Resistive MHD jet simulations with large resistivity
Miljenko Cemeljic, Jose Gracia, Nektarios Vlahakis, Kanaris Tsinganos
aa r X i v : . [ a s t r o - ph . S R ] J un Resistive MHD jet simulations with largeresistivity
Miljenko ˇCemelji´c, Jose Gracia, Nektarios Vlahakis and Kanaris Tsinganos
Abstract
Axisymmetric resistive MHD simulations for radially self-similar ini-tial conditions are performed, using the NIRVANA code. The magnetic diffusivitycould occur in outflows above an accretion disk, being transferred from the underly-ing disk into the disk corona by MHD turbulence (anomalous turbulent diffusivity),or as a result of ambipolar diffusion in partially ionized flows. We introduce, inaddition to the classical magnetic Reynolds number Rm, which measures the im-portance of resistive effects in the induction equation, a new number Rb, whichmeasures the importance of the resistive effects in the energy equation. We find twodistinct regimes of solutions in our simulations. One is the low-resistivity regime, inwhich results do not differ much from ideal-MHD solutions. In the high-resistivityregime, results seem to show some periodicity in time-evolution, and depart signifi-cantly from the ideal-MHD case. Whether this departure is caused by numerical orphysical reasons is of considerable interest for numerical simulations and theory ofastrophysical outflows and is currently investigated.
In Vlahakis & Tsinganos (1998) general classes of self-consistent ideal-MHD so-lutions have been constructed. In Vlahakis et al. (2000) Blandford & Payne (1982)model was analysed, and the problem with the terminal wind solution (which wasnot causally disconnected from the disk) has been solved. The common deficiencyof all radially self-similar models, a cut-off of the solution at small cylindrical radiiand also at some finite height above the disk because of a strong Lorentz force closeto the system’s axis has been corrected numerically. A search in the numerical sim-
Fig. 1
The initial setup, which is slightly modified analytical solution, is shown in the
Left panel.The solid lines represent logarithmically spaced isocontours of density. It is also shown in colourgrading, in red to violet colour, for the logarithm of density -1 to -4, respectively. In the
Right panelshown is, in the same grading, the solution with large magnetic diffusivity. It does not reach station-ary state, and shows some periodicity in time evolution. The dashed lines depict poloidal magneticfield lines, and the dotted lines depict the fast magnetosonic, Alfven and slow magnetosonic criticalsurfaces, top to bottom, respectively.Miljenko ˇCemelji´cTIARA, Academia Sinica, National Tsing Hua University, No. 101, Sec. 2, Kuang Fu Rd.,Hsinchu 30013, Taiwan e-mail: [email protected]
Jose GraciaSchool of Cosmic Physics, Dublin Institute for Advanced Studies, 31 Fitzwilliam Place, Dublin 4,Ireland e-mail: [email protected]
Nektarios Vlahakis & Kanaris TsinganosIASA and Section of Astrophysics, Astronomy and Mechanics, Dpt. of Physics,Univ. of Athens, Panepistemiopolis 15784 Zografos, Athens, Greece e-mail: vlahakis,[email protected] esistive MHD jet simulations with large resistivity 3 ulations for solutions at larger distances from the disk has been performed in Graciaet al. (2006) with NIRVANA code (version 2.0, Ziegler, 1998), and similar resultswere obtained also using the PLUTO code in Matsakos et al. (2008). Extension inthe resistive-MHD has been investigated in ˇCemelji´c et al. (2008) using the NIR-VANA code and some of results we present here. Results of these investigationscould also have implications in the numerical simulations of magnetospheric inter-action in vicinity of the young stellar objects, where the resistivity plays importantrole.Our numerical simulations are initiated by the slightly modified analytical solu-tions for radially self-similar flow from Vlahakis et al. (2000), and then evolved inthe resistive MHD simulations by NIRVANA code. Our initial setup is shown in theleft panel of Fig.1.
In addition to the magnetic Reynolds number Rm=VR/ h , which describes influenceof the magnetic diffusivity h in the induction equation, we introduced a new number,which describes the influence in the energy transport equation-see Fig.2. It can bewritten in terms of Rm and plasma beta as Rb=Rm b /2. It is the ratio of the pressureterm over the Joule heating term in the energy equation. When Rb is smaller or closeto unity, which can happen even when Rm is much larger than unity, the energydissipation becomes important. It might define one additional mode of resistive- Z / R R/R Fig. 2
Value of b / ( V R / V R ) for the analytical solution used as initial setup here. This quantitygives the critical value of magnetic diffusivity h that corresponds to Rb=1. Miljenko ˇCemelji´c, Jose Gracia, Nektarios Vlahakis and Kanaris Tsinganos MHD solutions, indicated in our search for eventual onset of super-critical resistiveregime.
The resistive MHD jets are similar to ideal-MHD solutions for a finite range of mag-netic diffusivity, in which they reach a well defined stationary state. This state onlyslightly differs from the initial state, as expected, since the initial setup was slightlymodified analytical stationary solution. Departure from the ideal-MHD regime oc-curs for larger values of magnetic diffusivity, above some critical value. One such
Fig. 3
Reconnection and re-shaping of the magnetic field in the vicinity of the young stellar ob-ject. Initially pure stellar dipole field reshapes into the stellar and disk open field during the time-evolution. The time is measured in the number of rotations at the inner disk radius, which is atR i =3.0 in these simulations. Without the substantial resistivity, reconnection does not occur andsimulations terminate because of numerical reasons.esistive MHD jet simulations with large resistivity 5 result is shown in the right panel of Fig.1. We note possible existence of the dis-tinct super-critical regime in magnetic diffusivity in our simulation for the outflowsinitialised with a self-similar analytical solutions. We also define the new character-istic number, which describes the influence of the resistivity on the energy transportequation. Physical parameters and the eventual periodicity of the super-critical resis-tive solutions are currently under investigation. Such solutions might be interestingfor investigations of accretion flows in the vicinity of young stellar objects, wherethe magnetic resistivity seems to play important role.In the Fig.3 we show one case in numerical simulations of magnetospheric inter-action in the closest vicinity of young stellar object ( ˇCemelji´c et al., 2009). Thesesimulations have been performed with code ZEUS347, which is our resistive versionof Zeus-3D code (Fendt & ˇCemelji´c, 2002). Magnetic reconnection shows to playessential role in re-shaping the initial stellar dipole, which enables the launching ofoutflows. In our numerical simulations, if the resistivity is too small, reconnectionwill not occur. Therefore, we need to investigate parameter space for resistivity, andwe need to understand what are the effects of large, and not only negligible or verysmall resistivity. Acknowledgements
This work was supported in part by EC’s Marie Curie Actions-Human Re-source and Mobility within the JETSET network under contract MRTN-CT-2004005592. M ˇC ex-presses gratitude to TIARA/ASIAA in Taiwan for possibility to use their Linux clusters and JET-SET for supporting this collaboration.