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4/1/2011
The fusion of large nuclei to form elements heavier than carbon
requires extremely high temperatures to overcome the large
electromagnetic repulsion of these nuclei.
Stars 3
This happens only in high-mass stars, where the crushing weight
of the outer layers of these stars makes these conditions possible.
Notes compiled by
In these stars, nuclear fusion proceeds to its theoretical end point,
after which the core of the star collapses catastrophically, setting
p
explosion.
p
off a supernova
Paul Woodward
Department of Astronomy
University of Minnesota
While on the main sequence, a high-mass star establishes a higher
temperature in its hydrogen burning core than is found at the
center of a star like the Sun.
At this higher temperature, hydrogen nuclei (protons) have enough
energy to slam into carbon, nitrogen, and oxygen nuclei as well as
into other protons.
The C, N, and O nuclei, even though they make up only about 2%
of the core, act as catalysts for hydrogen fusion into helium.
That is, the concentrations of C, N, and O are left unchanged by
the fusion reactions, but they permit hydrogen to fuse into helium
through a chain of reactions, called the CNO cycle, that makes the
helium production rate far higher than would be possible through
the proton-proton chain alone.
p of the CNO cycle
y are shown on the next slide.
The 6 steps
Just as for the proton-proton chain, 4 protons are replaced,
ultimately, by one helium nucleus.
Thus the energy produced by one trip through this reaction chain is
the same as that produced by the proton-proton chain; however,
the rate at which this energy is produced is greater.
The rate of nuclear energy generation in a high-mass star is so
great that the flux of photons carrying that heat outward through
the star is enormous.
A star of more than 2 solar masses goes through the same stages
that we have described for stars like the Sun, but of course much
more rapidly.
Although photons are massless, they do carry momentum, which
they can impart to the stellar matter through which they move,
bouncing many times back and forth from its electrons, ions, and
atoms.
However, helium burning begins in these massive stars gradually,
not by means of a helium flash. The core temperatures for these
stars are so high that degeneracy pressure plays no role up to this
point.
photons to the ggas ggenerates a
This momentum transfer from the p
phenomenon we call radiation pressure.
y a few hundred thousand yyears,, or even less,, helium
After only
becomes exhausted in the core of a high-mass star.
Since normal gas pressure is created by the collisions of atoms
with other atoms, transferring momentum, it is natural to consider
this same sort of process, but now involving atoms and photons, as
generating a pressure.
Fusion then proceeds in a helium-burning shell around the inert
carbon core, and a hydrogen-burning shell is located still further
out.
In very high mass stars, radiation pressure can be more important
than normal gas pressure in supporting the outer layers.
Intermediate mass stars, between 2 and 8 solar masses, are
prevented by degeneracy pressure from fusing iron. These stars
blow away their outer layers and end up as white dwarfs.
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For a high mass star, with more than 8 solar masses, degeneracy
pressure never halts the collapse of its carbon core.
The core temperature reaches the 600 million K needed to fuse
carbon into heavier elements.
Carbon burning may last only as long as a few hundred years.
As each stage of core burning ceases, the core collapses still
further, becomes still denser and hotter, and a still heavier element
begins to be produced.
produced
The final stages of nuclear fusion in the core of such a star are
complex. Helium captures are some of the simpler reactions that
occur (see next slide), but ultimately even heavy nuclei can fuse
with other heavy nuclei.
Some of the fusion reactions produce free neutrons, which may
fuse with heavy nuclei to make many of the elements we find on
Earth.
Ultimately, the core of a high mass star begins to resemble an
onion, with an whole sequence of shells burning various elements.
In the final days of such a star, iron is produced in a siliconburning core.
Each time the star’s core collapses further, the surrounding shell
burning intensifies, and the star’s outer layers inflate further.
Each time the core ignites again, the outer layers may contract a
bit.
However, the changes in overall luminosity are not as great for
such a star as they are for a star like the Sun in moving from the
main sequence through its subsequent giant phases.
In the H-R diagram, a high mass star thus tends to move in a zigzag fashion across the upper part of the diagram, toward the realm
of the red supergiants.
Fig. 16.17
Life tracks on the
H-R diagram from
main-sequence
star to
red supergiant
for selected
high mass stars.
(from models by
A. Maeder and
G. Meynet.)
Betelgeuse, Orion’s upper left shoulder star, is the best known red
supergiant. Its radius is 800 times that of the sun, or about 4 times
the distance from the Sun to the earth.
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The sequence of episodes of production in the core of ever heavier
elements ceases with the production of iron.
The nuclear particles are more tightly bound in iron than in any
other nucleus (and therefore iron has the least mass per nucleon of
any nucleus).
It is therefore impossible to generate any additional energy by
fusing more nuclear particles with iron nuclei. In fact, to do this
requires that energy be injected, not produced.
One might then wonder where all those heavier elements, like lead
and uranium that occur naturally on Earth, come from. We will get
to that presently.
Once iron accumulates in the core of a high mass star, its end is
near.
Iron piles up in the core until its degeneracy pressure can no longer
support it against gravity.
