the story of star birth shantanu basu university of western ontario cap lecture, uwo, april 2, 2003
TRANSCRIPT
The Story of Star Birth
Shantanu Basu
University of Western Ontario
CAP Lecture, UWO, April 2, 2003
Understanding our Origins
The Galaxy
Molecular Clouds
Disorderly
Complex
Nonlinear
Giant Molecular Cloud in Orion
Infrared view
From IRAS satellite
Molecular Clouds
Order?
Solomon et al. (1987)
From CO (J=1-0) maps.
2
1/ 2
2
2 0
3 32 0
2 5
if constant.
T
MM G
R
R R
Theory: equilibrium =>
1/ 2S
approx. true empirically = 1-dimensional velocity dispersion.
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.
Magnetic Fields and PolarimetryŠ
Background Star emits Unpolarized Continuum
Result: Observed -vector is parallel to plane-of-the-sky component of .
EB
B
ee
Most Likely Orientation
Least Likely Orientation
Polarization of Background Starlight by Magnetically Aligned Grains
E
B
(Partial) Polarization Observed
Courtesy A
. Goodm
an
Taurus Dark Cloud Complex ( 1 - 10 pc scales)
Magnetic Field Strength Data
From measurements of the Zeeman effect.
Data from Crutcher (1999)
12/12
GB
Let mN Empirically, see
B In particular,
Best fit => 1.6.
Note: =1 =>gravitational potential energy = magnetic energy.
Dimensionless mass-to-flux ratio
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.
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: 6
3
3 10 G on pc scales
10 cm/s.i ee
B
jv v
n e
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
Magnetic Pressure and Tension
2
1
4
1.
8 4
L
jf B B B
c
BB B
B
sn
B of bar magnet
B near solar surface
2 2
ˆ ˆIf .8 4L
c
B BB Bs f n
n R
Magnetic pressure gradient Magnetic tension due to finite radius of curvature Rc.
Magnetohydrodynamic Waves
2
4 c
B
RMagnetic tension
Alfven waves propagate like a wave on a tensioned string.
Propagation speed restoring term
inertial term
Alfven speed20 .
4A
Bv
Other wave modes include longitudinal motions as well.
Empirical evidence for MHD Waves/Turbulence
Basu (2000)
1
1
/ 2 , where
where4
,
.A
Ac
B
v
mn
Bv
1Best fit 0.45.c
i.e., Alfvenic motions in molecular clouds?
Outflows
MHDWaves
Thermal Motions
MHDTurbulence
InwardMotions
SNeH II Regions
Scenario for a Molecular Cloud B
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 2 / 2
0 0, 0 sech for .
ˆ( , 0) .
z H
z
z t z H e z H
B z t B z
• Cloud is bounded by a hot external medium
•Add nonlinear driving force near z = 0 =>
Kudoh & Basu (2003)
.1.0for 2sin),( 000 HzztatzF a
(Spitzer 1942)
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 andhot medium
Simulationbox
z
Molecular cloud
Hot medium
Kudoh & Basu (2003)
Basic MHD equations in 1.5 dimensions
2
0
1
8
1
4
0
0
4
z
yz zz z
y y yz z
z
yy z z y
z
vt z
Bv v Pv g
t z z z
v v Bv B
t z z
T Tv
t zB
v B v Bt z
gG
zkT
Pm
mass continuity
z-momentum
y-momentum
isothermality
magnetic induction
self-gravity (Poisson’s eqn.)
ideal gas law
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 H0 .
in this model.1,,30 00
20 HcHca ss
Parameters:
A Model for Turbulent Molecular Clouds
A snapshot.
Averaged.
A Model for Turbulent Molecular Clouds
Time average within the standard cloud.
Rms speeds increase toward cloud boundary.
21,
2 yv2
,8
yB
21
,2 zv nkT
Transverse standing wave => boundary is a node for By, antinode for vy.
Results for an ensemble of clouds with different turbulent driving strengths:
.50,40,30,20,10 02
0 Hca s
Solid circles => half-mass position
Open circles => edge of cloud
1/ 2Z
0.5 Av
Correlations of Global Properties
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.
221.
8 2y
y
Bv
2 2.y zv v
0.5 Av 1/ 2Z
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.
Outflow Model
Tomisaka (2002)
Critical interplay of rotation and magnetic field
Red = Magnetic field lines
Solid black = isodensity contours
Arrows = velocity vectors
Molecular or Dark Clouds
"Cores" and Outflows
Stages of Star Formation
Jets and Disks
Extrasolar System
1 p
c
Expansion Wave
Static outer core
Free-fall onto point mass
Region of infall moves outward at sound speed cs. Instantaneous radius of expansion wave is r = cst.
Based on model of Shu (1977)
Mass infall rate 3
.scdM
dt G
Q. But when does it end? How is the mass of a star determined?
sr c t
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.
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 image Gravitational field vectors
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?