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GEOPHYSICAL RESEARCH LETTERS, VOL. 35, L10106, doi:10.1029/2008GL033793, 2008

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Characteristic size and shape of the mirror mode structures in the solar wind at 0.72 AU T. L. Zhang,1,2 C. T. Russell,3 W. Baumjohann,1 L. K. Jian,3 M. A. Balikhin,4 J. B. Cao,2 C. Wang,2 X. Blanco-Cano,5 K.-H. Glassmeier,6 W. Zambelli,1 M. Volwerk,1 M. Delva,1 and Z. Vo¨ro¨s7 Received 27 February 2008; revised 9 April 2008; accepted 24 April 2008; published 29 May 2008.

[1] We investigate the structure of mirror modes in the solar wind at 0.72 AU using Venus Express magnetic field measurements. The mirror mode structure is identified as the presence of magnetic depression or magnetic ‘‘holes’’ in the solar wind with little or no directional change across them. We determine the characteristic size and shape of these structures by examining their durations as a function of the orientation of the magnetic field to the solar wind flow. The mirror mode structure is best fitted with an ellipsoid of revolution, and the resultant shape of the mirror mode structure is a prolate spheroid, or in other words, a rotational ellipsoid. We introduce two parameters, namely the width across the field and the eccentricity to give a full description of the size and shape of the structures. We find that the mirror mode structures in the solar wind are twodimensional and are more elongated along the magnetic field direction. Citation: Zhang, T. L., et al. (2008), Characteristic size and shape of the mirror mode structures in the solar wind at 0.72 AU, Geophys. Res. Lett., 35, L10106, doi:10.1029/2008GL033793.

Winterhalter et al. [1994] were the first to relate mirror mode structures to the linear magnetic hole in the solar wind. [3] Several past studies have investigated mirror mode structures in the solar wind at various heliocentric distances. For example, Winterhalter et al. [1994] examined the mirror mode structures between 1 AU and 5.4 AU, Sperveslage et al. [2000] studied magnetic holes between 0.3 AU and 17 AU. More recently, Stevens and Kasper [2007] investigated magnetic holes at 1 AU in detail using both magnetic field and plasma data. However, all previous studies define the mirror mode structure size by a single dimension only. In fact, one might expect mirror mode structures to have two characteristic lengths, one along the magnetic field and one cross the magnetic field. In order to study the evolution of the mirror mode structure in the solar wind, it is important to determine its characteristic lengths. In this paper, we make the first attempt to determine the characteristic size and shape of the mirror mode structure at 0.72 AU.

2. Observations 1. Introduction [2] Mirror mode waves occur in many space plasma regimes from the solar wind [Winterhalter et al., 1994], to cometary cones [Russell et al., 1987], planetary magnetosheath [Tsurutani et al., 1982; Baumjohann et al., 1999] and mass loading magnetospheres [Russell et al., 1998, 2006]. In the solar wind, these waves are found to be a type of the magnetic holes. In general, magnetic holes in the solar wind are isolated intervals with depressed field magnitude during a short duration of seconds or 10s seconds [Turner et al., 1977]. When there is no or little change in the magnetic field direction across the hole, it is called linear magnetic hole. In their comprehensive study of magnetic holes, 1 Space Research Institute, Austrian Academy of Sciences, Graz, Austria. 2 State Key Laboratory of Space Weather, Chinese Academy of Sciences, Beijing, China. 3 Institute of Geophysics and Planetary Physics, University of California, Los Angeles, California, USA. 4 Automatic Control and Systems Engineering, University of Sheffield, Sheffield, UK. 5 Institute of Geophysics, UNAM, Ciudad Universitaria, Coyoacan, Mexico D.F., Mexico. 6 Institut fu¨r Geophysik und Extraterrestrische Physik, Technical University Braunschweig, Braunschweig, Germany. 7 Institute for Astro- and Particle Physics, University of Innsbruck, Innsbruck, Austria.

