Magnetic Fields: Recent Progress and Future Tests

1. Magnetic Fields: Recent Progress and Future Tests Shantanu Basu The University of Western Ontario EPoS 2008, Ringberg Castle, Germany July 29, 2008

2. Collaborators: Glenn E. Ciolek (RPI, USA) Takahiro Kudoh (NAO, Japan) Eduard I. Vorobyov (ICA, Canada) Wolf Dapp (UWO) James Wurster (UWO) Many Thanks to Poster 02 Model for L1689B and magnetic field line curvature of OMC1

3. Molecular Clouds: Subcritical or Supercritical?

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

5. MC Accumulation Constraints Mestel (1999), Stellar Magnetism, and earlier papers quotes 103 above, not 150. Bottom line: Highly supercritical MC and rapid formation time t is trouble!

6. GMC Fields align with Galactic B Direction parallel to galactic plane H. Li et al. (2006)

7. 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. Goldsmith et al. (2008), 12CO emission Striations of gas emission consistent with magnetically-dominated envelope.

8. Pipe Nebula Magnetically regulated cloud formation? Pipe (and Taurus)  formed by flow or contraction along B? Alves, Franco, & Girart (2008)

9. Most mass is in the low density envelope Perseus Molecular Cloud Subcritical common envelope? Also turbulent. Highly ionized? Kirk, Johnstone, & Di Francesco (2006) Cores only at AV > 5 mag, threshold for shielding of UV?

10. Ambipolar Diffusion time in MC’s Much larger than geometric cross sec. due to polarizability of H2 For CR ionized regions For UV ionized envelopes, xi is ~ 10-4 and tAD is very long  effective flux freezing.

11. m  1 is interesting! For CR ionized sheet, with half thickness Z0. ambipolar diffusion time numbers from Ciolek & Basu (2006)

12. Magnetic Fields and Origin of the CMF/Massive Stars Preferred fragmentation mass can vary dramatically even with anarrowrange of m0. Standard value for CR ionized region Ciolek & Basu (2006)

13. Magnetic Fields and Origin of the CMF/Massive Stars Basu, Ciolek & Wurster (2008), arXiv: 0806.2482 Column density and velocity vectors (unit 0.5 cs) Note irregular shapes with NO strong turbulence. Periodic isothermal thin-sheet model.Initial small amplitude perturbations. B is initially normal to sheet.

14. CMF’s for fixed MTF Narrow lognormal-like. High-mass slope much steeper than observed CMF/IMF. Distributions peak at different values for each m0. “Core” = enclosed region with Basu, Ciolek, & Wurster (2008)

15. Magnetic Fields and Origin of the CMF/Massive Stars Add results from a range of models with m0=0.5 to m0 = 2.0. Get a broad distribution of core masses if m0 varies in a single cloud. Data from Nutter & Ward-Thompson (2007) Basu, Ciolek & Wurster (2008) Cumulative histogram of 1524 cores from over 400 separate simulations

16. Magnetic Field Line Curvature Reveals IC’s Weak Critical Basu, Ciolek & Wurster (2008)

17. Modes of Subcritical Fragmentation standard quasistatic AD nonlinear flow accelerated AD; Li, Nakamura Turbulence accelerated AD; Fatuzzo, Adams, Zweibel, Heitsch. flux freezing  no collapse These apply to CR ionized regions. Basu, Ciolek, Dapp, & Wurster (2008)

18. Turbulent Fragmentation with B and Ambipolar Diffusion Thin disk approximation Li & Nakamura (2004) time unit = 2 Myr; box width = 3.7 pc (a)-(e) subcritical (m0 = 0.83) model, (f)-(h) supercritical (m0 = 1.25) model. vk2~ k -4 spectrum – really a large-scale flow note filamentarity and velocity vectors

19. 3D Turbulent Fragmentation with B and AD Nonlinear IC Linear IC Nonlinear initial velocity field allowed to decay rms amplitude trans-Alfvénic Gas density in midplane (z=0) A vertical slice of gas density Kudoh & Basu (2008) using 64 x 64 x 40 cells box width = 2.5 pc

20. 3D Turbulent Fragmentation with B and AD What’s really happening? b is a proxy for m. Early turbulent compression Then, higher density region evolves with near vertical force balance Rapid contraction when/where Kudoh & Basu (2008)

21. 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).

22. Super-Alfvénic Turbulence ↔ Highly Filamentary, Large Velocities supercritical mtoflx ratio super-Alfvénic turbulence Decaying initial supersonic velocity perturbations in two thin-sheet models. Each compression leads to rapid, high velocity, efficient collapse (no rebound) subcritical mass-to-flux ratio trans-Alfvénic turbulence Basu, Ciolek, Dapp, & Wurster (2008)

23. 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.

24. Future Trends – MC Formation 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. Black arrows are velocity vectors. B field initially along x-direction. Ambipolar diffusion not included.

25. 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”. Initial mag. field strength time

26. Future Trends – Toward Global nonideal MHD Models 3D with ambipolar diffusion, in a patch of a larger cloud. turbulent diffuse halo supercritical dense cores fragmented nearly critical sheet Nakamura & Li (2008) Magnetic field lines in orange

27. Future Trend - Observing 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. Observations Simulations

28. Focus on Single Objects Also Important OMC-1 Schleuning (1998) Angle (degrees) This massive star forming region fit by mildly supercritical model. Angle (degrees) Poster 02, Wolf Dapp & S. Basu AU

29. The Later Stage of Core Collapse Girart, Rao, & Marrone (2006)

30. Catastrophic Magnetic Braking if Field is Frozen Lever arm is relatively very BIG! No Keplerian disk forms. Allen, Li, & Shu (2003)

31. Disk Formation with Magnetic Field Flux freezing disk forms only if m≥ 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. Mellon & Li (2008)

32. Magnetic dissipation Ambipolar diffusion 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. Ohmic Dissipation 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.

33. 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)

34. Thin Sheet collapse with Ambipolar D. & Ohmic D. Tassis & Mouschovias (2007) AD dominates OD dominates m (mtf ratio) Calculation stops when central star mass ~ 0.01 solar mass. Mass to flux ratio > 100 times critical value within ~ 1 AU radius.

35. 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.

36. 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.