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

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

3. BOUNDARY CONDITIONS Colloquium: STScI April 08

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

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

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

7. 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

8. 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. 2002 1- The Initial Mass Function (IMF)

9. 2- Stellar Multiplicity Most (~70%) stars are single! Beichman & Tanner Multiplicity is a function of stellar mass Lada 2006 Fundamental Boundary Conditions

10. INITIAL CONDITIONS

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

13. 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

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

15. Seeing the Light Through the Dark

18. 10 pc

21. Core Maps after wavelet decomposition RAWWavelet Decomposed

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

23. Stars Distribution of core masses

24. 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

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

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

27. Radio Molecular Lines and the Nature of the Cores

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

29. Rathborne et al. 2007 NH 3 Line Survey NH 3 detections indicate n(H 2 ) > 10 4 cm -3

30. Rathborne et al. 2007 NH 3 Line Survey NH 3 detections indicate n(H 2 ) > 10 4 cm -3 Radially Stratified Cores

31. Subsonic Supersonic  NT (km/s)

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

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

36. 0.18 km/s P thermal / P NT ~ 10-14!! Barnard 68 is a thermally supported Cloud!

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

39. P total = P thermal + P NT ISM

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

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

42. 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)

43. IC 348 Taurus Luhman 2004 Luhman et al. 2003 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

44. IC 348 Taurus Luhman 2004 Luhman et al. 2003 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

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

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

47. 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

48. 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

49. 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

50. 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

51. What determines the Star Formation Rate?

52. Lombardi, Lada & Alves 2008

53. 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

54. 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

55. 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:

56. 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 )

57. 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 )

58. Conclusions: 1- Distribution of core masses similar to stellar IMF but shifted to higher masses by factor of 3-4. 2- 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

59. 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

60. The End !

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