magnetic fields: recent progress and future tests shantanu basu the university of western ontario...
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Magnetic Fields: Recent Progress and Future Tests
Shantanu BasuThe University of Western Ontario
EPoS 2008, Ringberg Castle, GermanyJuly 29, 2008
Collaborators:
Glenn E. Ciolek (RPI, USA)Takahiro Kudoh (NAO, Japan) Eduard I. Vorobyov (ICA, Canada)Wolf Dapp (UWO)James Wurster (UWO)
Poster 02
Model for L1689B and magnetic field line curvature of OMC1
Many Thanks to
Molecular Clouds: Subcritical or Supercritical?
1/ 22 GB
1, 1, or 1 ?
Progenitors are H I CloudsHeiles & Troland (2008)
Column density
Blos
20 -210 cm
subcritical
supercritical
Flux freezing in HI gas Critical or supercritical MC formation requires significant accumulation of mass ALONG the magnetic field.
MC Accumulation Constraints
1/2 6 3
1
6 3 6
150 pc,2 1 3 10 G 1 cm
150 km/s.1 3 10 G 1 cm 10 yr
B B nL
G
L B n tv
t
Mestel (1999), Stellar Magnetism, and earlier papers quotes 103 above, not 150.
Bottom line: Highly supercritical MC and rapid formation time t is trouble!
GMC Fields align with Galactic B
H. Li et al. (2006)
Direction parallel to galactic plane
Goldsmith et al. (2008), 12CO emission
Striations of gas emission consistent with magnetically-dominated envelope.
Taurus Molecular CloudHeyer et al. (2008): Pol. maps → low plasma beta in envelope subcritical ? Most mass is in low density envelope (Goldsmith et al. 08), so probably, yes.
Pipe Nebula
Alves, Franco, & Girart (2008)
Magnetically regulated cloud formation?
Pipe (and Taurus) formed by flow or contraction along B?
Most mass is in the low density envelope
Kirk, Johnstone, & Di Francesco (2006)
Perseus Molecular Cloud
Subcritical common envelope? Also turbulent. Highly ionized?
Cores only at AV > 5 mag, threshold for shielding of UV?
Ambipolar Diffusion time in MC’s
2
2
21
2, where
1.4i
AD ni ni i iHA ni i H
mLn w
v m m
2 2 25
4 3 71.65 10 yr
0.1 pc 10 G 10 cm 10n i
AD
n xL B
For CR ionized regions
For UV ionized envelopes, xi is ~ 10-4 and AD is very long effective flux freezing.
Much larger than geometric cross sec. due to polarizability of H2
1 is interesting!
1/ 27 4 -310 10 cmi nx n
numbers from Ciolek & Basu (2006)
AD
0,g m
s
Z
c
0, 10g m
s
Z
c
ambipolar diffusion time
For CR ionized sheet, with half thickness Z0.
Magnetic Fields and Origin of the CMF/Massive Stars
Ciolek & Basu (2006)
22
, ,4g m g mM
Preferred fragmentation mass
can vary dramatically even with a narrow range of ,0
1/27
4 3
0.2
1010 cm
ni
i
nx
,0 0 flux freezingni
Standard value for CR ionized region
Magnetic Fields and Origin of the CMF/Massive Stars
Basu, Ciolek & Wurster (2008), arXiv: 0806.2482
0 1.1
0 2.0
0 0.5
Periodic isothermal thin-sheet model. Initial small amplitude perturbations. B is initially normal to sheet.
0' / (2 ), etc.x x Z
Column density and velocity vectors (unit 0.5 cs)Note irregular shapes with NO strong turbulence.
Narrow lognormal-like. High-mass slope much steeper than observed CMF/IMF.
“Core” = enclosed region with
.20, nn
Basu, Ciolek, & Wurster (2008)
Distributions peak at different values for each
CMF’s for fixed MTF
Magnetic Fields and Origin of the CMF/Massive Stars
Basu, Ciolek & Wurster (2008)
Data from Nutter & Ward-Thompson (2007)
Add results from a range of models with =0.5 to 0 = 2.0.
Cumulative histogram of 1524 cores from over 400 separate simulations
Get a broad distribution of core masses if 0 varies in a single cloud.
10 0 2
B
B
Critical Weak
Magnetic Field Line Curvature Reveals IC’s
Basu, Ciolek & Wurster (2008)
Modes of Subcritical Fragmentation
Basu, Ciolek, Dapp, & Wurster (2008)
standard quasistatic AD
flux freezing no collapse
Turbulence accelerated AD; Fatuzzo, Adams, Zweibel, Heitsch.
nonlinear flow accelerated AD; Li, Nakamura
These apply to CR ionized regions.
50 02 / 2 10 yrst Z c
Turbulent Fragmentation with B and Ambipolar DiffusionThin disk approximation Li & Nakamura (2004)
(a)-(e) subcritical (0.83model, (f)-(h) supercritical ( = 1.25model.
vk2~ k -4 spectrum – really a large-scale flow
note filamentarity and velocity vectors
time unit = 2 Myr; box width = 3.7 pc
3D Turbulent Fragmentation with B and AD
Kudoh & Basu (2008)
42 kvk
Nonlinear initial velocity field
rms amplitude
0 0.5
yr102 50 t
Gas density in midplane (z=0)
A vertical slice of gas density
Nonlinear IC
Linear IC
using 64 x 64 x 40 cells
allowed to decay
box width = 2.5 pc
3 Alfv c va s
trans-Alfvénic
3D Turbulent Fragmentation with B and AD
Kudoh & Basu (2008)
What’s really happening?
.4
Bv Bnt
ni B B Bn
28 2csB
2 3/2 22
2 2 2L LL n i n
ADv B BniA
is a proxy for .
