Download Stellar Remnants White Dwarfs Neutron Stars

Stellar Remnants
White Dwarfs
Neutron Stars
Black Holes
1
Announcements
q  Homework # 5 is due today.
q  Homework # 6 starts today, Nov
15th. Due on Tuesday, Nov 22nd.
2
Assigned Reading
Chapters: 64.4, 65.2, 67, 68.
3
White Dwarfs
v  End-product of evolution of stars
with mass < 8 Msun
v  Most of the mass of a typical star
is ejected outward (planetary
nebula)
v  Remaining core (made of Helium,
or Carbon+Oxygen) has a mass
M<1.4 Msun (i.e., similar to the mass
of our Sun) and a radius roughly like
the Earth.
WD Sirius B
v The density of such system is about
300,000 times greater than the average
Incredible density!
density of basaltic rocks on the Earth
v Over 97% of all stars will become
white dwarfs
16 tons per cubic
inch!
4
White Dwarfs are luminous enough to be routinely observed
with the HST. The Universe is still too `young to contain 5
Black Dwarfs.
What Supports White Dwarfs?
n 
n 
There is no fusion to counter
gravitational collapse. Eventually,
the electrons are forced to be close
together.
Electrons cannot be packed too
closely (a principle from Quantum
Mechanics, called the Pauli Exclusion
Principle):
•  There are only 2 different `flavors’
of electrons, so only 2 can occupy
the same energy level.
n 
The `packed’ (degenerate)
electrons oppose additional
gravitational collapse:
•  White dwarfs are thus supported
by electron degeneracy
Think of putting
tennis balls in a
shrinking box!
6
What Happens if We Add Mass to a
White Dwarf?
n 
The most common White Dwarfs (made
of Carbon+Oxygen) can be thought of a
crystalline lattice of Carbon and Oxygen:
•  This would be a giant diamond!
•  Crystalline structure confirmed in 2004
by studying WD pulsations.
n 
However, as you add mass, at Mass=
1.4 Msun, gravitational pressure is too
high for electrons to support it.
Electrons start combining with protons,
forming neutrons:
•  a neutron star is born!
•  The mass of 1.4 Msun, above which you
cannot have a white dwarfs is called the
Chandrasekhar limit (which earned the
physicist Chandrasekhar a Nobel Prize in
1983)
7
Neutron stars
n 
n 
A neutron star --- a giant
nucleus --- is formed from
the collapse of a massive
star (1.4 Msun < Mcore < 3
Msun).
Supported by neutron
degeneracy pressure (same
Pauli Exclusion Principle that
applies to electrons).
n 
Neutron stars rotate
very rapidly
(conservation of
angular momentum
n 
n 
Only about 10 km in
radius.
A teaspoon full would
contain 108 tons!
Very hot and with very
strong magnetic field
8
Jocelyn Bell
Neutron stars
discovered as
Pulsars,
thanks to their rapid
rotation
9
SNR N157B in the LMC
n 
pulsar
n 
16ms period
The fastest young
pulsar known
10
Pulsars, neutron stars’ light
houses
n 
n 
n 
Why do they rotate fast?
Conservation of Angular
Momentum: A.M. = M x v x R
Pulsar: A fast rotating,
magnetized neutron
star.
The jets’ existence is
due to the rotation and
to the presence of
magnetic fields.
Emits both strong
radiation (radio) and
jets of high-energy
particles.
11
Rotation of Neutron Stars
n 
Angular Momentum Conservation:
•  A.M. = MvR
n 
M = Mass of Neutron Star; v = Rotation Speed;
R = Radius
•  A neutron star has a radius about 100,000
times smaller than that of the Sun.
•  To compensate for the smaller radius, the
rotation speed has to increase by 100,000
times.
•  The rotation period decreases by (100,000)2.
Thus, instead of rotating in ~25 days, the Sun
would rotate about 5,000 times per second!
12
13
14
15
16
17
Pulsar Evolution
§ 
§ 
§ 
§ 
Pulsars emit radiation (0.1%) and high
energy plasma (99.9%): they loose energy
The rotational energy re-supplies the energy
lost from the pulsar radiation.
Eventually, pulsar slows down, radio beams
become weaker.
Many pulsars not observable
•  Beams do not sweep Earth,
•  Slowed down
Too quickly due to ultra strong magnetic fields, or
v  Reached their final stage of `invisible neutron stars .
v 
18
The Limit of Neutron Degeneracy
(What Happens if We Add Mass to a Neutron Star?)
n 
n 
n 
The upper limit on the mass of stars
supported by neutron degeneracy
pressure is about 3.0 MSun (predicted
by Lev Landau)
If the remaining core contains more mass,
neutron degeneracy pressure is
insufficient to stop the gravitational
collapse.
Nothing can stop the collapse; the stellar core
becomes a black hole!
19
Black holes
n 
When the ball of neutrons collapses,
it forms a singularity – a small region
in space with small volume and the
mass of the parent material.
A singularity has infinite density;
nothing can escape, not even light!
The most interesting aspects of a black hole are not what it’s
20 it.
made of, but what effect is has on the space and time around
If an object is incredibly dense and compact, we find that it can
trap light in
vesc
2GM
=
R
G = Gravitational Const.;
M = Mass; R = Radius
If Vesc=c,
the Sun
would
need to be
only 3 km
in radius
21
The gravity near Black Holes is
so strong to bend space, time,
and light!
