Dusty Dark Nebulae and the Origin of Stellar Masses Colloquium: STScI April 08

The Unsolved Problem of Star Formation Boundary Conditions & Initial Conditions Dusty Dark Nebulae and the Origin of Stellar Masses Colloquium: STScI April 08

BOUNDARY CONDITIONS Colloquium: STScI April 08

Compositions, Luminosities, Temperatures, Sizes, & Masses BOUNDARY CONDITIONS Colloquium: STScI April 08

Compositions, Luminosities, Temperatures, Sizes, & Masses BOUNDARY CONDITIONS Colloquium: STScI April 08

Compositions, Luminosities, Temperatures, Sizes, & Masses BOUNDARY CONDITIONS Colloquium: STScI April 08

Compositions, Luminosities, Temperatures, Sizes, & Masses  Once formed, the entire life history of a star is essentially predetermined by a single parameter: the star’s initial mass.  The IMF (the frequency distribution of stellar masses at birth) plays a pivotal role in the evolution of all stellar systems from clusters to galaxies. BOUNDARY CONDITIONS The Initial Mass Function (IMF) = first fundamental boundary condition Colloquium: STScI April 08

HBL DBL Completeness limit Brown Dwarfs Sun The IMF exhibits a broad peak between 0.6 and 0.1 M  suggesting a characteristic mass associated with the star formation process. Brown Dwarfs account for only 1 in 5 objects in IMF! Fundamental Boundary Conditions Muench et al The Initial Mass Function (IMF)

2- Stellar Multiplicity Most (~70%) stars are single! Beichman & Tanner Multiplicity is a function of stellar mass Lada 2006 Fundamental Boundary Conditions

INITIAL CONDITIONS

Stars form in Dense, Dark Cloud Cores Initial Conditions = Basic physical properties of starless cores: mass, size, temperature density, pressure, kinematics

The Team Members: Harvard-Smithsonian CfA: Charles Lada Gus Muench Jill Rathborne Calar Alto Observatory: Joao Alves Carlos Roman-Zuniga European Southern Observatory: Marco Lombardi Basic Properties of the Pipe Cloud: Distance: 130 pc Mass: 10 4 M  SIze: ~3 x 14 pc Star Formation Activity: Insignificant The Pipe Nebula Project Alex Mellinger

Extinction and the Identification and basic properties of dense cores. INITIAL CONDITIONS:

Seeing the Light Through the Dark

10 pc

Core Maps after wavelet decomposition RAWWavelet Decomposed

Distribution of core masses ( 159 cores ) Alves, Lombardi, Lada 2007

Stars Distribution of core masses

Probability Density Function for the Pipe Core Mass Function Pipe CMF IMFs x 3.3 Alves, Lombardi & Lada 2007 Star Formation Efficiency is the Key The IMF derives directly from the CMF after modification by a constant SFE

Mean Core Densities Median Core Density = 7000 cm -3 Lada et al. 2007

Mass – Radius Relation Constant Column Density: M ~ R 2 (Larson’s Laws)

Radio Molecular Lines and the Nature of the Cores

 stem = 0.26 km/s Core to Core Velocity Dispersion (C 18 O)  bowl = 0.28 km/s Muench et al. 2007

Rathborne et al NH 3 Line Survey NH 3 detections indicate n(H 2 ) > 10 4 cm -3

Rathborne et al NH 3 Line Survey NH 3 detections indicate n(H 2 ) > 10 4 cm -3 Radially Stratified Cores

Subsonic Supersonic  NT (km/s)

Dense cores are thermally supported! Such cores must evolve on ACOUSTIC timescales!!

B 68: Radial Density Profile  max = 6.9  0.2 Critical Bonnor-Ebert Sphere

0.18 km/s P thermal / P NT ~ 10-14!! Barnard 68 is a thermally supported Cloud!

Broderick, Keto, Lada & Narayan, 2007 B68 Core Pulsation

P total = P thermal + P NT ISM

Core structure is set by the requirement of pressure equilibrium with external medium! Lada et al. 2007

Pressure and the Origin of Core Masses: From CMF to IMF

The BE Critical Mass corresponds approximately to the characteristic mass of the core mass function! Origin of Cores: Thermal Fragmentation in a Pressurized Medium Non-equilibrium Equilibrium M BE = 1.15 (n s ) -0.5 T 1.5 (solar masses)

IC 348 Taurus Luhman 2004 Luhman et al P/k ~ 10 5 P/k ~ 10 6 From CMF to IMF: Setting the Mass Scale of the IMF The effect of increasing External Pressure m BE = C x a 4 (P surface ) -0.5

