N Yoshida
email: n.yoshida@pat.gp.tohoku.ac.jp

H Nakagawa

N Terada

J S Evans

N M Schneider

S K Jain

T Imamura

Jean-Yves Chaufray

H Fujiwara

Justin Deighan

J.-Y Chaufray

B M Jakosky

Seasonal and latitudinal variations of dayside N2/CO2 ratio in the Martian thermosphere derived from MAVEN IUVS observations

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Introduction

Planetary atmospheres are generally characterized by a compositional boundary, called the homopause, below which gases are well-mixed by eddy diffusion (homosphere) and above which gases are diffusively separated according to their own scale heights by molecular diffusion (heterosphere). In the heterosphere, the mixing ratio of lighter species is expected to increase with altitude above the homopause. The location of the homopause altitude influences the thermospheric composition and thereby the escape of species to space.

In addition, the fractionation between the homopause and the exobase determines the relative abundance of species that escape to space and the total atmospheric loss from the isotope record [START_REF] Jakosky | Mars Atmospheric Loss and Isotopic Fractionation by Solar-Wind-Induced Sputtering and Photochemical Escape[END_REF][START_REF] Jakosky | Mar's atmospheric history derived from upper-atmosphere measurement of 38 Ar/ 36[END_REF][START_REF] Lammer | Isotopic fractionation by gravitational escape[END_REF][START_REF] Chassefière | Mars atmospheric escape and evolution; interaction with the solar wind[END_REF][START_REF] Slipski | Argon isotopes as tracers for martian atmospheric loss[END_REF].

Early measurements of atmospheric composition in the Martian thermosphere were performed by the neutral mass spectrometers mounted on the aeroshell of Viking 1 and 2 landers [START_REF] Nier | Composition and Structure of Mars' Upper Atmosphere: Results From the Neutral Mass Spectrometers on Viking 1 and 2[END_REF]. Viking observed vertical profiles of CO 2 , N 2 , Ar, CO, and O 2 in the range between 120 and 200 km. The Viking observations showed that the relative abundance of lighter species increases with altitude due to diffusive separation. After the Viking observations, the Mars Atmosphere and Volatile EvolutioN (MAVEN) spacecraft measures atmospheric composition in detail in the thermosphere using in-situ and remote-sensing instruments; e.g., the Neutral Gas and Ion Spectrometer (NGIMS) [START_REF] Mahaffy | The Neutral Gas and Ion Mass Spectrometer on the mars Atmosphere and Volatile Evolution Mission[END_REF] and the Imaging UltraViolet Spectrograph (IUVS) (McClintock et al., 2014). In the beginning of MAVEN mission, vertical profiles of several species observed by both the NGIMS and IUVS instruments confirmed diffusive separation in the thermosphere [START_REF] Mahaffy | Structure and composition of the neutral upper atmosphere of Mars from the MAVEN NGIMS investigation[END_REF][START_REF] Withers | Changes in the thermosphere and ionosphere of Mars from Viking to MAVEN[END_REF][START_REF] Evans | Retrieval of CO 2 and N 2 in the Martian thermosphere using day glow observations by IUVS on MAVEN[END_REF].

Vertical profiles between the Viking and MAVEN observations are different in both scale heights and background temperature. The scale heights of CO 2 are larger in the MAVEN NGIMS measurements (15 km) than from Viking (10 km), with corresponding temperatures of 270 K and 180 K, respectively [START_REF] Withers | Changes in the thermosphere and ionosphere of Mars from Viking to MAVEN[END_REF]. [START_REF] Withers | Changes in the thermosphere and ionosphere of Mars from Viking to MAVEN[END_REF] mentioned that the warmer temperature observed by MAVEN is due to the Sun-Mars distance and the solar cycle. Vertical profiles of N 2 /CO 2 observed by the Viking probes and MAVEN/IUVS are compared in [START_REF] Evans | Retrieval of CO 2 and N 2 in the Martian thermosphere using day glow observations by IUVS on MAVEN[END_REF]. Diffusive separation of the two species is more effective in the Viking observations and the difference with IUVS observations is obvious above 140 km altitude. It is noted that the comparison of atmospheric composition by [START_REF] Evans | Retrieval of CO 2 and N 2 in the Martian thermosphere using day glow observations by IUVS on MAVEN[END_REF] was conducted in the beginning of the MAVEN mission. The vertical profile measurements by IUVS aboard MAVEN have now been taken for over three Martian Years, allowing an investigation into compositional distribution and variation of N 2 and CO 2 densities in the thermosphere of Mars.

