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Stellar Evolution - Chapter 12 and 13
The Lives and Deaths of Stars
White dwarfs, neutron stars and black holes
During the early stages of a star formation the objects are called a protostars. The
internal temperature is not high enough to produce fusion. These objects radiate
energy away in the form of light. That energy comes from gravitational energy
converted to heat.
Once they reach the Main
Sequence, The temperature is
high (10 million K) and
fusion starts. The contraction
stops because gravity and
internal pressure caused by
the energy released from
fusion exactly balance each
other (hydrostatic
equilibrium)
Nuclear reactions occur at
exactly the right rate to
balance gravity.
Remember that a stars’
mass determines its
luminosity
Evolution of a Sun-like star
(A star with the mass similar to the Sun)
Nuclear reactions slowly convert
H to He in the core.
That is called core hydrogen
burning. Burning here means
fusion
Newly formed stars are typically:
~91% Hydrogen (H)
~9% Helium (He)
In the Sun’s core, the conversion of
H to He will take ~10 billion years
(its Main Sequence lifetime).
Composition of a Sun-like star.
What happens when
the core Hydrogen is
used up?
Nuclear reactions stop.
Core pressure decreases.
Core contracts and gets hotter heating overlaying layers.
4H  1He burning moves from the
core to a hot “shell” surrounding
the core.
Post-Main Sequence evolution
•4H  1He reactions occur
faster than before; the shell is at
a higher temperature.
•The hot shell causes the outer
layers to expand and cool!
•The star gets brighter (more
luminous)!
•The star moves off the Main
Sequence, …up the “Red
Giant” branch.
Ascension up the red giant branch
takes ~100 million years.
What happens in the core as
it continues to contract and
get hotter?
Remember why Hydrogen burning
requires 107 K (10 million K)?
(Protons repel each other.)
Helium nuclei (2 protons) repel each
other even more…
In order to collide and fuse it is
necessary higher temperatures (The
nuclei need higher velocities!)
Helium begins to fuse into Carbon at >108 K (100 million K).
(Helium nuclei have 2 protons and two neutrons. Carbon nuclei have 6
protons + 6 neutrons.)
This reaction is called “triple alpha” = 3He  C
(Alpha particle: Nucleus of He)
The Helium Flash:
After the core reaches 108 K (100 million
K) (stage 9), Helium “ignites” to make
Carbon.

The onset of this burning causes the
temperature to rise sharply in a runaway
explosion – it is called Helium Flash

Eventually the core expands, density
drops and equilibrium is re-established

Core structure is now readjusted during
Helium core burning and total luminosity
is actually decreased (Radius decrease,d
temperature increases

During core Helium burning, the star is
on the Horizontal Branch (Stage 10).

