Transcript PPT - JMMC

The inner -magnetized- regions
of accretion discs
Jonathan Ferreira - LAOG (France)
Collaborators:
N. Bessolaz, C. Zanni, P. Garcia, C. Combet,
S. Cabrit, C. Dougados, F. Casse
Outline
I- Large scale magnetic fields in circumstellar discs
II- The magneto-rotational instability (MRI), dead zone and disc
ionization issues
III- Jet Emitting Discs (JEDs) vs Standard Accretion Discs
(SADs)
IV- Star-disc interactions and the stellar spin-down issue
V- Concluding remarks
I- Magnetic fields around YSOs
CTTs are oriented randomly with respect to local Bz
(Ménard & Duchêne 2004)
BUT
- sources with only discs: parallel
- sources with strong outflows: perpendicular
(Strom et al 86)
 Suggests strong impact of large scale Bz in jet
formation. But B required in discs for « viscosity »
via MRI, (Balbus & Hawley 91, Lesur & Longaretti 2006)
How strong is this field?
Infall stage: a decoupling matter/field must be at work.
- ideal MHD (B  n) gives far too strong fields
- ambipolar diffusion (also Banerjee & Pudritz 06) :
L  1 au
L  0.1 pc 
B

n




16-18
-3
5
-3
Heiles
et
al.
93


n

10
cm
n  10 cm
 Basu & Mouschovias 94 
13

B  100 G 
B  10 G

 Crucial issue of matter ionization (unsolved yet)
Presence of Bz will be an assumption and amount of flux F= pBzr2
a free parameter (IAU Grenoble 2007: now also a motto from F. Shu)
We expect however F M (Virial theorem and Jeans mass).
Effects of Bz on a SAD (1)
- Can it drive a jet ?
No
Magnetic field bending is not enough to launch jets
Blandford & Payne (82) jets require Br+/Bz > 1
This is possible only with a magnetic Reynolds
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number
But in a SAD, turbulent « viscous » torque gives
and in turbulent media nv~nm …
Lubow et al. 94a
Heyvaerts, Priest & Bardou 96
Ogilvie & Livio 98
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Effects of Bz on a SAD (2)
- Does it affect accretion ?
Yes
=> no large scale torque (magnetic braking) if Bz small
<< 1
if disc magnetization
<< 1
Thus, « magnetic braking » is negligible in weakly magnetized
accretion discs.
=> BUT, B triggers the magneto-rotational instability (Balbus &
Hawley 91) giving rise to the turbulent radial transport of
angular momentum
Magnetic field advection in SADs
A SAD can transport Bz such as to increase the
disc magnetization
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towards the center :
Diffusion equation
leads to
Since
where
one gets
Ferreira et al 06a, A&A
with e~ 1 for typical values of d
Note: the only real issue is
ionization and B/plasma coupling
A picture for the innermost disc regions
Jet Emitting Disc with ~ equipartition large scale Bz field
Ferreira & Pelletier 95
=> Existence of high Bz recently confirmed by spectro-polarimetric
observations around FU Or (~ kG @ 0.05 AU) Donati et al 05, Nature
II- Magneto-Rotational Instability,
dead zone and disc ionization
Flows in differential rotation:
B= 0
- small perturbation: ang momentum Wr2= Cst
=> centrifugal force pulls back to equilibrium (Rayleigh)
Chandrasekhar 53
Velikhov 59
Balbus & Hawley 91