The Martian homopause altitude was considered to be located around 120 and 130 km from observations by the Viking landers [START_REF] Nier | Composition and Structure of Mars' Upper Atmosphere: Results From the Neutral Mass Spectrometers on Viking 1 and 2[END_REF]. However, numerical simulations after this suggested that the Martian homopause altitude varies due to the atmospheric global circulation [START_REF] González-Galindo | A ground-toexosphere Martian general circulation model: 1. Seasonal, diurnal, and solar cycle variation of thermosphere temperatures[END_REF], and the saturation of small-scale gravity waves, planetary-scale waves, and thermal tides [START_REF] Imamura | Convective generation and vertical propagation of fast gravity waves on Mars: One-and two-dimensional modeling[END_REF][START_REF] Leovy | Control of the Homopause Level[END_REF]. Recently, [START_REF] Jakosky | Mar's atmospheric history derived from upper-atmosphere measurement of 38 Ar/ 36[END_REF] and [START_REF] Slipski | Variability of Martian turbopause altitudes[END_REF] In addition to homopause altitude variations, it is noted that Mars' thermospheric temperature is variable because solar extreme ultraviolet (EUV) irradiance changes with time and it is absorbed above ~100 km altitude. [START_REF] Gröller | MAVEN/IUVS stellar occultation measurements of Mars atmospheric structure and composition[END_REF] showed diurnal temperature variations for a pressure level of 3×10 -5 Pa (around 130 km) and for latitudes below 50° over one Martian year in their Figure 19. The average temperature between 12:00 and 16:00 local time (LT) is ~170 K, but observed temperatures showed broad variability between ~150 and ~200 K. [START_REF] Gröller | MAVEN/IUVS stellar occultation measurements of Mars atmospheric structure and composition[END_REF] mentioned that the relatively large variability could be due to variations with latitude and season. [START_REF] Bougher | The structure and variability of Mars dayside thermosphere from MAVEN NGIMS and IUVS measurements: Seasonal and solar activity trends in scale heights and temperature[END_REF] implied that long-term variations of temperature in the Martian dayside upper thermosphere correlate with solar EUV irradiance at Mars. The observed temperature range corresponding to scale heights over 150 -180 km in [START_REF] Bougher | The structure and variability of Mars dayside thermosphere from MAVEN NGIMS and IUVS measurements: Seasonal and solar activity trends in scale heights and temperature[END_REF] is 170 to 240 K. [START_REF] Thiemann | Mars thermospheric variability revealed by MAVEN EUVM solar occultations: Structure at aphelion and perihelion and response to EUV forcing[END_REF] also showed the correlation between thermospheric temperature and solar EUV irradiance using solar occultations of EUV irradiance at Mars. The thermospheric temperature has an impact on vertical profiles of atmospheric composition because each gas has its own scale height above the homopause altitude, H=kT/mg, where k is the Boltzmann constant, T is temperature, m is molecular mass according to species, and g is gravity. Therefore, the atmospheric composition above the homopause can be affected by the thermospheric temperature.

In addition, the atmospheric composition at the homopause would vary associated with variations of mixing ratio near the surface. Due to the tilt of the rotation axis, Mars poles become cold enough for CO 2 to condense out during local fall and winter, with CO 2 subliming from the poles during local spring and summer. The change in atmospheric mass results in variations of surface pressure with two peaks at L s ~ 60° and L s ~ 270° each year, corresponding to times when the greatest amount of CO 2 is in the atmosphere [START_REF] Hess | The annual cycle of pressure on Mars measured by Viking Landers 1 and 2[END_REF]. Both of two Viking landers observations showed a similar variation in pressure at the surface, although an absolute value of pressure is different due to their locations. Similar seasonal peaks of surface pressure were obtained by Mars Pathfinder lander, Phoenix lander, and Mars Science Laboratory (MSL) [START_REF] Martínez | The modern near-surface Martian climate: A review of in-situ meteorological data from Viking to Curiosity[END_REF]Ordonez-Etxeberria et al., 2017).

When the main atmospheric constituent condenses out, trace gases that do not condense out with the CO 2 , such as Ar and N 2 , are relatively enhanced (i.e., their mixing ratio increases).

Mixing ratio of N 2 at Gale crater was measured by MSL [START_REF] Trainer | Seasonal Variations in Atmospheric Composition as Measured in Gale Crater, Mars[END_REF]. A maximum mixing ratio of N 2 appears when the surface pressure is minimum. The seasonal variation of mixing ratio of N 2 at the surface is about ±10% [START_REF] Trainer | Seasonal Variations in Atmospheric Composition as Measured in Gale Crater, Mars[END_REF]. Note that the mixing ratio of trace gases varies with location and time, due to transport by advection and mixing. A strong depletion of mixing ratio of trace gases, such as CO and Ar, occurs in the summertime polar regions, associated with sublimation of CO 2 polar caps (e.g., [START_REF] Smith | The climatology of carbon monoxide and water vapor on Mars as observed by CRISM and modeled by the GEM-Mars general circulation model[END_REF][START_REF] Sprague | Mars' atmospheric argon: Tracer for understanding Martian atmospheric circulation and dynamics[END_REF]. Around the winter polar region, an enhancement of mixing ratio of trace gases is expected. Such variations might affect the atmospheric composition above the homopause.

In this study, we aim to investigate variations of atmospheric composition in the thermosphere and to reveal drivers of the variations. We use remote-sensing data for this study, which enables us to distinguish geophysical and geometrical effects owing to a wider coverage than in-situ observations, for better understanding the drivers of the variations in the thermosphere.

The outline of this paper is as follows. In Section 2, we describe the dataset used in this study. The seasonal, local time, and latitudinal variations of N 2 /CO 2 are shown in Section 3. We discuss the drivers of N 2 /CO 2 variation, inferred homopause altitudes from IUVS observations, and comparisons with model predictions in Section 4. Finally, our conclusions are summarized in Section 5.