Post-Main Sequence evolution
Relative sizes of main-sequence, red giant, and
horizontal branch stars.
Stage 7
Stage 9
Stage 10
Structure of Stars in Different Evolutionary Stages
Stage 10 - Helium-to-Carbon burning
occurs stably in core, with Hydrogen-toHelium burning in shell…
Carbon
Helium
…until the core Helium runs out….
in just 20-50 million years…
Carbon
Helium
Carbon
Helium
The increased shell burning
causes the outer layers to
expand and cool (again).
The star moves up the
asymptotic giant branch
(in only ~10,000 years!) to
stage 11.
becoming a red supergiant
•During this phase, Heliumto-Carbon burning creates a
Carbon core, which starts to
contract and heat up.
•Then He burning moves to a
shell
•with H burning in an outer
shell.
What do you suppose happens next in the core?
For a Sun-like star:
nothing….
Why?
Solar mass stars cannot squeeze and heat the
core enough to ignite Carbon. It will need to
reach a temperature of 600 million K to ignite
carbon
So what does happen?
With no more production of energy in
the core, the carbon core continues to
contract and heat.
Shell He burning grows more intense.
He flashes occur in the shell.
Surface layers pulsate and are finally
ejected (slowly, at ~10s of km/s).
The hot core collapse into a tiny
object called White Dwarf.
White Dwarf
And a Planetary Nebula appears! (The
expanding emission line nebula
heated by intense radiation from the
hot white dwarf)
Planetary Nebulae have nothing
to do with planets.
It is the last stage of the
evolution of a star with a mass
close to the Sun.
White Dwarf
The white dwarf has a
temperature of about 120,000
K. It radiate UV emission . The
emission excite the gas and the
gas glows
They emit line radiation (hot,
low pressure gas) but in size
they are much smaller than the
emission nebulae (HII regions)
Planetary nebula
They are important sources
of heavy elements (C, N and
O), which contaminate
interstellar clouds and will
go into the next generation
of stars.
White dwarfs have about the
Sun’s mass (the rest of the mass
was expelled).
The white dwarf is an object
about the size of the Earth!
(~0.01 solar radii, 12,000 km)
The collapse is stopped due to
electron degeneracy pressure
Density: ~1 million g/cm3 !!
Very low luminosities (small
radius)
(L = 4R2 T4)
What eventually happens
to a white dwarf?
It gets cooler and fainter
(at the same radius).
This is the End:
•White Dwarf fades away. It doesn’t
produce more energy, it dissipate the
energy stored in its mass. Because of
the small radius (small surface), it
takes a long time to cool off.
•Planetary Nebula dissipates into
interstellar space.
•End of story for stars like the Sun.
Summary:
What happens to higher mass stars?
Gravity squeezes and heats the
core. The temperature needs to
increase enough to be able to
ignite Carbon, around 600
million K
Then it will continue fusing
Oxygen, then Neon…as each
fuel gets exhausted in the core,
its burning moves to a shell.
Concentric fusion shells form an
“onion skin” structure.
Important!
The formation of an Iron
core is the last stage…
Reaching the conversion to Iron marks the end of the life of a massive star
Why is Iron formation the end of the line?
Hydrogen
Creating elements
heavier than Iron
requires energy!
With no more sources
of energy, and the Iron
fusion taking energy
from the core…
The pressure that
support the star’s core
is lost…
The core quickly
collapses under its own
weight….
The mass is too large and the
electron degeneracy pressure
cannot stop the collapse
Protons and electrons are crushed
together in the collapsing core,
making neutrons.
Eventually, the neutrons are so close
together they “touch” . They generate
the neutron degeneracy pressure
The densities reach 100 trillion g/cm3
(at those densities the whole Earth would fit in a football stadium!!)
The collapsing neutron
core then bounces!
Supernova
An explosive shock wave
propagates outward,
expelling all outer layers.
The Crab Nebula
This supernova was recorded
by Chinese astronomers in
1054 AD.
It was BRIGHT!
It was seen in daylight!
Crab Nebula
(Supernova remnant)
The Crab Nebula
(M1) is located in the
Taurus constellation.
The distance is about
6,500 ly
The age is about
1,000 years
The relative
magnitude is +8.4
Supernova ejecta like
this spread heavy
elements throughout
the Galaxy.
Heavier elements,
heavier than iron are
created during the
supernova explosion
A composite image of the Crab nebula from images of
Chandra (X-rays), Hubble (Visual) and Spitzer (IR)
The central object (core
of star) is a rotating
neutron star with a
strong magnetic field.
The object is called a
pulsar
The Crab pulsar (first
detected at radio
wavelength) has a
rotation period of 33
milliseconds!
Neutron Star size compared
to New York City
What happen to the core?
Composition of the core:
Neutrons
Mass: 1 – 3 MSun
Radius: ~10 km (6 miles)
Density: 1017 kg/m3
The core rotates fast
1 cm3 weighs as much as Mt. Everest!
Neutron stars also spin very rapidly… Why?
Why the core (neutron star) rotates fast?
The angular momentum L is
conserved:
Lbefore = Lafter
mvR = mVr
Mass stays the same
Most neutron stars rotate in less than a
second!