The iron core of a high mass star is first supported against gravity
by degeneracy pressure, an expression of the inability of
electrons in the core to be squeezed into too small a space.
However, as the iron continues to pile up in the core, and the core
shrinks further, it becomes possible for electrons to combine
with protons to form neutrons, releasing neutrinos in the
process.
Once this starts, it proceeds apace.
In a fraction of a second, an iron core with a mass about equal to
that of our Sun and a size larger than that of the Earth can
collapse to form a ball of neutrons just a few kilometers across!
This is like the fusion reaction to end all fusion reactions, the final
core is essentially a giant nucleus!
This neutron core is supported against gravity by the degeneracy
pressure of the neutrons (like electrons, two of them can’t be in
the same place at the same time either).
The gravitational collapse of the core releases an astronomical
amount of energy.
The supernova explosion momentarily floods the material
surrounding the core with neutrons.
The energy released can be more than 100 times the energy the
Sun will radiate over its entire 10-billion-year lifetime.
Elements heavier than iron can be made in neutron capture
reactions which absorb rather than produce energy.
This energy, much of it in the form of neutrinos produced from the
combination of electrons and protons, drives a shock front into the
outer layers of the star.
As far as we know, this is the source of elements like lead which,
although rare, nevertheless can be found on earth in quantities
sufficient to provide bullets for a world war or two.
These layers
Th
l
are then
h heated
h
d andd accelerated
l
d outward,
d making
ki this
hi
gas radiate light with a brilliance comparable to 10 billion suns for
a short period (days) and causing the gas ultimately to mix with
the surrounding interstellar medium.
If indeed we are correct that elements heavier than helium are
generated in stars, returned to the interstellar gas through stellar
winds, planetary nebula ejection, and through supernova
explosions, then on the average older stars should have smaller
proportions of these elements. This is indeed the case. The oldest
stars, in globular clusters, typically have only 0.1% of their mass
in such heavy elements, while recently formed stars have between
2% and 3% of their masses in these elements.
This gas, which may later become incorporated in new stars,
contains the heavy elements created in the massive star as well as
heavy elements created during the star’s final moments, when free
neutrons are abundant and react with other nuclei.
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We also think that heavy element fusion in stars involves the
capture of helium nuclei, which have two protons and two
neutrons.
Thus we predict that there should be a greater relative abundance
of heavier elements with even numbers of protons.
This is indeed the case, as is shown on the next slide.
The Crab Nebula, shown on the next slide, is the remnant of a
recent supernova, a star that exploded in 1054.
We know this date precisely, because it was recorded by the
Chinese.
At the center of the Crab nebula there is a pulsar, a rapidly rotating
neutron star.
This confirms our theoretical ideas that such objects
j
should remain
after a supernova explosion.
Other supernovae in our galaxy during the last 1000 years
occurred in 1006, 1572, and 1604.
We observe many such explosions in other galaxies.
The Crab Nebula, in Taurus,
M1, or NGC 1952,
Hubble
Space
Telescope
WFPC2.
Exploded
1054.
The Crab Nebula, in Taurus,
M1, or NGC 1952,
central pulsar
seen in
X-rays and
optical
light.
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The Crab Nebula, in Taurus,
M1, or NGC 1952,
central pulsar
seen in
X-rays
(2008)
The supernova observed by Tycho Brahe in 1572, known as
Tycho’s supernova, left behind an expanding remnant called
Cas A.
A sequence of detailed radio observations of this remnant have
been carried out that allow us to make a very short movie showing
its expansion.
Tycho
Brahe’s
Supernova
Optical and radio observations of Tycho’s Supernova Remnant,
VR53A.
VLA Radio Image of
the Cas A Supernova
Remnant
Chandra satellite
X-ray image
of Cas A
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The galaxy is actually littered with bubbles in the interstellar
medium which have been formed by supernovae.
Supernova HD 56925
(from Astronomy, Jan., 1992, p. 49)
A particularly beautiful old supernova remnant is the Cygnus
Loop, which covers a huge region of the sky.
The Cygnus Loop, NGC 6960-92, in red light with 48-inch Schmidt
Another old supernova remnant, which also has a pulsar in it, is
the Vela supernova remnant.
The Vela Supernova Remnant -- Royal Observatory, Edinburgh
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If we want to see supernovae in our lifetimes, we must look in
other galaxies.
Supernovae can rival entire galaxies in brightness, so you might
think they would be easy to spot.
Here’s an example. Apparently somebody was watching back in
1941.
The Vela pulsar -- Chandra X-ray observatory
The pulsar is moving through the SN remnant in the direction of arrow
Supernova in NGC 4725, a type Sb/SBb galaxy in Coma Bernices.
Two views, May 10, 1940 and January 2, 1941.
Supernova
in NGC 4096
1961
(Lick Observatory)
Supernova in NGC 4303
during and before outburst (1964)
The Hubble Space Telescope images on the next slide pinpoint
three distant supernovae, which exploded and died billions of
years ago. Scientists are using these faraway light sources to
estimate if the universe was expanding at a faster rate long ago
and is now slowing down.
