The Venus Express mission has completed over four years in polar orbit about Venus with periapsis altitudes as low as 180 km. On each orbit around periapsis the fluxgate magnetometer samples the magnetic field at 128 Hz. The data reveal short-lived bursts with peak-to-peak amplitudes up to 1.5 nT in the frequency range 42 to 60 Hz. These signals are whistler mode waves with burst durations of about 100 ms and Poynting vectors similar to terrestrial whistler mode signals generated by atmospheric lightning when detected in the ionosphere. We have examined the occurrence of these bursts as a function of background magnetic field strength, altitude, latitude and local time. The burst rates are highest for magnetic fields of 15–30 nT, at altitudes near 215 km, and at local times near the terminators. The characteristics of these signals are consistent with generation in the dynamic Venus atmosphere, entry into the ionosphere, propagation along the ionospheric magnetic field, and ultimately damping in the ionospheric plasma.
 The possible existence of lightning on Venus was first supported by observational data from the Venera 11, 12, 13, and 14 missions. The landers were instrumented with electromagnetic coil antennas capable of detecting ELF and VLF signals during their descent through the atmosphere and after they landed on the surface [Ksanfomaliti, 1979]. The Pioneer Venus Orbiter, operating contemporaneously, was instrumented with an electric antenna capable of detecting impulsive signals at the ELF-VLF frequencies 100 Hz, 730 Hz, 5.4 kHz and 30 kHz [Scarf et al., 1980] and a fluxgate magnetometer that allowed the direction and strength of the background field to be determined [Russell et al., 1980]. Both the electric sensor in the ionosphere and the four electromagnetic sensors in the atmosphere (below the ionosphere) saw the impulsive ELF and VLF signals that one would expect from lightning [Taylor et al., 1979; Russell et al., 1988a, 1988b, 1989, 1990; Russell, 1991; Ksanfomaliti, 1983]. These signals were attributed to lightning in the clouds at about 60 km [Russell, 1991]. They were not correlated with the locations of suspected volcanic peaks or any geographic location. Rather, these signals were correlated with local time much like terrestrial lightning [Russell et al., 1988c].
 At the end of the mission when the Pioneer Venus Orbiter penetrated the bottom of the ionosphere into the atmosphere, it saw strong impulsive signals unaffected by the effects of entry of the electromagnetic wave into the ionosphere [Strangeway et al., 1993]. The VLF measurements told a very consistent story. Regardless of whether the signals were detected in the ionosphere or the atmosphere, or whether they were seen by electric or magnetic antennas, the same impulsive signals with similar electromagnetic energy fluxes were detected.
 Venus lightning has been inferred from other measurements as well. It has been interpreted to be responsible for optical flashes seen from orbit on Venera 9 [Krasnopolsky, 1980] and from a ground-based telescope on Earth [Hansell et al., 1995]. Radio frequency signals seen on the Galileo flyby were attributed to lightning [Gurnett et al., 1991]. Moreover, Krasnopolsky [1983, 2006] has reported nitric oxide in the Venus atmosphere at levels that imply production by lightning activity comparable to that on Earth. While not everyone who has undertaken a search for lightning-associated signals has found them, there are many possible reasons for a null detection in any investigation. In the case of optical flashes, possible causes of non-detection include masking and scattering by the ever-present clouds and searches in regions where the electromagnetic detectors suggest the flash rate is low.
 The electromagnetic energy flux of the waves seen by Pioneer Venus (PVO) in the atmosphere on the orbits near the end of mission was used to calculate what the strength of the signals due to lightning would be if they were detected in the ionosphere. We note that we can calculate the wave energy flux from either the electric field or the magnetic field if we know the index of refraction or equivalently the wave speed. The electric and magnetic fields in an electromagnetic wave are related by the expression δE = VpδB, where δE and δB are the electric and magnetic fields in V/m and T, respectively, and Vp is the phase velocity in m s−1. In the Venus atmosphere, δE = cδB, where c is the speed of light. When the wave enters the ionosphere, the electrons interact with waves propagating in the whistler mode, resulting in a velocity lower than the speed of light. As a result, the magnetic field grows relative to the electric field and since the energy of the wave flux is proportional to the square of the wave amplitude, the energy is carried mainly by the magnetic component. On Pioneer Venus, that carried an electric antenna, the Poynting flux was calculated from the electric field [Russell et al., 1989]. As expected, the waves were stronger in the atmosphere [Strangeway et al., 1993]. On the Venus Express mission, we expect the magnetic components of the waves to be stronger in the ionosphere than in the atmosphere below but we have not yet entered that region on Venus Express to verify this in the manner of the Pioneer Venus test above.
