Wavelet analysis of magnetic field fluctuations in the

magnetosheaths of the outer planets

Ezequiel Echer Divisão de Geofísica Espacial, INPE

12201-970, São José dos Campos, SP

E-mail: eecher@dge.inpe.br

Abstract: Magnetic field fluctuations in the dayside magnetosheaths of the outer planets are

studied in this work with wavelet analysis. Pioneer-10 and 11, and Voyager-1 and 2, magnetic

field magnitude (Bo) data are used to study the low frequency oscillations in the

magnetosheaths of Jupiter, Saturn, Uranus and Neptune. It was found that these oscillations

are highly non-stationary, have different characteristics for each planet and occur

preferentially in the period range of ~ 5-20 min.

Keywords: wavelet transform; planetary magnetospheres; magnetosheath oscillations

1 Introduction

A planetary magnetosheath is the region between the bow shock and the

magnetopause/ionopause/planetary obstacle, which is filled by the shocked solar wind plasma

(compressed, heated, decelerated and deflected solar wind flow). The plasma flow lines diverge

around the planetary obstacle. At the internal boundary of this region, where the magnetosheath

plasma encounters the magnetopause, energy is transferred from the solar wind to the

magnetosphere [10,14].

Both the position and shape of the magnetopause and of the bow shock depend on the solar

wind and internal magnetosphere conditions. The magnetosphere shape, size and position of the

boundaries can be quite variable, especially for the outer planets [9,10,11]. At the outer planets,

a strong thermal anisotropy is expected from the bow shock until the subsolar magnetopause

[9,11]. In agreement with these conditions, the outer planet magnetosheaths are observed to be

dominated by mirror mode oscillations [6,9,10,11,17,18], although other wave modes, such as

ion cyclotron waves, can also be observed [4,6,16,17,18].

Mirror mode oscillations are pressure balance structures observed in planetary magnetosheaths.

They are observed as decreases in the magnetic field magnitude. The angular change across the

magnetic dip of the mirror mode structure is almost zero. Their quasi-periodical appearance in

the spacecraft frame is due to solar wind convection, since they are non-propagating

oscillations [16, 17, 18]. These structures are generated by ion instability temperature

anisotropy (higher temperature in the perpendicular to the magnetic field direction). They have

been noted first at Earth, and then in the Jupiter and Saturn magnetosheaths [16].

Ion-cyclotron waves arise from the resonant wave-particle interaction, where waves gain energy

from particles [19]. Charged particles are scattered by wave fields, and particle’s momentum

and energy change through this process.

Foreshock and magnetosheath waves at Uranus and Neptune were previously studied with

wavelet analysis [9]. It was found that the waves present in these regions are large-amplitude,

highly non-stationary, magnetic field oscillations, and with periods longer than the H+

cyclotron period. In this work, the wavelet analysis is used to study the non-stationary characteristic of magnetic field Bo fluctuations in the outer planet (Jupiter, Saturn, Uranus and

Neptune) magnetosheaths.

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2 Data and Methodology

2.1 Data

In this work, magnetometer data are used to study magnetosheath fluctuations. These data were

obtained from the Planetary Data Service (http://pds.jpl.nasa.gov) [8]. The periods selected for

the wavelet analysis were the inbound dayside magnetosheath crossings of the outer planets

from the following missions: Pioneer-10 (Jupiter), Pioneer-11 (Jupiter and Saturn), Voyager-1

(Jupiter and Saturn) and Voyager-2 (Jupiter, Saturn, Uranus and Neptune). The data resolution

available from these spacecraft was 0.2-0.8 s from Pioneer-10 and 11, and 1.92s from Voyager-

1 and 2. In order to have a more homogeneous dataset and to remove a few data gaps, all the

data were 3-sec averaged. The magnetometer experiments are described in the literature:

Pioneer-10 and Pioneer-11 [12], Voyager-1 and 2 [1].

