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.)
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
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
Observations a) Kinetic+ Thermal energy vs. gravity Larson, 1981 Caselli et al. 2002
magnetic energy vs. gravity b) magnetic energy vs. gravity Myers & Goodman 1988
Observations suffer some uncertainty Crutcher et al L183L1544L43 obs cor factor of /4 by missing B // factor of 1/3 due do core morphology
The simulations (vazquez-Semadeni et al. 2005) TVD code (Kim et al. 1999) 3D grid, 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)
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 ( )
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
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
Supercritical cloud 10 n n 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
Gravity vs. Other energies
Comparison with the ‘’classical’’ indicators
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 n n 0
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.
Morphology and characteristics of the ‘’Numerical’’ Ba 68 core Mass = 1.5 M Size = pc nt = 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 ?
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
Virial balance vs. ‘’classical’’ indicators c vs. magnetic/gravity B= 45.8B= 14.5 B= 4.6
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
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
CO clump N 2 H + core Mesurering surface terms ??
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