- Email: [email protected]
Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars
Available online at www.sciencedirect.com
ScienceDirect Advances in Space Research xxx (2019) xxx–xxx www.elsevier.com/locate/asr
Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars A.M.S. Franco a,⇑, M. Fra¨nz b, E. Echer a, M.J.A. Bolzan c a
National Institute for Space Research (INPE), Sao Jose dos Campos, Brazil b Max Planck Institute for Solar System Research, Goettingen, Germany c Federal University of Jataı´, Jataı´, Brazil
Received 19 February 2019; received in revised form 27 August 2019; accepted 5 September 2019
Abstract Wavelet analysis was employed to identify the major frequencies present in the plasma oscillations in the Martian magnetosheath. We have selected magnetosheath crossings and applied the Morlet wavelet transform to the electron density and temperature data, obtained from the Analyzer of Space Plasmas and Energetic Atoms experiment (ASPERA-3), onboard the Mars Express (MEX). In a study of 9667 magnetosheath crossings observed from 2005 to 2016, we have found 22,912 frequencies with high wave power between 5 and 60 mHz for the electron density data, For about 2/3 of the high wave power periods (63.3%), the most energetic frequencies were identified in the range 5–20 mHz. The analysis of the electron temperature data led to similar results, with 61.9% of the highest power frequencies in the 5–20 mHz range. No significant influence of the solar cycle on the frequencies of ULF waves has been observed in our analysis. The frequencies obtained here are near the Oþ gyrofrequency. The main fact that controls the ion gyroradius is the interplanetary magnetic field that is compressed around the planet. Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Induced magnetosphere of Mars; ULF waves; Wavelet transform
1. Introduction Near the Mars orbit, according to the Parker spiral model, the interplanetary magnetic field (IMF) should lie at an angle of 56° from the Mars-Sun line (Luhmann et al., 2018, 2004; Luhmann, 1995). Since the solar wind is perturbed by the passage of interplanetary shock waves, the planet can be reached by ion and energetic electron flows, which are associated with these shock waves or to solar flares. With the absence of an intrinsic magnetic field, the interaction between the solar wind and the Mars environment occurs directly with the upper ⇑ Corresponding author at: National Institute for Space Research, Av. dos Astronautas, 1.758 - Jardim da Granja, Sa˜o Jose´ dos Campos, 12227010, Brazil (A.M.S. Franco). E-mail address: [email protected] (A.M.S. Franco).
atmosphere and ionosphere of the planet. Thus, its magnetosphere is an induced one (Cloutier and Daniell, 1973; Cloutier and Daniell, 1979; Kivelson and Bagenal, 2007; Echer, 2010). Low frequency (LF) waves were observed for the first time in the plasma environment of Mars through measurements of the plasma wave system experiment (PSW) operated by the Phobos-2 spacecraft (Sagdeey and Zakharov, 1989). Plasma waves that are generated at the boundary layers, such as Alfven, fast mode and electromagnetic ion cyclotron waves, can be considered the most important for carrying energy over extended distances (Ergun et al., 2006). Russell et al. (1990) studied waves with frequencies below 0.5 Hz at the upstream region of Mars using Phobos spacecraft measurements. Waves at the proton gyrofrequency are observed in that region, and these waves were
https://doi.org/10.1016/j.asr.2019.09.009 0273-1177/Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
2
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
observed independently of whether the IMF formed a connection to the bow shock. The source of these waves can be ionized hydrogen from the exosphere via ionization by solar wind electrons, photoionization or charge exchange. Fowler et al. (2017) studied the wave power in the electric and magnetic field at Mars space environment for several frequency ranges (Ultra Low Frequencies (ULF): 0.01– 0.05 Hz; LF: 1–5 Hz; medium frequencies: 5 Hz and high frequency: 1–5 kHz) using data from Mars Atmosphere and Volatile Evolution (MAVEN) mission. Those authors have shown that high wave power is observed in the ULF range. The Martian magnetosheath is filled by compressional magnetohydrodynamic (MHD) waves. The interaction between the solar wind and heavy ions of the planetary plasma results in the generation of strong MHD bi-ion waves (Dubinin et al., 1997). These waves are related to the exchange of periodic momentum between the proton flux and heavy ions. They can be intensified and produce multiple shocklets (Dubinin et al., 1998; Nagy et al., 2004). Sauer et al. (1998) observed an oscillation characteristic of the dynamical exchange between the proton and heavy ions in the magnetosheath of Mars. It was also observed that non-linear MHD bi-ion waves can evolve to several shocklets. Espley et al. (2004) studied low frequency waves in the plasma regions of the induced magnetosphere of Mars (magnetosheath, magnetic Pile-up Region (MPR) and magnetotail). Through observations of the Magnetometer/Electron Reflectometer (MAG/ER) instrument onboard of the Mars Global Surveyor (MGS), compressional and elliptically polarized waves were observed at the dayside of the magnetosheath. The wave vector presented an angle higher than 60° in relation to the mean magnetic field. Such oscillations presented dominant frequencies significantly lower than the proton gyrofrequency in the magnetosheath. In the nightside magnetosheath the oscillations are more variable and sometimes present circular polarization, but in general they are transversal. The magnetic perturbations are left-hand elliptically polarized, they are also observed in some regions in the dayside of the magnetosphere (Espley et al., 2004). The waves propagate at smaller angle (less than 30°) relative to the mean magnetic field. Those oscillations present variable frequencies. The main frequencies observed are with a factor of 2 (0.2–0.004 Hz) less than the local proton gyrofrequency, but frequencies that exceed the proton gyrofrequency can also be observed. Ruhunusiri et al. (2015), using data from the ion analyzer and from the magnetometer instruments of MAVEN mission characterized low frequency waves in the Mars magnetosphere through the analyses of the transport ratios. They observed that Alfven and fast modes are more common than the mirror modes in the magnetosheath. They also observed that slow modes were less frequent than the others. Winningham et al. (2006) also studied low frequency waves in different regions of the Martian magnetosphere, such as: the magnetosheath, magnetotail and
magnetic cusps. The analysis was done using electron oscillation data obtained from observations of the electron spectrometer of the ASPERA-3 instrument onboard ESA Mars Express spacecraft (MEX). In the magnetosheath, oscillations in the electron flux present a frequency peak between 0.01 and 0.02 Hz, which corresponds to the oxygen gyrofrequency in that region. Their results also suggest that the bow shock may be the source of those oscillations, although it was observed that the magnetosheath and the magnetosphere night side region also respond to those oscillations. Lundin et al. (2011) observed that the average magnitude of magnetosheath waves is up to ten times higher than the wave magnitude observed in the density of Oþ ions and expected that ULF wave power is correlated with the Oþ outflow. These observations showed a first indication of the relation between the ULF wave power and atmospheric loss on Mars. Frequencies between 2 and 3 mHz have been observed as fundamental to oscillations in density and velocity time series (Gunell et al., 2008), and they are observed in regions where there is a velocity shear in the plasma flow. Fowler et al. (2017) have studied wave power in the electric and magnetic field data in various frequency bands. Their results show that high wave power was observed in the range of ULF, mainly in the region of the magnetosheath. They also have observed that energetic waves with high Poynting fluxes (2–16 Hz) between ~1011 and 108 mW2 reach the upper ionosphere. From that study it can be concluded that part of the power of waves observed in the magnetosheath can propagate down to regions below the Martian ionopause. The study of wave propagation is very relevant due to the fact that they have an important role in the energy and momentum transfer between the solar wind and the Mars magnetosphere (Ergun et al., 2006). Consequently, these waves are related to the processes of atmospheric loss at Mars via interaction with the solar wind. Knowing the importance to study fluctuations in Mars magnetosheath, the aim of this work is to determine the main frequency of plasma oscillations in the Mars magnetosheath. 2. Data In order to develop this work, plasma data obtained through the electron spectrometer (ELS) of the Analyzer of Space Plasma and Energetic Atoms (ASPERA-3) instrument onboard MEX spacecraft have been used. MEX was launched by the European Space Agency (ESA) in the beginning of July 2003 and it has arrived at Mars in December of the same year. It is still operating in orbit around the planet as of August 2019. The MEX orbit has an elliptical trajectory around Mars, with an inclination of 86.35° and a period of about 6.75 h. This eccentric elliptical orbit has an altitude of about 250 km at the periapsis and 10142 km at the apoapsis (Chicarro et al.,
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
3
2004). The main objective of the MEX mission is to study the interaction between the solar wind and Mars, its atmosphere, surface and subsurface. The MEX spacecraft operates with 7 instruments, which provide information on the atmosphere, ionosphere, surface and interior (Chicarro et al., 2004). One of these instruments is the ASPERA-3, which was used in our study. The goals of the ASPERA-3 instrument are to investigate the interaction of the solar wind with the Mars atmosphere, as well as to characterize the plasma environment and neutral gas of the planet using measurements of the ions, electrons and energetic neutral atoms. The main objective is to study the impact of the solar wind-Mars interaction on the atmosphere/ionosphere and the evolution of the Martian atmosphere (Barabash et al., 2006). ASPERA-3 is composed of four sensors, two Energetic Neutral Atoms (ENA) sensors, an Ion Mass Analyser (IMA) and an electron spectrometer (ELS) (Barabash et al., 2004). The ELS is a sensor that provides electron measurements in a 2D plane with a resolution of 4 s in an energy range between 0.01 and 20 keV. The sensor consists of a collimator system followed by a high standard top-hat electrostatic analyzer in a compact spherical design (Barabash et al., 2004, 2006). Since the ion spectrometer has a time resolution of only 192 s we use these data only to support the identification of plasma boundaries.