Images of SN 1997cj are in the left hand column; SN 1997ce, in
the middle; and SN 1997ck, on the right. All images were
taken by
y the Hubble telescope’s
p Wide Field and Planetary
y
Camera 2. The top row of images are wider views of the
supernovae. The supernovae were discovered in April 1997 in a
ground-based survey at the Canada-France-Hawaii Telescope on
Mauna Kea, Hawaii.
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Once the supernovae were discovered, the Hubble telescope was
used to distinguish the supernovae from the light of their host
galaxies. A series of Hubble telescope images were taken in
May and June 1997 as the supernovae faded. Six Hubble
telescope observations spanning five weeks were taken for each
supernova. This time series enabled scientists to measure the
brightness and create a light curve. Scientists then used the
light curve to make an accurate estimate of the distances to the
s perno ae Scientists combined the estimated distance with
supernovae.
ith
the measured velocity of the supernova’s host galaxy to
determine the expansion rate of the universe in the past
(5 to 7 billion years ago) and compare it with the current rate.
These supernovae belong to a class called Type Ia, which are
considered reliable distance indicators. Looking at great
distances also means looking back in time because of the finite
velocity of light. SN 1997ck exploded when the universe was
half its present age. It is one of the most distant supernovae
ever discovered (at a redshift of 0.97), erupting 7.7 billion years
ago. The two other supernovae exploded about 5 billion years
ago. SN 1997ce has a redshift of 0.44; SN 1997cj, 0.50. SN
1997ck is in the constellation Hercules;
Herc les; SN 1997ce is in Lynx,
L n
just north of Gemini; and SN 1997cj is in Ursa Major, near the
Hubble Deep Field.
Credits: Peter Garnavich, Harvard-Smithsonian Center for
Astrophysics, the High-z Supernova Search Team, and NASA
The most spectacular supernova of recent years was the one in
1987 that happened in a close companion galaxy of our own,
the Large Magellanic Cloud.
This supernova explosion rejuvenated the careers of an entire
generation of aging supernova buffs.
Amazingly, the outburst was actually detected on earth by two
neutrino detectors, corroborating our view that the supernova
shock is driven
dri en by
b an astounding
asto nding fl
flux of these eextremely
tremel weakly
eakl
interacting particles.
Supernova 1987A and the
Tarantula Nebula
Supernova 1987A progenitor star -- Anglo-Astral. Tel. Board
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Hubble Space
Telescope mosaic of
SN1987A and its
surroundings
Supernova 1987A light curve -- European Southern Observatory
The ring structures around this supernova look very much like the
structures observed in some planetary nebulae, like the
Hourglass Nebula, for example.
Perhaps the star that exploded had already lost much of its outer
layers in strong stellar winds before it blew up.
The precursor star was blue, not red, and this suggests mass loss
before the explosion.
One possibility, suggested by Chris Burrows, is that the two rings
might be “painted” by a high-energy beam of radiation or
particles, like a spinning light-show laser beam tracing circles
on a screen.
The source of the radiation might be a previously unknown stellar
remnant that is a binary companion to the star that exploded in
1987. Images taken by Hubble show a dim object in the
position of the suspected source of the celestial light show.
The striking Hubble picture actually shows three rings. The
smaller “center” ring of the trio was seen previously. The larger
pair of outer rings were also seen in ground-based images, but
their interpretation was not possible until the higher resolution
Hubble observations.
Though all of the rings probably are inclined to our view (so that
they appear to intersect), they probably are in three different
planes. The small bright
p
g ringg lies in a plane
p
containingg the
supernova; the two rings lie in front and behind it.
To create the beams illuminating the outer rings, the remnant
would need to be a compact object such as a black hole or
neutron star with a nearby companion. Material falling from the
companion onto the compact object would be heated and
blasted back into space along two narrow jets, along with a
beam of radiation.
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As the compact object spins it might wobble or precess about its axis,
like a child’s top winding down. The twin beam would then trace
out great circles like jets of water from a spinning lawn sprinkler.
If the rings are caused by a jet, however, the beams are extremely
narrow (collimated to within one degree). The jet model explains
why the rings appear to be mirror imaged, and why they appear to
be symmetrical about a point offset from the center of the
explosion.
Burrows got the idea for the beam explanation when he noticed that
where a ring appears brighter, an equally bright region appears on
opposite ring. By connecting lines between the similar clumps on
opposite rings Burrows found a common center. However, it is
offset from the heart of the supernova ejecta. When Burrows did a
detailed inspection of the HST image, he found a dim object which
may be the source of the beam at the predicted location. The
object is about 1/3 light-year from the center of the supernova
explosion.
From previous HST observations and images at lower resolution
taken at ground-based observatories, astronomers had expected to
see an hourglass-shaped bubble being blown into space by the
supernova’s progenitor star. The rings are probably on the surface
of the hourglass shape.
