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ASTR377:
A six week marathon
through the firmament
Week 4, May 10-13, 2010
by
Orsola De Marco
[email protected]
Office: E7A 316
Phone: 9850 4241
Overview of the course
1.
Where and what are the stars. How we perceive them, how we
measure them.
2.
(Almost) 8 things about stars: stellar structure equations.
3.
The stellar furnace and stellar change.
5.
Stellar death: stellar remnants.
6.
When it takes two to tango: binaries and binary interactions.
Core contraction and
shell ignition
• What changes first?
m = (X/mH + Y/mHe + Z/mZ)-1
where mH= 1 proton / 2 particles= ½
mHe=4 protons / 3 particles=4/3
mZ=A protons / A/2 particles = 2
 m will grow when H is running out, why?
• Pressure decreases, core shrinks, density and
temperature increase and hydrostatic
equilibrium is restored.
• This increases e in a shell around the core.
(When the Sun joined the main sequence it
had 0.7LSun).
… and surface expansion
• The H-depleted core contracts slightly as thermal support
dwindles.
• The photosphere keeps radiating and with lesser L supply would
like to contract also, but core contraction increases the thermal
energy and the layers just above the core heat up enough for H
(which is still plentiful just outside the H-depleted core) to ignite.
This moves the fusion engine of the star closer to the surface and
increases the thermal pressure closer to the surface so that
surface expands.
• At first this expansion cools the star, but as ions recombine and
molecules form, the opacity rises and convection stars. This carries
the increased L to the surface and the star brightens.
• The radius of the Sun will increase in this way to about ~160Ro. Its
temperature will drop to ~3000K and its luminosity will rise to
~2200Lo.
An aside
• Any change in stellar evolution, can, at least in
principle, have different consequences.
• For instance: The ignition of the shell results in a
higher luminosity (because the shell burns at higher
temperature), so why does the star not go up on the
HRD instead of right?
• Shell generates energy at a rate higher than can be
radiated so the luminosity does not increase. Instead,
the envelope above the shell heats up and expands.
• Only later, when the energy is transported out by the
very efficient method of convection, will the luminosity
increase.
On the HRD:
Back to clusters’ HRDs
On the (red) giant branch:
the first dredge-up
• The expanding envelope is cool enough for molecules to
form so that the opacity goes up and envelope convection
sets in.
• As the convective layer grows and extends from H-burning
shell to surface, it brings to the surface the by products of H
burning (a different N and 13C/12C abundances), which can
now be observed. This is called the first dredge up (some
stars can have up to three dredge up episodes in the course
of their evolution).
• When convection sets in the luminosity of the star grows
rapidly as this is the most efficient method of transporting
energy outward.
The Hyashi track
• As the envelope expands the star gains U (U
becomes less negative). By the Virial theorem
the star cools and elements recombine reducing
the thermal pressure. The star therefore
contracts again to maintain equilibrium.
• There is no hydrostatic equilibrium
with a fully recombined star.
• This results in a lower limit for
stellar temperature. No star in
hydrostatic equilibrium can be
cooler.
The tip of the red giant branch
• The He core is contracting till one of two things
happen: (1) Tc and rc rise to ignition
temperatures [more massive stars] or (2)
electron degeneracy sets in, so the core
pressure does not depend on temperature: as
the He core grows and heats up it cannot
change size [less massive stars].
• Eventually Tc rises enough for degeneracy to
be lifted and pressure to be once again related
to temperature. A sudden pressure wave is
liberated and the core has a He flash.
Degeneracy
• If the core collapse squeezes electrons
beyond a certain threshold before the
temperature is higher than the He-fusion
temperature of ~108 K, then degeneracy
pressure becomes relevant.
• Maxwell v distribution predicts too many
electrons at low velocity/energy than
allowed by the Pauli uncertainty
principle (see plot in hand-outs).
• Those electrons are pushed to higher
energy. The pressure provided is
independent of temperature:
Pdeg
5/3
n
 h2 e
me
(Board demo)
On to He fusion
• Bottleneck: there are no stable elements of
mass number 5 or 8, so He + p, or He + He,
likely to happen in an H and He-rich
environment, end up in products that vanish
immediately.
