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Stars 1
review of discussion of star
clusters
Notes compiled by
Paul Woodward
Department of Astronomy
University of Minnesota
Fig. 15.12
Main sequence
masses and
lifetimes.
1
2
The short main sequence lifetimes of massive stars, together with
the nearly simultaneous formation of all the cluster stars, tells
us that for an old cluster, all the massive stars will have left the
main sequence.
A younger cluster will have more massive stars still located on
th main
the
i sequence, burning
b i hydrogen
h d
in
i their
th i cores.
If our theory of stellar structure and evolution is good enough, we
may then calculate the main sequence lifetime of the most
massive cluster star still on the main sequence, and we will
then have the age of all the stars in the cluster.
We may use this technique to date each cluster.
cluster
We can also look for consistency of this theoretical calculation with other
knowledge in order to reinforce our confidence in the theory. For example,
globular clusters in the galaxy’s halo, which we believe to be very old for
other reasons, turn out indeed to be very old when dated by this method.
Also, the Pleiades, which still has some of its original nebulosity, is indeed
young.
Fig. 15.19
An H-R
diagram for the
stars of the
Pleiades.
Pleiades
Note that the
upper main
sequence stars
are missing.
3
Fig. 15.19
An H-R diagram for
the stars of the
Pleiades.
Note that the upper
main sequence stars
are missing.
This diagram uses
recent data from the
Hipparcos satellite.
Fig. 15.12
Main sequence
masses and
lifetimes.
The main
sequence turnoff
point for the
Pleiades is at
spectral type B6,
which has a main
sequence lifetime
of about 100
million years.
4
Stars from 4
clusters with very
different ages.
h + χ Persei
is only about 14
million
illi years old.
ld
Stars at the main
sequence turn-off
point for NGC 188
are slightly more
massive and
luminous than the
Sun, indicating an
age of 7 billion
years.
5
As the main sequence turnoff points for globular clusters indicate,
these clusters are indeed ancient.
They are indeed so old that their stars formed from gas that was
not yet enriched in heavy elements by the explosions and
winds of earlier generations of stars.
The different chemical compositions of globular cluster stars
means that we must take particular care in interpreting their
main sequence turnoff points.
This is illustrated on the next slide.
In fact
fact, globular clusters are some of the oldest things we have
been able to find to date. They are so old that they have been
used to constrain estimates of the age of the universe (the
universe must be at least as old as its globular clusters).
6
Old Clusters of Different Heavy Elements Abundances
If we put all these H-R diagrams together, we see that indeed our
picture of stellar evolution and our interpretation of the main
sequence as marking the core hydrogen burning phase of a
star’s life is consistent.
7
Stars 2
Notes compiled by
Paul Woodward
Department of Astronomy
U i
University
i off Minnesota
Mi
8
We now begin looking at stars by tracing their lives, beginning
with their formation out of huge interstellar gas clouds and
ending with their expulsion of their outer envelopes or simply
with an explosion.
This subject is covered in your textbook in Chapter 17.
You should review that chapter thoroughly.
When discussing the formation of the solar system, we already
talked quite a lot about the early stages of the star formation
process, going from a large cloud of interstellar gas to a
protostar surrounded by a protoplanetary disk.
Therefore we will skip that part of the story here.
Fig. 16.3 Artist’s concept of a collapsing stellar disk.
9
The bipolar jets emanating from compact objects at the centers of
rotating disks of gas, as shown on the previous slide, seem to be a
common feature of all such systems, big and small.
We will encounter them again when we discuss double star
systems,
t
andd yett again
i when
h we discuss
di
the
th nuclei
l i off galaxies.
l i
This is a feature of astronomy, we find again and again close
similarities in the behavior of systems that differ in scale by
factors as large as a thousand or even a million. The key point is
that these systems do not differ in any fundamental aspects other
than sheer scale.
10
If we think about the glob of a larger gas cloud that collapses to
form a single star, we can distinguish 4 stages of this
contraction process under gravity, once this glob has
contracted sufficiently to establish its distinct identity. We
consider its collapse
p beginning
g
g after it has become opaque
p q to
radiation, so that it makes sense to talk about its “surface,” the
surface region from which light can escape into space.
