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Magnetic pressure driven jet flow in young stellar systems
Kurt Liffman, CSIRO and Swinburne University of Technology Acknowledgement: ATNF/CASS Astrophysics Group Cosmic Magnetism Conference; 8th June 2010


Meteorites: Foundation Stones of the Planets
Cross section of the Allende carbonaceous chondrite
Chondrules formed ~ million years after CAIs

Chondrules
(melt objects)

1800 K Calcium Aluminium Inclusion (CAI) (condensates) 2000 K

CAIs ­ some of the first solids to form in the solar system ~ 4.57 billion years ago

Surrounding matrix (contains high temperature condensates) 500 K

Igneous rocks surrounded by "cold" sedimentary material. "Hot" rocks surrounded by "cold" material


Formation: local or non-local process?
Chondrules ­ first noted in 1802; first formation theory in 1877 approximately 20 formation theories developed since 1877 Two classes of theory

non-local

local formation

Meteoriticists ­ various lines of evidence (e.g. meteorites are from the asteroid belt: ~ 3 AU from the Sun) suggest local formation Astrophysicists ­ most energy at or near the inner rim of the disk: non-local


What is the Jet Flow Model?
Skinner (1990), Liffman (1991/2), Cameron (1994), Liffman & Brown (1995/6), Shu et al. (1996)

Nuth III J. A., 2001 American Scientist, 89, 228-235


Jet Processing of an Accretion Disk
· · · · Lifetime 106- 107 years Lifetime outflow mass ejected 0.1 M outflow "rock" mass ejected 10-3 - 10-4 M Total rock mass of the planets 10-4 M




10% fall back implies 10-4 - 10-5 M returned to the solar nebula

1000 AU Predictive Theory: Chondrules/CAI formed over a 107 year period. (Liffman 1992) Chondrules/CAI to be found in comets (Skinner 1990, Liffman, Shu et al.)


Stardust Mission
Dust particles obtained from a Kuiper Belt (i.e. ~ 40 AU) comet Same pattern as seen in meteorites: High formation temperature (> 1400K) rocks surrounded by cold material ­ in this case, ice. Chondrules and CAIs also found in Comet Wild 2 Nakamura et al. (2008) strongly suggest non-local formation. At 40 AU high temperature heating is difficult to understand

Brownlee et al. (2006)


Observations - forsterite dust formed in the interior disk regions surrounding Sun-like stars
Abraham et al. Nature 2009

"star burst" produces forsterite (Mg2SiO4) grains from amorphous dust within or around ~ 0.5 AU from the star These type of grains are observed in comets. Non-local formation!


"Modelling" the Jet Model ­ Inner Disk

x


Jet

Sun R R
*
t

R

o

Disk gas gas & dust R
d

Not to Scale

What is the jet flow mechanism?

Will consider magnetic pressure, instead of ceRrifugally driven nt co


Protostellar/T Tauri Jets
Two basic models:

Flow || to B

Why the dichotomy? MPD model Flow to B


Star-Disk Electric Circuit ­ J, B, E
Relative motion between the disk and stellar magnetic field generates an electric field

Rt ­ truncation radius Rco ­ co-rotation radius B* - stellar magnetic field j ­ current density

Nothing wrong with the MHD description, but the J, B, E description may provide some different insights.


Star-Disk Electric Circuit

Toroidal magnetic field induced within the disk


Magnetic Scale Height
The z component of the steady state momentum equation

hydrostatic (v = 0), isothermal form: which has the solution

where


Magnetic Scale Height
For the magnetically confined disk there is a distance from the central plane of the disk, HB, where the density of the disk goes to zero

Although this is the true height of the disk, it has a problem:

A more consistent definition gives the e-folding magnetic scale height, hB.

