Statistical study of low-frequency magnetic field fluctuations near Venus during the solar cycle

Transcription

1 PUBLICATIONS RESEARCH ARTICLE Key Points: The spatial distributions of fluctuation properties are presented under three typical solar activity periods The properties of fluctuations are solar cycle dependent The transfer of momentum and energy near Venus can be affected by solar activity Correspondence to: T. L. Zhang, Citation: Xiao, S. D., T. L. Zhang, and G. Q. Wang (2017), Statistical study of low-frequency magnetic field fluctuations near Venus during the solar cycle, J. Geophys. Res. Space Physics, 122, , doi:. Received 8 JAN 2017 Accepted 30 JUL 2017 Accepted article online 3 AUG 2017 Published online 18 AUG American Geophysical Union. All Rights Reserved. Statistical study of low-frequency magnetic field fluctuations near Venus during the solar cycle S. D. Xiao 1,2, T. L. Zhang 3,4, and G. Q. Wang 3 1 CAS Key Laboratory of Geospace Environment, University of Science and Technology of China, Hefei, China, 2 Space Science Institute, Macau University of Science and Technology, Macao, China, 3 Harbin Institute of Technology, Shenzhen, China, 4 Space Research Institute, Austrian Academy of Sciences, Graz, Austria Abstract We statistically investigate the solar cycle dependence of the magnetic field fluctuations in the frequency range MHz based on Venus Express data. We present the spatial distributions of fluctuation properties during three typical periods of the solar cycle, and a comparative study is also performed. With the increase of solar activity, the magnetic field is still quiet in the magnetotail region and the wave intensity becomes weaker in the magnetosheath. The transverse component of fluctuations becomes stronger in the magnetosheath region and weaker in the tail region. The proportion of circularly polarized components to incoherent noise of the fluctuations decreases in the magnetosheath region. The proportion of dominant parallel propagation fluctuations tends to be larger in the nightside magnetosheath, and more perpendicular propagation component is shown in the tail region. 1. Introduction Since there is not a global intrinsic magnetic field at Venus, the solar wind interacts directly with the highly conducting ionosphere and an induced magnetosphere is formed by currents induced in the ionosphere by the draping of the interplanetary magnetic field (IMF) [e.g., Phillips and McComas, 1991; Zhang et al., 2007, 2008a]. The magnetic field fluctuations in the plasma environment near Venus play an important part in the transfer of momentum and energy in the interaction processes of the solar wind with Venus. Therefore, it is important to study the properties and sources of fluctuations so as to advance our understanding of this complex interaction. Some prior observations [e.g., Glassmeier and Espley, 2006] studied the low-frequency magnetic field fluctuations at multiple planets, such as Venus [e.g., Luhmann et al., 1983; Guicking et al., 2010] and Mars [e.g., Espley et al., 2004]. The fluctuations convected from the upstream waves have been observed by Hoppe and Russell [1982], and Luhmann et al. [1983] suggested that the quasi-parallel bow shock is an important source of the fluctuations in the Venusian magnetosheath. Espley et al. [2004] observed predominantly compressional, elliptically polarized, and quasi-perpendicularly propagating fluctuations in the dayside Martian magnetosheath, which were identified as mirror mode waves. And in the nightside Martian magnetosheath, predominantly transverse, elliptically polarized, and quasi-parallel propagating fluctuations were found, which were associated with ion cyclotron instabilities that arise from solar wind and pickup ions. In the tail and magnetic pileup region of Mars, the fluctuations may be a mixture of multiple wave modes. Guicking et al. [2010] investigated the properties of low-frequency magnetic field fluctuations near Venus during solar minimum. The magnetic fluctuations consistent with short large-amplitude magnetic structures were observed by Collinson et al. [2012] in the Venusian foreshock, and the fluctuations would be convected back toward the bow shock and magnetosheath by the solar wind. The spatial distributions of the fluctuation properties near Venus are similar to the observations near Mars [e.g., Espley et al., 2004], which is also a planet without an intrinsic magnetic field. Ruhunusiri et al. [2015] have also investigated the lowfrequency plasma waves near Mars. They found that Alfvén waves are the most dominant wave mode in the upstream region and the Martian magnetosheath, fast waves are found frequently near the bow shock and the magnetic pileup boundary, and mirror and slow waves, on the other hand, occur much less frequently. Ruhunusiri et al. [2015] also investigated the low-frequency waves near Mars response to upstream solar wind conditions. They found that the Alfvén and fast wave occurrences vary dominantly near the Martian bow shock in response to the solar wind dynamic pressure. The fluctuations near Venus can also be strongly controlled by the conditions in the upstream solar wind. During the passage of a slow Interplanetary Coronal Mass Ejection (ICME) on Venus, Collinson et al. [2015] found that foreshock whistler mode waves XIAO ET AL. FLUCTUATIONS NEAR VENUS IN SOLAR CYCLE 8409