1. First, the surface temperature of the gas cloud is very low, but
its surface area is very large. As it contracts, liberating
gravitational potential energy as heat, this heat is radiated
away into space very efficiently.
efficiently The luminosity of the gas
cloud is therefore very high, perhaps as much as 100 times as
high as it will be once the star reaches the main sequence and
begins burning hydrogen in its core. However, this radiation,
because of the low surface temperature of the cloud, will
appear mostly in the infrared.
2. Second, as the gas cloud continues to collapse, radiating into
space essentially all of the heat generated from gravitational
potential energy release, its surface temperature warms only
slightly. However, as the collapse proceeds, the surface area
of the cloud is diminished,, so that its luminosityy is diminished
accordingly. This stage lasts only a few million years (for a
protostar of about one solar mass).
3. Third, release of gravitational potential energy, together with
the reduced radiating surface area, cause the interior of the
protostar to heat steadily. In this third stage the core
temperature exceeds a few million degrees K,
K so that
hydrogen fusion to form helium begins in the center and
significantly slows the continuing collapse of the protostar.
Continued shrinkage and continued heating give slight
increases in the luminosity over about 10 million years (for a
one solar mass protostar).
11
4. Fourth, shrinkage of the protostar and increase of the rate of
fusion in its core continue for a few tens of millions of years
until the fusion rate finally establishes gravitational
equilibrium, and the star is said to be on the main sequence.
F whatever
For
h t
it is
i worth,
th we can plot
l t suchh a protostellar
t t ll
evolutionary track on the H-R diagram.
Stars of different masses of course follow different tracks on the
diagram, but they all follow the same 4 stages of protostellar
evolution outlined above.
12
Fig. 16.6
Life tracks
from protostar
to main
sequence star
f stars off
for
different
masses.
You may remember that we said previously that the H-R diagram
for the Pleiades cluster indicates that the cluster is about 60
million years old.
You may also remember that this determination was made from
th main
the
i sequence turn-off
t
ff point.
i t
There were some stars in the cluster on the main sequence, and
some more massive stars had already begun to move off to the
right of the main sequence.
However, the least luminous stars in the cluster, the lowest mass
stars were mostly located a bit above the main sequence.
stars,
sequence
Now you can understand that these low-mass stars have not yet
reached the main sequence for the Pleiades cluster. The
previous slide indicates that only stars of about one solar mass
or more have had time to reach the main sequence by now.
13
From observing star clusters, we can roughly determine the
relative frequencies of formation of main sequence stars of
different masses.
This initial mass function, as it is called, strongly favors lowmass stars.
t
For every star formed between 10 and 100 solar masses, we find
roughly 10 stars between 2 and 10 solar masses, and a few
hundred stars below half a solar mass.
We have never conclusively seen any star of greater than about
100 solar masses.
masses
It is believed, as the British astronomer Eddington pointed out,
that a star of such great mass would generate so much energy
in its core that the outward streaming radiation would tear it
apart. (People still argue about this.)
We are not sure where the star formation story ends on the low
mass end of the scale.
As very low mass protostars (say, below 0.08 solar masses)
contract under gravity, we believe that a bizarre physical
phenomenon
h
called
ll d degeneracy
d
pressure would
ld halt
h lt the
th
collapse before efficient, self-sustaining hydrogen fusion
could begin in the core.
Such low mass stars fill the gap between stars and planets.
It is not clear whether Jupiter-sized objects form individually from
collapsing gas clouds
clouds, without being planets forming within
the protostellar disks of larger objects.
Such a “star,” or “brown dwarf,” with 0.05 solar masses, Gliese
229B, was discovered orbiting a “real” star, Gliese 229A in
1995.
14
The brown dwarf Gliese 229B.
This object was detected with a 1.5 m telescope on the ground (left) but the Hubble Space
Telescope provided a much sharper image (right). The small companion, Gliese 229B, has a
mass of only 20 to 50 times that of Jupiter. Gliese 229B is the companion of an ordinary
star, but it has a luminosity of only 2 to 4 millionths that of the sun. Its spectrum resembles
that of Jupiter. It has a lot of methane and a surface temperature of 600ºC to 700ºC.
