In the
astronomical case we use the motion
of the Earth around the Sun to get our two views. A nearby star will appear to
move a larger angle in the sky than a distant star.Main themes of this section will be
There are a number of ways of measuring the distance to a star. We will only deal with one method: "Parallax", which is the most basic.
The idea behind parallax is that if you look at objects at different distances from two different places then your view is slightly different. If you change your point of view nearby things move more than distant things.
You can demonstrate this with your fingers
In the
astronomical case we use the motion
of the Earth around the Sun to get our two views. A nearby star will appear to
move a larger angle in the sky than a distant star.
The angles involved are very small: a fraction of a second of arc
Distances in astronomy are usually measured in "parsecs".
1 parsec = 3 x 1018 cm, or 3.26 light years..
Typical star separations are of order 1 pc.
Nearest star is a Centauri, 4.3 ly, 1.3 pc.
We
see the Milky Way as a band of light in the sky.
Closer
inspection shows it to be made up of lots of individual stars
Tully movie (80 Megabytes quicktime); Tully Movie (27 megabytes mpg)
Galaxy contains clusters of stars, and nebulas
There is diffuse interstellar matter between all the stars, plus dense concentrations of gas (sometimes called nebulae) in certain places. These dense clouds are sometimes places where new stars are being formed. Interstellar matter consists of a mixture of gas (mainly hydrogen) and dust grains, which may be made from ice crystals, or minerals.
Because
of dust extinction it is not obvious where the center of the galaxy is just by
looking at it: We get a much better impression when we look at infrared images
which are much less affected by dust.
The
Milky Way is actually a disk galaxy. We are located about 8500 parsecs (25000
light years) light years from the center in the disk of the galaxy. We do not
have an accurate map of the Galaxy, but guess that it would look like the
following galaxies if viewed from outside
The galaxy is held together entirely by gravity. Each star orbits around the center of the galaxy.
Stars in the disk all move in the same direction. Stars in the halo have
randomly oriented orbits.
The
Sun moves at about 220 km/sec
around the center.
This give is a period of about 240 million years for one orbit.( back to the
dinosaur age)
Stars at different distances from the center of the galaxy move at different
speeds. This process is called differential
rotation. It leads to mixing up of stars.
Since we know the period and the size of the Sun's orbit around the center of the galaxy we can use Newton's law of gravity to determine the mass of the Milky Way.
There are about 1011 solar masses with the radius of the Sun, plus some more outside. most of this is stars: about 10% is interstellar matter. Since the average mass of a star is about 0.5 solar masses, there must be about 2 x 1011 stars in our Galaxy. We can only see a small fraction of them because of extinction
With very few exceptions we do not see details of stars. They are not star-shaped; we assume they are round like the Sun.
Many of the properties of the stars we can determine in ways similar to that we used to understand the Sun:
Distance comes from parallax for nearby stars, and extensions of the parallax principle for more distant ones
Luminosity: comes from knowing a star's brightness and distance, then applying the inverse square law of illumination. We usually measure luminosity by comparing a star with the Sun. There is an enormous range in the luminosities of stars, from million of times brighter to thousands of times fainter. There are many more faint ones than luminous ones.
Temperature of photospheres comes from using Wien's Law - in other words measuring the color of the star. There is a second method that examines the spectra of stars, and classifies them into spectral types, such as types O, B, A, F, G K M etc. This is discussed in the book, but we are going to drop this part of the course. Temperatures range from around 2000 K to around 100,000K.
Composition of stars comes from analyzing lines in their spectra. Most stars are like the Sun in being dominated by hydrogen and helium, but the amount of the "trace" elements varies.
Masses of stars.
The only reliable way to measure the mass of a star is to measure the gravitational force it produces. To measure the gravitational force you need to watch how something moves when it is close to the star. In principle we could do this by watching planets around the star, but in practice planets are usually too faint to be seen. We therefore study binary stars, where we have two stars orbiting around each other. Strictly speaking they are orbiting around their center of mass.
There are several types of binary star, depending on what we can actually measure.
When we actually see the stars moving around each other it is called a visual
binary. An example is the star Sirius,
which has a faint white dwarf companion. They take about 50 years to orbit each
other.
By studying the period and the size of the orbit it is possible to get the mass of the stars using Newton's law of gravity. Sometimes one of the stars is too faint to be seen, and one apparently sees one star orbiting about "nothing" , similar to the method used to measure the mass of a planet.. In these cases we can get some, but not all, of the information about the masses of the stars.