Copyright 2008 by the American Geophysical Union. 0094-8276/08/2008GL033793$05.00

[4] Venus Express, a planetary mission to Venus, spends its majority orbital time, typically 20 to 22 hours per day, in the solar wind due to the small size of the Venus induced magnetosphere. Thus it provides an excellent data set to study the magnetic holes in the solar wind at 0.72 AU. In this study we examine the 1 Hz magnetic field measurement made from May 2006 to December 2006 by the Venus Express magnetometer [Zhang et al., 2006]. In total, 216 days of data are available for this study. [5] To identify mirror mode structures, the magnetic field data are continuously scanned one data point at a time with a ±150 s interval on either side of that point. If this point is the minimum for this 300 s interval, then we designate it as the local Bmin and calculate the average B and standard deviation d for this interval. The directional change angle w across the feature is calculated from the starting and ending vectors of the magnetic hole defined by the nearest vectors to the edge of the hole with a magnitude larger than B – d. In this study, we use criteria Bmin/B < 0.75 and w < 15° to define the linear magnetic holes. We note that these conditions are slightly more relaxed than the conditions used in previous studies [Winterhalter et al., 1994; Sperveslage et al., 2000]. The mirror mode structure in the solar wind might occur either as an isolated magnetic hole or train of closed spaced magnetic holes. The train of holes is defined if there is at least a second comparable magnetic hole in the 300 s interval. We further expand the initial 300 s window and search all magnetic holes with spacing less than 150 s

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Figure 1. A typical example of the mirror mode structure in the solar wind characterized by the depressed magnetic field magnitude with little field directional change across the depression region. In addition, all field components shall approach zero.

Figure 3. Magnetic hole duration as a function of the orientation of the magnetic field to the solar wind flow represented by ratio of Bx to B. Small crosses are the 791 events selected for this study. Diamonds are the medians for each 0.1 Bx/B bin. The depicted curve is the best fitted elliptical function of y2 = 142 x2 + 29.

and all these holes will be counted as the same train of magnetic holes. In this study, a train of magnetic holes will be counted as a single event and will be represented only by the largest hole in the group. Finally, all automatically selected events are subjected to visual inspection. We select only unambiguous events with relatively steady ambient field background and we require all field components to approach zero at the field magnitude minimum as illustrated

in Figure 1. More examples of magnetic hole events are shown in Figure 2. [6] Out of 216 days of data used in this study, we obtain 791 events. This gives occurrence rates of 4.2 per day when taking into account the typical 3 hour data gap per day when the spacecraft spends is inside Venus magnetosheath. While the obtained occurrence rate is much higher than given in earlier observations [e.g., Sperveslage et al., 2000],

Figure 2. More examples of the mirror mode structures in the solar wind. 2 of 4

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Figure 4. Dependence of the normalized lengths on the orientation of the magnetic field to the solar wind flow. The depicted curve is the best fitted elliptical function of y2 = 9793 x2 + 1733. we note that we have taken a slightly higher up limit of 0.75 for Bmin/B instead of 0.5 as used in previous studies. In fact, if we take the Bmin/B = 0.5 as the upper limit in selecting event, we would have 311 events and an occurrence rate of 1.6 per day which is similar to the rate obtained by Sperveslage et al. [2000]. However, as indicated by Figure 2 (top), an upper limit of Bmin/B = 0.5 would exclude this event which have the same mirror mode structure as others.

3. Geometry of the Mirror Mode Structures [7] Mirror mode structures embedded in solar wind are expected to be stationary in the frame of solar wind [e.g., Treumann et al., 2004]. As the solar wind sweeps by spacecraft with a typical velocity of 400 km/s, the observational duration of the magnetic hole gives a measurement of the length of the mirror mode structure. The length in kilometres, or its normalized counterpart such as length in gyro radii, has been used to characterize the size of the magnetic holes in previous studies [e.g., Sperveslage et al., 2000]. However, as we mentioned above, we expect the structure to be field-aligned and have different scale length along and across the magnetic field. Since the solar wind magnetic field directions are highly variable and moreover the average field direction varies with heliocentric distance, one has to consider the field-control in studying the evolution of the mirror mode structure at various heliocentric distances. [8] We determine the characteristic size and shape of the mirror mode structures in the solar wind by examining their durations as a function of the orientation of the magnetic field to the solar wind flow. Figure 3 shows the distribution of the magnetic hole duration as a function of BX/B for both isolated and multiple holes. Here B is the average field magnitude for the event interval and BX is the X component (along the Venus-Sun direction, i.e., along the solar wind flow) of the magnetic field at the beginning of the hole. Small crosses are the individual events and diamonds are the medians duration for each the