2 can strengthen 100 times with respect to the typical power, and the dayside magnetosheath is filled with strong fluctuations convected from the foreshock and the bow shock. Also, prior studies have reported that the magnetic fluctuations near Venus are affected by upstream IMF orientations [e.g., Luhmann et al., 1983; Volwerk et al., 2008; Du et al., 2009b, 2010], which is also found near the Earth [e.g., Luhmann et al., 1986; Song and Russell, 1997; Du et al., 2009a]. The magnetic field fluctuations near Venus are generated mainly from two types of sources: convection from upstream foreshock and local generation [e.g., Luhmann et al., 1983; Du et al., 2010]. As Du et al. [2010] reported, the locally generated fluctuations, which can be generated from the ion cyclotron instability owing to ion pickup, are observed in the magnetosheath under the condition of IMF quasi-perpendicular to the solar wind flow. The fluctuations are found to be elliptically polarized, transverse component dominant, and propagating parallel to the background magnetic field. While, under the condition of IMF quasi-parallel to the solar wind flow, the fluctuations in the Venusian magnetosheath can be convected from the foreshock, and no clear polarization tendency can be observed. The statistical properties of ULF fluctuations in the upstream of Venus were investigated by Shan et al. [2016]. They found that the transverse component dominates and most fluctuations display nearly circular or slightly elliptical polarization. In addition, propagation angles of these ULF fluctuations are mainly less than 30 with respect to the mean magnetic field direction. They also reported that the backstreaming ion in the Venusian foreshock is an important source for the generation of fluctuations. The solar wind conditions vary during the solar cycle, and the fluctuations near Venus would be affected. The solar cycle dependence of proton cyclotron waves in the upstream solar wind at Venus has been reported by Delva et al. [2008, 2015], and it is found that there are more upstream proton cyclotron waves at Venus during solar maximum compared to solar minimum. In addition, the fluctuations near Venus can be generated locally due to the solar wind interaction with the pickup ionospheric ions [e.g., Russell et al., 2006; Du et al., 2009b, 2010]. Hence, the variations of the ionosphere also have an important effect on the fluctuations near Venus. Some previous studies [e.g., Bauer and Taylor, 1981; Elphic et al., 1984; Kar et al., 1986] have reported that the solar cycle variation of the EUV flux plays an important part in the solar wind interaction with Venus and that the Venusian ionosphere is dependent on EUV variations. Their results suggest that the Venusian ionosphere becomes stronger with the increase of solar activity. The Venusian ionosphere and also the magnetic barrier, acting as a dayside-induced magnetosphere formed by the IMF piling up in the dayside inner magnetosheath, at solar minimum are significantly lower in altitude than that at solar maximum [Zhang et al., 2008b]. The altitude of the ionosphere at the terminator is ~900 km at solar maximum [Zhang et al., 1991] and ~250 km at solar minimum [Zhang et al., 1990]. The altitude of the magnetopause (magnetic barrier upper boundary) at the terminator is ~1700 km at solar maximum [Zhang et al., 1991] and ~1000 km at solar minimum [Zhang et al., 2008b]. Therefore, it could be expected that the magnetic field fluctuations near Venus are also solar cycle dependent. Thereby, this work aims to investigate the solar cycle dependence of the fluctuations properties. 