SBC Science Module 04 Measuring and Classifying Stars Paper

Module 04 – Measuring and Classifying StarsThe Hertzsprung-Russell diagram is an important tool in the classification of stars and the understanding
stellar evolution. The H-R diagram was discovered independently by two astronomers in early 20th
century using observations of star luminosity and surface temperature. With this lab exercise, you will
use Stellarium to collect stellar information and then form your own H-R diagram and see if you can find
how stars are group into different luminosity classes.
Background Question – Describe the four major groups of stars and where they are located on the H-R
diagram.
Object: Explain the purpose of this laboratory assignment in your own words. What do you think you will
accomplish or learn from this exercise?
Hypothesis: Write a simple hypothesis connected to different stars and the H-R diagram that you will be
able to test up the Stellarium software (for example, most bright stars visible in the night are
supergiants)
Procedure:
1) Open the Stellarium software. Open the Sky and Viewing options window (F4). Under the “Sky”
tab, uncheck the Atmosphere and Dynamic eye adaption.
2) Select the Landscape tab and uncheck “Show ground”.
3) For this lab, you will need to record the spectral class and absolute magnitude of a group of near
stars and a group of the brightest stars in the night sky. For each star, open the Search window
(F3) and enter the star’s name. Click on the star and look at the displayed information at the
upper right. Record the star’s spectral class and absolute magnitude in the chart. Some
information has already been include in the chart.
4) Repeat step 3 for each of the stars on the list.
5) Plot each of your stars on the H-R diagram below. Denote each star by their listed star number
and mark the nearest in red and the brightest stars in blue.
6) Using the H-R diagrams in Chapter 12 as a reference, mark out where the main sequence line,
giant branch, supergiants branch, and white dwarfs region would be on your H-R diagram.
Q1: Based on the location of the Sun on your H-R diagram, what luminosity group (main
sequence, giant, supergiant, or white dwarf) does the Sun belong to?
Q2: What stars did you find to be supergiants?
Q3: What luminosity group and spectral classes are most nearby stars?
Q4: What luminosity groups and spectral classes do most of the bright stars belong to?
Q5: Is there any part of the H-R diagram that you do not find any stars?
7) Continue using Stellarium if you need further information to test your individual hypothesis. If
you need further direction, please ask your instructor.
Conclusion: In 1-2 paragraphs, explain if your observations and data support or conflict with your
hypothesis and if you have met your assignment objective. Was there any portion of the assignment
that was particularly interesting or difficult?
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Brightest Stars in the
Night Sky
Star
Sirius A
Canopus
Alpha Centauri A
Arcturus
Vega
Capella A
Rigel
Procyon A
Betelgeuse
Hadar
Altair
Aldebaran
Spica
Antares A
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Nearest Stars
Star
Sun
Proxima Centauri
Alpha Centauri A
Alpha Centauri B
Barnard’s Star
Wolf 359
Lalande 21185
Sirius A
Sirius B
Epsilon Eri
61 Cyg A
61 Cyg B
Spectral Class
Absolute Magnitude
Spectral Class
G2
M6
Absolute Magnitude
4.8
15.6
K1
M4
M6
M2
5.7
13.2
16.7
10.5
wd use B1
11.2
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Procyon A
Procyon B
wd use A6
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Module 04 – The Lives and Death of Stars
Astronomy is, arguably, at its heart a study of the stars. We turn now to those basic units of the universe,
beginning with our very own star, the sun.
Why Does the Sun Shine?
The sun is the ultimate source of all life on Earth. It dominates our sky and has played a huge role in
various societies throughout history. However, it wasn’t until the beginning of the 20th century that we
truly understood what powers the sun.
Nuclear Fusion in the Sun
After discarding various options (including a burning lump of wood or coal, or heat resulting from
gravitational collapse) as infeasible, given the sun’s long lifetime and incredible output, astronomers
finally found a mechanism that explains the sun’s energy: nuclear fusion.
