Magnetic Fields in Star and Planet Formation Frank H. Shu UCSD Physics Department Stars to Planets -- University of Florida 12 April 2007

Outline and Logic of Talk Cloud core characterized by dimensionless mass- to-flux ratio collapses to form star + disk. Some loss of flux during collapse results in for system. Most of the mass ends up in the star; almost all of the flux, in the disk. Therefore, known mass of star implies calculable flux in disk. Self-contained theory of MRI for viscous/resistive spreading yields disk radius needed to contain flux trapped in disk as function of age t. Predictions for with f < 1 (sub-Keplerian rotation) of disk. Implications for disk- and X-winds, funnel-flows, and planetsimal formation.

Catastrophic Magnetic Braking if Fields Are Perfectly Frozen Allen, Li, & Shu (2003) – Initial rotation in range specified by Goodman et al. (1993). Some braking is needed, but frozen-in value is far too much (no Keplerian disk forms).

Ohmic Dissipation of Split Monopole Yields Central Region of Low Uniform Field M⊙,M⊙, Contours of constant F L /F G Magnetic field lines Shu, Galli, Lizano, & Cai (2006)

NGC 1333 IRS 4A Girart et al. (2006); Gonzalez et al. (2007) Best fit:

Mean-Field MHD of Accretion Disks in Star Formation Model equations: Lubow, Papaloizou, & Pringle (1994); Shu & Li (1997) Shu, Galli, Lizano, Glassgold, & Diamond (2007)

MRI Turbulence in Magnetized Accretion Disks Turbulent viscosity: Turbulent resistivity: No previous MRI simulation is both global and has a nonzero net magnetic flux. Reason why MRI simulations systematically give too small aviscosity compared to astrophysical systems (cf. King, Livio, & Pringle 2007). Shakura-Sunyaev viscosity with magnetic pressure replacing gas pressure.

Four Astronomical Models Steady-state solution: Models: ObjectT TauLMPFU OriHMP M * /M ¤ M * M ¤ /yr 1x x x x10 -4 t age /yr3x10 6 1x x10 5 D MD /M¤MD /M¤ f R  /AU ,520 J D ( M ¤ AU km/s) binary? ,700 binary? 0 = 4

Magnetic Fields and Surface Densities Both LMP and TT have ~ 1 G field at 3 AU, compatible with chondrules in meteorites. LMP and HMP have several to tens of mG fields at 100 &1000 AU (check with masers) FU Ori has kG at 0.05 AU, compatible with measurement by Donati et al. (2005). These authors also find rotation to be sub-Keplerian by factor of 2 to 3, compatible with f = Surface density of neither LMP nor TT looks like minimum solar nebula. The profile inferred from solids probably results from recycling of hot rocks near the protosun (Stardust sample-return mission).

Implications for X-wind/Funnel Flow/Planetesimal Formation Inward press of disk field resisted by outward press of squeezed magnetosphere. Change of magnetically coupled layers from sub- Kepler to super-Kepler with change in sign of, i.e with change from outward bend to inward bend of field lines. (Inner edge helps.) X-winds are better focused and faster with f < 1/3. Planetesimals probably form only in dead zones Shu, Lizano, Galli, & Cai (2007)