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

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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CLUSTER observations of mirror mode events

2-3 s duration

~30 s duration

Lucek et al., 2001

The magnetic field variations are almost linearly polarized parallel to the main field direction

ISEE-1 observations of mirror mode events

Tátrallyay & Erdős, 2005

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 :

MM2

MM1

10 min case study

B/N anti-correlation

{Automatedtests

Solar wind

MM1

MM2

6 hour case study

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

Sign of Z Sign of Y

MM1 test over a fixed magnetosheath gridEpoch superposition normalised to the total number of magnetosheath crossings

MM2 test over a fixed magnetosheath gridEpoch superposition normalised to the total number of magnetosheath crossings

Sign of Z Sign of Y

MM2+plasma data existenceMM1+MM2

Sign of Y Sign of Y

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

... 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

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

Verigin’s model for the bow shock (cont’ed)

And ∆, Rs, Mas also come from non-linear equations ...

rBS : position of the bow shock

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

Total number of 5 minmagnetosheath crossings

Relative number mirrormode events

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.

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

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

Comparaison CLUSTER / ISEE : occurrence frequency 2

dawn dusk

Dawn/dusk asymmetry

Comparaison CLUSTER / ISEE : amplitude distribution

Dawn/dusk asymmetry

dawn dusk

Conclusion 1

Occurrence peak is duskward, close to the sheath

Conclusion 2

Amplitude peak is dawnward

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

Mirror modes

Non

Whereas mirror mode occurrence is not sensitive to Ms

Dependence on IMF orientation

Average Parker spiral

Dependence on IMF orientation

Average Parker spiral

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

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

Conclusion 3

Occurrence increases with solar wind Ma

Conclusion 4

Occurrence is favoured by IMF orientation perpendicular to the average Parker spiral

...

Comparaison CLUSTER / ISEE : amplitude distribution 1

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 !

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.)