Unlike the processes in nuclear power plants here on Earth, which involve very large atomic nuclei
splitting apart to release energy (nuclear fission), the sun’s core produces energy by combining, or fusing,
small nuclei to make larger ones. In particular, four hydrogen nuclei (single protons) fuse via a series of
steps to make one helium nucleus (two protons, two neutrons), some other subatomic particles, and
energy. The steps by which this transformation occurs in the sun (there’s a slightly different series of
steps at work in more massive stars) is known as the proton-proton chain. A high temperature (that is, a
high average speed for the particles) is required to overcome the repelling force of two like charges
(remember that like charges repel, unlike charges attract, and that protons have positive charge). When
the protons that are reacting are moving fast enough, they can overcome this electric repulsion and bind
together.
At the beginning of the chain, two protons smash into each other to become a deuterium nucleus (one
proton, one neutron), sometimes called “heavy hydrogen,” because it still has a +1 charge like normal
hydrogen, but has almost twice the mass. Two even smaller particles (called a positron and a neutrino)
also result from this reaction. The second step involves another hydrogen nucleus (proton) colliding with a
deuterium nucleus, which results in a helium-3 nucleus (two protons – which makes it helium – and one
neutron) and a gamma ray. (Helium-3 is not a common isotope under earthlike conditions.)
After two instances of each of these steps, two helium-3 nuclei can smash together to fuse into a helium4 nucleus (“normal” helium, with two protons and two neutrons) and an extra two protons. The overall
result then, is four hydrogen nuclei in, one helium nucleus (plus two positrons, two neutrinos, and two
gamma rays) out. The energy that comes out of the reaction is thus carried away as electromagnetic
radiation (“light” – the gamma rays) and the kinetic energy of the escaping neutrinos.
Energy Transport
The next obvious question is: How does all that energy get from the core to the surface of the sun? Deep
in the core, the matter is so hot and dense that the photons (gamma rays) from the fusion reactions can’t
travel farther than a fraction of a millimeter before colliding with an electron and being sent in a different
direction. The resulting random walk keeps the energy within the radiation zone for hundreds of
thousands of year, working its way gradually outward to the convection zone and finally out into space.
Although the photons produced at the core take nearly a million years to make their way to the sun’s
surface, the neutrinos are a different story. These sub-atomic particles interact so weakly with other
matter that the vast majority of them fly straight out of the sun as if it weren’t even there. The difficulty in
studying such energetic particles and our own incomplete understanding of the physics involved made
solar neutrinos one of the biggest puzzles in astronomy for decades. New advances in nuclear physics
have solved the conundrum, though, and now we are more certain than ever that we have a good
understanding of the processes inside the sun.
Structure of the Sun
Interior Layers
Inside the sun, as we have already seen, we can talk about different layers, depending on the processes
at work. The core is where the nuclear fusion occurs. Its temperature is approximately 15 million K.
Immediately outside the core is the radiation zone (see above) in which all the energy is transported
almost entirely by photons. The temperature is around 10 million K, and it extends about two-thirds of the
way toward the surface.
Above the radiative zone is a layer called the convection zone, where energy is transported by the
circulation of the plasma itself. In other words, the hot plasma at the bottom of the layer (at that depth, a
mere 2 million K) rises, cools, and then sinks to begin the process again. The top of the convection zone
is what we see as the surface of the sun, and is known as the photosphere. From here, energy escapes
as thermal radiation from a 5800 K body, peaking in the yellow/green region of the visible spectrum.
The Solar Thermostat
One of the most important phenomena inside the sun is the careful balance between the inward crush of
gravity due to its great mass and the outward blast of energy from the nuclear inferno. Each layer of the
sun must have that “equal but opposite” interplay of forces to maintain the status quo. This stable state is
called hydrostatic equilibrium or gravitational equilibrium.
The give and take between forces is actually quite remarkable. It is a self-regulating process that
maintains a steady fusion rate in the core. For example, if the reaction rate were for some reason to drop,
gravity would start to win the battle between forces, and the core would begin to contract. Due to the
contraction (the conversion of gravitational potential energy into thermal energy), the core would then
heat up. The hotter environment would send particles hurtling into each other at a higher speed, thus
increasing the reaction rate back to normal.
The reverse is also true. An increased rate would heat the core, pushing the layers outward and
spreading the particles out, cooling them. The particles would collide somewhat less, reducing the
reaction rate to normal again. With this natural thermostat, the sun continues its core fusion at a steady
rate as long as there is nuclear fuel.
Solar Activity
From the surface, there are several interesting phenomena we can see. Some have been known for
centuries, and others are more recent discoveries.
