ИКИ РАН, г. Москва, Россия

ИКИ РАН, г. Москва, РоссияИКИ РАН, г. Москва, Россия

О ВЛИЯНИИ ДАВЛЕНИЯ И НАТЯЖЕНИЯ СИЛОВЫХ ЛИНИЙ МАГНИТНОГО ПОЛЯ В МАГНИТОШИТЕ НА ПОЛОЖЕНИЕ И ФОРМУ ГЕОМАГНИТОПАУЗЫ

М.И. Веригин, Г.А. Котова, М.И. Веригин, Г.А. Котова, В.В. Безруких, А.П. РемизовВ.В. Безруких, А.П. Ремизов

Девятая конференция П 22 и ОФН 15«Физика плазмы в солнечной системе»

10 - 14 февраля 2014 г., ИКИ РАН

• 331 magnetopause crossings by Prognoz, Prognoz 2-6, 9 dated from 1972 to 1983 • 2625 magnetopause crossings by Interball 1 during 1995 and 1999

Data usedData used

-70 -60 -50 -40 -30 -20 -10 0 10 20

10

20

30

Xgipm , Re

Y2gipm+ Z2

gipm , Re

Prognoz Prognoz-2 Prognoz-3 Prognoz-4 Prognoz-5 Prognoz-6 Prognoz-9 Interball-1

, or

We use simple analytic model

)(2arctan)( 00 xrR

DDxy

2tan

2)( 2

02

2

0y

RDryx

with r0 – magnetopause subsolar distance, R0– nose curvature radius. This expression has finite asymptotic magnetotail diameter D and reasonably approximates distant Prognoz-9 magnetotail crossings.

Same shape was used 40 years ago by Howe & Binsack (JGR, 77, 3334-3344,1972) for modeling Explorer 33 & 35 magnetopause observations

GIPM magnetopause anisotropyGIPM magnetopause anisotropy

0

90

180

270

0 4 8 12 16 20

1.8 nP < V2 < 2.2 nP

0

90

180

270

0 4 8 12 16 20

0.8 nP < V2 < 1.2 nP

0

90

180

270

0 4 8 12 16 20

2.8 nP < V2 < 3.2 nP

0

90

180

270

0 4 8 12 16 20

3.7 nP < V2 < 4.3 nP

R yG IPM = 13 .8R zG IPM /R yG IP M = 0 .94

R yG IP M = 14 .06R zG IP M /R yG IPM = 0 .98

R yG IP M = 15.56R zG IP M /R yG IP M = 0 .96

R yG IPM = 17 .48R zG IPM /R yG IPM = 0 .95

• Magnetopause is compressed by about 5% in the direction perpendicular to the plane formed by Vsw and IMF vectors

• The compression may be a result of the tension of magnetosheath magnetic field lines draping the magnetopause

Verigin et al., Geom.& Aeron.,Verigin et al., Geom.& Aeron.,49, No.8, 1176-1181, 2009 49, No.8, 1176-1181, 2009

Relative role of magnetic field tension and pressure Relative role of magnetic field tension and pressure at the magnetopause noseat the magnetopause nose

General MHD equations

• Magnetic field pressure at the magnetopause is typically more important than the magnetosheath magnetic field line tension pressure

0)div( V

4),(

8),(

2 BBVV

Bp

0)div( B 0],rot[ BV

04

),(412

div22

BVBV

BpV

;

For VB upstream flow, along the post-shock stagnation line

0

4812

22

yBBBpV x

Magnetic pressure term Field line tension term

1

88

22 BB

where - subsolar magnetosheath thickness

RB

yBB x 1

44

2

whereR - magnetosheath field line curvature radius

12

Rpressuretension

because sw

bsbsmp RRR

Evidence of magnetic field pressure influence and Evidence of magnetic field pressure influence and simplified model of simplified model of bvbv dependence of the MP location dependence of the MP location

5 5 THEMISTHEMIS orbiters, Dusik et al., orbiters, Dusik et al., JGR, 2010JGR, 2010

An unusually low SW ram pressure (and, hence, low Ma) period in 2007–2008 with the peak at 1.4 nPa whereas 2 nPa is a typical value.

