1. The Story of Star Birth Shantanu Basu University of Western Ontario CAP Lecture, UWO, April 2, 2003

2. Understanding our Origins

3. The Galaxy

4. Molecular Clouds Disorderly Complex Nonlinear Giant Molecular Cloud in Orion Infrared view From IRAS satellite

5. Molecular Clouds Order? Solomon et al. (1987) From CO (J=1-0) maps. Theory: equilibrium => approx. true empirically  = 1-dimensional velocity dispersion.

6. Effect of Magnetic Fields Mathewson & Ford (1970) Polarized starlight yields information about plane-of-sky component of interstellar magnetic field. 1950’s – Chandrasekhar, Fermi use polarization data to estimate interstellar B strength ~ few  G (1 G = 10 -4 T). Similar estimate from cosmic ray data by Schluter, Biermann, Alfven, and Fermi.

7. Magnetic Fields and Polarimetry

8. Courtesy A. Goodman Taurus Dark Cloud Complex ( 1 - 10 pc scales)

9. Magnetic Field Strength Data From measurements of the Zeeman effect. Data from Crutcher (1999) Empirically, see In particular, Best fit => Note:  =1 => gravitational potential energy = magnetic energy. Dimensionless mass-to-flux ratio

10. Key Questions of the Early Stages of Star Formation How does matter arrange itself within interstellar clouds? Clarify the role of B and turbulence. Are clouds in approximate equilibrium between magnetic and turbulent support vs. gravity? Can we explain the observed correlations between , R, B, n ? What is the dissipation time scale of MHD turbulence? If much less than cloud lifetime, why is it commonly observed? Are driving sources adequate? How do star-forming cores get established within clouds? Inefficiency of star formation.

11. Why Magnetic Fields? Q. Why no large scale electric field? A.Overall charge neutrality in plasma means that E is shorted out rapidly by moving electric charges. In contrast, the required currents for large scale B can be set up by tiny drifts between electrons and ions. Finally, once large scale B is set up, it cannot be shorted out by (nonexistent) magnetic monopoles, nor can the very low resistivity dissipate the currents in a relevant time scale. Maxwell’s equations:

12. Flux Freezing In a highly conducting plasma cloud, contraction generates currents that make the magnetic field inside grow stronger, so that magnetic flux is conserved. The magnetic field lines are effectively “frozen” into the matter. Self-inductance

13. Magnetic Pressure and Tension B of bar magnet B near solar surface Magnetic pressure gradient Magnetic tension due to finite radius of curvature R c.

14. Magnetohydrodynamic Waves Magnetic tension Alfven waves propagate like a wave on a tensioned string. Propagation speed Alfven speed Other wave modes include longitudinal motions as well.

15. Empirical evidence for MHD Waves/Turbulence Basu (2000) i.e., Alfvenic motions in molecular clouds?

16. Outflows MHD Waves Thermal Motions MHD Turbulence Inward Motions SNe H II Regions Scenario for a Molecular Cloud

17. A New Computational Model of MHD Turbulence Numerical solution of equations of ideal magnetohydrodynamics,.i.e., fluid equations + Maxwell’s equations in low frequency limit Start with one-dimensional self-gravitating equilibrium state Cloud is bounded by a hot external medium Add nonlinear driving force near z = 0 => Kudoh & Basu (2003) (Spitzer 1942)

18. self-gravity perturbation Molecular cloud Magnetic field line Schematic picture of our simulation A sinusoidal perturbation is input into the molecular cloud. Magnetic field line Low-density and hot medium Simulation box Molecular cloud Hot medium Kudoh & Basu (2003)

19. Basic MHD equations in 1.5 dimensions mass continuity z -momentum y -momentum isothermality magnetic induction self-gravity (Poisson’s eqn.) ideal gas law

20. A Model for Turbulent Molecular Clouds Kudoh & Basu (2002) Highlights: Cloud expands due to turbulent pressure, achieves “steady state” between t = 10 and t = 40; later contracts when forcing discontinued at t = 40. Outer cloud undergoes largest amplitude oscillations. Resolution: 50 points per length H 0. in this model. Parameters:

21. A Model for Turbulent Molecular Clouds A snapshot. Averaged.

22. A Model for Turbulent Molecular Clouds Time average within the standard cloud. Rms speeds increase toward cloud boundary. Transverse standing wave => boundary is a node for B y, antinode for v y.

23. Results for an ensemble of clouds with different turbulent driving strengths: Solid circles => half-mass position Open circles => edge of cloud Correlations of Global Properties

24. What Have We Learned? Clouds can be in a time-averaged balance between turbulent support and gravity. Inner cloud obeys equipartition of transverse wave energy, Transverse modes dominate, Outer low density part of cloud undergoes large longitudinal oscillations, and exhibits transverse (Alfvenic) standing wave modes. Correlations and naturally satisfied. Further progress includes two- and three-dimensional simulations – need to scale to multi-processor systems, e.g., SHARCNET.

25. What Happens Next? Motte et al. (1998) HH47 jet seen by HST Young stellar object and disk - HST Local collapse of cores intensifies rotation and magnetic field strength. Rotation => disks Rotation + magnetic field => jets.

26. Outflow Model Tomisaka (2002) Critical interplay of rotation and magnetic field Red = Magnetic field lines Solid black = isodensity contours Arrows = velocity vectors

27. Molecular or Dark Clouds "Cores" and Outflows Stages of Star Formation Jets and Disks Extrasolar System 1 pc

28. Expansion Wave Static outer core Free-fall onto point mass Region of infall moves outward at sound speed c s. Instantaneous radius of expansion wave is r = c s t. Based on model of Shu (1977) Mass infall rate Q. But when does it end? How is the mass of a star determined?

29. Key Questions of the Late Stages of Star Formation What sets the size scale of a collapsing region? Inefficiency of star formation. Do cores undergo fragmentation during collapse? Does most collapsing material land on a disk first? If so, how does accretion from disk onto star proceed? Jet/outflow formation and its interaction with disk dynamics. After a central point mass (the star!) forms, an expansion wave moves outward – when does it stop? This sets the maximum possible mass of a star.

30. Clues to the Mass Scale New two-dimensional MHD simulation (Basu & Ciolek 2003) – calculate nonlinear evolution of cloud column density integrated along mean field direction; no turbulent driving; periodic domain; initially critical mass-to-flux ratio  =1)  Column density imageGravitational field vectors

31. Final Thoughts Fundamental question: how does matter arrange itself within interstellar molecular clouds? The role of magnetic fields and MHD turbulence is critical MHD simulations of turbulent support and core formation provide insight into the early stages of star formation Various groups have developed models for individual stages of the star formation process Progress can be made with high dynamic range simulations that tie together many different stages An ultimate question: how are stellar masses determined?