The electron density profiles of the Martian dayside M2 layer can be used to investigate the thermal structure of the lower thermosphere since they are dominated by photochemical processes. Krymskii et al. (2003, 2004) retrieved Hn from the MGS electron density profiles by assuming a parabolic electron density distribution in the vicinity of the M2 peak; they showed the presence of Hn longitude variations. Zou et al. (2011) also estimated Hn from the MGS electron density profiles using the Taylor decomposition of the electron density with respect to altitudes to analyze seasonal variations of the neutral atmosphere. In this study, we used a Chapman-α function that can well describe the electron density profiles of a photochemical equilibrium layer to estimate Hn. As shown in Fig. 3, the gridded mean Hn varies from ~ 9 km to ~ 14 km under the selected condition, basically consistent with the previous results (e.g., Krymskii et al. 2003, 2004; Zou et al. 2011).
The amplitudes of thermal tides should increase with increasing altitudes according to the classical tidal theory (Chapman and Lindzen 1970); in contrast, the actual condition is that thermal tides undergo dissipation when propagating upwards (e.g., Withers et al. 2003). As shown in Fig. 3l, Hn longitude variations can reach ~ 20% in the lower thermosphere, which is much higher than the longitude variations of the neutral temperature at lower altitudes (e.g., Banfield et al. 2000). That is to say, tide wave amplitudes increase when propagating upwards into the lower thermosphere. For the ionosphere, Fang et al. (2021) recently analyzed longitude variations of the ionospheric electron densities above the M2 peak measured by the MAVEN mission. Their results indicated that longitude variation amplitudes of ionospheric electron density also trend to increase with increasing altitude; the longitude variations can reach ~ 15% near 200 km, significantly larger than the ~ 8% longitude variation of the electron density at the M2 peak presented in this study. It is notable that Fang et al. (2021) showed that the amplitude of the wave-1 is comparable to those of the wave-2 and -3, which are two dominant longitude components in this study. This is possibly due to the different observational conditions and sampling modes of the two types of measurements, especially Fang et al. (2021) used the MAVEN measurements near 20°S while in this study we used the MGS measurements at high northern latitudes.
Topographic fluctuations are generally prominent on Mars, which were suggested to be the primary reason for atmospheric longitude variations (e.g., Forbes et al. 2002; Moudden and Forbes 2008b). Figure 5a shows Martian topography changes. The topography changes are much more significant at mid- and low-latitudes than at high latitudes; the most notable changes are two asymmetrical plateaus. Withers et al. (2003) and Moudden and Forbes (2008b) performed Fourier decompositions to the Martian topography and compared the decomposed zonal components with those of the MGS neutral density to relate atmospheric longitude variations to the topography. Their comparisons were for large latitudinal scales and indicated relevance between atmospheric longitude variations and the topography, with emphasis on low- and mid-latitudes. This study is confined to the longitude variations at high northern latitudes. The Fourier decomposition was also applied to the topography. As shown in Fig. 5b, the Fourier amplitudes of the longitude variations are significantly larger at low- and mid-latitudes than at high latitudes. The dominant longitude components include the wave − 1, − 2, and − 3, and the wave − 2 is more prominent in the northern hemisphere. The selected MGS radio occultation measurements are located at higher northern latitudes, as indicated by the red dashed box in Fig. 2. Figure 5c shows that the wave − 1, − 2, and − 3 are also dominant components at middle to high northern latitudes, and the mean amplitude of wave − 3 is somewhat lower than those of wave − 1 and − 2. Nonlinear modulation of topographic longitude wave-n to the solar forcing should induce apparent longitude wave-n variation in the atmosphere as seen at a fixed LST (e.g., Forbes et al. 2002). That is to say, the topographic longitude components are not fully consistent with those of hmM2, NmM2, and Hn (Fig. 4), which mainly manifests as that a dominant longitude variation component in the topography, the wave − 1, is not prominent in hmM2, NmM2, and Hn. Then, what is the manifestation of the relevance between the ionospheric and thermospheric longitude structures and the topography in the selected data set? We took the dominant wave − 3 in the ionosphere and thermosphere to further analyze. A notable feature of the topographic wave− 3 is that the wave − 3 phase changes with latitude; it shifts westwards with increasing latitude in the latitudinal range of ~ 50°N to ~ 80°N and turns to shift eastwards beyond ~ 80°N. Figure 5d presents the topographic wave − 3 in the latitudinal range of the MGS measurements to show these phase shifts. Latitude variations of the wave-3 in hmM2, NmM2, and Hn are presented in Fig. 5e–g, respectively, for comparison; where the data are extended to a larger LST range (LST < 6.7) to include those MGS measurements at higher latitudes to investigate the effect of the topographic wave − 3 phase turning at 80°N. It is interesting that similar phase shifts and turning appear in the three parameters, consistent with the topography. It is notable that the LST of the MGS measurements significantly increases with increasing latitude beyond ~ 80°N in the extended date set, which also contributes to the eastward wave − 3 phase shift in the MGS measurements at higher latitudes. The DE2 and SE1 tide components were suggested to be primarily responsible for the wave-3 longitude variations, and SE1 was thought to be more important at high latitudes (e.g., Cahoy et al. 2007; Forbes et al. 2002; Moudden and Forbes 2008b; Withers et al. 2003). Taking Hn for example, the wave-3 phase shifts eastwards ~ 48° form 80°N grid to 86°N grid. The calculated mean LST of the gridded data changes ~ 2.1 h from 80°N grid to 86°N grid, which corresponds to a wave-3 phase eastward shift of 10.5° (21°) for DE2 (SE1), significantly lower than the observed 48° phase shift. Thus, the observed turning of the phase shift at 80°N should be related to the topography. Based on simulations, Wilson (2002) also indicated westward phase shift of the wave-3 in neutral density with increasing latitude at high northern latitudes. The similar phase shifts in ionospheric and thermospheric longitude variations and in the topography indicate a commonality between them. Exciting and upward propagating efficiency may be different for various tide wave modes (e.g., Wang et al. 2006). Thus, the difference in the dominant longitude components between the three parameters and the topography is possibly due to that various topography modulated wave modes have discrepant exciting and propagating efficiencies.