Sunspots and Prominences
One of Galileo’s most startling discoveries was that the face of the sun was not unblemished, as everyone
assumed. Even with his small telescope, he was able to see darker regions, known today as sunspots.
Sunspots appear dark only in comparison with the surrounding plasma. They are still quite bright, but they
are cooler and thus appear fainter than the majority of the sun’s surface. We have learned over time that
sunspots are associated with magnetic fields. They usually come in sets of two, magnetic north and
south, connected by a looping magnetic field. Sometimes the gas of the sun’s outer layers gets trapped in
such a loop, and can be seen as a solar prominence.
Flares and Other Storms
Sometimes the magnetic field lines on the sun’s surface change drastically and rather suddenly. In such
cases, the released energy can cause a solar flare – a storm of X-rays and nearly light-speed charged
particles. Flares and other such activity can disrupt certain electrical technologies on Earth, as well as
producing auroras by interacting with our planet’s magnetosphere.
Module 04 – The Lives and Death of Stars
Now that we’ve seen how the nearest star works, we can generalize a bit to the other stars in the sky.
We’ll start by looking at the main physical characteristics by which we can classify them.
Luminosity
Looking at the sky, one of the first things we can notice about the stars is that some are brighter than
others. There are three possible explanations: (1) they are all the same brightness but are at different
distances, (2) they are all at the same distance but each has a different brightness, or (3) they are both
different brightness and distances. It turns out the third case is correct.
We can measure the distances of the nearest stars directly through a phenomenon known as stellar
parallax. As Earth moves through its orbit, the nearest stars shift a miniscule amount compared to the
background stars. The amount of as star’s shift tells us its distance. Once we know distance, we can find
the true brightness of a star from its distance and apparent brightness.
Astronomers usually talk about a star’s intrinsic brightness in terms of its total energy output, or
its luminosity (energy per second, or power). Because the light leaving a star spreads out with distance,
the total power per unit area decreases with distance from the source. As it traverses space, a star’s light
is spread across spheres of ever-increasing size. The surface area of a sphere depends on the square of
its radius; therefore, the apparent brightness of a star (its power spread across a given area) drops off by
the square of the distance. This is known as the inverse-square law for light.
This figure shows the phenomenon in more detail. As it leaves the star, light must first pass through a
sphere of space with a radius of 1 AU. The same total amount of light will cross through the 2-AU-radius
sphere. However, the larger sphere (with a radius twice as large) has a surface area four times as big.
The light, spread out over four times the area, thus appears four times fainter. Similarly, by the time it
passes through the sphere with radius of 3 AU, the light is covering an area nine (32) times as large, and
looks 9 times fainter. We see, then, that a star’s brightness changes with the square of the distance from
the star (the same holds true for any object emitting light).
A survey of stars in our Galaxy shows a vast range of luminosities. We can compare them by using the
sun’s luminosity (Lsun) as a baseline. The sun is really kind of an average star in this respect. The
brightest single stars we know can be a million times brighter than the sun (106 Lsun), while the faintest
are a ten-thousandth as bright (10-4 Lsun).
Temperature
Remember from Module 03 that an object’s thermal spectrum can tell us its temperature. As we saw with
the sun, the light that we see comes from the photosphere (the “surface”). The same is true of other stars;
only the light from the surface escapes. Thus we only see the thermal signature of the surface (that is,
the surface temperature). When we view stars in the sky, we see a wide range of temperatures as well as
of luminosities. Since temperature is directly related to color (the wavelength at which the most energy is
emitted), this makes for a lovely display of red (cool), yellow (medium), or blue (hot) stars.
When astronomers first began analyzing stellar (absorption) spectra, they noticed that the lines made by
hydrogen were stronger in some stars than others. Stars were soon being classified by their spectral
type – a letter assigned according to the strength of the hydrogen lines in their spectra. That system alone
soon proved inadequate, as more data were gathered. Within a few years, a new order for the spectral
classes had been adopted: OBAFGKM. (The mnemonic that generations of astronomy students have
used to remember this order is “Oh, Be A Fine Girl/Guy, Kiss Me!” You may want to try inventing your
own.)
