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Compressible MHD turbulence in molecular clouds

Compressible MHD turbulence in molecular clouds. Lucy Liuxuan Zhang Prof. Chris Matzner University of Toronto. Dynamics of molecular clouds - I. Problem: expected cloud collapse time ≤ 3x10 6 yrs expected cloud lifetimes ≥ 3x10 7 yrs Environment: n H2 =10 3 /cm 3 , T=10K, ∂E/∂t=0.4L ☼

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Compressible MHD turbulence in molecular clouds

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  1. Compressible MHD turbulence in molecular clouds Lucy Liuxuan Zhang Prof. Chris Matzner University of Toronto

  2. Dynamics of molecular clouds - I • Problem: • expected cloud collapse time ≤ 3x106 yrs • expected cloud lifetimes ≥ 3x107 yrs • Environment: • nH2=103 /cm3, T=10K, ∂E/∂t=0.4L☼ • L=2pc, cs≈0.2 km/s → ts≡L/cs≈10Myr • va ≥ σv » cs • isothermal approximation • existence of B field and turbulence motions

  3. Dynamics of molecular clouds - II • Possible solution (current opinions) • Turbulence as “turbulent pressure” to support the cloud from self-gravity • Magnetic fields as cushion to reduce dissipation rate • Supersonic, sub-alfvenic turbulence persists for more than flow crossing time over cloud size L

  4. Intro hydrodynamics • Lagrangian (SPH) • Eulerian (grid-based) • Advantages • large dynamical range in mass • Computationally faster by several orders of magnitude • Easy to implement and to parallelize • Basic principal: solve the integral Euler equations on a Cartesian grid by computing the flux of mass, momentum and energy across grid cell boundaries

  5. Equations (no source term) • ∂tρ+(ρv)=0 • ∂t(ρv)+(ρvv+Pδ-bb)=0 • ∂te+[(e+P)v-bb·v]=0 • e=ρv2/2+p/(γ-1)+b2/2 • ∂tb= x (v x b) • ·b=0 • P=p+b2/2 P total pressure, p gas pressure, є thermal

  6. Our numerical model - ISOTHERMAL • Adiabatic version: • “A Free, Fast, Simple and Efficient TVD MHD code” by Ue-Li Pen, Phil Arras, ShingKwong Wong (astro-ph/0305088 2003) • Isothermal version (γ=1): • Eq(4) does not make sense!! • But then, we don’t have to solve for energy separately to update the pressure because p=ρcs2 where cs is constant in space & time. • Eq(4) e=ρv2/2+p/(γ-1)+b2/2 and the quantity p drop out from the system • Eq(7) P=ρcs2+b2/2→ P=ρcs2+b2/2.

  7. Energy dissipation in MHD turbulence • Molecular clouds: • Isothermal, constant cs in space and time • Initial conditions: • Cubic, periodic box of size L • Plasma of uniform density ρ0 • Uniform B field B0=(B0,0,0) where b0=(ρ0cs2/β)1/2=B0/(4π)1/2 • Velocity perturbation δv: • Time intervals ∆t = 0.001 ts • Realization of Gaussian random field • Power spectrum |δv2|  k6 exp(-8k/kpk)2, kpk=8(2π/L) • ·δv=0 divergenceless • ∫ρδv=0 zero net momentum • ∂tE =103ρ0L2cs3 → ∆E= ∂tE · t energy normalization

  8. Some results (partial) • Comparison with “Dissipation in compressible magnetodydrodynamic turbulence” by Stone, Ostriker, Gammie • Є=Єk+Єb+Єth • Єth=p/(γ-1), γ=1 → Єth=ρcs2 log(ρ/ρ0)

  9. Open questions • Can molecular clouds be supported against gravitational collapse solely by magnetic turbulence? • If not, how important a role MHD turbulence plays? • What other mechanisms are realistic?

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