The Energy Balance of The Energy Balance of Clumps and Cores in Clumps and Cores in

Molecular CloudsMolecular Clouds Sami DibSami Dib CRyA-UNAMCRyA-UNAM

Enrique Vázquez-Semadeni (CRyA-UNAM)Enrique Vázquez-Semadeni (CRyA-UNAM)Jongsoo Kim (KAO-Korea) Jongsoo Kim (KAO-Korea) Andreas Burkert (USM)Andreas Burkert (USM)Thomas Henning (MPIA)Thomas Henning (MPIA)Mohsen Shadmehri (Ferdowsi Univ.) Mohsen Shadmehri (Ferdowsi Univ.)

The Energy Balance of The Energy Balance of Clumps and Cores in Clumps and Cores in

Molecular CloudsMolecular Clouds Sami DibSami Dib CRyA-UNAMCRyA-UNAM

Enrique Vázquez-Semadeni (CRyA-UNAM)Enrique Vázquez-Semadeni (CRyA-UNAM)Jongsoo Kim (KAO-Korea) Jongsoo Kim (KAO-Korea) Andreas Burkert (USM)Andreas Burkert (USM)Thomas Henning (MPIA)Thomas Henning (MPIA)Mohsen Shadmehri (Ferdowsi Univ.) Mohsen Shadmehri (Ferdowsi Univ.)

Why is the energy balance of clouds Why is the energy balance of clouds important ?important ?

On which scales are they grav. On which scales are they grav. bound/unbound (fragmentaion theories) ?bound/unbound (fragmentaion theories) ?

How much mass is in the bound/unbound How much mass is in the bound/unbound cores and clumps ?cores and clumps ?

• SFESFE

• Stellar Stellar multiplicity multiplicity

• IMF vs CMD 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

S

c dSnB

Observations Observations a) Kinetic+ Thermal energy vs. gravitya) Kinetic+ Thermal energy vs. gravity

14.02 92.0

2L

LGM Larson, Larson,

19811981

Caselli et al. Caselli et al. 20022002

b) magnetic energy vs. magnetic energy vs. gravitygravity

Myers & Myers & Goodman 1988Goodman 1988

Observations suffer some uncertainty

Crutcher et al. 2004

L183 L1544 L43

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

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

dt

dWEEE

dtId

magmagKthKth

21

221

2

2

V

thth dVpE23

s

ithith dSnpr21

V

K dVvE 2

2

1 s

jjiiK dSnvvr 21

V

mag dVBE 2

81

s

jijimag dSnTr21

V

E dVrI 2

S

ii dSnvr 2V

ii dVgxw

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

10 n0

100 n0

1000 n0

Mrms = 10 = 1Lbox = 4LJ ~ 4 pcn0 = 500 cm-3

B0 = 4.5 Gc = 8.8

Gravity vs. Other energies

Comparison with the ‘’classical’’ indicators

Non-magnetic cloud

Mrms = 10Lbox = 4LJ ~ 4 pcn0 = 500 cm-3

B0 = 0 Gc = 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

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= 45.8 B= 14.5

B= 4.6

Virial balance vs. ‘’classical’’ indicators vir vs. (kinetic+thermal)/gravity

Large scatter,No specific correlation

vir very ambiguous

B= 45.8B= 14.5

B= 4.6B= 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

CO clump

N2H+ core

Mesurering surface terms ??

gracias por su atención