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PHYS 3380 - Astronomy
The Chandrasekhar Limit
The more massive a white dwarf, the smaller it is.
 Pressure becomes larger, until electron degeneracy pressure can
no longer hold up against gravity.
WDs with more than ~ 1.4 solar
masses can not exist!
PHYS 3380 - Astronomy
Summary of 1 M evolution
･On Main Sequence, Sun evolves slowly due to the changing chemical composition of
its core - the Sun gets hotter and increases in luminosity (moving to the left and up in
the HR diagram).
･After the hydrogen is used up in the core, the helium core contracts, and heats the
hydrogen rich layer just outside of the core. The hydrogen ignites in the shell around
the core and the Sun moves to the right in the HR diagram.
･When the outer layers of the Sun become convective, the luminosity of the Sun
shoots up and the Sun becomes a Red Giant.
･The core continues to contract and heat up
･ The core of the Sun is supported by the hot (normal) gas of helium nuclei produced
by the hydrogen burning and by degenerate electrons; the electrons already occupy
many of the available energy levels up to very high energies - it will take a lot of heat in
order to increase the energy of even 1 electron. The fractional increase in the kinetic
energy of the electrons will be very small for a given amount of heat input. So, the
pressure due to the electrons does not change very much for a given amount of heat
input -the core of the Sun will not expand strongly in response to the ignition of the
helium.
PHYS 3380 - Astronomy
･The temperature of the core rises (really the temperature of the helium nuclei gas
rises) as the reactions turn-on - the reaction rate goes up - the temperature of the
helium nuclei in the core goes up - the rate of reactions goes up - and so on.... Until
ignition of helium burning - helium flash lasts for a few minutes or less with a peak core
luminosity of up to 1 x1011 L.
･The helium flash shuts down because, eventually, as you add enough heat to the gas,
you can excite electrons to higher energy states and you eventually spread the
electrons out over a large enough range of states to make the gas normal. (obey the
perfect gas law).
･The helium flash occurs in stars less massive than around 2.25 M.
･After the helium flash, the star quiescently burns what is left of the helium in its core
(for a time ~ 10 - 20 % as long as its Main Sequence lifetime).
･When the helium is converted into carbon and oxygen, the core again contracts,
ignites helium burning in a shell around the core, expands, cools, and moves to the
right in the HR diagram.
PHYS 3380 - Astronomy
･When the star becomes convective, it moves up the AGB greatly increasing in
luminosity at roughly constant temperature. Low mass stars are not, however,
massive enough to reach the ignition temperature of carbon before the core becomes
completely supported by degenerate electron pressure (which halts the contraction).
･The nuclear evolution of the Sun ends at this point and the star is now ready to enter
into its final stages of evolution; at this time the star is AGB star characterized by a
carbon-oxygen core, surrounded by a helium burning shell and a hydrogen burning
shell.
• For stars whose mass is greater than 2.25 M, the electrons in their cores are not
degenerate at the time of helium ignition and so there is no helium flash and they
settle into a stage of quiescent helium burning before they approach the AGB.
•Star cools and moves left on the H-R diagram possibly generating a planetary nebula
•He-burning shell keeps dumping C and O onto the core. C,O core collapses and the
matter becomes degenerate.
•Star becomes a white dwarf
PHYS 3380 - Astronomy
Summary of 1 M evolution
Approximate typical
timescales
Phase
Main-sequence
Subgiant
Redgiant Branch
Red clump
AGB evolution
PNe
WD cooling
 (yrs)
9 x109
3 x108
1 x109
1 x 108
~5x106
~1x105
>8x109
PHYS 3380 - Astronomy
Summary of 1 M evolution
Approximate typical
timescales
Phase
Main-sequence
Subgiant
Redgiant Branch
Red clump
AGB evolution
PNe
WD cooling
 (yrs)
9 x109
3 x109
1 x109
1 x 108
~5x106
~1x105
>8x109
PHYS 3380 - Astronomy
Lagrangian Points
Lagrangian points (or libration points) five positions in an orbital configuration
where a small object affected only by
gravity can maintain a stable orbital
configuration with respect to two larger
objects (like a satellite with respect to
the Sun and Earth). Mark positions
where the combined gravitational pull
of the two large masses provides
precisely the centripetal force required
to orbit with them.
