Transcript 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 ≤ 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
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
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
Equations (no source term)
1. ∂tρ+(ρv)=0
2. ∂t(ρv)+(ρvv+Pδ-bb)=0
3. ∂te+[(e+P)v-bb·v]=0
4. e=ρv2/2+p/(γ-1)+b2/2
5. ∂tb= x (v x b)
6. ·b=0
7. P=p+b2/2
P total pressure, p gas pressure, є thermal
Our numerical model - ISOTHERMAL
 Adiabatic version:
“A Free, Fast, Simple and Efficient TVD MHD code”
by Ue-Li Pen, Phil Arras, ShingKwong Wong (astroph/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.
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
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)
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?