Although this progression in the spectra made more sense when arranged this way (as opposed to the
original, alphabetical order), astronomers didn’t understand why. Some 15 years later, a young woman at
Harvard Observatory realized the sequence was directly related to surface temperature (where O stars
are hottest, and M stars are coolest). This discovery proved invaluable to astronomers, who use it to this
day in the form of the H-R Diagram.
Mass
The final property of stars we will discuss here is mass. As with the other characteristics, we find that the
sun is average in this sense. Again using the sun’s mass (Msun) for comparison, we find that stars range
from a truly immense 150 Msun to a relatively tiny 0.08 Msun (which is only about 80 times as massive as
Jupiter).
How do we know the masses of stars? We can’t bring them into a lab and weigh them on a scale, but we
can measure their masses by using Newton’s version of Kepler’s Third Law (see Week 2). Many stars
form in binary systems, in which two stars orbit each other. If we can find their orbital period and
separation, we can then calculate their masses. Through various methods that depend on how distinctly
we can see the individual stars, we have been able to calculate the masses of a wide variety of stars.
The Hertzsprung-Russell Diagram
Invented early in the 20th century and named after the two men who independently devised it,
the Hertzsprung-Russell (H-R) diagram is one of the most powerful analytical tools in astronomy today.
What’s On an H-R Diagram?
Part of the beauty of an H-R diagram is its simplicity. On the horizontal axis is spectral type as discussed
above (OBAFGKM). Since spectral type relates directly to temperature, we can also consider this axis to
plot temperature, though it goes “backwards,” with the hottest stars on the left and the coolest on the
right, following the spectral sequence. On the vertical axis, we plot luminosity (or sometimes apparent
brightness), with brightest at the top. From this simple layout, we get an astonishing amount of
information, starting with the distinct groupings of stars in different areas.
The Main Sequence
The most striking pattern on the H-R diagram is known as the main sequence. Ninety percent of all stars
fall in this region, which is a slightly curved line from upper left (hot and bright) to lower right (cool and
faint). The vast majority of stars are found in this part of the diagram because this is where they spend the
vast majority of their time. A star that is fusing hydrogen in its core as its energy source – a “normal” star will fall on the main sequence. Therefore, this stable stage of a star’s life is often called its main sequence
lifetime.
The length of any given star’s main sequence lifetime depends only on its mass. This correlation can be
explained by the fact that a more massive star has greater gravity to compress its core, which makes the
core hotter. A hotter core consumes its nuclear fuel more rapidly, and so hot, blue, bright, massive main
sequence stars have the shortest lifetimes. In contrast, the cool, red, faint, low-mass stars should live on
the main sequence for up to 100 billion years, which is nearly ten times the current age of the universe.
Giants and Dwarfs
There are some stars that don’t fall on the main sequence on an H-R diagram. Two groups lie above
(brighter) and to the right (cooler) of it. Because these stars are cooler, they look red. However, as they
are much brighter than the main sequence, we know they must be much larger to put out so much light
from such a cool surface. Therefore, such stars are known as giants (or sometimes red giants)
or supergiants, depending on their diameters. They are stars in their first death throes after the main
sequence.
On the opposite side of the diagram, the lower left (hot and faint), we find a special group also named for
both color and size. These objects are very hot, giving off a whitish color, but faint. For the same reason
bright, cool stars had to be large, a hot-yet-faint star must be small. These so-called white dwarfs are
only about the size of Earth, and are the last embers of dead sun-like stars.
Finding Cluster Ages
One of the most interesting uses for an H-R diagram is providing a means to find the age of a group of
stars. Stars tend to form in clusters, and when we see a cluster, we know the member stars must all be
approximately the same age (within a few million years, which is small when compared to total lifetime).
Given what we know about how long each spectral type spends on the main sequence, this gives us a
clever tool for determining age.
Remember that the more massive (brighter and hotter) a star is, the shorter its main sequence lifetime.
When a star uses up its hydrogen, its temperature and brightness change, and it appears to move off the
main sequence in the H-R diagram. By looking at a cluster’s diagram and seeing which stars are just
peeling away from the main sequence (the main sequence turnoff point), we can tell which stars have
already evolved off the main sequence and which are just ending their lifetimes, thus aging the whole
cluster. Since all the stars formed at the same time, the main sequence lifetime of a star at the turnoff
must be the overall age of the cluster.