2.2 Wavelet analysis

The Wavelet Transform (WT) is a very powerful tool to analyze non-stationary signals. It

permits the identification of main periodicities in a time series and time variation each

frequency [3, 5, 7, 15]. The WT of a discrete data series is defined as the convolution between

the time series with a scaled and translated version of the wavelet function chosen. By varying

the wavelet scale and translating in time, it is possible to construct a picture showing the

amplitude of any characteristics versus scale and how this amplitude varies with time. To

analyze quasi-sinusoidal periodicities, the Morlet wavelet transform is usually used, because it

can detect variations in the periodicities of geophysical signals in a continuous way along time

scales [15]. The Morlet Wavelet is a plane wave modulated by a Gaussian , 24

1 2

)0(

η

η

ηπψ

−−

= ee oiw ,

where ωo is dimensionless frequency and ηo is dimensionless time.

3 Results and Discussion

The Pioneer-11 spacecraft had its closest approach at Saturn on 1 September 1979. This

spacecraft discovered that Saturn had a dipolar field. The magnetopause was found at ~20

Saturn radii (RS) and several bow shock (BS) crossings were observed [13]. There was an

inbound BS crossing at 12:15 UT on 31 August 1979, an outbound BS crossing at 13:20 UT on

31 August 1979, a BS crossing at 18:15 UT on 31 August 1979, and a magnetopause crossing

at 21:55 UT on 31 August 1979. Two magnetosheath intervals are defined from that period:

12:20-13:10 UT/31 August 1979 (50 min) and another from 18:20-21:50 UT/31 August 1979

(3h 30 min). Thus the first magnetosheath is limited by two solar wind intervals while the

second magnetosheath interval terminates at the magnetopause.

Figure 1 shows mirror mode structures in the Saturnian magnetosheath [16,18]. Data are

magnetic field magnitude and angular components. The bow shock is crossed at ∼ 18:00 UT

and the magnetopause at ∼ 22:00 UT on 31 August 1979. It is noted that there are little or no

mirror mode oscillations for the first third of the magnetosheath crossing. Mirror modes start to

form at ∼ 19:00 UT and have their largest amplitudes close to the magnetopause. These

features of mirror mode amplitudes are typical of planetary magnetosheath mirror mode

structures [18].

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Figure 1: Mirror modes in the Saturnian magnetosheath

observed by Pioneer 11 on day 243, 1979. These structures

have the largest amplitudes close to the magnetopause [18].

Figure 2 shows the wavelet spectrum for Bo during the Pioneer-11 Saturn magnetosheath

crossing showed in Figure 1. The wavelet spectrum shows high-frequency variations in the first

half interval near the bow shock (BS), and lower frequencies near the magnetopause crossing.

For Bo, significant periods around 2-3 min and 3-10 min are seen in the wavelet spectrum

during the 2nd

half interval.

Figure 2: Wavelet spectrum of the magnetic field Bo

fluctuations in the Saturn’s magnetosheath (interval

from Figure 1)

However, the high-frequency oscillations in the first part of the spectrum are much weaker than

the large amplitude low frequency waves close to the magnetopause. In order to have a better

resolution of these high frequency waves, this magnetosheath interval was split in two sub-

intervals. Figure 3 shows the wavelet spectra for these sub-intervals. One can now better see

both the high frequency oscillations near the bow shock and the low frequency waves near the

magnetopause.

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Figure 3: Wavelet spectra of the magnetic field Bo

fluctuations in the Saturn’s magnetosheath (interval

from Figure 2 split in two)

Figure 4 shows the wavelet spectrum of Bo (Voyager-2 data) for the Uranus’ magnetosheath for

24 January 1986 [2]. The Bo wavelet spectrum shows intermittent ~30 s -2 min oscillations,

especially around the time of the large pulse in Bo (08:40 UT). A continuous signal is seen at

~3-10 m, during the first half interval, and another continuous signal is seen around 20 min.

Figure 4: Wavelet spectrum of the magnetic field Bo

fluctuations in the Uranus magnetosheath [2].

Table 1 presents a summary of the main periods found through the wavelet analysis for the

outer planet magnetosheath Bo fluctuations. Columns are: planet/spacecraft; interval of

magnetosheath crossings (Universal Time, UT); main periods found with wavelet analysis, in

hours (h), minutes (min) and seconds (s).

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Table 1 – Summary of the outer planet magnetosheath intervals studied in this work. Columns

show planet/spacecraft, interval of magnetosheath crossing and main periods found with

wavelet analysis. Periods are given in hours (h), minutes (min), and seconds (s).

