Measuring The Stars

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Chapter 10

• Measuring The Stars

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Parallax
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Parallax

• tan p B/d -gt d B/tan p
• (d B/p for small p)
• D pc 1AU/parcsec (pc parsec)
• 1 pc 3.26 ly
• Distance limit 50 pc
• Hipparcos satellite 100 pc

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Inverse Square Law of Light

• Luminosity (L)
• Apparent Brightness or Flux (f)
• f L/d2

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Inverse Square Law of Light

• f L/4pd2
• Therefore, if we know
• The flux (f) of a star.
• The distance (d) to a star.
• we can determine the luminosity of the star.
• 1 L? 3.9 x 1026 W

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Stellar Temperature

• Wiens Law
• lmaxT 3 x 10-3 mK

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Stellar Temperature

• Stellar spectra can tell us the temperatures of
  the stars!

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Spectral Classification

• Original classification strength of Hydrogen
  Balmer lines.
• A stars strongest Balmer lines.
• Q stars weakest Balmer lines.
• Now organized by temperature O B A F G K M
• (O, Be a Fine Gal/Guy, Kiss Me)
• O stars hottest
• M stars coolest
• 10 subclasses (0, 1, 9)
• The Sun is a G2 star!

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Stellar Spectra
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Stellar Radii

• Luminosity total power radiated
• Intensity power/unit area
• Therefore luminosity area x intensity
• Stephan-Boltzmann Law I sT4
• Surface area of a sphere A 4pr2
• L 4pr2sT4
• In the correct units L r2 T4
• (when L, r, and T are given in solar
  units L?, r?, T?)

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HR diagram

• If we know
• The surface temperature of stars
• The absolute luminosity of stars
• We can plot surface temp (color) vs. abs.
  Luminosity

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Selection Effects

• What type of stars are visually most common?
• O B main-sequence
• Giants and supergiants
• Selection Effect

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Selection Effects

• What type of stars are actually most common?
• Lower main-sequence red dwarfs
• White dwarfs
• (Very luminous stars actually quite rare!)

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Spectroscopic Parallax

• For d gt 100pc
• If we know
• The temperature of a star (based on its spectra).
• What type of star it is (based on spectral lines
  widths).
• we can find its position on the HR diagram.
• we can determine its luminosity (as labeled on
  the HR diagram).
• Then, if we also know
• The stars flux (as measured from Earth).
• we can determine its distance (using the
  inverse square law of light).
• Distance limit 10 kpc

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Stellar Masses

• Mass lt--gt Gravity!
• Binary Stars
• Center of Mass
• Keplers 3rd Law
• P2 a3 -gt 1 a3/P2 (Const. factor of
  1)
• Period (P) time in years
• Avg. distance (a) AU
• In general
• MA MB a3/P2 (mass Solar Masses)
• (For Earth-Sun system MSun 1 M? and MEarth is
  small.)

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Visual Binary Systems
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Spectroscopic Binary Systems
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Eclipsing Binary Systems
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Spectroscopic EclipsingBinary Systems

• We can determine
• Orbital Period (P)
• Orbital Velocities (v)
• Radii of Orbits (a)
• Masses of the stars (M)
• Spectroscopic Doppler Shift only measures
  radial motion -gt only get lower limit to mass.
• Eclipsing Can also determine diameters of the
  stars. (D)

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Mass-Luminosity Relation
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Main-Sequence Lifetimes

• Stellar Lifetime Stellar Mass/Stellar
  Luminosity
• (t M/L or t 1/M2)
• An O5 star (40 M?) has a MS lifetime of only 1
  million years.
• Our Sun (a G2 star) has a MS lifetime of 10
  billion years.
• An M0 star (0.5 M?) has a MS lifetime of 56
  billion years!

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HR Diagram Relations

• Main Sequence