Module 04 – The Lives and Death of Stars
We have seen that stars come in a wide variety of masses, sizes, temperatures, and luminosities. Now
we will look more closely about how a star’s basic characteristics impact its life cycle.
Star Formation
Previously, we examined the way the solar system formed, from a cloud of gas and dust, gravity slowly
winning over the gas pressure, and collapsing into a spinning disk. All stars form in essentially this way,
starting from a cold, dense cloud. Such a stellar nursery must begin cold so that the motions of the gas
particles are somewhat slow and the resulting pressure is low enough for gravity to take hold. Similarly,
the cloud needs to be relatively dense so that the gravitational attraction among particles can be stronger.
A cloud of this nature is called a molecular cloud, because at the low temperatures involved, hydrogen
atoms can combine into hydrogen molecules (H2). Molecular clouds tend to begin with a mass of a few
thousand Msun, and thus several stars usually form together. This fact explains why we see so many star
clusters. Once the larger stars begin to shine (fusing hydrogen in their cores), much of the remaining gas
is blown away by strong stellar winds and radiation pressure, exposing the young cluster to view in visible
light.
It has become one of the most famous images of modern times. The following image, taken with the
Hubble Space Telescope in 1995, shows evaporating gaseous globules (EGGs) emerging from pillars of
molecular hydrogen gas and dust. The giant pillars are light years in length and are so dense that interior
gas contracts gravitationally to form stars. At each pillars’ end, the intense radiation of bright young stars
causes low density material to boil away, leaving stellar nurseries of dense EGGs exposed. The Eagle
Nebula, associated with the open star cluster M16, lies about 7000 light years away. The pillars of
creation were again imaged by the orbiting Chandra X-ray Observatory, and it was found that most EGGS
are not strong emitters of X-rays.
As each little piece of cloud collapses, it forms a protostar, which will not be a star until it becomes hot
enough to begin hydrogen fusion. Conserving angular momentum, the protostar will spin faster as it
contracts, and form a protoplanetary disk in which its own planets might form. Many also produce jets of
high-speed gas that stream out in tight beams along the protostar’s rotation axis. The process that
creates these jets is not well understood, though. Until fusion kicks in, material from the cloud continues
to fall onto the protostar, increasing its mass. Once fusion begins, though, gravitational collapse slows to
a stop, as the star’s interior comes to a stable balance, with the energy produced in the core matched by
that radiated from the surface.
The Fate of Low-Mass Stars
Low-mass stars are those with masses of about 8 Msun or less. Their main sequence lifetimes – about
90% of a star’s entire lifespan – go essentially just like the sun’s, fusing hydrogen via the proton-proton
chain (for those of ~2 Msun or less). It’s once the hydrogen fuel runs out that things get interesting.
The Red Giant Phase
Without fuel for the nuclear reactions, the core can no longer produce enough pressure to counteract
gravity, and it begins to collapse. In the process, it heats up, as do the surrounding layers. Soon, the layer
of fresh, unused hydrogen immediately outside the original core heats up enough to begin fusion
(hydrogen shell fusion, because that layer is like a shell around the core). The temperature is high
enough that the reactions go at a much faster rate than during the star’s main sequence lifetime, and thus
put out a lot more energy. The result is more heat being added to the outer layers, and those layers
expand and cool in reaction. In brief, the exhaustion of the core’s hydrogen fuel leads to a core collapse
that heats the next layer of hydrogen enough to fuse, which in turn heats the outer layers of the star and
causes them to get big and cool off. The cooler gas looks redder, earning such stars the designation red
giants.
This process will continue, shrinking the core and expanding the outer layers, until the core gets hot
enough (100 million K) to start helium fusion. However, the density of the core is so high, the gas doesn’t
act like it would under more normal conditions (because it is in a state known as electron degeneracy see below). It acts more like a solid than a gas, so that the rising temperature does not make the
degenerate core expand in response. So as the helium fusion reactions produce more energy, the gas
continues to heat up and increase the reaction rate in a vicious cycle. This runaway reaction is known as
the helium flash.
The helium flash dumps so much energy into the core in such a short time that the gas becomes nondegenerate, and the core expands again. All this energy pushes the hydrogen shell outward, expanding
and cooling it as well. The outer layers cool and contract, leaving the photosphere slightly warmer than in
the red giant phase. Nearly at the end of its life, the star is now fusing helium in its core, and hydrogen in
a shell just outside that. On the H-R diagram, this star will track to the left, maintaining the same
luminosity, but having a hotter surface temperature. At this stage, the star is known as a horizontal branch
star.
