The Power-Law Tail in the Initial Mass Function (IMF) of Stars Basu & Jones, 2004, MNRAS Letters, in press Fundamental questions: Can the IMF be described by a lognormal distribution? Or, is there a power-law tail? What is the generation mechanism of the IMF distribution? If multiplicative factors determine stellar mass, central limit theorem => lognormal distribution probability distribution function

The Orion Nebula A great laboratory for IMF studies nearby, away from Galactic plane lots of young stellar objects, low mass stars detectable wide range of stellar density Trapezium stars near center => symptomatic of more general phenomenon of mass segregation?

IMF of Orion Nebula Cluster (ONC) Squares = histogram of masses of 696 stars (Hillenbrand 1997) binned in increments D log m = 0.2. Dash-dotted line : best fit lognormal to complete histogram – c2 minimized but implied probability = 4.75 x 10-12! Dotted line: best fit lognormal for M < MO – c2 implies probability 0.134. Solid line: best fit straight line for M > MO – slope =

IMF of Orion Nebula Cluster (ONC) Look for region dependent variations – mass segregation? Lognormal good fit for M < Msun. Power-law present for M > Msun in all regions. Most massive stars make slope shallower in some regions. Bottom line: only significant evidence for mass segregation comes from the five stars near the center (Trapezium stars plus one other).

A Minimum-Hypothesis Model Reed (2002,2003) – similar model for distribution of incomes, city sizes. Protostellar condensation masses initially drawn from a lognormal distribution (circles) Accretion growth dm(t)/dt = gm. Fixed time of growth => continued lognormal distribution (diamonds) Above accretion law but an exponential distribution of accretion times t, i.e.,

A Minimum-Hypothesis Model Solid line is analytically derivable: Expect since both rates controlled by external medium.

Another Growth Law Dashed line: sequence of bounded isothermal equilibria (Bonnor-Ebert) for external pressure Pext. Dash-dot line: same but for higher external pressure. Dashed line well described by Geometric accretion =>

Alternate Growth Law Squares => a power-law tail with varying index; average value –1.6. Protostellar condensation masses initially drawn from a lognormal distribution (circles) Accretion growth dm(t)/dt =g1m2/3. Fixed time of growth (diamonds). Above accretion law but an exponential distribution of accretion times t, i.e.,

Conclusion Even if the central limit theorem ensures a lognormal distribution of protostellar condensation masses at birth – subsequent accretion growth (proportional to some power of mass) coupled with a distribution of accretion times, will skew the distribution toward having a power-law tail.