• As the Tc rises 8Be, although unstable, can
be formed at a rate high enough to result in
a non zero abundance of this element which
can then react with another 4He.
The triple alpha chain
(I had forgotten to give you the reactions last week….)
2
12
6
C He O  
4
2
16
8
(Only a little)
The triple alpha chain
(one more thing….)
• The energy of one reaction (3xHe=C) is
7.3MeV (compared with ~25MeV for H
burning reaction). So the energy per He
particle is 10% of what it was for H
(7.3/3 MeV).
• This plus the actual supply of He in the
core of a star
for16a much shorter
12 make
4
C
He
O


6
2
8
time burning He in the core.
2
The horizontal branch
• After He ignition the star returns to a
main-sequence like structure, except
slightly smaller, hotter and more
luminous.
• We call these core-helium burning stars
“Horizontal Branch (HB) stars” or even
“clump stars”.
• The HB lasts about 100 million years.
Core He exhaustion
Iben 1971
• Core helium
exhaustion proceeds
in a way which is
very similar to the
hydrogenexhaustion. The star
eventually expands,
rejoins the Hayashi
track. It is now on the
Asymptotic Giant
Branch.
The Asymptotic Giant Branch
• Expansion proceeds as for the RGB. The star
ascends once again the Hayashi track.
• At the base of the AGB we have a second
dredge-up episode.
• There are two active shell sources, He and H.
• Mass-loss is at its peak and mostly dust
driven.
• Helium shell flashes in the latter phase of the
AGB.
Mass-loss
• We know stars lose mass looking at
giant’s spectra.
• We know that white dwarfs, which
descend from 1-10Mo stars, have a
mass in the range ~0.5-1.0Mo with
most of them having M~0.6Mo. So
there is a mass deficit.
Mass-loss
• In 1977 Dieter Reimers
expressed the mass-loss
from a giant in this way:
.
M   1.4 1013
L /L R /R
Myr 1
M / M
where   1
Does it work for the Sun?
• This is an empirical
formula, derived from
fitting data.
• It embodies no real
physics, though of
course should be
explainable by
physics.
Mass-loss
• If the cause of the mass loss is the radiation
pressure, i.e., the stellar luminosity. Think of
it as the fraction of stellar energy (L) used to
counter binding energy (U) of the star: L/U,
or L/gR.
.
M   1.4 1013
where   1
L /L
Myr 1
(g /g )(R /R )
Mass-loss
• Reimers mass-loss is OK for RGB stars,
but fails for AGB stars, which have dusty
atmospheres (he did not observe many/any
AGB stars because they are dusty).
• During the thermally-pulsating AGB the
mass-loss rate surges from 10-7 Mo/yr to
about 10-4 or even 10-3 Mo/yr. We call this
phase the superwind.
• The mass-loss geometry also seems to
change.
• Both the cause of the superwind and the
geometry change remain unclear.
Mass-loss causes/helping agent.
•
•
•
•
•
Radiation pressure.
Radiation pressure on dust.
Pulsations.
Binarity.
Magnetic fields.
Massive stars MMS≥12-15Mo
• The Blue Loop = the HB for
massive stars.
• After He exhaustion, the
contraction of the C and O
core eventually reaches
fusion temperatures to make
Mg.
• For MMS<2.5-5Mo a
degenerate C-O core
develops. This may
eventually lead to a C-flash
(similar to the He-flash).
• This procedes through
consecutive stages of fusion
till the byproduct is Fe.
Characteristics of
massive stars
• The initial mass function dictates that
there are very few massive stars.
• The lifetime of a 7Mo star is 30 Myr.
• Sizes of massive stars on the main
sequence and as giants.
• Spectra type is O (B) and they have
hydrogen rich atmospheres (as usual).
Wolf-Rayet stars
• Recognised in 1867 by Charles
Wolf and Georges Rayet as
stars having bright lines. Why?
• They are very rare.
Georges Rayet French 1839 1906
Wolf-Rayet stars: spectra
• Emission lines are caused by large envelopes
where ions scatter photons into the line of sight.
