Ambipolar Diffusion Effects on the Weakly Ionized Turbulence - - PowerPoint PPT Presentation

Ambipolar Diffusion Effects on the Weakly Ionized Turbulence Molecular Clouds

UC-HIPACC: The Future of AstroComputing Conference

San Diego Supercomputer Center December 16 - 17, 2010

Pak Shing Li Astronomy Department, UC Berkeley

Collaborators: Chris McKee (UC Berkeley) Richard Klein (LLNL, UC Berkeley) Robert Fisher (Univ. of Massachusetts at Dartmouth )

Molecular Clouds

Magnetic field in MCs

• ≤ 21 μG in MCs, magnetically supercritical (M/Mc=1.4~2.1) Troland & Crutcher (2008)
• ~ 6 μG in CNM, magnetically subcritical

Heiles & Troland (2005)

• Approximate equipartition: 1.3 < Eturb/Emag < 1.9

Supersonic turbulent MCs

• Broad molecular line widths in MCs: 1 ~ 10 km/s

Zuckerman & Palmer (1974)

• Line width - size relation: v  l0.5  P(k)  k-2 Larson (1981), Passot et al. (1988)
• Hierarchical filamentary and clump structures Low et al. (1984), Scalo (1984),

Stenholm (1984), Elmegreen & Scalo (2004)

Weintraub et al. (2000) Goldsmith et al. (2008) Carina Nebula

MHD turbulence

3 1

• 1

6

9.58 10 (μG) rads 1 10 s 1

ci i in in ci n

eB Z B m c t t    

 

      

Ideal or Non-Ideal?

7

10

i i n

n x n



 

Caselli (1998), Bergin et al. (1999)

• neutrals depend on coupling:

Ambipolar Diffusion

Mestel & Spitzer (1956)

Slow AD-driven Quasi-Static Star Formation Process: tAD ~ 10 tff

Spitzer (1968), Nakano & Tademaru (1972), Mouschovias (1976, 1977, 1979), Nakano & Nakamura (1978), Shu (1983), Lizano & Shu (1989), Fiedler & Mouschovias (1992,1993), …

Ideal MHD: ionized gas frozen with magnetic field Weakly Ionized MCs (ions + neutrals):

• ions are frozen with B-field

Numerical Method (ZEUS-MP + AD)

               

; ; ; 1 ; 4 ;

n i n n i i n n AD i n n n n n i i i i i i i i n n i AD i n i n

v v t t v v v P g t v v v P g B B t B v v t v B v B v                                                      

2-Fluid Semi-Implicit Method:

Tóth (1995), Mac Low & Smith (1997)

3

/ 10

i Ai i n

t x v   



     

Heavy-Ion Approximation:

γAD ρi = const. χi ≡ ρi/ρn

• Criterion:

fI « fD  fL => RAD(lvi) » MAi

2

• AD Reynolds number

AD 2

4 R ( )

AD i n AD AD dyn

v t t B      

≤ 1 weak coupling » 1 strong coupling Li, McKee, Klein (2006) Isothermal Li et al. (2008)

Models Parameters

Five 5123, no gravity, 600,000 CPU hours RAD (l0) : 0.12, 1.2, 12, 120, 1200

Li, McKee, Klein, & Fisher (2008): 1283, 2563, and one 5123

• Model parameters: Mrms = 3, β = 0.1, k = 1~2, T = 10K, periodic boundaries
• Convergence studies in time, resolution, and ionization mass faction χi
• Convergence studies in power spectral indexes

0.5 1 1.5 2 1 1.01 1.02

tf UB / UB,0

• 4
• 3
• 2
• 1

1 1.005 1.01 1.015

log10 i <UB> / UB,0

i = 0.01 speedup = 100 RAD(lvi) » MAi

2

10

• 1

10 10

1

10

2

10

3

1 1.5 2 2.5

RAD(l0) n

nv,i nv,n nB

Burgers Spectrum Iroshnikov-Kraichnan Spectrum

I II III

Velocity Power Spectral Index

I: ideal MHD RAD   II: standard AD RAD › MA

2

III: strong AD MA

2 › RAD › MAi 2

McKee, Li, & Klein (2010)

Ideal MHD → ← Pure HD

10 10

1

10

2

1 2 3 4 5 6

RAD(DMC) N

10 10

1

10

2

1 2 3 4 5 6

RAD(DMC) N

RAD of 27 Observed Molecular Clouds

Crutcher (1999) McKee, Li, & Klein (2010)

10

• 1

10 10

1

10

2

10

3

1 1.5 2 2.5

RAD(l0) n

nv,i nv,n nB

Burgers Spectrum Iroshnikov-Kraichnan Spectrum

I II III

Crutcher (1999)

I: ideal MHD RAD   II: standard AD RAD › MA

2

III: strong AD MA

2 › RAD › MAi 2

McKee, Li, & Klein (2010)

Ideal MHD → ← Pure HD

Velocity Power Spectral Index

Clump Mass function and Mass/Flux Ratio

Padoan & Nordlund (2002), Padoan et al. (2007) Hennebelle & Chabrier (2008, 2009)

2

• x

4lnm+σ N(m)dm=C 1+erf m dm 2 2σ            

• n

v

P (k)=k

Turbulence Fragmentation:

McKee, Li, & Klein (2010)

RAD(l0) = 1200

X Z

RAD(l0) = 12

X Z

RAD(l0) = 0.12

X Z

1 2 3 4 5 6 7 2 4 6 8 10 12 2 4 6 8 10 12

Morphological Change of Turbulence Gas with AD

I II III ↑B

Conclusions

• 2-fluid semi-implicit + heavy-ion approximation is fast and works well on

turbulence simulations!

AD Reynolds Number RAD(lvi) » MAi

2

Li, McKee, & Klein (2006), Li et al. (2008)

• Many statistical properties (e.g. velocity and density power spectra, density

PDF) of the magnetized turbulence system change as a function of RAD, which is a good parameter on measuring how important AD is.

Li et al. (2008)

• AD is still important in weakly ionized MCs at small length scale and that

leads to important astrophysical implication on many aspects of the MCs (e.g. morphological change, clump mass function, mass/flux ratio, ions & neutrals line width ratio, correction of Chandrasekhar-Fermi method, turbulence enhancement to AD diffusion, AD heating, …) when AD is strong.

McKee, Li, & Klein (2010), Li, McKee, & Klein (2011)