The Energy Balance of Clumps and Cores in Molecular Clouds
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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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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.)


The energy balance of clumps and cores in molecular clouds sami dib

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


The energy balance of clumps and cores in molecular clouds sami dib

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


The energy balance of clumps and cores in molecular clouds sami dib

Observations

a) Kinetic+ Thermal energy vs. gravity

Larson, 1981

Caselli et al. 2002


The energy balance of clumps and cores in molecular clouds sami dib

b) magnetic energy vs. gravity

Myers & Goodman 1988


The energy balance of clumps and cores in molecular clouds sami dib

Observations suffer some uncertainty

factor of /4 by missing B//

factor of 1/3 due do core morphology

Crutcher et al. 2004


The energy balance of clumps and cores in molecular clouds sami dib

  • 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)


The energy balance of clumps and cores in molecular clouds sami dib

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 ()


The energy balance of clumps and cores in molecular clouds sami dib

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


The energy balance of clumps and cores in molecular clouds sami dib

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


The energy balance of clumps and cores in molecular clouds sami dib

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


The energy balance of clumps and cores in molecular clouds sami dib

Gravity vs. Other energies


The energy balance of clumps and cores in molecular clouds sami dib

Comparison with the ‘’classical’’ indicators


The energy balance of clumps and cores in molecular clouds sami dib

Non-magnetic cloud

Mrms = 10

Lbox = 4LJ ~ 4 pc

n0 = 500 cm-3

B0 = 0 mG

mc = infty.

10 n0

100 n0

1000 n0


The energy balance of clumps and cores in molecular clouds sami dib

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.


The energy balance of clumps and cores in molecular clouds sami dib

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 ?


The energy balance of clumps and cores in molecular clouds sami dib

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


The energy balance of clumps and cores in molecular clouds sami dib

Virial balance vs. ‘’classical’’ indicators c vs. magnetic/gravity

B= 45.8

B= 14.5

B= 4.6


The energy balance of clumps and cores in molecular clouds sami dib

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


The energy balance of clumps and cores in molecular clouds sami dib

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


The energy balance of clumps and cores in molecular clouds sami dib

Mesurering surface terms ??

CO clump

N2H+ core


The energy balance of clumps and cores in molecular clouds sami dib

gracias por su atención


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