MAVEN IUVS

We use limb observations from IUVS aboard MAVEN. The MAVEN orbit is elliptical with apoapsis near 6000 km and periapsis near 160 km altitude, with a 4.5-hour period. IUVS limb measurements are taken near periapsis below 500 km altitude for dayglow observations in the far and mid-UV regime (115 -340 nm) [START_REF] Jain | The structure and variability of Mars upper atmosphere as seen in MAVEN/IUVS day glow observations[END_REF]. Dayglow emissions of CO 2 + Ultraviolet Doublet (UVD) at 288 -289 nm [START_REF] Jain | The structure and variability of Mars upper atmosphere as seen in MAVEN/IUVS day glow observations[END_REF][START_REF] Evans | Retrieval of CO 2 and N 2 in the Martian thermosphere using day glow observations by IUVS on MAVEN[END_REF] and N 2 Vegard-Kaplan bands (VK) at 258.0 -287.5 nm [START_REF] Stevens | New observations of molecular nitrogen in the Martian upper atmosphere by IUVS on MAVEN[END_REF] are used to retrieve CO 2 and N 2 densities, respectively from 100 to 200 km with an altitude resolution of 5 km [START_REF] Evans | Retrieval of CO 2 and N 2 in the Martian thermosphere using day glow observations by IUVS on MAVEN[END_REF][START_REF] Stevens | New observations of molecular nitrogen in the Martian upper atmosphere by IUVS on MAVEN[END_REF]. To understand variations of atmospheric composition in the thermosphere, it is better to use non-reactive species that do not vary spatially and temporally. N 2 is weak in photochemical reactivity and non-condensable. The CO 2 density can vary due to photochemistry and meteorology of the condensation as CO 2 ice clouds, but these effects should be negligible because CO 2 is the dominant species in Mars' atmosphere. Since the effect of sublimation and condensation from the polar ice caps is well understood as the variation of surface pressure, CO 2 variations can be corrected using a knowledge of surface pressure. Thus, we analyze the number densities of CO 2 and N 2 to investigate the mixing ratio in the thermosphere. It is noted that [START_REF] Evans | Retrieval of CO 2 and N 2 in the Martian thermosphere using day glow observations by IUVS on MAVEN[END_REF] adopted an upper limit of 60° for Solar Zenith Angle (SZA) over concerns that the retrievals may be biased at larger SZA values due to anisotropy effects (i.e. variation in solar illumination along the slant path). The upper limit has since been raised to 75° because no evidence of a bias has been seen in retrievals for SZAs up to this revised limit. This is not surprising, since CO 2 + UVD and N 2 VK are optically thin such that most of the airglow signal originates from within a few scale heights of the tangent point, or the airglow peak, whichever is larger. In general, contributions along the slant path within two scale heights of a tangent point of 130 km will have an SZA within ~ 6° of the SZA at the tangent point. We use the dataset of level 2 version 13 revision 1 provided in the Planetary Data System (PDS).

In the level 2 dataset, CO 2 densities are provided at fixed altitude bins centered at 130, 140, 150, and 170 km, whereas N 2 densities are provided at 125, 137, 153, and 173 km.

The uncertainties of CO 2 densities are small (less than 10%) whereas those of N 2 densities are relatively large, typically up to 40% below 140 km and above 160 km. Below 140 km altitude, there is a possibility of contamination by solar stray light in the N 2 VK emission bands. On the other hand, above 160 km, the intensity of N 2 VK emission becomes dimmer, resulting in a reduced signal-to-noise ratio in the N 2 VK emission and corresponding increased uncertainties of retrieved N 2 densities. In this study, we confine our analysis to ~140 km where the densities have the smallest uncertainties. We interpolate the N 2 density between 137 and 153 km onto the CO 2 altitude grid and evaluate the mixing ratio at 140 km.

Data we applied in this study have uncertainties in N 2 /CO 2 less than 50%. Under the given constraint, uncertainties of N 2 /CO 2 at 140 km used for this study are in the range of 15% to 50% with a mean value of 37%. These variations are explained below.

Seasonal variation

Figure 3 demonstrates a seasonal trend of the CO 2 , N 2 number densities, and N 2 /CO 2 ratio at 140 km. Each color represents a specific local time bin, including 8:00 -10:00, 12:00 -14:00, and 16:00 -18:00, and symbols represent observed MYs. Figures 3(a

Local time variation

Figure 4 shows the short-term variations of IUVS observations vs. local time during three seasons. We selected three groups L s = 30° -70° in MY 33, L s = 120° -160° in MY 33, and L s = 340° -40° in MY 33 to 34 because those well cover the range from morning terminator to evening. In all three groups, local time of IUVS observation varies from evening to morning for each period as shown in Figure 1. We have to note that data taken during L s = 240° -300° in MY 33 have wide local time coverage, however, we didn't select this group since observation during this period included data at high southern latitudes (> ~65°S) which are sunlit throughout the sol (i.e. there is no night). The results presented in In Figures 4(d) and 4(e), observed CO 2 and N 2 densities have their maximum around noon. That would be a result of local time variation. A similar local time variation of Ar density is found in the upper thermosphere [START_REF] Gupta | Dawn-dusk asymmetries in the martian upper atmosphere[END_REF]. On the other hand, CO 2 and N 2 densities in Figures 4(a), 4(b), 4(g), and 4(h) don't have any clear peaks around noon.

It could be that the effects of season and local time on number density cannot be distinguished from these datasets. Nevertheless, Figures 4(c), 4(f), and 4(i) show that N 2 /CO 2 become minimum around noon and increase toward the dawn side. N 2 /CO 2 around dawn is larger than that at noon by a factor of 1.6 on average. This suggests that N 2 /CO 2 at 140 km has a local time variation. In order to verify the local time effect on CO 2 , and N 2 densities and N 2 /CO 2 ratio, additional data are needed.

Latitudinal variation

Additionally, we have investigated latitudinal dependences of CO 2 , N 2 , and N 2 /CO 2 .