Balbus 2003, ARA&A
B
B≠ 0
- perturbation: magnetic torque Ff= JrBz < 0
=> W < WK(r) : destabilizing effect which amplifies
the deviation (with Bz or Bf)
BUT magnetic tension is stabilizing Fr= JfBz > 0
∂t ur = (W2  W2K)r + Fr/r => B must be small
radius
MRI: dispersion relation
Balbus & Hawley 91
Axisymmetric modes, incompressible flow, isothermal disc, homogeneous Bz,
no radial modes
Instability if w2<0
The most unstable mode has a dynamical growth rate
In an accretion disc l< lmax= h => VA < Wh = Cs
Thus, an equipartition field ( ~ 1) quenches the MRI.
MRI: turbulent transport
In a SAD, radial angular momentum transport is due to a turbulent
« viscosity » n,giving rise to an accretion rate
Mass conservation
Angular momentum conservation
Where the « viscous » tensor is (Shakura & Sunyaev 73)
= r< ur uf> - < Br Bf>/0
Energy equation: Q- = sT4 = Qe with
Alpha prescription:
n=av Cs h
av= sRf/P0
Numerical simulations av ~ 1/2 (Lesur & Longaretti 07)
MRI: the role of Ohmic resistivity
Previous arguments/calculations neglected the Ohmic resistivity h
(electron-ions collisions):
- any wavelength l will be dissipated on a time scale l2/h
- the growth rate of a magnetic perturbation is l/VA
 MRI is quenched whenever l2/h < l/VA
In a disc, relevant wavelengths are l<lmax= h
Gammie 96
 MRI quenched at all scales when Rm = h VA/h < 1
Critical threshold is hard to define precisely (eg Fleming et al 2000)
< Bz > = 0 Rmcrit = h Cs/h ≈ 104
< Bz > ≠ 0 Rmcrit = h Cs/h ≈ 102
To conclude: MRI sets in only if Rm = h VA/h between 1 and 100
av between 10-3 and 1 ? (av ~ 1/2)
The dead zone
Gammie 96
MRI quenched at all scales when Rm = h VA/h < 1
Estimates:
r VA2 ≈ avP= av r Cs2 => VA ≈ av1/2 Cs
Ionization fraction x = ne/nH
Hayashi 81
Rm
=> Around 1 au, Rm < 1 for x < 10-13
How small is x ?
Collisional ionization (ions K, Na) requires T> 1000 K => r < 0.1 au (SAD)
At large distances, ionization due to Cosmic Rays, but absorbed when S>So =
100 g cm-2 (Umebayashi & Nakano 81)
 A layered accretion disc: active surface + inner dead zone?
An unsteady accretion ?
Only active upper zones with Sa =So will undergo MRI:
 The disc accretion rate
Gammie 96
varies like Sa na
Sa =103 g cm-2 is a constant: Macc varies like na # T r3/2
Temperature T(r) depends on opacity regimes (eg. Bell & Lin 94)
Thus Macc(r) is a function of the radius.
 Mass accumulation in the dead zone frontier?
 Time dependent disc accretion rate (eg. self-gravity sets-in, or heating and
ionization) ?
We are facing a difficulty: need for a self-consistent model taking into account
both macro (fluid laminar equations) and microphysics (turbulence +
ionization states)…
Models of disc ionization
Glassgold et al 97: only X-rays, disc = Minimum Solar Nebula
S(r) = 1700 R-3/2 g cm-2
T(r) = 280 R-1/2 K
=> dead zone between 1- 10-30+ au
Fromang et al 02: only X-rays, disc = av standard (shallower gradients)
av = 0.001
=> all the disc is « dead »
av = 0.01 Ma= 10-8 Msun/yr => dead zone between 0.2-100 au
av = 0.1 Ma< 10-7 Msun/yr => no dead zone
Matsumura & Pudritz 03: X-rays, CR and radioactivity, disc = Chiang & Goldreich 97
