Multidimensional Models of Magnetically Regulated Star Formation

1. 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

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

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

4. 2D simulation box Dense core Gravitational collapse leads to cores. Indebetouw & Zweibel (2000) Basu & Ciolek (2004) Li & Nakamura (2004) MHD simulation: 2-dimensional Structure of the z-direction is integrated into the plane  2D approximation. Magnetic field line Low density and hot gas Molecular cloud

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

6. 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. Initially critical mass-to-flux ratio  balance between gravity and magnetic restoring forces. But neutrals slip past ions/magnetic field. likely low SFE Column density Mass-to-flux ratio m

7. 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) 0.1 pc Horizontal slice through a core.

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

9. MHD Models of Gravitational Instability Taurus, C18O (Nanten telescope) Relate to observed maps? 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)

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

11. 1-D Magnetohydrodynamic (MHD) equations Ideal MHD (mass) (z-momentum) (y-momentum) (magnetic field) (self-gravity) (gas) (isothermality)

12. Density Evolution Kudoh & Basu (2003) a Driving is terminated at t =40 t0. The density plots at various times are stacked with time increasing upward. Input constant amplitude disturbance during this period. Turbulent driving amplitude increases linearly with time between t=0 and t=10t0.

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

14. Power spectrum of a time snap shot Power spectrum as a function of a wave number (k) at t =30t0. Power spectrum of vy Power spectrum of By driving source Note that there is significant power on scales larger than the driving scale ( ). Kudoh & Basu (2005)

15. 1D simulation box 2D simulation box Dense core Back to 2-D model. What happens deep within collapsing cores? MHD simulation: 2-dimensional Structure of the z-direction is integrated into the plane  2D approximation. Magnetic field line Low density and hot gas Molecular cloud

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

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

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

19. 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)