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