End State
Just as hydrogen fusion produces helium, helium fusion creates carbon. When the helium in the heliumfusing core runs out, the same set of processes as before will begin. The core collapses, heating a shell
of helium that begins fusing, and a shell of hydrogen outside the helium shell. Without core fusion, the
core and shells contract and heat up, pouring energy into the outer layers and causing them to expand.
However, another round of fusion never begins in the core. Although the core will continue to heat as it
collapses under the crush of gravity, degeneracy pressure (again, see below) will stop the infall before
temperatures rise to the approximately 600 million K necessary to begin carbon fusion.
With the energy released from double-shell fusion and the vast size of the star’s outer layers making the
core’s gravitational hold on them weaker, the star begins to puff off its upper portions with its own stellar
wind. The end result is a bare core with a spherical (or roughly spherical) cloud of gas and dust around it.
Such a cloud is known as a planetary nebula because its disk-like shape through a telescope.
What of the core, though? Without fusion to balance the inward pull of gravity, what keeps it from
collapsing completely? The answer is a phenomenon called electron degeneracy pressure. When
electrons get packed together tightly enough, a quantum mechanical effect causes them to gain
momentum (essentially, to move faster). Although this motion produces pressure, the amount of pressure
has nothing to do with the temperature of the degenerate material, which is why a low-mass star suffers a
helium flash (above). In the end, then, a low-mass star leaves its hot, electron degenerate core exposed
to space. The slowly cooling ember is then known as a white dwarf.
The Fate of High-Mass Stars
Some of the processes that a low-mass star experiences also occur in high-mass stars. However, there
are some key differences.
Supergiants and Heavy Elements
All main sequence stars fuse hydrogen into helium in their cores. Stars with masses greater than about 2
Msun, however, undergo fusion via a process called the CNO cycle (named for the carbon, nitrogen, and
oxygen that are involved as catalysts). The CNO cycle is much more efficient than the proton-proton
chain, which explains the faster use of fuel (shorter lifetimes) and greater energy output (higher
luminosities) of high-mass stars. Once core hydrogen is depleted in a high-mass star, the same core
collapse and exterior expansion that we saw in low-mass stars begins. Being so large and bright to begin
with, it expands into a supergiant. There is no helium flash because the star’s higher gravity increases
the core temperature enough to begin helium fusion before degeneracy sets in.
The biggest difference happens when the core helium is gone. Stars greater than about 8 Msun are
massive enough that their cores reach the temperature necessary to begin carbon fusion. In fact, such
stars will continue to fuse new nuclear fuels (and add new shells of old-fuel fusion above the new core)
until their interiors are layered like an onion, with iron building up in the core as the final nuclear product.
Iron is a special element. Its nuclear particles are bound together so efficiently that neither any fusion
(combination of nuclei) nor fission (splitting of a nucleus) reaction will extract any energy. Changing an
iron nucleus into something else needs energy to be added. In the core of a massive star, then, a build-up
of iron is a death warrant. No further fusion reactions can produce any energy to counteract gravity, and
in one last, glorious instant, gravity wins.
Going Out with a Bang
Massive stars are the embodiment of the old adage about wanting to “live fast, die young, and leave a
beautiful corpse.” Having used its fuel in only a few tens or hundreds of millions of years, a massive star
that has fused its core into iron nuclei has no chance against the onslaught of gravity. Although electron
degeneracy pressure can briefly support the core, gravity overcomes it and the whole star collapses
catastrophically, in an explosive event called a supernova.
An incredible amount of energy is released in the explosion; a supernova can outshine an entire galaxy
for a few days. The electrons, protons, and neutrons in the core all get compressed so intensely during
implosion that the electrons and protons smash together and form neutrons and neutrinos. Neutrinos fly
out of the core at nearly the speed of light, taking much of the converted gravitational potential energy
with them. The core is left as a huge ball of neutrons (upheld this time by neutron degeneracy pressure)
known as a neutron star, while the blast of outgoing neutrinos drives a shock wave that ejects the star’s
outer layers out into space. We see evidence not only in the supernovae we observe, but also in
the supernova remnants (SNRs) that have been identified throughout the Galaxy. SNRs can be truly
spectacular, and certainly live up to the title of “beautiful corpse.”
