In this study we primarily utilize data from the MESSENGER Magnetometer instrument [Anderson et al., 2007] to identify and classify KH waves at the magnetopause. Following MOI, MESSENGER has been in an eccentric orbit around the planet, with an 82.5° inclination to the orbital plane, an apoapsis of ∼7 RM from the planet center, and a periapsis of ∼1.1 RM. The apoapsis, initially located at ∼15:00 magnetic local time (MLT), progresses during the mission and makes a full revolution around Mercury's equatorial plane over the Mercury year. After an initial verification period, the Magnetometer instrument became fully operational on 22 March 2011. To avoid introducing any bias in the statistics connected to the spacecraft trajectory, we have limited our analysis to one complete Mercury year (88 Earth days), starting on 23 March and ending on 20 June 2011.
 On the basis of terrestrial KH wave signatures, together with the KH wave observations during M3, we anticipate two dominant features in the wave patterns: sawtooth wave oscillations and/or periodic inbound and outbound magnetopause crossings. The sawtooth-like wave pattern, which is frequently observed in both the plasma and magnetic field data at Earth's magnetopause [e.g., Fairfield et al., 2007; Hasegawa et al., 2009], has been interpreted as a gradual transition through a mixing region on the leading edge of a rolled up KH vortex, followed by an abrupt transition at the stable trailing edge [Fairfield et al., 2007]. Large-scale boundary oscillations due to a KH wave train in the linear stage of the instability are more difficult to separate from non-KH phenomena, such as boundary motions due to variations in solar wind pressure. In order to adequately determine the KH nature of these types of waves, a full minimum variance analysis of a series of consecutive boundary layer crossings is required [e.g., Fairfield et al., 2000].
 During the 23 March to 20 June 2011 time period, we found evidence for six large-amplitude sawtooth-shaped wave trains, all of them in the postnoon and evening sectors of the magnetosphere. The spacecraft trajectory for each wave observation is given in Figure 1. The details of two examples are given in sections 3.1 and 3.2, and a statistical study of all six events is given in section 3.3.
Figure 1. Overview of MESSENGER's trajectory for the observed wave events. The trajectories in Mercury solar magnetospheric (MSM) coordinates for the full duration of the wave observations are shown by black lines, and the spacecraft position at the end of each event is given by a colored circle. The dashed lines show approximate locations of the magnetopause and the bow shock in (top left) the Z = 0, (top right) X = 0, and (bottom left) Y = 0 planes. At bottom right, events are given in the X-R plane, where R = √(Z2 + Y2) is the radial distance from the X axis. Data from MESSENGER's third Mercury flyby are included on all panels for comparison.
Download figure to PowerPoint
3.1. Example 1: 15 May 2011
 On 15 May 2011, MESSENGER's periapsis was located on the postnoon side of the planet, inside the dayside magnetosphere, at approximately 14:50 MLT, as shown in Figure 2. An overview of the magnetic field measurements is given in Figure 3. The spacecraft approached the equatorial plane from the north. Soon after the spacecraft's closest approach (CA) to the planet at 09:11:50 UTC, the Magnetometer recorded an extended interval of strong oscillations in the magnetic field, B, with a periodicity of 30–40 s. The amplitude of the perturbations was at its strongest nearest CA, starting at 45° magnetic latitude, approximately 1 RM from the dipole center, with a peak-to-peak value of ∼20 nT, and then decreased smoothly as MESSENGER traveled toward the postnoon side of the magnetosphere. The oscillations died out for an interval of ∼2 min in the middle of the dayside magnetosphere, ∼09:20:30–09:22:30 UTC, although an approximate wave pattern could still be discerned in By and Bz during this period.
Figure 2. Overview of the Kelvin-Helmholtz (KH) wave observation on 15 May 2011. The panels show, from top to bottom, the X, Y, and Z components in MSM coordinates and the absolute magnitude of the magnetic field. The vertical dashed line marks the approximate position of the magnetopause (MP) crossing.
Download figure to PowerPoint
Figure 3. A closer view of the KH waves of 15 May 2011. The first and second panels show the FIPS spectrogram of energy E per charge Q for the measured proton flux and the sodium ion count rate, respectively. The third–sixth panels follow the same format as in Figure 2.
