IMPRS Solar System School Retreat, Apr 29 – May 2, 2013 Sun-planet connection Y. Narita Space Research Institute Austrian Academy of Sciences Chap. 1 Plasma Chap. 2 Sun Chap. 3 Earth Chap. 4 Planets 1 Ionization of atomic hydrogen gas H → p + e- 1AU corona 13.6 eV = 158 000 K Other ionization sources? 2 Magnetohydrodynamics Flow velocity evolution Simplified pressure balance Magnetic field evolution 3 Pressure balance realizations (a) Hydrostatic equilibrium (b) Hydromagnetic equilibrium Φ grav p pdyn mag pth (c ) Rotating body (d) Radiative transfer Φ Φgrav grav prad 4 Energy conversion processes Eth shock wave cooling solar wind E heating kin Erad reconnection contraction T-tauri stars dynamo Eddinton luminosity waves and E turbulence mag Egrv 5 Heat energy transport Caveat! Additional energy loss due to neurtino escape 6 Exercise Is the electrical conductivity in interplanetary plasma (at 1 AU) better than that of iron Fe (107 Ω-1 m-1)? How many meaningful units are there for expressing pressure? 7 Solution Is the electrical conductivity in interplanetary plasma (at 1 AU) better than that of iron Fe (107 Ω-1 m-1)? -1 2 -3 The resistivity formula (η=σ = me νc / ne e ) using ne= 10 cm -7 6 -1 -1 and νc = 10 Hz (Te = 0.3 MK) yields σ = 10 Ω m . It is less conductive than iron but is almost on the same order. How many meaningful units are there for expressing pressure? Pa (pascal) N/m2 (force per area) J/m3 (energy density) kg ms-1 / m2 s (momentum flux) 8 Chap. 2 Sun Heat production Solar luminosity from gravitational contraction from nuclear fusion Is the core hot enough for fusion? … Yes but only possible through tunnel effect Reaction process (pp-chain, CNO-cycle) neutrinos heat 9 Heat transfer to the surface F Frad cnv Lⵙ Core Radiative transport Convective transport Surface Corona 15 MK 6000K 1 MK ν Tachocline Chromosphere Energy conversion Eth → Ekin →Emag Model construction ● Spherical symmetry ● Hydrostatic equilibrium ● Equation of state? 10 Excursion to astrophysics Main sequence stars Low-mass (M) red dwarf, 0.1-0.5 Mⵙ Sun-like (G) 0.5-1.5 Mⵙ core - conv High-mass (O,B) 1.5 Mⵙ or higher core - rad - conv core+conv - rad High-mass stars live much shorter although they have more fuel. Why? 11 Convection zone slow Buoyancy + Coriolis effect Taylor column Twisting magnetic field lines (“alpha”) v fast Differential rotation B Stretching field lines (“Omega”) Rad B v Cnv Cause of 11-year (or 22-year) perioditicy? 12 Corona Proposed heating mechanisms: shock waves, nanoflares, Alfven waves, ... Thermal expansion of coronal gas → solar wind (Eth → Ekin) Slice along the rot axis Slice cutting the rot axis Thomson scattering Vsw = cs 10Rⵙ 13 Heliosphere 14 Exercise 1. Estimate the lifetime of the sun. 2. Is the number density of solar neutrino coming to Earth higher than 1 cm-3? 15 Solution 1. Estimate the lifetime of the sun. -13 (Fuel amount) = (Mⵙ / mp) [protons] x 26/4 [MeV] x 1.6 x 10 [J/MeV] 26 (Consumption rate) = Lⵙ = 4 x 10 [J/s] (Lifetime) = (Fuel) / (Consumption) = 2.9 x 1018 [s] = 0.9 x 1011 [yr] 2. Is the number density of solar neutrino coming to Earth higher than 1 cm-3? Use solar constant and reaction rate (2 neutrinos per 26 MeV). Neutrino number flux is F = 1.36 x 103 [J/m2s] / (13 [MeV] x 1.6 x 10-13 [J/MeV]) = 6.5 x 1010 [particles / cm2s] Number density (on using the light speed c) is n = F/c = 2.18 x 106 [particles m-3] = 2.18 [particles cm-3]. It is slightly more than one particle per cm3. 16 Chap. 3 Earth Earth's magnetic field boundary Time scale of reaction against solar wind change? 17 Magnetosphere Equlibrium picture Solar wind plasma 10 RE ● How does the tail form? - Friction model vs. reconnection model ● Where is the pressure balance applicable? And what kind of pressure? 18 Magnetic field transport Friction model (Axford & Hines, 1961) v with shear v B B Reconnection model (Dungey, 1961) v v Bearth B reconnected Bsun 19 Magnetospheric dynamics Geomagnetic storm Auroral substorm jet compression reconnection Phenomenon with sudden increase Phenomenon with the southward direction of solar wind pressure (CME, CIR) of interplanetary magnetic field Dayside compression ~ minutes Dayside reconnection ~ minutes Nightside compression ~ hours Tail reconnection ~ 40 minutes after dayside reconnection Recovery ~ days Recovery ~ hours 20 Exercise 1. What can be used as a proxy of past Earth climate and solar activity on the time scale from 1000 to 10,000 years? Earth climate … Solar activity … 2. Draw footprint motion of Earth's magnetic field line in the arctic region. Friction model Reconnection model 12h 12h 18h 6h 18h 6h 0h 0h viewed from north pole axis to the ionosphere 21 Solution 1. What can be used as a proxy of past Earth climate and solar activity on the time scale from 1000 to 10,000 years? Earth climate … Oxygen 18 isotope abundance in stalagmite Solar activity … Carbon 14 isotope abundance in tree ring (Neff et al., Nature, 411, 290, 2001) 2. Draw footprint motion of Earth's magnetic field line in the arctic region. Friction model Reconnection model 12h 12h dayside reconnection friction at flank of magnetopause 18h 6h 18h 6h 0h 0h tail reconnection viewed from north pole axis to the ionosphere 22 Chap. 4 Planets Obstacle types Magnetized body Umagnetized body With atmosphere Earth Venus, Mars Gas giants (J, S) Titan, Enceladus Icy planets (U, N) Ganymede Without atmosphere Mercury Earth moon 23 Dipole axis and magnetosphere size Merc Earth 2 R pl 10 Rpl J, S U, N 25 R 70 Rpl (J), 20 Rpl (S) pl 24 Mercury Rocky planets Induced magnetosphere Venus 2 Rpl No inosophere Earth but substorm- like events Mars 1%-10% Rpl No planetary magnetic field 10 Rpl Substorm, aurora 1%-10% Rpl Crustal magnetic field 25 Gas giants (Jup,Sat) Centrifugal force Liquid, metalic hydrogen envelope? 10-hour rotation Satellites as plasma source (Io, Enceladus) Aurora, radio wave, synchrotron emission 26 Icy planets (Ura, Nep) pole-on pole-off solar wind solar wind Planet formation beyond ice limit Large tilt angle → pole-on magnetosphere Aurora, radio wave emission 27.