A solar terminator wave is discovered in neutral thermosphere densities. The data originate from the accelerometer experiment on the CHAMP satellite between 2001 and 2007. During solar minimum conditions the phase fronts of the dusk terminator wave during Northern Hemisphere summer extend from about −60° to almost +30° latitude, at an angle of about 30° with respect to the terminator. The density amplitudes are of order ±3–6%, and the horizontal wavelength is of order 3,000 km. The dusk terminator wave is generally more well-defined than that near dawn, is more prominent during solar minimum than solar maximum, and during solstice as opposed to equinox. This wave is also found in similarly-analyzed output from the Kyushu University General Circulation Model that extends from the surface to the exobase. At solar minimum the model wave amplitude is similar to that observed, but with a horizontal wavelength close to 2,000 km. Analytic theory predicts a typical horizontal wavelength of 1,000 km. While there have been several reports of ionospheric waves in connection with the solar terminator, this appears to be the first such observation in the neutral thermosphere. In addition, the orientations of the dawn and dusk terminator waves are such that the maximum equatorial density perturbation occurs near midnight; therefore, some previous observations of the so-called “midnight temperature maximum” may contain contributions attributable to the terminator wave.
 In February 1970, Chimonas and Hines  predicted that the solar eclipse of March 7, 1970, would generate gravity waves as the cooling region associated with the shadow moved at supersonic speeds through the atmosphere. They theorized that the gravity waves would build up into a bow wave, much like a rapidly moving boat produces a bow wave on the water surface. They specifically predicted that a traveling ionospheric disturbance (TID) would be generated in connection with the eclipse. A TID was indeed observed in total electron content (TEC) [Davis and da Rosa, 1970], and interpreted as possibly being connected with the eclipse passage. Chimonas  subsequently developed a mathematical framework for the gravity wave characteristics, and Chimonas and Hines  demonstrated consistency between their theory and the observations of Davis and da Rosa .
 Drawing an analogy with the eclipse, Beer  put forth the idea that the solar terminator might similarly serve as a generator of gravity waves. Raitt and Clark  quickly responded with an analysis of electron temperature data from ESRO-1A that appeared to confirm Beer's prediction. They consistently found wavelike oscillations in electron temperature near the terminator with a distribution of horizontal wavelengths which peaked near 1,000 km. They also found wave amplitudes to be much larger in the dawn versus dusk sector, but acknowledged that this could have been an altitude effect due to the eccentricity of the satellite orbit. More recently, Vasylyev and Sergeev  studied in detail the waves generated in the troposphere by the moving terminator, but do not extend their solutions into the upper atmosphere. Galushko et al.  also reported measurement of traveling ionospheric disturbances (TIDs) associated with the terminator using the Millstone Hill incoherent scatter radar.
 As noted by Galushko et al. , among all the sources of gravity waves, the solar terminator holds a special status, as it is a source that is well-defined and predictable. As such, it represents a “natural laboratory” experiment wherein theory and measurement can be compared. In this paper, it is our objective to establish observationally the characteristics of the solar terminator wave in the thermosphere, at different seasons and levels of solar activity. To date, to the authors' knowledge, this is the first reported measurement of a terminator wave in the neutral thermosphere. In addition, we provide a numerical simulation with the Kyushu University General Circulation Model (GCM) that replicates the salient features of our measurements.
2. Data and Model
 The neutral density data analyzed here were derived from accelerometer measurements on the CHAMP satellite between 2001 and 2007, and are separated into 3 levels of solar activity according to 81-day mean values of the 10.7 cm solar radio flux: 70–100 (SSMIN); 100–150 (SSAVG); and 150–225 (SSMAX). The data extend from −87° to +87° latitude, span altitude regions from 440 ± 40 km during 2001 to 340 ± 10 km during 2006, and have an 80-km horizontal resolution along the orbit. In addition, the ascending and descending portions of the orbit each precess through all local times every ≈260 days, so that complete local time sampling is achieved every ≈130 days. High-pass filtering was applied along the orbit to extract density residuals with horizontal scales between about 160 km (the minimum observable scale at this resolution) and 4800 km. In the following we work with relative residual densities, that is, the ratio of the high-pass filtered densities to the trend that is removed, in order to minimize the effects of altitude variations. For details concerning these density data and related errors, filtering techniques, etc., see Bruinsma et al. [2004, 2006] and Bruinsma and Biancale .
 The GCM used in this study extends from the surface to the exobase and contains a full set of physical processes appropriate for the troposphere, stratosphere, mesosphere and thermosphere [Miyoshi and Fujiwara, 2003]. The version used here is the same as the GCM used by Miyoshi and Fujiwara [2003, 2008] except for the horizontal resolution. The vertical resolution is 0.4 scale heights above the tropopause, and the horizontal resolution is T42 (the maximum horizontal wave number is 42), corresponding to a grid spacing of 2.8° latitude by 2.8° longitude. Therefore, horizontal scales of order 600 km or greater can be resolved.
