Star Clusters

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Star Clusters

• Ay 16 Lecture 11
• March 6, 2008

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Star Clusters

• Types
• Distances (Space Motions, Parallax )
• Dynamics
• Relaxation
• Masses (Virial Theorem)
• Stellar Populations
• HR Diagrams Pop I and II

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Star Clusters

• Four Basic Types
• Globular (round bound)
• Open (irregular bound)
• Association (irregular, not bound)
• HII Region (very young, irregular)
• (? other young eg. GMC clusters)

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? Cen
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G1

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Palomar 1
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NGC 188
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h ? Per
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CYG OB2
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ORION
Trapezium
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NGC2237
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Globulars (15-20,000)
M87 David Malin AAT
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Spatial Distribution of Globular Clusters

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• Distribution of
• HII Regions in
• The Milky Way

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M31

• UV

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Stars Move.

• 
  v total velocity
• 
  vR radial vel
• 
  vT tangential
• 
  velocity
• vT v sin ? tan ? vT/vR
  

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Proper Motion

• ? (radians/s) vT(km/s)/d(km)
• but radians/sec is a bad unit, never
  mind km!
• So convert km/s to parsecs/yr and radians to
  arcsec
• multiply by 3.156x107s/yr / 3.086x1013 km/pc
• and by 206265/radian
• vT 4.74? (arcsec/yr)
  d(pc)
• or d vT/4.74 ?
• or, if we know ?, d vR tan ? / 4.74 ?
  

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Moving Cluster Method

• Compare the proper motion of a cluster with the
  rate at which its size changes.
• Clusters appear to be heading towards particular
  points on the sky.

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We need the radial velocity, vr, the proper
motion, ?, and the angle to the convergent point,
?.
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Today --- Hipparcos

• High Precision Parallax Collecting Satellite
• 2.4 million stars measured, 118,000
• with high
  precison
• parallaxes
  better
• than 0.001
  arcsec
• Hyades
  distance
• 46.34 /-
  0.27 pc
• ESA 1993

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Also, get distances from HR diagrams.

• Magnitudes --gt apparent luminosity is
  proportional to 1/d2
• Color is essentially distance independent
• (except when dust gets in the way)
• So --- slide HR diagrams for similar clusters to
  get offset between a cluster of a known distance
  and an unknown.

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Cluster Timescales

• Stars still move! How fast/long?
• Cluster dynamics can be
• described in terms of two
• important parameters

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Timescales

• Size r (pc)
• Stellar Velocity or velocity dispersion
• (the distribution of velocities w.r.t.
• the cluster mean) ? (km/s)
• Simplest time scale crossing time
• tC r/? 106 years r(in pc)/ ?( in km/s)

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Relaxation Time

• tr relaxation time, time to establish
  dynamical equilibrium
• Estimate by collision time for stars in the
  cluster. If n the stellar density
• v average stellar velocity
• r impact parameter
• By geometry n (?r2) v tr 1
• ? tr 1/n?r2v

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The Virial Theorem

• For a relaxed system, i.e. one that is
• bound, time invariant on average
• With well defined kinetic and potential energies
• lt K gt -1/2 ltUgt

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HR Diagrams

• Ejnar Hertzsprung
• Henry Norris Russell
• 1906/1913
• Studied star clusters
  and
• nearby stars

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HR Diagrams

• Complete Color-Magnutide diagrams can give you
  cluster distances
• cluster ages
• cluster metallicities