To constrain the local time effects found in Figure 4, local time is limited from 10:00 to 14:00.

We selected the datasets that cover more than 60 degrees in latitude. Latitudinal dependences are investigated for observation in L s = 80° -100° and L s = 340° -360°. In Figure 5 In the northern summer, CO 2 densities become larger toward the northern polar region, which are 3.4×10 9 cm -3 around 45°S on average and 8.6×10 9 cm -3 around 25°N on average.

Although N 2 densities have relatively large uncertainties, N 2 densities slightly increase toward the northern polar region, which are 3.5×10 8 cm -3 around 45°S on average and 4.3×10 8 cm -3 around 25°N on average. A larger amplitude of CO 2 density variations than that of N 2 density drives the latitudinal dependence of N 2 /CO 2 . The dayside N 2 /CO 2 ratio in the northern summer is larger in the southern hemisphere (~0.11 around 45°S on average) and smaller in the northern hemisphere (~0.05 around 25°N on average). On the other hand, in the northern spring, these latitudinal dependences disappear. Because both CO 2 and N 2 densities have a similar latitudinal variation, N 2 /CO 2 is almost constant with latitude. On the other hand, it is noteworthy that both CO 2 and N 2 densities in the southern hemisphere observed in MY 32 (red dots) are slightly higher than those in MY 33 (black dots). Higher densities in MY 32 might be associated with inflation at the upper atmosphere due to solar EUV heating in MY 32, for which EUV irradiance is about two times larger as seen in Figure 2(a). Our observation suggests that the latitudinal variation of N 2 /CO 2 in the thermosphere has a strong seasonal dependence.

Discussion

Drivers of seasonal variation

In order to reveal drivers of the seasonal variations of N 2 /CO 2 at 140 km, we have examined seasonal variations of surface N 2 /CO 2 , thermospheric temperature, and homopause altitude. To infer the effects of these parameters on N 2 /CO 2 at 140 km, we use the same method described in [START_REF] Mahaffy | Structure and composition of the neutral upper atmosphere of Mars from the MAVEN NGIMS investigation[END_REF], [START_REF] Jakosky | Mar's atmospheric history derived from upper-atmosphere measurement of 38 Ar/ 36[END_REF], and [START_REF] Slipski | Variability of Martian turbopause altitudes[END_REF]. Under assumptions of isothermal atmosphere and hydrostatic equilibrium, we can estimate vertical profiles of CO 2 and N 2 densities using observed densities at 140 km and thermospheric temperature. A vertical profile of mixing ratio is obtained from the CO 2 and N 2 profiles, which is expected to match the mixing ratio in the homosphere at the homopause altitude. The mixing ratio in the homosphere is assumed to be the mixing ratio at the surface.

Therefore, densities of CO 2 and N 2 at 140 km observed from IUVS are functions of the surface N 2 /CO 2 , thermospheric temperature, and homopause altitude. For the sake of simplicity, a plausible range of these parameters to explain the observed N 2 /CO 2 at 140 km is evaluated under the assumption that the other two parameters are fixed. We constrain the geometry from 10:00 to 14:00 in LT and from 45°S to 45°N in latitude to derive these parameters. Under the given constraints, mean values of N 2 /CO 2 at 140 km derived from IUVS are 0.033 near perihelion (between L s = 230° and 270°) and 0.056 near aphelion (between L s = 50° and 90°), respectively. The results of our parameter study are summarized in Table 1.

We find that the surface N 2 /CO 2 is required to vary by ~70% between 0.016 and 0.027 with season in order to explain the observed variation of N 2 /CO 2 at 140 km between 0.033 and 0.056 if we assume an isothermal temperature of 180 K and a constant homopause altitude of 120 km. The seasonal variation of inferred surface N 2 /CO 2 shows a similar trend with observed variation of N 2 /CO 2 at 140 km, with a minimum value near perihelion and a maximum value near aphelion. In contrast, the typical surface value of mean N 2 /CO 2 ratio is 0.0272 and surface N 2 mixing ratio has a seasonal variation in ±10%, which are measured by MSL [START_REF] Trainer | Seasonal Variations in Atmospheric Composition as Measured in Gale Crater, Mars[END_REF]. Since we restricted the data between 45°S to 45°N here, an enhancement and a depletion of mixing ratio of trace gases around the polar region are out of scope. [START_REF] Trainer | Seasonal Variations in Atmospheric Composition as Measured in Gale Crater, Mars[END_REF] showed that N 2 mixing ratio has its maximum at L s ~ 160° and a second maxima at L s ~ 0°, responding to the condensation of the CO 2 polar cap [START_REF] Hess | The annual cycle of pressure on Mars measured by Viking Landers 1 and 2[END_REF]Ordonez-Etxeberria et al., 2017;[START_REF] Martínez | The modern near-surface Martian climate: A review of in-situ meteorological data from Viking to Curiosity[END_REF]. However, two peaks of N 2 mixing ratio shown in [START_REF] Trainer | Seasonal Variations in Atmospheric Composition as Measured in Gale Crater, Mars[END_REF] do not agree with the timing and magnitude of seasonal variation of inferred surface N 2 /CO 2 from this study. For these reasons, the seasonal variation of surface N 2 /CO 2 cannot explain the observed N 2 /CO 2 variation at 140 km.