Which has the desired property that

Bz 0 hB h


Example: X-ray Binary

Liffman and Bardou (1999)


Star-Disk Torque

Liffman (2007)

The J, B, E model - same as the MHD answer for the torque on the disk from the star

Suppose there is a trans-field, short-circuit ­ perhaps due to Gravity Drift


Gravitational Drift
Gravitational Drift drives a radial current that short circuits the star-disk current

Drift Velocity

Gravitational Drift Current

Liffman (2007)


Short-Circuit ­ Toroidal Field
The radial transfield currents produce toroidal fields above and below the disk. jвB flow points away from the disk.

acceleration region starts near the top of the disk (z = z0)

Assume jr is a constant with z
toroidal field

acceleration region finishes when the radial current is exhausted (z = zT)

Liffman (2007)


Short Circuit ­ Total Force

Integrate jrвB over volume ­ total force is independent of jr variation with z

This implies that the ejection speed of the gas is independent of jr variation with z


Short-Circuit ­ Ejection Speed

Potentially high exhaust speed


Acceleration Region: Flow Speed
The z component of the steady state momentum equation

We can obtain a general flow speed "Bernoulli-like" equation

This allows us to deduce solutions for distance, speed, density of the flow as a function of time

Liffman et al. (2011)


Toroidal Fields?
How can toroidal fields drive the flow? Intuitive model

Step 1 Step 2

Step 3


Predictions
This simple theory leads to a number of, potentially, observable predictions (1) The ejection speed of the flow increases as one approaches the star

(2) Stellar rotation period may be a fundamental period of the flow (3) The flow starts at Rt and ends at "Ro" when the transfield current runs out

Current balance equation


Predictions
Mass ejection is proportional to mass accretion

Mass ejection rate and speed increases as the inner edge approaches the star

Star

Jet Flow
Rt

Rco


Predictions
Mass ejection is proportional to mass accretion

Mass ejection rate and speed increases as the inner edge approaches the star

Star
Rt

Rco


Predictions
Mass ejection is proportional to mass accretion

Jet Flow Star
Rt Rco


Laboratory Magnetic Jet Flows

Fastest speed listed in the literature ~ 200 km/s


Professor Aleksej Ivanovich Morozov


Conclusions
(1) Much of the solid material in the solar accretion disk underwent thermal processing with radial transport (2) A solar bipolar jet flow/rim wind could have provided the formation and transport mechanism for this material (3) Mass ejection is proportional to mass accretion (4) Toroidal fields may power the jet flows. (5) Jet flows produced at the inner rim of the disk (6) Mass ejection rate increases as the inner edge of the disk approaches the star and decreases as the inner edge approaches the co-rotation radius (7) Inner disk is compressed by the jet flow Meteorites may offer a way of deducing the mechanism for magnetically-driven outflows


CSIRO Material Science and Engineering Kurt LIffman Research Group Leader Phone: 03 9252 6167 Email: Kurt.Liffman@csiro.au

Thank you
Contact Us Phone: 1300 363 400 or +61 3 9545 2176 Email: enquiries@csiro.au Web: www.csiro.au


MHD Equations
Mass Conservation Momentum Conservation Maxwell Stress Tensor Energy Conservation Equation of State Ohm's Law And Maxwell's Equations


Energy Conservation
We want the conservative form: which Q is a flow constant Steady state isotropic pressure

+

Infinite conductivity Equation of State

+




V || B v B

+ other flow constants



where De Laval Nozzle Equation


Converging/Diverging Nozzle

vin



vthroat

vout


VB

B v






Magnetic Nozzle
where
Fast Magnetosonic Speed


AlfvИn Speed





CA and C

S

and




So there exists the possibility of high speed flow, relatively low temperature flow in a magnetic jet.



Radial Transport of Processed Material in Circumstellar Disks

The dust in the ISM has an amorphous structure. Inner disk dust ~ 90% crystalline silicate. Outer disk dust ~40% crystalline silicate

The dust in inner disks is more processed. Evidence suggests that the dust is processed in the centre of the disk and then moves radially outwards.

Van Boekell et al. 2004


Transport mechanisms from the inner to outer sections of the accretion disk
transport mechanism from the inner to outer regions of YSO accretion disks

http://amesteam.arc.nasa.gov/Research/disks_science.html

Outflow Transport (Skinner, Liffman, Shu &c) Turbulent Eddy Advection (Morfill and Volk 1984)


Photo-evaporation and YSO disks
Photo-evaporation gives the gravitational radius: Rg ~ 1 AU (Liffman 2003) Photoevaporation splits the disk into an inner and outer disk (Gorti et al 2009) Not to Scale Jet Outer Disk Inner Disk Sun R Photo-evaporative wind Rg ~ 1 AU ~10 AU

*

If there is not disk then turbulent convective transfer might have a problem