PHY3 Astrophysics

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PHY3 - Astrophysics

• Lesson 3
• Hertzsprung-Russell diagram, Ceiphid variables

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Hertzsprung-Russell Diagram

• Astronomers looked for correlations between
  stellar properties.
• Make plots of one intrinsic property vs. another
  intrinsic property.
• An intrinsic property is one that does not depend
  on the distance the star is from the Earth (e.g.,
  temperature, mass, diameter, composition, and
  luminosity).
• By the beginning of the 20th century, astronomers
  understood how to measure these intrinsic
  properties.

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Hertzsprung-Russell Diagram

• In 1912, two astronomers, Ejnar Hertzsprung
  (1873-1967) and Henry Norris Russell (1877-1957),
  independently found a surprising correlation
  between temperature (colour) and luminosity
  (absolute magnitude) for 90 of the stars.
• These stars lie along a narrow diagonal band in
  the diagram called the main sequence.
• This plot of luminosity vs. temperature is called
  the Hertzsprung-Russell diagram or just H-R
  diagram for short.

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• This H-R diagram has plotted luminosity in units
  of the Suns luminosity (Lsun 3.9 x 1026 W).
• Note that more luminous stars are also more
  massive.

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Mass and luminosity

• Luminosity is roughly proportional to mass raised
  to the power of 3.5.

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Life on the Main Sequence

• Stars on the Main Sequence are burning hydrogen
  into helium within their cores. Eventually they
  run out of fuel and die. As they die they leave
  the Main Sequence.
• The Sun has enough fuel to live on the Main
  Sequence for 10 Billion years. Stars with greater
  mass have more fuel to burn, but they also have
  much higher luminosities.
• A star with twice the mass of the Sun has a
  luminosity which is 16 times greater than the
  Sun. So despite having twice the mass to fuse it
  will use it up 16 times faster than the Sun. It's
  lifetime will therefore be 2/16 1/8th that of
  the Sun Just over a Billion years.

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Life on the Main Sequence

• More massive stars live even shorter lives. A
  star with a mass 30 times the Sun's would live on
  the Main Sequence for only a few million years.
  This is a very short time in a Cosmic sense.
• Stars with very low mass have such low
  luminosities that they may live for 10s - 100s of
  billions of years on the Main Sequence.

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• The other 10 of the stars in the H-R diagram do
  not follow the relationship.

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• The giant and supergiant stars are in the upper
  right of the diagram.
• These stars must be large in diameter because
  they are very luminous even though they are cool.
  They have a huge surface area over which to
  radiate their energy.
• The white dwarfs are at the opposite end in the
  lower left of the diagram.
• They must be very small in diameter (only about
  the diameter of the Earth) because even though
  they are hot, they are intrinsically dim. They
  have a small surface area and so the sum of the
  total radiated energy is small.

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Colour and magnitude

• The H-R diagram is also called a colour-magnitude
  diagram because the absolute magnitude is usually
  plotted vs. the colour.
• Magnitude is another way of measuring brightness
  and originated with the ancient Greeks.
• Bright stars are magnitude 1 and the dimmest
  stars which could be seen with naked eye are
  magnitude 6.
• The Sun has a magnitude of 26.7!
• Obviously this apparent magnitude does not tell
  us how bright the star is as it does not take
  into account how far away it is.
• Astronomers define the absolute magnitude of a
  star as the apparent magnitude it would have if
  it were a distance of 10 parsec from Earth.
• The absolute magnitude of stars range from 10 to
  15.

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Colour and magnitude

• Astronomers have also been classifying stars by
  their spectral type (i.e. the colour of light
  they emit).
• In effect this is using ?max to classify stars by
  their temperatures T.

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Colour and magnitude

• Seven classes are recognised today.
• OBAFGKM when ranked in order of decreasing
  temperature.
• Oh Be A Fine Girl Kiss Me!

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Measuring great distances

• The H-R diagram can be used to find the distance
  to distant stars.
• Measure the temperature using Wiens Law.
• Use the H-R diagram to predict luminosity L.
• Measure the intensity I of the star.
• Use to calculate the
  distance D.

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Cepheid variables

• Henrietta Leavitt (in 1912) discovered how
  brightness of some stars could be used to
  calculate their distances.
• The brightness of these stars rise and fall in a
  regular way with periods ranging from hours to
  weeks.
• Some Cepheid variables are close enough for
  distances to be measured by parallax. Leavitt
  calculated the absolute magnitude of these stars
  and discovered a relationship between absolute
  magnitude (luminosity) and its period.
• Astronomers now use this relationship to
  calculate distances of Cepheid variables which
  are too far away to have any detectable parallax.
  This has been crucial in determining the scale,
  structure and age of the Universe.