Variations on a Theme
For the most part, all stellar lives can be described by the processes outlined above. However, sometimes
variations arise. For example, for the most massive of stars, not even neutron degeneracy pressure is
strong enough to stop the core’s collapse once fusion stops. The implosion then continues, and creates
a black hole.
Another set of unusual circumstances can arise in a close binary system, in which two stars orbit each
other with a relatively small separation. As the more massive member expands into its giant stage, the
outermost layers of its atmosphere can enter the gravitational influence of its companion, in effect
siphoning off the giant and spiraling down onto the companion. A mass exchange process like this can
lead to several interesting phenomena.
Module 04 – The Lives and Death of Stars
The stellar graveyard is populated with truly bizarre objects. Here we explore them in a bit more detail.
White Dwarfs
Basic Characteristics
As we’ve already seen, white dwarfs are the remnants of low-mass stars that have puffed off their outer
layers, and are upheld against their own weight by electron degeneracy pressure. The inert core of a lowmass star, a white dwarf thus is composed primarily of carbon, the “ash” from the helium fusion reactions
at the end of that star’s life.
However, this matter is anything but ordinary. It’s so incredibly dense that only a teaspoon of white dwarf
material would weigh several tons on Earth (leading to the mnemonic phrase, “ten tons per teaspoonful”).
In practical terms, that means that a 1 Msun white dwarf would only be about the size of Earth!
Another peculiarity of a white dwarf is that adding more mass actually makes it smaller. Unlike, say, a
cake – in which more mass means a bigger cake – adding material to a white dwarf increases the inward
gravitational pressure and compresses the dead star further. The particles need to be packed more tightly
together to provide the counter-pressure required to hold up the white dwarf.
If enough matter gets piled onto a white dwarf, then eventually, just like in the collapsing core of a
massive star, the degenerate electron pressure will not be sufficient to bear its own weight. Calculations
show that the greatest mass that can be supported is 1.4 Msun. This upper limit on the size of a white
dwarf is called the white dwarf limit (known among astronomers as the Chandrasekhar limit, after the
man who first calculated it).
White Dwarfs in Binaries
When a white dwarf is part of a binary system in which there is mass exchange (see previous lecture
page), some unusual phenomena can occur. As material spirals onto the white dwarf, conservation of
angular momentum causes it to spin faster and flatten out, forming an accretion disk. Hydrogen from the
companion’s atmosphere gradually forms a layer on the surface of the white dwarf, compressed to high
density and heated by its gravity. When the temperature at the bottom of this hydrogen layer reaches 10
million K, hydrogen fusion ignites, causing a few-week-long flash of thermonuclear activity.
This nova blows off the majority of the material that has accreted onto the white dwarf and creates a nova
remnant. After the explosion dies down, accretion from the companion continues, and the process begins
again.
Sometimes matter accretes onto a white dwarf that is near the white dwarf limit, and adds enough mass
to take it over the limit. In such a case, the temperature inside the white dwarf finally rises enough to start
carbon fusion. Fusion races through the white dwarf in an instant, and without any upper layers to
counteract the sudden output of energy, it destroys itself in an explosion called a white dwarf
supernova (as opposed to a massive star supernova, discussed earlier). White dwarf supernovae are
actually extremely useful to astronomers, because they can be used as “standard candles” (they are all
essentially the same brightness, because they result from the explosion of a 1.4 Msun white dwarf) for
determining distances.
Neutron Stars
Basic Characteristics
Formed in a massive star supernova, a neutron star is another strange breed of stellar corpse. Made up
entirely of neutrons, and held up by neutron degeneracy pressure (which has the same fundamental
quantum mechanical basis as electron degeneracy pressure, except with a different kind of particle), a
neutron star is much like an enormous atomic nucleus. Its density is even more incredible than a white
dwarf’s. The same 1 Msun that was squeezed down to the size of the Earth to make a white dwarf would
all have to be in a sphere about the size of a city to be a neutron star. As you might guess, a neutron star
also has an upper limit on its mass. Current calculations show that neutron degeneracy pressure could no
longer support an object with a mass somewhere between 2 and 3 Msun.