0 40 80 120 160

0

1

2

3

4

88

222 STSH BBVk

bv

a

a

bv

a

bv

SinkM

kMSin

kMSinVk

2

2

2

2

2

22

21441

STtSWSH BBB 4 ISEE 3 empiric relation

Crooker et al., JGR, A12, 1982

Simplified model :-reasonably described magnetopause nose cone angle dependence found by Dusik et al., 2010-additionally described the magnetopause crossings by geostationary GOES 10 & 12 orbiters under very high IMF and SW ram pressure

Tatrallyay et al., Ann. Geophys., 30, 1675, 2012Tatrallyay et al., Ann. Geophys., 30, 1675, 2012

Simplified model disadvantage - theoretically unjustified simple addition of magnetic and thermal pressure at the subsolar magnetopause.

More accurate total thermal & magnetic pressure More accurate total thermal & magnetic pressure evaluation at the stagnation pointevaluation at the stagnation point

0 0.4 0.8 1.2 1.6 2M s / M a

0.8

0.9

1

1.1

1.2

1.3

/ V

2

= kV 2 (1 + 16

( M sM asinbv)

4/3)

3-D MHD calculations by Stahara, Pl.Sp.Sci., 50, 421, 2002.

Proxy for total thermal & magnetic field pressure at the stagnation point,

as deduced from Stahara’ s 3-D MHD calculations, and implemented in our

magnetopause model presented at previous IKI conference of 2013.

Is this proxy reasonable enough for MHD flows with Ms 6 ???

Ms = 6

Solution of MHD flow after the curved shock Solution of MHD flow after the curved shock in Lagrangian variablesin Lagrangian variables

-0.2 0 0.2 0.4

-0 .6

-0 .4

-0 .2

0

0.2

0.4

0.6

0.8 M s = 5 M a = 4

bv = 30o

B

V

m

i

jnjm

nm

k

jijm

kk

i

jjk

i

ux

uBgB

ux

uBgB

ux

upg

tx

~

41

41~1

2

2

MHD equations in Lagrangian variables

tux

uxBg

tB

tB

k

i

j

m

mjki

i

21

,,,, 21 tuuxx ii ,,,, 21 tuu tuupp ,,, 21 ,,,, 21 tuuBB ii

- start point position at the BS - time of the bow shock crossing

2,1, u

3u21

11

gg - preshock plasma density

k

i

j

i

jk ux

uxg

- covariant components of the space metric tensor

- metric tensor contravariant components and determinant

gandg jk

AND - Rankine-Hugoniot relations at the BS

Final result – EXACT ANALYTIC SOLUTION for several first terms of xi , Vi , Bi , p, expansion over t

An example of MHD flow lines after the BS as calculated in Lagrangian variables. NOTE that the cavity in the flow (“magnetosphere”) is self-organized after the predefined curved shock.

Shugaev, Kalinchenko, XY Moscow MHD conf., V2, p.618, 2005

Comparison of stagnation pressure distributions Comparison of stagnation pressure distributions in ( Min ( Mss , M , Maa ) plane ) plane

, ,

Lagrangian equations analytic solution MHD proxy

2 3 4 5 6 7 8 9 10

Sonic M ach num ber

2

3

4

5

6

7

8

9

10

Alfv

enic

Mac

h nu

mbe

r

322

2

22

611 bv

a

s SinMMVk

2 3 4 5 6 7 8 9 10

Sonic M ach num ber

2

3

4

5

6

7

8

9

10

Alfv

enic

Mac

h nu

mbe

r

O-O-O-ps ! ! !