It is also found that a plausible range of the variation of thermospheric temperature cannot explain the observed N 2 /CO 2 variation when we assume a constant surface mixing ratio to be 0.020 [START_REF] Mahaffy | Abundance and Isotopic Composition of Gases in the Martian Atmosphere from the Curiosity Rover[END_REF] and two cases of homopause altitudes (110 and 120 km). In the case of an assumed homopause altitude at 110 km (120 km), the thermospheric temperature is required to vary between 193 and 403 K (129 and 269 K), a difference of 210 K (140 K), due to the variation of N 2 /CO 2 at 140 km. However, previous observations suggested that the dayside upper thermospheric temperature varies by ~70 K in the range from 170 to 240 K due to the effects of changing heliocentric distance and solar cycle [START_REF] Bougher | The structure and variability of Mars dayside thermosphere from MAVEN NGIMS and IUVS measurements: Seasonal and solar activity trends in scale heights and temperature[END_REF]. In addition, [START_REF] Bougher | Comparative terrestrial planet thermospheres 3. Solar cycle variation of global structure and winds at solstices[END_REF]2015) determined the seasonal variation of the exobase temperature to be ~40 K under the solar moderate condition (F 10.7 = 130) using numerical modeling. In addition to the upper thermosphere, temperature in the lower thermosphere around ~130 km observed in [START_REF] Gröller | MAVEN/IUVS stellar occultation measurements of Mars atmospheric structure and composition[END_REF] varies between ~150 and ~200 K. The inferred range of thermospheric temperatures (210 K and 140 K) are clearly out of the plausible range reported by these previous studies and not sufficient to explain the observed seasonal variation of N 2 /CO 2 at 140 km.

Thus, we propose that variations in homopause altitudes are most likely needed to reproduce the observed seasonal variation of N 2 /CO 2 at 140 km altitude. Under the assumption of a constant surface mixing ratio of 0.020 and two cases of isothermal temperatures (150 and 200 K), inferred homopause altitudes are estimated between ~110 and ~130 km. Analysis of observations by MAVEN/NGIMS suggested that homopause altitudes on the dayside are located between ~100 and 140 km [START_REF] Slipski | Variability of Martian turbopause altitudes[END_REF]. Their inferred homopause altitudes have seasonal differences of ~30 km. Inferred homopause altitudes in this study show a reasonable agreement with the results reported by [START_REF] Slipski | Variability of Martian turbopause altitudes[END_REF].

Consequently, we conclude that variations of the homopause altitude could be the dominant driver of changes in N 2 /CO 2 in the thermosphere.

Estimation of homopause altitude

Hereafter, we determine homopause altitudes considering the variations of surface N 2 /CO 2 and thermospheric temperature. Here, we use the N 2 /CO 2 ratio at 50 km altitude, in the homosphere, predicted by Mars Climate Database (MCD) version 5.3 [START_REF] Millour | The Mars Climate Database (Version 5.3). Scientific Workshop "From Mars Express to ExoMars[END_REF] instead of the surface N 2 /CO 2 . As the input for the MCD, IUVS observation geometries shown in Figure 1 are applied, and an average condition of solar EUV flux and a typical dust climatology are used. The mean mixing ratio of N 2 in the MCD is designed to match the observational result by MSL/SAM [START_REF] Mahaffy | Abundance and Isotopic Composition of Gases in the Martian Atmosphere from the Curiosity Rover[END_REF]. N 2 /CO 2 reported in Mahaffy et al. MSL in [START_REF] Mahaffy | Abundance and Isotopic Composition of Gases in the Martian Atmosphere from the Curiosity Rover[END_REF]. Temperatures corresponding to an altitude of 175 km are determined from Chapman fits to CO 2 + UVD brightness profiles observed by IUVS [START_REF] Lo | Nonmigrating tides in the Martian atmosphere as observed by MAVEN IUVS[END_REF][START_REF] Bougher | The structure and variability of Mars dayside thermosphere from MAVEN NGIMS and IUVS measurements: Seasonal and solar activity trends in scale heights and temperature[END_REF]. We have applied the 8607 profiles whose temperatures are valid.

We assume an isothermal atmosphere and thus the temperature at 175 km is applied at all altitudes. The standard deviation of derived temperatures is ~50 K, which reflects a combination of atmospheric phenomena, such as nonmigrating tides (e.g., [START_REF] Lo | Nonmigrating tides in the Martian atmosphere as observed by MAVEN IUVS[END_REF] and thermal tides (e.g., [START_REF] Stevens | Martian mesospheric cloud observations by IUVS on MAVEN: Thermal tides coupled to the upper atmosphere[END_REF]. A temperature deviation of ~50 K corresponds to a deviation of ~10 km in the inferred homopause altitudes. Values of observed N 2 /CO 2 at 140 km would not be expected to be lower than N 2 /CO 2 in the homosphere based on an assumption of a well-mixed homosphere, thus we exclude these values from the ensemble data when inferring homopause altitudes. Although the number of excluded profiles is 17, that is negligible compared with the total number of profiles (9258). Inferred homopause altitudes, shown in Figure 6(c), are located between ~60 and 140 km. The uncertainty of inferred homopause altitudes is ± ~8 km based on the uncertainty of N 2 /CO 2 at 140 km by IUVS, which is ~37% on average. The inferred homopause altitudes clearly have an anti-correlation with the variations of N 2 /CO 2 at 140 km.