Passive disc with Ma=0 (more consistent)
=> Ionization CR > X-rays (unless kTX ≈ 5-10 keV)
=> dead zone between 0.2- 3 au
=> Results highly depend only chosen value So ≈ 103 g cm-2
=> Interesting proposition: low massive planets formed in dead zone?
But is there really a « dead zone » ?
Fleming & Stone 03
Magnetic energy
Ohmic resistivity
h(z)
Maxwell stress
The dead zone is
not quite « dead »
Reynolds stress
Kinetic energy
Turbulent mixing
and mass exchange
between the 2
regions…
III- Jet Emitting Discs (JEDs)
Why do jets need to be magnetized anyway ?
See Ferreira, Dougados, Cabrit 2006, A&A, 453, 785
1000 AU
B: only necessary in the acceleration zone
not anymore in the asymptotic regime
Constraints from T Tauri Jets
Images: degree of collimation, evolution (HH objects)
Spectroscopy: jet kinematics (line profiles, PV diagrams) and
physical conditions such as density and temperature (line ratios).
=> Strong contrainsts on all MHD models
The 3 basic steady-state jet models
Blandford & Payne 82
Ferreira & Pelletier 93,95,97
Wardle & Königl 93
Casse & Ferreira 00, 04
Shu et al 94, 95
Fendt 9, 00
Shang et al 98, 02
Weber & Davis 68
Hartmann & McGregor 80
DeCampli 82
Sauty & Tsinganos 94, 02
 share the same physics: rotating body + large scale Bz
 Governed by the same set of MHD equations
 Apart the « extended disc wind » model, mass flux is imposed
=> Can observations discriminate between these models ?
First: are jets indeed rotating?
DG Tau
Observations
HST/STIS
Bacciotti et al 00
1.
The collimation degree increases with the
jet speed (higher closer to the axis)
2. Unresolved acceleration scale <20 au
=> MHD: launching radius at 2-3 au
(Anderson et al 03, Pesenti et al 04)
Putting all constraints together
Ferreira, dougados, Cabrit 2006
Observations:
- jet radius r
- velocity Vphi
- velocity Vp
Models:
-anchoring radius ro
- magnetic lever arm
=> l ~ 10 needed
 Jet velocity gradients incompatible with current X-wind models
 Observed mass fluxes incompatible with stellar winds only.
 IF velocity shifts are rotation: launching radius from 0.2 to 3 AU
Accretion-Ejection Systems
Axisymmetric jets are nested magnetic surfaces
of constant magnetic flux: a(r,z) = Cst
Blandford & Payne 82,
Ferreira & Pelletier 95
- Single fluid MHD description
- Non-relativistic equations (no light-cylinder)
- Steady-state
- Usually: polytropic energy equation
- Ideal MHD (no viscosity, no diffusivity)
A complex interplay between disc and jets is
necessary to assess the mass loading M
Ý  r
acc
=> Magnetized Accretion-Ejection Structure (MAES)
Governing MHD equations
• Mass
• Momentum
• Energy
• Perfect gas
• Ohm’s law
• Induction
Obtaining Self-Similar solutions
Separation of variables: all power-law indices are constrained
 using
requires
MÝacc  r
The magnetic field distribution is intimately linked with the disc
ejection efficiency (only radially self-similar class of solution
compatible with a Keplerian disc)
Propagation of a solution (Runge-Kutta for stiff equations) from disc
midplane, needs a matrix inversion with several singular points:
