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
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