3. Methodology 3.1. Boundary identification In order to develop the study of the ULF waves in the magnetosheath of Mars, it is necessary to know the location of the major plasma boundaries (bow shock, pile-up boundary [MPB], PhotoElectron Boundary [PEB]) of the magnetic environment of the planet. The major Martian plasma boundaries for the years between 2005 and 2013 have been identified by Han et al. (2014) using MEX data. In order to apply the study for the whole interval of the MEX mission (2004–2016), the boundaries of the years 2014, 2015 and 2016 had to be identified by Franco (2018). For 2004 we do not have a significant number of intervals with data for this analysis, so the data from this year were disregarded in this study. The MEX boundary catalog can be obtained from the MPI for Solar System Research. Here we briefly explain the method used to identify the boundaries in these previous studies. First, a list of data intervals where the MEX is at a maximum of 4 RM (Mars Radius) of distance of the planet for the interval of 7 h (approximately the duration of the MEX orbit) has been compiled using the CCATI software (Fraenz et al., 2016). After that, plots with the electron and ion spectra for each interval have been made. The identification of the boundaries in the plot is made manually following the same criteria defined by Martineczs et al. (2008).
Fig. 1. Example of the identification of plasma boundaries on Mars for the interval between 12:30 UT and 16:00 UT on January 09, 2015. The upper panel shows the electron spectrum and the bottom panel, the ion spectrum.
https://www.mps.mpg.de/planetary-science/marsexpress-aspera-3 (2019) Fig. 1 shows an example of the identification of the plasma boundaries of Mars following these criteria. The bow shock can be identified by a sudden increase in the temperature of the electrons and ions due the heating of the plasma at the bow shock of the planet. The MPB inbound crossings are characterized by a decrease in the magnetosheath (energetic) electron density and increase of planetary ions flux. In the ion spectrum, low energy ions are observed in the magnetic pile-up region (MPR), which helps to identify the boundaries of the region (MPB and PEB). The PEB is also identified where the flux of the energetic electrons and ions are very low and photo-electrons with energies 20–30 eV are observed. This boundary should be very close to the ionopause. The boundaries are selected visually by clicks on the screen in the region where the criteria are met. Selecting these boundaries, a file with the index of the boundary and the time where the MEX has crossed is generated. In the study of the ULF waves in the magnetosheath, we are interested in the intervals that correspond to that
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
4
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
region. Between 2014 and 2016 a total of 1766 magnetosheath crossings have been identified and added to the MEX list of magnetosheath crossings available, resulting in a total of 9667 magnetosheath crossings from 2005 to 2016. 3.2. Wavelet analysis The wavelet functions are used to analyze nonstationary signals (Morettin, 1992). Different from Fourier transform, which approaches a function by a linear combination of sinusoidal components (each corresponding to a different frequency), the wavelet functions wðtÞ, are generated from a simple generating function, which suffer expansions/contractions and translations in time. Those functions consist in a set of small waves, with a compact support, localized in time domains (space) and frequency (Bolzan, 2004). The wavelet functions are generated by expansion, wðtÞ ! wð2tÞ, and translations, wðtÞ ! wðt þ 1Þ, from a simple generating function, the wavelet-mother given by following equation: 1 tb p ffiffi ffi wa;b ðtÞ ¼ w ; ð1Þ a a where a is the scale (a > 0) and b is the position. In this work we used the Morlet wavelet given by (Torrence and Compo, 1998): t2
wðtÞ ¼ ein0 t e 2 ;
ð2Þ
where n0 is a constant angular frequency. The Wavelet Transform (WT) applied on a time series f(t) is defined as:
Z WT ða; bÞ ¼
f ðxÞwa;b ðtÞdt;
ð3Þ
where f(x) is a time series, wa:b ðtÞ is the wavelet function and wa;b ðtÞ represents the complex conjugate thereof. We used the Global Wavelet Spectrum (GWS) in order to identify the major periods (most energetic) in each magnetosheath crossing. The GWS is given by: Z 2 GWS ¼ jWT ða; bÞj db; ð4Þ
4. Results In order to determine the frequencies with most power in the low frequency window for plasma oscillations in the Mars magnetosheath, the WT was applied to 9667 magnetosheath crossings observed from 2005 to 2016 for electron density and electron temperature data. The data used in this analysis have a time resolution of 4 s and the Morlet wavelet a wave number (n0 ) of six, since its shape gives good-time localization. 4.1. Periodicities in electron density data Fig. 2 shows an example of the WT results applied to the electron density for the interval wherein the MEX crossed the Mars magnetosheath, between 02:45 UT and 03:06 UT on February 06, 2012. Fig. 2(a) shows the electron density time series. The wavelet spectrum power is shown in Fig. 2 (b), and in Fig. 2(c) the GWS, where we note the presence of three most energetic frequencies: 44 mHz, 11 mHz and 6.4 mHz. The GWS provides the power integrated in time
Amplitude² Fig. 2. Panel (a) N e data. Panel (b) Wavelet spectrum. (c) Global Wavelet Spectrum.