To evaluate the effect of an isothermal atmospheric assumption on the inferred homopause altitudes, we assume a constant gradient of temperature below 140 km but still an isothermal atmosphere above that altitude. The constant gradient of temperature is determined such that the temperature at 100 km should be 130 K (cf. [START_REF] Gröller | MAVEN/IUVS stellar occultation measurements of Mars atmospheric structure and composition[END_REF][START_REF] Forget | Density and temperatures of the upper Martian atmosphere measured by stellar occultations with Mars Express SPICAM[END_REF]. In this case, the inferred homopause altitudes are located between 105 and 140 km. It should be noted that the impacts of assuming a non-isothermal atmosphere on the inferred homopause altitude is strong below 105 km, where the inferred altitude increases by up to ~45 km and by ~19 km on average. However, even when the non-isothermal atmosphere is assumed, a seasonal variation similar to Figure 6(c) is obtained.

Recently, [START_REF] Franz | Initial SAM calibration gas experiments on Mars: Quadrupole mass spectrometer results and implications[END_REF] revised the volume mixing ratio of both N 2 and CO 2 measured by MSL, which suggests that the surface N 2 /CO 2 value is higher by a factor of ~1.5 than that measured by [START_REF] Mahaffy | Abundance and Isotopic Composition of Gases in the Martian Atmosphere from the Curiosity Rover[END_REF] and used by the MCD. We find that a factor of 1.5 increase in the surface mixing ratio uniformly increases the inferred homopause altitude by ~10 km.

Figure 7 shows time variations of pressure at 140 km as in Figure 2. As the pressure, CO 2 partial pressure derived from CO 2 density and temperature is applied. We assume an isothermal atmosphere; i.e., the temperature at 175 km derived from IUVS observations are used. Uncertainties of pressure are calculated from both that of CO 2 density and temperature, shown as gray bars. Pressure changes between ~4×10 -6 and ~3×10 -4 Pa and shows a seasonal sinusoidal trend; higher pressure appears around perihelion and lower pressure around aphelion. A similarity of seasonal trend between N 2 /CO 2 and pressure would suggest that N 2 /CO 2 variation at 140 km is mainly caused by variation of background pressure due to the inflation and contraction of the lower atmosphere. While we found that seasonal N 2 /CO 2 ratio varies at a given altitude, we could not identify the seasonal variation at a given pressure level. It is noted that the N 2 /CO 2 variation from MY 33 L s = 340° to MY 34 L s = ~30° is somewhat different to the pressure variation over the same period. This might imply that N 2 /CO 2 could also change slightly via other mechanisms.

The CO 2 density at the inferred homopause altitude, extrapolated from the CO 2 density at 140 km, is shown in Figure 8, which are extrapolated from CO 2 density at 140 km altitude. The average value is 2.6×10 11 cm -3 but it deviates between 10 10 and ~10 13 cm -3 .

Distributions of CO 2 density at the inferred homopause altitude suggest that dayside homopause altitude changes would be generated by two factors: (1) the inflation and contraction of the lower atmosphere due to changing of solar irradiance that changes the homopause altitude at a fixed pressure level, (2) eddy diffusion via turbulence related to atmospheric wave activity as reported by [START_REF] Slipski | Variability of Martian turbopause altitudes[END_REF] that changes the pressure level at the homopause. Although our study doesn't include dust storm events, the atmospheric heating due to the dust loading in the lower atmosphere, which absorbs the solar irradiation, could cause the change in homopause altitude and N 2 /CO 2 variation in the upper atmosphere.

We have also inferred the latitudinal dependence of homopause altitudes. In Figure 9, plots of inferred homopause altitude vs. latitude are shown for the same seasons as in Figure 5. In Figure 9(a), the inferred homopause altitudes in the northern summer decrease toward the southern winter polar region. The difference in altitudes between northern and southern hemispheres is about ~30 km. In Figure 9(b), the latitudinal dependence of inferred homopause altitudes in the northern spring disappears. This is the first observational evidence of a latitudinal dependence of dayside homopause altitudes, which matches well with model predictions by [START_REF] González-Galindo | A ground-toexosphere Martian general circulation model: 1. Seasonal, diurnal, and solar cycle variation of thermosphere temperatures[END_REF]. In their model, homopause altitude is defined where mixing ratio of CO 2 equals to 0.9. They mentioned that lower homopause altitudes in southern winter indicate a relative depletion of CO 2 in the upper atmosphere. Certainly, our observations showed that relative depletion of CO 2 in the southern hemisphere. [START_REF] González-Galindo | A ground-toexosphere Martian general circulation model: 1. Seasonal, diurnal, and solar cycle variation of thermosphere temperatures[END_REF] indicated that the depletion of CO 2 could result from the condensation of CO 2 due to colder temperatures or the meridional transportation of CO 2 -poor air from the upper thermosphere. Latitudinal asymmetrical heating in the lower atmosphere due to its season would also be a potential driver of the latitudinal dependence of homopause altitude. The driver of the latitudinal dependence of homopause altitudes, however, cannot be fully constrained by our study.