 The PVO values in the atmosphere were then used to design the data system of the fluxgate magnetometer on Venus Express (as described by Russell et al. ) to enable it to sample the waveforms of these electromagnetic waves. Venus Express was launched successfully in 2005 and inserted into Venus orbit in 2006. The expected bursts of electromagnetic signals started to be observed in the ionosphere when periapsis altitudes reached sufficiently low values shortly after orbit insertion [Russell et al., 2007]. These signals are polarized in a plane perpendicular to the magnetic field and rotate in a right-handed sense. They appear when the magnetic field dips into the atmosphere, i.e., departs from its usual (dayside) horizontal orientation [Russell et al., 2008a, 2011]. It is expected that such dipping would allow access of atmospherically generated signals to the ionosphere.
Figure 1a shows a sample of bursts seen on December 13, 2009 at 247 km altitude, 83° N latitude and 0810 LT. These waves are active for more than 2 s but the individual components of each last less than 100 ms. In this figure we have restored the constant background field to the filtered perturbation before performing our principal axis analysis. Thus the large component of the background field along the minimum variance direction accurately reflects the fact that the wave propagation vector is nearly along the magnetic field.
Figure 1b shows the hodogram over a 3.2 s span. The wave perturbation vectors appear to be confined to a plane whose normal is nearly parallel to the magnetic field. To classify a wave as a whistler mode event we conservatively require the out-of-plane power be less than 25% and the power in the maximum variance direction to be less than three times that of the intermediate direction. This ensures the waves are naturally occurring whistler mode waves. Few events fail this criterion. Most of the transient signals we see below 400 km are whistler mode waves.
Figure 1c shows a power spectrum of the signals transverse to the magnetic field after applying a bandpass filter that passes the frequency range 42 to 60 Hz [Russell et al., 2008b]. Comparison of the direction of rotation of the magnetic vectors with the background magnetic field direction shows that the multiple peaks in this spectrum are all right-hand polarized, as would be expected for whistler mode waves. We expect that each of the peaks in the spectrum corresponds to a burst in the time series shown in Figure 1a.
 In this paper we examine the amplitude and occurrence of such bursts during the nearly six Venus years of VEX operation, from orbit insertion to the end of 2009. To minimize spurious signals associated with the spacecraft and other instruments we analyze only in a passband from 42 to 60 Hz. When the noise in the maximum variance direction exceeds 0.2 nT half-amplitude we do not include the data in our analysis. When it is less than 0.2 nT, we record the number of whistler mode bursts and the duration of the analysis interval. We report on the statistics of the bursts as a function of background magnetic field strength, altitude, latitude, and local time. We defer the search for dispersion of the signals to a future study. Waves such as those shown in Figure 1 are very short in time and close to the instrument Nyquist frequency. This closeness produces hodograms with slowly rotating triangles of points rather than the expected circular pattern at frequencies far below the Nyquist frequency.
2. The Venus Express Orbit
Figure 2 shows the Venus Express orbit in the years 2006 and 2009. In the latter year, the periapsis is almost directly over the north pole and beginning to precess toward lower latitudes. This precessional motion was also experienced by Pioneer Venus, but its initial periapsis was much closer to the planetary equator. The magnetic draping pattern produced by the solar wind interaction with Venus leads to near-radial magnetic fields near midnight and allows whistler mode waves easy access from the atmospheric source region. Thus Pioneer Venus saw many lightning-associated whistler mode bursts when its periapsis moved through the night side as Venus orbited the Sun. Because the Pioneer Venus antenna was noisy in sunlight, only the night hours from dusk to dawn could be studied. In contrast, Venus Express, as demonstrated by Figure 1a (0810 LT), can detect events while in sunlight.