, ,

Lagrangian equations analytic solution MHD proxy

2 3 4 5 6 7 8 9 10

Sonic M ach num ber

2

3

4

5

6

7

8

9

10

Alfv

enic

Mac

h nu

mbe

r

32

2

22 61

a

bv

MSinVk

2 3 4 5 6 7 8 9 10

Sonic M ach num ber

2

3

4

5

6

7

8

9

10

Alfv

enic

Mac

h nu

mbe

r


, ,

MHD proxy

32

2

22 61

a

bv

MSinVk

2 3 4 5 6 7 8 9 10

Sonic M ach num ber

2

3

4

5

6

7

8

9

10

Alfv

enic

Mac

h nu

mbe

r

2 3 4 5 6 7 8 9 10

Sonic M ach num ber

2

3

4

5

6

7

8

9

10

Alfv

enic

Mac

h nu

mbe

r

MHD proxy

322

2

22

611 bv

a

s SinMMVk

Will be used onwards…

Total thermal & magnetic pressure at the stagnation pointTotal thermal & magnetic pressure at the stagnation pointand the magnetopause modeland the magnetopause model

rr00 = 10.81 = 10.81 RRee -1/6 -1/6 (a)(a)RR00 = 16.33 = 16.33 RRee -1/6-1/6

DD = 95.05 = 95.05 RRee -1/6-1/6

<<nn22>> = 1.347 = 1.347 RRee

rr00 = 10.89 = 10.89 RRee -3/16-3/16 (b) (b)RR00 = 16.55 = 16.55 RRee -3/16-3/16

DD = 97.13 = 97.13 RRee -3/16-3/16

<<nn22>> = 1.339 = 1.339 RRee

0 0.1 0.2 0.3 0.41 / M a

0.8

0.9

1

1.1

1.2

1.3

1.4

/ V

2

= kV2 (1 + ( 6 S in2 b v

M a2 )

2/3)

GEOMAGNETOPAUSE MODEL

)(2arctan)( 00 xrRD

Dxy

Correspondence to Prognoz’ observationsCorrespondence to Prognoz’ observations

-20 -10 0 10 20

10

20

30

0.6 nP

0.5 nP < V2 < 0.7 nP

-70 -60 -50 -40 -30 -20 -10 0 10 20

10

20

30

1.2 nP

1.1 nP < V 2 < 1.3 nP

-70 -60 -50 -40 -30 -20 -10 0 10 20

10

20

30

1.8 nP

1.7 nP < V 2 < 1.9 nP

-60 -50 -40 -30 -20 -10 0 10

10

20

30

3.0 nP

2.9 nP < rV2 < 3.1 nP

Power exponent correspondence to some other modelsPower exponent correspondence to some other models

-1 / 6.6 < -1 / 6 < -3 / 16 < -0.194Shue et al., 1998 Usual (a) Present model (b) Lin et al., 2010

• Построенная модель включает описание зависимости положения магнитопаузы от угла между направлениями солнечного ветра и межпланетного магнитного поля bv .

ВыводыВыводы

• С использованием данных о пересечениях магнитопаузы спутниками Прогноз, Прогноз 2-6, 9, Интербол и полного давления магнитного поля и плазмы в точке остановки, 2D положение этой границы может быть описано как: , , где

• Показано, что влияние натяжения силовых линий межпланетного магнитного поля у магнитопаузы в 2 / R меньше, чем влияние давления межпланетного магнитного поля (толщина магнитошита, R радиус кривизны магнитных силовых линий) .

)(2arctan)( 00 xrR

DDxy

rr00 = 10.89 = 10.89 RRee -3/16-3/16 RR00 = 16.55 = 16.55 RRee -3/16-3/16

DD = 97.13 = 97.13 RRee -3/16-3/16

• С использованием результатов 3D МГД моделирования обтекания магнитопаузы солнечным ветром (Stahara, 2002) и аналитического решения МГД уравнений в Лагранжевых переменных построено аналитическое выражение, описывающее полное давление набегающего потока плазмы в точке его остановки:

где

32

2

22 61

a

bv

MSinVk

)1(1

2

)1()1(

21

211

sM

k

Спасибо за внимание !

Спасибо за внимание !Девятая конференция П 22 и ОФН 15

«Физика плазмы в солнечной системе» 10 14 февраля 2014 г., ИКИ РАН

ИКИ РАН, г. Москва, Россия

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