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The Energy Balance of Clumps and Cores in Molecular Clouds Sami Dib

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

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The Energy Balance of Clumps and Cores in Molecular Clouds Sami Dib

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  1. The Energy Balance of Clumps and Cores in Molecular Clouds Sami Dib 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 • Stellar multiplicity • IMF vs CMD

  3. Classical grav. boundness parameters Jeans number : Jc = Rc / Lj with Lj= ( cs2/ G aver)1/2 if Jc > 1 core is grav. bound, collapse Jc < 1 core is grav. unbound Mass-to magnetic flux ratio : c= (M/)c/ (M/)cr c= Bm Rc2 Bm is the modulus of the Mean Magnetic field c < 1 : magnetic support, c > 1 no magnetic support. Virial parameter : vir= (5 c2 Rc/GMc), Mvir= 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. b) magnetic energy vs. gravity Myers & Goodman 1988

  6. Observations suffer some uncertainty factor of /4 by missing B// factor of 1/3 due do core morphology Crutcher et al. 2004

  7. The simulations(vazquez-Semadeni et al. 2005) • TVD code (Kim et al. 1999) • 3D grid, 2563 resolution • Periodic boundary conditions • MHD • self-gravity • large scale driving • Ma= 10, J=L0/LJ=4 • L0= 4pc, n0= 500 cm-3, T=11.4 K, cs=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 n0 :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 n0 :7.5 (+), 15(*), 30 (), 60 () and 100 () • for each identified clump we calculate • EVT terms • velocity dispersion : c specific angular momentum : jc • average density : naver virial parameter : vir • Mass : Mc characteristic size : Rc • Volume : Vc • Jeans number : Jc • Mass to magnetic flux ratio : c

  11. Supercritical cloud Mrms = 10 b = 1 Lbox = 4LJ ~ 4 pc n0 = 500 cm-3 B0 = 4.5 mG mc = 8.8 10 n0 100 n0 1000 n0

  12. Gravity vs. Other energies

  13. Comparison with the ‘’classical’’ indicators

  14. Non-magnetic cloud Mrms = 10 Lbox = 4LJ ~ 4 pc n0 = 500 cm-3 B0 = 0 mG mc = infty. 10 n0 100 n0 1000 n0

  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 cs average number density = 3.2×104 cm-3 Sharp boundaries Similar bean morphology But … Life time of the core ?

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

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

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

  20. 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. • Jc-therm./grav well correlated • c-megnetic/grav. Well correlated, but sign ambiguity • vir/thermal+kinetic/grav. Poorly correlated+sign ambiguity

  21. Mesurering surface terms ?? CO clump N2H+ core

  22. gracias por su atención

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