1446 Introductory Astronomy II

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1446 Introductory Astronomy II

• Chapter 11
• The Nature of Stars
• R. S. Rubins
  Fall, 2009

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The Lives of Stars 1

• Birth they are created from interstellar gas
  clouds.
• Life they shine from millions to hundreds of
  billions of years with the energy created by
  thermonuclear fusion.
• Death they die spectacularly, by one of several
  methods, which, for an isolated star, depends
  only on its mass.
• After the Sun, the nearest star to us (after the
  Sun) is Proxima Centauri, which is about 25
  trillion miles (4 ly) away, so that its light
  about 4 years to reach us.
• In all its stages, the life of a star is a battle
  between the inward pressure of gravity, which
  tends to collapse the star, and the net outward
  thermal pressure, which tends to expand the star.
• (Heating the air in a balloon causes it to
  expand.)

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The Lives of Stars 2

• Gravity is always present, but throughout its
  life, the star must continually replenish its
  thermal energy to prevent collapse.
• Both nuclear fusion, in which matter is converted
  to energy, and gravitational collapse, in which
  potential energy is lost, produce thermal energy.
• Ultimately, gravity secures at least a partial
  victory.
• Except for the most massive stars, which end
  their lives as black holes, gravitational
  collapse is ultimately stopped by a quantum
  mechanical effect, known as degeneracy pressure.
• The outcome for an isolated star depends on its
  birth mass.

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Total Luminosity

• The total luminosity L of a star is the total
  energy per second that it radiates into space.
• L depends only on its surface temperature T and
  radius R, and is given by
• L ? T4R2.
• The visual luminosity is the visible energy per
  second radiated into space.
• The apparent brightness is the visible energy per
  second which crosses unit area of a surface
  perpendicular to the light flow
• The variation of brightness with distance in
  space is given by
• apparent brightness ? 1/(distance)2.
• This is an example of an inverse-square law.
  

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Inverse Square Law
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Apparent Magnitude

• In the magnitude system, introduced by the Greek
  astronomer Hipparcos (2nd Century BCE), the
  brightest stars were given magnitude 1, the
  next brightest magnitude 2, and so on.
• In the modern system, the apparent magnitude m is
  a measure of the visual brightness of objects as
  measured from the Earth.
• Very bright objects have negative magnitudes
• e.g. MSun 26.7 , Mfull moon 12.5.
• Very dim objects have positive magnitudes
• e.g. MPluto 15 , Munaided-eye limit
  6.

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Apparent Magnitude Scale
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Absolute Magnitude

• The absolute magnitude M is a means of comparing
  the true brightnesses (or visual luminosities)
  of stars.
• This is done by calculating the apparent
  magnitude it would have if it were at a
  designated distance of 10 pc (parsec).
• Calculation of M, knowing m and the distance d.
• M m 5 log (d/10),
• where d is in pc, and log(10n) n.
• Example Find the absolute magnitude of star at a
  distance of
• 1000 pc, with an apparent
  magnitude of m 5.
• Solution
• M 5 5 log(1000/10) 5 5 log(102)
  5 (5x2) 5.

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H-R Diagram 1

• The two basic properties needed to characterize
  stars are
• i. the surface temperature T,
• ii. the luminosity L or the absolute
  magnitude M.
• In an H-R diagram,
• M or log L
• is plotted against
• T or the spectral type.
• Notes
• T increases from right to left (the left side is
  hotter).
• The spectral type is symbolized as follows by the
  letters
• O (hottest), B, A, F, G, K, M (coldest).

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Spectral Classes

• Major classification
• O B A F G
  K M
• oh be a fierce giraffe
  kick me
• hottest
  coolest
• Minor classification
• 0 1 2 3 4 5 6
  7 8 9
• hottest
  coolest
• A5 is hotter than G2.
• A3 is hotter than A6.
• B5 is hotter than A5.

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Annie Cannon and Spectral Type

• In the 1880s, Edward Pickering used female
  students to analyze star data at Harvard College,
  classifying 10,000 stellar spectra were
  classified with the letters A to O, based on the
  relative strengths of their H spectra, which he
  incorrectly assumed was proportional to the
  surface temperature of the star.
• The confused situation was sorted out by
  Annie Cannon, 20 years before Bohrs theory of
  the H atom gave a theoretical connection between
  spectral intensities and temperature.
• Reducing the number of letters to 7, she
  reorganized the scheme into its present form, and
  classified over 400,000 stars.
• She became the first woman to be awarded an
  honorary degree by Oxford University in England.

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Stellar Spectra 1
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Stellar Spectra 2
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H-R Diagram 2

• Satellite data are shown for almost 41,500 nearby
  stars.
• The thickness is due to the presence of star
  clusters of widely different ages.

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H-R Diagram 3
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H-R Diagram 4
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H-R Diagram 5
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Relative Sizes of Stars 1
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Relative Sizes of Stars 2
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Radii of Stars 1
1000 RSun
100 RSun
10 RSun
RSun
0.1 RSun
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Radii of Stars 2

• Luminosity L ? R2T4.
• White dwarfs are found in the lower left of the
  diagram. Since they are hot and have low
  luminosities, they must be very small.
• Their radii are about 0.01 RSun.
• Red giants and red supergiants lie mainly at the
  upper right of the diagram. Since they are cool
  and have high luminosities, they must be
  extremely large.
• Red giants have radii in the range 10 RSun to
  100 RSun.
• Red supergiants have radii from 100 RSun to
  1,000 RSun.
• Main sequence stars lie on a diagonal line from
  lower right(radius 0.1 RSun) to the upper left
  (radius 10 RSun).

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Luminosity Classes

• The Sun is a G2 V star.
• Aldeberan, a red giant, is a K5 III star.
• Regulus, a hot blue main sequence star, is a B7 V
  star.
• Betelgeuse, a red supergiant, is an M2 Ia star.

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Binary Stars Mass Measurement

• True binary stars are pairs of stars that orbit
  each other about their center of mass.
• About 1/2 of the objects in the night sky which
  appear to us as single stars, are actually binary
  stars.

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Binary System Kruger 60
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Large Separation Binary Stars

• While only a few low-mass binary star systems
  have been found with separations greater than 50
  AU, two such sets with separations of 1800 AU and
  5100 AU were discovered in 2007, with the latter
  pair taking about 500,000 years to complete one
  orbit.
• On a human scale, it would be equivalent to two
  baseballs orbiting each other at a distance of
  200 miles (which could only occur if there were
  no other matter in their neighborhood).

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Measurement of Mass

• There is no direct method of determining the mass
  of an isolated star, other than the Sun, the mass
  of which may be found from planetary motion.
• Newtons generalization of Keplers 3rd Law
  applied to a binary system gives
• Star masses of between about 0.1 MSun and 100
  MSun are normally found, although a star of mass
  120 MSun has recently been measured.

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Log (Luminosity) vs. Log (Main-Sequence Mass)

• The life of a star depends only on its birth
  mass, and hence on its main-sequence position on
  the H-R diagram.

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Main Sequence Masses (in solar masses)
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A Receding Spectroscopic Doublet
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Light Curves of Partially Eclipsing Binaries
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Light Curves of Totally Eclipsing Binaries