The position of a
black hole is
called a
`singularity ;
it is a `hole in
space!
Around this hole,
space is bent, like
placing a cannon ball
in the center of a
22
bed.
The Size of a Black Hole
n 
n 
The extent of a black
hole is called its event
horizon. Nothing
escapes the event
horizon!
The radius of the event
horizon is the
Schwarzschild radius
given by:
Rs = 2GM/c2
23
Some Examples of Black Hole Sizes
n 
n 
n 
A 3MSun black hole would have a Schwarzschild
radius of ~10km. It would fit in Amherst.
A 3 billion MSun black hole would have a radius
of 60 AU – just twice the radius of our solar
system.
Some primordial black holes may have been
created with a mass equal to that of Mount
Everest. They would have a radius of just
1.5x10-15 m – smaller than a hydrogen atom!
24
Some Odd Properties of Space
Around a Black Hole
n 
n 
Light emitted near the surface (event
horizon) of a black hole is redshifted as it
leaves the intense gravitational field.
For someone far away, time seems to runs
more slowly near the surface of a black
hole. An astronaut falling into a black hole
would seem to take forever to fall in.
25
Gravitational Redshifts
A photon will give up energy while climbing away from a
mass.
It is trading its own energy for gravitational potential energy.
26
Survey Question
If your buddy were falling into a black hole, what
kind of telescope would you need in order to see
him/her wave goodbye as they crossed the event
horizon?
1)  A large radio telescope.
2)  A large infrared telescope.
3)  A large visible light telescope?
4)  A large X-ray telescope?
27
Time runs more slowly in the
presence of a gravitational field.
1s
Strobe light
No gravitational field.
28
Time runs more slowly in the
presence of a gravitational field.
Observer is far away
from the gravitational
field
Strobe light
(according to the clock)
1s
Big gravitational field for the clock.
(same concept as the increased frequency of light as it escapes the
29
gravitational field)
Black Holes Don’t Suck!
n 
n 
Many people are under the
impression that the gravity of black
holes is so strong that they suck in
everything around them.
Imagine what would happen if the
Sun were to instantly turn into a
black hole. What would happen to
the Earth?
30
Black Holes Don’t Suck!
GM 1M 2
Fg =
2
d
n 
n 
n 
The masses of the Sun and Earth
don’t change (M1 and M2)
The Earth is the same distance from
the Sun as it was before (d = 1 AU)
Therefore, the force on the Earth
would remain exactly the same!
31
Black Holes Don’t Suck!
n 
So why are black holes so infamous?
•  The reason is that the mass is so compact
that you can get within a few kilometers of a
full solar mass of material. Today, if you
stood on the surface of the Sun, much of the
material is hundreds of thousands of
kilometers away. With a black hole, the
mass is so concentrated that you can get
very close to the full mass.
n 
Gravity strength is extreme near a B.H.
•  And so is the tidal field
32
The tidal forces
near a moderate
sized black hole
are lethal!
An astronaut (or
any other object)
would be
shredded.
33
How Do We `See’ A Black
Hole?
n 
n 
Short answer … we don’t.
But we can see:
•  either the lensing effect (bending of
light due to the extreme gravitational
fields)
•  or the radiation from the material falling
into a black hole.
34
Lensing (Light Bending)
from a Black Hole!
Gravitational lensing (a
prediction of Einstein’s General
Relativity)
36
Cygnus X-1 is one of the brightest Xray sources in the sky
HD 226868
Cygnus X-1
The blue supergiant is so large, that its outer atmosphere can be
drawn into the black hole. As the material spirals into the black
hole, it heats up to millions of degrees and emits X-ray radiation.
37
How do we `see Black Holes…
When matter falls into a B.H. it gets very,
very hot. It emits X-ray.
n  Candidate B.H.’s are powerful X-ray
emitters, especially if they show very rapid
variability (=small size)
n  They can also emit jets (similar to pulsars)
n 
Black Hole Jet in the
center of the galaxy
M87 (HST picture)
38
Survey Question
Your doomed friend remembers that s/he has a rocket that
s/he can use to temporarily stop her/his descent into the
black hole. With visions of heroism in your head, you tie
a rope to your waist and jump out of your spaceship to go
and rescue her/him. How does time appear (to you) to
progress for you and your friend as you approach her/
him?
1)  Your own time seems to run normally and your friend’s
time seems to run faster and faster as you approach him.
2)  Your own time seems to run slower and slower as you
fall and your friend’s time seems to continue to run at
the same slow rate.
39
Survey Question
Your doomed friend remembers that s/he has a rocket that
s/he can use to temporarily stop her/his descent into the
black hole. With visions of heroism in your head, you tie
a rope to your waist and jump out of your spaceship to go
and rescue her/him. How does time appear (to you) to
progress for you and your friend as you approach her/
him?
1)  Your own time seems to run normally and your friend’s
time seems to run faster and faster as you approach him.
2)  Your own time seems to run slower and slower as you
fall and your friend’s time seems to continue to run at
the same slow rate.
40