Early models of the contraction of protostars to form main
sequence stars were based upon rough scenarios like the one
we have just outlined.
The Japanese astronomer Hyashi built models assuming this sort
off “quasi-static”
“
i t ti ” evolution,
l ti that
th t is,
i a slow
l progress through
th
ha
series of physical states each of which was very nearly in
equilibrium.
Unfortunately, life is not this simple.
First Karl-Heinz Winkler, working in Germany, and later Frank
Shu at Berkeley,
Shu,
Berkeley worked out detailed models for the
formation of single solar mass stars that we now think are
basically correct.
15
These models reveal that the protostar is not in equilibrium, but
instead its surface is marked by an extremely strong shock
front, in which infalling gas from the surrounding cloud is
suddenly decelerated upon striking the surface of the protostar.
It is from this shock front that a huge amount of kinetic energy
from the infalling gas, just converted into heat in the shock, is
radiated into space.
The dynamics of this situation determines much of the internal
structure of the protostar. The loss of huge amounts of heat of
condensation from the shock, essentially before that energy
can become incorporated into the protostar,
protostar greatly affects the
course of such a protostar’s development.
These models, of course, did not include rotation or magnetic field
affects, which still remain to be treated properly in such work.
These theoretical studies have led us to the conclusion that the
internal structures of main sequence stars of different masses
are dramatically different.
High mass stars generate nuclear energy prodigiously in their
cores.
They produce so much energy so rapidly that “conduction” by
radiation diffusion cannot transport it outward fast enough.
Instead, we believe that their cores are fully convective.
Nevertheless, outside their cores, where the gas is still very
hot and ionized, radiation diffusion works well in carrying the
energy all the way out to the surface.
surface
Medium mass stars like our Sun transport liberated nuclear energy
outward from their cores by radiation diffusion. In a layer
near the surface, the gas becomes too opaque for efficient
radiation diffusion, and convection takes over.
16
Low mass stars are believed to be convective from their surfaces
right down to their cores.
Such stars with fast rotation rates can produce very powerful
flares as a result of the winding up of their magnetic fields by
their deep convection zones.
Proxima Centauri is such a “flare star.”
Low mass stars gradually burn their core hydrogen, reducing the
number of independent particles (four protons are replaced by
a single helium nucleus) in their cores.
In this process
process, their cores shrink,
shrink and they grow gradually a bit
more luminous (the sun is thought to have increased in
luminosity by perhaps 30% over the 4.7 billion years of the
Earth’s history to date).
17
In the Sun, hydrogen nuclei are combined to produce helium
nuclei (and extra energy in various forms).
Because helium nuclei usually have two protons and two
neutrons, we have to combine four hydrogen nuclei
(protons) to get one helium nucleus.
This is incredibly unlikely to happen in a single event.
Instead, it proceeds in stages, each involving only the collision
of two particles.
18
The previous slide illustrates the primary nuclear reaction chain
in the Sun.
It provides about 86% of the Sun’s energy.
Together with the alternate (second) reaction chain on the next
slide,
lid which
hi h iinvolves
l
berylium
b li
and
d li
lithium
hi
as intermediate
i
di
products, these two reaction sequences produce 98.5% of the
Sun’s energy.
The remainder of the Sun’s energy is produced by the CNOcycle, the third reaction chain (on the next slide) involving
carbon, nitrogen, and oxygen.
These alternate reaction chains are included here for correctness,
but all you need concern yourself with is understanding the
primary chain shown on the previous slide.
Do not memorize these
nuclear reactions. They are
given here for completeness
and to satisfy the curious.
19
Now let’s consider what happens to a star like the Sun when it
runs out of hydrogen fuel in its core.
It’s subsequent evolution is called the “red giant phenomenon,”
and it is one of the early triumphs of computational science.
I was stellar
It
ll evolution
l i models
d l that
h made
d us understand
d
d that
h redd
giant stars are not separate sorts of objects that have always
been that way since their formation. These computer models,
which take stars from one equilibrium state to the next, in
which the nuclear makeup is slightly altered by the star’s
burning, were the only way that we were able to figure out
that red giant stars are just the evolved states of main sequence
stars.