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
5
Fig. 3. MEX orbit (red) on 6 February 2012 in cylindrical coordinates. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
along a specific frequency. The frequency peaks identified in GWS correspond to the most energetic frequencies in the ULF range for each magnetosheath interval. Fig. 3 shows the MEX orbit (red) on 06 February 2012. The region marked in blue represents the region where the spacecraft crossed the magnetosheath and the wavelet transform was applied on the data (Fig. 2). This is an outbound orbit, and it is possible to observe in Fig. 2 that wave power intensifies strongly as the spacecraft approaches the bow shock. In Fig. 3 the orbit is shown using Mars Solar Orbital (MSO) coordinates system. The Mars-Sun line is defined as the +x direction and the origin is centered on Mars, y points opposite to Mars’ motion, and z completes the right-handed set pointing upward from the plane of the ecliptic into the northern hemisphere. The Y-axis in Fig. 3 represents the cylindrical radial distance pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q ¼ Y MSO 2 þ Z MSO 2 . The aim of this study is to find the most energetic frequencies of plasma oscillations in Mars magnetosheath. Then, the main frequencies are identified by the higher power peaks observed in the GWS. After applying the WT to the electron density during the 9667 magnetosheath crossings, 22,912 peaks of frequencies were identified in electron density data, which results in an average of 2.4 frequencies per interval. These were divided into ranges (from 5 to 60 mHz) to perform a statistical analysis. Frequencies lower than 5 mHz were disregarded, since they may be influenced by changes in the spacecraft potential (Espley et al., 2004; Lundin et al., 2011). Furthermore, considering that the spacecraft moves with a velocity of about 5 km/s, for frequencies lower than 5 mHz, 1000 km have been covered. Then, if three oscillations can be considered to characterize a wave, a total of 3000 km will be traveled,
Table 1 Number of peaks in the global wavelet spectrum presented in each range of frequencies for the electron density data. Frequencies (mHz)
number
Percentage (%)
5 < f 10 10 < f 20 20 < f 30 30 < f 40 40 < f 50 50 < f 60 Total
7704 6797 3342 2425 2630 14 22,912
33.6 29.7 14.6 10.6 11.5 0.1
which is much larger than the Martian magnetosheath, so that the spacecraft has crossed many plasma regimes for this distance (Lundin et al., 2011). Table 1 presents the ranges of frequencies used in this analysis, the number of peak frequencies identified in each range, and the corresponding percentage relative to the total number of frequencies identified between 5 and 60 mHz. Fig. 4 shows the histogram that was made from the results shown in Table 1. We can notice that the main frequencies observed in the electron density were in the range 5–10 mHz with 33.6%. Further, the second peak was observed in the range 10–20 mHz with 29.7% of the 22,912 frequencies identified. Considering those two ranges, we have found that 63.3% (about 2/3) of the frequencies occur in the interval of 5–20 mHz. 4.2. Periodicities in electron temperature data The same study that was made for the electron density was done for the electron temperature. Fig. 5 shows the
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
6
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
Fig. 4. Histogram of the percentage of the main frequencies in electron density in the magnetosheath of Mars.
Amplitude² Fig. 5. Panel (a) T e data. Panel (b) Wavelet spectrum. (c) Global Wavelet Spectrum.
WT results applied to the electron temperature for the same interval wherein the MEX crossed the Mars magnetosheath presented in Fig. 2. In Fig. 5(c) we note the presence of five main frequencies: 43 mHz, 25 mHz, 15 mHz, 9 mHz and 6.2 mHz. Applying the WT, 23,395 frequencies were identified in the electron temperature time series, an average of 2.4 frequencies per interval. Table 2 shows the total number of peaks in the global wavelet spectra in each range of frequencies. Table 2 and Fig. 6 present the range of main frequencies found. We observe that most of the peak frequencies are also located between 5 and 10 mHz with 32.8% of the cases. Considering two ranges (5–10 mHz and 10–20 mHz) as it was done for the frequencies of the electron density study, 61.9% of the principal frequencies are observed between 5 and 20 mHz, which is very similar to what we obtained for the electron density.
Table 2 Number of peaks in the global wavelet spectrum presented in each range of frequencies for the electron temperature data. Frequencies (mHz)
Number
Percentage (%)
5 < f 10 10 < f 20 20 < f 30 30 < f 40 40 < f 50 50 < f 60 Total
7676 6812 3238 2789 2877 3 23,395
32.8 29.1 13.8 11.9 12.3 <0.1
4.3. Solar cycle dependence investigation In the study of the Mars plasma environment, the phases of solar cycle have been found to influence the ion escape ratio (Modolo et al., 2005; Lundin et al, 2013,
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
7
Fig. 6. Histogram of the percentage of the main frequencies in electron temperature in the magnetosheath of Mars.
Fig. 7. Histograms with electron density (a) and electron temperature (b) ULF wave percentage in the range 5–20 mHz for each solar cycle phase (2005– 2016).
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
8
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
Dong et al., 2015), density and temperatures of the ionosphere (Sa´nches-Cano et al., 2016) and consequently the formation of the induced magnetospheric cavity. Since the ionospheric plasma pressure is higher during the solar maximum (high activity) phases of the solar cycle also the higher ionospheric pressure can withstand against the then higher solar wind flux (Sa´nches-Cano et al., 2017). A study looking for variation of those frequencies with the solar cycle has been developed here, where the main frequencies were divided into subintervals according to the solar cycle phases. In Fig. 7 histograms of the percentage of periods with higher wave power from electron density (a) and electron temperature (b) data in the range 5– 20 mHz for each solar cycle phase (2005–2016) are shown. In electron density data, in Fig. 7(a), the declining phases (this includes 2005, 2006, 2007 (cycle 23) and 2015, 2016 (Cycle 24)) have 61.7% of the peak frequencies in the global wavelet spectra in the interval 5–20 mHz. The minimum phase (2008 and 2009) has 65.5% of the peak frequencies in that range of frequencies. During the ascending phase the percentage is 64.8% (2010 and 2011) and while in the maximum (2012, 2013 and 2014) it is 63.4%. For electron temperature (Fig. 7(a)) a similar result has been found. During declining phases 60.6% of the frequencies identified are in the interval of 5–20 mHz. During the minimum phase 63.8% are in that range of frequencies. In the ascending and maximum phases 63.9% and 61.5% are in that range, respectively. After this analysis it is possible to conclude that there is no significant influence of solar cycle on the frequencies of ULF waves in the magnetosheath of Mars. 5. Discussion The results that were found in Sections 4.1 and 4.2 agree with the findings by Winningham et al. (2006), where they used the integrated electron energy flux to study the electron oscillations in the induced magnetosphere of Mars. Those authors also observed an energetic peak between 10 and 20 mHz in the magnetosheath. They have interpreted it as corresponding to the oxygen ion gyrofrequency in the Mars magnetosheath, calculated using data from the magnetometer from Mars Global Surveyor (Espley et al., 2004). It is important to mention that the energetic peaks found in this study do not correspond to single pulses because the algorithm used in this work excludes periods of high wave power caused by single pulses (for more details see Torrence and Compo, 1998). It is believed that for large scales (greater than the Debye Length kD ), the plasma should be electrically neutral, and the electron density approximately equal to the ion density (Ne ffi Ni). When ion wave modes of large scale develop, they carry with them the electrons which are associated with the oscillating ions. Then, the electrons assume their wavelike behavior. Electrons oscillate at higher frequency, but they also respond to lower frequencies to maintain quasi-equilibrium with positive ions. Therefore,
when we observe in the ULF domain, the electrons trace the movement of the ions and the wave modes thereof (Winningham et al., 2006). Lundin et al. (2011) also found out similar results where the most energetic frequencies are between 3 and 20 mHz of ULF waves at the magnetosheath. In the analysis of solar cycle variation, no significant influence was observed. 6. Summary and conclusion In this work, the main frequencies in plasma oscillation in Mars magnetosheath using electron density and temperature have been identified. The analysis was conducted for 11 years of the MEX mission (2005–2016). The dependence of the solar cycle in these frequencies was also analyzed. The following results were obtained in this paper: The Martian plasma boundaries catalog was updated, and plasma boundaries from 2014 to 2016 are now available for new researches. The main frequencies of plasma waves in the magnetosheath of Mars were identified for electron density and temperature from ELS/ASPERA-3/MEX data. The majority of peaks in the global wavelet spectrum of the electron density and temperature are in the range between 5 and 20 mHz. In the electron density spectra, 63.6% of a total of 22,912 energetic frequencies are in a range between 5 and 20 mHz and for electron temperature spectra 61.9% of those 23,395 frequencies identified were in that frequency range. Those frequencies are near the local oxygen gyrofrequency in the Mars magnetosheath. No clear influence of the solar cycle on the frequencies of ULF waves in the Mars magnetosheath was observed here. This study has been developed using plasma data observed by the MEX mission, and our results agree with previous works (Winningham et al., 2006; Lundin et al., 2011). An idea for a future work is to study the influence of the Mars orbital distance on the ULF wave generation. At Venus, closer to the Sun, the solar cycle will probably have a stronger effect on the ULF wave intensity, and this would also be an interesting future work to be developed. Acknowledgments AMSF would like thank the Sa˜o Paulo Research Foundation (FAPESP), Brazil, (projects 2016/10794-2 and 2017/00516-8) and the National Council for Scientific and Technological Development (CNPq), Brazil, (project 300234/2019-8) agencies for the support. The MJAB was supported by Goia´s Research Foundation (FAPEG), Brazil, (grant n. 201210267000905) and CNPq (grants n. 303103/2012-4). EE thanks CNPq (project 302583/20157) and FAPESP (2018/21657-1) for the support.