Many binaries are so far away that we cannot separate the stars with a
telescope, or directly measure the motions. In these cases we make use of the
Doppler shift of the spectral lines of the stars. This is called a spectroscopic
binary star. Depending on the relative brightness of the stars we may see
either one line or two lines showing.
In a few cases the spectroscopic binaries may be orbiting in such a way that
one star moves in front of the other, as in an eclipse. This is an eclipsing
binary. Eclipsing binaries are rare but they are very useful in that they
can give us information about the sizes of stars and even about their
shapes, sometimes.
Once we have measured a number of stars we can look for patterns connecting
the mass with other properties of the star. The most important result is that
for the majority of stars there is a simple law connecting them:
L=M3.5
For historical reasons, stars which follow this relationship are called Main Sequence Stars. They are all stars which are in the process of converting hydrogen to helium.
When we investigate them some more we find that
However we must note that not all stars lie on the Main Sequence, and we will later meet stars called "Red Giants" and "White Dwarfs" which do not obey the mass-luminosity law given above.
Astronomers often plot the temperature against luminosity in what is called an H-R diagram, which stands for "Hertzsprung-Russell" diagram
Where L is the luminosity of the star and M is its mass, both in terms of the
Sun. This means we can add one more result to our understanding of the main
sequence, namely that the hot, bright, large stars (top left) are more
massive than the faint, cool small ones. The range in main sequence masses is
about 0.2 - 60 times the mass of the Sun
00.21
Much of our understanding of stars comes from making computer models of how a large mass of gas of typical composition behaves under gravity. It is found that all the main sequence stars are turning hydrogen into helium in their cores. The mass is what determines where on the main sequence a star is. Once a star of a given mass starts it will stay more or less at the same place on the main sequence for a long time. The luminosity and temperature of the star do not change much as the fraction of helium in the core increases.
96:20
Eventually, however, there will be a shortage of fresh hydrogen in the core of the star. For the Sun this is about 10 billion years. For other stars we can make use of the fact that the mass of a star is a measure of the total amount of "fuel" it has, while the luminosity is a measure of the rate at which the star is consuming fuel.
The lifetime is therefore proportional to Mass/Luminosity.
The high mass stars therefore have the shortest lifetimes
In a star like the Sun hydrogen fusion lasts for 10 billion years. The Sun stays on the main sequence during this time, but it slowly increases in size and luminosity over that time. The change is so slow that life on Earth is not affected by these changes.
In about 5.5 billion years or so, so much helium "ash" that no more hydrogen burning can take place. The center collapses and gets hotter, and helium now starts to be converted by another nuclear reaction to make carbon.
This reaction takes place very quickly, giving off a lot of energy, so that
the luminosity of the Sun increases comparatively rapidly. The extra heat causes
the Sun to expand to a much larger radius. It becomes a red
giant star
The Sun would engulf Mercury and look enormous in the sky. The temperature of the Earth would get so high that life would certainly be extinguished.
Red giant stars tend to have strong stellar winds, blowing gas back into the
interstellar medium, Mass loss is a major feature of the late stages of stars'
lives.
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Some stars in these late stages of their lives become
variable.
The balance between pressure and gravity is no longer stable, and they grow and
shrink with periods ranging from days to many years. As the stars grow and
shrink they change their surface temperatures so move around on the H-R diagram.
A medium mass star ends its life by ejecting a large fraction of itself into space to form a planetary nebula.
These have nothing whatever to do with planets: the name comes because some
of the first to be found in the 19th century looked a bit like images
of Uranus. Modern photos show much more detail.
HST images of planetary nebulae
The star that is left behind is essentially the core of the red giant star that made the nebula. It is therefore small and hot, and in a totally different part of the H-R diagram..
The central star of a planetary nebula is so hot it gives off lots of ultraviolet radiation that ionizes the gas around it. The gas is heated to about 10,000 K by the ultraviolet radiation from the central star.
The gas has an emission line spectrum
Eventually the gas drifts away from the star to form part of the interstellar medium, to form new stars.
The central star of a planetary nebula has some very unusual properties. It is called a white dwarf.
White dwarf stars have masses like that of the Sun, but
sizes
like that of the Earth. Their density is equivalent to about one ton per
teaspoonful. The surface gravity is about 100,000 times that of Earth, It would
take as much energy to climb four inches high on a white dwarf as to climb Mount
Everest on earth.
