AST 541 The Stellar Initial Mass Function

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AST 541The Stellar Initial Mass Function

• Feng Dong
• December 3rd, 2004

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A First Look
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IMF?

• Initial Mass Function The mass distribution of
  stars ever formed in disk, clusters, etc
• 1. time-independent
• 2. continuous
• Why is it important?
• 1. a link between stellar and galactic
  evolution
• 2. insights on theories of star
  formation

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Outline

• Pioneering Work by Salpeter 1955.
• A Systematic Study on IMF. (MillerScalo 1979
  Scalo 1986 Scalo 1998)
• Recent Advance in Both Observation and Theory.
  (Kroupa 2002 Larson 2003 Chabier 2004 )

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Salpeter 1955 A First Probe into the Luminosity
Function and IMF

• Formation rate of stars in the solar neighborhood
  has been constant.
• IMF is a smooth function of mass, independent of
  time.
• Stars do not change their mass appreciably in the
  main sequence.
• Most stars are poorly mixed and move off the MS
  when about 12 of the mass has been burned from
  hydrogen into helium.

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From LF to IMF

• Total Luminosity Function
• Original Mass Function
• Original Luminosity Function
• Linking the Present to Past

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A Power Law IMF

• For log(m/m?) between -0.4 and 1.0
• ?(m) 0.03(m/m?)(-1.35)

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MillerScalo 1979Scalo 1986

• 1. Present-Day Luminosity Function. (number of
  all stars per pc3 and absolute mag)
• 2. Present-Day Mass Function, or PDMF. (number
  of MS stars per pc2 and logm)
• 3. Initial Mass Function, or IMF. (number of
  stars ever formed in the disk per pc2 and logm)

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Present-Day Luminosity Function
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Mass-Luminosity Relation
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Scale Heights
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Correction for Non-MS Stars
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Resulting PDMF and Uncertainties
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PDMF, Birthrate and IMF (1)

• Stellar Creation
  Function. (per unit area)
• Define
  then
• ?
• Relative Stellar Birthrate. (in units
  of average birthrates)

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PDMF, Birthrate and IMF (2)

• since ?
• For stars with MS lifetime greater than the age
  of the Galaxy, the PDMF and IMF are identical.
  

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IMFs from Trial Birthrates

• For
• A Taylor series to first
• order

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Continuity Constraint
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Additional Constraints
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Final IMF within Birthrate Range
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Some Derived Quantities

• Cumulative Number Distribution of IMF
• Present Birthrate of Stars (per yr pc2 logM)
• Cumulative Mass Distribution of IMF
• with Oort Limit Any Missing Mass?
• mass to light ratio

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On Star Formation Theory

• Fragmentation Model
• IMF may reflect the initial mass
  distribution of protostellar fragment masses,
  with fragments evolving independently of each
  other
• Fragments Interaction Model
• IMF may be a signature of certain
  interactions of protostellar fragments with
  ambient gas and with each other

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Revisit of The Two basic Assumption

• Is the IMF Time Independent?
• Is the IMF continuous over mass?

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IMF Not Only for Field Stars
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IMF Power Law Index Statistics

• Is there a real variation? Or Just the
  uncertainties are so large?

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Some Recent Advance

• (Kroupa 2002 Larson 2003 Chabier 2004 )
• A uniform IMF in variable systems?
• What does it mean to theory of star formation.

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Chabrier 2004
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Kroupa 2002
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Summary

• The IMF can now be determined down to a few
  Jupiter masses, two orders of magnitudes below
  the limit of accuracy of Salpeter (1955).
• The IMF exhibits a similar behavior in various
  environments disk, young and globular clusters,
• spheroid but the uncertainties are still
  large