2. Data and Method Launched in November 2005, Venus Express [Titov et al., 2006; Svedhem et al., 2007] was inserted into a 24 h polar orbit around Venus in April 2006 and sent back science data until November Venus Express provides a good opportunity to study the solar cycle dependence of the magnetic field fluctuations near Venus. Figure 1 displays the 13 month Smoothed Monthly Total Sunspot Number (sunspot data from the World Data Center Sunspot Index and Long-term Solar Observations (SILSO), Royal Observatory of Belgium, Brussels) during the Venus Express mission, from April 2006 to November 2014, and a clear solar activity variation in this solar cycle is shown. The Sun entered solar minimum in and maximum in According to this variation of sunspot number, we choose three typical periods, as shaded in red, to investigate the solar cycle dependence of the low-frequency magnetic field fluctuations near Venus. As listed in Table 1, we choose the data from June 2008 to June 2009, with a mean sunspot number of ~3.2, to represent low solar activity condition; the data from August 2010 to July 2011, with a mean sunspot number of ~51, are used to represent the moderate solar activity condition; and the high solar activity condition is represented by the data from September 2013 to September 2014 with a mean sunspot number of ~ In the later section, the properties of low-frequency magnetic field fluctuations are examined in these three groups by using the magnetic field data with a resolution of 1 s from the Venus Express XIAO ET AL. FLUCTUATIONS NEAR VENUS IN SOLAR CYCLE 8410

3 Figure 1. The 13 month smoothed monthly total sunspot number during the Venus Express period, from April 2006 to November The red shaded areas show three typical solar activity periods in this solar cycle. magnetometer [Zhang et al., 2006] and a comparative study among them is also performed. The results show how the solar activity affects the properties of the low-frequency magnetic fluctuations near Venus. In consideration of the Venusian orbital motion around the Sun (~35 km/ s), the solar wind flow (~430 km/s) is not exactly parallel to the Sun-Venus line. The data in Venus solar orbital (VSO) coordinates, where the X axis points toward the Sun from Venus, the Y axis is chosen to be opposite to the Venusian orbital motion, and the Z axis is perpendicular to the ecliptic plane and toward north, are transformed to an aberrated VSO coordinate system (VSO α ), rotated around the Z axis with an average aberration angle of 5 and the X α axis is antiparallel to the solar wind flow. To examine the properties of fluctuations such as the wave intensity, ellipticity, polarization, and propagating direction, the spectral analysis method [e.g., McPherron et al., 1972; Means, 1972; Samson, 1973; Arthur et al., 1976; Song and Russell, 1999] is used in this study. First, the background magnetic field is determined as the low-pass-filtered data with a cutoff frequency of 0.01 Hz. Then, the magnetic field data can be converted into a mean field (MF) coordinate system. The MF coordinate system has its Z MF axis along the background magnetic field, and its Y MF axis is chosen to be perpendicular to the plane defined by the background magnetic field and the aberrated X (X α ) axis. Then the X MF axis is defined to complete the right-handed Cartesian coordinate system. The transverse component and compressional component of the fluctuations are distinguishable under the new MF coordinate system. To examine the fluctuations, the magnetic field data are continuously scanned in a 100 s window with an increment of 10 s. The magnetic field fluctuations near Venus are a mixture of multiple wave modes, and there are no clear principal frequencies. In this study, we present a statistical study of low-frequency magnetic field fluctuations near Venus, which is defined by the fluctuations near or below the proton cyclotron frequency [Espley et al., 2004]. The statistical analysis in this study is performed in the frequency range of 30 to 300 MHz based on the width of the observation window and the resolution of the data. The lower limit of the frequency range is determined by the width of the sliding window (100 s), which is set long enough to observe fluctuations and short enough to assume that the observation is in situ. The upper limit of the frequency range is determined by the resolution of magnetic field data (1 s) and corresponds to the typical proton cyclotron frequency in the Venusian magnetosheath. Hence, the frequency range covers all of the observable low-frequency fluctuations near Venus. As introduced by Song and Russell [1999], we can obtain the power spectral density matrix for the selected frequency range in each window as P ij ¼< B i ðωþb j ðωþ >, where i and j are the three components of the magnetic field in the MF system (i,j = x,y,z), and B(ω) is the Fourier transform of B(t). Then, the transverse power (P ) can be represented by P xx and P yy, and P zz corresponds to the compressional power (P ). Then, the principal axis analysis can be performed to find the minimum and maximum variance directions. In particular, the diagonalization of the real part of the power spectral matrix provides three eigenvectors (ξ 1, ξ 2, and ξ 3 ) and three eigenvalues (λ 1, λ 2, and λ 3 ) for the maximum, intermediate, and minimum variance directions. The propa- Table 1. The Data Sets Used in This Study to Represent Three Typical Solar Activity Periods gation direction of a wave can be Solar Activity Period Orbits Sunspot Number assumed to be the direction of the Low Jun 2008 to Jun minimum variance. Also, the spectral Moderate Aug 2010 to Jul matrix can be transformed into the High Sep 2013 to Sep principal axis system by the matrix XIAO ET AL. FLUCTUATIONS NEAR VENUS IN SOLAR CYCLE 8411