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
References Barabash, S., Lundin, R., Andersson, H., et al., 2004. ASPERA-3: analyser of space plasmas and energetic ions for Mars Express. In: Wilson, Andrew (Ed.), scientific coordination: Agustin Chicarro. Mars Express: the scientific payload. ESA SP-1240. ESA Publications Division, Noordwijk, Netherlands, pp. 121–139 (ISBN 92-9092-556-6). Barabash, S., Lundin, R., Andersson, H., et al., 2006. The analyzer of space plasmas and energetic atoms (ASPERA-3) for the Mars Express Mission. Space Sci. Rev. 126, 113–164. Bolzan, M.J.A., 2004. Analysis of wavelet transform applied in geophysical. Revista Brasileira de Ensino de Fı´sica 26, 37–41. Chicarro, A., Martin, P., Trautner, R., 2004. The Mars Express Mission: an overview. In: Wilson, Andrew (Ed.), scientific coordination: Agustin Chicarro. Mars Express: The Scientific Payload. ESA SP1240. ESA Publications Division, Noordwijk, Netherlands, pp. 3–16 (ISBN 92-9092-556-6). Cloutier, P.A., Daniell Jr., R.E., 1973. Ionospheric currents induced by solar wind interaction with planetary atmospheres. Planet. Spice Sci. 21, 463–474. Cloutier, P.A., Daniell Jr., R.E., 1979. An electrodynamic model of the solar wind interaction with the ionospheres of Mars and Venus. Planet. Space Sci. 27, 1111–1121. Dong, Y., Fang, X., Brain, D.A., et al., 2015. Strong plume fluxes at mars observed by MAVEN: an important planetary ion escape channel. Geophys. Res. Lett. 42, 1–9. Dubinin, E., Sauer, K., Baumgartel, K., Lundin, R., 1997. The Martian magnetosheath: phobos-2 observations. Adv. Space Res. 20, 149–153. Dubinin, E., Sauer, K., Baumgaertel, K., Srivastava, K., 1998. Multiple shocks near Mars. Earth Planets Space 50, 279–287. Echer, E., 2010. Planetary magnetosphere. Revista Brasileira de Ensino de Fı´sica 32 (2), 2301-2–2301-7. Ergun, R.E., Andersson, L., Peterson, W.K., Brain, D., Delory, G.L., Metchell, D.L., Lin, R.P., Yau, A.W., 2006. Role of Plasma Waves in Mars’ atmospheric Loss. Geophys. Res. Lett. 33, L14103. https://doi. org/10.1029/2006GL025785. Espley, J.R., Cloutier, P.A., Brain, D.A., Crider, D.H., Acun˜a, M.H., 2004. Observations of low-frequency magnetic oscillations in the Martian magnetosheath, magnetic pileup region and tail. J. Geophys. Res. 109, 1–12, 0148-0227/04/2003JA010193. Fowler, C.M., Andersson, L., Halekas, J., et al., 2017. Electric and magnetic variation in the near-Mars environment. J. Geophys. Res. Space Phys. 122, 8536–8559. Franco, A.M.S., 2018. A Study of Plasma Waves in the Induced Magnetospheres of Mars and Venus Thesis (Space Gephysics). National Institute for Space Research, Sa˜o Jose´ dos Campos, Brazil. Fraenz, M., Mouikis, C., Marghitu, O., Schroeder, O., Mcfadden, J., Roussos, E., Penou, E., 2016. CCATI Interface for Tplot data products Software-Package for Ampte IRM, Cluster CIS, Galileo PLS MAVEN, Messenger FIPS, MEX/VEX Aspera, PVO MAG, STEREO and the SPICE system. Available: http://www2.mps.mpg. de/projects/mars-express/aspera/ccati/ (access: Aug. 27, 2019). Gunell, H., Amerstorfer, U.V., Nilsson, H., et al., 2008. Shear driven waves in the induced magnetosphere of Mars. Plasma Phys. Controll. Fusion 50, 1–9.
9
Han, X., Fraenz, M., Dubinin, E., et al., 2014. Discrepancy between ionopause and photoelectron boundary determined from mars boundary determined from Mars express measurements. Geophys. Res. Lett. 41, 8221–8227. Kivelson, M.G., Bagenal, F., 2007. Planetary magnetospheres. In: Macfadden, Lucy-Ann, Weissman, Paul R., Johnson, T.V. (Eds.), Encyclopedia of the Solar System. Academic, San Diego, CA, pp. 519–539. Luhmann, J.G., Russell, C.T., Brace, L.H., Vaisberg, O.L., 1992. The Intrinsic Magnetic Field and Solar-Wind Interaction of Mars. In: Mars (A93-27852 09-91), pp. 1090–1134. Luhmann, J.G., 1995. Plasma interactions with unmagnetized bodies. In: Kivelson, M.G., Russell, C.T. (Eds.), Introduction to Space Physics. Cambridge Univ. Press, New York, pp. 203–226. Luhmann, J.G., Ledvina, S.A., Russell, C.T., 2004. Induced magnetospheres. Adv. Space Res. 33, 1905–1912. Lundin, R., Barabash, S., Dubinin, E., Winningham, D., Yamauchi, M., 2011. Low-altitude acceleration of ionospheric ions at Mars. Geophys. Res. Lett. 38, 1–11. Lundin, R., Barabash, S., Holmstroem, M., et al., 2013. Solar cycle effects on the ion escape from Mars. Geophys. Res. Lett. 40, 6028–6032. Martineczs, C., Fraenz, M., Woch, et al., 2008. Location of the bow shock and ion composition boundaries at venus-initial determinations from venus express aspera-4. Plane. Space Sci. 56, 780–784. Morettin, P.A., 1992. Waves and Wavelets: From Fourier Analysis to the Wavelet Analysis. Edusp, Sa˜o Paulo, p. 296. Modolo, R., Chanteur, G.M., Dubinin, E., Mattheuws, A.P., 2005. Influence of the solar EUV flux on the Martian plasma environment. Ann. Geophys. 23, 433–444. Nagy, A.F., Winterhalter, D., Sauer, K., et al., 2004. The plasma environment of Mars. Space Sci. Rev. 111, 33–114. Ruhunusiri, S., Halekas, J.S., Connerney, J.E.P., et al., 2015. Lowfrequency waves in the Martian magnetosphere and their response to upstream solar wind driving conditions. Geophys. Res. Lett. 42, 8917– 8924. Russell, C.T., Luhmann, J.G., Schwingenschuh, K., Riedler, W., Yeroshenko, Y., 1990. Upstream waves at Mars: phobos observations. Geophys. Res. Lett. 17, 897–900. Sa´nches-Cano, B., Lester, M., Witasse, O., et al., 2016. Solar cycle variations in the ionosphere of Mars as seen by multiple Mars express data sets. J. Geophys. Res. 121, 2547–2568. Sa´nches-Cano, B., Hall, B.E.S., Lester, M., et al., 2017. Mars plasma system response to solar wind disturbances during solar minimum. J. Geophys. Res. 122, 6611–6634. Sagdeey, R.Z., Zakharov, A.V., 1989. Brief history of the phobos mission. Nature 341, 581–585. Sauer, K., Dubinin, E., Baumgartel, K., 1998. Nonlinear MHD waves and discontinuities in the Martian magnetosheath observations and 2D biion MHD simulations. Earth Planets Space 50, 793–801. Torrence, C., Compo, G.P., 1998. A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 79 (1), 61–78. Winningham, J.D., Frahm, R.A., Sharber, J.R., et al., 2006. Electron oscillations in the induced martian magnetosphere. Icarus 182, 360– 370. (access: Aug. 27, 2019).