The hourglass was formed by a wind of slow-moving gas that was
ejected by the star when it was a red supergiant, and a much faster
wind of gas that followed during the subsequent blue supergiant
stage. The hourglass was produced by the fact that the stellar
wind from the red giant was denser in the equatorial plane of the
star. When the star reached the blue supergiant stage, the faster
winds tended to break out at the poles of the star.
Energetic radiation from the supernova explosion illuminated the
dense gaseous material in the equatorial “waist” of the hourglass,
causing it to glow -- thus explaining the central bright ring. The
two outer rings might be painted on the surface of the hourglass by
a very different process, by the beams from the stellar remnant.
In any case, the expanding ejecta are just now beginning to strike
the ring of material surrounding the star.
The first knot in the ring around the star began to light up in 1997.
Now the rest of the ring is beginning to light up.
It could shine extremely brightly for as much as a decade.
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A recent HST
photo, showing the
ring beginning to
shine brightly.
Bright areas on this
image mark the
regions of difference
between recent and
older photos of
SN1987A
The study of stellar evolution, and of supernova explosions in
particular, is almost totally dependent upon computer
simulation.
One of the supernova explosion simulations, performed by a
computer code built from one that I wrote, made the cover of
Physics Today a few years ago.
That same computer code was used to try to understand how heavy
elements processed only
onl in the deep stellar interior could
co ld have
ha e
gotten to the surface and been observed so soon after the
explosion. That simulation made the cover of Science
magazine, and it helped us to understand how the very heavy
elements get into the interstellar medium efficiently enough to
end up in stars like our own, and of course in planets like our
own even more importantly.
Convective instabilities in an
axisymmetric simulation of the
collapsed iron core of a 15-solarmass star just 70 msec before
supernova explosion. Neutinos from
electron capture in the core heat the
surrounding matter to produce
vigorous convection that triggers the
explosion. Colors indicate surviving
electron population per nucleon
(from about 0.1, green, to about 0.5,
red)
d) and
d arrows show
h velocities.
l iti
An
A
accretion shock, briefly stalled, at
the red-purple boundary liberates
protons from heavy nuclei. (Adam
Burrows, John Hayes, and Bruce
Fryxell, University of Arizona)
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This
computation
of the same
fluid
instability
that mixes
the layers of
processed
gas in a
supernova
explosion
was
performed
with our
code to
match a lab
experiment.
Stars 4
Notes compiled by
Paul Woodward
Department of Astronomy
University of Minnesota
We will begin by briefly reviewing the life histories of low-mass
and high-mass stars that we have been discussing.
The low-mass stars burn hydrogen in their cores on the main
sequence, burn hydrogen in shells around inert helium cores as
subgiants and red giants, burn helium in their cores and hydrogen
in shells as helium-burning stars on the “horizontal branch” in
the H-R diagram, burn helium and hydrogen in shells around
inert carbon cores as red giants again, and finally shed their outer
l
layers
as planetary
l t
nebulae,
b l exposing
i their
th i carbon
b cores,
supported by electron degeneracy pressure, as white dwarfs.
A white dwarf is extremely dense. Two dice made from white
dwarf material would weigh 5 tons, about as much as 3 cars (see
next slide). A solar mass is packed into the volume of the earth.
The more massive a white dwarf is, the smaller it is, up to a limit,
the Chandrasekhar limit of 1.4 solar masses, after which a
white dwarf must collapse to form a neutron star.
The size of the white dwarf Sirius B compared to the Earth and Sun
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We now review the life history of a massive star.
It is roughly the same, except much faster, up to the generation of an
inert carbon core. However, in a massive star, the carbon core is
much hotter, so that it is not supported by electron degeneracy
pressure but by the pressure that comes from heat energy.
The carbon core ultimately reaches the 600 million degrees K
needed for fusion of carbon, and the star keeps burning,
developing a whole series of nuclear burning shells around an
iron core.
The final catastrophe for a massive star comes when the electrons in
its iron core, unable to support the star by their degeneracy
pressure, are forced to combine with the protons to form neutrons
(and neutrinos).
Neutron stars can pack a solar mass into a sphere only 10 km
across!
They are like gigantic nuclei held together not by the strong
nuclear force, but by gravity.
A paper clip made from neutron star material would outweigh Mt.
Everest!
The escape velocity from a neutron star’s surface is about half the
speed of light, and photons which do emerge do so with a
gravitational redshift that increases their wavelengths by about
15%.
The core collapses suddenly to form a neutron star, or possibly a
black hole, releasing vast energy in the form of neutrinos.
When the iron core of a massive star collapses to form a neutron
star, its angular momentum remains unchanged, while its size is
dramatically reduced.
Even if it was hardly rotating at all as an iron core, by the time it
ends up as a neutron star, it is bound to be spinning rapidly.
During its collapse, the magnetic field in the core is carried along
with the material, forcing the magnetic field lines very closely
g
and thus amplifying
p y g the field strength
g mightily.
g y
together
Right after the neutron star is formed, we can expect its magnetic
field to be as much as a trillion times that of the Earth.
