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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

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
- Stellar multiplicity
- IMF vs CMD

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

Observations

a) Kinetic+ Thermal energy vs. gravity

Larson, 1981

Caselli et al. 2002

b) magnetic energy vs. gravity

Myers & Goodman 1988

Observations suffer some uncertainty

factor of /4 by missing B//

factor of 1/3 due do core morphology

Crutcher et al. 2004

- 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)

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 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 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

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

Gravity vs. Other energies

Comparison with the ‘’classical’’ indicators

Non-magnetic cloud

Mrms = 10

Lbox = 4LJ ~ 4 pc

n0 = 500 cm-3

B0 = 0 mG

mc = infty.

10 n0

100 n0

1000 n0

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 = 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 ?

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

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

B= 45.8

B= 14.5

B= 4.6

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

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

Mesurering surface terms ??

CO clump

N2H+ core

gracias por su atención