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
ScienceDirect Advances in Space Research xxx (2019) xxx–xxx www.elsevier.com/locate/asr
Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars A.M.S. Franco a,⇑, M. Fra¨nz b, E. Echer a, M.J.A. Bolzan c a
National Institute for Space Research (INPE), Sao Jose dos Campos, Brazil b Max Planck Institute for Solar System Research, Goettingen, Germany c Federal University of Jataı´, Jataı´, Brazil
Received 19 February 2019; received in revised form 27 August 2019; accepted 5 September 2019
Abstract Wavelet analysis was employed to identify the major frequencies present in the plasma oscillations in the Martian magnetosheath. We have selected magnetosheath crossings and applied the Morlet wavelet transform to the electron density and temperature data, obtained from the Analyzer of Space Plasmas and Energetic Atoms experiment (ASPERA-3), onboard the Mars Express (MEX). In a study of 9667 magnetosheath crossings observed from 2005 to 2016, we have found 22,912 frequencies with high wave power between 5 and 60 mHz for the electron density data, For about 2/3 of the high wave power periods (63.3%), the most energetic frequencies were identified in the range 5–20 mHz. The analysis of the electron temperature data led to similar results, with 61.9% of the highest power frequencies in the 5–20 mHz range. No significant influence of the solar cycle on the frequencies of ULF waves has been observed in our analysis. The frequencies obtained here are near the Oþ gyrofrequency. The main fact that controls the ion gyroradius is the interplanetary magnetic field that is compressed around the planet. Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.
Keywords: Induced magnetosphere of Mars; ULF waves; Wavelet transform
1. Introduction Near the Mars orbit, according to the Parker spiral model, the interplanetary magnetic field (IMF) should lie at an angle of 56° from the Mars-Sun line (Luhmann et al., 2018, 2004; Luhmann, 1995). Since the solar wind is perturbed by the passage of interplanetary shock waves, the planet can be reached by ion and energetic electron flows, which are associated with these shock waves or to solar flares. With the absence of an intrinsic magnetic field, the interaction between the solar wind and the Mars environment occurs directly with the upper ⇑ Corresponding author at: National Institute for Space Research, Av. dos Astronautas, 1.758 - Jardim da Granja, Sa˜o Jose´ dos Campos, 12227010, Brazil (A.M.S. Franco). E-mail address: [email protected] (A.M.S. Franco).
atmosphere and ionosphere of the planet. Thus, its magnetosphere is an induced one (Cloutier and Daniell, 1973; Cloutier and Daniell, 1979; Kivelson and Bagenal, 2007; Echer, 2010). Low frequency (LF) waves were observed for the first time in the plasma environment of Mars through measurements of the plasma wave system experiment (PSW) operated by the Phobos-2 spacecraft (Sagdeey and Zakharov, 1989). Plasma waves that are generated at the boundary layers, such as Alfven, fast mode and electromagnetic ion cyclotron waves, can be considered the most important for carrying energy over extended distances (Ergun et al., 2006). Russell et al. (1990) studied waves with frequencies below 0.5 Hz at the upstream region of Mars using Phobos spacecraft measurements. Waves at the proton gyrofrequency are observed in that region, and these waves were
https://doi.org/10.1016/j.asr.2019.09.009 0273-1177/Ó 2019 COSPAR. Published by Elsevier Ltd. All rights reserved.
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
2
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
observed independently of whether the IMF formed a connection to the bow shock. The source of these waves can be ionized hydrogen from the exosphere via ionization by solar wind electrons, photoionization or charge exchange. Fowler et al. (2017) studied the wave power in the electric and magnetic field at Mars space environment for several frequency ranges (Ultra Low Frequencies (ULF): 0.01– 0.05 Hz; LF: 1–5 Hz; medium frequencies: 5 Hz and high frequency: 1–5 kHz) using data from Mars Atmosphere and Volatile Evolution (MAVEN) mission. Those authors have shown that high wave power is observed in the ULF range. The Martian magnetosheath is filled by compressional magnetohydrodynamic (MHD) waves. The interaction between the solar wind and heavy ions of the planetary plasma results in the generation of strong MHD bi-ion waves (Dubinin et al., 1997). These waves are related to the exchange of periodic momentum between the proton flux and heavy ions. They can be intensified and produce multiple shocklets (Dubinin et al., 1998; Nagy et al., 2004). Sauer et al. (1998) observed an oscillation characteristic of the dynamical exchange between the proton and heavy ions in the magnetosheath of Mars. It was also observed that non-linear MHD bi-ion waves can evolve to several shocklets. Espley et al. (2004) studied low frequency waves in the plasma regions of the induced magnetosphere of Mars (magnetosheath, magnetic Pile-up Region (MPR) and magnetotail). Through observations of the Magnetometer/Electron Reflectometer (MAG/ER) instrument onboard of the Mars Global Surveyor (MGS), compressional and elliptically polarized waves were observed at the dayside of the magnetosheath. The wave vector presented an angle higher than 60° in relation to the mean magnetic field. Such oscillations presented dominant frequencies significantly lower than the proton gyrofrequency in the magnetosheath. In the nightside magnetosheath the oscillations are more variable and sometimes present circular polarization, but in general they are transversal. The magnetic perturbations are left-hand elliptically polarized, they are also observed in some regions in the dayside of the magnetosphere (Espley et al., 2004). The waves propagate at smaller angle (less than 30°) relative to the mean magnetic field. Those oscillations present variable frequencies. The main frequencies observed are with a factor of 2 (0.2–0.004 Hz) less than the local proton gyrofrequency, but frequencies that exceed the proton gyrofrequency can also be observed. Ruhunusiri et al. (2015), using data from the ion analyzer and from the magnetometer instruments of MAVEN mission characterized low frequency waves in the Mars magnetosphere through the analyses of the transport ratios. They observed that Alfven and fast modes are more common than the mirror modes in the magnetosheath. They also observed that slow modes were less frequent than the others. Winningham et al. (2006) also studied low frequency waves in different regions of the Martian magnetosphere, such as: the magnetosheath, magnetotail and
magnetic cusps. The analysis was done using electron oscillation data obtained from observations of the electron spectrometer of the ASPERA-3 instrument onboard ESA Mars Express spacecraft (MEX). In the magnetosheath, oscillations in the electron flux present a frequency peak between 0.01 and 0.02 Hz, which corresponds to the oxygen gyrofrequency in that region. Their results also suggest that the bow shock may be the source of those oscillations, although it was observed that the magnetosheath and the magnetosphere night side region also respond to those oscillations. Lundin et al. (2011) observed that the average magnitude of magnetosheath waves is up to ten times higher than the wave magnitude observed in the density of Oþ ions and expected that ULF wave power is correlated with the Oþ outflow. These observations showed a first indication of the relation between the ULF wave power and atmospheric loss on Mars. Frequencies between 2 and 3 mHz have been observed as fundamental to oscillations in density and velocity time series (Gunell et al., 2008), and they are observed in regions where there is a velocity shear in the plasma flow. Fowler et al. (2017) have studied wave power in the electric and magnetic field data in various frequency bands. Their results show that high wave power was observed in the range of ULF, mainly in the region of the magnetosheath. They also have observed that energetic waves with high Poynting fluxes (2–16 Hz) between ~1011 and 108 mW2 reach the upper ionosphere. From that study it can be concluded that part of the power of waves observed in the magnetosheath can propagate down to regions below the Martian ionopause. The study of wave propagation is very relevant due to the fact that they have an important role in the energy and momentum transfer between the solar wind and the Mars magnetosphere (Ergun et al., 2006). Consequently, these waves are related to the processes of atmospheric loss at Mars via interaction with the solar wind. Knowing the importance to study fluctuations in Mars magnetosheath, the aim of this work is to determine the main frequency of plasma oscillations in the Mars magnetosheath. 2. Data In order to develop this work, plasma data obtained through the electron spectrometer (ELS) of the Analyzer of Space Plasma and Energetic Atoms (ASPERA-3) instrument onboard MEX spacecraft have been used. MEX was launched by the European Space Agency (ESA) in the beginning of July 2003 and it has arrived at Mars in December of the same year. It is still operating in orbit around the planet as of August 2019. The MEX orbit has an elliptical trajectory around Mars, with an inclination of 86.35° and a period of about 6.75 h. This eccentric elliptical orbit has an altitude of about 250 km at the periapsis and 10142 km at the apoapsis (Chicarro et al.,
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
3
2004). The main objective of the MEX mission is to study the interaction between the solar wind and Mars, its atmosphere, surface and subsurface. The MEX spacecraft operates with 7 instruments, which provide information on the atmosphere, ionosphere, surface and interior (Chicarro et al., 2004). One of these instruments is the ASPERA-3, which was used in our study. The goals of the ASPERA-3 instrument are to investigate the interaction of the solar wind with the Mars atmosphere, as well as to characterize the plasma environment and neutral gas of the planet using measurements of the ions, electrons and energetic neutral atoms. The main objective is to study the impact of the solar wind-Mars interaction on the atmosphere/ionosphere and the evolution of the Martian atmosphere (Barabash et al., 2006). ASPERA-3 is composed of four sensors, two Energetic Neutral Atoms (ENA) sensors, an Ion Mass Analyser (IMA) and an electron spectrometer (ELS) (Barabash et al., 2004). The ELS is a sensor that provides electron measurements in a 2D plane with a resolution of 4 s in an energy range between 0.01 and 20 keV. The sensor consists of a collimator system followed by a high standard top-hat electrostatic analyzer in a compact spherical design (Barabash et al., 2004, 2006). Since the ion spectrometer has a time resolution of only 192 s we use these data only to support the identification of plasma boundaries.