It is noticeable from Fig. 5e–g that the longitude variation phases of the three parameters are different from each other; especially the wave − 3 peaks of NmM2 are significantly asynchronous with those of hmM2 and Hn. Then, how do the ionosphere and thermosphere couple under the forcing of the topography modulated non-migrating tides? Fig. 6a further presents the wave-3 phases (ψ3 in Eq. (2)) of NmM2, hmM2, and Hn for comparison. Differences between the phases are evident. Taking NmM2 for reference, the phase difference between hmM2 and NmM2 is ~ 40°, and that between Hn and NmM2 is ~ 60°, just a half of a wave-3 cycle (120° in longitude). Previous studies presented the phase discrepancies between the longitude variations of different neutral parameters. Withers et al. (2011) developed a formalism to explain the phase difference between neutral temperature and atmospheric pressure, where the phase difference was attributed to the vertical change of the longitude variation amplitude of atmospheric pressure. England et al. (2019) presented the phase difference between the longitude variations of neutral temperature and atmospheric density. In this study, NmM2 primarily depends on the CO2 density at hmM2 and Hn corresponds to the averaged neutral temperature in the vicinity of hmM2, they are related to the state of the lower thermosphere at similar height levels. The ionization peak forms at the height where atmospheric optical depth [Eq. (3)] reaches one according to the Chapman theory that assumes the atmosphere is isothermal and horizontally stratified (Rishbeth and Garriott 1969):
$$\tau =\sigma n{H}_{n}\bullet \mathrm{sec}\chi ,$$
(3)
where σ is absorption cross section, n is neutral density, and χ is the solar zenith angle. That means the ionization peak occurs at a constant atmospheric pressure level (Eq. (4)) for a fixed solar zenith angle:
$$P=nk{T}_{n}=n{H}_{n}mg,$$
(4)
where k is the Boltzmann constant, Tn is neutral temperature, m is molecular mass, and g is the gravity acceleration. Simulations (González-Galindo et al. 2013) showed that the Martian M2 peak at the subsolar point is nearly located at the same atmospheric pressure level through a Martian year. Thus, NmM2 variation should be negatively correlated with Hn variation in view of that NmM2 is positively correlated with n. That means longitude variations of NmM2 and Hn should be in anti-phase, just as presented in Fig. 6a. This result indicates that longitude variations of Hn driven by non-migrating tides modulate the concurrent longitude variations of NmM2 according to the Chapman theory, although the Martian atmosphere is longitudinally varying and is not strictly isothermal (the neutral temperature in the lower thermosphere can increase by tens of Kelvin from ~ 120 km to ~ 160 km, e.g., Cui et al. 2018; Fox et al. 1996; Mendillo et al. 2011).
hmM2 is positively correlated with the neutral scale height according to the Chapman theory (Rishbeth and Garriott 1969). Longitude variations of the ionosphere can be attributed to those of Hn, then longitude variations of hmM2 should be in-phase with those of Hn. However, they are also not in-phase in observations (see Figs. 3 and 6a). The atmospheric optical depth increases with decreasing altitude, and for an ionization layer dominated by photochemical processes, hmM2 corresponds to the height where the atmospheric optical depth equal to one. The atmospheric optical depth is related to the column content of ionized neutral composition downward from atmospheric top. The atmospheric column content depends on the underlying atmospheric temperature, which determines the expansion or contraction of the overlying atmosphere (e.g., Bougher et al. 2001; Zou et al. 2011; González-Galindo et al. 2013). Thus, hmM2 mainly depends on the neutral temperature below the M2 peak, which controls the atmospheric column content above the M2 peak. For the actual Martian atmosphere (in which neutral temperature changes with increasing altitudes), this neutral temperature should be the effective one of the underlying atmosphere mostly lower than hmM2, as revealed by Zou et al. (2011) that the effective neutral scale height between the lower atmosphere and the ionospheric peak is the primary driver for hmM2 variations. That means the height level of the atmospheric temperature determining hmM2 is lower than the height level of Hn. Thus, the difference of the wave − 3 phase between hmM2 and Hn indicates vertical change of the longitude variation phase of neutral temperature. Although both SPWs, which can be generated from nonlinear atmospheric wave–wave interactions (e.g., Forbes et al. 2020), and non-migrating tides can cause atmospheric longitude variations, the observed wave phases of the thermosphere and ionosphere under the selected condition is consistent with vertical non-migrating tide propagation, since the wave − 3 of hmM2 should be in-phase with that of Hn if the longitude variations are caused by SPWs (their phases keep constant with varying altitude).
