ИКИ РАН, г. Москва, Россия

1. О ВЛИЯНИИ ДАВЛЕНИЯ И НАТЯЖЕНИЯ СИЛОВЫХ ЛИНИЙ МАГНИТНОГО ПОЛЯ В МАГНИТОШИТЕ НА ПОЛОЖЕНИЕ И ФОРМУ ГЕОМАГНИТОПАУЗЫ М.И. Веригин, Г.А. Котова, В.В. Безруких, А.П. Ремизов ИКИ РАН, г. Москва, Россия Девятая конференция П 22 и ОФН 15 «Физика плазмы всолнечной системе» 10 - 14 февраля 2014 г., ИКИ РАН

2. 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 r0 – magnetopause subsolar distance, R0– 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

3. 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

4. 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 Field line tension term where D-subsolarmagnetosheath thickness whereR-magnetosheath field line curvature radius because • Magnetic field pressure at the magnetopause is typically more important than the magnetosheath magnetic field line tension pressure

5. Evidence of magnetic field pressure influence and simplified model of bvdependence of the MP location ISEE 3 empiric relation Crooker et al., JGR, A12, 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 • Tatrallyay et al., Ann. Geophys., 30, 1675, 2012 An unusually low SW ram pressure (and, hence, low Ma) period in 2007–2008 with the peak at 1.4 nPa whereas 2 nPa is a typical value. Simplified model disadvantage - theoretically unjustified simple addition of magnetic and thermal pressure at the subsolar magnetopause. 5 THEMIS orbiters, Dusik et al., JGR, 2010

6. More accurate total thermal & magnetic pressure evaluation at the stagnation point 3-D MHD calculations by Stahara, Pl.Sp.Sci., 50, 421, 2002. 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 ???

7. 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 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. Final result – exact analytic solution for several first terms of xi , Vi , Bi , p, rexpansion over t Shugaev, Kalinchenko, XY Moscow MHD conf., V2, p.618, 2005

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

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

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

11. Total thermal & magnetic pressure at the stagnation point and the magnetopause model GEOMAGNETOPAUSE MODEL r0 = 10.89 ReP-3/16 (b) r0 = 10.81 ReP-1/6 (a) R0 = 16.55 ReP-3/16 R0 = 16.33 ReP-1/6 D = 97.13 ReP-3/16 D = 95.05 ReP-1/6 <dn2> = 1.339 Re <dn2> = 1.347 Re

12. Correspondence to Prognoz’ observations Power exponent correspondence to some other models -1 / 6.6 < -1 / 6 < -3 / 16 < -0.194 Shue et al., 1998 Usual (a) Present model (b) Lin et al., 2010

13. Выводы • Показано, что влияние натяжения силовых линий межпланетного магнитного поля у магнитопаузы в 2D / R меньше, чем влияние давления межпланетного магнитного поля (D- толщина магнитошита, R радиускривизны магнитных силовых линий). • С использованием результатов 3D МГД моделирования обтекания магнитопаузы солнечным ветром (Stahara, 2002) и аналитического решения МГД уравнений в Лагранжевых переменных построено аналитическое выражение, описывающее полное давление набегающего потока плазмы в точке его остановки: где • С использованием данных опересечениях магнитопаузы спутниками Прогноз, Прогноз 2-6, 9, Интербол и полного давления P магнитного поля и плазмы в точке остановки, 2D положение этой границы может быть описано как: , , где r0 = 10.89 ReP-3/16 R0 = 16.55 ReP-3/16 D = 97.13 ReP-3/16 • Построенная модель включает описание зависимости положения магнитопаузы от угла между направлениями солнечного ветра и межпланетного магнитного поляbv.

14. Спасибо за внимание ! Девятая конференция П 22 и ОФН 15 «Физика плазмы всолнечной системе» 10  14 февраля 2014 г., ИКИ РАН