Planet/spacecraft Interval (UT) Wavelet results

Jupiter/Pioneer-10 23:16 26 Nov 1973 - 19:50 27 Nov 1973 6s-3 min

6-25 min

~50 min

1-2 h

Jupiter/Pioneer-10 04:00 01 Dec 1973 - 13:00 01 Dec 1973 6-20 s

6-15 min

~50 min

Jupiter/Pioneer-11 04:00 26 Nov 1974 - 02:00 27 Nov 1974 2-6 min

10-40 min

1-2 h

Jupiter/Pioneer-11 08:30 27 Nov 1974 - 12:30 27 Nov 1974 5-20 min

> 1 h

Jupiter/Pioneer-11 14:00 28 Nov 1974 - 13:00 29 Nov 1974 3-10 min

15-30 min

1-2 h

2-3 h

Jupiter/Voyager-1 14:35 28 Feb 1979 - 19:53 28 Feb 1979 1-4 min

5-20 min

25 min

30-40 min

1-1.5 h

Jupiter/Voyager-1 12:28 01 Mar 1979 - 19:55 01 Mar 1979 2-10 min

6-12 min

25-40 min

30-60 min

Jupiter/Voyager-2 18:00 03 Jul 1979 - 23:00 04 Jul 1979 1-2 min

6-25 min

30 min

Saturn/Pioneer-11 12:20 31 Aug 1979 - 13:10 31 Aug 1979 15-45 s

50 s-2 min

Saturn/Pioneer-11 18:20 31 Aug 1979 - 21:50 31 Aug 1979 2-3 min

3-10 min

Saturn/Voyager-1 23:45 11 Nov 1980 - 01:30 12 Nov 1980 3 min

5-10 min

15-20 min

Saturn/Voyager-2 13:45 24 Aug 1981 - 17:00 24 Aug 1981 40 s-3 min

10-20 min

Saturn/Voyager-2 18:40 24 Aug 1981 - 20:10 24 Aug 1981 40s-1.5 min

10-20 min

Saturn/Voyager-2 00:40 25 Aug 1981 - 06:50 25 Aug 1981 2-3 min

5-12 min

20-25 min

Uranus/Voyager-2 08:00 24 Jan 1986 – 09:45 24 Jan 1986 1-2 min

5-10 min

20-25 min

Neptune/Voyager-2 14:40 24 Aug 1989 - 18:00 24 Aug 1989 3-5 min

5-10 min

10-20 min

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4 Conclusions

Wavelet analysis was applied to the Bo data of Pioneer-10 and 11, and Voyager-1 and 2

spacecraft during their inbound trajectory in the magnetosheaths of the four outer planets. The

aim was to identify the main frequencies and to study the non-stationary features of the

magnetosheath Bo fluctuations. The main results found are:

1 – Jupiter: there is a continuous signal at ~1-1.5 h; main periods occur at 5-10, 10-25 min;

sporadic high-frequencies are seen at periods < 1min.

2 – Saturn: there are 5-10 min oscillations at the 2nd

half intervals of the crossing (close to the

magnetopause); 1-2 min waves occur at the first half interval close to the BS. The

magnetosheath intervals without magnetopause crossings (Voyager-2 intervals 1 and 2) show a

different spectrum: the main continuous frequencies are observed at ~12-25 min, with sporadic

oscillations at 1-3min.

3 – Uranus: there is a highly pulsating field, with sporadic and high-frequency (1-2 min

variations); the main periods are seen at 5-10 min in the magnetosheath region closest to the

BS; fluctuations with longer periods are seen at 20-25min.

4 – Neptune: the main frequencies are seen at 5-10 and 10-20 min in the 2nd part of the

magnetosheath crossings, close to the magnetopause; high-frequency waves (3-5 min) are

observed close to the bow shock. Magnetic field structures become broader, lower in frequency

and larger in amplitude from the BS to the magnetopause.

In conclusion, the outer planet dayside magnetosheaths are dominated by non-stationary, large

amplitude, low-frequency, ~5-20 min magnetic field Bo oscillations.

