Download THE LIFE CYCLES OF STARS (3)

BENDIGO U3A 2012
Keith Thompson
THE LIFE CYCLES OF STARS (2) The Main Sequence
Illust Galactic Cluster
In our first talk we looked at the way stars are born out of huge clouds of gas and dust
in the Milky Way.
We saw that they were born as clusters of stars and we looked
at several such clusters.
Each containing up to a few hundred stars.
These form
a local concentration of matter and act as a gravitational centre that holds the group
loosely together. Each star in the cluster will orbit about the common centre of
mass taking many years to do so. The cluster is loosely bound and slowly stars will
escape, wander from the group, and will mingle with the rest of the stars in the
galaxy.
While the cluster exists as a cluster it forms a powerful tool to help us understand how
stars function.
Illust Hayashi Tracks
Notice how the stars form along a line on the Brightness-Temperature diagram.
This line was discovered experimentally from observations of stars well before the
theory of star condensation was worked out, and in fact the end point of the
calculations was made to be this line. How it was discovered is the subject of today's
talk.
We shall need to understand how we measure the brightness of stars, their colour and
distance.
STELLAR MAGNITUDE SYSTEM
The ancient Babylonians 1800 BC put together the first star catalogues. The Greek
Hipparchus (180-125 BC) and later Claudius Ptolemy in Alexandria about 150 AD
classified stars according to their apparent brightness to the eye, dividing them six
into classes of brightness. The brightest stars were called first magnitude, the
somewhat dimmer stars were second magnitude, even dimmer were third magnitude,
down to sixth magnitude which were the faintest stars visible. ( We have to
remember these early astronomers suffered the same eye defects as we have but did
not have corrective spectacles. Consequently they did not often see stars as points of
light. The brighter stars actually appeared bigger. So for “magnitude” read size.
Galileo, when he first used his telescope on the stars, noticed and commented that his
telescope magnified the gaps between the stars more than it magnified the stars
themselves. He was convinced that the sizes of stars were optical illusions. In reality
they were points of light. )
This subjective classification lasted until the 19th century when quantitative
measurements were possible. It was discovered that the brightest stars were about
100 times brighter than the dimmest stars visible by naked eye. It was further
discovered that the classifications differed by a constant ratio of brightness and since
there were 5 classification jumps the ratio was convenient to be 5 100 = 2.511886.
For our purposes about 2½. Thus a 1st magnitude star is 2½. Times brighter than a 2nd
magnitude star which is 2½. Times brighter than a 3rd mag star and so on. In
Bendigo you are not likely to be able to see a 6th mag star due to light pollution. You
would need to be outback away from all lights with no moon and be dark adapted for
½ an hour.
Once the stars were placed on a measurable numerical scale the scale was extended in
three ways
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Extension to brighter and dimmer stars.
Most stars fitted on the scheme but some were extra bright and became 0th magnitude
i.e. brighter that 1st magnitude, or even negative magnitudes, brighter still, and with a
telescope were seen new stars invisible to the naked eye. These would have large
positive magnitudes.
Illust magnitude scale
Here we see the scale extended to –26 the brightness magnitude of the sun and +28
the dimmest expected (when this book was published) for the Hubble space telescope.
It is an unfortunate historical relic from the Greeks that the magnitude scale is upside
down. The brighter the star the less its numerical magnitude.
Extension to Fractional magnitudes
Illust southern cross3
Illust southern cross mags
With care in measurement we can quote magnitudes to a few decimal places . One
decimal place means a precision of 10% two places of decimals means a precision of
1% . With care and training a visual observer can estimate magnitudes to  0.2 of a
magnitude. This is about 20% accuracy.
Extension to colour
When photography was used to record stars it was quickly realized that the early
photographic plates were sensitive to blue light but not to red light. Consequently it
was possible that photographing a bright red star (Betelgeuse) together with a fainter
blue star (Rigel) the blue star would record the brighter on the photographic plate.
This led to a completely new scale called photographic magnitudes
m ph as distinct
from the visual magnitude m v . This opened up the possibility of describing the
colour of a star by its colour index C = m ph - m v Bluish stars would record
brightly on film with a lower magnitude (remember upside down scale) than in the
visual. This made the colour index negative.
Red stars on the other hand would
record poorly on film and appear dimmer with a higher photographic magnitude than
visual. The colour index would be positive. Compare these two stars in the
constellation of Orion. V = magnitude as seen visually (yellow light), B in blue, I in
infra red.
Illust Orion Betelgeuse
SAO 113271 M0
V=0.58 B-V = 1.500 so B= 2.08 (dim in blue)
V-I = 2.32 so I = -1.74 (bright in IR)
Distance 131 pc = 427 LY
Rigel
`
SAO 131907 B8p
V = 0.28 B-V = -0.030 so B=0.25 (bright in blue)
V-I = 0.03 so I = 0.25 (dim in IR)
distance = 237 pc = 772 LY
When instruments were made sensitive enough to record starlight the same
measurements were made with filters.
With a yellow filter in the path the
instrument recorded essentially the visual magnitude, now called just V. With blue
filter in it mimicked the old photographic magnitude now called B.
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B-V could be measured for stars and was a measure of their colour and hence surface
temperature.
The Distances of Stars
The ancient Greeks thought all stars were at the same distance fixed to a huge crystal
sphere just outside the boundaries of the solar system. They could not conceive the
immense distances we now know and partly for this reason they rejected the idea of
the Earth going round the sun (heliocentric theory) because they could detect no
parallactic shift in stellar positions. Later when the heliocentric theory was accepted
it was realized that the stars were at immense but unknown distances.
It was important to know the size of the solar system or the distance the Earth was
from the sun.
This was found first by measuring the parallax of Mars. Then timing the transits of
Venus across the sun's disk in 1761, 1769, 1874 and 1882.
We now know the size
of the solar system by bouncing radar beams off Venus.
By using the radius of the Earth's orbit (150,000,000 km) we can attempt parallax
measures on nearby stars.
This began in the early 1800's with no great accuracy
until the end of 19th century. Here are some measurements of the parallax of Alpha
Centauri, the brighter of the two pointers to the cross.
Alpha Centauri
1832-3
1.14"  0.11"
1839-40
0.913"  0.064"
1860-4
0.880"  0.068"
0.521"  0.066"
1881-2
0.76"  0.013"
1881-3
0.676"  0.027"
The modern accepted value is 0.745"
Despite these difficulties parallaxes were measured and distances calculated. A new
unit of distance was coined.
If a star has a parallax of 1" arc then its distance is 1
Parsec (pc).
If it has a parallax of 0.5" arc its distance is 2 parsecs and so on.
Distance in Parsecs =
1
" arc _ parallax
1 Parsec = 3.26 Light years = 3.086  1013 km
Once it was possible to measure the distances to stars it became possible to correct
their brightness for distance.
Some nearby stars might appear bright only because
they are near; some dim distant stars may be in themselves very bright. What we
needed was a way to correct for the distance to give an "absolute magnitude".
It
was decided that 10 parsecs was the standard distance and the absolute magnitude of a
star is that magnitude it would appear if we could transport it from wherever it is to 10
parsecs away. If M is the absolute magnitude and m the apparent measured
magnitude then there is a simple expression
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Absolute Magnitude
=
M
=
m – 5log 10 (d(pc)/10)
The absolute magnitude of a star is how bright it is intrinsically in itself.
very important thing to know.
This is a
STELLAR SPECTRA
We have all seen sometime a rainbow, which takes the sun's light and splits it into its
various colours.
Illust Fire Rainbow
We can do the same with a prism or other devices.
Illust Fraunhofer spectrum
Fraunhofer found dark lines crossing the sun's spectrum. He was not the first to see
them but was the first to catalogue them. He named them A,B,C,D,……. He did not
know what caused them. These dark lines mean something. We now know each one
is caused by some element in the light source. The dark line in the Yellow is known as
the D Line of Sodium Two lines in the blue/violet are called H and K lines of
Calcium. Other lines are caused by iron and magnesium and all kinds of elements.
With modern instruments we can spread the spectrum out and find many lines .
Each element produces its own unique set of lines; a kind of optical fingerprint.
By knowing which lines are in the spectrum you know which elements are on the star.
In fact Helium was discovered on the sun in this way before known on Earth.
Illust Solar Echelle Spectrum
Here we can see the dark line in the red due to Hydrogen. It is called H  . The D
line of Sodium is revealed here as being two lines close together D 1 and D 2 The H
and K lines of Calcium are deep in the blue./violet.
When people started taking spectra of stars the results were very confusing. There
were so many different spectra. In the early 1900's astronomer E.C.Pickering at
Harvard College set up a system to photograph the spectra of as many stars as
possible and classify them. A weak prism was placed in front of the telescope lens
and this turned every star image into a tiny spectrum.
Illust Objective Prism Spectra
Each little spectrum on the plate needs microscopic examination
Pickering found that ladies were much better at this job than men (and cheaper) and
had an army known as the Harvard Ladies. They tried to classify the spectra into
types.
Illust Harvard Ladies
They started by examining the hydrogen lines only and classifying according to how
strong they were. Thus began a sequence of A, B,C, ….. types.
Nothing of any
sense came out of this until one Annie Jump Cannon rearranged the order and
merged some classifications until she got a smooth transition from one classification
to another.
Illust Annie Jump Cannon
The order when rearranged was OBAFGKM.
This has given rise to certain
mnemonics such as Oh Be A Fine Girl Kiss Me.
Or less sexist and more
Australian, Ordinarily Beetles And Fleas Give Kangaroos Malaria.