As the neutron star rotates, and its magnetic fields are whipped
around by that rotation, somehow beams of radiation are driven
out along the directions of the magnetic poles.
When the magnetic poles do not coincide with the rotation axis,
these beams of radiation sweep around like a lighthouse beam.
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Fig. 17.9b
This artwork likens a
pulsar (top) to a
lighthouse (bottom).
If a pulsar’s radiation
beams, channeled by
its magnetic field, are
not aligned with its
rotation axis, these
beams will sweep
through space. We
see a pulse of
radiation each time
such a beam sweeps
by us, hence the name
“pulsar.”
Fig. 17.9a
Fig. 17.8
These time-lapse
photos of the pulsar in
the Crab Nebula,
which lies to the upper
left of the unrelated
star at the center, show
how the pulsar flashes
on and off about
abo t 30
times a second.
(Jocelyn Bell was at the controls when the pulses first appeared)
(the controls, and the instrument, were conceived by her thesis
advisor, Anthony Hewish, who was awarded the Nobel Prize)
The Crab Nebula, shown on the next slide, is the remnant of a
recent supernova, a star that exploded in 1054.
We know this date precisely, because it was recorded by the
Chinese.
At the center of the Crab nebula there is a pulsar, a rapidly rotating
neutron star (rotating 30 times per second).
This confirms our theoretical ideas that such objects should remain
after a supernova explosion.
explosion
The Crab Nebula, in Taurus,
M1, or NGC 1952,
Hubble
Space
Telescope
WFPC2.
Exploded
1054.
Other supernovae in our galaxy during the last 1000 years
occurred in 1006, 1572, and 1604.
We observe many such explosions in other galaxies.
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The Crab Nebula
The colorful photo on the left in the next slide shows a groundbased image of the entire Crab Nebula. The nebula, which is 10
light-years across, is located 7,000 light-years away in the
constellation Taurus. The green, yellow and red filaments
concentrated toward the edges of the nebula are remnants of the
star that were ejected into space by the explosion.
At the center of the Crab Nebula lies the Crab Pulsar -- the
collapsed core of the exploded star. The Crab Pulsar is a rapidly
rotating neutron star – an object only about six miles across, but
containing more mass than our Sun. As it rotates at a rate of 30
times per second the Crab Pulsar's powerful magnetic field
sweeps around, accelerating particles, and whipping them out
into the nebula at speeds close to that of light.
The blue glow in the inner part of the nebula -- light emitted by
energetic electrons as they spiral through the Crab’s magnetic
field -- is powered by the Crab Pulsar.
The picture on the right shows a Hubble Space Telescope image of
the inner parts of the Crab. The pulsar itself is visible as the left
of the pair of stars near the center of the frame. Surrounding the
pulsar is a complex of sharp knots and wisp-like features. This
image is one of a sequence of Hubble images taken over the
course of several months.
months This sequence shows that the inner
part of the Crab Nebula is far more dynamic than previously
understood. The Crab literally “changes it stripes” every few
days as these wisps stream away from the pulsar at half the
speed of light.
The Hubble Space Telescope photo was taken Nov. 5, 1995 by the Wide Field
and Planetary Camera 2 at a wavelength of around 550 nanometers, in the
middle of the visible part of the electromagnetic spectrum.
Credit: Jeff Hester and Paul Scowen (Arizona State University), and NASA
The three pictures shown on the next slide are taken from a series
of Hubble Space Telescope images. They show dramatic
changes in the appearance of the central regions of the Crab
Nebula. These include wisp-like structures that move outward
away from the pulsar at half the speed of light, as well as a
mysterious “halo” which remains stationary, but grows brighter
then fainter over time. Also seen are the effects of two polar
jets that move out along the rotation axis of the pulsar. The
most dynamic feature seen -- a small knot that “dances
dances around
around”
so much that astronomers have been calling it a “sprite” -- is
actually a shock front (where fast-moving material runs into
slower-moving material) in one of these polar jets.
The telescope captured the images with the Wide Field and Planetary Camera 2
using a filter that passes light of wavelength around 550 nanometers, near the
middle of the visible part of the spectrum. The Crab Nebula is located 7,000
light-years away in the constellation Taurus.
Credit: Jeff Hester and Paul Scowen (Arizona State University), and NASA
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As the neutron star at the center of the Crab Nebula spins on its
axis 30 times a second, its twin searchlight beams sweep past
the Earth, causing the neutron star to blink on and off. Because
of this flickering, the neutron star is also called a “pulsar.” In
addition to the pulses, the neutron star’s rapid rotation and
intense magnetic field act as an immense slingshot, accelerating
subatomic particles to close to the speed of light and flinging
them off into space.
In a dramatic series of images assembled over several months of
observation, Hubble shows what happens as this magnetic
pulsar “wind” runs into the body of the Crab Nebula. The
glowing, eerie shifting patterns of light in the center of the Crab
are created by electrons and positrons (anti-matter electrons) as
they spiral around magnetic field lines and radiate away energy.
This lights up the interior volume of the nebula, which is more
than 10 light-years across.
