Parameter StudyParameter StudyIn Disk Jet Systems:In Disk Jet Systems:

AuthorsAuthors::Tzeferacos PetrosTzeferacos Petros11, Ferrari Attilio, Ferrari Attilio11, Mignone Andrea, Mignone Andrea1,21,2, , Bodo GianluigiBodo Gianluigi22, Massaglia Silvano, Massaglia Silvano11, Zanni Claudio, Zanni Claudio33

1Dipartimento di Fisica Generale, Universita’ degli Studi di Torino,Italy2INAF/Osservatorio Astronomico di Torino,Italy3Laboratoire de l’Observatoire de Grenoble,France

5th JetSet school, Galway, DIAS, 5th JetSet school, Galway, DIAS, Ireland, 12.01.2008 Ireland, 12.01.2008

: A Focus on Equipartition

OverviewOverview

IntroductionIntroduction

Numerical Setup/ParametersNumerical Setup/Parameters

ResultsResults

ConclusionsConclusions

Constrains on YSOsConstrains on YSOs

YSO Jets YSO Jets Well CollimatedWell Collimated Magnetically driven Magnetically driven Length 0.1-10 pcLength 0.1-10 pc Age ~10Age ~1055 yr yr Temperature ~ 10Temperature ~ 1033-10-1044 00K K Velocity ~ 100-300 km sVelocity ~ 100-300 km s-1-1

dM/dt ~ 10dM/dt ~ 10-9 -9 - 10- 10-7 -7 MMsunsun yr yr--

11

(Bally & Reipurth, 2002)(Bally & Reipurth, 2002)

Central Object &Disk Central Object &Disk

The majority are low mass The majority are low mass stars (<5 Mstars (<5 Msunsun))

Surrounded by accretion disks Surrounded by accretion disks (rad~10(rad~1022 -10 -1033AU)AU)

dMdMaccacc/dt ~10/dt ~10-8-8 -10 -10-6 -6 MMsunsun yr yr-1-1

t t survivalsurvival~ 10~ 1066-10-107 7 yryr

(Siess et al. 1998)(Siess et al. 1998)

Initial conditionsInitial conditions(tabulating the disk)(tabulating the disk)

Radial Self Similarity at the equator (Blandford & Payne.1982)Radial Self Similarity at the equator (Blandford & Payne.1982)

Assume equatorial symmetry (r axis)Assume equatorial symmetry (r axis)

Assume axisymmetry (z axis)Assume axisymmetry (z axis)

Fill the domain from bottom to top solving the equilibrium Fill the domain from bottom to top solving the equilibrium equations for both directions, using a second order equations for both directions, using a second order approximation approximation

Over impose a static hot corona in equilibrium with the disk’s Over impose a static hot corona in equilibrium with the disk’s surfacesurface

boundary conditionsboundary conditions(equatorial & axial symmetry, open boundaries)(equatorial & axial symmetry, open boundaries)

ª =43Bz0r2

0

µrr0

¶3=4 m5=4

(m2 + z2=r2)5=8(1)

We define at the borders of the domain and the sink the behavior of primitive variables

R,Z axis → equatorial & axial symmetry The “open” boundaries assume outflow condition (zero gradient) for all variables except for Vphi

and the magnetic field

Ghost zones of the sink region are treated as the respective boundaries of the domain

Uniform Resolution [256,768]

Pluto Code

(Mignone et al. 2007)

ParametersParameters

ª =43Bz0r2

0

µrr0

¶3=4 m5=4

(m2 + z2=r2)5=8(1)

Normalization of the MHD equations yields 7 Normalization of the MHD equations yields 7 non-dimensional parameters that can be non-dimensional parameters that can be chosen arbitrarily (almost !!! ) chosen arbitrarily (almost !!! )

ª =43Bz0r2

0

µrr0

¶3=4 m5=4

(m2 + z2=r2)5=8(1)

S

K

C

V }

Calculated at z=0}2

2

B

P

m : initial field inclination(Blandford & Payne criterion)

αm : resistivity parameter (Shakura & Sunyaev. 1973)

f : cooling function (currently all ohmic heating is radiated away)

δ : corona to disk density ratio

χm : anisotropy parameter

Case 0Case 0 Case 1Case 1 Case 2Case 2 Case 3Case 3 Case 4Case 4 Case 5Case 5

μμ 0.10.1 0.30.3 11 33 0.30.3 0.30.3αα 11 11 11 11 0.10.1 0.10.1χχmm 33 33 33 33 100100 33

← ← Magnetic Magnetic field lines field lines

(on the background(on the backgroundis displayed the is displayed the

logarithm of density)logarithm of density)

PoloidalPoloidal current current →→

Case1Case1

Evolved outflow & magnetic fieldEvolved outflow & magnetic field

case0 case1 case2 case3 case4 case5 case0 case1 case2 case3 case4 case5

((μμ study) (anisotropy) study) (anisotropy)

acceleration of the outflow, crossing acceleration of the outflow, crossing the critical surfacesthe critical surfaces

casecase00 case1 case1 case2 case3 case2 case3

The alfvenic The alfvenic surface is surface is crossed only crossed only for values for values small values of small values of μμ ) ) at at leastleast within the within the computation- computation- al box.al box.

