Astrophysics and Space Sciences Transactions www.astrophys-space-sci-trans.net 1810-6528 1810-6536 5 1 2009 10.5194/astra-5-31-2009 http://www.astrophys-space-sci-trans.net/5/31/2009/ http://www.astrophys-space-sci-trans.net/5/31/2009/astra-5-31-2009.html http://www.astrophys-space-sci-trans.net/5/31/2009/astra-5-31-2009.pdf 31 34 2009-08-06 Analytical solutions for anisotropic MHD shocks V. Génot CESR, Université de Toulouse (UPS) & CNRS (UMR5187), Toulouse, France A new method to analytically solve the anisotropic MHD system of equations describing shock transitions is presented. As this system is known to be under-determined (there is more unknown parameters than available equations) free parameters must be chosen. From observational contraints it appears that the magnetic amplitude jump is a good candidate as it is generally available more frequently and more precisely than other jump variables. With this approach we obtain an explicit expression for the density compression ratio for arbitrary upstream parameters and shock geometry. Downstream anisotropy and pressure are also calculated. The results are tested against an other approach and compared with observations from the Earth's bow shock and the solar wind termination shock. Burlaga L. F., Ness N. F., and Acũna M. H.: Trains of magnetic holes and magnetic humps in the heliosheath, Geophys. Res. Lett., 33, L21106, doi:10.1029/2006GL027276, 2006. Chao, J. K. and Goldstein, B.: Modification of the Rankine-Hugoniot Relations for Shocks in Space, J. Geophys. Res., 77, 5455–5466 , 1972. Chao, J. K., Zhang, X. X., and Song, P.: Derivation of temperature anisotropy from shock jump relations: Theory and observations, Geophys. Res. Lett., 22, 17, 1995. Génot, V.: Mirror and firehose instabilities in the heliosheath, Astroph. J., 687, 119–122, 2008. Génot, V., Budnik, E., Hellinger P., Passot T., Belmont G., Trávní\v cek,~P., Sulem P.-L., Lucek, E., and Dandouras, I.: Mirror structures above and below the linear instability threshold: Cluster observations, fluid model and hybrid simulations, Ann. Geophys., 27, 601–615, 2009. Hudson, P. D.: Discontinuities in an anisotropic plasma and their identification in the solar wind, Planet. Space Sci., 18, 1611–1622, 1970. Lerche, I., Pohl, M., and Schlickeiser, R.: Turbulent adiabatic shock waves and diffusive particle acceleration, J. Plasma Phys., 64, 459–474, 2000. Liu, Y., Richardson, J. D., Belcher, J. W., and Kasper, J. C.: Temperature anisotropy in a shocked plasma: mirror-mode instabilities in the heliosheath, Astroph. J., 659, 65–68, 2007. Siewert, M. and Fahr, H.-J.: A Boltzmann-kinetical description of an MHD shock with arbitrary field inclination, Astron. Astrophys., 485, 327–336, 2008. Vogl, D. F., Biernat, H. K., Erkaev, N. V., Farrugia, C. J., and Mühlbachler, S.: Jump conditions for pressure anisotrophy and comparison with the Earth's bow shock, Nonlin. Proc. Geophys., 8, 167–174, 2001. Whang, Y. C., Burlaga L. F., Wang Y.-M., and Sheeley Jr. N. R.: The termination shock near 35° latitude, Geophys. Res. Lett., 31, L03805, doi:10.1029/2003GL018679, 2004. Winterhalter, D., Kivelson M. G., Walker R. J., and Russell C. T.: The MHD Rankine-Hugoniot jump conditions and the terrestrial bow shock - A statistical comparison, Adv. in Space Res., 4, 287–292, 1984.