3. Methodology 3.1. Boundary identification In order to develop the study of the ULF waves in the magnetosheath of Mars, it is necessary to know the location of the major plasma boundaries (bow shock, pile-up boundary [MPB], PhotoElectron Boundary [PEB]) of the magnetic environment of the planet. The major Martian plasma boundaries for the years between 2005 and 2013 have been identified by Han et al. (2014) using MEX data. In order to apply the study for the whole interval of the MEX mission (2004–2016), the boundaries of the years 2014, 2015 and 2016 had to be identified by Franco (2018). For 2004 we do not have a significant number of intervals with data for this analysis, so the data from this year were disregarded in this study. The MEX boundary catalog can be obtained from the MPI for Solar System Research. Here we briefly explain the method used to identify the boundaries in these previous studies. First, a list of data intervals where the MEX is at a maximum of 4 RM (Mars Radius) of distance of the planet for the interval of 7 h (approximately the duration of the MEX orbit) has been compiled using the CCATI software (Fraenz et al., 2016). After that, plots with the electron and ion spectra for each interval have been made. The identification of the boundaries in the plot is made manually following the same criteria defined by Martineczs et al. (2008).
Fig. 1. Example of the identification of plasma boundaries on Mars for the interval between 12:30 UT and 16:00 UT on January 09, 2015. The upper panel shows the electron spectrum and the bottom panel, the ion spectrum.
https://www.mps.mpg.de/planetary-science/marsexpress-aspera-3 (2019) Fig. 1 shows an example of the identification of the plasma boundaries of Mars following these criteria. The bow shock can be identified by a sudden increase in the temperature of the electrons and ions due the heating of the plasma at the bow shock of the planet. The MPB inbound crossings are characterized by a decrease in the magnetosheath (energetic) electron density and increase of planetary ions flux. In the ion spectrum, low energy ions are observed in the magnetic pile-up region (MPR), which helps to identify the boundaries of the region (MPB and PEB). The PEB is also identified where the flux of the energetic electrons and ions are very low and photo-electrons with energies 20–30 eV are observed. This boundary should be very close to the ionopause. The boundaries are selected visually by clicks on the screen in the region where the criteria are met. Selecting these boundaries, a file with the index of the boundary and the time where the MEX has crossed is generated. In the study of the ULF waves in the magnetosheath, we are interested in the intervals that correspond to that
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
4
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
region. Between 2014 and 2016 a total of 1766 magnetosheath crossings have been identified and added to the MEX list of magnetosheath crossings available, resulting in a total of 9667 magnetosheath crossings from 2005 to 2016. 3.2. Wavelet analysis The wavelet functions are used to analyze nonstationary signals (Morettin, 1992). Different from Fourier transform, which approaches a function by a linear combination of sinusoidal components (each corresponding to a different frequency), the wavelet functions wðtÞ, are generated from a simple generating function, which suffer expansions/contractions and translations in time. Those functions consist in a set of small waves, with a compact support, localized in time domains (space) and frequency (Bolzan, 2004). The wavelet functions are generated by expansion, wðtÞ ! wð2tÞ, and translations, wðtÞ ! wðt þ 1Þ, from a simple generating function, the wavelet-mother given by following equation: 1 tb p ffiffi ffi wa;b ðtÞ ¼ w ; ð1Þ a a where a is the scale (a > 0) and b is the position. In this work we used the Morlet wavelet given by (Torrence and Compo, 1998): t2
wðtÞ ¼ ein0 t e 2 ;
ð2Þ
where n0 is a constant angular frequency. The Wavelet Transform (WT) applied on a time series f(t) is defined as:
Z WT ða; bÞ ¼
f ðxÞwa;b ðtÞdt;
ð3Þ
where f(x) is a time series, wa:b ðtÞ is the wavelet function and wa;b ðtÞ represents the complex conjugate thereof. We used the Global Wavelet Spectrum (GWS) in order to identify the major periods (most energetic) in each magnetosheath crossing. The GWS is given by: Z 2 GWS ¼ jWT ða; bÞj db; ð4Þ
4. Results In order to determine the frequencies with most power in the low frequency window for plasma oscillations in the Mars magnetosheath, the WT was applied to 9667 magnetosheath crossings observed from 2005 to 2016 for electron density and electron temperature data. The data used in this analysis have a time resolution of 4 s and the Morlet wavelet a wave number (n0 ) of six, since its shape gives good-time localization. 4.1. Periodicities in electron density data Fig. 2 shows an example of the WT results applied to the electron density for the interval wherein the MEX crossed the Mars magnetosheath, between 02:45 UT and 03:06 UT on February 06, 2012. Fig. 2(a) shows the electron density time series. The wavelet spectrum power is shown in Fig. 2 (b), and in Fig. 2(c) the GWS, where we note the presence of three most energetic frequencies: 44 mHz, 11 mHz and 6.4 mHz. The GWS provides the power integrated in time
Amplitude² Fig. 2. Panel (a) N e data. Panel (b) Wavelet spectrum. (c) Global Wavelet Spectrum.
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
5
Fig. 3. MEX orbit (red) on 6 February 2012 in cylindrical coordinates. (For interpretation of the references to color in this figure legend, the reader is referred to the web version of this article.)
along a specific frequency. The frequency peaks identified in GWS correspond to the most energetic frequencies in the ULF range for each magnetosheath interval. Fig. 3 shows the MEX orbit (red) on 06 February 2012. The region marked in blue represents the region where the spacecraft crossed the magnetosheath and the wavelet transform was applied on the data (Fig. 2). This is an outbound orbit, and it is possible to observe in Fig. 2 that wave power intensifies strongly as the spacecraft approaches the bow shock. In Fig. 3 the orbit is shown using Mars Solar Orbital (MSO) coordinates system. The Mars-Sun line is defined as the +x direction and the origin is centered on Mars, y points opposite to Mars’ motion, and z completes the right-handed set pointing upward from the plane of the ecliptic into the northern hemisphere. The Y-axis in Fig. 3 represents the cylindrical radial distance pffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffiffi q ¼ Y MSO 2 þ Z MSO 2 . The aim of this study is to find the most energetic frequencies of plasma oscillations in Mars magnetosheath. Then, the main frequencies are identified by the higher power peaks observed in the GWS. After applying the WT to the electron density during the 9667 magnetosheath crossings, 22,912 peaks of frequencies were identified in electron density data, which results in an average of 2.4 frequencies per interval. These were divided into ranges (from 5 to 60 mHz) to perform a statistical analysis. Frequencies lower than 5 mHz were disregarded, since they may be influenced by changes in the spacecraft potential (Espley et al., 2004; Lundin et al., 2011). Furthermore, considering that the spacecraft moves with a velocity of about 5 km/s, for frequencies lower than 5 mHz, 1000 km have been covered. Then, if three oscillations can be considered to characterize a wave, a total of 3000 km will be traveled,
Table 1 Number of peaks in the global wavelet spectrum presented in each range of frequencies for the electron density data. Frequencies (mHz)
number
Percentage (%)
5 < f 10 10 < f 20 20 < f 30 30 < f 40 40 < f 50 50 < f 60 Total
7704 6797 3342 2425 2630 14 22,912
33.6 29.7 14.6 10.6 11.5 0.1
which is much larger than the Martian magnetosheath, so that the spacecraft has crossed many plasma regimes for this distance (Lundin et al., 2011). Table 1 presents the ranges of frequencies used in this analysis, the number of peak frequencies identified in each range, and the corresponding percentage relative to the total number of frequencies identified between 5 and 60 mHz. Fig. 4 shows the histogram that was made from the results shown in Table 1. We can notice that the main frequencies observed in the electron density were in the range 5–10 mHz with 33.6%. Further, the second peak was observed in the range 10–20 mHz with 29.7% of the 22,912 frequencies identified. Considering those two ranges, we have found that 63.3% (about 2/3) of the frequencies occur in the interval of 5–20 mHz. 4.2. Periodicities in electron temperature data The same study that was made for the electron density was done for the electron temperature. Fig. 5 shows the
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
6
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
Fig. 4. Histogram of the percentage of the main frequencies in electron density in the magnetosheath of Mars.