Only in cases Only in cases 0,1 the outflow 0,1 the outflow becomes becomes super fastsuper fast

acceleration mechanism (acceleration mechanism (ІІBBphi phi ІІ /B/Bpp))

case0 case1 case2 case3case0 case1 case2 case3

(only grad Bphi)(only grad Bphi) (only co-rotation)(only co-rotation)

magnetically driven!

The ratio between Bφ and Bp gives a good perspective of the dominant mechanism

|Bφ| /Bp<1 →co-rotation, centrifugal acceleration

|Bφ| /Bp>1 →gradient of Bφ along the field lines is the main accelerating mechanism

In all: Magneto-centrifugal acceleration

case0case0 case1case1 case2case2 case3case3 case4case4 case5case5

2Mj/2Mj/ΜΜaa 0.190.19 0.270.27 0.360.36 ((0.990.99)) 0.560.56 0.380.38

ξξ 0.080.08 0.110.11 0.150.15 ((~1~1)) 0.280.28 0.180.18

MjMj 0.0070.007 0.0130.013 0.0100.010 (0.013)(0.013) 0.0110.011 0.0170.017

MaccMacc 0.0740.074 0.0940.094 0.0490.049 (0.029)(0.029) 0.0430.043 0.0890.089

Ejection efficiencyEjection efficiency

In all cases we In all cases we calculated the final calculated the final ratio 2 (dMej/dt) / ratio 2 (dMej/dt) / (dMacc/dt) as well as (dMacc/dt) as well as the ejection index the ejection index ξξ

In all cases but case3 In all cases but case3 we have a plateau in we have a plateau in the time evolution of the time evolution of the ratiothe ratio

The ejection indexThe ejection indexincreases as the increases as the plasma plasma beta decreases beta decreases

Low diffusivity cases Low diffusivity cases show elevated indexes show elevated indexes in comparison to in comparison to case1case1

* A well known signature of * A well known signature of the magneto-centrifugal the magneto-centrifugal acceleration mechanism is acceleration mechanism is the transformation of the transformation of magnetic (poynting flux) to magnetic (poynting flux) to kinetickinetic

* This is shown in cases * This is shown in cases 1,2 from the poynting over 1,2 from the poynting over kinetic flux ratio that is high kinetic flux ratio that is high near the disk drops by 1-2 near the disk drops by 1-2 orders of magnitude (less orders of magnitude (less than unity) at higher than unity) at higher altitudesaltitudes

Energy transformation Energy transformation along the outflowalong the outflow

>We have super alfvenic outflows for cases 0,1,2,4,5 and the final velocity >We have super alfvenic outflows for cases 0,1,2,4,5 and the final velocity reached is of the expected order of magnitude (~100-150 Km sreached is of the expected order of magnitude (~100-150 Km s -1-1)* . Only )* . Only cases 0, 1 become superfast in the domain. cases 0, 1 become superfast in the domain.

> The acceleration mechanism is magneto-centrifugal, mainly megnetic > The acceleration mechanism is magneto-centrifugal, mainly megnetic pressure for low pressure for low μμ and and co-co-rotation rotation for high for high μμ.. > The outflow collimates through hoop stress (no artificial collimation)> The outflow collimates through hoop stress (no artificial collimation)

> Accretion rates are of the order of 10> Accretion rates are of the order of 10-8-8 M Msunsun y y-1-1 whereas ejection rates are whereas ejection rates are

~10~10-9-9 M Msunsun y y-1 -1 * *

> Mass ejection efficiency increases with > Mass ejection efficiency increases with μμ. .

ConclusionsConclusions

> Significant increase in the ejection efficiency is observed for for low a > Significant increase in the ejection efficiency is observed for for low a configurations (in agreement with Zanni et al. 2007) configurations (in agreement with Zanni et al. 2007)

> The highly anisotropic / low resistivity configuration settles in a steady > The highly anisotropic / low resistivity configuration settles in a steady outflow configuration (as predicted in Casse & Ferreira 2000a) outflow configuration (as predicted in Casse & Ferreira 2000a)

> Straying away from equipartition brings either distorted magnetic field > Straying away from equipartition brings either distorted magnetic field topologies (weak collimation) or inefficient acceleration (inability to cross topologies (weak collimation) or inefficient acceleration (inability to cross critical surfaces)critical surfaces)

> Returning current sheet at the innermost region of the disk as well as some > Returning current sheet at the innermost region of the disk as well as some artificial heating due to dissipation in the disk’s surface produces elevated artificial heating due to dissipation in the disk’s surface produces elevated mass loading thus it is explained the higher values of mass loading thus it is explained the higher values of ξξ..

ConclusionsConclusions

Go raibh maith agat Go raibh maith agat (presumably “thank you”)(presumably “thank you”)

for your attention!for your attention!

ReferenceReference

ª =43Bz0r2

0

µrr0

¶3=4 m5=4

(m2 + z2=r2)5=8(1)

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