When hydrogen is exhausted in the core of a star like the Sun, the
inert helium there does not generate further nuclear energy, so
it contracts under the crushing weight of the gas above it.
The contraction of the helium core releases gravitational potential
energy, so it actually heats up.
The layers above the core, which still contain unburnt hydrogen,
contract and heat up as well.
The layer
Th
l
off hydrogen
h d
just
j above
b
the
h helium
h li
core becomes
b
so hot
h
that it begins to burn, and this process actually generates more
nuclear energy than the core hydrogen burning did when the
star was on the main sequence.
The star can eventually increase in luminosity by up to 4 orders of
magnitude. This process takes about a billion years, for a star
like the Sun, and longer for less massive stars.
In order to radiate all this luminosity into space, the layers above
the hydrogen burning shell expand enormously (by about a
factor of 100 in radius) and become fully convective.
20
The now far greater surface area produces the much greater
luminosity, ironically, at a somewhat reduced surface
temperature.
The star has thus become a red giant.
A newly
As
l produced
d d hhelium
li
adds
dd to the
h mass off the
h inert
i
core, its
i
greater gravity causes it to shrink still further.
The hydrogen burning shell shrinks along with the core, growing
hotter and denser.
This makes the hydrogen burning rate increase in the shell, which
increases the star
star’ss luminosity still further.
further
This vicious cycle feeds upon itself until the temperature in the
helium core reaches about 100 million degrees K, at which
point helium nuclei can fuse in the core to produce carbon.
The process by which the core of a star can get hotter, rather than
cooler, once its source of nuclear heat generation ceases is a
bit odd, but we can understand it as follows.
We begin when nuclear reactions are continually generating heat
in the core.
This heat produces pressure, which supports the core against
gravity at its present radius.
The heat generation is balanced by escape of heat due to radiation,
conduction, or convection from the surface region of the core.
So the pressure, the gravity, and the radius of the core remain
constant.
Now suppose that the nuclear reactions shut off from lack of
further fuel.
The escape of heat does not shut off.
21
The escaping heat would cause the core to cool off, if only its
gravity and its radius were to remain constant, as before.
But the escape of heat causes a reduction of the pressure
supporting the core, so that it contracts under its gravity.
W can think
We
hi k off this
hi contraction
i as generating
i ordered
d d inward
i
d
motion, which has an associated kinetic energy derived from
the liberation of gravitational potential energy.
We can also think of the inward moving material as colliding with
other material moving inward and toward it, so that the kinetic
energy of the ordered motion is transformed into kinetic
energy of disordered motion, which we call heat.
This additional heat will raise the pressure of the gas.
If the pressure rises enough, the collapse will stop, or at least
pause or slow, since heat continues to escape from the surface.
How much added pressure does it take to arrest the collapse?
You might think that all we have to do is to replace the heat
energy that escaped from the surface of the core with heat
energy generated in the collapse from release of gravitational
potential energy.
But this cannot be true, since the collapse makes the core smaller.
The core’s mass is still the same, but now its smaller size means
that its gravity is stronger.
This in turn means that we need more pressure than before in
order to support it at this smaller size.
Therefore, if the collapse is slowed and nearly stopped, we know
that the pressure must be higher than before.
In fact, the temperature, which is proportional to the ratio of the
pressure to the density, must be higher to counter the stronger
gravity at this smaller core radius.
22
Once hydrogen fusion ignites in a shell around the core, it
eventually burns much more brightly than the hydrogen
burning in the star’s core.
We can understand this also.
The energy generation rate we had with core hydrogen burning
had to be sufficient to provide enough pressure to hold up all
the material overlying the core against the crush of gravity. It
had to do this while matching the rate at which energy was
escaping from the star through its surface.
Now the energy generated in the hydrogen burning shell must still
support
pp all this overlying
y g material as well as the dead weight
g
of helium accumulating in the core.
The helium must be heated sufficiently by the hydrogen burning
shell to hold itself and the overlying material up. It’s like
trying to carry on your shoulders a child who keeps growing
older and heavier – it is quite a burden.
