A theoretical study on the O+ ions of the Martian magnetosphere

CHINESE ASTRONOMY AND ASTROPHYSICS ChineseAstronomy

PERGAMON

and Astrophysics

A theoretical

23 (1999)

377-383

study on the O+ ions of the

Martian

magnetospheret

*

LIU Zhen-xingl SHI Jian-kuil T. L. Zhang2 ‘Center for Space Science and Applied Research, Beijing 100080 ‘Space

Research

Institute,

Austrian A-8010

A theoretical

Abstract along that

magnetic the

field.

magnetic

both

is made

2) that,

as 2 increases,

increase,

3) that

on the Ot

from

field consists

the

density

Martian

values of the intrinsic with increasing

both

the density

and flux decrease

the intrinsic

magnetic

areocentric

the magnetotail,

and flux are the smaller,

magnetic Martian

field.

Thus,

by observing

magnetosphere

distance,

the density

one may learn about

field. It is found

areocentric first,

distance, then

slowly

field, the fast the density

and flux fall with increasing the density

assuming

field and an induced

and flux decrease

the stronger

12,

and flux profiles

ionosphere,

of an intrinsic

are made for different

the density

Inffeddgasse

Gmz, Austria

field lines emanating

Martian

Calculations

1) that

study

of Sciences,

Academy

and 4) at a given distance the greater

in

the intrinsic

and flux distributions

the size of the intrinsic

in the

field of the

planet. Key

words:

Martian

magnetosphere-O+

ions -intrinsic

magnetic

field

1. INTRODUCTION The

Martian

Later,

magnetic

it was discovered

in the magnetotail is the smaller

field, that

plasma

is relatively

the greater

and magnetopause

there exists strong.

the pressure

were first

also a permanent The

magnetotail

discovered

bow-shock. is compressible

of the solar wind 12-‘l.

0275-1062/99/$

- see front matter

SO275-1062(99)00068-5

@

1999 Elsevier Science B.V.

All rights reserved.

field

and its thickness

In the region beyond

t Supported by National Natural Science Foundation (No. 49884002) Received 1998-01-16: revised version 1998-04-06 * A translation of Acta Astron.Sin. Vol. 40, No. 1, pp. 76-82, 1999

PII:

in 1965[‘1.

The magnetic

2.8Rm

378

SHI Jim-kui

(Rm=radius

of Mars), the Interplanetary

et al. / Chinese

Astronomy

and Astrophysics

23 (1999)

377-383

Magnetic Field (IMF) dominates151, but there is

still some evidence of a small intrinsic magnetic field of Mars. Analysis of the data obtained by spacecraft Phobos-2 shows that, in the Martian magnetotail,

there is a plasma sheet that is mainly formed by Ot

ions originating

Martian ionosphere16v71, as well as hydrogen ions and heavier ionsls~gl. According to the analysis of the data obtained by different spacecraft,

from the

the dipole mo-

ment of Mars ranges from about 2 x lOi T m3 to about 2x 101r T m31g-i11. What, then, is the correct value? So far, there is no answer. Because the data on the Martian magnetic field come from those regions that the spacecraft happen to pass by, the question of the structure of the magnetosphere, the intrinsic dipolar moment and dynamics await further observations combined with theoretical studiesliz]. There have been some theoretical papers on the position and formation of the Martian magnetopause, and some on the effect of temperature on the ion distributionl’31. In the present study, on the basis of the distribution function obtained by solving the dynamic equation, we study the O+ ion density and flux distributions along the field line for a set of assumed dipole moments. It is found that the ion distribution depends on the Martian intrinsic field. Hence we can hopefully deduce the Martian magnetic moment from the observation of the ion distribution.

2. PHYSICAL

MODEL

Because the atmosphere of the Mars is thinner than that of the Earth, we can easily imagine a base surface So on Mars with the following properties. Below So, the ions are in diffusive equilibrium. Above it, because collision can be ignored1 14v151the guiding center approximation is valid and we have: 1) the ion gyration radius and period are much smaller than the characteristic distance and time scale of field variation, 2) the conductivity along the field line is infinite, so the parallel electric field can be neglected, 3) gravity is much less than the magnetic force, and 4) the ion drift velocity is much less than the ion total velocity. Therefore, above So, the conditions in the geo-magnetosphere stated in Refs.[15,16] are satisfied, and Eq. (2) of Ref. [16] on the guiding center is valid. Consider a magnetic flux tube (‘Yield line” in this paper always refers to a tube axis). Suppose the guiding center of the ions at the base So take a cone distribution in the velocity space (Eq. (5) of Ref. [IS]). Th en we can write the ion distribution function f along the field line (the number of guiding centers per unit length of the tube and unit time interval) es

fb,u,,,u~)

=

Cexp( -

0,

+M(u$+ u”I> T

E,,

+

0 ),

(0 < e,,E

>

E,) (1)

@>~,E
where s is the coordinate along the field line, UJIand til are the velocity components parallel and perpendicular to the field line, M is the ion mass, and d is the gravitational potential. T = To + Eo, To and Eo being the ion temperature and energy at Se, B and Bm are the ion

SHI Jian-kui

et al. / Chinese

magnetic

and Astrophysics

23 (1999)

377-389

value, E and E,,, = Eo - 9 are the ion kinetic

pitch angle and its maximum threshold.

