Corresponding author: C. T. Russell, Institute of Geophysics and Planetary Physics, University of California, Los Angeles, CA 90095-1567, USA. (firstname.lastname@example.org)
 The occurrence of electrical discharges in planetary atmospheres produces high temperatures and pressures enabling chemical reactions that are not possible under local thermodynamic equilibrium conditions. On Earth, electrical discharges in clouds produce nitric oxide. Similar abundances of nitric oxide exist in the Venus atmosphere, but the existence of extensive electrical activity in its substantive cloud system is not as firmly established. To determine the strength and occurrence rate of lightning, the Venus Express mission included dual magnetometers sampling at 128 Hz to detect the electromagnetic signals produced by lightning. We report herein evidence of the apparent overflight of electrical storms by the Venus Express spacecraft. These observations reveal two types of signals reaching the spacecraft: one in the ELF band that exhibits dispersion and travels along the magnetic field, and one in the ULF band that appears to travel vertically across the magnetic field from below.
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 Venus’ extensive cloud cover and rapid atmospheric circulation, evidenced by its 4-day winds, has led to attempts to measure the electromagnetic waves and optical flashes associated with lightning on the Venera landers and orbiters [Ksanfomaliti, 1983], the Pioneer Venus Orbiter [Russell, 1991], and the Vega balloons [Sagdeev et al., 1986]. The landers observed the expected electromagnetic signals in the ELF and VLF bands, as did the Pioneer Venus Orbiter. The Vega balloons, floating in the cloud deck, did not see lightning flashes optically, but flashes were observed from above by Venera 9 orbiter's visible spectrometer [Krasnopolsky, 1980] and a terrestrial telescope [Hansell, 1995]. The Galileo spacecraft's radio wave antenna picked up emissions interpreted to be lightning [Gurnett et al., 1991], but the Cassini radio wave system did not see signals indicative of Earth-like lightning [Gurnett et al., 2001]. To help resolve the question of the existence of Venus lightning, the Venus Express (VEX) orbital mission included a fluxgate magnetometer with sufficient bandwidth to measure the waveforms’ expected low-frequency portions of electromagnetic waves associated with lightning [Zhang et al., 2006].
 It is important to determine the occurrence rate of lightning on Venus because the temperature and pressure in a lightning discharge allows chemical reactions that do not occur under local thermodynamic equilibrium conditions, such as the production of nitric oxide. The amount of nitric oxide observed spectroscopically in the Venus atmosphere is consistent with lightning energetics similar to that on Earth [Krasnopolsky, 2006].
 On Earth, lightning produces a broad range of frequencies from below the Schumann resonances, which begin at 7.8 Hz [Sentman, 1995] to the VLF range. These signals are seen in the ionosphere [Simões et al., 2011], even though the Schumann resonances are nominally a resonance in the waveguide between the conducting planet and the conducting ionosphere. The highest frequency we can resolve on VEX is 64 Hz. Thus, if the spectrum of electromagnetic waves produced by Venus lightning is similar to that of Earth's lightning, the Venus Express observations should resemble the waves in the upper ULF and lower ELF frequency range occupied by the Schumann resonances, possibly influenced by propagation in the waveguide between the planet and ionosphere. In the Venus ionosphere, the highest frequency electromagnetic wave that can propagate in the ELF band is about 700 Hz, the gyrofrequency of electrons in a 25 nT magnetic field, which is typical for the Venus ionosphere at the VEX periapsis altitude [Daniels et al., 2012]. Pioneer Venus detected electric field variations in its lowest frequency channel, 100 Hz, that were clearly electromagnetic in nature, propagating along the magnetic field, and present only when the magnetic field was significantly inclined to the horizontal. Electromagnetic waves generated in the atmosphere are refracted vertically, as they slow down on reaching the ionosphere. An inclined field allows the wave to propagate into it. These earlier results have been summarized by Russell . In this paper we wish to extend our understanding of Venus lightning using Venus Express magnetic measurements that have been cleaned with an improved technique that enables us to study a wider bandwidth than was possible in our earlier papers [Russell et al., 2007, 2008a, 2008b; Daniels et al., 2012].
2 Venus Express Measurements
 The Venus Express magnetometer is sampled at 128 Hz, which allows reconstruction of waveforms up to 64 Hz. The frequency band in which lightning-associated signals were expected contains much noise from the spacecraft, which was derived from the Mars Express spacecraft that had not carried a magnetometer. Initial studies were restricted to a narrow frequency band from 42 to 60 Hz in which these interfering signals were minimal [Russell et al., 2008a]. These limited bandwidth studies revealed the presence of occasional short bursts (hundreds of milliseconds) of electromagnetic signals that were right-hand, nearly circularly polarized, with phase fronts propagating at a small angle to the magnetic field [Russell et al., 2007]. The signals were seen only when the magnetic field dipped by ~17 or more degrees to the horizontal, allowing signals to enter the ionosphere [Russell et al., 2008b]. Studies of these short bursts of signals showed that the amplitudes of the waves were largest at low altitudes in the ionosphere where the electron density was expected to be greatest and the wave speed slowest, consistent with propagation in the whistler mode [Daniels et al., 2012]. Waves can be observed at all local times with the magnetometer, unlike with the Pioneer Venus electric field detector, whose noise level was too high in sunlight to detect signals produced by lightning during the daytime. Only in eclipse on the nightside of the planet could the signals attributed to lightning be seen on the Pioneer Venus Orbiter.