One might think this burden of the helium core might be light.
No way.
All this hellium is really, really close together. It finds itself
extremely gravitationally attractive. Keeping its nuclei and
electrons whipping around fast enough so that it does not
come completely together is a difficult job requiring lots and
lots of energy.
23
24
Because helium nuclei have twice the charge of hydrogen nuclei,
they repel each other more strongly.
They must therefore be moving faster in order to strike each other
hard enough to overcome this repulsion and form beryllium.
(The beryllium would split back into two helium nuclei, but
under the conditions in a helium burning stellar core another
helium nucleus can come along before this happens, so that a
stable carbon nucleus can be created.)
Helium fusion in a red giant star ignites suddenly, in what is
called a helium flash.
When the helium first ignites, the core is supported by degeneracy
pressure, and its total pressure does not increase much as its
temperature, and the helium fusion rate, shoot up.
After the helium flash, the core does expand against gravity,
expanding and cooling the hydrogen burning shell.
25
Degeneracy pressure is a concept that will pop up again and again
in our discussions of stellar evolution.
It can be understood, at least qualitatively, by the following
analogy.
Think about a room.
Now put a whole lot of billiard balls into the room. Just pour
them in until they fill up, say, a quarter of the room’s volume.
They will be in the lower quarter of the room.
If you try to squeeze them so that they take up less volume, you
will probably be unable to do so (let’s say that you can’t
squeeze hard enough to pulverize them,
them so that all the little
spaces between them can be filled with the powder produced).
The billiard balls now act like helium gas exerting degeneracy
pressure. The billiard balls are touching. You can’t get them
any closer to each other no matter how hard you push.
Now let’s put some energy into this system of billiard balls by
picking them up and throwing them every which way.
Let’s imagine that we can do this somehow without getting hit,
although the billiard balls will all hit each other.
The billiard balls have a lot more kinetic energy of disordered
motion than before. They are a lot hotter.
And they must now take up a lot more room.
If you were to turn a winch and pull the ceiling of the room
downward, you could make the billiard balls take up less room
But this would take a lot of work, because the billiard balls would
be hitting the ceiling pretty hard
hard, especially as the volume
available to them got closer and closer to a quarter of the
original room volume (when they would all be touching once
again).
Without crushing the billiard balls, you could not make them take
up less volume than a quarter of the original room.
26
Degeneracy pressure is like the force of resistance that the billiard
balls exert when they are all touching and you try to squeeze
them into a smaller volume.
Normal gas pressure is like the force that the billiard balls exert
against the ceiling of the room as you lower it with your winch
against the force of their bouncing off of it.
it
Normal gas pressure is strong, but you can overcome it if you
press hard enough, and you can make the gas squeeze into a
smaller volume.
Degeneracy pressure is stronger, in the sense that you cannot
overcome it and squeeze the material into a smaller volume
unless
l you squeeze so hard
h d that
th t the
th material
t i l changes
h
its
it
fundamental nature. An example of such a change is when the
particles of the material fuse into different particles that take
up less space. This is like pulverizing the billiard balls, or like
combining protons with electrons in a star to form neutrons,
which take up dramatically less space, believe it or not.
Fig. 16.10a
Core structure of a helium-burning star.
27
Fig. 16.10b
Relative sizes of a low-mass star as a main-sequence star,
a red giant, and as a helium-burning star.
It turns out that the helium burning cores of all low-mass stars
fuse helium into carbon at about the same rate. Therefore
these stars all have about the same luminosity.
However, these stars can have different masses, based upon how
much mass they started out with and how much mass they lost
in stellar winds during their red giant phases.
Stars that lost more mass end up with smaller radii and higher
surface temperatures.
These helium burning stars therefore occupy a horizontal branch
in the H-R diagram of a star cluster.
28
The core helium of a low-mass helium-burning star runs out in
about a hundred million years.
Once helium is exhausted in the core, the core again shrinks and
heats up, helium begins burning in a shell around this core,
and hydrogen continues burning in a shell around the helium
region.
Once again the luminosity increases to new heights as the core
size shrinks, and the outer layers of the star puff up again to a
greater extent than ever.