Figure 1 illustrates the mean (i.e., averaged over all available orbits for a given level of solar activity) relative residual densities plotted in a geographic latitude vs. local time contour format. Information on data binning is provided in the caption to Figure 1. We illustrate Northern Hemisphere (NH) summer results for the 3 levels of solar activity defined previously, and also include the SH summer result (Figure 1, bottom left) for solar minimum. Note that all panels in Figure 1 are centered on noon except for Figure 1, bottom right, which is centered on midnight for an alternative perspective of the terminator feature to be described below. The daytime structures are characterized by two bands of enhanced densities on both sides of the equator; we presume these to be related to ordering of the neutral density distribution in magnetic coordinates related to the equatorial ionization anomaly (EIA), as already noted by Liu et al. . Taking Figure 1, top left, corresponding to NH summer and SSAVG as an example, the feature of interest here is the banded structure inclined about 30° with respect to the dusk terminator. This feature extends from 30°N to poleward of 60°S, with amplitude excursions of order ±3–6%. The density amplitudes are slightly larger during SSMIN, and during SSMAX amplitudes are smaller and do not extend over as wide a latitude range. Similar behavior is found during equinox (not shown), although the terminator wave is less well-defined than during solstice. The solar cycle dependence may be a result of using relative density residuals, but may also reflect differences in the effect of molecular diffusion on vertically-propagating waves (see later discussion). Also CHAMP is orbiting at mean latitudes roughly 100 km lower during SSMIN as opposed to SSMAX. A terminator wave is also apparent before dawn in Figure 1, although it is generally less well-defined and extensive than at dusk. One is reminded that these results are obtained by averaging over several cycles of complete local time sampling, and combining ascending and descending data separated by several months. Therefore, the terminator wave illustrated here really is a persistent feature. It is possible that smaller-scale waves that might have existed but that were not in phase between various orbits, may have been averaged out.
 Similarly-filtered GCM densities at 400 km altitude (Figure 2) reveal very similar terminator waves in terms of amplitude, orientation, latitudinal extent and dusk vs. dawn asymmetry. Additional smaller-scale waves are also seen. An additional perspective is provided in Figure 3. Refer to the dashed rectangle normal to the dusk terminator wave phase fronts in Figure 2. Smoothed averages of the relative density residuals in this box were computed for both the CHAMP and GCM data and these are illustrated in Figure 3. Note that the amplitudes are similar, about ±2–4% after smoothing out smaller-scale structures, with similar wavelengths depending which maxima or minima are used: 2800–3600 km for CHAMP and 1800–2300 km for the GCM.
 Finally, note that the orientations of both the dawn and dusk terminator waves are such that the maximum density perturbation near the equator occurs within a few hours of midnight (see Figure 1). Using e.g. MSISE90 [Hedin, 1991] a 4% relative density perturbation translates to 5K (20K) exosphere temperature perturbations at SSMIN (SSMAX). Thus, the terminator wave may contribute to some observations of the so-called “midnight temperature maximum (MTM)” at low latitudes [Herrero and Spencer, 1982; Herrero et al., 1983, 1993]. However, the wave-like signature of the terminator wave (see Figure 3) suggests that its generation mechanism might be different than the ion-drag-related enhancement of subsidence heating around midnight that has been suggested to produce the MTM [Mayr et al., 1979].
4. Discussion and Conclusions
 The dayside thermosphere constitutes a density or pressure bulge moving westward with the phase speed of the Sun (about 450 ms−1 at the equator). In connection with the dawn and dusk terminator discontinuities, one can imagine the terminator waves to be analogous to bow or wake waves (or solitons) produced by a surface ship. The speed of sound near 400 km is of order 500 ms−1 (700 ms−1) at SSMIN (SSMAX), and thus the terminator moves subsonically at these altitudes.
 A theoretical basis exists for the observations and simulations reported here, although most published work exists in the Russian literature. English summaries of the salient results are provided by Somsikov , Somsikov and Ganguly , and Galushko et al. . The main points are that gravity waves can be generated by a terminator moving at sub-sonic speeds, and that at midlatitudes between 180–600 km altitude the generated waves have typical periods and spatial scales of order 30 minutes and 1000 km, respectively. This typical horizontal scale is roughly a factor of 3 less than the scales revealed by CHAMP, although multi-orbit averaging has probably only revealed the longest-wavelength and most phase coherent of the terminator waves. The largest horizontal scale seen in the GCM is closer to theory, but smaller-scale waves are also seen, especially near dawn. Given the experimental and GCM results provided here, further refinement of analytic theory may be possible.
 The precise reasons why the terminator wave is inclined to the terminator, sometimes extends to the dayside of the terminator, and is larger in the winter hemisphere than the summer hemisphere remain to be determined. We speculate the following. The terminator wave depicted in our figures may be partially driven in-situ, but may also be the result of excitation at lower altitudes and transmission upwards as a spectrum of waves. As these waves propagate vertically and possibly obliquely, they will be affected differently by dissipation and mean winds that also vary with geographic location, local time and season. In addition the phases of these waves will change with height. The terminator wave that we observe thus likely bears the aggregate signatures of these effects.
 The terminator waves seen here are different than those measured by Galushko et al.  since their waves were most prominent in the post-dawn sector, only occurred below 300 km, and furthermore their measurements were made at equinox which may also be a factor. Somsikov and Ganguly  note a number of plasma instability processes that might give rise to wave-like structures in electron densities near the terminator, so it does not necessarily follow that neutral and plasma terminator waves are one and the same phenomenon. Theory also predicts a region between about 120–180 km where non-propagating (decaying) waves are produced, and a third region at lower altitudes (<100 km) where a supersonic terminator excites both acoustic and gravity waves. A much more comprehensive analysis of our GCM results is planned for future work, wherein we will further elucidate height, latitude and seasonal characteristics of the solar terminator waves, degree of conformity with theoretical expectations, and possible interpretation of previously-reported measurements of the midnight temperature maximum as manifestations of terminator wave effects.
 J. Forbes was supported by grant ATM-0719480 from the National Science Foundation as part of the Space Weather Program. The efforts of Xiaoli Zhang in preparing the final figures are much appreciated.