Parameter Study

1
Parameter Study
In Disk Jet Systems

A Focus on
Equipartition
AuthorsTzeferacos 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
lObservatoire de Grenoble,France
2
Overview

• Introduction
• Numerical Setup/Parameters
• Results
• Conclusions

3
Constrains on YSOs

• YSO Jets
• Well Collimated
• Magnetically driven
• Length 0.1-10 pc
• Age 105 yr
• Temperature 103-104 0K
• 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 (lt5 Msun)
• Surrounded by accretion disks (rad102 -103AU)
• dMacc/dt 10-8 -10-6 Msun yr-1
• t survival 106-107 yr
• (Siess et al. 1998)

4
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 disks surface

5
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)
6
Parameters

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

Case 0 Case 1 Case 2 Case 3 Case 4 Case 5
µ 0.1 0.3 1 3 0.3 0.3
a 1 1 1 1 0.1 0.1
?m 3 3 3 3 100 3
f cooling function (currently all ohmic heating
is radiated away)
Calculated at z0
d corona to disk density ratio
m initial field inclination (Blandford Payne
criterion)
am resistivity parameter (Shakura
Sunyaev. 1973)
?m anisotropy parameter
7
? Magnetic field lines(on the
backgroundis displayed the logarithm of
density)Poloidal current ?
Case1

8
Evolved outflow magnetic field

• case0 case1 case2 case3
  case4 case5
• (µ study)
  (anisotropy)
  

9
acceleration of the outflow, crossing the
critical surfaces
The alfvenic surface is crossed only for
values small values of µ ) at least within the
computation- al box. Only in cases 0,1
the outflow becomes super fast

• case0 case1 case2
  case3

10
acceleration mechanism (?Bphi ? /Bp)
magnetically driven! The ratio
between Bf and Bp gives a good perspective of the
dominant mechanism Bf /Bplt1
?co-rotation, centrifugal acceleration
Bf /Bpgt1 ?gradient of Bf along the field lines
is the main accelerating mechanism In
all Magneto-centrifugal acceleration

• case0 case1 case2
  case3
• (only grad Bphi)
  (only co-rotation)

11
Ejection efficiency
case0 case1 case2 case3 case4 case5
2Mj/?a 0.19 0.27 0.36 (0.99) 0.56 0.38
? 0.08 0.11 0.15 (1) 0.28 0.18
Mj 0.007 0.013 0.010 (0.013) 0.011 0.017
Macc 0.074 0.094 0.049 (0.029) 0.043 0.089
In all cases we calculated the final ratio 2
(dMej/dt) / (dMacc/dt) as well as the ejection
index ? 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
12
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
13
Conclusions
gtWe 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. gt The acceleration mechanism is
magneto-centrifugal, mainly megnetic pressure for
low µ and co-rotation for high µ. gt The outflow
collimates through hoop stress (no artificial
collimation)gt Accretion rates are of the order
of 10-8 Msun y-1 whereas ejection rates are 10-9
Msun y-1 gt Mass ejection efficiency
increases with µ.

14
Conclusions

gt Significant increase in the ejection efficiency
is observed for for low a configurations (in
agreement with Zanni et al. 2007) gt The highly
anisotropic / low resistivity configuration
settles in a steady outflow configuration (as
predicted in Casse Ferreira 2000a) gt
Straying away from equipartition brings either
distorted magnetic field topologies (weak
collimation) or inefficient acceleration
(inability to cross critical surfaces)gt
Returning current sheet at the innermost region
of the disk as well as some artificial heating
due to dissipation in the disks surface produces
elevated mass loading thus it is explained the
higher values of ?.
15
Go raibh maith agat (presumably thank you)for
your attention!
16
Reference
1 Zanni, C., Ferrari, A., Rosner, R., et al.,
2007, AA, 469, 811 2 Mignone, A., Bodo, G.,
Massaglia, S., et al., 2007, ApJS, 170, 228 3
Ferreira, J. Pelletier, G., 1995, AA, 295,
807 4 Ferreira, J., 1997, AA, 319, 340 5
Casse, F. Ferreira, J. 2000a, AA, 353, 1115
6 Ferrari, A., 1998, ARAA, 36,539 7
Ferrari, A., 2004, ApSS, 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,
AA, 24, 337 11 Powell, K.G., Roe P.L.,
Linde, T.J., Gombosi, T.I. DeZeew, D.L., 1999,
JCP, 154, 284