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0.1 BX/B bins. To estimate the asymptotic durations along the field (BX/B = 1) and cross the field (BX/B = 0), we find the best fit curve to the median durations. The depicted curve is an ellipse fit to the medians. It is evident that the mirror mode structure is highly elongated. The obtained mirror mode structure at 0.72 AU has a typical duration of 13 s along the field and about 5 s across the field. [9] For each individual event, the mirror mode structure length along the solar wind flow can be obtained by assuming a typical solar wind velocity of 400 km/s. In order to take into account of the magnetic field effect on the size of the mirror mode structure, we normalize the length along the solar wind flow for each individual event by the solar wind proton gyro radius. Here we calculate the proton gyro radius by assuming a typical solar wind temperature of 100000 K at solar minimum. Figure 4 shows the distribution of the normalized mirror mode structure lengths as a function of BX/B. The best-fit elliptical curve gives a major axis length of this spheroid is 107 rp and the minor axis length is 42 rp. Thus the shape of the mirror mode structure is best represented by a prolate spheroid, a rotational ellipsoid having two axes of equal length across the equatorial plane. The ellipticity, or eccentricity, of the structure is 0.92. The elongation ratio of the major axis and minor axis of this rotational ellipsoid is 2.55.

4. Concluding Remarks [10] In this study we examine the characteristic size and shape of the mirror mode structures in the solar wind at 0.72 AU using Venus Express magnetic field measurements. We found the mirror mode structure is of a shape of a rotational ellipsoid elongated along the interplanetary magnetic field line. Herein we introduce two parameters, namely the width across the magnetic field and the eccentricity to characterize the geometry of the mirror mode structure in the solar wind. The width perpendicular to the field is found to be 47 rp and the structure is elongated along the magnetic field with an eccentricity of 0.92. [11] Our observed mirror mode structure occurrence rate is much higher than earlier studies. This increased rate is at least partly due to our relaxing the upper limit of Bmin/B to 0.75 in event selection. However, as shown in Figure 2, event in the 0.5 < Bmin/B < 0.75 range behaves the same as event in Bmin/B < 0.5 range. Thus it is justified to increase the up limit of Bmin/B in event selection. Furthermore, it is reasonable to believe that the mirror mode structure exist beyond our limitation of Bmin/B < 0.75 and thus the mirror mode occurrence rate should be even higher than what we obtained here. However, in studying the mirror mode waves, we are more interested in the relative value of the occurrence rate than the absolute one. In other words, we are interested in comparing the occurrence rate at different heliocentric distances and different times of the solar rotation or phase of the solar cycle to get the underlying physics of the mirror-mode evolution. Finally, we note that the occurrence of the mirror mode structures spread apparently equally between 0 to 1 of BX/B (Figures 3 and 4). However, taking into account the IMF Parker’s spiral angle of 37°, or equivalent to about 0.8 of BX/B, at 0.72 AU, it seems that the mirror modes occurs preferably when the IMF is oriented at an extremely large angle to the solar wind

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flow. Thus further study on the correlation of occurrence rate on the solar wind condition is needed, but it is beyond the scope of this paper. [12] Acknowledgments. The work at UCLA was supported by the National Aeronautics and Space Administration under research grant NNG06GC62G. The work in China was supported by NNSFC project 40628003 and by 973 Program 2006CB806305. This work in Austria was partially supported by the Austrian Wissenschaftsfonds under grant P20131-N16.

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