The Hubble team finds that material doesn’t move away from the
pulsar in all directions, but instead is concentrated into two
polar “jets” and a wind moving out from the star’s equator.
The most dynamical feature in the inner part of the Crab is the
point where one of the polar jets runs into the surrounding
material forming a shock front. The shape and position of this
feature shifts about so rapidly that astronomers describe it as a
“dancing
g sprite,”
p , or “a cat on a hot plate.”
p
The equatorial wind appears as a series of wisp-like features that
steepen, brighten, then fade as they move away from the pulsar
to well out into the main body of the nebula.
The Crab Nebula, in Taurus,
M1, or NGC 1952,
central pulsar
seen in
X-rays and
optical
light.
The Crab Nebula, in Taurus,
M1, or NGC 1952,
central pulsar
seen in
X-rays
(2008)
A pulsar has also been found in the center of the Vela supernova
remnant.
Once we knew that pulsars existed, it proved easy to search for
them, and lots of them were found.
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Close Binary Stars
Notes compiled by
Paul Woodward
Department of Astronomy
University of Minnesota
The Vela Supernova Remnant -- Royal Observatory, Edinburgh
A large fraction of stars are located in binary systems.
Binary stars are born at the same time and evolve separately
according to the principles of stellar evolution theory laid out
earlier.
However, when the more massive of the two stars evolves off the
main sequence toward its giant star phase, very interesting
things can happen if the two stars are orbiting each other at a
sufficiently small separation.
separation
We will discuss here only the case of close binary stars.
During the main sequence stage of both stars’ lives, tidal forces
alter the shapes of the stars, so that when the stars are closest to
each other they become elongated, with the elongation
directions along the line joining their centers. This is because
each star attracts the near side of the other more than it does the
far side.
The periodic elongation of the two stars upon closest approach
results in friction within each star, even though the stars are
made of gases.
These frictional forces are minimized when the two stars orbit
each other in circular orbits and rotate synchronously, so that
they each always present the same face to each other. The
action of the frictional forces therefore leads ultimately to such
a state.
(This process is familiar from our study of the moons of Jupiter. It
also is at work in locking the Earth’s Moon’s rotation rate to its
orbital period, so that we always see the same face of the
Moon.)
The following slide shows a Roche diagram.
The lines on the diagram are equipotential surfaces.
The diagram is drawn in the equatorial plane of two orbiting stars in
a binary system, and the diagram is drawn in a frame of reference
rotating with the stars’ orbital motion.
That is, in the diagram, the centers of the two stars remain fixed at
the two points labeled M1 and M2 .
The lines drawn in the diagram are actually the intersections of
equipotential surfaces with the equatorial plane of the two stars.
Along each equipotential line, there is no effective gravitational force
felt in the direction of the line; instead, the effective gravity (the
gravity with the centrifugal force of the orbital motion taken into
account) pulls only in the direction perpendicular to the line.
(from Shu, The Physical Universe)
This means that no effective gravitational potential energy is
liberated or gained by moving along an equipotential line.
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Thus, an object, like a star, made of gas free to move around must
have its surface lie along an equipotential line.
If this were not so, some of the gas on the surface could move in
such a way as to fill an area of vacuum and at the same time
liberate gravitational potential energy.
The lines in the Roche diagram have their weird shapes partly
because the two stars are orbiting about each other. Centrifugal
g from this rotation are included in the diagram’s
g
forces arising
equipotential lines. In this rotating frame of reference, the net
forces on a particle which is located on an equipotential line are
in the direction perpendicular to the line. We call these net
forces on a particle the effective gravity at that particle’s
location.
The point labeled L1 on the Roche diagram is the point at which
the effective gravity vanishes. That is, a particle at this
Lagrangian point feels no net attraction to either star.
(from Shu, The Physical Universe)
The surfaces of constant pressure in stars that are motionless in the
orbit frame of reference must coincide with the equipotential surfaces
(the effective gravity has no component along the equipotential)
The surfaces of constant density in stars that are motionless in the orbit
frame of reference must coincide with the equipotential surfaces, because
these are surfaces of constant pressure.
(from Shu, The Physical Universe)
The equipotential surfaces in the Roche diagram must be surfaces of
constant pressure.
If this were not so, then pressure differences along these surfaces,
unopposed by the effective gravity, would set up motions in the
stars’ gas that would tend to eliminate the pressure differences.
Thus if the stars have been orbiting each other for a long time, we
can be sure that the pressures have equalized on the equipotential
surfaces.
If the gas density were to vary along the equipotential surfaces, then
the greater weight of gas above one point on the surface would
cause the pressure there to be greater than at another point.
Again, these pressures would equalize by means of gas motions
driven by the pressure differences.
The result is that the equipotential surfaces are also surfaces of equal
pressure, density, and temperature.
(from Shu, The Physical Universe)
The surfaces of the two stars orbiting each other, which are of
course surfaces where the density passes through some
relatively small value, must therefore be equipotential surfaces.
The Roche diagram therefore indicates that if the radii of the stars
are both small compared to their mutual separation, then the
surfaces of the stars are roughly spherical.