 Due to the high-latitude periapsis of the orbit of Venus Express, low-altitude observations are limited to a small region around the north pole. This region is complementary to that of Pioneer Venus and gives us new insight into the lightning generation process as we will show below. The nature of the orbit causes the altitude and latitude to be negatively correlated, and thus steps must be taken to ensure trends due to one are not mistakenly attributed to the other. This coverage is illustrated in Figure 3a which shows the altitude and latitude of bursts detected in the study period when the background field lay between 15 and 30 nT (for reasons explained in the next section). We call this the full data set. For Figure 3b, if there were more than one burst in a five-second interval only the position of the strongest is shown. We call this the reduced data set. An example of such an interval is illustrated in Figure 1a. In both Figures 3a and 3b we have drawn a black box around the region from 80 to 90° latitude and 180 to 300 km altitude. Since this region has the most homogenous coverage, we restrict our study of spatial variations to this box in the following analysis so we do not interpret altitude-related changes as latitude-related changes and vice versa.
3. The Effect of the Background Magnetized Plasma
 The propagation of whistler mode waves depends on the strength of the magnetic field, the direction of the wave normal relative to the magnetic field and the ambient electron density. First, these waves do not propagate if their frequency is above the electron gyrofrequency. Their wave normal surfaces undergo a topological change at half the electron gyrofrequency and at the lower hybrid frequency about 0.02 times the electron gyrofrequency. In Figure 4a we show the rate of occurrence of bursts with amplitudes greater than 0.2 nT. The left-hand panel shows the full data set and the right-hand panel the reduced data set. We find that the waves are not detected at the spacecraft unless the field strength is above about 10 nT. This is equivalent to a local electron gyrofrequency only five times the wave frequency in the 42–60 Hz band we are analyzing. We expect the magnetic field becomes weaker at lower altitudes so it is reasonable to infer that the waves simply cannot propagate to the spacecraft from below when the field at the spacecraft is of the order of 10 nT or less. The burst rate also decreases at high field strength. The reason for this latter decrease may simply be that the waves travel faster at high field strength since for constant energy flux (Poynting vector) the amplitude must decrease as the wave speeds up. In a region of typical solar-minimum ionospheric density of 104 cm−3 at a field strength of 20 nT, the group velocity of 50 Hz waves is 97 km·s−1 while at 40 nT the group velocity is 147 k·ms−1. We note that lower electron densities also result in faster wave propagation so that if the magnetic field and electron density are anti-correlated (as is often observed in plasmas where the total pressure is nearly constant) then the amplitude correlation with B here could also be the result of a changing electron density. We discuss this in more detail in section 5 below. The solid line in Figure 4a gives the number of observations in each bin. While the number does decrease at high field strength, the total observation time is of sufficient size to ensure a statistically accurate rate at all field strengths shown. The burst rate in the right-hand panel is lower than in the left-hand panel because the reduced data set is smaller than the full since only one burst is allowed to be included per five-second interval.
 In Figure 4b we show the average amplitude as a function of background magnetic field in the same format. The amplitude follows the same general trend as the burst rate. The largest bursts occur at field strengths in the range of 15 to 20 nT and decrease at higher field strengths where the waves are expected to be traveling faster. As in Figure 4a, the solid line denotes the total observation time. We can show that the change in burst rate and average amplitude is consistent with a gradual weakening of the signal with increasing background field with the display in Figure 4c, where we normalize the number of occurrences in each amplitude bin by the total number of bursts in each field strength bin. This variation is consistent with burst strengths being very weak when the background field is below 15 nT, peaking sharply between 15 and 30 nT, and gradually weakening as the background field continues to increase. For the rest of this paper we restrict our analysis to periods when the background magnetic field is between 15 and 30 nT.
3.2. Burst Rate and Amplitude Versus Altitude
 Keeping the region of interest to latitudes above 80° N and altitudes below 400 km where we have more uniform spatial coverage and restricting our analysis to times when the magnetic field is between 15 and 30 nT, we can now investigate the spatial variation of signal strength and occurrence rate. Figure 5a shows the burst rate and observation time versus altitude in our study volume. Again, we have many thousands of seconds of data in each bin as shown by the solid line. The rate is low below 200 km, rises sharply between 200 and 225 km, and then decreases with altitude, reaching very low levels by 400 km. Again, the full data set is given in the left-hand panel and the reduced data set in the right-hand panel.