Download figure to PowerPoint
 As the spacecraft approached the magnetopause, the oscillations reappeared, first as small-amplitude fluctuations in all components of the magnetic field, and soon thereafter as large-amplitude oscillations with variations up to nearly 40 nT peak to peak in the Bx component together with a sawtooth-like wave pattern in By. All wave activity stopped about 1 min before the magnetopause crossing (encountered at ∼09:31:20) at the same time that the plasma count rate increased toward magnetosheath values. No further wave activity was seen after that time. The magnetic field remained strongly northward throughout the magnetosheath and in the solar wind for more than an hour after the wave encounters.
 A close-up view of the magnetic field signatures of the KH waves is shown in Figure 3, together with supporting plasma data from MESSENGER's Fast Imaging Plasma Spectrometer (FIPS) [Andrews et al., 2007]. The pattern indicates that large, nonlinear (plausibly rolled up) plasma waves were present inside the dayside magnetopause, penetrating on the order of 0.25 RM (∼600 km) into the magnetosphere, or almost a third of the distance to the planetary surface. The spatial extent of the waves was thus similar to that for the KH event seen during the third flyby, but the full spatial structure is in this case difficult to determine as the spacecraft trajectory was not confined to the planet's equatorial plane. The plasma measurements also showed clear periodic signatures of magnetosheath plasma at each wave encounter. The repeated pattern of the particle observations inside the magnetopause indicates that magnetosheath plasma was already being merged into the magnetosphere by KH waves in the postnoon sector of the magnetopause. Although no magnetic field perturbations are visible on the magnetosheath side of the magnetopause, periodic variations in the proton count rate by up to a factor of 2 are present in the plasma data. There is also a periodic pattern in the density of sodium ions that is consistent with the magnetic field oscillations. Notable Na+ count rates are visible throughout most of the boundary layer when the plasma and magnetic field are magnetospheric, but no clear signature of Na+ is seen when the magnetosheath plasma is present. These observations imply that the increased H+ count rates are actual encounters with magnetosheath plasma, and not the signature of compressional waves propagating inward from the KH-unstable boundary [e.g., Pu and Kivelson, 1983a, 1983b].
 The absolute magnitude of the field showed a two peak feature similar to that reported by Sundberg et al.  and was particularly visible during the time period 09:26–09:28. This pattern is indicative of the increase in the magnetic pressure at the edge of a vortex that is required to balance the centrifugal force acting on the plasma [Miura, 1997; Hasegawa et al., 2009; Nishino et al., 2011] and can be interpreted as a sign of the rolled up nature of the waves.
 A closer analysis of the wave pattern in the low-altitude region (09:14:00–09:17:40) shows an extremely stable wave pattern, primarily transverse albeit with a compressional component. The pulsations in minimum variance coordinates [Sonnerup and Scheible, 1998] and the associated magnetic hodogram are given in Figures 4 and 5, respectively. We have here applied a quadratic detrending of the data in order to remove the influence of the overall changes in the magnetic field magnitude and direction over the time period analyzed. The waves were elliptically polarized with an ellipticity of 0.6, and the approximate directions of maximum, intermediate, and minimum variance in MSM coordinates were (−0.9, 0.3, 0), (0.3, 0.8, 0.5), and (−0.2, −0.5, 0.9), respectively. The direction of minimum variance was clearly defined, with a ratio between the minimum and intermediate variance eigenvalues of 9.2, and the ratio of maximum to intermediate eigenvalue was 2.5. As the spacecraft MLT was steady at ∼15:00 throughout the observations, and the pulsation frequency was relatively constant, it is a reasonable assumption that the high- and low-latitude wave oscillations are on near-conjugate field lines. The low-altitude oscillation would thus be the signature of field-aligned waves propagating downward from the KH instability region toward the planetary surface.
Figure 4. Close-up of the low-altitude pulsations. The figure shows, from top to bottom, the maximum (B1), intermediate (B2), and minimum (B3) variance components and the absolute magnitude of the magnetic field after a quadratic detrending of the data. A 1 s smoothing filter has been applied to the data.
Download figure to PowerPoint
3.2. Example 2: 17 June 2011
 Another KH event was recorded on 17 June 2011. As shown in Figure 1, MESSENGER was in an inbound trajectory on the dusk side at around 17:00 MLT and crossed the magnetopause at ∼00:50 UTC, 1 RM north of the orbital plane. The magnetic field measurements for this event are given in Figure 6. The magnetopause transition is characterized by a change in the magnetic field properties from the high-frequency fluctuations typical of the magnetosheath to the smoother magnetospheric field components [e.g., Sundberg et al., 2011]. There is also an increase in the average X component of the field, but otherwise the field properties were continuous across the boundary.
