1. The Energy Balance of Clumps and Cores in Molecular Clouds Sami Dib Sami Dib CRyA-UNAM CRyA-UNAM Enrique Vázquez-Semadeni (CRyA-UNAM) Jongsoo Kim (KAO-Korea) Andreas Burkert (USM) Thomas Henning (MPIA) Mohsen Shadmehri (Ferdowsi Univ.)

2. Why is the energy balance of clouds important ? On which scales are they grav. bound/unbound (fragmentaion theories) ? How much mass is in the bound/unbound cores and clumps ? SFE SFE Stellar multiplicity Stellar multiplicity IMF vs CMD IMF vs CMD

3. Classical grav. boundness parameters Jeans number : J c = R c / L j with L j = (  c s 2 / G  aver ) 1/2 if J c > 1 core is grav. bound, collapse J c < 1 core is grav. unbound Mass-to magnetic flux ratio :  c = (M/  ) c / (M/  ) cr  c =  B m R c 2 B m is the modulus of the Mean Magnetic field  c 1 no magnetic support. Virial parameter :  vir = (5  c 2 R c /GM c ), M vir =  vir M If  vir < 1  object is Grav. Bound  vir > 1  object is Grav. Unbound

4. Observations a) Kinetic+ Thermal energy vs. gravity Larson, 1981 Caselli et al. 2002

5. magnetic energy vs. gravity b) magnetic energy vs. gravity Myers & Goodman 1988

6. Observations suffer some uncertainty Crutcher et al. 2004 L183L1544L43  obs 2.6 2.3 1.9  cor 0.9 0.8 0.6 factor of  /4 by missing B // factor of 1/3 due do core morphology

7. The simulations (vazquez-Semadeni et al. 2005) TVD code (Kim et al. 1999) 3D grid, 256 3 resolution Periodic boundary conditions MHD self-gravity large scale driving Ma= 10, J=L 0 /L J =4 L 0 = 4pc, n 0 = 500 cm -3, T=11.4 K, c s =0.2 km s -1 different  = Mass/magnetic flux Stanimirovic & Lazarian (2001) Ossenkopf & Mac Low (2002) Dib & Burkert (2005) Dib, Bell & Burkert (2006) Koda et al. (2006)

8. Clump finding algorithm Is done by identifying connected cell which have densities above a defined threhold. thresholds are in unit of n 0 : 7.5 (+), 15(*), 30 (  ), 60 (  ) and 100 (  )

9. The virial theorem applied to clumps and core in 3D numerical simulations. (EVT) (e.g., McKee & Zweibel 1992; Ballesteros et al. 1999; Shadmehri et al. 2002) volume terms surface terms

10. Clump finding algorithm Is done by identifying connected cells which have densities above a certain threhold. thresholds are in unit of n 0 : 7.5 (+), 15(*), 30 (  ), 60 (  ) and 100 (  ) for each identified clump we calculate EVT terms velocity dispersion :  c specific angular momentum : j c average density : n aver virial parameter :  vir Mass : M c characteristic size : R c Volume : V c Jeans number : J c Mass to magnetic flux ratio :  c

11. Supercritical cloud 10 n 0 100 n 0 1000 n 0 M rms = 10  = 1 L box = 4L J ~ 4 pc n 0 = 500 cm -3 B 0 = 4.5  G  c = 8.8

12. Gravity vs. Other energies

13. Comparison with the ‘’classical’’ indicators

14. Non-magnetic cloud M rms = 10 L box = 4L J ~ 4 pc n 0 = 500 cm -3 B 0 = 0  G  c = infty. 10 n 0 100 n 0 1000 n 0

15. Non-magnetic cloud - Larger number of clumps than in MHD case. - Suggests that B reduces SFE by reducing core formation probability, not by delaying core lifetime.

16. Morphology and characteristics of the ‘’Numerical’’ Ba 68 core Mass = 1.5 M  Size = 0.046-0.078 pc  nt = 0.018 km s -1 = 1/10 c s average number density = 3.2×10 4 cm -3 Sharp boundaries Similar bean morphology But … Life time of the core ?

18. Virial balance vs. ‘’classical’’ indicators J c vs. thermal/gravity Mag. cases: average slope is 0.60c B= 45.8 B= 14.5 B= 4.6 B= 0

19. Virial balance vs. ‘’classical’’ indicators  c vs. magnetic/gravity B= 45.8B= 14.5 B= 4.6

20. Virial balance vs. ‘’classical’’ indicators  vir vs. (kinetic+thermal)/gravity Large scatter, No specific correlation  vir very ambiguous B= 45.8 B= 14.5 B= 4.6 B= 0

21. Conclusions clumps and cores are dynamical out-of equilibrium structures the surface terms are important in the energy balance not all clumps/cores that are in being compressed are gravitationally bound No 1-to-1 match between EVT grav. boubd ojbects and objects bound according to the classical indicators. J c -therm./grav well correlated  c -megnetic/grav. Well correlated, but sign ambiguity  vir /thermal+kinetic/grav. Poorly correlated+sign ambiguity

22. CO clump N 2 H + core Mesurering surface terms ??

23. gracias por su atención