Multidimensional Models of Magnetically Regulated Star Formation Shantanu Basu University of Western Ontario Collaborators: Glenn E. Ciolek (RPI), Takahiro Kudoh (NAO, Japan), Eduard I. Vorobyov (UWO) Submillimeter Astronomy, CfA, June 15, 2005

Onishi et al. (2002) Taurus Molecular Cloud 5 pc velocity dispersion sound speed distance = 140 pc

magnetic force gravity MHD wave pressure Turbulence Magnetic field line Cloud Magnetized Interstellar Cloud Schematic Picture

Magnetic field line MHD simulation: 2-dimensional Low density and hot gas Molecular cloud Structure of the z-direction is integrated into the plane  2D approximation. 2D simulation box Indebetouw & Zweibel (2000) Basu & Ciolek (2004) Li & Nakamura (2004) Gravitational collapse leads to cores. Dense core

Two-Fluid 2-D MHD Equations (some higher order terms dropped) Magnetic thin-disk approximation. Basu & Ciolek (2004)

MHD Model of Gravitational Instability Basu & Ciolek (2004) - Two-dimensional, uniform grid, periodic; normal to mean B field. Small perturbations added to initially uniform state. Column density Mass-to-flux ratio  Initially critical mass-to-flux ratio  balance between gravity and magnetic restoring forces. But neutrals slip past ions/magnetic field. likely low SFE

MHD Model of Gravitational Instability Infall motions are subsonic. Maximum Similar to infall speeds in cores where measured, e.g., Tafalla et al. (1998), Williams et al. (1999), Lee et al. (1999, 2001, 2004) Horizontal slice through a core. 0.1 pc

MHD Model of Gravitational Instability Basu & Ciolek (2005) Negligible Weak Strong in all images - intermediate time scale ~ 4 Myr - supersonic infall - moderate elongation - large spacing - longest time scale ~ 50 Myr - subsonic infall - mildest elongation - small spacing - shortest time scale ~ 2 Myr - supersonic infall - greatest elongation - smallest spacing

MHD Models of Gravitational Instability Relate to observed maps? Taurus, C 18 O (Nanten telescope) Further effects necessary? - core spacing - core masses, shapes - polarization patterns - magnitude of infall motions - turbulent motions (Li’s talk) - 3D, non-periodic important for turbulence - microphysics (ionization, heating/cooling)

Magnetic field line MHD simulation: 1-dimensional Self-gravity Magnetic field line Driving force Molecular cloud Hot medium 1D simulation box Low density and hot gas Molecular cloud 2D simulation box Kudoh & Basu (2003) A model for turbulent motions

1-D Magnetohydrodynamic (MHD) equations (mass) (z-momentum) (y-momentum) (magnetic field) (self-gravity) (gas) (isothermality) Ideal MHD

Input constant amplitude disturbance during this period. The density plots at various times are stacked with time increasing upward. Turbulent driving amplitude increases linearly with time between t=0 and t=10t 0. Driving is terminated at t =40 t 0. a Density Evolution Kudoh & Basu (2003)

Linewidth-Size Relation from Ensemble of Cloud Models Kudoh & Basu (2002) Most power concentrated on largest scales. Large scale oscillations survive longest after internal driving discontinued. Velocity dispersion (  ) vs. Scale of the clouds Consistent with observations Time-averaged gravitational equilibrium Filled circles = half-mass position, open circles = full-mass position for a variety of driving amplitudes. Linewidth- size relation

Power spectrum of a time snap shot Power spectrum as a function of a wave number (k) at t =30t 0. Note that there is significant power on scales larger than the driving scale ( ). Power spectrum of B y Power spectrum of v y Kudoh & Basu (2005) driving source

Magnetic field line MHD simulation: 2-dimensional 1D simulation box Low density and hot gas Molecular cloud Structure of the z-direction is integrated into the plane  2D approximation. 2D simulation box Back to 2-D model. What happens deep within collapsing cores? Dense core

Zoom in to simulate the collapse of an intially slightly nonaxisymmetric supercritical core Basu & Ciolek (2004) Core to Protostar + Disk Vorobyov & Basu (2005)

Disk Formation and Protostellar Accretion Vorobyov & Basu (2005) Ideal MHD 2-D (r,  simulation of rotating supercritical core. See poster (#76, downstairs) on this subject! Logaritmically spaced grid; inner zone width 0.3 AU.

Spiral Structure and Episodic Accretion Vorobyov & Basu (2005) FU Ori events Spiral arms create a strong centrifugal disbalance  bursts of mass accretion; 0.01 to 0.05 solar masses are accreted.

Summary Two-dimensional simulations of magnetically-regulated fragmentation: - core properties depend on magnetic field strength - infall speeds subsonic for critical and subcritical cases; for star formation. - maximum infall speeds supersonic for supercritical case; for star formation. One-dimensional simulations of turbulence: - stratified cloud has largest (supersonic) speeds in outermost parts - significant power generated on largest scales even with driving on smaller scales. Collapse of nonaxisymmetric rotating cores: - leads to centrifugally balanced disk  spiral structure  burst of enhanced accretion  spiral structure regenerated …. cycle continues due to continued mass infall from envelope. (poster Vorobyov & Basu)