Amplitude² Fig. 5. Panel (a) T e data. Panel (b) Wavelet spectrum. (c) Global Wavelet Spectrum.
WT results applied to the electron temperature for the same interval wherein the MEX crossed the Mars magnetosheath presented in Fig. 2. In Fig. 5(c) we note the presence of five main frequencies: 43 mHz, 25 mHz, 15 mHz, 9 mHz and 6.2 mHz. Applying the WT, 23,395 frequencies were identified in the electron temperature time series, an average of 2.4 frequencies per interval. Table 2 shows the total number of peaks in the global wavelet spectra in each range of frequencies. Table 2 and Fig. 6 present the range of main frequencies found. We observe that most of the peak frequencies are also located between 5 and 10 mHz with 32.8% of the cases. Considering two ranges (5–10 mHz and 10–20 mHz) as it was done for the frequencies of the electron density study, 61.9% of the principal frequencies are observed between 5 and 20 mHz, which is very similar to what we obtained for the electron density.
Table 2 Number of peaks in the global wavelet spectrum presented in each range of frequencies for the electron temperature data. Frequencies (mHz)
Number
Percentage (%)
5 < f 10 10 < f 20 20 < f 30 30 < f 40 40 < f 50 50 < f 60 Total
7676 6812 3238 2789 2877 3 23,395
32.8 29.1 13.8 11.9 12.3 <0.1
4.3. Solar cycle dependence investigation In the study of the Mars plasma environment, the phases of solar cycle have been found to influence the ion escape ratio (Modolo et al., 2005; Lundin et al, 2013,
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
7
Fig. 6. Histogram of the percentage of the main frequencies in electron temperature in the magnetosheath of Mars.
Fig. 7. Histograms with electron density (a) and electron temperature (b) ULF wave percentage in the range 5–20 mHz for each solar cycle phase (2005– 2016).
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
8
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
Dong et al., 2015), density and temperatures of the ionosphere (Sa´nches-Cano et al., 2016) and consequently the formation of the induced magnetospheric cavity. Since the ionospheric plasma pressure is higher during the solar maximum (high activity) phases of the solar cycle also the higher ionospheric pressure can withstand against the then higher solar wind flux (Sa´nches-Cano et al., 2017). A study looking for variation of those frequencies with the solar cycle has been developed here, where the main frequencies were divided into subintervals according to the solar cycle phases. In Fig. 7 histograms of the percentage of periods with higher wave power from electron density (a) and electron temperature (b) data in the range 5– 20 mHz for each solar cycle phase (2005–2016) are shown. In electron density data, in Fig. 7(a), the declining phases (this includes 2005, 2006, 2007 (cycle 23) and 2015, 2016 (Cycle 24)) have 61.7% of the peak frequencies in the global wavelet spectra in the interval 5–20 mHz. The minimum phase (2008 and 2009) has 65.5% of the peak frequencies in that range of frequencies. During the ascending phase the percentage is 64.8% (2010 and 2011) and while in the maximum (2012, 2013 and 2014) it is 63.4%. For electron temperature (Fig. 7(a)) a similar result has been found. During declining phases 60.6% of the frequencies identified are in the interval of 5–20 mHz. During the minimum phase 63.8% are in that range of frequencies. In the ascending and maximum phases 63.9% and 61.5% are in that range, respectively. After this analysis it is possible to conclude that there is no significant influence of solar cycle on the frequencies of ULF waves in the magnetosheath of Mars. 5. Discussion The results that were found in Sections 4.1 and 4.2 agree with the findings by Winningham et al. (2006), where they used the integrated electron energy flux to study the electron oscillations in the induced magnetosphere of Mars. Those authors also observed an energetic peak between 10 and 20 mHz in the magnetosheath. They have interpreted it as corresponding to the oxygen ion gyrofrequency in the Mars magnetosheath, calculated using data from the magnetometer from Mars Global Surveyor (Espley et al., 2004). It is important to mention that the energetic peaks found in this study do not correspond to single pulses because the algorithm used in this work excludes periods of high wave power caused by single pulses (for more details see Torrence and Compo, 1998). It is believed that for large scales (greater than the Debye Length kD ), the plasma should be electrically neutral, and the electron density approximately equal to the ion density (Ne ffi Ni). When ion wave modes of large scale develop, they carry with them the electrons which are associated with the oscillating ions. Then, the electrons assume their wavelike behavior. Electrons oscillate at higher frequency, but they also respond to lower frequencies to maintain quasi-equilibrium with positive ions. Therefore,
when we observe in the ULF domain, the electrons trace the movement of the ions and the wave modes thereof (Winningham et al., 2006). Lundin et al. (2011) also found out similar results where the most energetic frequencies are between 3 and 20 mHz of ULF waves at the magnetosheath. In the analysis of solar cycle variation, no significant influence was observed. 6. Summary and conclusion In this work, the main frequencies in plasma oscillation in Mars magnetosheath using electron density and temperature have been identified. The analysis was conducted for 11 years of the MEX mission (2005–2016). The dependence of the solar cycle in these frequencies was also analyzed. The following results were obtained in this paper: The Martian plasma boundaries catalog was updated, and plasma boundaries from 2014 to 2016 are now available for new researches. The main frequencies of plasma waves in the magnetosheath of Mars were identified for electron density and temperature from ELS/ASPERA-3/MEX data. The majority of peaks in the global wavelet spectrum of the electron density and temperature are in the range between 5 and 20 mHz. In the electron density spectra, 63.6% of a total of 22,912 energetic frequencies are in a range between 5 and 20 mHz and for electron temperature spectra 61.9% of those 23,395 frequencies identified were in that frequency range. Those frequencies are near the local oxygen gyrofrequency in the Mars magnetosheath. No clear influence of the solar cycle on the frequencies of ULF waves in the Mars magnetosheath was observed here. This study has been developed using plasma data observed by the MEX mission, and our results agree with previous works (Winningham et al., 2006; Lundin et al., 2011). An idea for a future work is to study the influence of the Mars orbital distance on the ULF wave generation. At Venus, closer to the Sun, the solar cycle will probably have a stronger effect on the ULF wave intensity, and this would also be an interesting future work to be developed. Acknowledgments AMSF would like thank the Sa˜o Paulo Research Foundation (FAPESP), Brazil, (projects 2016/10794-2 and 2017/00516-8) and the National Council for Scientific and Technological Development (CNPq), Brazil, (project 300234/2019-8) agencies for the support. The MJAB was supported by Goia´s Research Foundation (FAPEG), Brazil, (grant n. 201210267000905) and CNPq (grants n. 303103/2012-4). EE thanks CNPq (project 302583/20157) and FAPESP (2018/21657-1) for the support.
