The Story of Star Birth

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
Giant Molecular Cloud in Orion Infrared view
Disorderly Complex Nonlinear
From IRAS satellite
5
Molecular Clouds
Order?
From CO (J1-0) maps.
Theory equilibrium gt
Solomon et al. (1987)
s 1-dimensional velocity dispersion.
approx. true empirically
6
Effect of Magnetic Fields
Mathewson Ford (1970)
Polarized starlight yields information about
plane-of-sky component of interstellar magnetic
field.
1950s Chandrasekhar, Fermi use polarization
data to estimate interstellar B strength few mG
(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.
Empirically, see
In particular,
Best fit gt
Data from Crutcher (1999)
Dimensionless mass-to-flux ratio
Note m1 gt
gravitational potential energy magnetic energy.
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 s,
  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?

1. 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.
Maxwells equations
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.
12
Flux Freezing
Self-inductance
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.
13
Magnetic Pressure and Tension
B near solar surface
B of bar magnet
Magnetic tension due to finite radius of
curvature Rc.
Magnetic pressure gradient
14
Magnetohydrodynamic Waves
Alfven waves propagate like a wave on a tensioned
string.
Propagation speed
Magnetic tension
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
Scenario for a Molecular Cloud
SNe
H II Regions
17
A New Computational Model of MHD Turbulence
Kudoh Basu (2003)

• Numerical solution of equations of ideal
  magnetohydrodynamics, .i.e., fluid equations
  Maxwells equations in low frequency limit
• Start with one-dimensional self-gravitating
  equilibrium state

(Spitzer 1942)

• Cloud is bounded by a hot external medium
• Add nonlinear driving force near z 0 gt

18
Schematic picture of our simulation
Magnetic field line
Low-density and hot medium
Hot medium
Simulation box
Molecular cloud
self-gravity
Molecular cloud
perturbation
A sinusoidal perturbation is input into the
molecular cloud.
Magnetic field line
Kudoh Basu (2003)
19
Basic MHD equations in 1.5 dimensions
mass continuity
z-momentum
y-momentum
isothermality
magnetic induction
self-gravity (Poissons eqn.)
ideal gas law
20
A Model for Turbulent Molecular Clouds
Resolution 50 points per length H0 .
Parameters
in this model.
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.
Kudoh Basu (2002)
21
A Model for Turbulent Molecular Clouds
A snapshot.
Averaged.
22
A Model for Turbulent Molecular Clouds
Time average within the standard cloud.
Transverse standing wave gt boundary is a node
for By, antinode for vy.
Rms speeds increase toward cloud boundary.
23
Correlations of Global Properties
Results for an ensemble of clouds with different
turbulent driving strengths
Solid circles gt half-mass position Open circles
gt edge of cloud
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?
HH47 jet seen by HST
Motte et al. (1998)
Local collapse of cores intensifies rotation and
magnetic field strength. Rotation gt
disks Rotation magnetic field gt jets.
Young stellar object and disk - HST
26
Outflow Model
Red Magnetic field lines Solid black
isodensity contours Arrows velocity vectors
Tomisaka (2002)
Critical interplay of rotation and magnetic field
27
Stages of Star Formation
28
Expansion Wave
Static outer core
Region of infall moves outward at sound speed cs.
Instantaneous radius of expansion wave is r cst.
Free-fall onto point mass
Mass infall rate
Q. But when does it end? How is the mass of a
star determined?
Based on model of Shu (1977)
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 (m1).

Column density image
Gravitational 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?