 To mitigate the effects of noise sources on VEX, the magnetometer team installed two triaxial sensors: one on the spacecraft deck and one at the end of a 1 m boom [Zhang et al., 2006]. The former magnetometer can be used to identify noise sources to be removed from the records of the outer sensor.
 Recently, we have constructed an algorithm to use the inboard sensor to detect the interfering signals and remove them from the outboard sensor, producing a relatively clean signal over the entire frequency range from 0 to 64 Hz, the Nyquist frequency. Fourier analysis is used to detect the interfering signals on the inboard sensor. If the same interference is found at the outboard sensor, it is removed using inverse transforms. Our tests of this procedure show that minimal interfering tones remain.
 Figure 1 shows 27 s of cleaned data near periapsis at 380 km near the north pole in the early afternoon. The measurements have been rotated into a radial, east, and northward coordinate system, and high-pass filtered with a corner frequency of 3 Hz. The background magnetic field not shown has an unusually large vertical component of up to 15 nT, which we presume assists the waves seen to penetrate the ionosphere over a wide frequency range on this day. The signal is occasionally dominated by low-frequency signals and at other times by higher frequency signals. The bottom trace is the filtered field strength. While at high frequencies the signals tend to be stronger in the components than in the field strength, this appears not to be the case at low frequencies. To address the spectral characteristics of the data, we examine dynamic spectra in the next section.
3 Spectral Analysis
 Very occasionally, as here, the signals we identify with possible electrical activity are present, with temporal variations, for tens of seconds. When this occurs, we can study the signal's behavior in frequency-time space in a dynamic spectrum. By examining the real and imaginary cross spectral matrices [Means, 1972], we can calculate not only the power spectral density of the transverse component of the waves (perpendicular to the background field) and the compressional power (along the background field), but also properties such as ellipticity of the oscillating magnetic field and direction of propagation of the waves’ phase fronts relative to the magnetic field, which are robust diagnostics of the wave mode and hence the source of the waves. In particular, the quadrature spectral density matrix, which consists solely of products of out-of-phase components, can be used to compare with the direction of the magnetic field to determine if the wave polarization is left-handed or right-handed [Means, 1972]. This “sign” is added to the ellipticity so that right-handed waves have positive ellipticity and left-handed waves have negative ellipticity. The quadrature spectral matrix is also used to determine the direction of propagation of the circularly polarized power. Comparisons of this direction with the minimum variance direction obtained from the eigenvalues of the in-phase variance show agreement for transversely polarized signals.
 We show such an analysis in the form of a dynamic spectrum in Figure 2, where we have calculated the transverse power spectral density in nT2/Hz from 0 to 64 Hz. This calculation is made by summing the power seen by the three orthogonal sensors and removing the compressional component of the signal. The spacecraft is at a local time of 1330, a latitude of 78°N, and an altitude of 380 km, moving southward at 8 km · s–1.
 The extended wave activity on this pass shows power in two bands, initially 0–20 Hz and 25–50 Hz, with the ELF signals dropping in frequency and amplitude with time. We will refer to the lower frequency waves as the ULF band and the higher frequency waves as the ELF band. The upper frequency band is right-hand circularly polarized and this characteristic is clearly evident even in weak signals, while the low-frequency waves are linearly polarized.
 Examination of the direction of propagation, plotted in Figure 2, shows that, while the waves in the high-frequency band are propagating along the magnetic field, the apparent directions of propagation in the low-frequency band are at large angles to the magnetic field. The mottled appearance of the low-frequency spectrum of propagation angles is consistent with the inability of the program to define a direction of propagation for a linearly polarized wave whose ellipticity is close to zero. We emphasize that the propagation vector is ill defined because of the intrinsic properties of the waves. The data have large coherence (≥ 0.5) and therefore a high signal-to-noise ratio. We note that if the source is beneath the spacecraft in the atmosphere, the large discontinuity in the index of refraction at the bottom of the ionosphere would refract the waves vertically so that they would propagate nearly perpendicular to the magnetic field. The strongest of the linear signals occur from about 0620:21 to 0620:23, suggesting this is the center of the active region, but weak lower frequency signals do persist both before and after this period. The occasional simultaneous ELF waves propagating along the magnetic field and the lower-frequency ULF waves seem to be from different source regions because the temporal behavior of the amplitudes of the two signals differs. The detection of the former waves depends on a magnetically controlled propagation path because they are propagating along the field and must be so guided at this frequency. Because at these frequencies any guided waves must be at least elliptically polarized, their direction of polarization can be determined. Similarly, the linear waves must be propagating nearly perpendicular to the field to be linearly polarized. Sources directly below the spacecraft would have the most direct access to the spacecraft and produce the strongest signals of this type.