Acknowledgements

The author would like to thank to the Brazilian FAPESP (2007/52533-1) and CNPq (PQ-

301233-2011-0) agencies for financial supports. The author would also like to acknowledge the

Planetary Data System of NASA's Office of Space Science for high-resolution magnetic field

data and to the C. Torrence and G. P. Compo for the wavelet routine

(http://atoc.colorado.edu/research/wavelets/).

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References

[1] Behannon, K .W., M. H. Acuna, L. F. Burlaga, R. P. Lepping, N. F. Ness, F. M. Neubauer,

Magnetic field experiments for Voyagers 1 and 2, Space Science Reviews, 21, 235-257,

1977.

[2] Echer, E., Foreshock and magnetosheath waves at Uranus and Neptune studied with

wavelet analysis, Advances in Space Research, 44, 1030-1037, 2009.

[3] Echer, E., Wavelet analysis of ULF waves in the Mercury’s magnetosphere, Revista

Brasileira de Geofísica, 28, 175-182, 2010.

[4] Fairfield, D. H, Magnetic fields of the magnetosheath, Reviews of Geophysics, 14, 117-134,

1976.

[5] Grinsted, A., J. C. Moore, S. Jevrejeva, Application of the cross wavelet transform and

wavelet coherence to geophysical time series, Nonlinear Processes in Geophysis, 11, 561-

566, 2004.

[6] Hasegawa, A., Drift mirror instability in the magnetosphere, Phyiscs of Fluids, 12, 2642-

2650, 1969.

[7] Kumar, P. and Foufoula-Georgiou, E., Wavelet Analysis for geophysical applications,

Reviews of Geophysics, 35, 385, 1997.

[8] McMahon, S. K., Overview of Planetary Data System, Planetary and Space Science, 44, 3-

12, 1996.

[9] Richardson, J. D., The magnetosheaths of the outer planets, Planetary and Space Science,

50, 503-517, 2002.

[10] Russell, C.T. The dynamics of planetary magnetosphere,Planetary and Space Science. 49,

1005–1030, 2001.

[11] Russell, C. T. , Outer planet magnetospheres: a tutorial, Advances in Space Research, 33,

2004-2020, 2004.

[12] Smith, E. J., C. P. Sonett, Extraterrestrial magnetic fields: achievements and opportunities,

IEEE Trans. on Geoscience Electronics, GE-4, 154-171, 1976.

[13] Smith, E. J., L. Davis Jr., D. E. Jones, P. J. Coleman Jr., D. S. Colburn, P. Dyal, C. P.

Sonett, Saturn’s magnetosphere and its interaction with the solar wind, Journal of

Geophysical Research, 85, 5655-5675, 1980.

[14] Spreiter, J. R. et al, Hydromagnetic flow around the magnetosphere, Planetary Space

Science, 14, 223-253, 1966.

[15] Torrence, C. and G. P. Compo, A practical guide to wavelet analysis, Bulletin of the

American Meteorological Society, 79, 61-78, 1998.

[16] Tsurutani, B. T., E. J. Smith, R. R. Anderson, K. W. Ogilvie, J. D. Scudder, D. N. Baker,

S. J. Bame, Lion roars and nonoscillatory drift mirror waves in the magnetosheath, Journal

of Geophysical Research, 87, 6060-6072, 1982.

[17] Tsurutani, B. T., G. S Lakhina, O. P. Verkhoglyadova, E. Echer, F. L. Guarnieri, Magnetic

Decreases (MDs) and mirror modes: two different plasma beta changing mechanisms,

Nonlinear Processes in Geophysics, 17, 5, 467-479, 2010.

[18] Tsurutani, B. T., G. S. Lakhina, O. P., Verkhoglyadova, E., Echer, F. L., Guarnieri, Y. C.

Narita, D. O. Constantinescu, Magnetosheath and heliosheath mirror mode structures,

interplanetary magnetic decreases, and linear magnetic decreases: Differences and

distinguishing features, Journal of Geophysical Research, 116, p. A02303, 2011.

[19] Tsurutani, B. T. and Lakhina, G. S., Some basic concepts of wave-particle interactions in

collisionless plasmas, Rev. Geophys., 35, 491-502, 1997.

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