GEM Tutorial: The Magnetosheath
S M Petrinec
Lockheed Martin Advanced Technology Center, Palo Alto, CA
GEM Summer Workshop: 20-27 June 2009
1
Outline
• What is the magnetosheath?
• Outer boundary (bow shock)
• Shock jump conditions
• Asymptotic cone angle
• Standoff position (nominal and special cases)
• Bow shock shape
• Inner boundary (magnetopause)
• Plasma parameters along inner boundary
• Sources of accelerated flows
• Within the magnetosheath
• Historical studies
• Theory and analytic models
• Synoptic maps
• Summary
GEM Summer Workshop: 20-27 June 2009
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What is the magnetosheath?
The magnetosheath is the region of
space between a planetary obstacle
(magnetopause or ionopause) and a
detached bow shock; which exists to
slow and divert the super-magnetosonic
solar wind plasma flow around the
planetary obstacle.
Figure from Van Allen, J., "Magnetospheres, Cosmic
Rays, and the Interplanetary Medium", in The New
Solar System, [1991], pg. 29.
GEM Summer Workshop: 20-27 June 2009
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Outer boundary (Bow shock)
From An Album
of Fluid Motion
by Milton Van
Dyke
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Outer boundary (Bow shock)
Rankine Hugoniot relations:
Zhuang and Russell, JGR, 1981
Petrinec and Russell, Space Sci. Rev., 1997
Define X = r∞/r
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Outer boundary (Bow shock)
Shock jump conditions:
Petrinec and Russell, Space Sci. Rev., 1997
GEM Summer Workshop: 20-27 June 2009
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Outer boundary (Bow shock)
Shock jump conditions:
X = 1 (trivial solution)
Analytic solutions exist! (one real root; two complex roots)
Petrinec and Russell, Space Sci. Rev., 1997
GEM Summer Workshop: 20-27 June 2009
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Outer boundary (Bow shock)
Petrinec and Russell,
Space Sci. Rev., 1997
GEM Summer Workshop: 20-27 June 2009
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Outer boundary (Bow shock)
Shock jump conditions:
Petrinec and Russell,
Space Sci. Rev., 1997
GEM Summer Workshop: 20-27 June 2009
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Outer boundary (Bow shock)
Shock jump conditions:
Petrinec and Russell,
Space Sci. Rev., 1997
GEM Summer Workshop: 20-27 June 2009
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Outer boundary (Bow shock)
Shock jump conditions:
These solutions describe
the jump in MHD jump
conditions across the
shock, but don’t provide
any information as to the
shape or size of the bow
shock
Petrinec and Russell,
Space Sci. Rev., 1997
GEM Summer Workshop: 20-27 June 2009
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Outer boundary (Bow shock)
Asymptotic angle:
Sonic Mach cone angle (y = asin(1/MS))
Petrinec and Russell, Space Sci. Rev., 1997
Good to know, but still doesn’t
provide any information as to the
shape or size of the bow shock
GEM Summer Workshop: 20-27 June 2009
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Outer boundary (Bow shock)
Bow shock location: Standoff position
Alvin Seiff at NASA Ames
Hypervelocity Free Flight Facility (1966)
GEM Summer Workshop: 20-27 June 2009
Shock distance in front of a sphere:
δ/Rn = 0.78r∞/r
Seiff, NASA SP-24, 1962
13
Outer boundary (Bow shock)
Bow shock location: Standoff location
John Spreiter
Bow shock
Spreiter et al., Planet. Space Sci., 1966
GEM Summer Workshop: 20-27 June 2009
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Outer boundary (Bow shock)
Bow shock location: Standoff location
(Low solar wind Mach numbers)
Historical theories of shock wave standoff
location in air using hydrodynamics
(Petrinec, Planet. Space Sci., 2002)
GEM Summer Workshop: 20-27 June 2009
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Outer boundary (Bow shock)
Bow shock location: Standoff location
(Low solar wind Mach numbers)
Spreiter and Rizzi,
Acta Astron., 1974
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Outer boundary (Bow shock)
Bow shock location: Standoff location
(Low solar wind Mach numbers)
Dms/amp = 3.4X-0.6
Dms/amp = 1.1X
Cairns and Lyon, JGR, 1995
GEM Summer Workshop: 20-27 June 2009
Cairns and Lyon, JGR, 1996
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1
Outer boundary (Bow shock)
9
8
7
6
Bow shock location: Standoff location
(Low solar wind Mach numbers)
1.1*X
(gasdynamic experiments)
1.1*(2X/(1 + g)(1 - X)) (Farris and Russell)
5
4
3
Farris and Russell (1994) conjecture:
For large upstream sonic Mach numbers:
r∞/r (=X)
(g-1)/(g+1)
and
Ms2/(1-Ms2)
(g-1)/(g+1)
Downstream and upstream sonic
Mach numbers are simply related
(Landau and Lifshitz, 1959):
Ms2 = (2+(g-1)Ms∞ 2)(2gMs∞ 2-(g-1))
D/DOB
2
0.1
9
8
7
6
5
4
3