A contour plot of the effective potential
due to gravity and the centrifugal force of
a two-body system in a rotating frame of
reference. The arrows indicate the
gradients of the potential around the five
Lagrange points—downhill toward them
(red) or away from them (blue).
PHYS 3380 - Astronomy
Mass Transfer in Binary Stars
In a binary system, each star controls a finite region of space,
bounded by the Roche Lobes (or Roche surfaces).
Lagrange points = points of
stability, where matter can
remain without being pulled
towards one of the stars.
Matter can flow over from one star to another through the
Inner Lagrange Point L1.
PHYS 3380 - Astronomy
Recycled Stellar Evolution
In some binary systems - less massive star
has become a red giant - more massive
star is still on main sequence - Algol
paradox
Caused by mass transfer
-in a binary system can
significantly alter the stars’ masses
and affect their stellar evolution.
PHYS 3380 - Astronomy
White Dwarfs in Binary Systems
X-ray
emission
T ~ 106 K
Binary consisting of WD + MS or Red Giant star
=> WD accretes matter from the companion
Angular momentum conservation => accreted
matter forms a disk, called accretion disk.
Matter in the accretion disk heats up to ~ 1 million K
=> X-ray emission => “X-ray binary”.
PHYS 3380 - Astronomy
Nova Explosions
Hydrogen accreted
through the accretion
disk accumulates on the
surface of the WD
Nova Cygni 1975
 Very hot, dense layer
of non-fusing hydrogen
on the WD surface
 Explosive onset of H
fusion
 Nova explosion
PHYS 3380 - Astronomy
Recurrent Novae
Most novae are recurrent on time scales ranging from 1,000 to 100,000 years
• recurrence interval for a nova is less dependent on the white dwarf's
accretion rate than on its mass
• massive white dwarfs - powerful gravity - require less accretion to
fuel an outburst than lower-mass ones
• the interval is shorter for high-mass white dwarfs.
RS Ophiuchi eruption in Feb 2006
PHYS 3380 - Astronomy
GK Persei
PHYS 3380 - Astronomy
Supernovae
In the 1930’s supernovae were recognised as a separate class of
objects to novae (meaning new stars).
• So-called by Fritz Zwicky, after Edwin Hubble estimated distance to
Andromeda galaxy (through Cepheids)
• Hence the luminosity of the “nova” discovered in 1885 in Andromeda
was determined
• Supernovae outbursts last for short periods: typically months to a few
years
• Typical galaxies like the Milky Way appear to have a rate of 1-2
supernovae per 100 years
• But as they are extremely bright - even small telescopes can detect
them at large cosmic distances
• Historical accounts of supernovae in our galaxy are coincident with
supernovae remnants now visible
PHYS 3380 - Astronomy
What is a Supernova ?
Stars which undergo a tremendous explosion, or sudden brightening.
During this time their luminosity becomes comparable to that of the entire
galaxy (which can be ~1011 stars)
SN1998bu in M96: left - reference image, right - BVI colour image
PHYS 3380 - Astronomy
Supernovae in the Milky Way
European and far eastern written records of the following Galactic events:
Supernova Remnant Year
Peak Visual
mag
CasA
1680
?
Kepler
1604
-3
Tycho
1572
-4
3C58
1181
-1
Crab
1054
-4
SN1006
1006
-9
• Supernova remnants observable in optical, radio and X-ray for
thousands of years
PHYS 3380 - Astronomy
The Crab nebula - optical (red)
and X-ray (lilac) composite
Death of a massive star
Tycho’s supernova remnant in
X-rays
Explosion of a white dwarf
The
Menagerie
Supernova
Remnant
Cassiopeia A Supernova Remnant
Kepler’s Supernova Remnant
Cygnus Loop Supernova Remnant
PHYS 3380 - Astronomy
The Observed Types of Supernovae
Supernovae explosions classified into two types according to their
observed properties. The two main types are Type I and Type II which are
distinguished by the presence of hydrogen lines in the spectrum.