Figure 5b shows a complementary plot of burst amplitude occurrence versus altitude where we normalize the occurrences of each amplitude in an altitude bin by the total number of bursts in the bin. Again the full data set is shown in the left-hand panel and the reduced data set in the right-hand panel. As would be expected from Figure 5a, the amplitudes of the bursts seen below 200 km are weak. This is consistent with the electron density decreasing, which would cause the signal to propagate more rapidly and have a smaller amplitude or the magnetic field decreasing preventing the signal from reaching the spacecraft from below. Because Venus Express is operating in the deepest solar minimum since the Dalton minimum in the early 1800 s [Russell et al., 2010], we suspect that the electron density in the lower ionosphere of Venus is much weaker than seen during the Pioneer Venus epoch. However, without a Langmuir probe or other such instrument capable of measuring electron density on Venus Express we cannot confirm this hypothesis. At altitudes above 225 km, the electron density could also be decreasing allowing the waves to travel faster and reducing their amplitude without changing the energy flux. Between 225 to 250 km and 350 to 375 km, the percentage of amplitudes above 0.24 nT has decreased by about a factor of 2. Bursts over 0.29 nT make up about 25% in the former bin, but none are detected in the latter. By 375 to 400 km we see no bursts above 0.24 nT. To decrease this much solely from a density change, affecting the amplitude but preserving the Poynting vector, would require a density drop of a factor of 16. This is possible in the lower EUV conditions of the solar minimum at this time, but some attenuation of the wave energy flux with altitude may also play a role. Pioneer Venus measurements taken on the nightside detected a decrease of the median energy flux over this altitude range by about a factor of 4 [Russell et al., 1989]. This fall-off in the observed electromagnetic energy flux was used as further evidence that the energy's source was at or below the bottom of the ionosphere. This is consistent with the Venus Express measurements and we believe it too is due to a reduction of energy flux with increasing altitude.
4. Local Time and Latitude Dependence
 Above we have shown that there is relatively minimal variation in the occurrence rate and strength of the whistler mode bursts with altitude in the range 200 to 300 km and magnetic field strength between 15 and 30 nT. Thus we use these ranges to further subdivide our data into bins of local time and latitude. In Figure 6, we show the burst rates in three-hour bins of local time in each of two latitude ranges: 80 to 85°N and 85 to 90°N. The top panel shows the full data set and the bottom panel the reduced data set. The observation time in each bin is shown by the solid lines. There are minima in occurrence at night and during the day and maxima over the terminators. The lower latitude range maximizes over the dawn terminator and the higher range over the dusk terminator. We need more data to verify this unexpected difference.
 If we calculate the burst rate as a function of latitude averaged over all local times we obtain the distribution shown in Figure 7. Again the full data set is shown on top and the reduced data set on the bottom. Moving away from the pole, the burst rate increases fastest around 83°N. 83°S seems to be close to the average edge of the southern polar vortex and is associated with a change in the slope of the zonal wind velocity [Luz et al., 2011]. This is consistent with lightning discharges in the atmosphere. The large difference in the local time behavior at the two latitudes examined in Figure 6 suggests that the latitude variation is not well determined by our sparse data set. To test this we divided the data into three independent sets, each containing one-third of the observation time and calculated the average and probable error of the mean. These are included on both plots. It is clear that the rates at lower latitudes are not well determined. Thus we can say little about the possible connection of these signals to the polar vortex. Furthermore, there is a second more plausible cause for the decrease toward the poles as discussed in the next section.
 Finally we can divide the data into three local time sectors (dayside, nightside, and terminators) and examine their altitude dependencies. We analyze each 3-h local time bin separately to judge the statistical accuracy of the altitude dependence using the full data set, as shown in Figure 8. We note that this diagram separates the data into 81 separate bins so the count in each is low. Thus we should only consider trends as accurate; the exact rates are going to be uncertain. The data clearly show that the burst rate is greatest on average at 200–225 km. At this altitude, the average rate does not change greatly with local time except at night, where the rate seems to be lower at this altitude and all other altitudes (with at most one exception in the 0130–0430 LT sector). These altitude distributions again are consistent with a lightning source in the atmosphere. Also shown in Figure 8 is the distribution of the background magnetic field strength, which increases with altitude on the dayside. On the terminator, however, the increase with altitude is reduced and at night the altitude dependence is weak. This is consistent with the draping configuration of the magnetic field that produces a horizontal field at low altitudes on the dayside, with a direction more along the solar wind flow direction at high altitudes away from the subsolar region with a larger resulting compression of the magnetic field. On the nightside the field is more aligned with the anti-solar direction at all altitudes.
