Magnetic Fields: Recent Progress and Future Tests Shantanu Basu The University of Western Ontario EPoS 2008, Ringberg Castle, Germany July 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?

Progenitors are H I Clouds Heiles & Troland (2008) Column density B los subcritical supercritical Flux freezing in HI gas  Critical or supercritical MC formation requires significant accumulation of mass ALONG the magnetic field.

MC Accumulation Constraints Mestel (1999), Stellar Magnetism, and earlier papers quotes 10 3 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), 12 CO emission Striations of gas emission consistent with magnetically- dominated envelope. Taurus Molecular Cloud Heyer 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 A V > 5 mag, threshold for shielding of UV?

Ambipolar Diffusion time in MC’s For CR ionized regions For UV ionized envelopes, x i is ~ and  AD is very long  effective flux freezing. Much larger than geometric cross sec. due to polarizability of H 2

 1 is interesting! numbers from Ciolek & Basu (2006) ambipolar diffusion time For CR ionized sheet, with half thickness Z 0.

Magnetic Fields and Origin of the CMF/Massive Stars Ciolek & Basu (2006) Preferred fragmentation mass can vary dramatically even with a narrow range of    Standard value for CR ionized region

Magnetic Fields and Origin of the CMF/Massive Stars Basu, Ciolek & Wurster (2008), arXiv: Periodic isothermal thin-sheet model. Initial small amplitude perturbations. B is initially normal to sheet. Column density and velocity vectors (unit 0.5 c s ) Note irregular shapes with NO strong turbulence.

Narrow lognormal-like. High-mass slope much steeper than observed CMF/IMF. “Core” = enclosed region with 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.

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.

Turbulent Fragmentation with B and Ambipolar Diffusion Thin disk approximation Li & Nakamura (2004) (a)-(e) subcritical (    0.83  model, (f)-(h) supercritical (   = 1.25  model. v k 2 ~ 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) Nonlinear initial velocity field rms amplitude 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 trans-Alfvénic

3D Turbulent Fragmentation with B and AD Kudoh & Basu (2008) What’s really happening?  is a proxy for . Early turbulent compression Then, higher density region evolves with near vertical force balance Rapid contraction when/where

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 ratio trans-Alfvénic turbulence supercritical mtoflx ratio super-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 Initial mag. field strength

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 Angle (degrees) AU Angle (degrees) Poster 02, Wolf Dapp & S. Basu This massive star forming region fit by mildly supercritical model. 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 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. 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 ratio) 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 ~10 6 yr Local (periodic) highly turbulent models predict very large infall and have other drawbacks. Future  global approaches, including ambipolar diffusion.