Comparison of densities and composition with Mars Climate Database predictions

Figure 10 shows a comparison of densities of CO 2 and N 2 , and N 2 /CO 2 derived from IUVS observations with those predicted by the MCD using an average solar EUV input and a typical dust climatology for the corresponding geometries of the IUVS observations. IUVS observations are shown as black dots. The gray bars represent uncertainties of IUVS observations. The MCD predictions are shown as red dots. The MCD well reproduces the seasonal variation of N 2 /CO 2 derived from IUVS observations throughout the observation period. However, the MCD overestimates the N 2 /CO 2 value at 140 km by a factor of two. The possible reason for this discrepancy is that the homopause altitude is too low in the MCD. As can be seen in Figure 10, the MCD shows large discrepancies of N 2 densities between L s = 30° and L s = 70° in MY 33 with an opposite trend in the N 2 densities between L s = 340° and L s = ~40° in MY 33 to 34. The opposite trend found in this study suggests that the treatment of minor species in the model is not perfect, and further investigation is required to explain the contradiction with the observations reported here (private communication with F. González-Galindo, E. Millour, & F. Forget). Further studies of discrepancies between the model and observations offer opportunities to improve our understanding of atmospheric composition in the upper atmosphere.

Conclusions

In this paper, we have investigated dayside N 2 /CO 2 at 140 km using MAVEN/IUVS limb scan observations from October 2014 to May 2018. We find that N 2 /CO 2 at 140 km significantly varies in the range of 0.02 to 0.20 and clearly exhibits seasonal and latitudinal dependences. Seasonal dependence is observed throughout the MAVEN mission, which shows a sinusoidal trend that N 2 /CO 2 is largest near aphelion (~0.063 on average between 50° and 90° in L s ) and smallest near perihelion (~0.031 on average between 230° and 270° in L s ).

A latitudinal dependence of N 2 /CO 2 is found in the northern summer. N 2 /CO 2 increases toward the southern winter hemisphere by a factor of two (between latitude 45°S and 25°N).

Meanwhile, the latitudinal dependence of N 2 /CO 2 disappears in the northern spring.

In order to reveal the drivers of seasonal variations of N 2 /CO 2 at 140 km, we have examined the effects of surface N 2 /CO 2 , thermospheric temperature, and homopause altitude.

Homopause altitudes inferred from IUVS under the assumption of an isothermal atmosphere and a fixed surface N 2 /CO 2 are estimated to vary between 100 and 130 km. The altitudes of inferred homopause and seasonal trends agree reasonably well with [START_REF] Slipski | Variability of Martian turbopause altitudes[END_REF]. The variations of the homopause altitude could be the dominant driver of changes in N 2 /CO 2 ratios in the thermosphere. In addition, we inferred homopause altitudes by considering the variations of both surface N 2 /CO 2 and thermospheric temperature by combining the MCD predictions with IUVS observations. Our inferred homopause altitudes vary between ~60 and 140 km altitude throughout the MAVEN mission and exhibit an anti-correlation with a seasonal sinusoidal trend of N 2 /CO 2 at 140 km. Distributions of CO 2 density at the inferred homopause altitude suggest that dayside homopause is mainly controlled by inflation and contraction of the lower atmosphere. Variations of observed N 2 /CO 2 ratio at 140 km are associated with CO 2 number density, namely pressure, at 140 km. Thus, we suggest that inflation of the lower atmosphere near perihelion causes an increase in the dayside homopause altitude and a decrease in the mixing ratio of N 2 in the upper atmosphere. Our results show, for the first time, the clear evidence for a latitudinal dependence of homopause altitudes in the northern summer. The inferred homopause altitudes in the northern summer decrease toward the southern winter polar region. The difference in altitudes between northern and southern hemispheres is about ~30 km. On the other hand, the latitudinal dependence of inferred homopause altitudes in the northern spring disappears.

We have compared IUVS observational results with model predictions of N 2 /CO 2 from MCD v5.3. The MCD well reproduces the seasonal variation of N 2 /CO 2 derived from IUVS observations throughout the MAVEN mission. However, the MCD overestimates IUVS N 2 /CO 2 values by a factor of two. A possible reason for this discrepancy is that the homopause altitude is systematically low in the MCD. The observation of the N 2 mixing ratio at 140 km by MAVEN/IUVS offers a source for improvements to atmospheric composition in global circulation models.

IUVS observations imply significant impacts to the variations of the homopause altitude on atmospheric composition in Mars' upper thermosphere. Our results support the idea that atmospheric composition in the exosphere varies with the homopause altitude.

Understanding the influence of the homopause altitude on the escape of minor species should be clarified in future work. Corresponding CO 2 partial pressure is calculated to be based on IUVS observations both CO 2 density at 140 km and temperature at 175 km under the assumption for isothermal atmosphere.

  reported substantial variations of the homopause altitude by using vertical profiles of N 2 / 40 Ar observed by NGIMS. The inferred homopause altitudes are located between 60 and 140 km. Slipski et al. (2018) demonstrated the possibility of a seasonal change in homopause altitude at noon by ~30 km, with the largest values observed between L s = 240° and 360° and the smallest values between ~50° and 180°. Slipski et al. (2018) also showed the latitudinal dependence of homopause altitudes, but a clear latitudinal dependence predicted in González-Galindo et al. (2009) was not obtained because latitudinal and local time effects could not be distinguished due to the NGIMS observing geometry.