2
0.01
0.01
2
3
4
5
6 7 8 9
2
3
4
5
0.1
r/r (=X)
6 7 8 9
1
So,
D/DOB = 1.1(2X)/((1+g)(1-X))
= 1.1((g-1) Ms∞ 2+2)/(g+1)(Ms∞ 2-1))
GEM Summer Workshop: 20-27 June 2009
Farris and Russell, JGR, 1994
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Outer boundary (Bow shock)
Bow shock location: Standoff location
(Low solar wind Mach numbers)
(Petrinec, Planet. Space Sci., 2002)
GEM Summer Workshop: 20-27 June 2009
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Outer boundary (Bow shock)
Bow shock location: Standoff location
(Low solar wind Mach numbers)
GEM Summer Workshop: 20-27 June 2009
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Outer boundary (Bow shock)
Bow shock location: Standoff location
(Low Alfvén Mach number, qBn = 0)
De Sterck and Poedts, Astron. Astrophys., 1999
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Outer boundary (Bow shock)
Bow shock shape
Farris et al., GRL, 1991
Bow shock
Good approximation for the dayside shock,
but since it is an ellipsoid and does not
asymptote, is not appropriate for the
nightside.
Other empirical Earth bow shock models:
Fairfield, JGR, 1971
Formisano, Planet. Space Sci., 1979
Slavin and Holzer, JGR, 1981
Peredo et al., JGR, 1995
GEM Summer Workshop: 20-27 June 2009
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Outer boundary (Bow shock)
Bow shock shape
GEM Summer Workshop: 20-27 June 2009
Peredo et al., JGR, 1995
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Outer boundary (Bow shock)
Distant bow shock shape
Farris and Russell
model
Khurana and Kivelson, JGR, [1994]
Cairns and Lyons
model
Khuarana and Kivelson model for asymptotic flaring angle correction used to
extend various dayside bow shock models (Bennett et al., JGR, 1997)
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Outer boundary (Bow shock)
Bow shock shape at low Mach number
Fairfield et al., JGR, 2001
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Inner boundary (Along the magnetopause)
Hydrodynamic parameters along inner boundary
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Inner boundary (Along the magnetopause)
Hydrodynamic parameters along inner boundary
GEM Summer Workshop: 20-27 June 2009
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Inner boundary (Along the magnetopause)
Plasma parameters along inner boundary
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Inner boundary (Along the magnetopause)
MHD features – slow mode shock and plasma depletion layer
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Inner boundary (Along the magnetopause)
Sources of accelerated flows
GEM Summer Workshop: 20-27 June 2009
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Inner boundary (Along the magnetopause)
Sources of accelerated flows
VA
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Inner boundary (Along the magnetopause)
Sources of accelerated flows
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Inner boundary (Along the magnetopause)
Sources of accelerated flows
Lavraud et al., GRL,
2007
Accelerations are calculated along the
streamlines according to the steady state
MHD momentum equation
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Within the magnetosheath
Spreiter et al., Planet. Space Sci., 1966
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Within the magnetosheath
Spreiter et al., Planet. Space Sci., 1966
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Within the magnetosheath
Analytic models of the magnetosheath
magnetic field
Kobel and Flückiger, JGR, 1994
Romashets et al., JGR, 2008
Surface shapes:
Bow shock and magnetopause are modeled as paraboloids with a common focus,
(halfway between the magnetopause nose and the Earth center)
Procedure:
Procedure:
Determine a magnetosheath scalar
magnetic potential for which:
Determine a magnetosheath vector
magnetic potential for which:
• The normal magnetic field
component is conserved across the
bow shock
• The magnetic field is tangential to
the magnetopause.
• Current-free within the
magnetosheath region
• The normal magnetic field
component is conserved across the
bow shock
• Magnetic field is coplanar across the
bow shock
• The magnetic field change decreases
to zero across the distant
downstream bow shock
• The magnetic field is tangential to
the magnetopause
• Non-zero currents are allowed within
the magnetosheath
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Within the magnetosheath
Spacecraft used: Geotail (magnetosheath), Wind (solar wind)
Span of time: 4/1996 – 10/2005
Magnetosheath passes: 2894 (bs-bs, mp-bs, mp-mp)
-40
20
Magnetosheath samples
rotated by solar wind flow velocity direction,
transformed from GSE to GSM coordinates, and
normalized by the convected
solar wind dynamic pressure.