Astronomy

TO and EO are constants

and 8,

is determined

by the ion pitch

379

energy

and its

angle and the

field at So.

Let us assume that 8, is small. ion linear density at s can be written

Then, as

we have ul

< ~11and, along the field line, the

and the ion flux along the field line as J(s)

s,u,,,u+I

= jju,,f( u

In Eqs. (2) and (3), U is the region in the velocity phase space, 0 < B,, E > Em (shown shaded in Fig. 1). Considering the conservation of magnetic Aux, the normalized ion linear density at s (the ratio of the ion linear density at s to that at SO) can be written as

N(s)

where Bo = B(Q), flux as ntu:(s)

B n(s) = Fo n(q))

du/,dui. u/r

(4)

and the normalized

ion u.L

B J(s) = & J(sO)

3. FEATURES

9

OF ION

According to the observations, an induced field ~T[‘gl~l:

DISTRIBUTION

the Martian &

Fig. 1

(5)

m

magnetic

* D(cos8/r2)

Schematic diagram showing the region of integration

AND field consists

DISCUSSION of an intrinsic

field and

+ g;-

&>O

(O
&
CT <

6 < 27)

here, m is the Martian intrinsic moment, 6 is the co-latitude and r is the areocentric distance. The observational data suggest that BT is between 10 and 20nT; let BT = 15nT. From the observations on the density of the Martian atmosphere, we take the areoc.entric distance of So to be 1.1 Rm, so as to ensure that the plasma is thin enough for the ions to satisfy the guiding center approximation. Also, according to the observations, we take T = 2000 K,

380

Ee = 2.5eV

SHI Jian-kui

and 0,

et al. / Chinese

Astronomy

= 45’ in our calculation.

and Astrophysics

23 (1999)

If we take Eo several

377-383

times larger or Brn any

value between 15O-55O, the result will be nearly the same. We take a right-handed system XYZ, with X pointing to the Sun, and Z to the north magnetic pole. The ion density and flux distributions in the meridian plane are calculated and the results are as follows. 3.1 The Distribution

of O+ Ions along the Magnetic

Field Lines

The results of our calculation for Ot ions show that the Ot ion density and flux along the magnetic line decrease with increasing areocentric distance. The density distributions of Ot ions along field lines at different co-latitudes are shown in Fig.2 (the Martian magnetic moment is taken to be 9x 1011 Tm3 in the calculation). In Fig.2, from left to right the curves correspond to field lines at co-latitudes iO" , 20°, 30° and 40°, respectively. Fig. 2 shows that the density of O+ ions along the field line decreases with increasing areocentric distance at any co-latitude. At co-latitude 10’ the density decreases quickly in the region -X < 0.5Rm and more slowly in the region -X > 0.5 Rm. The region of fast decrease gets larger with 4.0 2.0 0.0 increasing co-latitude: from -X < 0.5Rm -XfRm at colatitude 10’) to -X < 2.0 Rm at colatitude 40’. Fig. 2 Ot ion density distribution along It can be seen from Fig. 2, that the higher different field lines the c&latitude, the lower the final level of normalized density.

“*+

0.01

The variation the density.

of the flux of O+ ions along the field line is similar

to the variation

of

Figs. 3(a) and (b) display, respectively, the normalized O+ ion density and flux as 2 varies on the meridian plane at X = -3.0 Rm. Again, we have taken the Martian magnetic moment to be 9 x 1O1i T m3 in the calculation. The curve in Fig. 3(a) shows that the normalized 0 + ion density first decreases with increasing 2, then, after a certain distance, it increases. The curve in Fig. 3(b) shows that the normalized O+ ion flux behaves in a similar manner. Physically, it is reasonable that the flux of Ot should decrease along a field line. The Ot ions in the Martian magnetosphere mainly come from the ionosphere rather than the solar wind. The transport of the ions from the ionospheric region to the magnetosphere is controlled by gravity. So, if the change of the velocity is small, we can say that the larger the areocentric distance, the fewer the ions and the smaller the ion flux will be. On the other hand, the field lines of different co-latitudes are differently configured, so the ion distributions along different field lines will be different.