However, if the stellar radii are large, then the stars’ shapes can be
g y distorted by
y their mutual ggravitational attraction.
highly
One limiting case is when both stars are so large that they are just
touching. Then each star is said to fill its Roche lobe, and the
two stars look like the 3-D representation of the Roche lobes in
the second slide.
This analysis leads to a standard classification of binary stars,
which is given on the third slide.
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(from Shu, The Physical Universe)
(from Shu, The Physical Universe)
(from Shu, The Physical Universe)
(from Shu, The Physical Universe)
(from Shu, The Physical Universe)
(from Shu, The Physical Universe)
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(from Shu, The Physical Universe)
(from Shu, The Physical Universe)
The semidetached binary star Algol, in the constellation Perseus,
consists of a 3.7 solar mass star on the main sequence and a 0.8
solar mass star that is a subgiant.
One would expect the more massive star in the pair to have
evolved more rapidly, leaving the main sequence first.
One must therefore conclude that the 0.8 solar mass subgiant has
transferred much of its originally far larger mass to its main
sequence companion
companion.
The main sequence star is now far more massive, and its evolution
rate will therefore be accelerated.
Before its companion leaves its giant phase, it is possible that the
main sequence companion will grow into a giant, presumably
transferring mass back to create a common envelope star
system.
First stage in the evolution of an Algol-type binary system.
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Second stage in the evolution of an Algol-type binary system.
Third stage in the evolution of an Algol-type binary system.
Stage 1
Stage 2
Fig. 16.24
Artist’s
conception of the
development of
the Algol close
binary system.
Stage 3
The Algol system is a semidetached binary in which the star with
the smaller radius is a main sequence star.
Algol is already fairly interesting, but things can get even more
exotic if the smaller, companion star is a white dwarf.
Because a white dwarf is so compact, the stream of gas from a
giant star companion that fills its Roche lobe will liberate a
large amount of gravitational potential energy in falling all the
way down toward the surface of the white dwarf.
Because the infalling gas will have some orbital angular
momentum, and because this angular momentum will be
preserved, the stream of gas will miss the tiny white dwarf,
whipping around it in an elliptical orbit (see illustration on
second slide).
Since the gas stream will remain in the equatorial plane, it must
strike itself after missing the white dwarf surface, leading to the
formation of an accretion disk.
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(from Shu, The Physical Universe)
Second stage in the formation of an accretion disk.
The stream of matter dissipates much of its kinetic energy, but its
angular momentum remains.
First stage in the formation of an accretion disk.
The stream of matter misses the companion and strikes itself.
(from Shu, The Physical Universe)
A close, low-mass binary star, which in this case is also a cataclysmic variable star system.
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Fig. 17.3 A red giant star
with a white dwarf
companion
There is not as yet an adequate understanding of why gas in an
accretion disk tends to slowly spiral into the center, ultimately
falling onto the surface of the central object.
In order to spiral in, angular momentum must be removed from the
gas, generally through some process or processes that transport
it outward through the disk.
These processes are not well understood, but we can (and many
astronomers do) think about these processes as frictional
di i i
dissipation.
Kepler’s laws demand that the inner parts of the disk orbit much
more rapidly about the central object than the outer parts.
Frictional or viscous forces try to make the disk rotate as a solid
body, which requires that the central regions lose and the outer
regions gain angular momentum.
A constant stream of gas therefore lands on the central white dwarf
from the inner part of the accretion disk.
Fig. 17.4 A mechanism for nova outbursts
Fig. 17.4 A mechanism for nova outbursts
The hydrogen-rich gas from the giant star companion of the white
dwarf therefore ultimately lands on the surface of the white
dwarf.
As more and more hydrogen-rich gas piles up on the white dwarf,
it ultimately becomes dense and hot enough for the hydrogen to
fuse into helium.
The hydrogen shell burning causes the white dwarf to suddenly
flare up
up, for a few weeks
weeks, as a nova.
nova
Such a nova outburst can be as luminous as 100,000 Suns.
Heat and pressure from this explosive hydrogen burning at the
surface of the white dwarf forces material near the surface out
into space, where it can be visible as a nova remnant.
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Nova Herculis (1934), showing large change in brightness
between March 10 and May 6 of 1935.
The nova remnant, after the initial outburst dies down, may be
most luminous in the infrared.
The expanding shell of gas cools as it expands, but still radiates
strongly in the infrared.
A typical nova light curve
With each nova outburst, the white dwarf in a binary system can
gradually grow more massive. (However, the most recent research
on this subject challenges this idea.)
Ultimately, it reaches a mass, near Chandrasekhar’s famous white
dwarf mass limit of about 1.4 solar masses, where it can no longer
support itself against gravity by means of electron degeneracy
pressure.
At this critical point, it begins to collapse, growing hotter as it
liberates gravitational potential energy.
Because the white dwarf is degenerate, once the temperature required
to ignite carbon fusion is reached, this fusion begins explosively.