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009
A.M.S. Franco et al. / Advances in Space Research xxx (2019) xxx–xxx
References Barabash, S., Lundin, R., Andersson, H., et al., 2004. ASPERA-3: analyser of space plasmas and energetic ions for Mars Express. In: Wilson, Andrew (Ed.), scientific coordination: Agustin Chicarro. Mars Express: the scientific payload. ESA SP-1240. ESA Publications Division, Noordwijk, Netherlands, pp. 121–139 (ISBN 92-9092-556-6). Barabash, S., Lundin, R., Andersson, H., et al., 2006. The analyzer of space plasmas and energetic atoms (ASPERA-3) for the Mars Express Mission. Space Sci. Rev. 126, 113–164. Bolzan, M.J.A., 2004. Analysis of wavelet transform applied in geophysical. Revista Brasileira de Ensino de Fı´sica 26, 37–41. Chicarro, A., Martin, P., Trautner, R., 2004. The Mars Express Mission: an overview. In: Wilson, Andrew (Ed.), scientific coordination: Agustin Chicarro. Mars Express: The Scientific Payload. ESA SP1240. ESA Publications Division, Noordwijk, Netherlands, pp. 3–16 (ISBN 92-9092-556-6). Cloutier, P.A., Daniell Jr., R.E., 1973. Ionospheric currents induced by solar wind interaction with planetary atmospheres. Planet. Spice Sci. 21, 463–474. Cloutier, P.A., Daniell Jr., R.E., 1979. An electrodynamic model of the solar wind interaction with the ionospheres of Mars and Venus. Planet. Space Sci. 27, 1111–1121. Dong, Y., Fang, X., Brain, D.A., et al., 2015. Strong plume fluxes at mars observed by MAVEN: an important planetary ion escape channel. Geophys. Res. Lett. 42, 1–9. Dubinin, E., Sauer, K., Baumgartel, K., Lundin, R., 1997. The Martian magnetosheath: phobos-2 observations. Adv. Space Res. 20, 149–153. Dubinin, E., Sauer, K., Baumgaertel, K., Srivastava, K., 1998. Multiple shocks near Mars. Earth Planets Space 50, 279–287. Echer, E., 2010. Planetary magnetosphere. Revista Brasileira de Ensino de Fı´sica 32 (2), 2301-2–2301-7. Ergun, R.E., Andersson, L., Peterson, W.K., Brain, D., Delory, G.L., Metchell, D.L., Lin, R.P., Yau, A.W., 2006. Role of Plasma Waves in Mars’ atmospheric Loss. Geophys. Res. Lett. 33, L14103. https://doi. org/10.1029/2006GL025785. Espley, J.R., Cloutier, P.A., Brain, D.A., Crider, D.H., Acun˜a, M.H., 2004. Observations of low-frequency magnetic oscillations in the Martian magnetosheath, magnetic pileup region and tail. J. Geophys. Res. 109, 1–12, 0148-0227/04/2003JA010193. Fowler, C.M., Andersson, L., Halekas, J., et al., 2017. Electric and magnetic variation in the near-Mars environment. J. Geophys. Res. Space Phys. 122, 8536–8559. Franco, A.M.S., 2018. A Study of Plasma Waves in the Induced Magnetospheres of Mars and Venus Thesis (Space Gephysics). National Institute for Space Research, Sa˜o Jose´ dos Campos, Brazil. Fraenz, M., Mouikis, C., Marghitu, O., Schroeder, O., Mcfadden, J., Roussos, E., Penou, E., 2016. CCATI Interface for Tplot data products Software-Package for Ampte IRM, Cluster CIS, Galileo PLS MAVEN, Messenger FIPS, MEX/VEX Aspera, PVO MAG, STEREO and the SPICE system. Available: http://www2.mps.mpg. de/projects/mars-express/aspera/ccati/ (access: Aug. 27, 2019). Gunell, H., Amerstorfer, U.V., Nilsson, H., et al., 2008. Shear driven waves in the induced magnetosphere of Mars. Plasma Phys. Controll. Fusion 50, 1–9.
9
Han, X., Fraenz, M., Dubinin, E., et al., 2014. Discrepancy between ionopause and photoelectron boundary determined from mars boundary determined from Mars express measurements. Geophys. Res. Lett. 41, 8221–8227. Kivelson, M.G., Bagenal, F., 2007. Planetary magnetospheres. In: Macfadden, Lucy-Ann, Weissman, Paul R., Johnson, T.V. (Eds.), Encyclopedia of the Solar System. Academic, San Diego, CA, pp. 519–539. Luhmann, J.G., Russell, C.T., Brace, L.H., Vaisberg, O.L., 1992. The Intrinsic Magnetic Field and Solar-Wind Interaction of Mars. In: Mars (A93-27852 09-91), pp. 1090–1134. Luhmann, J.G., 1995. Plasma interactions with unmagnetized bodies. In: Kivelson, M.G., Russell, C.T. (Eds.), Introduction to Space Physics. Cambridge Univ. Press, New York, pp. 203–226. Luhmann, J.G., Ledvina, S.A., Russell, C.T., 2004. Induced magnetospheres. Adv. Space Res. 33, 1905–1912. Lundin, R., Barabash, S., Dubinin, E., Winningham, D., Yamauchi, M., 2011. Low-altitude acceleration of ionospheric ions at Mars. Geophys. Res. Lett. 38, 1–11. Lundin, R., Barabash, S., Holmstroem, M., et al., 2013. Solar cycle effects on the ion escape from Mars. Geophys. Res. Lett. 40, 6028–6032. Martineczs, C., Fraenz, M., Woch, et al., 2008. Location of the bow shock and ion composition boundaries at venus-initial determinations from venus express aspera-4. Plane. Space Sci. 56, 780–784. Morettin, P.A., 1992. Waves and Wavelets: From Fourier Analysis to the Wavelet Analysis. Edusp, Sa˜o Paulo, p. 296. Modolo, R., Chanteur, G.M., Dubinin, E., Mattheuws, A.P., 2005. Influence of the solar EUV flux on the Martian plasma environment. Ann. Geophys. 23, 433–444. Nagy, A.F., Winterhalter, D., Sauer, K., et al., 2004. The plasma environment of Mars. Space Sci. Rev. 111, 33–114. Ruhunusiri, S., Halekas, J.S., Connerney, J.E.P., et al., 2015. Lowfrequency waves in the Martian magnetosphere and their response to upstream solar wind driving conditions. Geophys. Res. Lett. 42, 8917– 8924. Russell, C.T., Luhmann, J.G., Schwingenschuh, K., Riedler, W., Yeroshenko, Y., 1990. Upstream waves at Mars: phobos observations. Geophys. Res. Lett. 17, 897–900. Sa´nches-Cano, B., Lester, M., Witasse, O., et al., 2016. Solar cycle variations in the ionosphere of Mars as seen by multiple Mars express data sets. J. Geophys. Res. 121, 2547–2568. Sa´nches-Cano, B., Hall, B.E.S., Lester, M., et al., 2017. Mars plasma system response to solar wind disturbances during solar minimum. J. Geophys. Res. 122, 6611–6634. Sagdeey, R.Z., Zakharov, A.V., 1989. Brief history of the phobos mission. Nature 341, 581–585. Sauer, K., Dubinin, E., Baumgartel, K., 1998. Nonlinear MHD waves and discontinuities in the Martian magnetosheath observations and 2D biion MHD simulations. Earth Planets Space 50, 793–801. Torrence, C., Compo, G.P., 1998. A practical guide to wavelet analysis. Bull. Am. Meteorol. Soc. 79 (1), 61–78. Winningham, J.D., Frahm, R.A., Sharber, J.R., et al., 2006. Electron oscillations in the induced martian magnetosphere. Icarus 182, 360– 370.
Please cite this article as: A. M. S. Franco, M. Fra¨nz, E. Echer et al., Wavelet analysis of low frequency plasma oscillations in the magnetosheath of Mars, Advances in Space Research, https://doi.org/10.1016/j.asr.2019.09.009