Hydrogen lines
No hydrogen


Type II
Type I




Lightcurve and spectra properties
Si
He
No He or Si




II-P, II-L, IIn, IIb, II-p
Ia
Ib
Ic
PHYS 3380 - Astronomy
Example Spectra of Type Ia and Type II Supernovae
H
H
No H or He
H
S
Ca
Typical Type II supernova
observed within a few weeks of
explosion
Si
Typical Type Ia supernova
observed near maximum light
(i.e. when supernova is at its
brightest)
PHYS 3380 - Astronomy
From H Burning to Core-Collapse in Massive (> 8 M) Stars
• H in core consumed forming He core
surrounded by H-burning shell
• He core contracts forming He-burning core
surrounded by a H-burning shell
• Core of 12C and 16O produced, surrounded
by He and H burning shells.
• The core will again contract and the
temperature will rise, allowing C and O
burning to Mg and Si.
• Process continues, with increasing Z, building up heavier and heavier elements
until the iron group elements of Ni, Fe and Co are formed. The core is
surrounded by a series of shells at lower T, and lower 
• Iron core ultimately collapses, triggering an explosion that destroys the star: a
supernova
PHYS 3380 - Astronomy
Energy Production
Nuclear fusion can produce
energy up to the production
of iron.
Nuclear reactions that use
iron cannot produce energy
- nuclear reactions can
only produce energy only
if proceed from from less
tightly bound nuclei to
more tightly bound nuclei
Binding energy
due to strong
force = on short
range, strongest
of the 4 known
forces:
electromagnetic,
weak, strong,
gravitational
PHYS 3380 - Astronomy
Core Collapse
• Fe core contracts as no nuclear fusion occurring, and e– become degenerate gas.
• When core mass > MCh (Chandrasekhar mass) the e– degeneracy pressure is less
than self-gravity and core contracts rapidly (for Fe: MCh1.26 M )
Result:
• Gas is highly degenerate, hence as core collapses T rises unconstrained, and
reaches threshold for Fe photodisintegration
56
Fe 134 He  4n 100MeV
• Reaction is highly endothermic - collapse turns into almost free fall.
• Infall continues, T rises, and photon field energetic enough to photodissociate He

He  2n  2 p  25MeV
• Core contracts further, density becomes high enough for e– capture
e  p  n   e
• Neutrinos escape, removing more energy from core and accelerating collapse  takes milliseconds
complete collapse
• Neutron gas becomes degenerate at densities of ~1018 kg m-3
• Neutron degeneracy pressure sufficient to balance gravity; however core has actually

overshot the equilibrium point and undergoes a slight bounce, creating a shock wave
which slams into the collapsing outer layers of the star.
• “Proto-neutron star" begins to form at the core
PHYS 3380 - Astronomy
Shock wave stalls within ~0.03 s - supernova problem
- inward flowing matter smothers shock wave and pushes it back
into the star
What actually causes the explosion?
- neutrinos reenergize the shock wave
Two stages of collapse:
-Dynamic stage (collapse, neutronization) – only e are emitted,
accounting for/carry 1-3% of the binding energy (duration - 10 ms).
e  p  n   e
- Cooling stage – all neutrino flavours are emitted which carry (9698)% of binding energy, duration - about 10 s.

e  e     
e    e    
e  nucleon  e     nucleon
PHYS 3380 - Astronomy
Core collapse phase so dense and energetic that only neutrinos are able
to escape the collapsing star.
- Most of gravitational potential energy of the collapse gets converted
to 10 second neutrino burst
- releases about 1046 joules
- Stellar gas so dense that it is actually
slightly opaque to neutrinos
- ~1% of neutrino energy (1045 J)
reabsorbed by the star
- along with turbulent convection
processes (convective overturn),
reaccelerates shock wave producing
an explosion.
