From Clouds to Cores: Magnetic Field Effects on the Structure of Molecular Gas Shantanu Basu University of Western Ontario, Canada Collaborators: Takahiro Kudoh (UWO) Carol Jones (UWO) Glenn Ciolek (RPI) John Dubinski (Toronto) Star Formation 2002, Taiwan, June 12, 2002

Magnetic Field Strength Data Crutcher (1999) and Basu (2000) A better correlation Best fit slope = 0.47 Best fit slope = D velocity dispersion

Magnetic Field Strength Data Two separate correlations Best fit => (1) However, (2) Dimensionless mass-to-flux ratio As found by Myers & Goodman (1988) Pressure of self-gravityTurbulent pressure

Magnetic Field Strength Data Using B los, best fit implies i.e., Alfvenic motions in molecular clouds? e.g., Myers & Goodman (1988), Bertoldi & McKee (1992), Mouschovias & Psaltis (1995).

A Model for Turbulent Molecular Clouds Kudoh & Basu (2002) Numerical solution of MHD equations in 1-D. Start with Spitzer 1-D equilibrium state Cloud has a moving boundary Density stratification due to gravity Add nonlinear forcing near z = 0 => nonzero Highlights: Cloud expands due to turbulent pressure, achieves “steady state”; later contracts as forcing discontinued. z/H t / t cross,0

A Model for Turbulent Molecular Clouds Turbulent driving => At half-mass position z 1/2, simulation yields Kudoh & Basu (2002)

Dense Cores Tafalla et al. (1999) The specific case of L1544: Tafalla et al. (1999) & Williams et al. (1999) => spectra imply over a range of scales r ~ 0.02 – 0.1 pc. Apparent starless core with low turbulence.

A Model for L1544 Magnetic field model with ambipolar diffusion. Contraction of supercritical core => infall speed ~ 0.1 km/s for r ~ 0.01 – 0.1 pc. Oblate model flattening + observed elongation => implied inclination angle  = 74 o. Supercritcal core (  ~ 2) and  = 74 o => estimate B los. Ciolek & Basu (2000)

Zeeman Data for L1544 Ciolek & Basu (2000) predict B los = 16  G within r = 0.06 pc. Crutcher & Troland (2000) measure B los = 11 +/- 2  G within r = 0.06 pc. CT (2000) measurement not sensitive to inner region where B los > 25  G, therefore “measured field consistent with the model prediction”.

Polarization Data for L1544 Ward-Thompson et al. (2000) – Polarized submillimeter emission Angular offset  = 29 o +/- 6 o between apparent minor axis and apparent B direction. Inconsistent with pure oblate model.

Magnetic Field Projection for Triaxial Cores Basu (2000) Projected B field (dashed) and density contours (solid) for triaxial body (  = 0.3,0.6) seen from three viewing angles. Probability distribution function for offset angle .

Intrinsic Shapes of Cores Can invert observations of projected axis ratios to get an intrinsic shape distribution. Recent Data: Lee & Myers (1999) - compile projected b/a for 406 cores (optical selection). Jijina, Myers, & Adams (1999) - b/a for 264 cores (NH 3 maps). Analysis: Jones, Basu, & Dubinski (2001); Jones & Basu (2002) - invert these and other distributions to obtain intrinsic shapes. Previously, Ryden (1996) – several catalogs of 19 – 89 each.

Intrinsic Shapes of Cores Data for NH 3 cores, Jijina et al. (1999) Two key features of all observed distributions: (1)Significant decline towards p = 1. (2)Broad peak near p = 0.5 – Property (1) incompatible with pure oblate or even pure prolate objects. Triaxiality required for a better fit. Jones, Basu, & Dubinski (2001)

Intrinsic Shapes of Cores Jones, Basu, & Dubinski (2001) A uniform distribution of triaxial axis ratios  = c/a,  = b/a does not provide a good fit. Assuming triaxial ellipsoids (Binney 1985), any distribution of ratios  = c/a,  = b/a yields a distribution of observed axis ratios p for a large number of random viewing angles. Instead, assume Gaussian distributions of  and  and find distributions of projected axis ratio p.

Intrinsic Shapes of Cores Gaussians with centers at      width  = 0.1. Best fit using    analysis =>      inverse    values Best fit   is much smaller than    => cores primarily flattened in one direction => triaxial but nearly oblate. Broad peak favors near-oblate triaxial objects. Jones, Basu, & Dubinski (2001)

Shapes of Cores: The Bottom Line Near-oblate triaxial distributions provide best fit in all cases! Jones & Basu (2002)

Triaxial Cores Galli et al. (2001) – nonaxisymmetric equilibrium- L1544 overlay Origin Effect of large scale turbulence? Triaxial equilibria? Gravitationally driven effect? Implication Leads naturally to multiple star formation? Nakamura & Li (2002) – nonaxisymmetric collapse

Summary Magnetic field strength data imply an ensemble of turbulent clouds satisfying We have performed global 1-D ideal MHD simulations of turbulent molecular clouds. Stay tuned for Kudoh’s talk! Results agree with above relation; adjusts to value slightly greater than  v, which itself is related to the driving force. Oblate MHD supercritical core model for L1544 makes reasonable prediction for B los. Angular offset of B direction with apparent minor axis => triaxiality. Detailed analysis of large cloud core data sets show that cores indeed triaxial but nearly oblate.