IC 348 Taurus Luhman 2004 Luhman et al P/k ~ 10 5 P internal = P thermal + P NT + B 2 /8π The effect of decreasing internal Pressure x 2 m BE = C x a 4 (P surface ) -0.5 From CMF to IMF: Setting the Mass Scale of the IMF  (a effective ) 2 = P internal

High Pressure Regions: Embedded Cluster Cores P/k ~ 10 6 –10 7 K cm -3

Multiplicity increases with stellar mass Multiple Stars Single Stars Fundamental Boundary Condition #2: Stellar Multiplicity

ORIGIN OF THE IMF: **m BE = Constant x a 4 (P surface ) -0.5 Bonnor-Ebert Mass Scale - CMF{logm} = c 1  (log{m/m 0 }, s i ); m 0 = m BE ** IMF{logm} = c 2  (log{m/m 0 }, s k ); m 0 =SFE m BE

ORIGIN OF THE IMF: **m BE = Constant x a 4 (P surface ) -0.5 Bonnor-Ebert Mass Scale - CMF{logm} = c 1  (log{m/m 0 }, s i ); m 0 = m BE ** IMF{logm} = c 2  (log{m/m 0 }, s k ); m 0 =SFE m BE

ORIGIN OF THE IMF: **m BE = Constant x a 4 (P surface ) -0.5 Bonnor-Ebert Mass Scale - CMF{logm} = c 1  (log{m/m 0 }, s i ); m 0 = m BE ** IMF{logm} = c 2  (log{m/m 0 }, s k ); m 0 =SFE m BE Yield = M dg x SFE = b(t) x Δt M dg = mass of dense gas (n>10 4 ) b(t) = stellar birthrate

What determines the Star Formation Rate? (E. Lada 1991) Most stars form in clusters Stars form exclusively in dense (n > 10 4 cm -3 ) gas

What determines the Star Formation Rate?

Lombardi, Lada & Alves 2008

What determines the Star Formation Rate? On GMC scales, the amount of gas ( M DG ) at high density (>10 4 cm -3 ) and high extinction (A V > 6-10 mag;  gas > 100 M  pc -2 ) SFR =  SF M DG /  SF Conjecture: SFR ~ M DG  SF =  ff ~ (G  ) -1/2 for n = 10 4 cm -3 :  ff = 3 x 10 5 yrs = constant

What determines the Star Formation Rate? On GMC scales, the amount of gas ( M DG ) at high density (>10 4 cm -3 ) and high extinction (A V > 6-10 mag;  gas > 100 M  pc -2 ) SFR =  SF M DG /  SF if  SF ~ (G  ) -1/2 then SFR ~  3/2 Conjecture: Gao & Solomon 2004 SFR ~ M DG

What determines the Star Formation Rate? if  SF ~ (G  ) -1/2 then SFR ~  3/2 Conjecture:  SFR = A (  gas ) 1.6 Kennicutt 1998 Schmidt-Kennicutt Law On GMC scales, the amount of gas (M DG ) at high density (>10 4 cm -3 ) and high extinction (A V > 6-10 mag;  gas > 100 M  pc -2 )  DG ~ (  gas ) 1.6 On the other hand:

What determines the Star Formation Rate? Conjecture:  SFR = A (  gas ) 1.6 Kennicutt 1998 Schmidt-Kennicutt Law P gas ~ (a eff ) 2 On GMC scales, the amount of gas (M DG ) at high density (>10 4 cm -3 ) and high extinction (A V > 6-10 mag;  gas > 100 M  pc -2 )

What determines the Star Formation Rate? Conjecture:  SFR = A (  gas ) 1.6 Kennicutt 1998 Schmidt-Kennicutt Law P gas ~  G (  gas ) 2  SFR ~ (P gas ) n ; n = ¾ (?) On GMC scales, the amount of gas (M DG ) at high density (>10 4 cm -3 ) and high extinction (A V > 6-10 mag;  gas > 100 M  pc -2 )

Conclusions: 1- Distribution of core masses similar to stellar IMF but shifted to higher masses by factor of SFE ≈ 25-30% 3- Cores are DENSE CORES 4- Cores are THERMALLY supported 5- Cores are PRESSURE CONFINED: P surface = P external 6- BE mass  CMF characteristic mass: thermal fragmentation under PRESSURE

ORIGIN OF THE IMF: **m BE = Constant x a 4 (P external ) -0.5 Bonnor-Ebert Mass Scale The IMF produced in a star forming event may be determined by only a few very basic physical parameters, e.g., Temperature and External Pressure. The IMF produced in a star forming event may be determined by only a few very basic physical parameters, e.g., Temperature and External Pressure. - CMF{logm} = c 1  (log{m/m 0 }, s i ); m 0 = m BE ** IMF{logm} = c 2  (log{m/m 0 }, s k ); m 0 =SFE m BE

The End !

Pressure Pressure ! Pressure Three things to remember from this talk: