Data used 331 magnetopause crossings by Prognoz Prognoz

Data used • 331 magnetopause crossings by Prognoz, Prognoz 2 -6, 9 dated from 1972 to 1983 • 2625 magnetopause crossings by Interball 1 during 1995 and 1999 We use simple analytic model , or with r 0 – magnetopause subsolar distance, R 0– nose curvature radius. This expression has finite asymptotic magnetotail diameter D and reasonably approximates distant Prognoz-9 magnetotail crossings. Same shape was used 40 years ago by Howe & Binsack (JGR, 77, 3334 -3344, 1972) for modeling Explorer 33 & 35 magnetopause observations

GIPM magnetopause anisotropy • Magnetopause is compressed by about 5% in the direction perpendicular to the plane formed by Vsw and IMF vectors • The compression may be a result of the tension of magnetosheath magnetic field lines draping the magnetopause Verigin et al. , Geom. & Aeron. , 49, No. 8, 1176 -1181, 2009

Relative role of magnetic field tension and pressure at the magnetopause nose For V B upstream flow, along the post-shock stagnation line General MHD equations ; Magnetic pressure term where D - where R - Field line tension term subsolar magnetosheath thickness magnetosheath field line curvature radius because • Magnetic field pressure at the magnetopause is typically more important than the magnetosheath magnetic field line tension pressure

Evidence of magnetic field pressure influence and simplified model of bv dependence of the MP location ISEE 3 empiric relation Crooker et al. , JGR, A 12, 1982 Simplified model : - reasonably described magnetopause nose cone angle dependence found by Dusik et al. , 2010 - additionally described the magnetopause crossings by geostationary GOES 10 & 12 orbiters under very high IMF and SW ram pressure An unusually low SW ram pressure (and, hence, low Tatrallyay et al. , Ann. Geophys. , 30, 1675, 2012 Ma) period in 2007– 2008 with the peak at 1. 4 n. Pa Simplified model disadvantage whereas 2 n. Pa is a typical theoretically unjustified simple addition of value. 5 THEMIS orbiters, Dusik et al. , JGR, 2010 magnetic and thermal pressure at the subsolar magnetopause.

More accurate total thermal & magnetic pressure evaluation at the stagnation point Ms = 6 Proxy for total thermal & magnetic field pressure at the stagnation point, as deduced from Stahara’ s 3 -D MHD calculations, and implemented in our magnetopause model presented at previous IKI conference of 2013. Is this proxy reasonable enough for MHD flows with Ms 6 ? ? ? 3 -D MHD calculations by Stahara, Pl. Sp. Sci. , 50, 421, 2002.

Solution of MHD flow after the curved shock in Lagrangian variables MHD equations in Lagrangian variables - start point position at the BS - time of the bow shock crossing - preshock plasma density - covariant components of the space metric tensor - metric tensor contravariant components and determinant AND - Rankine-Hugoniot relations at the BS Final result – EXACT ANALYTIC SOLUTION for several first terms of xi , Vi , Bi , p, r expansion over t Shugaev, Kalinchenko, XY Moscow MHD conf. , V 2, p. 618, 2005 An example of MHD flow lines after the BS as calculated in Lagrangian variables. NOTE that the cavity in the flow (“magnetosphere”) is self -organized after the predefined curved shock.

, , Comparison of stagnation pressure distributions in ( Ms , Ma ) plane Lagrangian equations analytic solution O-O-O-ps ! ! ! MHD proxy

, , Comparison of stagnation pressure distributions in ( Ms , Ma ) plane Lagrangian equations analytic solution MHD proxy

, , Comparison of stagnation pressure distributions in ( Ms , Ma ) plane MHD proxy Will be used onwards…

Total thermal & magnetic pressure at the stagnation point and the magnetopause model GEOMAGNETOPAUSE MODEL r 0 = 10. 81 Re P -1/6 (a) R 0 = 16. 33 Re P -1/6 D = 95. 05 Re P -1/6 <dn 2> = 1. 347 Re r 0 = 10. 89 Re P -3/16 (b) R 0 = 16. 55 Re P -3/16 D = 97. 13 Re P -3/16 <dn 2> = 1. 339 Re

Correspondence to Prognoz’ observations Power exponent correspondence to some other models -1 / 6. 6 Shue et al. , 1998 < -1 / 6 Usual (a) < -3 / 16 < Present model (b) -0. 194 Lin et al. , 2010