5. Discussion and Conclusions
 The first five years of Venus Express operation have provided magnetic observations of whistler mode waves in the Venus ionosphere that both complement the electric field measurements of Pioneer Venus and confirm the hypothesis that atmospheric lightning is the source of these electric and magnetic bursts. The signals definitely propagate in the whistler mode and have a similar electromagnetic energy flux as whistler waves due to lightning observed in the terrestrial ionosphere [Russell et al., 2011]. These waves appear in the ionosphere when the magnetic field deviates sufficiently from the horizontal to enable vertically propagating, lightning-generated waves to couple to the ionospheric magnetic field [Russell et al., 2011].
 In this paper, we now have obtained enough whistler mode bursts to determine their spatial variation in amplitude and occurrence rate. We have attributed these principally to variations in the speed of the waves rather than to attenuation of the wave energy, consistent with what we found for signals with whistler mode properties in the Pioneer Venus data [Russell et al., 1989]. We expect that the collisionless ionospheric plasma in which the spacecraft is orbiting produces very little damping because the electron temperature is quite low and the observed waves are propagating nearly parallel to the magnetic field. The temperature remains low despite potential energy sources (such as the whistler mode waves themselves) because the magnetic field connects the collisionless ionospheric plasma to the collisional upper atmosphere below the spacecraft which can absorb all the energy added to the ionosphere at higher altitudes [Strangeway, 1997a, 1997b].
 The whistler mode is the only plasma wave mode with a magnetic component at these frequencies [Stix, 1962]. As we see from Figure 8, the typical magnetic field strength is about 25 nT. The center of the band of frequencies we analyze is 50 Hz and a typical electron density near 250 km altitude at solar minimum is about 104 cm−3. Here the phase speed of our waves will be about 60 km·s−1 and the group velocity about 111 km·s−1. At higher altitudes using Figure 9 obtained by radio occultation measurements on Pioneer Venus Orbiter by Brace and Kliore , we see the density is 1.5 × 103 cm−3 at 300 km altitude and the phase speed will increase to about 156 km·s−1 and the phase speed to about 288 km·s−1. If the energy flux of the waves we are seeing were perfectly constant, the wave amplitude we measure would decrease as the wave speed increased. The Venus Express measurements have been obtained during the most extreme solar minimum of the space age [Russell et al., 2010] so the variation of density with altitude may even be more severe than shown for the solar minimum of 1986. Figure 10 also shows Pioneer Venus radio occultation data but here as a function of solar zenith angle. This shows that when the Venus Express data are obtained from solar zenith angles of 75 to 90°, the densities are even lower than the average ionospheric density at lower latitudes. Finally, Figure 11 shows the strong dependence of electron density on the solar EUV flux which varies with solar activity.
 In short we can understand altitude and latitude variations of the Venus Express whistler mode amplitudes quite well based on the PVO measurements of ionospheric density. We also note the rapid decrease in density with decreasing altitude at the bottom of the ionosphere. During the unusual solar minimum of 2006–2009, the density should have been smaller than shown in Figures 9, 10 and 11 and at higher altitudes. This explains why the low-altitude signals are weak. The waves are increasing in speed as the density declines as the spacecraft approaches the bottom of the ionosphere.
 Finally, these observations from Pioneer Venus provide an alternate explanation of the reduction in wave occurrence as the pole is approached in Figure 7. The density is lower in the region and the waves must be traveling faster. Again this causes the wave amplitude to drop even though the wave energy flux has not changed. Occam's razor, the philosophy that the simplest explanation that fits the facts is to be preferred, then would imply that it is most probable that the ionospheric electron density is the principal controlling factor for all the spatial variations we see, including the local time variation. Not only are the signal rate variations consistent with control of the wave speed by the electron density, but this control also means that all our observations of amplitude variations in space and with the magnetic field strength are consistent with an atmospheric source of the signals.
 The evolution of the Venus Express orbit will allow us to explore lower latitudes in future years but its precession is slow. Future operations may also be able to shorten the orbital period and thus increase low-latitude coverage. This will help improve the resolution of the latitudinal variation.
 This work was supported by the National Aeronautics and Space Administration under research grant NNX10AV29G.