Early turbulent compression
5/2 quickly as L LAD Then, higher density region evolves with near vertical force balance
1/2 more slowlyAD
Rapid contraction when/where 1.
Thin Sheet vs. 3D
Bottom line: 3D nonideal MHD fragmentation simulations confirm basic features of thin sheet models: kinematics, fragment spacings, etc.
Kudoh, Basu, Ogata, & Yabe (2007) confirm gravitational fragmentation (small-amplitude) models of Basu & Ciolek (2004), Basu et al. (2008)
Kudoh & Basu (2008) confirm turbulent fragmentation models of Li & Nakamura (2004), Nakamura & Li (2005).
Super-Alfvénic Turbulence ↔ Highly Filamentary, Large Velocities
Basu, Ciolek, Dapp, & Wurster (2008)
subcritical mass-to-flux ratiotrans-Alfvénic turbulence
supercritical mtoflx ratiosuper-Alfvénic turbulence
Each compression leads to rapid, high velocity, efficient collapse (no rebound)
Decaying initial supersonic velocity perturbations in two thin-sheet models.
Velocity Fields Tell the Story
Conclusion 1: These differences are testable!
Conclusion 2: Highly turbulent Fourier space driving in periodic boxes is NOT the way to go. Models of turbulence require GLOBAL approach.
Future Trends – MC Formation
Black arrows are velocity vectors. B field initially along x-direction. Ambipolar diffusion not included.
Fabian Heitsch’s talk, and e.g. Heitsch et al. (2007)
Molecular cloud formation and evolution starting from converging H I flows. Not periodic. No Fourier space driving. Thermal instability (and other instabilities) occur.
Left: inclusion of B field; Hennebelle et al. (2008), Banerjee et al. (2008). See poster 01 by Robi Banerjee. Use AMR codes.
Cluster Forming Region with B
Price and Bate (2008)
SPH simulation of cluster forming region with supercritical flux-frozen magnetic field. Leads to lower star formation efficiency and creation of magnetically dominated “voids”.
time
Initi
al m
ag.
field
str
engt
h
Future Trends – Toward Global nonideal MHD Models
Nakamura & Li (2008)
turbulent diffuse halo
fragmented nearly critical sheet
supercritical dense cores
Magnetic field lines in orange
3D with ambipolar diffusion, in a patch of a larger cloud.
Future Trend - Observing Simulations
Observations
Simulations
1. Star Formation Taste Tests, Alyssa Goodman, Focus group, Thursday.
2. Helen Kirk’s talk today. “Observe’’ magnetic turbulent ambipolar diffusion simulations. Compare relation of core velocity dispersion to that of the surrounding region.
Focus on Single Objects Also Important
Ang
le (
degr
ees)
AU
Ang
le (
degr
ees)
Poster 02, Wolf Dapp & S. Basu
This massive star forming region fit by mildly supercritical model.
01.0 2.0
OMC-1 Schleuning (1998)
The Later Stage of Core Collapse
Girart, Rao, & Marrone (2006)
Catastrophic Magnetic Braking if Field is Frozen
Allen, Li, & Shu (2003)
No Keplerian disk forms.
Lever arm is relatively very BIG!
Disk Formation with Magnetic Field
Mellon & Li (2008)
Flux freezing disk forms only if ≥ 100 ! Shown on left.
Can such a highly supercritical region be achieved, and within 100 AU of protostar?
Black lines represent magnetic field. Centrifugal disk enclosed by white line.
Magnetic dissipation
Ambipolar diffusion
Ohmic Dissipation
2
2 2
1AD
A ni
L
v B
Neutral-ion colliison time. More generally, neutral-charged-grain collisions too. Grains in turn affect ion numbers. In AD, field does not decay but neutrals do not advect field fully.
2
4OD
cL
Resistivity. Depends on e-i and e-n collisions generally. A true decay of currents and magnetic field. Eventually more effective than AD in reducing central flux.
3D Nested Grid Simulation with Ohmic Dissipation
Machida et al. (2007)
Also, talk by Ralph Pudritz today
Calculation stops when central star mass ~ 0.01 solar mass. Mass to flux ratio > 100 times critical value within ~ 1 AU radius.
based on Nakano et al. (2002)
Thin Sheet collapse with Ambipolar D. & Ohmic D.
(
mtf
rat
io)
Tassis & Mouschovias (2007)
AD dominates OD dominates
Calculation stops when central star mass ~ 0.01 solar mass. Mass to flux ratio > 100 times critical value within ~ 1 AU radius.
Is B too strong in the late phases?
• How do observed disks form? Magnetic dissipation may not resolve MB catastrophe• Alternate explanations may be needed: outflow blows away envelope and eliminates angular momentum coupling? Main disk forms after outflow begins?• A 3D calculation with magnetic dissipation (microphysics can be tricky) that can model the full accretion phase is necessary for the future.
Role of B in the Early Phases
• Interplay of gravity, magnetic fields, and ambipolar diffusion yields a broad CMF, including massive cores. This process is independent but not mutually exclusive of competitive accretion and turbulent fragmentation.
• Magnetic field line curvature at core edges may be used as a proxy for measuring ambient mass-to-flux ratio
• Hard to avoid conclusion that overall cloud mass-to-flux ratios are close to critical value. Common envelope likely slightly subcritical but entire cluster forming regions (OMC1) may be supercritical
• Three-dimensional simulations confirm the mode of Turbulence Accelerated Magnetically Regulated Fragmentation. Formation of quiescent cores in ~106 yr
• Local (periodic) highly turbulent models predict very large infall and have other drawbacks. Future global approaches, including ambipolar diffusion.