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V. Génot, E. Budnik, C. Jacquey, J.A. Sauvaud, I. Dandouras, CESR, Toulouse, France
E. Lucek, Imperial College, London, UK
CDPP and ISSI 81 teams
Statistical study of mirror mode events in the Earth magnetosheath
Cluster Workshop, Finland, September 2006
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Goal
- Obtain the spatial distribution of mirror mode events- as a function of the normalized distance between the magnetopause and the bow shock, and angles- in relation with conditioning parameters of the solar wind- by testing different identification methods based on magnetic and/or plasma parameters- compare with previous studies using ISEE-1 data :
-Tátrallyay & Erdős, 2005- Verigin et al., 2006
Data : 5 years of CLUSTER observations
- 4sec FGM data (and preliminary tests with 0.2sec)- Onboard CIS/HIA moments- Held in a multi-instrument, CLUSTER specialised database : DD-CLUSTER
manunja.cesr.fr/DD_SEARCH
General outline
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Tools offered by CDPP
- A multi-mission database
- Analysis prototype with-Conditionnal search-Customized plots-Basic space physics tools-Uploading of your own files-Web service access to remote databases
CDPP at CESR
Visit cdpp.cesr.fr
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CLUSTER observations of mirror mode events
2-3 s duration
~30 s duration
Lucek et al., 2001
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The magnetic field variations are almost linearly polarized parallel to the main field direction
ISEE-1 observations of mirror mode events
Tátrallyay & Erdős, 2005
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Identification methods
Mirror threshold test
• β(T/T// - 1) > 1
• β>1 [3]
MVA test
• δB/B > 0.15
• Angle(Max. Var., B) < 20°
MM1 MM2
Identification of mirror mode events is a long standing problem because :- Slow modes and mirrors have both anti-correlated B and N signatures- Mirror mode and ion cyclotron mode both grow on temperature anisotropy
Different methods have been developed : transport ratio (Song et al. 1994, Denton et al. 1995, 1998), minimum variance analysis (should be used with caution as pure mirror modes are linearly polarized), 2- and 4- satellite methods (Chisham et al. 1999, Génot et al. 2001, Horbury et al. 2004), 90° degree B/Vz phase difference (Lin et al. 1998), ...
In our analysis we used 2 tests :
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MM2
MM1
10 min case study
B/N anti-correlation
{Automatedtests
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Solar wind
MM1
MM2
6 hour case study
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Lin’s Test
90° degree phase difference between B and the ‘out of coplanarity plane’ velocity component.
Only the mirror mode satisfies this relation.
Ref: Lin et al., JGR, 1998
... but bad coherence !
Anti-correlation OKin the range 0.02-0.06 Hz
Alternative method
Mean phase = 94°
B/N anti-correlation
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Sign of Z Sign of Y
MM1 test over a fixed magnetosheath gridEpoch superposition normalised to the total number of magnetosheath crossings
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MM2 test over a fixed magnetosheath gridEpoch superposition normalised to the total number of magnetosheath crossings
Sign of Z Sign of Y
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MM2+plasma data existenceMM1+MM2
Sign of Y Sign of Y
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Solar Wind = blackMM2 + (MM1-true) = redMM2 + (MM1-false) = blue
Sign of Y Sign of Y
Solar Wind = blackMM2+(B/N anti-correlation true) = redMM2+(B/N anti-correlation false) = blue
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... But these preliminary tests lacked a proper normalization.
Indeed, one needs to use real distance to the shock and magnetopause.
This was done with :- a model shock and magnetopause- a model shock and real magnetopause
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Verigin’s model for the bow shock
Uses :- GIPM reference frame- Shue et al., 1998 magnetopause model (needs ρV2, Bz)- upstream parameters : Ma, Ms, θbv
dawn/duskassymmetry
Verigin et al., 2001, 2003, 2006
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Verigin’s model for the bow shock (cont’ed)
And ∆, Rs, Mas also come from non-linear equations ...
rBS : position of the bow shock
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Fractional distance across the model magnetosheath
For a position r inside the magnetosheath, the fractional distance is between 0 (MP) and 1 (BS)
F=1
F=0
F=0
F=1
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Total number of 5 minmagnetosheath crossings
Relative number mirrormode events
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Magnetosheath crossing are not counted as mirror events
real
real_final
model
... but bow shock crossings may be counted in. Checking with B/N anti-correlation will cancel this uncertainty.