Computer models show that the helium burning in the shell spikes
upward every few thousand years in a series of thermal
pulses.
For a one solar mass star, this stage can last less than a million
years.
29
In order to ignite carbon in the core of such a star, the temperature must rise to
about 600 million degrees K.
For low-mass stars, degeneracy pressure halts the shrinkage of the core before
this very high temperature can be reached.
Such stars have huge stellar winds, and during the thermal pulses, carbon can
b ddredged
be
d d up ffrom th
the core andd bbrought
ht to
t the
th surface
f
andd into
i t the
th wind
i d
by convection.
Red giants with high carbon concentrations in their atmospheres are called
carbon stars.
Such carbon in the stellar wind can form dust grains, because of the very low
surface temperatures of these stars.
During the final stages of the evolution of a low-mass star, the wind from the
star becomes very great.
Ultimately, all the mass of the envelope surrounding the inert, degenerate
carbon core is ejected to form a nebula, which is set aglow by the
ultraviolet radiation of the cooling, but still very hot core.
Thi lluminous
This
i
nebula
b l iis called
ll d a planetary
l t
nebula.
b l
The degenerate carbon core is called a white dwarf.
The textbook discusses what humans might do 5 billion years hence, when the
Sun begins to become a subgiant, and the rest. This discussion is
interesting enough to warrant reading, once. But 5 billion years is a long
time.
Th nextt slide
The
lid summarizes
i
the
th life
lif story
t
off a low-mass
l
star,
t before
b f
we go on to
t
look at some planetary nebulae.
30
The Owl Nebula, on the following slide, gives an idea why these
nebulae, formed by mass ejections from dying stars, are called
planetary nebulae – with poor telescopes they look like
planets.
31
Planetary Nebula, the “Owl”
in Ursa Major (NGC 3587)
A small collection of Hubble Space Telescope images of planetary
nebulae is shown on the next few slides. The mass of gas
ejected from a star in this manner can be up to 75% of the total.
The first of these planetary nebulae, the Stingray Nebula, is so
young that only 20 years ago its gas was not hot enough to emit
light However
light.
However, the temperature of the central star has increased
rapidly, so we will be able to witness the formation of this
planetary nebula, a process that may take only 100 years or so.
The ultraviolet light from the central white dwarf star causes the
surrounding nebula to glow.
32
The Stingray Nebula,
or Henize 1357,
HST image.
The Egg Nebula, CRL 2688, is likely to have first appeared a few
hundred years ago.
The arc structures in this nebula, visible on the next slide, have
been interpreted as shells of gas ejected previously by the
central star at intervals of perhaps 100 to 500 years (could these
have been the periodic helium flashes predicted by stellar
evolution models?).
In the infrared (shown on the second slide), there is a dumbbell
structure of molecular hydrogen. Matter streams out along the
polar axis at 100 km/sec and collides with previously ejected
gas moving at only 20 km/sec.
km/sec
The matter in the two polar streams darkens the centers of the two
cones of visible light from the central star.
33
The Egg Nebula, CRL 2688
The Hourglass Nebula, MyCn18, discovered by Margaret Mayall
and Annie Cannon, at first fits the standard model of planetary
nebula formation.
The idea is that matter is ejected from the central star in wind-like
flows that are episodic, and that grow faster and faster.
We believe that the earlier ejected matter is denser at the equator
than at the poles, and that it therefore channels the new, more
rapidly ejected gas into an hourglass shape.
The Hourglass Nebula shows this structure beautifully, with the
walls of the hourglass showing detailed structure that may either
be related to the episodes of the earlier,
earlier slower winds or to the
interaction of an energetic stream of gas with the walls of this
channel.
The Hourglass Nebula is at a distance of 8,000 light-years.
34
Hubble
Space
Telescope
image of
the
Hourglass
Nebula,
MyCn 18.
“Snowplow” model of planetary Nebula
35
Internal structure of main sequence star and helium burning star
Internal structure of one solar mass star in second red giant stage
36
This shows how long a
star like the sun spends in the
various stages we have
The ultimate fate of a star depends mainly upon the mass that it
had when it was on the main sequence, burning hydrogen to form
helium in its core.
37