0
ZaGSM [RE]
10
0
-10
2
2 1/2
(YaGSM +ZaGSM ) ×Sign(YaGSM)
-20
-20
-30
20
-20
-10
0
10
20
30
YaGSM [RE]
40
20
0
-20
XaGSM [RE]
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-40
Caveats:
1. 5-min averages not all statistically independent
2. Orbital bias:
10 RE perigee – subsolar region more often
sampled during low s.w. pressure
30 RE apogee – flanks more often sampled at
high s.w. pressure
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Within the magnetosheath
Potential problems (placing boundaries):
• Misidentification
• Solar wind pressures not accurate (nH+, nHe++, etc.)
• Wind spacecraft too far off Sun-Earth axis
• Estimated solar wind convection time incorrect
• Short-term oscillations of the boundaries not accounted for
• Discontinuities in the solar wind and traveling through the magnetosheath
GEM Summer Workshop: 20-27 June 2009
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Within the magnetosheath
Geotail MGF observations
-30
IMF within 10° of
Parker-Spiral angle
2
-30
1
2 1/2
(and |Bz| < (Bx +By ) /2)
1
IMF within 10° of
Parker-Spiral angle
2
2 1/2
(and |Bz| < (Bx +By ) /2)
2
1
1
2
-20
-20
2
3
-10
-10
YaGSM [RE]
YaGSM [RE]
2
4
0
10
0
10
3
4
4
3
20
20
2
2
2
30
30
2
20
10
0
-10
XaGSM [RE]
GEM Summer Workshop: 20-27 June 2009
-20
-30
20
10
0
-10
-20
-30
XaGSM [RE]
39
Within the magnetosheath
IMF directions 10° - 30° from radial
-30
-20
-20
-10
-10
YaGSM [RE]
YaGSM [RE]
-30
IMF within 10° of
Parker-Spiral angle
2
2 1/2
(and |Bz| < (Bx +By ) /2)
0
10
20
20
30
30
10
0
-10
XaGSM [RE]
GEM Summer Workshop: 20-27 June 2009
-20
-30
2 1/2
0
10
20
2
(and |Bz| < (Bx +By ) /2)
20
10
0
-10
-20
-30
XaGSM [RE]
40
Within the magnetosheath
Geotail MGF observations
-30
IMF within 10° of
perpendicular to
solar wind flow direction
2
2 1/2
(and |Bz| < (Bx +By ) /2)
2
-30
IMF within 10° of
perpendicular to
solar wind flow direction
2
2 1/2
(and |Bz| < (Bx +By ) /2)
3
2
2
2
3
3
-20
-20
Petrinec and Russell,
Space Sci. Rev, 1997
3
-10
YaGSM [RE]
YaGSM [RE]
-10
3
0
10
0
10
5
4
4
20
3
3
20
4
2
3
2
30
20
30
10
0
-10
XaGSM [RE]
GEM Summer Workshop: 20-27 June 2009
-20
-30
20
10
0
-10
-20
-30
XaGSM [RE]
41
Within the magnetosheath
Geotail MGF observations
-30
IMF within 10° of
Parker-Spiral angle
2
1
2 1/2
(and |Bz| < (Bx +By ) /2)
1
2
1
1
2
-20
Petrinec and Russell,
Space Sci. Rev, 1997
2
3
-10
YaGSM [RE]
2
4
0
10
3
4
4
3
20
2
2
2
30
2
20
10
0
-10
XaGSM [RE]
GEM Summer Workshop: 20-27 June 2009
-20
-30
42
Within the magnetosheath
Geotail MGF observations
-30
IMF within 10° of
parallel to solar wind
flow direction
2
2 1/2
(and |Bz| < (Bx +By ) /2)
2
3
-30
3
2
2
2
2
3
-20
3
IMF within 10° of
parallel to solar wind
flow direction
2
2 1/2
(and |Bz| < (Bx +By ) /2)
-20
1
2
2
-10
2
2
YaGSM [RE]
YaGSM [RE]
-10
0
4
0
2
3
10
3
10
2
3
20
20
2
2
2
30
30
2
20
10
0
-10
XaGSM [RE]
GEM Summer Workshop: 20-27 June 2009
-20
-30
20
10
0
-10
-20
-30
XaGSM [RE]
43
Within the magnetosheath
Spreiter et al., PSS 1966
Geotail CPI observations
4
3
-30
2
2.5
3
1
1.5
-20
nmsheath/nsw
(all conditions)
2
-10
YaGSM [RE]
2.5
2.5
1
0
1
10
1.5
1.5
20
1
2.5
2
0.5
30
1
20
10
0
-10
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June[R
2009
E]
-20
-30
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Within the magnetosheath
Geotail CPI observations