 At late times during this event, most signals reach the spacecraft mainly by propagating along the magnetic field in a right-handed sense and the linear low-frequency waves are weak. We interpret this behavior as indicating that at the end of this period, the spacecraft was no longer near a lightning source.
 The properties of the signals observed on 15 April 2007, are as expected for the generation of electromagnetic waves in the atmosphere and the propagation of signals into the Venus ionosphere, where the magnetic field is about 25 nT and the electron density, based on earlier Pioneer Venus data, ranges from 103–104 cm–3 [Brace and Kliore, 1991]. The only electromagnetic wave that can reach the spacecraft at frequencies in the bandwidth studied here is the whistler-mode wave, whose magnetic and electric perturbations rotate around the magnetic field in the same direction as electrons rotate around the field, referred to as right-hand polarization. The whistler-mode wave can propagate at any direction to the magnetic field below the lower hybrid frequency [Stix, 1962]. In a proton-electron plasma, this frequency is close to the geometric mean of the proton and electron gyrofrequencies or about 16 Hz here. If the plasma ions were singly charged oxygen, the lower hybrid frequency would drop to about 4 Hz. The transition from omnidirectional propagation to guided propagation along the field is gradual with increasing wave frequency, with the range of forbidden, near-perpendicular propagation angles growing slowly with wave frequency. Hence, we do not expect the change in wave properties with frequency to be abrupt or precisely at the lower hybrid frequency. However, it does seem to be well-defined in this case.
 Below one-quarter of the electron gyrofrequency, the group velocity of whistler-mode waves increases with increasing frequency. This allows high frequencies to arrive before low resulting in the characteristic dispersion of terrestrial lightning-generated whistlers [Eckersley, 1935]. The Venus waves also show some hint of the dispersion expected for whistler-mode waves in the top panel of Figure 2. To illustrate this better, Figure 3 shows 8 s of dynamic spectra of the transverse power with the same analysis parameters as in Figure 2, but with twice the display rate, i.e., every 0.125 s. The expected group dispersion for whistler-mode waves with parallel propagation and frequencies well below the electron gyrofrequency is
where fce and fpe are the electron gyrofrequency and electron plasma frequencies, t and s are time and distance, f is the wave frequency and t0 is the signal generation time [Eckersley, 1935]. If we assume path lengths of 600 and 300 km, and plasma and electron gyrofrequencies of 1 MHz and 1 kHz, we get the two theoretical dispersion curves shown on top of the data in Figure 3. The figure shows that a dispersive origin for the time variations at this time is consistent with a nearby source of the waves.
 We note in passing that this central energy in this burst must extend above 64 Hz. Referring back to the middle panel in Figure 2, the ellipticity of this burst appears to drop at highest frequencies while this behavior is not observed at the highest frequencies of other bursts. The most reasonable explanation of this phenomenon is aliasing of the signals above the Nyquist frequency into the analysis band. This reverses the direction of rotation of the waves that were detected by the magnetometer above 64 Hz, but were sampled at a rate too low to reconstruct them. Pioneer Venus data, of course, detected whistler mode events at 100 Hz, so we are confident that there are signals at frequencies above the Venus Express analysis band [Russell, 1991], as this event suggests.
5 Concluding Remarks
 The cleaning of the VEX magnetic measurements over a wider bandwidth has enabled us to identify two signals that appear to be associated with electrical activity in the atmosphere. The first type is guided by the magnetic field and appears to be able to enter the ionosphere where there is a substantial vertical magnetic field. It occurs at about 20 Hz and above, to which we refer as ELF waves. The second signal occurs at lower frequencies (ULF), which need not be guided by the field and could be from activity below the spacecraft. The ULF waves may provide a more direct way of deducing the amount of electrical activity in the Venus atmosphere albeit limited to the near polar regions by VEX's periapsis location. Finally, the spectrograms do provide an indication of the expected dispersion of whistler waves, but, as expected, this dispersion is small.
 We thank the Venus Express project team for the development, cruise, orbit insertion, and operations of the spacecraft at Venus, as well as the magnetometer development group and data processing personnel at the Austrian Academy of Science, Space Research Institute in Graz, for the instrument and data delivery. The work at the University of California, Los Angeles, was supported by NASA under research grant NNX10AV296.