The percentage magnitudes of the longitude variations of the parameters also differ from each other, as presented in Fig. 3j–l. Figure 6b further shows the wave-3 percentage amplitudes [A3 in Eq. (2)] of NmM2, hmM2, and Hn for comparison. The percentage amplitudes of Hn are nearly twice as large as those of NmM2. The latitudinally averaged ratio of Hn amplitudes to NmM2 amplitudes is ~ 2.3, similar to the ratio of their total longitude variation magnitudes (Fig. 3). For a Chapman-α layer NmM2 is proportional to Hn−1/2, which means a change of the neutral scale height ΔHn/Hn will cause a smaller change of the electron density ΔNmM2/ NmM2 with a magnitude of half that of ΔHn/Hn. Thus, the wave-3 amplitude ratio of Hn to NmM2 is basically consistent with the Chapman-α layer. A possible reason for the smaller difference is that the mean height of the altitudinal range (− 10 km to 20 km around hmM2) used for fitting Hn is higher than hmM2. The percentage amplitudes of the longitude variations of hmM2 are much smaller than those of Hn. hmM2 linearly depends on the neutral scale height according to the Chapman theory:
$${h}_{m}{M}_{2}\left(\chi \right)={h}_{m}{M}_{2}\left(\chi =0\right)+{H}_{n}^{^{\prime}}\bullet \mathrm{ln}\left(\mathrm{sec}\chi \right),$$
(5)
where χ is the solar zenith angle; in view of the vertical changes of neutral temperature, Hn’ is the effective neutral scale height of the atmosphere below the M2 peak. Since the value of hmM2 is dominated by the base value of χ = 0 (e.g., Morgan et al. 2008), the percentage variation of hmM2 caused by the change of the neutral scale height is much smaller than that of the neutral scale height.
The observed wave phases of Hn and hmM2 indicate the presence of the effect of upward propagating non-migrating tides, which is consistent with Cahoy et al. (2007), who presented vertical phase shifts of ionospheric longitude waves using the MGS electron density profiles. Owing to the vertical change of wave phase associated with tides, the dominant longitude variations should be weakened when integrating the electron densities with respect to altitudes, since out-of-phase longitude variations of the electron densities at different altitudes counteract partially. Thus, we calculated the total electron content of partial M2 layer (TECp, in units of TECu, 1TECu = 1016 electrons/m2) to investigate its longitude variations. In view of hmM2 varies with longitude and latitude under the selected condition (see Fig. 3), for each electron density profile a TECp value was obtained by integrating the electron densities in the altitudinal range of − 15 km to 25 km around the M2 peak, where a main portion of the M2 layer locates. TECp data were also gridded according to the operation used in Fig. 3. Figure 7a shows longitude and latitude variations of the gridded mean TECp and Fig. 7b presents the corresponding standard deviations of the gridded TECp. TECp varies primarily with latitude due to the change of the solar zenith angle, which is similar to NmM2 (see Fig. 3), while its longitude variation appears to be not as evident as that in NmM2. Figure 7c presents the longitude variation using the residual TECp after removing zonal averages (△TECp). As expected, the aforementioned wave − 3 and − 2 are not evident in △TECp, and the longitude variation of △TECp is basically equivalent to the standard deviation of the gridded TECp in amplitude. Figure 7d further shows the amplitudes of the longitude wave − 1 to − 6 of △TECp. There is seems no a wave component that can be dominant at different latitudes. The amplitudes of others wave components can be comparable to those of wave − 3 and − 2. Thus, the analysis for △TECp further supports that ionospheric longitude variations are related to upward propagating non-migrating tides.
The above analyses indicate that the observed ionospheric longitude variations are the results of the coupling between the ionosphere and thermosphere through photochemical processes under the forcing of topography modulated thermal tides. For this coupling, the neutral scale height is the key atmospheric parameter determining ionospheric longitude variations. The relationship between ionospheric and thermospheric longitude variations conforms to the Chapman theory and vertical propagation of non-migrating thermal tides. The results suggest that longitude variation of NmM2 can be used as a quantitative indicator for that of the thermal structure in the lower thermosphere (for both amplitude and phase).