3d curvature determination for the bastille interplanetary ... · 3d curvature determination for...

3D curvature determination for the BastilleInterplanetary Shock:

Multi-Satellite Triangulation

T. Terasawa1, S. Kawada1, F. M. Ipavich2, C. W. Smith3, R. P. Lepping4, J. King4, A. J. Lazarus5, and K. I. Paularena5

1 U of Tokyo, 2 U of Maryland, 3 Bartol Res. Inst., U of Delaware, 4 GSFC/NASA, 5 MIT

Originally scheduled as a poster (abstract, page 20),then moved to the oral session 20 March, AM by LOC.

The shock normal direction…...important basic information describing the shock properties

Determination of the shock normal:conceptually simple, but not straightforward in reality

→ e.g., Russell et al.(2000) JGR 105, 25143-

For example,it is believed that the acceleration process ofelectrons emitting type II radio bursts dependscritically on the shock angle.

Determination of the shock normal direction

Trace image

flare/CME shock arrival

The Bastille day flare in 2000 …. IPS arrived on the next day(average speed … 1AU/28hours ~ 1500 km/s)

Lessons from the study of the Bastille IP shock … ACE, SOHO,WIND,GEOTAIL and IMP-8 were all in the upstream solar wind!

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satelliteconstellation

on 15 July 2000

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We are going to show the results of


on 15 July 2000

1. The conventional methods based on the single satelliteobservation (minimum variance, etc.)2. 4-satellite method for the plane surface model3. 5-satellite method for the spherical surface model4. 5-satellite method for the plane surface model withconstant dVshock/dt (time derivative of the shock speed)

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[nT]

the Bastielle interplanetary shock on 15 July 20003 of 5 satellites gave the magnetic field data

● magnetic minimum variance/Geotail: nG = (-0.82, +0.42,+0.39) phi~153o , theta~23o

● WIND best fit (Lepping et al., 2001, Solar Phys. 204, 287): nw = (-0.93, +0.26,+0.26) phi~164o , theta~15o

local determination of the shock normal direction

nw and nG agree(they make an angle ~ 13o

which is within a typical error range.)

The conventional methods give consistent answers:

W

G

phi (longitudinal angle)

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on 15 July 2000and

shock arrival times

SOHO and IMP8gave the plasma data.(IMP8 magnetometer was not working during this event, unfortunately.)

4 satellites determine shock parameters if the shock has a plane surface.

IPS

velocity ~ Vs (constant)

direction ~ n

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plane surface model

Russell et al., 1983; Horbury, Invited talk on the first day

shock normal direction (phi, theta)

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175170165160155150145

GTL MVM WIND

with planer shock assumption A-S-G-W A-S-8-W A-S-G-8 S-G-8-W A-G-8-W

theta_n

phi_n

4-satellite method for plane shocks

Best fit normals by conventional methods

plane surface model--- results

longitudinal angle

latitudinalangle

The result with the largestdeparture from theconventional methods doesnot depend on the IMP8timing uncertainly.

spherical surface modelformulation (1)

Rc(t) = Rc0 + Vs・t

(Xc,Yc,Zc)

S1

S2

S3

S4

S5

center

5-satellite method for spherical shocks

5-satellite method for spherical shocks



(Xc,Yc,Zc)

S1

S2

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S4

S5

center

Rc0 + Vs t1 = [ (X1-Xc)2 + (Y1-Yc)2 + (Z1-Zc)2]1/2

Rc0 + Vs t2 = [ (X2-Xc)2 + (Y2-Yc)2 + (Z2-Zc)2]1/2

Rc0 + Vs t3 = [ (X3-Xc)2 + (Y3-Yc)2 + (Z3-Zc)2]1/2

Rc0 + Vs t4 = [ (X4-Xc)2 + (Y4-Yc)2 + (Z4-Zc)2]1/2

Rc0 + Vs t5 = [ (X5-Xc)2 + (Y5-Yc)2 + (Z5-Zc)2]1/2

five unknowns (Rc0, Vs, Xc, Yc, Zc) and five equations

→ solvable (We need iterations to treat nonlinearity of Vs)

Let us take the S1 position as the origin of the new coordinate.Then we have,

Rc0 = [ Xc2 + Yc2 + Zc2]1/2 (1)Rc0 + Vs (t2 - t1) = [ (X2-Xc)2 + (Y2-Yc)2 + (Z2-Zc)2]1/2 (2)Rc0 + Vs (t3 - t1) = [ (X3-Xc)2 + (Y3-Yc)2 + (Z3-Zc)2]1/2 (3)Rc0 + Vs (t4 - t1) = [ (X4-Xc)2 + (Y4-Yc)2 + (Z4-Zc)2]1/2 (4)Rc0 + Vs (t5 - t1) = [ (X5-Xc)2 + (Y5-Yc)2 + (Z5-Zc)2]1/2 (5)