4 Figure 2. Spatial distributions of the observational coverage under (a) low (sunspot number ~ 3.2), (b) moderate (sunspot number ~ 5.1), and (c) high (sunspot number ~ 109.9) solar activity conditions. The horizontal axis (X α ) represents the distance from the center of Venus along the solar wind flow, and the vertical axis indicates the distance from the solar wind flow ((Y α 2 + Zα 2 ) 1/2 ). The Sun is to the left. The bin size is RV. The black solid and dashed lines indicate the positions of the bow shock and ion composition boundary [Martinecz et al., 2009], respectively. of the three eigenvectors T as P 0 = T 1 PT. After that, the polarization parameters can be calculated easily through the new matrix P 0 [Fowler et al., 1967]. It is important to note that the method will be invalid if the minimum and intermediate eigenvalues are very close. In this work, the cases with λ 2 /λ 3 < 2 will be ignored in the statistical analysis, following a prior work of Espley et al. [2004]. 3. Results To investigate the solar cycle dependence of the magnetic field fluctuations near Venus, the data during three typical periods under different solar activity conditions obtained by Venus Express are chosen. Figure 2 shows the observational coverage during different solar activity periods with bin size R V (R V is one Venus radius ~ 6052 km, and the figure format is used in all spatial distribution figures throughout this paper). The color indicates the number of observational cases in each bin. In the cylindrical coordinates, the horizontal axis denotes the distance from the center of Venus along the solar wind flow, while the vertical axis denotes the distance from the solar wind flow. The black solid line and dashed line indicate the positions of the bow shock and ion composition boundary, respectively, based on the models from Martinecz et al. [2009] observed near solar minimum. The clear orbit variation of Venus Express is shown in Figure 2. The data cover the regions of magnetosheath and magnetotail. Thereby, the solar cycle dependence of the lowfrequency magnetic field fluctuations in these regions can be discovered. Figure 3 shows the magnetic field strength distributions under different solar activity conditions in the cylindrical coordinates. The bin sizes of all distributions of fluctuation properties are the same as Figure 2, and the data are binned through the median values, which can be able to remove the outliers resulting from extreme cases like ICMEs. The magnetic barrier characterized by a strong magnetic field in the dayside Figure 3. Spatial distributions of the magnetic field strength under different solar activity conditions. The format is the same as in Figure 2. XIAO ET AL. FLUCTUATIONS NEAR VENUS IN SOLAR CYCLE 8412

5 Figure 4. Spatial distributions of the relative total power of the fluctuations (P T / B 2 ) under different solar activity conditions. The format is the same as in Figure 2. magnetosphere [e.g., Zhang et al., 1991] and the induced magnetotail in the nightside magnetosphere are shown clearly. Figure 3 exhibits a solar cycle-dependent IMF near Venus, as reported by Luhmann et al. [1993], and also the solar cycle-dependent magnetic barrier. Compared to the solar minimum model, indicated by black lines, the bow shock shows farther away from Venus during solar maximum. Also, it is obvious that the induced magnetotail covers a larger region under high solar activity, which has been reported by some prior papers [e.g., Xiao et al., 2016] Wave Intensity Figure 4 shows the spatial distributions of the wave intensity under different solar activity conditions. As described above, the total power (P T ) is the sum of the transverse power (P ) and the compressional power (P ). In consideration of the strength of background magnetic field, the wave intensity is indicated by the relative wave power scaled by the square of background magnetic field (P T / B 2 ). As shown in Figure 4, with the solar activity increasing, the fluctuations in the magnetosheath region become weaker. However, the tail region is still quiet compared with the magnetosheath during the whole solar cycle Transverse and Compressional Ratio Figure 5 shows the spatial distributions of the transverse and compressional ratio under the different solar activity conditions. Based on the power spectral density matrix, the transverse and compressional ratio is defined by (P P )/P T. This parameter indicates whether the transverse or compressional component of fluctuations is dominant. A positive (negative) ratio means that the transverse power is higher (lower) than the compressional power. The range of this ratio is from 1 to 1, and a ratio of 1 (1) indicates that this fluctuation is purely compressional (transverse). As shown in Figure 5, the fluctuations near Venus have a higher transverse power than the compressional power. Especially in the region of nightside magnetosheath, the Figure 5. Spatial distributions of the transverse and compressional ratio of fluctuations (P P ǁ )/P T under different solar activity conditions. The format is the same as in Figure 2. XIAO ET AL. FLUCTUATIONS NEAR VENUS IN SOLAR CYCLE 8413

6 Figure 6. Spatial distributions of the ellipticity of fluctuations under different solar activity conditions. The format is the same as in Figure 2. The majority of the values fall into the range from 0.3 to 0.7, which is chosen to set the color bar. ratio is over 0.5 and increases with the solar activity increasing. That means the transverse fluctuation is dominant in the nightside magnetosheath region, and the proportion of the dominant transverse fluctuations tends to be larger during high solar activity. Meanwhile, the transverse and compressional ratio shows a decrease in the tail region with the solar activity increasing. This means that the dominant transverse component of fluctuations becomes weaker during high solar activity in the tail region Ellipticity The ellipticity of fluctuations is defined by the ratio of the minor and major axes of the polarization ellipse for qffiffiffiffiffiffiffi the plane wave and can be calculated from the eigenvalues as [Song and Russell, 1999]. The value of ellipticity is between 0 and 1. It is equal to 0 for the linear polarized fluctuations and 1 for the circle polarized fluctuations. The spatial distributions of ellipticity under the different solar activity conditions are displayed in Figure 6. The fluctuations in the tail region are moderately polarized. Compared with the tail region, the fluctuations in the magnetosheath have a larger ellipticity, which means that there are more circle polarized fluctuations in the magnetosheath. With the solar activity increasing, the ellipticity of fluctuations in the magnetosheath shows a decrease. This means that relatively more linear polarized fluctuations occur in the magnetosheath during high solar activity Degree of Polarization A fluctuation can be divided into a completely polarized component and an unpolarized component. The degree of polarization is chosen to describe the proportion of a fluctuation that is polarized, defined by the fraction of the total intensity contributed by the completely polarized component. The degree of λ 2-λ 3 λ 1-λ 3 Figure 7. Spatial distributions of the degree of polarization of fluctuations under different solar activity conditions. The format is the same as in Figure 2. The majority of the values fall into the range from 0.3 to 0.8, which is chosen to set the color bar. XIAO ET AL. FLUCTUATIONS NEAR VENUS IN SOLAR CYCLE 8414

7 Figure 8. Spatial distributions of the angles between the wave vector directions (k) and the background magnetic field (B BG ) under different solar activity conditions. The format is the same as in Figure 2. polarization has its range from 0 to 1. A degree of 1 means that the fluctuation is a monochromatic signal, completely polarized signal with all the properties of the fluctuation independent of time. A degree of 0 means that the fluctuation is incoherent noise, completely unpolarized signal with no coherence between its components. With the method reported by Fowler et al. [1967], the degree of polarization is calculated based on the coherency matrix of fluctuations, which is decomposed into polarized and unpolarized portions. The spatial distributions of the degree of polarization are shown in Figure 7 under the different solar activity conditions. Compared with the tail region, the fluctuations in the magnetosheath have a lower degree of polarization, which means that more unpolarized fluctuations are generated in the magnetosheath. With the solar activity increasing, the polarized component of fluctuations in the magnetosheath shows a slight increase Wave Vector Direction The wave vector direction is an important property of fluctuations. As described above, the wave vector direction can be assumed to be the direction of minimum variance. To be noted, the propagation direction can be better determined with a higher ratio of the intermediate to the minimum eigenvalue (λ 2 /λ 3 )[Song and Russell, 1999]. Considering both the volume of data and the validity of the results, we only choose the cases with λ 2 /λ 3 > 2, as Espley et al. [2004] used in their Martian plasma environment analysis. Figure 8 shows the spatial distributions of the angle between the wave vector direction (k) and the background magnetic field under the different solar activity conditions. The fluctuations in the dayside magnetosheath have almost perpendicular propagation. And with the solar activity increasing, more and more quasi-perpendicular propagating waves are generated in that region, also in the tail region. However, the fluctuations in the nightside magnetosheath have mainly quasi-parallel propagation, and more and more quasi-parallel propagating waves are generated with solar activity increasing. Figure 9. Histograms of cone angles, which are the angles between the IMF and the X α axis, under different solar activity conditions. XIAO ET AL. FLUCTUATIONS NEAR VENUS IN SOLAR CYCLE 8415

8 4. Discussion and Conclusion Venus is considered to be a sister planet of Earth; nevertheless, it has no intrinsic magnetic field, and the solar wind interacts with the Venusian ionosphere directly. The induced magnetosphere of Venus is formed by the IMF draped around the ionosphere. Since the Venusian ionosphere is mainly modulated by the solar EUV radiation, the solar cycle variation of the EUV flux plays an important part in the solar wind interaction with Venus [e.g., Bauer and Taylor, 1981; Elphic et al., 1984; Kar et al., 1986]. Shan et al. [2016] reported that the backstreaming ion in the Venusian foreshock is also an important mechanism of the generation of fluctuations. They found that the transverse component dominates fluctuations in the upstream of Venus, most fluctuations in the upstream solar wind display nearly circular or slightly elliptical polarization, and the propagation angles are mainly less than 30. Similar statistical properties of upstream fluctuations are also shown in Figures 5, 6, and 8. The conditions in the upstream solar wind are also solar cycle dependent. As Delva et al. [2015] reported, during near solar maximum, the higher ratio of planetary to solar wind proton density, higher EUV (which increases the ionization in the Venus exosphere), and lower solar wind proton density lead to more proton cyclotron waves at Venus. Du et al. [2010] found that low-frequency magnetic field fluctuations near Venus show different properties under the different IMF orientations. Figure 9 shows the histograms of cone angles, defined as the angle between the IMF and the X α axis, during three typical periods of the solar cycle. The IMF of an orbit is represented by the average value during the interval between 5 min before and after the apoapsis, which is always located in solar wind. As shown in Figure 9, we found that the distribution of cone angles has no obvious variations coincided with solar activity. Based on the distributions, the IMF orientations cannot be an important mechanism of the solar cycle dependence of the fluctuation properties. In addition, some prior works statistically studied the space weather effects on the IMF [e.g., Vech et al., 2015], and they found that the cone angle becomes larger during ICMEs. The occurrence rate of ICMEs is solar cycle dependent, and ICMEs would have an effect on the IMF and also the fluctuations near Venus. However, these outliers resulting from ICMEs are effectively removed because the data are binned through the median. Therefore, the variation of ICMEs also cannot be a mechanism of the solar cycle dependence of the fluctuation properties in this work. As described above, the sources of fluctuations in the Venusian magnetosheath and magnetotail, including the convection from the upstream solar wind [e.g., Shan et al., 2016] and the pickup ions from the exosphere [e.g., Russell et al., 2006], are solar cycle dependent. Therefore, we can infer that the distributions of fluctuation properties are solar cycle dependent. Indeed, almost all aspects of the Venus plasma environment are controlled by the solar activity. Of course, a separate study specifically considering the EUV intensity at Venus would be needed to clearly establish a dependence on EUV, which is not the focus of the present paper. In this work, the magnetic field data have been examined during three typical solar activity periods, as shown in Table 1, to investigate the low-frequency fluctuations near Venus. Then we are able to examine the solar cycle-dependent properties of the fluctuations near Venus. The wave intensity, transverse and compressional ratio, ellipticity, degree of polarization, and wave vector direction of the magnetic fluctuations were calculated in the frequency range of 30 to 300 MHz. Then the spatial distributions of these properties were given under different solar activity conditions, and a comparative study was performed. Our results show that the magnetic field is still quiet during the whole solar cycle in the tail region compared to the other regions. In Figures 4b and 4c, we can find clear red regions of high relative wave intensity in the dayside very low altitude region. The altitude of the ionosphere at solar maximum (~900 km at the terminator [Zhang et al., 1991]) is significantly higher than that at solar minimum (~250 km at the terminator [Zhang et al., 1990]). The orbit of Venus Express [Titov et al., 2006] has a periapsis altitude of 250 to 350 km at 80 north latitude during the first few years and then lower. Thereby, the spacecraft enters the ionosphere and stays there for a much longer period at solar maximum. This high relative wave intensity region may develop because a larger number of data in the ionosphere, with strong fluctuations and relatively weaker magnetic fields (Figure 3), are obtained during higher solar activity periods. As Figure 4 shows, with the solar activity increasing, the wave intensity becomes weaker in the magnetosheath. In Figure 5, the transverse and compressional ratio shows an increase in the magnetosheath and a decrease in the magnetotail. This means that the transverse component of fluctuations becomes stronger in the magnetosheath region and weaker in the tail region. Figure 6 shows that the ellipticity decreases with the solar activity increasing in the magnetosheath. That means that more linear polarized fluctuations are XIAO ET AL. FLUCTUATIONS NEAR VENUS IN SOLAR CYCLE 8416

9 generated. As shown in Figure 7, the degree of polarization in the magnetosheath region slightly increases with the solar activity increasing, which means that the unpolarized component of fluctuations decreases. And the variation of the distributions of angle between the wave vector direction and the background magnetic field (see Figure 8) indicates that the dominant parallel propagation component of fluctuations in the nightside magnetosheath increases and more perpendicular propagation components are generated in the tail region, with the solar activity increasing. This work aims to present the solar cycle dependence of the properties of fluctuations near Venus. Some prior works [Guicking et al., 2010; Du et al., 2010] have reported similar distributions of fluctuation properties under low solar activity at Venus. Espley et al. [2004] reported a similar work at Mars under moderate solar activity. Their results show that the spatial distributions of the fluctuations properties at Mars are similar to the ones at Venus, which has been mentioned by Guicking et al. [2010]. By using both magnetic field and ion moments data, Ruhunusiri et al. [2015] further confirm that the Alfvén waves are the main wave mode in the Martian magnetosheath, fast waves are found frequently near the bow shock and the magnetic pileup boundary, and mirror and slow waves occur much less frequently. The increase of transverse and compressional ratio, the decrease of ellipticity, and the decrease of the propagation angle of fluctuations in the magnetosheath with increasing solar activity can be interpreted as an increase of the occurrence rate of the Alfvén waves with increasing solar activity. Based on our figures, the spatial distributions of fluctuation properties show some variations during solar cycle. The investigation of the mechanisms leading to this solar cycle dependence is beyond the scope of the paper and is left to future work. The statistical results suggest that the transfer of momentum and energy in the plasma environment near Venus can be affected by solar activity and the transfer process would have some variations during solar cycle. Acknowledgments This work in China was supported by NSFC grant and supported by the Science and Technology Development Fund of Macao SAR (008/ 2016/A1 and 039/2013/A2). Venus Express magnetic field data are available in the ESA s Planetary Science Archive (ftp://psa.esac.esa.int/pub/mirror/venus-express/), and sunspot data are obtained from the World Data Center SILSO ( References Arthur, C. W., R. L. McPherron, and J. D. Means (1976), A comparative study of three techniques for using the spectral matrix in wave analysis, Radio Sci., 11, , doi: /rs011i010p Bauer, S. J., and H. A. 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