The matter in a white dwarf is not like ordinary matter (solids, liquids,
gases) at all. There is no pressure in the normal sense. The star is held up by
something called degeneracy pressure, which is something you can only understand
from quantum mechanics.
White dwarfs do not do anything. They shine energy into space, but have no way of replacing it. So they slowly cool down; their color becomes redder and they eventually become a "black dwarf" and too difficult to detect. This takes billions of years. The galaxy is probably full of black dwarfs that we have almost no chance of detecting.
High mass stars have the most interesting deaths.
In high mass stars things do not stop with the formation of carbon. Other thermonuclear reactions can take place to make even more complicated atoms.
Among the important reactions are carbon turning into oxygen and oxygen turning into silicon. These reactions take place much more quickly the larger the atoms.
Many of the most common elements heavier than hydrogen and helium are formed this way. The insides of high mass supergiant stars are the only places we know of in the Universe where these atoms can be made in substantial quantities.
Later in this course we will learn that when the Universe was formed it first contained only hydrogen. Helium was formed in the first few minutes of the Universe, but only a negligible quantity of any other element.
The carbon that our bodies are made out of and the oxygen that we breathe were all made inside stars that existed before the solar system was formed. These atoms were blown out into space from the stars, and collected to make a new cloud that formed the solar system.
But you can't make all elements this way. Thermonuclear fusion can only take place if the total mass of the new elements that are formed are less than the total mass of the elements forming them. If this is so then energy can be released.
When you examine the physical properties of nuclei you find that you can make all the elements up to number 26 (iron) in this way, but to make anything with a higher atomic number you need to supply energy, which is very hard to do, as the energy has to be made available under very intense conditions.
As far as we know, the only way to make these elements is in a supernova, so we will take a look at what a supernova is.
There is a curious relationship between the radius and the mass of a white
dwarf star. The more mass it has the smaller it is. When it gets to a mass of
1.4 solar masses the white dwarf has a zero radius, which effectively says that
it can't be a white dwarf anymore. This limit is called the Chandrasekhar
limit. If the core of a star tries to form a white dwarf with
a mass greater than this limit it keeps on collapsing to ever smaller size
giving off enormous amounts of energy. Because of Newton's law of gravitation,
the smaller something gets the more energy it gives out.
The collapse of the core of a high mass star gives rise to a supernova.,
which is an extremely powerful explosion of a star when its core collapses. The
star brightens by millions of times in a few hours, with no warning to
astronomers. This only happens in our galaxy a few times a century, and usually
in a place where we cannot see it. There was one in the Magellanic Clouds (the
nearest small galaxy to the Milky Way galaxy) in 1987.the light from a supernova
fades over a period of a year or
so.
Three major things happen in a supernova:
the outer layers of the star get blown out into space to form the nebula.
The Crab Nebula (right) is one of the most famous
of these. It is the result of a supernova explosion that was seen by Chinese
astronomers in the year 1054. It is slowly expanding and gives off powerful
radio waves and X-rays as well as light. The gas spreads out into space and
eventually fades away. Other examples:
Tycho's
remnant, Neutron stars are much smaller than white dwarfs. A
typical
neutron star is 10 - 15 km (6 - 10 miles) across, with the mass of several
times that of the Sun. The density is 108 tons per cubic centimeter.
The material of a neutron star is similar to the nucleus of an atom. A way of
understanding the neutron star is to think of gravity being so strong as to
collapse the atoms themselves so that their nuclei combine.
They were predicted theoretically in the 1930s, based on calculations using quantum mechanics, but it was originally believed that they were unobservable because they are so small.
But in 1967
pulsars were discovered. These
are sources of a intense radio emission that flash off and on with periods of a
few seconds down to fractions of a second. A small number are also visible
pulsars.
Pulsars flash for the same reason that a lighthouse flashes. The radio waves are produced in a region of magnetic field that surrounds the neutron star. Their fast rotation is another example of the law of conservation of angular momentum. If the sun (which now rotates once a month) collapsed to the size of a neutron star it too would spin in a small fraction of a second.
The ultimate fate of a neutron star is to slow down and fade away
Above about 3 solar masses even neutron stars are unstable. The gravitational force is so strong that no physical force can halt the collapse. (Remember that the closer that objects are the stronger the force). It seems that eventually we get infinite density in zero volume. This is called a singularity. Is this a paradox?
