1. 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

2. 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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4. CLUSTER observations of mirror mode events 2-3 s duration ~30 s duration Lucek et al., 2001

5. The magnetic field variations are almost linearly polarized parallel to the main field direction ISEE-1 observations of mirror mode events Tátrallyay & Erdős, 2005

6. Identification methods Mirror threshold test β  (T  /T // - 1) > 1 β  >1 [3] MVA test δB/B > 0.15 Angle(Max. Var., B) < 20° MM1MM2 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 :

7. MM2 MM1 10 min case study B/N anti-correlation { Automated tests

8. Solar wind MM1 MM2 6 hour case study

9. 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 OK in the range 0.02-0.06 Hz Alternative method Mean phase = 94° B/N anti-correlation

10. Sign of Z Sign of Y MM1 test over a fixed magnetosheath grid Epoch superposition normalised to the total number of magnetosheath crossings

11. MM2 test over a fixed magnetosheath grid Epoch superposition normalised to the total number of magnetosheath crossings Sign of ZSign of Y

12. MM2+plasma data existence MM1+MM2 Sign of Y

13. Solar Wind = black MM2 + (MM1-true) = red MM2 + (MM1-false) = blue Sign of Y Solar Wind = black MM2+(B/N anti-correlation true) = red MM2+(B/N anti-correlation false) = blue

14. ... 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

15. Verigin’s model for the bow shock Uses : - GIPM reference frame - Shue et al., 1998 magnetopause model (needs ρV 2, Bz) - upstream parameters : Ma, Ms, θ bv dawn/dusk assymmetry Verigin et al., 2001, 2003, 2006

16. Verigin’s model for the bow shock (cont’ed) And ∆, Rs, Mas also come from non-linear equations... r BS : position of the bow shock

17. 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=1

18. Total number of 5 min magnetosheath crossings Relative number mirror mode events

19. 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.

20. Statistical studies of mirror mode occurrence and characteristics Comparaison CLUSTER / ISEE MissionISEECLUSTER Time range10 y5 y Time resolution 4 s Fractional distance range 0-1 Zenith angle range 20°-100°20°-90° No coverage in the subsolar region close to the nose Uncertainty close to the bow shock remains

21. 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

22. Comparaison CLUSTER / ISEE : occurrence frequency 2 dawndusk Dawn/dusk asymmetry

23. Comparaison CLUSTER / ISEE : amplitude distribution Dawn/dusk asymmetry dawn dusk

24. Conclusion 1 Occurrence peak is duskward, close to the sheath Conclusion 2 Amplitude peak is dawnward

25. 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 Typemirrornon mirrorsolar wind Number of events6363574058523 alpha/proton density 0.04530.04480.0496 ram pressure (nPa) 2.332.121.84 Ma10.918.177.64 Ms8.688.498.65

26. Mirror modes Non Whereas mirror mode occurrence is not sensitive to Ms

27. Dependence on IMF orientation Average Parker spiral

28. Dependence on IMF orientation Average Parker spiral

29. 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

30. Ma=12.13 Ramp=2.44 Bz=-0.038 Ma=11.05 Ramp=1.94 Bz=-0.30 Ma=10.08 Ramp=2.33 Bz=-0.33 Ma=10.74 Ramp=2.42 Bz=0.06

31. Conclusion 3 Occurrence increases with solar wind Ma Conclusion 4 Occurrence is favoured by IMF orientation perpendicular to the average Parker spiral

32. ...

33. Comparaison CLUSTER / ISEE : amplitude distribution 1

35. 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 !

36. 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.)