Binary and Multiple Star Systems Star Clusters

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Binary and Multiple Star SystemsStar Clusters
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Learning GoalsWhat We Should Know

• What are eclipsing, spectrum, and spectroscopic
  Binary Stars
• How are Binary Stars used to determine stellar
  masses
• What is the explanation of Nova Stars
• What are the different types of star clusters
• How are star clusters evidence the stars are
  constantly forming
• How do globular clusters show stellar evolution
• How is the distance to star clusters determined

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13 Star Clusters

• Reading Assignments
• Pathways to Astronomy, Schneider Arny
• Units 69
• Online Resources Course Website

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Multiple Star Systems

• Two or more stars gravitationally bound
• Types
• optical double stars
• Physical binaries
• Visual binary
• spectroscopic binary
• eclipsing binary
• astrometric binary
• Semi major axis .1 to 100 AU
• Mass 0.5 to 20 Ms

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• Co-orbiting stars orbit about center of mass
• Relationships
• a a1 a2
• Keplers 3rd Law m1 m2 a3/p2
• m2/m1 a1/a2
• Determination of Mass of Stars

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Period and Semi-major Axis

• Visual or Eclipsing Binary
• Period repetition of position or eclipse
• Spectroscopic Binary
• Period from repetition of Doppler shift
• Orbital velocity form Doppler shift
• Semi-major axis
• Visually
• Calculate from period and velocity

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Example

• Suppose p0.9 y, a10.3 a21.8
• M1 M2 (2.1)3/(0.9)2 11.4 Ms
• M1/M2 1.8/0.3 6
• 6 M2 M2 11.4 Ms
• M2 (11.4/7) Ms 1.62 Ms
• M1 6 Ms 9.77 Ms

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Doppler Effect

• Shift of Wavelength (frequency) due to motion
  toward or away from observer
• Blue Shift (shorter wavelength)
• Motion toward observer
• Red Shift (longer wavelength)
• Motion away from observer
• Velocity is a fraction of speed of light
• v C ( ??/?)

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Example

• The normal wavelength of Ha 656.3 nm
• Suppose it is observed in the spectrum of a star
  as 656.17 nm.
• This is a blue shift object has a velocity
  toward the observer
• V c ((656.3-656.17)/656.3)
• V 3x105 (0.13/656.3) 59.4 km/s

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Eclipsing Binaries and Stellar Size
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Percentage of Multiple Star Systems
Members of System of Stars
1 41
2 41
3 14
4 3
5 1
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Formation of Multiple Star Systems

• Fission splitting of fast rotation protostar
• Capture gravitation attraction of one star for
  another passing by
• Sub-fragmentation during gravitation collapse

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Binary Systems with Mass Transfer

• Roche surface
• Evolution of one star to giant stage
• Outer atmosphere of star fills lobe
• May transfer mass into lobe of second star
• Nova stars addition of mass from one star to
  another that may be a WD
• WD gains mass and ignites Hydrogen burning and a
  nova type explosion

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Contact binaries

• 0.8 to 5 Ms
• Roche limits touch
• WD partner receives mass from other partner
• Form through fission of rotating protostar
• Very short periods
• Old pulsars binary systems with mass transfer
  that speeds up rotation of neutron star

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Star Clusters and Associations

• 3 Types
• Open (Galactic) clusters
• Star Associations
• Globular Clusters

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Typical Characteristics
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Milky Way Galaxy

• Shape
• Size
• Sun Location
• Halo

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Open (Galactic) Clusters

• 100 to 1000 stars
• 5 to 50 pc size
• Young stars, star forming clouds of gas
• Break apart with time due to individual motions
• Separate in about 100 million years
• 2 stars (5 and 5.5 km/s)
• Relative velocity
• 0.5 x 0.2 108 107 AU 4 pc
• Quickly dissipate over time

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Star Associations

• More open and fewer stars
• 10 to 100 stars
• 10 to 100 pc
• contain O and B or T-Tauri stars
• star forming region
• OB associations
• T associations

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Globular Clusters

• Massive and stars are very close together
• (average distance is 0.5 ly for 106 cluster)
• distance of proxima centauri is 1.29 pc (4.2 ly)
• Exist in halo of the galaxy
• Very old 12 14 billion years old
• formed early in the history of the galaxy

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Distance to Stars via Clusters

• Methods
• Parallax up to 50 pc
• Extended to a few 100 by satellite methods
• Main-Sequence Fitting
• (brightness plot apparent brightness and then
  adjust to get the brightness ratio and hence the
  distance)

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Example

• Suppose we observe a variable star with a period
  of 10 days in star cluster of unknown distance
• The apparent magnitude is 13.5
• Check Cepheid Variable Properties
• the absolute magnitude of the Cepheid star is
  -0.5 (550 Ls)

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Variable Stars

• Stars in the instability strip
• Bright high luminosity
• Relationship between brightness period and
  luminosity or absolute magnitude
• Cepheid Variables
• Periods of 3 to 50 d
• Luminosity 200 Ls for type II, 1000 Ls for type
  I
• RR Lyrae stars
• Periods 0.3 to 1 d
• Luminosity 100 Ls

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Example

• m-M 13.5 (-.5) 14
• BR 2.51214
• DR 2.51214/2 2.5127 630
• Dist 10DR 6300 pc

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Corrections for Interstellar Reddening

• Dust in nebula
• Calculate from the amount of reddening of spectra
• Clusters are closer that they appear

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Using Clusters to Understand Stellar Evolution

• Plot cluster on HR diagram
• all stars are at about the same distance
• can assume that apparent magnitudes are in the
  same relationship as absolute magnitudes or
  luminosities
• If we know distance to cluster we know luminosity
• Observe the cluster on HR diagram , ms, giants,
  etc.
• Assume that there is little or no second
  generation star formation

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• MS turn off point indicates age of cluster
• Figure 22.5

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Globular clusters

• Very old turn off at the age of Sun
• Little or no O, B and A stars
• Smaller stars so clusters have a reddish color
• Age 12 14 billion years
• Implications for halo of our galaxy
• Spread in ages of 2 to 3 billion years
• Globular shapes
• More spherical (slightly flattened) not
  dominated in evolution by rotation
• Slow rotation

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• Globular clusters are a source of strong x-ray
  radiation
• Closeness leads to possible mass exchanges and
  hence x-ray emissions
• Heavy element fractions near zero

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Questions