SHI &an-E& et al. / Chinese

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and Astrophysics

23 (1999)

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0.20 -X=3Rm

-X=3Rm

;;; -g

0.15

ii

L

0.10

1.0

0.0

2.0

3.0

0.0

1.0

Fig. 3 The distribution

Results

of O+ ion density (a) and flux (b) along the Z-direction

for Different

of our calculation

field line will be different

3.0

Z/Rm

Z/Rm

3.2 Ion Distribution

2.0

Assumed

show that

Martian

the ion density

if we take different

Magnetic

Moments

and flux distributions

values of the Martian

magnetic

along

moment

the

in our

calculation. The O+ ion density

distributions

and 30 x 1011 T m3 are displayed Fig. 4 shows that, the density 40%

to

of its in

and,

about

1.00 I_

for m = 5 x 1O1l T m3,

value

, the density

9x101rTm3 quickly

10’ for m = 5,10,15

decreases slowly and, in the the density decreases to

magnetotail, about

along the field line at co-latitude

in Fig. 4.

20%

the

of

If m = at Se. decreases more

magnetotail,

its

m=5E21

value

at

m = 14x 1O’l T m3, it decreases quickly and, in the magnetotail,

m=9E21

falls Se.

If

z z

0.10 :

In = 1.4 E 22

even more by one or-

der of magnitude. If m = 28 x 1Ol1 T m3, it decreases more quickly still and decreases by two orders of magnitude totail. ment

Thus,

in the magne-

the size of the intrinsic

has a decided

influence

density profile. Results of our calculation that

the moment

mo-

I

0.01 0.0

1.0

on the ion also show

has an influence

on the

ion flux distribution along the field line. Figs. 5(a) and (b) show the variation of O+ ion density and flux as a function

2.0

I

I 30

40

- X/Rm Fig.4

The Ot density profile along the

field line for 4 different values of the intrinsic magnetic moment

of the intrinsic

moment

at the point X = -3Rm

382

SHI J&n-k&

et al. / Chinese

Astronomy

and Astropfiysics

23 (1999)

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on the field line of co-latitude 10’. It can be seen that both the density and the flux decrease (the latter more quickly) with increasing magnetic moment. As the moment increases from 5x 1021 to 30 x 1021 G cm3, the ion density decreases by more than one-half order of magnitude, and the flux, by more than one order of magnitude.

‘.OO 7

0.4

-X=3Rm

0

-X=3Rm

0.01

10

20

30

’

I

0

20

(b)

(a) Fig.5

40

m/lx 1021G*cm3

m/lx @G-cm3

The Ot density (a) and flux (b) at -X

= 3Rm and co-latitude 10’ as a

function of the intrinsic magnetic moment m

Since we have taken the Martian magnetosphere to consist of an intrinsic field and an inductive field, and the ions mainly move along the field line, so the motion of the ion is controlled by the field line and therefore by the intrinsic moment. With a stronger intrinsic field, the field lines will be more strongly curved towards the planet, more ions will be trapped in the near-Mars space, so resulting in smaller ion density and flux in the magnetotail. Thus, it is reasonable that the ion density and flux should decrease with increasing intrinsic moment. Knowing the ion distribution as a function of the intrinsic moment, we can hopefully learn something about the latter by observations of the former.

4. SUMMARY

In the present study, the O+ ion density and flux distributions in the Martian magnetosphere are investigated from the distribution function obtained by solving the dynamic equation. And the influence of the intrinsic moment on the density and flux distributions along the field line is also considered. The results are as follows. (1) The density and flux of O+ ions along the field lines decrease with increasing areocentric distance. In the magnetotail, the density and flux vary with the 2 coordinate.. (2) If the Martian intrinsic field is strong, the density and flux of the ions along the field line will decrease quickly with increasing distance and the normalized density and flux will

SHI Jian-kai

be low. If the Martian

et al. / Chinese Astronomy

intrinsic

slowly, and the normalized

and Astrophysics

field is weak, the density

density

23 (1999)

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and flux of the ions will decrease

and flux will be high.

(3) In the Martian magnetotail, the ion density and flux decrease with increasing intrinsic moment. This fact may be used to deduce the Martian magnetic moment from the observed ion distribution. Two final points should be made. 1. To deduce the moment from the ion distribution is possible only when the relevant observation is sufficiently accurate. This point will be further studied in another paper. 2. The present calculation is based on the configuration of the Martian magnetosphere model of Ref. [17] (Eq. (6)), w h ere the tilt of the induced field is neglected. If the solar wind is in a different direction, the configuration will be changed. The effect of the tilt on the ion distribution will be investigated in another paper. ACKNOWLEDGMENTS This work is supported dation of China grant under 49884002.

by the National

Nature

Science

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