Chapter 19 The Nature of the Stars

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Guiding Questions

• How far away are the stars?
• What evidence do astronomers have that the Sun is
  a typical star?
• What is meant by a first-magnitude or
  second-magnitude star?
• Why are some stars red and others blue?
• What are the stars made of?
• As stars go, is our Sun especially large or
  small?
• What are giant, main-sequence, and white dwarf
  stars?
• How do we know the distances to remote stars?
• How does our Sun evolve?
• How can we find the temperature, power, and size
  of stars from their spectra?

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Careful measurements of the parallaxes of stars
reveal their distances.

• The brightness of a star is not a good indicator
  of distance.
• e.g., Polaris is closer than Betelgeuse but
  Betelgeuse appears brighter.
• Distances to nearby stars can be measured using
  parallax.
• Parallax is the apparent change in the position
  of an object do to a change in observing position.

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Stellar Parallax As Earth moves from one side of
the Sun to the other, a nearby star will seem to
change its position relative to the distant
background stars. d 1 / p d distance to
nearby star in parsecs p parallax angle of that
star in arcseconds
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If a stars distance is known, its Luminosity can
be determined from its brightness.

• A stars luminosity can be determined from its
  apparent brightness if its distance is known.
• L/L? (d/d?)2 x (b/b?)
• Where L? the Suns luminosity

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Luminosity Function As stars go, our Sun is
neither extremely luminous nor extremely dim.
It is somewhat more luminous than most nearby
stars of the 30 stars within 4 pc, only three
have a greater luminosity.
Luminosity of Sun L? 3.86 X 1026 W
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Greater distances can be measured with Cepheid
variables
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Cepheids compress, heat up, and brighten
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Periods reveals Luminosity of Cepheids
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Measure a stars Luminosity -gt find its distance
from its apparent brightness.

• As you get farther and farther away from a star,
  it appears to get dimmer.
• Luminosity, L, doesnt change
• Apparent brightness, b, does change following the
  inverse square law for distance.
• b L / (4pd2)
• Intensity Power/Area

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Astronomers often use the magnitude scale to
denote brightness.

• Historically, the apparent magnitude scale runs
  from 1 (brightest) to 6 (dimmest).
• Today, the apparent magnitude scale extends into
  the negative numbers for really bright objects
  and into the 20s and 30s for really dim objects.
• Absolute magnitude, on the other hand is how
  bright a star would look if it were 10 pc away.

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Astronomers often use the magnitude scale to
denote brightness.
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A stars color depends on its surface temperature.
Wiens law l(m) 3 x 10-3 T(K) The hotter the
object, the shorter the wavelength of its
brightest light
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UBV photometry is the process of systematically
looking at intensity emitted by a star in three
wavelength (color band) regions. U ultraviolet,
B blue, V visual
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The spectra of stars reveal their chemical
compositions as well as surface temperatures.

• In the late 19th Century, Harvard astronomers
  obtained spectra for hundreds of thousands of
  stars.
• Annie Jump Cannon grouped stellar spectra into a
  classification scheme of spectral types A through
  O.

• Today we recognize the spectral types O, B, A, F,
  G, K, and M as running from hottest to coolest.

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The spectra of stars reveal their chemical
compositions as well as surface temperatures.
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The spectra of stars reveal their chemical
compositions as well as surface temperatures.

• O B A F G K M
• hottest to coolest
• bluish to reddish
• Further refined by attaching an integer, for
  example F0, F1, F2, F3 F9 where F1 is hotter
  than F3
• An important sequence to remember
• Our Best Astronomers Feel Good Knowing More
• Oh Boy, An F Grade Kills Me
• Oh Be a Fine Girl (or Guy), Kiss Me

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Strengths of absorption lines (our Sun is a G2
and has strong FeII and Ca II lines)
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Stars come in a wide variety of sizes

• Stefan-Boltzmann law relates a stars energy
  output, called LUMINOSITY, to its temperature and
  size.
• Flux Intensity Power/Area sT4
• LUMINOSITY Power Flux Area 4pR2 sT4
• LUMINOSITY is POWER, or Energy/time, measured in
  joules per second
• The Stefan-Boltzman constant, s 5.67 X 10-8 W
  m-2 K-4
• Small stars have low luminosities unless they are
  very hot.
• Cool stars must be very large in order to have
  large luminosities (e.g. Red Giants).

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Hertzsprung-Russell (H-R) diagrams reveal the
different kinds of stars.
HR DIAGRAM Absolute magnitude vs
temperature or luminosity vs spectral type
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Hertzsprung-Russell (H-R) diagrams reveal the
different kinds of stars.

• Main sequence stars
• Stars in hydrostatic equilibrium found on a line
  from the upper left to the lower right.
• Hotter is brighter
• Cooler is dimmer
• Red giant stars
• Upper right hand corner (big, bright, and cool)
• White dwarf stars
• Lower left hand corner (small, dim, and hot)

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Determining the Sizes of Stars from an HR Diagram

• Main sequence stars are found in a band from the
  upper left to the lower right.
• Giant and supergiant stars are found in the upper
  right corner.
• Tiny white dwarf stars are found in the lower
  left corner of the HR diagram.

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Luminosity classes
Details of a stars spectrum reveal whether it is
a giant, a white dwarf, or a main-sequence star.

• Class I includes all the supergiants.
• Class V includes the main sequence stars.
• The Sun is a G2 V

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Luminosity increases with mass, in main-sequence
stars.
Bigger is brighter!
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Luminosity increases with temperature, in
main-sequence stars.
Bigger is hotter!
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When core hydrogen burning ceases, a
main-sequence star becomes a red giant
.

• When all of the hydrogen in the core has been
  depleted, the interior can no longer repel the
  inward pull of gravity.
• The core heats under pressure, causing the outer
  layers to expand and swell.
• These outer layers get farther from the hot core
  and cool, resulting in a red color.

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H-R diagram shows Suns evolution.
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Guiding Questions

• How far away are the stars?
• What evidence do astronomers have that the Sun is
  a typical star?
• What is meant by a first-magnitude or
  second-magnitude star?
• Why are some stars red and others blue?
• What are the stars made of?
• As stars go, is our Sun especially large or
  small?
• What are giant, main-sequence, and white dwarf
  stars?
• How do we know the distances to remote stars?
• How does our Sun evolve?
• How can we find the temperature, power, and size
  of stars from their spectra?