Stars

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Stars

• Sun is nearest one 8 light minutes from the
  Earth. Next nearest, 4 light years away!
• From spectra, we can get temperature,
  composition, density
• Next? Diameters, Luminosities (how much energy
  they radiate), and Masses.
• But, first we need to be able to determine
  their distances.

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• Parallax can use this technique to measure
  distances to the nearest stars
• Greeks attempted to measure stellar parallax, but
  failed. Why?
• Distance from the size of the angular shift
• D 1 / P
• Where D is the distance in parsecs (about 3.3
  light years), and P is ½ the angular shift (in
  seconds of arc)
• 1 parsec 206265 A.U.

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• Nearest star (other than the Sun) a Centauri P
  0.76 seconds of arc, D 1.31 parsecs (4.29
  light years)
• Atmospheric blurring (seeing) limits detection
  (smallest shift that can be detected is 0.002
  seconds of arc, but smallest that can be used
  accurately is 0.02 seconds of arc (50 parsecs)
• Hipparcos Satellite (1989) measured 120,000
  stars, accurate to 0.001 seconds of arc (less
  accurate measurement for millions stars)

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• Proper Motion with parallax shifts, the stars
  return to the same position when the Earth
  returns to the same place in orbit But Stars
  are moving (including the Sun)
• Proper motion can indicate distance
• Small proper motion could be a low transverse
  velocity, but could be distant star
• Large proper motion star must be nearby

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Intrinsic Brightness

• Previously, discussed apparent visual magnitude
  (mv) but, stars radiate different amounts of
  energy.
• Absolute Visual Magnitude, Mv, the magnitude a
  star would have (in visible light) if it we
  viewed from a distance of 10 parsecs.
• -- mv Mv -5 5log10(D), and mv Mv is
  called the distance modulus.
• Bigger the distance modulus, the more distant the
  star.

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• D 10 to the power (mv Mv 5)/5
• Also, Suns mv -26.5, distance 1 A.U.
• (or, 0.000005 parsecs)
• Mv 5 5 log (0.000005) 26.5 5.0
• Luminosity energy/time. Since Mv is only for
  the wavelengths of visible light, need to adjust
  for full range of E.M. spectrum.
• Absolute Bolometric Magnitude (for the Sun, Mbol
  4.7)
• Can measure energy output of the Sun (solar
  constant). And, we know the distance to the Sun.
  So can get the Luminosity of the Sun,
• Lsun 4p D2 Intensity of Sun 4 x 1026
  joules/sec
• Other stars 10-4 to 105 times Lsun

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Diameters of Stars

• All, but a few, appear as pinpoints of light
  (even in Hubble images)
• But, if you know L and T, can get diameter
• First, each square meter of a stars surface
  radiates (approximately) like a black-body (E s
  T4), so
• L 4p R2 s T4,
• Can use Sun as a reference point
• L/Lsun (R/Rsun)2 (T/Tsun)4
• What does this indicate? If a star is cool (low
  T), but luminous (big L), it must be large (big
  R).

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Hertzsprung-Russell (H-R) Diagram

• Stars are different sizes, temperatures,
  luminosities
• H-R diagram is a plot of Luminosity (or absolute
  magnitude) versus Temperature (or spectral type
  O,B,A,F,G,K,M)
• Note these are not linear plots exponential
  factors are used.
• movement on a H-R diagram is not change of
  location it is a change in the relationship
  between L and T (happens as stars evolve).

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• Spectral Line widths are affected by collisional
  broadening
• Broad profiles dense gas
• Narrow profiles lower density gas
• Main Sequence stars are relatively small and
  dense
• Giant Stars are large, less dense

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• Luminosity Classes
• Ia bright supergiants
• Ib supergiants
• II bright giants
• III giants
• IV subgiants
• V main sequence
• Sun is a G2V star

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Spectroscopic Parallax

• Determine spectral class (O, B, A, F.)
• Determine Luminosity class (Ia .V)
• Find on an H-R diagram
• Get Absolute Magnitude
• Determine distance from distance modulus
• (mv Mv)

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• What types of stars are there, how common are the
  different types
• Stellar Density Function
• Number of types per cubic parsec
• M dwarfs and White dwarfs are most common
• Hot, Large stars are rare

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Binary Stars

• Many (most) stars are found in multiple star
  systems stars orbit the center of mass of the
  system
• Visual Binaries stars may be a few arc
  seconds from each other. Orbital periods
  typically decades
• Optical Doubles two stars along same
  sight-line, but distant from one another (fairly
  rare occurrence)

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• Apparent relative orbit what you observe of
  the stars motion reason its apparent? Could
  be tipped (inclined)
• Need true relative orbit
• Center of apparent orbit is the same as that of
  the true orbit
• The two stars obey Keplers laws
• The brighter star will be at one focus
• Line through the focus and center is the major
  axis
• Problems if the stars are too close, hard to
  measure the separation accurately too far apart?
  Orbital period is too long to measure

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• Why are we doing this to get stellar masses
• If R distance to center of mass, then
• MA/MB RB/RA
• To get total Mass, need separation (in A.U., to
  use Keplers laws)
• Average distance semi-major axis of the true
  relative orbit
• Get separation in seconds of arc
• Need to know distance to get separation in A.U.
  then get Period in years.

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• Small angle formula
• (Angular separation/206265) (linear separation/
  distance)
• Form of Keplers 3rd Law
• MA MB a3/P2, where Ms are in solar masses, a
  is in A.U., and P is in years.
• Only one mass appears in Keplers law of
  planetary motion, Why?

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• Astrometric Binaries one of the stars is too
  faint to detect
• Discovered by wobble in proper motion of the
  visible star the center of mass of the system
  will move in a straight line
• Led to the discovery of Sirius B
• Sirius A has mass 2.35 Msun
• Sirius B has mass 1.17 Msun
• But, B is 9 magnitudes fainter than A!
• Radius is about the same size as Earths Sirius
  B is a White Dwarf

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• Spectroscopic Binaries too close to separate
  visually, but spectrum shows evidence of two
  stars
• If both stars are bright enough, spectrum shows
  two sets of lines.
• Double Line system as stars move, lines shift
  (due to Doppler effect) can plot a radial
  velocity curve
• If you have P, then v x P 2pR
• But, cant tell of orbit is inclined, only get
  lower limit to masses (but, can get the ratio of
  the masses,
• vA/vB MB/MA

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• Single Line spectroscopic binaries get a number
  related to the mass of the invisible star, the
  total mass, and inclination, but cant get it
  sorted out.
• Again, still have the problem of unknown
  inclination of the double-line systems
• With a large sample, can get a statistical
  estimate of the masses (of a particular spectral
  class, for example)

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• Eclipsing Binaries Algol is the most famous
• Stars orbit the center of mass in (nearly) the
  same plane
• From Doppler shifts get velocities
• From light curve get the orbital inclination
  (especially if the eclipses are full)
• Thus, can get true velocities from the radial
  velocities
• Diameters? Know the velocity and duration of the
  eclipse d v x t
• Problems? Elliptical orbits, partial eclipses,
  and the stars can distort and heat each others
  atmospheres

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• Mass and Diameter give you the density
• If star is a sphere Density 3 M / 4 p R3
• Giant stars 0.1 0.01 grams /cubic cm
• Super giants 0.001 0.000001 g/cc
• White Dwarfs 2 x 106 g/cc
• Main Sequence stars show a mass-luminosity
  relation
• L M3.5
• Masses range from 0.08 Msun to 50 Msun
• Luminosities 10-6 to 106 Lsun