Paularena et al., JGR, 2001
4
3
-30
2
2.5
3
1
1.5
-20
nmsheath/nsw
(all conditions)
2
-10
YaGSM [RE]
2.5
2.5
1
0
1
10
1.5
1.5
20
1
2.5
2
0.5
30
1
20
10
0
-10
GEM Summer Workshop: 20-27XaGSM
June[R
2009
E]
-20
-30
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Within the magnetosheath
Spreiter et al., PSS 1966
Geotail CPI observations
0.9
-30
0.8
-20
Vmsheath/Vsw
(all conditions)
0.7
-10
YaGSM [RE]
0.6
0
0.6
10
0.7
20
0.8
0.7
30
20
0.8
10
0
-10
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June[R
2009
E]
-20
-30
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Within the magnetosheath
Cluster comparison:
Longmore et al., Ann. Geophys. (2005)
0.9
-30
-30
0.9
0.8
0.8
0.9
0.8
0.9
-20
0
0.8
Velocity Ratio
ZaGSM > 0
-10
YaGSM [RE]
Velocity Ratio
ZaGSM < 0
-10
YaGSM [RE]
-20
0.8
10
0
10
0.6
0.7
0.7
20
20
0.7
0.7
0.8
0.7
0.8
0.8
0.7
0.8
30
20
10
0
-10
XaGSM [RE]
30
-20
-30
20
10
0
-10
-20
-30
XaGSM [RE]
Authors conclude that higher
velocities are seen in the dusk
magnetosheath north of the
equator; higher in the dawn
south of the equator. Not
supported by Geotail
observations.
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Within the magnetosheath
Low solar wind Mach number; IMF along Parker spiral
-30
-30
5
4
5
5
4
4
-20
4
3
3
2
-20
2
1
1 2
4
Magnetosheath Alfvén
Mach number
1
1
Conditions:
Solar wind MA < 5
Northward IMF
Equatorial IMF direction within
20° of Parker spiral angle
1
YaGSM [RE]
1
0
Magnetosheath Alfvén
Mach number
2
-10
YaGSM [RE]
-10
5
2
3
3
1
3
Conditions:
Solar wind MA < 5
Southward IMF
Equatorial IMF direction within
20° of Parker spiral angle
0
1
1
10
10
20
2
2
3
3
1
2
3
3
3
1
3
2
30
20
1
20
2
30
10
0
-10
XaGSM [RE]
GEM Summer Workshop: 20-27 June 2009
-20
-30
20
2
3
3
10
0
-10
-20
-30
XaGSM [RE]
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Within the magnetosheath
High solar wind Mach number; IMF along Parker spiral
-30
-30
4
3
-20
4
4
-20
5
5
4
3
Magnetosheath Alfvén
Mach number
2
YaGSM [RE]
3
0
Conditions:
Solar wind MA > 5
Northward IMF
Equatorial IMF direction within
20° of Parker spiral angle
1
-10
YaGSM [RE]
-10
Magnetosheath Alfvén
Mach number
3
10
Conditions:
Solar wind MA > 5
Southward IMF
Equatorial IMF direction within
20° of Parker spiral angle
2
0
1
10
2
2
4
20
3
3
2
2
20
3
4
4
3
5
4
5
2
4
2
4
4
3
30
4
4
5
30
3
5
3
5
4
5
20
10
0
-10
XaGSM [RE]
GEM Summer Workshop: 20-27 June 2009
-20
-30
20
10
0
-10
-20
-30
XaGSM [RE]
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Summary
The magnetosheath contains many features. Some are fairly wellunderstood, while others are not. Observations are very important
for determining the weaknesses, and for constraining analytic and
MHD models. The difficulty with in situ observations is placing
them in spatial context with respect to the boundaries, and
accurately matching with the solar wind.
The most prevalent physical phenomena in the outer
magnetosheath include plasma compression, diversion, and heating,
beams, and plasma instabilities. The inner edge of the
magnetosheath is where the slow mode discontinuities and plasma
depletion layers occur. The interaction between the solar wind and
the magnetosphere (primarily via the reconnection process) also
occurs at the inner edge of the magnetosheath.
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