As the fusion reactions liberate nuclear energy in the form of heat,
the thermal pressure is insufficient to expand the material and
reduce the nuclear reaction rate. Electron degeneracy pressure still
dominates. Consequently, the nuclear fusion rate shoots up almost
instantly, and there is an explosion. The white dwarf explodes as a
white dwarf supernova.
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We have already discussed neutron stars and pulsars as the
remnants of the supernova explosions of massive stars.
Particularly interesting things can happen when neutron stars are
located in binary systems.
Just like white dwarfs, neutron stars can cause the formation of
accretion disks around themselves when mass is transferred
from a giant companion star that tries to expand past the limits
of its Roche lobe.
lobe
However, when hydrogen-rich gas falls onto the surface of a
neutron star, immensely more gravitational potential energy is
released than when the same amount of gas falls onto a white
dwarf.
The accretion disks around neutron stars are therefore hotter and
more luminous than those around white dwarfs, and they emit
huge quantities of X-rays (a very energetic form of light).
Fig. 17.11
Matter
accreting
onto a
neutron star
adds angular
momentum,
increasing
the neutron
star’s rate of
spin.
As the material from the accretion disk falls onto the neutron star,
it imparts what remains of its angular momentum to the neutron
star.
The result is that the neutron star spins faster and faster as it
accretes more and more material.
The neutron star can end up spinning hundreds of times per
second, and thus earn the name millisecond pulsar.
The X-ray emission from an X-ray binary, as a binary system
with an accreting neutron star is called, can come in powerful
bursts. These bursts come from episodes of helium fusion at the
base of the thin, meter-thick layer of hydrogen-rich material on
the surface of the neutron star. Each burst lasts only a few
seconds.
X-ray binaries are concentrated in the disk of the Galaxy, just like
the stars, gas, and dust of the Galaxy.
A neutron star accreting mass steadily in a binary system could
ultimately become a black hole.
A supernova explosion of a massive star could also leave a black
hole behind, rather than a neutron star.
In either of these ways, a binary system could end up with a black
hole in it.
The classic candidate for such a system is the X-ray binary Cygnus
X-1.
This system contains an extremely bright star with an estimated
mass of 18 solar masses. Doppler shifts of its spectral lines
indicate that this star orbits an unseen companion with a mass of
about 10 solar masses.
Even with the various uncertainties in these mass estimates, the
companion seems well above the neutron star mass limit of
about 3 solar masses.
Fig. 17.15b An artist’s concept of the Cygnus X-1 system.
The X-rays come from the high temperature gas in the accretion
disk surrounding the black hole.
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The upper limit to the possible mass of a neutron star is not precisely
known, but we believe that it is less than 3 solar masses.
The possible states of matter above nuclear density are
fundamentally unknown to us.
Above this mass limit, we believe that neutron degeneracy pressure
can no longer support the object against its own gravity.
Nevertheless, regardless of what form matter might take within a
collapsing neutron star, we believe that nothing could halt the
collapse. The increasing heat of the material, due to the release
of gravitational potential energy, actually acts as an additional
source of gravitational force, through Einstein’s mass-energy
relationship.
Remember that the electrons in a white dwarf at the white dwarf
mass limit become so energetic that they can combine with the
protons to form neutrons, a far denser state of matter, leading to
the collapse of the white dwarf against gravity.
Just so, presumably, the neutrons of a neutron star near the neutron
star mass limit become so energetic that they can combine with
each other to produce more massive baryons (the family of
particles to which neutrons and protons belong), which take up
less space. The neutron star would then collapse further under its
gravity.
This time, however, we believe that the collapse would take the
neutron star literally “out of sight” to form a black hole.
We believe that collapse into a black hole is therefore inevitable.
The form that the matter of the former neutron star takes once it
disappears from our view is in a sense irrelevant, since we could
perform no experiments to verify theoretical ideas on this
subject. The results of such experiments would need to be
communicated to us from within the black hole, but not even
light can escape the gravitational force there.
We can think of a black hole as mass that is so concentrated that gravity
is so strong near it that even light is deflected so greatly that it orbits
the mass concentration rather like the way the planets orbit the Sun.
A black hole has what we call an event horizon, beyond which events
are unobservable to us.
Inside the event horizon, gravity is so strong that the escape velocity
exceeds the speed of light.
Even light cannot escape from within the event horizon.
Light loses energy upon working its way out from a strong gravitational
field. This energy loss takes the form of a redshift, and we call it the
gravitational redshift.
Fig. 17.12 (a) A 2-D representation of “flat” space-time.
The circumference of each circle is 2π times its radius.
radius
(b) A 2-D representation of the “curved” space-time around a black
hole. The black hole’s mass distorts space-time, making the
radial distance between two circles larger than it would be in a
“flat” space-time.
Light emitted directly outward from the location of the event horizon is
infinitely redshifted, that is, it reaches locations far from the black
hole redshifted to infinite wavelength (zero energy), and is thus
invisible.
We will discuss all this more in a later lecture.
3 Solar mass black
hole with photon
sphere, event
horizon,
Schwarzschild
radius, incoming
light
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