• The Doppler effect shifts photons to higher and
lower energies generating broad emission lines.
• The region of the
envelope between
the core and the
observer absorbs
radiation creating
a blue-shifted
component to the
emission line
(called the Pcygni
profile).
Wolf-Rayet stars: mass-loss
• WR stars are either dominated by N lines
(called WN stars) or by carbon lines (called
WC stars). The latter category has no
hydrogen in their atmosphere!
• The loss of the H envelope is due to huge
mass-loss (we can measure the mass loss by
looking at the spectral lines).
• The origin of the mass-loss is, once again not
well identified, but it is certainly due to
radiation pressure.
The Eddington limit
It is the luminosity for which gravity is
balanced by radiation pressure.
LEdd =
4Gm p cM
e
LEdd  1.3 10 38 (M / M ) erg/sec

(Board derivation)
Luminous Blue Variables
• This is once again something to
do with mass-loss. The most
massive stars seem to go
through unstable phases where
not just the huge WR mass
loss, but something altogether
huger takes place. A real
outburst (not a supernova) that
loses many solar masses in a
short time.
• LBVs might be the most
massive stars where radiation
pressure is at the limit for stellar
stability.
• We observe these LBV nebulae
around WR stars.
• Sometime, they have bipolar
shapes (e.g., e Car) and a
binary cause is suspected.
M1-67
e Carinae
The end of the line: Fe
• Massive stars keep fusing core elements till the core
is made of iron, which does not liberate energy by
fusion because it has the
highest
binding
energy per
nucleon
(nothing is
more tightly
bound).
What
happens
then?
Supernovae observations
• Six historical
Supernovae in
the last 1000
years within an
angle of 60 deg
near the plane:
about 1/28 SN/yr.
Supernovae observations
• Extragalactic
supernovae
observed in
modelrn times: MV
~ -19 mag or
L~1010Lo.
• Time integrated
output 1049 ergs –
similar to a middle
sized galaxy!
SN 1999by
http://www.konkoly.hu/staff/tothi/sn1999by.html
Supernovae observations
• Two types of lightcurves
(Type I and type II),
though Type II are quite
variable. Type I always
have the same scaled
brightness (more in 2
weeks!)
• Type II happen in spiral
galaxies (young
populations) while Type I
happen also in elliptical
galaxies (old populations).
• Type I are 1/300 per year,
type II are 1/100 per year.
SN 1999by
http://www.konkoly.hu/staff/tothi/sn1999by.html
Four types of spectra
•
•
•
•
Type I have no H lines, type II
do.
Type Ia,b,c have strong silicon,
strong helium and weak silicon,
respectively.
Type II, Ib, Ic derive from
massive star collapse – they
occur in elliptical galaxies
(which host younger
populations) in proximity to HII
regions. They have intermediate
type elements from the many
stages of nuclear burning.
Type Ia are something else…
Supernovae Type II
•
•
•
•
When the Fe core grows above the Chandrasekhar limit, electron
degeneracy cannot stop the collapse and the core is now in free fall.
Fe atoms are “smashed” by photons in a process called photodisintegration. This requires energy.
Also, e- and p recombine to form n and neutrinos. The particle density
decreases and neutrinos take energy out. The Fe core collapse in free
fall.
As all the e- and p recombine to n the collapse is suddenly halted by n
pressure (we have made a neutron star).
Pdeg
•
•
5/3
n
 h2 n
mn
When the neutron density rises nutrons are puched closers and closer
till the strong nuclear force becomes repulsive. This makes the core
suddenly more rigid and sends a pressure wave out. This
pressure/shock
 wave is sent out from the core that ejects the envelope.
Note that the U to form a neutron star is approximately the one released
in the SN explosion: GM2/R~30x1052 erg.
Nucleosynthesis past the
Fe elements
• Nuclei build up by accretion of
neutrons. Heavy nuclei have low
binding energies and tend to decay.
The decay liberates energy.
• Building nuclei heavier than Fe
requires energy, but in the supernova
environment there is plenty of energy
to forge these elements.