 In contrast to the 15 May event, the main wave activity is seen on the magnetosheath side of the magnetopause (as determined from the overall magnetic field properties), where sawtooth oscillations with amplitudes close to 150 nT show clear signs of a KH wave train propagating along the magnetopause boundary. Once inside the magnetosphere, the wave properties changed to a more sinusoidal character, with smoother variations in the field. In this event, the magnetospheric wave pattern is observable deep into the magnetosphere, on the order of 0.4 RM from the magnetopause. The oscillations were visible until the spacecraft reached 57° magnetic latitude, approximately 1.13 RM from the dipole center. Although the oscillation period was relatively stable, the waves did not show the same clear wave structure as the low-altitude pulsations on 15 May. This difference is possibly a result of variability in the solar wind properties during the wave observations, as the 15 May observations showed an unusually stable northward-directed magnetic field in both the magnetosheath and the solar wind. Periodic variations in the H+ density are also visible during this wave event, but they are not as clearly correlated with the magnetic field as during the 15 May event because the wave and sampling frequencies are similar in magnitude. An increase in the proton flux is seen in the low-altitude portion of the wave pattern (∼00:55–00:59 UTC). This increase may be the signature of magnetosheath ions that have been introduced into the magnetosphere at the magnetopause through the KH waves and then consequently guided by the magnetospheric field toward lower latitudes. Verification of this inference requires a thorough analysis of the plasma data, however, and is beyond the scope of the present study.
3.3. Event Selection and Statistics
 Six large-amplitude KH wave trains were identified in the Magnetometer data over the selected time period. The events were identified on the basis of large-amplitude fluctuations (>50 nT) in the magnetic field showing that a continuous series of sawtooth waves are present at the magnetopause. A few events during which minor KH wave structures were observed but the KH wave motion was not the main source of the measured magnetic field fluctuations are not included further here. MESSENGER also measured a few consecutive inbound/outbound magnetopause crossings. Although these may be related to the KH instability (as shown by Fairfield et al.  and Otto and Fairfield ), they require a long period of continuous observations for the KH structure to be adequately determined. As we cannot ascertain that this magnetopause motion is not due to compression and expansion of the magnetosphere driven by pressure fluctuations in the solar wind, we have chosen not to include such events in the analysis.
 The details of the identified events are given in Table 1. Data from the third Mercury flyby are also included as a comparison. The spacecraft trajectory for each wave observation is shown in Figure 1.
Table 1. Characteristics of Kelvin-Helmholtz Waves Observed at Mercurya
|Date||DOY||Time Interval||MLT, h||MSH Bz||Mean Period||Maximum Amplitude|
|29 Sep 2009||272||21:27–21:29||21||Variable||17 sb||40 nT|
|15 May 2011||135||09:13–09:30||15.5||North||36 s||100 nT|
|11 Jun 2011||162||12:26–12:37||19||North||12 s||135 nT|
|12 Jun 2011||163||00:28–00:36||19||North||20 s||70 nT|
|15 Jun 2011||166||13:10–13:20||18||North||15 s||120 nT|
|17 Jun 2011||168||00:45–00:58||17||North||17 s||150 nT|
|19 Jun 2011||170||23:33–23:43||16||North||24 s||75 nT|
 Histograms of the measured wave periods are shown in Figure 7. All events show a relatively stable wave period in the approximate range 10–40 s, with a typical variation within ±10 s of their mean value (except for a few outliers in the data). The third Mercury flyby is not included here as the wave signature differs greatly from those for the other events; see the work of Boardsen et al.  and Sundberg et al.  for details. All events apart from that during were accompanied by a northward magnetic field in the magnetosheath and a relatively smooth transition in the magnetic field properties from the magnetosheath to the magnetosphere.
Figure 7. Histograms of the observed wave periods for the six events observed during MESSENGER's first Mercury year in orbit. The median and mean values of the periods for each wave event are marked by dotted and dashed-dotted lines, respectively.
Download figure to PowerPoint
 A majority of the events were observed during a time interval 8 d in length during which MESSENGER was crossing the duskside magnetopause in the 17:00–19:00 MLT section of the magnetosphere. The events that were farthest tailward were marked by sawtooth oscillations that appeared to be primarily located in the magnetosheath, but the magnetospheric field was less affected by the waves than for the dayside events.