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A resolution of the magnetic braking catastrophe during the second collapse

A resolution of the magnetic braking catastrophe during the second collapse. Wolf B. Dapp & Shantanu Basu. cc2yso UWO, May 17, 2010 – Wolf Dapp. Protostellar disks. www.hubblesite.org. Magnetic flux and angular momentum problem.

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A resolution of the magnetic braking catastrophe during the second collapse

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  1. A resolution of the magnetic braking catastrophe during the second collapse Wolf B. Dapp & Shantanu Basu cc2yso UWO,May 17, 2010 – Wolf Dapp

  2. Protostellar disks www.hubblesite.org

  3. Magnetic flux and angular momentum problem • the resolution of those two problems are interlinked (preceding talks by Galli, Li) • cloud cores have ideal MHD cc2yso UWO,May 17, 2010 – Wolf Dapp

  4. Magnetic braking • coupling of disk’s magnetic field with external field • torsional Alfvén waves transfer angular momentum from disk to low-density external medium

  5. Ambipolar diffusion • ions gyrate around magnetic field lines • neutrals effectively ‘feel’ the magnetic field through collisions • they drift only slowly past the ions • dominant flux loss mechanism in the regime n < ~1010 cm-3 (c) 2006 Pearson Education, Inc., publishing as Addison Wesley

  6. Ohmic dissipation • if charged particles are not well-coupled to the magnetic field, collisions can knock them off, and flux is dissipated • dominant flux loss mechanism between ~1012 < n < 1015 cm-3(Nakano et al. 2002, Kunz & Mouschovias 2010)

  7. Introduction • Method and Initial State • Results • Future work • Summary Outline cc2yso UWO,May 17, 2010 – Wolf Dapp

  8. our approach common approach AU-sized sink cell resolution down to stellar sizes • AU-sized sink cells, only first core resolved • no disk formation found • a disk forms under the right conditions cc2yso UWO,May 17, 2010 – Wolf Dapp

  9. Method • axisymmetric, rotating, thin disk • logarithmic, adaptive grid, N = 1024, Drmin = 0.02 , resolving the 2nd core • ambipolar diffusion, ohmic dissipation, magnetic braking, and force-free external B • barotropic pressure-density relation • disk is hydrostatic in z-direction, incl point mass/disk gravity, magnetic pinching, thermal and external pressure cc2yso UWO,May 17, 2010 – Wolf Dapp

  10. Magnetic braking and ohmic dissipation from steady-state Alfvén wave propagation (Basu & Mouschovias 1994) resistivity, Machida et al. (2007), Nakano et al. (2002) ionization fraction cc2yso UWO,May 17, 2010 – Wolf Dapp

  11. Barotropic pressure-density relation Masunaga & Inutsuka (2000) secondcore Ionization of HI @13.6 eV Dissociation of H2 @4.5 eV geff = 1.1 second collapse g= 7/5 collapsing dense core “first core” cc2yso UWO,May 17, 2010 – Wolf Dapp

  12. central number density column density rotation rate external number density vertical magnetic field mass-to-flux ratio Temperature nc = 4.4 x 106 cm-3 Sc = 0.23 g cm-2 Wedge = 0.3 km s-1 pc-1 = 10-14 s-1 next = 103 cm-3 Bz = 200 mG m0 = 2 T = 10 K Initial state cc2yso UWO,May 17, 2010 – Wolf Dapp

  13. Introduction • Method and Initial State • Results • Future work • Summary Outline cc2yso UWO,May 17, 2010 – Wolf Dapp

  14. Results: Density profile second core Dapp & Basu (2010) ohmic dissipation first core flux-freezing added centrifg support under flux freezing magnetic wall prestellar infall profile, r -1 expansion wave, r -1/2 cc2yso UWO,May 17, 2010 – Wolf Dapp

  15. Results: Magnetic Field Dapp & Basu (2010) } 3 orders of magnitude difference magnetic wall cc2yso UWO,May 17, 2010 – Wolf Dapp

  16. Results: Mass-to-flux ratio Dapp & Basu (2010) cc2yso UWO,May 17, 2010 – Wolf Dapp

  17. Results: Angular velocity Dapp & Basu (2010) expansion wave, r -2 magnetic braking catastrophe cc2yso UWO,May 17, 2010 – Wolf Dapp

  18. Disk formation! • introduce sink cell (a few ) after 2nd core forms Dapp & Basu (2010) centrifugal balance • centrifugal balance is achieved cc2yso UWO,May 17, 2010 – Wolf Dapp

  19. Disk formation! • infall velocity plummets Dapp & Basu (2010) cc2yso UWO,May 17, 2010 – Wolf Dapp

  20. Disk formation! • disk fragments into ring Dapp & Basu (2010) classical Toomre instability cc2yso UWO,May 17, 2010 – Wolf Dapp

  21. very fast runs, allows for large parameter searches • Add non-axisymmetry or effective viscosity to stabilize disk / long-term disk evolution Future work cc2yso UWO,May 17, 2010 – Wolf Dapp

  22. we resolve the 2nd core • despite magnetic braking, a disk does form at a very early age, very close to the 2nd core • we can differentiate between prestellar and centrifugal disks • we resolve and identify features like • expansion waves in S,W • magnetic wall(s) • Ohmic dissipation • removes flux efficiently within 1st core, • effectively shuts off magnetic braking, • increases m-t-f ratio by ~103 Summary cc2yso UWO,May 17, 2010 – Wolf Dapp

  23. The End cc2yso UWO,May 17, 2010 – Wolf Dapp

  24. Thin-disk test • thin-disk model is justified within the 1st core, and in the prestellar profile outside • it’s not applicable within the 2nd core, as expected Z = r cc2yso UWO,May 17, 2010 – Wolf Dapp

  25. Initial profile • collapse profile with and • angular velocity goes as column density Dapp & Basu (2010) cc2yso UWO,May 17, 2010 – Wolf Dapp

  26. Expansion wave effects • gravitational field just outside the central stellar core instead of as further out • free-fall profile outside of star, • infall velocity • steady-state mass accretion • angular velocity now • angular momentum cc2yso UWO,May 17, 2010 – Wolf Dapp

  27. Mass-to-flux-ratio in the ISM Basu (2005) • observations consistent with m = 1 • assembled from ionized subcritical HI gas • problems with higher m: • accumulation length~1 kpc for m = 1 • accumulation speed10 km/s ↔ 10 pc/Myr • collapse as soon as m > 1 • large scale fields ordered • Emag ~ Egrav Alves et al. (2008) cc2yso UWO,May 17, 2010 – Wolf Dapp

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