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Application of the paraboloid model to the magnetospheres of Mercury, Earth, Saturn, and Jupiter .

Application of the paraboloid model to the magnetospheres of Mercury, Earth, Saturn, and Jupiter. Igor I. Alexeev and Elena S. Belenkaya. Content. Introduction. What is a paraboloid model?

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Application of the paraboloid model to the magnetospheres of Mercury, Earth, Saturn, and Jupiter .

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  1. Application of the paraboloid model to the magnetospheres of Mercury, Earth, Saturn, and Jupiter. Igor I. Alexeev and Elena S. Belenkaya International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  2. Content • Introduction. What is a paraboloid model? • Paraboloidal model of Mercury’s magnetic field and estimation of the magnetospheric currents contribution to the total field. • Jupiter magnetosphere, plasma magnetodisk. • Saturn magnetosphere. The magnetodisk increase with magnetosphere enhancement. • Conclusions International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  3. Rsm,kmRsm/ Rp Mercury 3 600 km 1.4 Earth 64 000 km10 flyby ~30 min one orbit12hours Saturn 1 723 700 km28 Jupiter 5 712 000 km80 International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  4. Magnetosphere parameters 4 International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  5. Paraboloid model of the Earth’s magnetosphere Alexeev, [1978], Belenkaya et al. [2005]. International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  6. Each current system generated its own field Normal to magnetopause magnetic field cancel BN = 0 not just for total field but for each separate current module Tailcurrent system BTN = 0 conserved tail lobe magnetic fluxΦ∞=const at x →-∞. Alexeev et al., Space Sci. Rev., 2003. Current systems which generated the magnetospheric magnetic field International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  7. Greene, J.M., and R. L. Miller, 1994. International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  8. Two magnetospheric currents systems Magnetopause current depends on: R1, ψ Ψ is the dipole tilt angle R1 is the magnetopause stand-off Tail currents and closure magnetopause currents dependent on: R1, R2, Δz, Φlobe R2 is the inner edge of tail current Φlobe is the tail lobe magnetic flux Δz is the vertical displacement of the tail current sheet Penetrated IMF term dependent on: kr is the reconnection “efficiency” International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  9. Mercury’s paraboloid magnetosphere model Mx,My,Mz, dx, dy, dz - dipole, Ψ is the dipole tilt, R1is the magnetopause stand-off, R2is the inner edge of tail current, Φlobeis the tail lobe magnetic flux, Δz is the vertical displacement, kris the reconnection “efficiency”, BIMF is the IMF vector. Alexeev et al., JGR, 2008 Alexeev et al. ,Icarus, 2010.