MHD critical points (ideal MHD jet)
• Slow
=> =B2/P
• Alfvén => where Mdot  r 
• Fast
=> g
Note: all parameters are constants
A typical super-FM solution
= 0.03
e= h/r= 0.03
am= 1
kBP= 0.12
lBP= 23
2Pjet
= 0.84
Pacc
Pdiss
= 0.16
Pacc
Ferreira & Casse 04, ApJL
Self-similar MAES
 = 0.005
 = 0.05
MÝacc  r
Ferreira 97
• Narrow parameter space: equipartition field 0.1 <  < 1 am~1
• All solutions recollimate (Blandford & Payne 82, Pelletier & Pudritz 92)
• A gradient in  could forbid it (Ferreira 97)
• All solutions (here sub-fast) terminate with a shock
Numerical studies of accretion-ejection
systems
In most numerical simulations the disc is a boundary condition and
mass loss imposed (eg. Ouyed & Pudritz 97,99,03, Pudritz et al 06,
Ustyugova 99, Krasnopolsky et al 99, 03, Anderson et al 05…)
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Casse & Keppens 02, 04
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Zanni et al 04, 07
=> Main results from self-similar calculations are confirmed by
MHD simulations where the disc is also computed.
JEDs vs SADs
(1) A JED is weakly dissipative: lack of disc emission (Ferreira &
Pelletier 93)
~ h/r << 1
(2) A JED is accreting faster : time scales and variability…?
with ms = ur/Cs ~ 1 in a JED,
ms= av h/r <<1 in a SAD
(3) A JED is thinner and less dense than a SAD with same Mdot:
JEDs vs SADs
(3) A JED is thinner and less dense
than a SAD with same Mdot:
 The SAD/JED transition
provides a trap stopping
migration of protoplanetary
cores (Masset et al 06)
 Different radial structure than a
SAD (planet formation?)
Optically thick
region
Optically thin
region
Combet & Ferreira, in prep
JEDs vs SADs
(3) A JED is thinner and less dense than a SAD with same Mdot:
 Different properties with respect to X-ray screening and
ionization (recombination time scales) => dead zone ?
Dead zone (Gammie 96) if
Rm= hVA/h < 1
=> translates into an ionization
rate (only coll. recomb)
Ferreira et al, in prep
kTX= 3.9 keV, LX=3 1030erg/s Mdot=10-7 Msun/yr
The need for a warm « corona »
Thin discs => enthalpy negligible in jets: « cold jet » models
In that case, l~ 50-100
•
Mass fluxes too low
< 10% observed
•
Velocities too high (Garcia et al 01a,b)
Higher mass fluxes with l~ 10 can only be done if some energy is
deposited at the disc surface (Casse & Ferreira 00b).
Warm jets from thin discs can
arise if
1. Stellar UV/X illumination
(Garcia et al, in prep)
2. Local dissipation of accretion
energy (coronal heating, Galeev
79, Heyvaerts & Priest 89)
IV- The star-disc magnetic interaction
See review in PPV
Alencar et al
(1) Evidences of a magnetospheric interaction (Edwards et al. 94, 98, Calvet
04, Muzerolle et al 01, Bouvier et al. 99, Günther et al 99, Johns-Krull et al 99,01, Feigelson
& Montmerle 99, COUP survey)
(2) T Tauri stars are slow rotators despite contraction + accretion
(Bertout et al 89, Bouvier et al 97, Rebull et al 02)
 Accretion must proceed AND help to remove stellar angular
momentum
=> What kind of magnetic configuration?
Rotational evolution of PMS stars
Bouvier et al. 97