Each classification was further subdivided. B type stars were subdivided into B0, B1,
B2,…….B9 before coming to A0, A1, etc
Illust main sequence spectra
These are what the spectra looked like to Annie J.Cannon
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The reason for this order was not known at the time. This classification was
published as The Henry Draper Catalogue which lists for some 300,000 stars their HD
number, stellar coordinates, visual magnitude, photographic magnitude and spectral
type. Henry Draper was a rich financier who paid for this.
Illust main sequence spectra2
This set in colour shows more easily the change in the hydrogen spectra and the
emergence of metal spectra.
The publication of the Henry Draper Catalogue by the Harvard College Observatory.
Placed a huge data bank in the hands of those interested in finding out how stars
work.
Distances for many stars were being found and for those stars in binary system (two
stars gravitationally bound in mutual orbit) stellar masses were found. (This is a
whole new area we might look at another time)
When absolute magnitudes were calculated it became clear that the hot blue O type
stars were the brightest and the most massive, and cool red M type stars the dimmest
and least massive.
In 1905 the Danish astronomer Ejnar Hertzsprung (1873-1967) published a paper
confirming these correlations. He published in tabular form just lists of numerical
data. He was puzzled that some G type stars were brighter than other G type of the
same spectral classification. This is intrinsic brightness corrected for different
distances. Because they were the same G type they would be the same colour index
and the same temperature. Therefore the brighter ones had to be bigger. He called
the brighter stars giants.
In 1913 Henry Norris Russell (1877-1957) independently came to the same
conclusions and published as a graph. He also found G type stars which were bright,
and G types that were much dimmer. He called the dimmer stars dwarfs.
Illust First HR Diagram
This diagram in its modern form has become one of the most fundamental diagrams
for understanding how stars function.
Illust HR diagram
This is a modern HR diagram constructed with data gather by the space telescope
Hipparchos (in memory of Hipparchus the Greek who made the first star catalogue).
Hipparchos obtained accurate photometric data and parallax data.
The main line running diagonally from top left to bottom right is called the main
sequence.
When Hertzsprung and Russell first made the HR diagram. It was believed that all
stars were born as hot blue massive O type stars at the top of the main sequence, and
that as they aged they slowly cooled and move down and that as they aged they
slowly lost mass (somehow) and cooled down. This was later realized to be wrong.
It has however left a linguistic legacy. O and B stars are called "early" and K and M
stars are "late".
B1 and B2 would be called "early B" but B8 and B9 would be
called "late B".
All stars are born on the main sequence somewhere. The massive stars are hot, blue
and bright, the least massive stars are cool, red and dim.
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THE AXES OF THE HR DIAGRAM
These may be labeled in a variety of ways but it is the same diagram.
They are essentially Brightness, (vertical) and spectral type (horizontal).
The horizontal axis may be in spectral type O,B,A,F,G,K,M.
or in temperature
units usually about 35000 K on the left to about 5000 K on the right, or it may be in
the colour index B-V with blue (negative) on the left to red (positive) on the right.
The vertical axis may be in absolute magnitude M v , or in luminosity compared to the
sun (L/L ) on a logarithmic scale, or if you restrict the diagram to stars in one
cluster you may even use apparent magnitude m . The reason for this is that the
difference between absolute magnitude M and apparent magnitude m would be
m – M = 5 Log 10 (d(pc)/10) = constant.
It has the effect of shifting all the points up or down the same amount.
The background to the HR diagram may also be coloured Blue to red (L to R).
WHAT KIND OF STARS ARE WHERE ON THIS DIAGRAM ?
Let us try to imagine how different sorts of stars will fit on this diagram. Let us pick
an average star like our sun. We shall (mentally) keep its size constant but vary its
surface temperature. Suppose we make it a cool star. Then being cool it will
radiate mostly in the red with long wavelength radiation (red hot only) and the total
light output will be small because it is cool. We may therefore place a cool averaged
size star on the right side of the diagram and somewhere below the middle. Now
suppose we keep it the same size but raise its surface temperature until it goes through
“white hot” to “blue hot”. Its colour will be blue so it will be on the left side of the
diagram and its brightness will have increased somewhat above average since it is
blue hot, so it will be above the middle of the left side. We see then that merely
raising the temperature of a star but keeping it the same size moves it across the
diagram leftwards and upwards. This diagonal line is roughly but not precisely the
main sequence.
On the true main sequence the star’s size also increases as we raise
its temperature. The main sequence then also slopes down from left to right due to a
combination of temperature and size changes. We may continue in this way to place
cool small red stars (Red dwarves) in the bottom right corner. Red supergiants will
be in the upper right corner, and very small hot stars (white dwarves) in the bottom
right corner.
The Hertzsprung Russell (HR) diagram is perhaps the most important tool for
describing the state of a star. Once a star is “placed” on the HR diagram it is
generally well categorised. If a star changes its characteristics we can plot its
evolution as a trail across various parts of the diagram. We may place a star by three
measurements. We must measure its apparent brightness (magnitude), and distance
and apply the distance correction to find its intrinsic brightness (absolute magnitude).
We must also measure either its colour (B-V) using photometry, or its spectral type
using a spectrograph.
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