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Statistical studies of mirror mode occurrence and characteristics
ComparaisonCLUSTER / ISEE
Mission ISEE CLUSTER
Time range 10 y 5 y
Time resolution
4 s 4 s
Fractional distance range
0-1 0-1
Zenith angle range
20°-100° 20°-90°
No coverage in the subsolar regionclose to the nose
Uncertainty close to the bow shock remains
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Comparaison CLUSTER / ISEE : occurrence frequency 1
Good agreement :Larger occurrence in the inner region of the magnetosheath, close to the magnetopause at larger ZA and closer to the middle of the sheath in the subsolar region
statistical artefact
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Comparaison CLUSTER / ISEE : occurrence frequency 2
dawn dusk
Dawn/dusk asymmetry
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Comparaison CLUSTER / ISEE : amplitude distribution
Dawn/dusk asymmetry
dawn dusk
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Conclusion 1
Occurrence peak is duskward, close to the sheath
Conclusion 2
Amplitude peak is dawnward
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Relations with conditioning parameters
• Record a magnetosheath event (mirror mode or not)• Compute delay from CLUSTER to ACE in Solar Wind recursively• Record associated Solar Wind parameters :
- Ma, Ms, alpha/proton density, ram pressure- IMF orientation
Type mirror non mirror solar wind
Number of events 6363 57405 8523
alpha/proton density
0.0453 0.0448 0.0496
ram pressure (nPa)
2.33 2.12 1.84
Ma 10.91 8.17 7.64
Ms 8.68 8.49 8.65
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Mirror modes
Non
Whereas mirror mode occurrence is not sensitive to Ms
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Dependence on IMF orientation
Average Parker spiral
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Dependence on IMF orientation
Average Parker spiral
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This relative number is higher for IMF direction perpendicular to the average Parker spiral.
As both orientations are symmetric as far as the magnetosphere / magnetosheath configuration is concerned, it may be an indication that highly perturbed solar wind conditions are more favourable for mirror mode development.
Indeed these events correspond to cases where ...
Dependence on IMF orientation
mirror mode events----------------------------
non mirror mode events
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Ma=12.13Ramp=2.44Bz=-0.038
Ma=11.05Ramp=1.94Bz=-0.30
Ma=10.08Ramp=2.33Bz=-0.33
Ma=10.74Ramp=2.42Bz=0.06
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Conclusion 3
Occurrence increases with solar wind Ma
Conclusion 4
Occurrence is favoured by IMF orientation perpendicular to the average Parker spiral
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...
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Comparaison CLUSTER / ISEE : amplitude distribution 1
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Conclusions• MM1 : mirror events seem located in the middle magnetosheath whereas previous studies (eg Tátrallyay & Erdös 2005 with 10 years of ISEE magnetic only data) showed them closer to magnetopause. However in our work near magnetopause events detected with the MM1 test are ‘averaged’ with magnetosphere crossings because we use a fixed magnetopause.
• MM2 : events tend to be closer to magnetopause
• Both MM1 & MM2 detected events are closer to the nose of the magnetosheath.
• A significant number of MM2 magnetosheath flank events exhibit B/N anti-correlation but do not satisfy the mirror instability threshold. They may be quasi-perpendicular slow modes; or non-linear mirror modes which exist below the linear threshold (bi-stability).
• Lin’s method should be re-calibrated before any firm conclusion could be drawn.
• About the tool : the automated search proved to be very powerful to obtain ‘quick & dirty’ results from which more in-depth analysis can be conducted. Its versatility makes it the perfect engine for long term, multi-mission and multi-instrument study in space sciences. CDPP will offer it online !
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Todo (a lot)
• No predefined magnetopause : use of a dynamic model to get rid of the ‘averaging’ problem
• Correlation of events with IMF/Solar wind plasma using ACE data
• To which extent is the mirror criterion satisfied ? Does it stay close to marginal stability ?
• Implement transport ratio method; improve the use of Lin’s test
• Distributions of amplitude/duration as functions of β, magnetopause/bow shock distance, ...
• Variation of anisotropy during mirror events : is the anisotropy effectively consumed ?
• Test of δB/ δT theoretical relations : differences between the fluid and the Landau-fluid approachs (Passot et al.)
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