T Tauri rotate at ≈ 10 % break-up (Bertout 89)

Velocity dispersion requires disc interaction (« disc locking »
paradigm)
The Gosh & Lamb configuration
(1) The disc-locking paradigm
(2) Accretion must still proceed
Gosh & Lamb 79
Cameron & Campbell 93, Li 96
Matt & Pudritz 04
-
Rt > Rco: star is spun down => accretion is prevented
-
Rt< Rco: star is spun up => accretion is allowed
But 2 major difficulties:
(i) Efficiency of disc viscosity??
(ii) Magnetic shear and reconnection
Aly 86
=> Loss of causal connection Lovelace et al 95, 99, Bardou & Heyvaerts 96
Uzdensky et al 02, Matt & Pudritz 05
Two (over-)simplified configurations
Camenzind 90, Shu et al 94a, 95
(Matt & Pudritz 05)
- Assumes Rt= Rco
- « X-wind » is actually a disc-wind from
a small disc region: no stellar spin-down
per se
(Uchida & Low 81, Hirose 97)
Ferreira, Pelletier, Appl 00
- Assumes Rt= RX = Rco
- « Reconnection X-winds » at the
magnetic neutral line: very efficient
stellar spin down (but unsteady events)
Heavy numerical simulations
Hayashi et al 96, Miller & Stone 97, Hirose et
al 97, Goodson et al 97,99, Kueker et al 03,
Romanova et al 02,03,04,05, Long et al 05, 06
von Rekowski & Brandenburg 04,05
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Zanni et al, in prep
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Funnel flows are a natural feature in a non force-free
magnetosphere, BUT lead to stellar spin up.
Main difficulties (and differences between works):
-Treatment of disc physics (mass, nv and nm)
-Boundary conditions at the star (!!)
-Numerical resolution
The disc truncation radius Rt
But why should Rt= Rco?
In fact, 2 conditions define
Rt < Rco:
(1) Accretion is halted
(1) Disc material is loaded
onto stellar field lines
 Pmag ~ Pth
 Bphi ~ Bz
(Bessolaz et al, to be subm)
=> Accretion funnels with B ~ 140 G only
at Rt= 2 R* (and no X-wind)
Torques on the accreting protostar
Gosh & Lamb configuration
is NOT established
- After some time, most field
lines are disconnected
from the star (nm≈ Csh)
- Final stage = 2 electric
circuits = 2 torques (+ no
X-wind !!)
(1) Positive torque due to
accretion (dominant)
(2) Negative torque due
to open field lines
(ready for wind…)
Zanni et al, in prep
Reconnection X-winds: Interplay of
dynamo + fossil fields








Protostellar core at break-up (Class 0)
Bipolar fossil field
t=0: dynamo produces a dipole field
Magnetic neutral line at RX= R*
Contraction of the protostar, spin-down
by the ReX-wind + accretion funnels
rx≈ rco increases (magnetosphere
expands)
Accretion rate onto the star is regulated
Stellar open field increases (Class I, II?)
Reconnection X-winds
ÝX
M
= 0.1
Ý
Macc
T = 3000 K
Stellar field
B  r
n
n=4
Ferreira, Pelletier, Appl 00
Momentum flux Vs Bolometric luminosity
Class 0
103 yr
104 yr
Class I
105 yr
Ferreira et al. 00
Bontemps et al. 95
Saturation mechanism for B*?
ÝX
M
= 0.1
Ý
Macc
T = 3000 K
B  r n
n=4




ReX-wind power diminishes in time with W*
The disc magnetic flux F must be limited otherwise B* too large, W* too low
One would expect a correlation between W* and F
Does the weak dispersion in stellar periods reflect a weak dispersion in disc
magnetic flux ? (remember F M)
V- Concluding remarks (1/3)
- Effects of large scale Bz are most probably very important in the
innermost disc zones
- MRI (accretion)
- jet launching (« disc winds »)
- star-disc interaction and possibility to drive ReX-winds
- planet migration halting
- Models have reached some maturity but
- numerical experiments needed to assess time-dependent
behavior and complex fields (eg Gregory et al, 06, 07)
- important issues such as ionization, thermodynamics left over
- challenge to find out observational constraints
V- Concluding remarks (2/3)
The « stellar angular momentum problem »
requires a wind as a sink:
 Accretion-powered stellard winds ?
 Reconnection X-winds ?
QuickTime™ and a
TIFF (LZW) decompressor
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Matt & Pudritz 05
Ferreira, Pelletier & Appl 00
Both scenarii suffer from lack of full dynamical calculations :
- Enhanced stellar winds require RA/R* > 14 !
- ReX-winds rely on a magnetic neutral line…
=> High quality MHD experiments + HRA observations are needed
V- Concluding remarks (3/3)
Time ?
Bz: an unavoidable ingredient ?
=> A possible evolutionary sequence for the disc magnetic field
Classes 0 and I:
• Mainly disc winds + ReX-winds (stellar spin-down)
Classes II (and III):
• Mainly « enhanced » (accretion-powered) stellar winds