Download Supernovas Neutron Stars and Black Holes

Supernovas Neutron Stars
and Black Holes
General properties
Calculation of the radius of the event
horizon for a black hole
Schwarzschild radius
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.
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
2Gmb
v
r
Mass of Earth
= 6.06 x 1024kg
Radius of Earth
1. Calculate the escape velocity of Earth
2. Calculate the escape velocity of a typical neutron star
(Diameter 20km
Density 4 x1017kgm-3)
=6.4 x 106m
Pulsars
Composition;
Mainly neutrons
Density 4 x1017kgm-3
Diameter c20km
dipole magnetic field strength c109 Tesla
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
Pulsar
Cassiopeia/Persius
0.715s
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
Pulsar in vulpecular
1.56ms
The periods of pulsars vary from a few
seconds down to a fraction of a second.
Period
(s)
0.865
3.25
This is simply a random selection from the
catalogue.
0.167
0.167
0.00576
0.375
0.402
3.44
1.24
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.
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!?)
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.
Singularity
Matter and light above the
event horizon can be seen.
Matter and light within the
event horizon cannot be
seen.
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.
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.
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.
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.
Schwarzschild Radius
Escape velocity relation
v
• 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;
2Gm
rb
Where the velocity of light is
the escape velocity and Rs
is the Schwarzschild radius
2Gm
c
Rs
2Gm
Rs  2
c
This derivation does not use general
relativity so is not absolutely
mathematically sound.
Schwarzschild Radius
2Gm
Rs  2
c
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?