  10. Module of the magnetic field for all flybys • Mariner 10 III • MESSENGER 1 • Mariner 10 I • MESSENGER 2 Model – solid curve Data - thin curve International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  11. MESSENGER Flyby 2, Oct. 6th, 2008|B|mod |B|M2σ =8.8 nT; Bx_mod , Bx_M2 • Magn_x • Tail_x • Dipole_x • Model_x • M2_x International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  12. Best fitting dipole parameters Parameters of the magnetospheric currents International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  13. MESSENGER Data from Mercury Orbit Mercury’s magnetic equator, determined on successive orbits as the point where the direction of the internal magnetic field is parallel to the spin axis of the planet, is well north of the planet’s geographic equator. Internal dipole (about 0.2 Mercury radii) or 480 km, northward of the planet’s center. Cortese to Sean C. Solomon (MESSENGER PI) http://messenger.jhuapl.edu/news_room/details.php?id=174 International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  14. Jupiter Io, 5.9 Ganymede, 14.9 Cusp?Callisto 26.3? Europe, 9.4 26 Nov 1998, HST, Clarke, BU, USA. International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  15. JupiterGalileo orbit and Cassini Flyby • Cassini flyby • Paraboloid magnetopause • Galileo orbit Alexeev, Belenkaya, 2005 International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  16. The Jovian magnetospheric magnetic field dependend on radial distance R as measured by Ulysses [Cowley et al., 1996] R-1power-law, dotted-dashed curve, and R-1,7 power-law, dashedcurve R-2power-law, solidcurve R-3joviandipolepowerlaw, dottedcurve. Allmodelcurveswere normalized onmeasuredfieldstrengthat 20 Rj- 62.2nT. International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  17. JupiterNoon-midnight meridian plane Magnetodisk plasma preserve the magnetic flux reconnectionacross the equatorial plane Meff=Mdip+Mdisk, Meff= 4 Mdip 17 International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  18. Saturn Cassini SOI model International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  19. “Sling” model by magnetodisk Slinger from the Balearic Islands with the sling 19 International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  20. Magnetodisk magnetosphere International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  21. Conclusions • Module magnetospheric structure results in universal magnetospheric model for all scales (5.7×106 km >R1>3×103 km) • Jupiter’s magnetosphere is most interesting object. It is a biggest in Solar System. The jovian magnetodisk doubled the magnetospheric size. • Determination of a Mercury’s magnetic dipole moment value gives 195.9±0.3 nTRM3. The root mean square deviation between the model and the observations amounts to σ = 10.5 nT. • We received the dipole northern offset up to ~0.18 RM. The dipole tilt angle is 3.2±0.1˚ 21 International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  22. Acknowledgements All observational data have been received by cooperation with • James A. Slavin, GSFC, Greenbelt, MD, USA • C. Robert Clauer, Tech. Univ. Virginia, USA • Stanley W.H. Cowley, Leicester Univ., UK. • Rene Prange, Observatory Medon, France. 22 International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  23. Thank you !!! International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  24. Conclusions • A new model of Mercury’s global magnetospheric current systems has been developed based upon the paraboloidal model. • The contributions of the external current systems into the total magnetic field along the spacecraft orbits are significant and must be taken into account when fitting the planetary dipole parameters. • Determination of a magnetic dipole moment value gives 195.9±0.3 nTRM3, that is consistent with both of the Mariner 10’s and MESSENGER 1 close Mercury encounters. The root mean square deviation between the model and the observations amounts to σ = 10.5 nT. • We received the dipole offset up to 0.166±0.001RMtoward the northern pole. In the equatorial plane the dipole offsets are smaller (dx = -0.021±0.001RMand dy = 0.021±0.001RM). The dipole tilt angle is 3.2±0.1˚, and the eastern longitude of the Mercury’s magnetic northern pole is 189.6±1.8˚. International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  25. Conclusions (Mercury) • A new model of Mercury’s global magnetospheric current systems has been developed based upon the paraboloidal model. • The contributions of the external current systems into the total magnetic field along the spacecraft orbits are significant and must be taken into account when fitting the planetary dipole parameters. • Determination of a magnetic dipole moment value gives 195.9±0.3 nTRM3, that is consistent with both of the Mariner 10’s and MESSENGER 1 close Mercury encounters. The root mean square deviation between the model and the observations amounts to σ = 10.5 nT. • We received the dipole offset up to 0.166±0.001RMtoward the northern pole. In the equatorial plane the dipole offsets are smaller (dx = -0.021±0.001RMand dy = 0.021±0.001RM). The dipole tilt angle is 3.2±0.1˚, and the eastern longitude of the Mercury’s magnetic northern pole is 189.6±1.8˚. International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  26. Igor Alexeev and E. Belenkaya Scobeltsyn Institute of Nuclear Physics, Lomonosov Moscow State University, Leninskie Gory, 119992 Moscow, Russia The paraboloid model applied to the magnetospheres of Mercury, Earth, Jupiter, and Saturn 26 International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  27. Polar oval diameters R1Meff/Mplθoval • Earth 10 RЕ 1.021.5о • Jupiter 80 Rj4.5 15.9о • Saturn22 Rs1.215.6о R1 is the subsolar distance in Rpl International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  28. Jupiter’s magnetospheric modelwith variable magnetopause flaring “Earth-like” Expanded Compressed International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  29. Mercury • Orbit 0.31 – 0.46 a.u. • RadiusRМ=2440 km • Density 5.3 t/m3 • 60% (mass) – Fe (core) • Temperature+430˚С (noon) -160˚ C (night) • Dipole moment~ 200 nTRm3 MM = 0.037%ME International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  30. MESSENGERhttp://messenger.jhuapl.edu/index.php • Total mass- 1.41.81.3 m 1100 kg (600kg – fuel and 508 kg devices and platform) • Power 390 – 640 Wt • Start 3 Aug 2004 6 gravitational maneuvers Earth (1), Venus (2), Mercury (3) Mercury Orbit Insertion March 18, 2011 12:45 a.m. UTC • Total length of the orbit 7.9·109 km (52.7 a.u.) 15 Sun orbits • Costs $446M ($1.5 from each USA citizen) International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  31. International Astrophysics Forum Alpbach 2011, 23 June, 17:10

  32. Greene, J.M., and R. L. Miller, 1994. International Astrophysics Forum Alpbach 2011, 23 June, 17:10

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