The range of rotational periods of
pulsars is from a few milliseconds to
about 4 seconds
Slow rotation v
Fast rotation V
Large radius R
Small radius r
Neutron stars have very strong magnetic fields… Why?
Magnetic field of neutron stars
Why neutron star have a very
intense magnetic field?
When the star collapses into a
neutron star, the plasma
(electrically charged ) that
make up the core of the star
carries and intensify the
magnetic field
The result is that a neutron star
rotates fast and have a very
intense magnetic field
The combination of these two characteristics leads to an
interesting phenomenon:
PULSARS
RA
Dec
The first pulsar, PSR1919+21was discovered in
1967 by then a graduate student, Jocelyn Bell in
England who measured this periodic radio signal
from an unresolved source (They were studying
scintillation of radio sources):
The observations were made with a radio telescope at 82 MHz (3.7 m
wavelength). The period of the pulsar is 1.337 seconds
In 1974, her advisor, Anthony Hewish, won the Nobel Prize in physics
for explaining it….. She was not a co-recipient of the award
A pulsar model
The Lighthouse model of a pulsar
1) Strong magnetic fields
lead to “hot spots” at the
magnetic poles.
2) Accelerated particles at
hot spots emit “beamed”
radiation. For most
pulsars the emission is in
the radio wavelengths
3) If the rotation axis is not
aligned with the
magnetic field axis, then
this “searchlight” rotates.
4) If Earth is in the path of
the rotating beam, for
every rotation, a pulse is
detected
An animation of the lighthouse
model of a pulsar
Are neutron stars the densest,
most compact object in the
universe?
Can a neutron star be crushed
further?
YES!
Neutron stars are also stable structures,
supported by neutron degeneracy pressure.
What do you suppose happens if the mass
exceeds 3 solar masses?
The structure is crushed, and now there is
nothing to halt the complete gravitational
collapse…!!
The structure becomes a Black Hole
The end of the life of stars of different masses
Diameter of a white dwarf ~
12,000 km diameter (~Earth
diameter)
Diameter of a neutron
star ~20 km across
???
Black holes are thought to be the endpoints of stars that
exceed 25-30 solar masses on the main sequence
•They are concentrations of mass where gravity is so strong
that nothing (including light) can escape!
•In terms of theory of relativity, the mass of the black hole
distort and curve the space-time and creates an extremely
deep gravitational well
•The mass will collapse into what is called in relativity as a
SINGULARITY.
•The radius and density of the resulting object cannot be
determined.
•The state of the matter inside cannot be described.
A small mass creates a small curvature
Einstein’s
“General Theory of Relativity”
Masses curve the space around them.
More mass  more curvature.
Roll a marble
A way to visualize the curvature of space
Due to the presence of the mass, the
trajectory of the marble is a curve  more
gravity.
Eventually (squeezing the mass even more) the escape velocity would be
equal to the speed of light (300,000 km/sec).
The trajectory of a light beam will be so distorted. The beam of light will
remain inside the gravity well
 Nothing could get out, including light!
That’s a
Black Hole.
The critical radius at which the escape velocity equals the speed of light is
called the Schwarzschild Radius.
This is considered the “radius” of a black hole. There is no “solid” surface at
that radius.
The sphere around the black hole at the Schwarzschild Radius is called the
“event horizon,” because no event inside that sphere can ever be seen,
heard or known by anyone outside.
A simulation of the distortion of the images of stars in the background
by a supermassive black hole (Gravitational lensing)
(Supermassive Blackhole: Masses in the range of million to billion solar masses)
Event horizon
Schwarzschild radii for different masses of black hole:
1 earth mass:
1 cm
1 solar mass:
3 km
106 solar masses:
3 x 106 km (0.02 AU)
109 solar masses:
3 x 109 km
e:What
would happen to the orbit of the Earth
if the Sun suddenly became a Black Hole?
Would the Earth get sucked in?
No!
 The Earth will be at the same distance, at one AU from a solar mass
black hole, it will feels the same gravitational attraction from the Sun at 1
AU.
 The gravitational force depends on the product of the masses and is
inversely proportional to the distance squared. The masses of the Sun (or
black hole) and the Earth are the same and the distance remain the same!!!
An example: The presence of a supermassive black hole in the
center of the Milky Way
• An animation of the
observation (in IR) of the center
of the Milky Way showing the
movement of stars around the
central supermassive black hole.
• The black hole (Located by the
star symbol in the animation) is
located in the center of the
Milky Way, in the constellation
Sagittarius, at a distance of
about 26,000 ly.
• The mass is about 4.3 million
solar masses
How can we determine the mass
of the black hole?
Newton version of Kepler 3rd
Law!
MBH = a3 / P2
P = Orbital period of a star orbiting the black hole
a = Radius of the orbit of the star
Mass of Black Hole = MBH