Astrophysics and Space Sciences Transactions www.astrophys-space-sci-trans.net 1810-6528 1810-6536 4 1 2008 10.5194/astra-4-7-2008 http://www.astrophys-space-sci-trans.net/4/7/2008/ http://www.astrophys-space-sci-trans.net/4/7/2008/astra-4-7-2008.html http://www.astrophys-space-sci-trans.net/4/7/2008/astra-4-7-2008.pdf 7 12 2008-03-05 On the validity of ideal MHD in the vicinity of stagnation points in the heliosphere and other astrospheres D. H. Nickeler nickeler@asu.cas.cz M. Karlický Astronomical Institute Ondřejov AV ČR, Czech Republic The paradigm of ideal MHD is investigated in the vicinity of null points of flows and magnetic fields. These null points determine the location and geometrical shape of the heliopause (or other astropauses). We investigate the question whether regular and stable solutions of the ideal MHD equations in the vicinity of null points of flow and magnetic field exist. This is done to test the validity of ideal MHD in the vicinity of flow and magnetic field of the plasma boundaries of stellar winds and their local interstellar medium. We calculate the general solutions of ideal MHD in the vicinity of magnetic null points and use the standard form of stagnation point flows to analyse all possible time evolutions of these plasma environments. We show that the solution space in 2-D consists almost exclusively of either exponentially (in time) growing velocity or magnetic fields, or collapse solutions. Regular solutions must be three-dimensional and seem to be unstable with respect to small perturbations. This is an argument that reconnection has to take place in such regions and that therefore nonideal terms in Ohm's law are necessary, allowing for reconnection. We conclude that the use of ideal MHD in the vicinity of singular points of flow and magnetic field has to be analysed very carefully with respect to simulation results as those simulations show numerical dissipation (resistivity). These simulations can therefore produce unphysical reconnection regimes. Thus one has to search for a realistic Ohm's law, allowing for reconnection at the heliospheric boundaries. Arnold, V I.: Ordinary differential equations, Springer, Berlin, 1992. Baranov, V B., Fahr, H.-J., and Ruderman,~M S.: Investigation of macroscopic instabilities at the heliopause boundary surface, Astron. Astrophys., 261, 341–347, 1992. Belov, N A.: Instability of a tangential discontinuity in a two-dimensional flow with a stagnation point, Fluid Dynamics, 32(2), 219–222, 1997. Bronstein, I N. and Semendjajew, K A.: Taschenbuch der Mathematik, Verlag Harri Deutsch, Thun und Frankfurt/Main, 1979. Chandrasekhar, S.: An introduction to the study of stellar structure, Dover Publications, New York, 1957. Contopoulos, J.: General Axissymmetric Magnetohydrodynamic Flows: Theory and Solutions, Astrophys. J., 460, 185–198, 1996. Emden, R.: Gas balls: Applications of the mechanical heat theory to cosmological and meteorological problems, Teubner, 1907. Fahr, H.-J., Fichtner, H., and Scherer, K.: Determination of the heliospheric shock and of the supersonic solar wind geometry by\vadjust means of the interstellar wind parameters, Astron. Astrophys., 277, 294–264, 1993. Fahr, H.-J., Grzedzielski, S., and Ratkiewicz, R.: Magnetohydrodynamic modeling of the 3-dimensional heliopause using the Newtonian approximation, Ann. Geophysicae, 6, 337–354, 1988. Hornig, G. and Schindler, K.: The problem of magnetic topology and its invariant definition, Phys. of Plasmas, 3(3), 781–791, 1996. Nickeler, D H., Goedbloed, J P., and Fahr, H.-J.: Stationary field-aligned MHD flows at astropauses and in astrotails, Astron. Astrophys., 454, 797–810, 2006. Nickeler, D. and Karlick\'y, M.: Are heliospheric flows magnetic flux- or line conserving?, Astrophys. Space Sci. Trans., 2, 63–72, 2006. Parker, E N.: Interplanetary dynamical processes, Interscience Publishers, New York, 1963. Parnell, C E., Smith, J M., Neukirch, T., and Priest, E R.: The structure of three-dimensional magnetic neutral points, Phys. of Plasmas, 3(3), 759–770, 1996. % Pogorelov, N.V., Zank, G.P., and %Ogino, T.: Three-dimensional features of the outer heliosphere due to coupling %between the interstellar and interplanetary magnetic fields. I. Magnetohydrodynamic %model:Interstellar perspective, Astrophys. J., 614, 1007-1021, 2004 Reitmann, V.: Reguläre und chaotische Dynamik, Teubner, Stuttgart Leipzig, 1996. Ruderman, M S.: Absolute and convective instability of tangential discontinuities in viscous fluids: Application to heliopause, Astrophys. and Space Science, 274, 327–341, 2000. Titov, V S. and Hornig, G.: Magnetohydrodynamic flows sustaining stationary magnetic nulls, Phys. of Plasmas, 7, 3542–3550, 2000. Zank, G.: private communication, 2007.