Properties of Stars

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Properties of Stars
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Star Names or Identification

• Constellations
• Star Name Constellation Name and brightness
  rank, i.e. 2nd brightest star in the
  constellation Orion is ß Orionis, practice dates
  from the Greeks (Bayer method)
• Proper names Betelgeuse, Sirius (Arab
  astronomers after the time of Ptolemy)
• Star Catalogs number for star (depends on the
  catalog), i.e. HD183143 (Henry Draper Catalog)

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Star Properties

• Distance
• Brightness/Luminosity
• Size
• Mass
• Temperature
• Composition

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Star Properties (cont)

• Rotation
• Magnetic Field
• Composition
• Motion
• Atmospheric Properties

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Distance to Stars

• Parallax
• Baseline is major axis of earths orbit (i.e. 2
  AU)
• Position (angle ) of star measured with respect
  to distant background stars gives parallax
  angle P
• Small angle formula give distance d
• Angle is arc seconds, d is in parsecs
• d 1/p

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Parallax Example

• Parallax angle p0.4
• d 1/0.4 2.5 parsecs
• 1 parsec 3.26 ly
• 1 parsec 206,265 AU

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Accuracy of Parallax Measurements

• Limited to about 0.01
• d 1/0.01 100 parsecs
• 100 Parsecs, 326 ly is small scale even for the
  Milky Galaxy (diameter 100,000 ly)

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Brightness, Magnitude, and Luminosity

• Hipparchus established a brightness scale for
  start the magnitude scale
• 1st magnitude brightest stars to 6th magnitude
  faintest visible
• Human perception is a fixed difference in
  brightness for each magnitude change
• Actual relationship is a fixed ratio of
  brightness
• Suppose a m2 star has a brightness B1 and a m3
  star has a brightness B2, then
• B1/B2 2.512

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Apparent Magnitude - m

• Now a third star has a magnitude m4 star has a
  brightness B3 such that
• B2/B3 2.512
• And
• B1/B3 (2.512)(2.512) (2.512)m3-m1
  (2.512)2
• 6.31
• Hence, star 1 is 6.31 times brighter than star 3

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Magnitudes

• A difference of 5 magnitudes is
• (2.512)5 100
• Every 5 magnitude difference is 100 in brightness
• Apparent Magnitude m depends on distance
• Two stars of the same intrinsic brightness, the
  one that is farther away will have a greater
  magnitude

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Magnitude and Brightness Ratio
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Magnitude and Distance

• Relationship of brightness and distance (inverse
  square law)
• B 8 1/d2
• Suppose we know the magnitude of two stars with
  the same intrinsic brightness and they are at
  different distances
• Using the difference in magnitude ?mm1-m2 we can
  find the distance ratio

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Magnitude and Distance Ratio
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Absolute Magnitude - M

• The apparent magnitude of a star at a fixed
  distance of 10 pc.
• If absolute and apparent magnitude of a star are
  known (big if) then the distance to the star can
  be found.
• Distance is 10 pc times the distance ratio

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Magnitude and Distance Ratio
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Example

• Suppose the absolute magnitude of a star is M
  4
• And the apparent magnitude of the star is 7,
  what is the distance to the star?
• M14, d110 pc, m27
• ?m m - M 7 (4) 3
• From the table if ?m 3 distance of star is 40 pc

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Luminosity

• Total Energy emitted by a star over all
  wavelengths
• L has units of Joules/second or watts
• Luminosity is an intrinsic property of a star
• Depends on size (area) and temperature
• Bigger stars more luminous
• Higher temperature stars more luminous

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Luminosity Temperature and Size

• Stefan-Boltzmann Law
• Energy output per square meter per second (w/m2)
• E ?T4
• Total energy output Luminosity
• E times area
• E (4 ? R2)
• Luminosity proportional to T4 and R2
• Luminosity of Sun
• Ls 4 x 1026 watts

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Luminosity Temperature and Size
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Sizes of Stars

• Eclipsing Binary Stars
• Binary stars or common (50 of stars)
• Light Curve (pp 381)
• Doppler Shift to Get Velocity
• Orbital Parameters
• Total mass of system
• Stellar diameters
• Simulation

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Rotation and Atmospheric Motions

• Doppler Effect
• Motion relative to observer changes wavelength
• Blue shift if object moves toward observer
• Red shift if object moves away from observer
• Velocity
• V c ??/?

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Magnetic Field

• Zeeman Effect
• Spectral lines are split into two lines
• States of electron spin axis
• Separation of spectral lines related to strength
  of magnetic field
• Map surface of the Star

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Stellar Spectral Classes

• Differences in the Spectra of Stars
• Observations of nearest Stars
• Observations of brightest Stars
• Representative Stars
• Spectra vary with Temperature and to a lesser
  extent composition

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Hertzsprung-Russell DiagramOrganizing Stellar
Data

• Diagram to Show relationship of brightness and
  spectral class
• Absolute Magnitude vs Spectral Class
• Luminosity vs Temperature

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Main Sequence Stars (17.3)
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Main Sequence

• Main Sequence stars that have reached a stable
  configuration in their evolution
• Russell Vogt Theorem equilibrium of main
  sequence star is determined by mass and
  composition
• Mass Luminosity Relationship

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Non-Main Sequence Stars

• White Dwarves
• Luminosity 0.0001 0.01 solar
• Temperature 5000 15,000 K
• Radii 0.01 solar
• Late stage of stellar evolution
• Giants and Super Giants
• Giants luminosity 10,000 100,000 solar
• Temperature 5,000 15,000 K
• Radii 10 100 solar
• Super (Red) Giants luminosity 10,000 100,000
  solar
• Temperature 2500 3500 K
• Radii 100 1000 solar