Modeling of the outer heliosphere with the realistic solar cycle Vladislav V. Izmodenov a,b,c, * , Yuri G. Malama b,c , Michael S. Ruderman d a Lomonosov Moscow State University, Department of Aeromechanics and Gas Dynamics, School of Mechanics and Mathematics, Leninskie Gory, Glavnoe Zdanie, Moscow 119899, Russia b Space Research Institute (IKI), Russian Academy of Sciences, Prosouznaya 84/32, Moscow, 117997, Russia c Institute for Problems in Mechanics, Russian Academy of Sciences, Prospekt Vernadskogo 101-1, Moscow, 119526, Russia d University of Sheffield, Department of Applied Mathematics, Hicks Building, Hounsfied Road, Sheffield S3 7RH, UK Received 1 November 2006; received in revised form 11 June 2007; accepted 14 June 2007 Abstract Time-dependent kinetic-continuum model of the solar wind interaction with the two-component local interstellar cloud (LIC) has been developed recently [Izmodenov, V., Malama, Y.G., Ruderman, M.S. Solar cycle influence on the interaction of the solar wind with local interstellar cloud. Astron. Astrophys. 429, 1069–1080, 2005a.]. Here, we adopted this model to the realistic solar cycle, when the solar wind parameters at the Earth’s orbit are taken from space data. This paper focuses on the results related to the termination shock (TS) excursion with the solar cycle that may help to understand Voyager 1 data obtained at and after the crossing of the termination shock and to predict the time of the TS crossing by Voyager 2. Ó 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. Keywords: Heliospheric termination shock; Heliospheric interface; Solar wind; Solar cycle; Interstellar H atoms 1. Introduction More than 30 years’ (three solar cycles) observations of the solar wind show that its momentum flux varies by fac- tor of 2 from solar maximum to solar minimum. It has been shown theoretically that such variations of the solar wind momentum flux strongly influence the structure of the heliospheric interface, the region were the solar wind interacts with the interstellar gas. Recent review on the modeling of the heliospheric interface is given in Izmode- nov and Baranov (2007). Most models of the heliospheric interface, which take into account the solar cycle effects, ignored the interstellar H atom component or took this component into account by using simplified fluid or multi-fluid approximations. These implications were adopted because it is difficult to solve a 6D (time, two dimensions in space, and three dimensions in velocity-space) kinetic equation for the inter- stellar H atom component. Recently, the non-stationary, self-consistent model of the heliospheric interface was developed by Izmodenov et al. (2003a, 2005a), Izmodenov and Malama (2004a,b). Izmodenov et al. (2005a) have studied the effects for the ‘ideal’ solar cycle. It was assumed that, at Earth’s orbit, the solar wind number density oscillates harmonically, while the bulk velocity and temperature remain constant. The per- iod of the harmonic oscillations was chosen to be 11 years. The solution of the system of Euler equations for plasma, and the kinetic equation for interstellar H atoms was found numerically with the periodic boundary condi- tions for the solar wind at the Earth’s orbit. The period of the solution is 11 years. The basic results for the plasma component are the following: (1) The solar cycle variation of the termination shock (TS) location is ±7 AU about its mean value. (2) The heliopause (HP) location varies by ±2 AU about its mean value. (3) The variation of the 0273-1177/$30 Ó 2007 COSPAR. Published by Elsevier Ltd. All rights reserved. doi:10.1016/j.asr.2007.06.033 * Corresponding author. Address: Lomonosov Moscow State Univer- sity, Department of Aeromechanics and Gas Dynamics, School of Mechanics and Mathematics, Leninskie Gory, Glavnoe Zdanie, Moscow 119899, Russia. Tel.: +7 495 4344189; fax: +8 499 739 95 31. E-mail addresses: izmod@ipmnet.ru, izmod@iki.rssi.ru (V.V. Izmode- nov). www.elsevier.com/locate/asr Advances in Space Research xxx (2007) xxx–xxx ARTICLE IN PRESS Please cite this article in press as: Izmodenov, V.V. et al., Modeling of the outer heliosphere with the realistic solar cycle, J. Adv. Space Res. (2007), doi:10.1016/j.asr.2007.06.033