PHYS 3380 - Astronomy
Testing the Model: SN1987A
Unique opportunity to test the core-collapse neutrino generating theory was
the supernova of February 1987 in the Large Magellanic Cloud.
Expected neutrino flux for the SN at this distance (about 50 kpc) was 1013 m2. How many detected ?
Two experiments (Kamiokande and IMB)
simultaneously detected neutrino burst,
and the entire neutrino capture events
lasted 12s. This occurred before the SN
was optically detected (or could have
become visible). Time for shock wave to
reach stellar surface (~1 hour).
Significant result of observations:
- neutrinos and antineutrinos both took the same time to arrive at earth difference in their arrival times less than 12 seconds.
 first empirical evidence that matter, antimatter, and photons all react
similarly to gravity, which was widely predicted by standard theories of
gravity but not previously tested directly.
PHYS 3380 - Astronomy
SN1987A - Confirmation of Core Collapse
Core-collapse of
Before
massive star
• Catalogued star SK69 202
• M=17M
• Teff=17000
• Log L/ L = 5.0
• Star has
disappeared
• Neutrinos confirm
neutron star
formation
• No pulsar or neutron
star yet seen
At maximum
PHYS 3380 - Astronomy
Precursor
Sanduleak -69° 202, the precursor to SN 1987A, was a blue
supergiant presumed to have a mass of about 15 - 20 solar masses.
- required some revisions to models of high mass stellar
evolution, which had suggested that supernovae would
result from red supergiants.
Now believe star was chemically poor in elements heavier than He
- contracted and heated up after phase as cool, red
supergiant during which it lost much of its mass into space
Remnant
- rings caused by interaction
of fast stellar wind with older
slower winds - shaped by
magnetic fields
- two older winds from red and
blue supergiant stages
Supernova 1987a Movie Link
Rings must be related to the supernova because the supernova is at their center. But
they could not have been ejected by the supernova explosion.
- inner ring must have been expanding for 20,000 years to grow to this radius
- must have been ejected 20,000 years before the supernova explosion.
Movie illustrates the actual three-dimensional shape of the triple-ring system.
Astronomers really don't know why it has this structure - is one of the outstanding
mysteries of SN1987A.
Some physical effect must determine the polar axis of the rings. Possibly rotation.
But rotation of what? Many astronomers now believe that the parent star of
SN1987A was actually a close binary system. Perhaps the inner ring was ejected
while the merger took place, 20,000 years before the explosion.
Rapidly brightening "hot spots" are appearing all around the ring. These
hotspots appear where the blast wave (a kind of "sonic boom") from the
supernova explosion first strikes parts of the dense ring that protrude
inward. It is expected that, ten years from now, the ring will be roughly 100
times brighter than it is today.
Light Echoes
Light emitted in directions other than directly toward us encountered
nearby interstellar clouds and then was reflected. Luminous arcs could be
observed around the supernovae, called 'light echoes'. The two main arcs
or rings observed are due to clouds located at a distance of about 300 and
1100 light-years in front of the supernovae.
The optical light curve of SN1987A for the
first 1400 days after the explosion
- continued to brighten for the first 100
days after the initial flash, reaching a
maximum brightness of about 3rd
magnitude, bright enough to see with the
naked eye.
- then faded rapidly, with the brightness
dropping by a factor of 2 every 77 days
for the first 500 days
- almost exactly the same rate observed
in laboratories for the decay of the
radioactive nucleus Cobalt-56 into the
stable nucleus Iron-56 (the half-life of
Cobalt-56 is 77 days).
Astronomers long suspected that supernova explosions were responsible for
the formation of the heavy elements in the universe
- strongest confirmation to date of the idea that supernova explosions really
did make the heavy elements
- for the first time, we could measure exactly how much Cobalt-56 was
made (0.07 Solar masses)