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Parameter Study. In Disk Jet Systems:. : A Focus on Equipartition. Authors : Tzeferacos Petros 1 , Ferrari Attilio 1 , Mignone Andrea 1,2 , Bodo Gianluigi 2 , Massaglia Silvano 1 , Zanni Claudio 3. 5th JetSet school, Galway, DIAS, Ireland, 12.01.2008.

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parameter study
Parameter Study

In Disk Jet Systems:

:A Focus on Equipartition

Authors:Tzeferacos Petros1, Ferrari Attilio1, Mignone Andrea1,2, Bodo Gianluigi2, Massaglia Silvano1, Zanni Claudio3

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

1Dipartimento di Fisica Generale, Universita’ degli Studi di Torino,Italy

2INAF/Osservatorio Astronomico di Torino,Italy

3Laboratoire de l’Observatoire de Grenoble,France

  • Introduction
  • Numerical Setup/Parameters
  • Results
  • Conclusions
constrains on ysos
Constrains on YSOs

YSO Jets

  • Well Collimated
  • Magnetically driven
  • Length 0.1-10 pc
  • Age ~105 yr
  • Temperature ~ 103-1040K
  • Velocity ~ 100-300 km s-1
  • dM/dt ~ 10-9 - 10-7 Msun yr-1

(Bally & Reipurth, 2002)

Central Object &Disk

The majority are low mass stars (<5 Msun)

Surrounded by accretion disks (rad~102 -103AU)

dMacc/dt ~10-8 -10-6 Msun yr-1

t survival~ 106-107 yr

(Siess et al. 1998)

initial conditions tabulating the disk
Initial conditions(tabulating the disk)
  • Radial Self Similarity at the equator (Blandford & Payne.1982)
  • Assume equatorial symmetry (r axis)
  • Assume axisymmetry (z axis)
  • Fill the domain from bottom to top solving the equilibrium equations for both directions, using a second order approximation
  • Over impose a static hot corona in equilibrium with the disk’s surface
boundary conditions equatorial axial symmetry open boundaries
boundary conditions(equatorial & axial symmetry, open boundaries)

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)


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

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


Calculated at z=0


δ: corona to disk density ratio

m : initial field inclination

(Blandford & Payne criterion)

αm: resistivity parameter

(Shakura & Sunyaev. 1973)

χm: anisotropy parameter

magnetic field lines on the background is displayed the logarithm of density poloidal current
← Magnetic field lines(on the backgroundis displayed the logarithm of density)Poloidal current →


evolved outflow magnetic field
Evolved outflow & magnetic field

case0 case1 case2 case3 case4 case5

(μ study) (anisotropy)

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

case0case1 case2 case3

The alfvenic surface is crossed only for values small values of μ )at leastwithin the computation- al box.

Only in cases 0,1 the outflow becomes super fast

acceleration mechanism b phi b p
acceleration mechanism (ІBphi І/Bp)

case0 case1 case2 case3

(only grad Bphi)(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


Ejection efficiency

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

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

The ejection index

increases as the plasma

beta decreases

Low diffusivity cases show elevated indexes in comparison to case1


Energy transformation along the outflow

* A well known signature of the magneto-centrifugal acceleration mechanism is the transformation of magnetic (poynting flux) to kinetic* This is shown in cases 1,2 from the poynting over kinetic flux ratio that is high near the disk drops by 1-2 orders of magnitude (less than unity) at higher altitudes



>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 s-1)* . Only cases 0, 1 become superfast in the domain. > The acceleration mechanism is magneto-centrifugal, mainly megnetic pressure for low μ and co-rotation for high μ.> The outflow collimates through hoop stress (no artificial collimation)> Accretion rates are of the order of 10-8 Msun y-1 whereas ejection rates are ~10-9 Msun y-1 *> Mass ejection efficiency increases with μ.



> Significant increase in the ejection efficiency is observed for for low a configurations (in agreement with Zanni et al. 2007) > The highly anisotropic / low resistivity configuration settles in a steady outflow configuration (as predicted in Casse & Ferreira 2000a) > Straying away from equipartition brings either distorted magnetic field topologies (weak collimation) or inefficient acceleration (inability to cross critical surfaces)> 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 mass loading thus it is explained the higher values of ξ.


[1] Zanni, C., Ferrari, A., Rosner, R., et al., 2007, A&A, 469, 811

[2] Mignone, A., Bodo, G., Massaglia, S., et al., 2007, ApJS, 170, 228

[3] Ferreira, J. & Pelletier, G., 1995, A&A, 295, 807

[4] Ferreira, J., 1997, A&A, 319, 340

[5] Casse, F. & Ferreira, J. 2000a, A&A, 353, 1115

[6] Ferrari, A., 1998, ARA&A, 36,539

[7] Ferrari, A., 2004, Ap&SS, 293, 15

[8] Blandford, R.D. & Payne, D.G., 1982, MNRAS, 199, 883

[9] Pudritz, R.E., Oyed, R., Fendt, C. & Brandenburg, A., 2006, in “Protostarts and Planets V”, B. Reipurth , D. Jewitt and K. Keil (eds.), University Arizona Press, Tucson, p. 277

[10] Shakura, N.I. & Sunyaev, R.A., 1973, A&A, 24, 337

[11] Powell, K.G., Roe P.L., Linde, T.J., Gombosi, T.I. & DeZeew, D.L., 1999, JCP, 154, 284