It may be, but in fact we can never see this, because a black hole is formed around the singularity preventing us from seeing it
(Show 35 minute segment of "Cosmos") 05.35
A black hole is a region of space from which light and matter cannot escape,
but they can enter it.. We can understand this in terms of the idea of escape
velocity. We know that the stronger the gravitational field around an object
(such as a planet) the higher the escape velocity. In a black hole the gravity
is so strong that the escape velocity is greater than the speed of light.
If the Sun were to collapse to form a black hole (which it cannot do) it would be a few km across. (The Earth would be 1 cm across). But our motion around the Sun would not be affected: at large distances from the sun Newton's laws still apply.
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03.36
How can we detect a black hole?
There are probably many black holes in the galaxy, but because they are so
dark we can only detect them when they are in a binary system. The star Cygnus
X-1 is the prototype of such a star. There is a visible star called HD226868
whose Doppler
shifts indicate that it is one of a pair of binary stars. Its companion is invisible
but has a mass too high to be a white dwarf or a neutron star. Also, the
companion it too faint to be a main sequence or giant star. So by a process of
elimination it can only be a black hole.
A corroborative piece of information is that the Cyg X-1 system gives off
very powerful X-rays. X-rays are a sign of gas at temperatures of millions of
degrees (Wien's law). The likeliest way of producing this emission is in an
accretion disk around the black hole. The black hole is so close to the other
star that it sucks gas off it, The gas is rotating as it falls and goes into a
disk where it heats up as it falls into the black hole. It is a paradox that
while Black holes themselves are infinitely dark, they can indirectly produce
enormous amounts of
power.
Black holes are also found in the nuclei of distant galaxies, and may be responsible for the most powerful objects in the Universe (Quasars). These pictures show jets emerging from the nucleus of the galaxy M87, where there is a black hole with a mass of 3 billion Suns.
There is also a moderate size black hole in the center of our own galaxy (3 million Suns) . We have to use infrared radiation to study the center of our galaxy because of all the dust in the way. We can estimate its mass by actually watching stars in orbit. The real data are taken about once a year; what you see is an animation of several years motions.
Link to stars orbiting our galactic center
Black holes were predicted from Einstein's theory of relativity. At the end of the nineteenth century it was discovered that the speed of light always is the same, even when emitted from a moving object. Einstein's theory resolves this paradox at the expense of introducing some strange behaviours when objects travel close to the speed of light.
For example, if you look at an object moving very fast, it appears shortened. Also the clocks in a moving object run more slowly. It sounds weird, but these effects can be measured - for example by carrying an atomic clock in a plane around the world.
Near a black hole there are other effects: time at different speeds depending on how strong the gravity is where you are. If you fall into a black hole you will accelerate and then be crushed and disappear. If you watch someone else fall into a black hole, you will see their time run more and more slowly, so that they never actually pass through the surface.
What about worm holes? Astrophysicists are skeptical whether one could move from one place in the Universe to somewhere else, but have not yet proved that it is impossible.
Many stars are members of clusters of hundreds or thousands of stars.
Example of
globular cluster and
open
cluster
We will discuss the differences between these below.
Astronomers assume that when you see a cluster of stars they were all formed at the same time. There are several reasons for believing this:
The stars in a cluster have a wide variety of masses. If they were born at the same time they must be at different evolutionary stages.
We can see this by plotting an HR diagram for all the stars in one particular cluster.
Here is an example of all the stars in the cluster NGC 2264.
HR diagram for NGC2264.
Note that
most of the stars are above the main sequence as predicted for a young cluster,
since they are still young and evolving onto the main sequence. This is a
cluster that is associated with clouds of gas and dust.
HR diagram for an old cluster:
High mass stars have moved off the
main-sequence
This
diagram shows HR diagrams for clusters of different ages. After
a cluster is born, more
or less all at the same time, the high mass stars go through their main sequence
lives more quickly than the low mass stars, so the overall appearance of the HR
diagram for the stars in the cluster changes. Astronomers use the HR
diagrams for clusters of stars to estimate the time since the cluster was
formed. This is one of the very few ways there is of estimating the ages
of stars.
96:24
There are two types of cluster:
Open clusters
The Pleaides or Seven Sisters (right) is a good example of an open cluster.
Globular
Clusters 
The reason for the difference between the two types of cluster is that Globular Clusters were formed when the Galaxy was young, and not many metals had been made inside stars. The open clusters were made more recently, when the interstellar matter is richer in metals.
Final comment:
Just about everything I have said about stellar evolution is in direct contradiction with fundamentalist theories of creation that require an age of 6000 years for the Universe. If the Galaxy is billions of years old we can understand
98:24 00.24
Cygnus Loop