Neutron stars can also be found in binary systems, and experience analogous conditions. When matter
forms an accretion disk around a neutron star, though, it has much farther to fall to reach the surface
(remember how much smaller a neutron star is than a white dwarf). As a result, it gets heated to
extremely high temperatures, and emits X-rays (leading to the term X-ray binaries). The infalling matter
apparently adds angular momentum to the neutron star, causing it to spin faster and faster as long as
material continues to accrete. Unlike a white dwarf binary, hydrogen fusion on the surface of the neutron
star is stable. A disruption comparable to a nova happens when helium fusion ignites. An extra burst of Xrays is produced for a period of hours or days before the X-ray burster settles back down.
Pulsars
One of the things that changes during a core’s collapse to a neutron star is that its rotation speeds up
(conservation of angular momentum again) and its magnetic field gets stronger (as the field lines are
compressed). Although the mechanism is not yet well understood, a neutron star can sometimes beam
radiation out along its magnetic poles. When the magnetic poles and rotation axis are offset, the result is
a lighthouse-like beam spinning through space. If one of these beams crosses our line of sight, we can
thus see a sort of pulse every time it sweeps past.
An object we see producing such regular pulses is called a pulsar, and can have a period anywhere from
a few seconds down to a few milliseconds. As some of its energy is beamed away, a pulsar will slow
down over time, until the beam becomes so weak it is no longer detectable. Adding this fact to the
random orientation of pulsar beams – that is, some of them will not cross our line of sight – we recognize
that although all pulsars are neutron stars, not every neutron star is a pulsar.
Black Holes
The Event Horizon and Singularity
The last member of our menagerie of stellar remnants is the oddity known as a black hole. When even
neutron degeneracy pressure is not enough to support a collapsing core’s weight, no force we know can
stop it. It collapses into a point of infinite density and zero radius known as a singularity. Our current
understanding of physics breaks down in the extreme conditions of a singularity, making it another as-yet
unsolved mystery.
Outside the singularity, though, we understand a bit better. Recall from Module 02 that the escape
velocity of an object depends on the distance from which an orbiting object tries to break away (as well as
on the mass of the object being orbited). In the case of a black hole, its mass is so concentrated that
there is a distance from the singularity at which the escape velocity exceeds the speed of light. Since the
speed of light is the universe’s ultimate speed limit, nothing – not even light itself – can escape from the
gravity of a black hole inside this distance. The sphere at which escape velocity equals the speed of light
is called the event horizon, and its radius (the Schwartzschild radius) depends on the black hole’s mass.
Any object has a Schwartzschild radius (yours is about the size of an atom); the reason a collapsed
stellar core can be a black hole and you cannot is that all the mass of an object must be inside the
Schwartzschild radius for such extreme conditions to arise.
Misconceptions
Contrary to popular belief, black holes do not act like huge cosmic vacuum cleaners, sucking up
everything nearby. At most distances, objects would simply orbit a black hole as if it were any other object
with the same mass. Only within about three times the Schwartzschild radius does gravity get strange
and act differently than Newton’s laws predict.
For example, a 10 Msun black hole has a Schwartzschild radius of around 30 km. Thus, you’d have to get
closer than about 90 km (less than the distance between Chicago and Milwaukee or between San
Francisco and Sacramento or between New York and Philadelphia) in order to experience any unusual
effects. Cosmically speaking, that’s an awfully small target to hit accidentally.
M4 cp
– Measuring and Classifying Stars
The Hertzsprung-Russell diagram is an important tool in the classification of stars and the
understanding stellar evolution. The H-R diagram was discovered independently by two astronomers
in early 20th century using observations of star luminosity and surface temperature. With this lab
exercise, you will use Stellarium to collect stellar information and then form your own H-R diagram
and see if you can find how stars are group into different luminosity classes.
For this project piece, use a computer simulation to measure the characteristics of a sample of stars
and then organize your data into a Hertzspung-Russel diagram. Please read through the assignment
background information and follow the steps listed in the lab assignment instructions. You will be
asked to form a hypothesis, state the lab objective, record your measurements and calculations, and
answer each of the lab questions.
Click here to download the instruction document for this piece of the project. Follow the instructions
contained within and submit your results as this project deliverable.
Submit your paper with a title page and in APA format.