1.24
The periods of pulsars vary from a few seconds down to a fraction of a second.
This is simply a random selection from the catalogue.

10. Black Holes
For stellar remnants of supermassive stars that explode (Ms>40) the result is a black hole.
A black hole is produced when the escape velocity of the stellar remnant exceeds the speed of light.
The limiting mass for the core remnant to form a black hole rather than a neutron star is around 2 solar masses.

11. Black Holes and General Relativity
As a black hole is formed the mass of the core exceeds the “neutron degeneracy pressure”
Gravitational theory suggest that at this the gravitational force is so extreme that the core itself must be squeezed to infinite density
This implies the existence of a singularity (mass with zero volume!?)

12. Properties of black holes
Event horizon
Above this singularity exists a region from which no light can escape as the escape velocity is too high.
This region has a boundary where the escape velocity is equal to the speed of light.
This is the event horizon.
Matter and light above the event horizon can be seen. Matter and light within the event horizon cannot be seen.
Singularity

13. Properties of black holes
Event horizon
Black holes have three properties which are detectable:
mass, electrical charge, angular momentum
Singularity
Black holes can tear apart matter which is close to them. This matter forms an “accretion disk” around the event horizon.

14. An accretion disk forms as matter spirals into a black hole.
X-rays are emitted at right angles driven by intense magnetic fields
Artists impression of a black hole as part of a binary pair.

15. This Hubble Space Telescope image contains three main features.
The outer white area is the core or centre of the galaxy NGC4261.
Inside the core there is a brown spiral-shaped accretion disk.
It has a mass one hundred thousand times as much as our sun.
Because it is rotating we can measure the radii and speed of its constituents,
and hence “weigh” the object at its centre.
This object is about as large as our solar system,
but weighs 1,200,000,000 times as much as our sun.
This means that gravity is about one million times as strong as on the sun.
Almost certainly this object is a black hole.

16. M87 is an active galaxy.
Near its core (or centre) there is a spiral-shaped disc of hot gas.
Although the object in the centre is no bigger than our solar system
it has a mass three billion times as much as the sun.
This means that gravity is so strong that light cannot escape.
We have a black hole. In the first figure, there is a diagonal line.
This is believed to be the passage out of particles which escape
along the axis of rotation and avoid being swallowed by the black hole.

17. Schwarzschild Radius
Escape velocity relation
This is the radius of the event horizon of a spherical black hole, from within which the strength of gravity is so strong that light cannot escape.
The radius at which a body would become a black hole;
Where the velocity of light is the escape velocity and Rs is the Schwarzschild radius
This derivation does not use general relativity so is not absolutely mathematically sound.

18. Schwarzschild Radius Questions:
What radius would the Earth have to be shrunk to if it were to become a black hole?
At what radius would the sun become a black hole?
There was a worry that hadrons in the LHC could produce mini-black holes. What is the necessary mass a proton
(radius ~10-15m) would have to acquire in order to become a black hole?