From (2)~(5), we have a set of nonlinear equations, X2Xc+Y2Yc+Z2Zc+Vs (t2 - t1) Rc0 = [ X2

2+Y22+Z2

2 - Vs2 (t2 - t1)2 ]/2 (2’) X3Xc+Y3Yc+Z3Zc+Vs (t3 - t1) Rc0 = [ X3

2+Y32+Z3


2+Y42+Z4


2+Y52+Z5

2 - Vs2 (t5 - t1)2 ]/2 (5’)

Note that if we fix Vs (2’)~(5’) are linear with respect to (Xc,Yc,Zc,Rc0).Our procedure is, therefore, (a) Solve (2’)~(5’) for a trial value of Vs, and obtain (Xc,Yc,Zc,Rc0). (b) Search Vs so that [Xc2 + Yc2 + Zc2]1/2 - Rc0 =0 is satisfied.


shock normal direction (phi, theta)

Best fit normals by conventional methods

longitudinal angle

latitudinalangle

plane surface model + spherical surface model70

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175170165160155150145

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with planer shock assumption A-S-G-W A-S-8-W A-S-G-8 S-G-8-W A-G-8-W

theta_n

phi_n

4-satellite method for plane shocks

5-satellite method(shock normal at the GEOTAIL position)

spherical surface modelshock normal direction

We have set the IMP8 timing correction at -20 secso as to make the shock normal direction consistent with thoseby the conventionalmethods.

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ock

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correction for IMP-8 timing (sec)

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Shock normal directiondepends on the choiceof the timing correctionsfor the IMP-8 data.

spherical surface model --- Rc and Vs

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Vs (projected tothe ecliptic plane)

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Curvature radiusof the shock surface

correction for IMP-8 timing (sec)

shock speed

If the shock surface is spherical …. 5 satellites needed



(Xc,Yc,Zc)

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However, we should also take into account of the casewhere the center is outside of 1AU and Vs<0,namely the shock has a concave shape shrinking in time.

Initially we expect that the center is inside of 1AU and Vs>0,namely the shock has a convex shape expanding in time.

spherical surfacemodel --- result

spherical surface model

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~1100 km/s(shock speed projected to the ecliptic plane)

solar wind

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Split plane shock model

splitting time correctionfor shock arrival times

at SOHO and GEOTAIL

An artificial model: split plane surface model

Choose the best splitting time:… agree with results from the conventional methods (WIND best fit,

Geotail MVM)

split plane surface model --- solution

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longitudinal angle ofthe shock normal vector

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concave convex

split plane shock model Geotail MVM WIND best fit

latitudinal angle ofthe shock normal vector

�

Splitting time correction (sec)

delay advance

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Split plane shock model

4-satellite methodSplit plane surface model

split plane surface model vs. spherical surface model

5-satellite methodspherical surface model

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These two results seem to be not inconsistent.

A : Leading edgeB : Core 1C : Core 2 A

B

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　 10:54 11:54

18 Jan 2000 CME SOHO/LASCO

Ahead of such a concaved-shape CME, the shock may also have a concave shape locally.

It may not be so crazy to think of a concaved-shape IPS:

Question to solar radio astronomers:Are there any peculiar type-II bursts relating toconcaved shocks?

5 satellites determine shock parameters if the shock hasa plane surface.

IPS

velocity ~ Vs = Vs0 + a・ t (a: constant)

direction ~ n

plane surface model with constant dVs/dt

S1

S2

S3

S4

S5

Physically unacceptable result:IPS was accelerated from

660 km/s (at ACE) to1330 km/s (at WIND)

Summary and comments・We have formulated a 5-satellite method in which the shockcurvature is derived from shock arrival times at these satellites.・The method is applied to obtain the curvature radius of the Bastilleinterplanetary shock in 2000.・This Bastille IPS seems to have had a concave shape locally when itarrived at the near-earth environment.

Application of the 5-satellite method: STEREO + 3 other spacecraft

possible Japan’s contribution to STEREO (in addition to the Solar-B collaboration)

around Earth … GEOTAIL(1992-?), SELENE (2005-)around Mars … NOZOMI (orbit insertion in Jan 2004)

3d curvature determination for the bastille interplanetary ... · 3d curvature determination for...

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