  We analyzed CO 2 and N 2 densities derived from IUVS limb scan observations from October 2014 to May 2018, which correspond to 9258 profiles. The tangential footprints of IUVS limb observation included in the analysis are shown in Figure1. The dayside measurements by IUVS have been performed in several groups of orbits during different seasons throughout the MAVEN mission. Local time is limited from 7:00 to 19:00 except for observations around the southern polar region. SZA is in the range from 0° to 75°. IUVS limb observations over the time period considered here provide good coverage in longitude, latitude, local time, and season.3 ResultsTime variations of IUVS observations vs. L s are shown in Figure2. Figure2(a) provides the Sun-Mars distance (blue line) and the orbit averaged solar EUV irradiance at 17 -22 nm observed by the Extreme UltraViolet Monitor (EUVM) (Eparvier et al., 2015) aboard MAVEN (black line). Figures 2(b)-2(d) show the observed CO 2 density, N 2 density, and N - 2 /CO 2 at 140 km, respectively. Colors correspond to the observed local time. Uncertainties are shown by gray bars. The dayside N 2 /CO 2 varies from 0.02 to 0.20, but variations of CO 2 density, N 2 density, and N 2 /CO 2 shown in Figure 2 include effects of season, local time, and latitude. A short-term variation of N 2 /CO 2 during L s = 30° -70° in Martian Year (MY) 33, L s = 120° -160° in MY 33, and L s = 340° -40° through MY 33 to MY 34, which correspond to orbits around 1800 -2200, 2900 -3500, and 4800 -5500, respectively, is seen in Figure 2(d).

Figure 4

 4 Figure 4 represent the combination of local time and seasonal variations, thus caution must be taken. Data taken during L s = 120°-160° in MY 33, the second column in Figure 4, correspond to an increasing of number density with season. Meanwhile, data taken during L s = 30°-70° in MY 33 and L s = 340°-40° in MY 33 to 34, the first and the third columns in Figure 4, correspond to a decreasing of number density with season.

  , plots of densities vs. latitude and N 2 /CO 2 vs. latitude in the northern summer (L s = 80° -100°) are shown in Figures 5(a) through 5(c), and in the northern spring (L s = 340° -360°) are shown in Figures 5(d) through 5(f), respectively. It is noted that the latitudinal variation observed in the northern spring contains observations during both MY 32 and MY 33. MYs in the northern spring are distinguished by color in Figure 5. Uncertainties are shown by gray bars.

(

  2013) is ~0.020 at L s = 187.5°. Figures6(a) and 6(b) show N 2 /CO 2 in the homosphere derived from the MCD and temperature at 175 km observed from IUVS, respectively, which are used to infer homopause altitudes. The MCD predicts N 2 /CO 2 values within the range between 0.012 and 0.022. The MCD N 2 /CO 2 obtained around L s = 270° in MY 33 (orbits near 4000) are remarkably low because N 2 /CO 2 has a gradient toward the higher latitude in the MCD. Roughly speaking, the MCD predictions of N 2 /CO 2 in the homosphere except for the data in the polar region are well matched with the observation of surface N 2 /CO 2 from

Figure 1 .

 1 Figure 1. The tangential footprint of IUVS limb observation analyzed in this paper. (a) Solar longitude (L s ; deg), (b) local time (hours), (c) SZA (deg), and (d) latitude (deg). The horizontal axis shows orbit number (bottom) and corresponding Earth date (top).

Figure 2 .

 2 Figure 2. Time variations of (a) solar EUV irradiance (mW m -2 ; black), the Sun-Mars distance (AU; blue), number densities (cm -3 ) of (b) CO 2 , (c) N 2 , and (d) N 2 /CO 2 at 140 km altitude. Uncertainties are shown by gray bars in (b, c, d). Colors in (b, c, d) represent the local time (hours) of observation. The lower horizontal axis shows L s and Mars Year (MY) and that of top shows corresponding Earth date.

Figure 3 .

 3 Figure 3. The variations of (a) CO 2 and (b) N 2 density, and (c) N 2 /CO 2 at 140 km altitude as a function of L s . IUVS observations are constrained at specific local time bins, including 8:00 -10:00 (purple), 12:00 -14:00 (light blue), and 16:00 -18:00 (yellow). Data obtained in MY 32, 33, and 34 are indicated with triangles, diamonds, and squares, respectively.

Figure 4 .

 4 Figure 4. Local time variations of CO 2 , N 2 , and N 2 /CO 2 at 140 km altitude. Uncertainties are shown by gray bars. Data shown are constrained to three seasons. (a, b, c) Observations from L s 30° to 70° in MY 33, which correspond with orbits around 1800 -2200. (d, e, f) Observations from L s 120° to 160° in MY 33, which correspond with orbits around 2900 -3500. (g, h, i) Observations from L s 340° to 40° in MY 33 through 34, which correspond with orbits around 4800 -5500.

Figure 5 .

 5 Figure 5. Latitudinal variations of CO 2 , N 2 , and N 2 /CO 2 at 140 km altitude. Uncertainties are shown by gray bars. Local time is limited from 10:00 to 14:00. (a, c, e) L s is limited between 80° and 100°, which corresponds to the northern summer. (b, d, f) L s is between 340° and 360°, which corresponds to the northern spring. MYs observed between 340° and 360° are distinguished by colors; red is MY 32 and black is MY 33.

Figure 6 .

 6 Figure 6. Time variations of (a) N 2 /CO 2 at 50 km, in the homosphere, predicted by the MCD, (b) temperature (K) at 175 km observed by IUVS, and (c) inferred homopause altitude (km)considering the effect of variations of N 2 /CO 2 in homosphere, isothermal thermospheric temperature, and N 2 /CO 2 at 140 km.

Figure 7 .

 7 Figure 7. The same as Figure 2 (b) but CO 2 partial pressure at 140 km altitude is shown.

  ) and 3(b) demonstrate that CO 2 and N 2 densities, distinguished by local time, vary with L s . Those variations correspond to the inflation and contraction of the lower atmosphere. It is noteworthy that variations in CO 2 densities have a larger amplitude than variations in N 2 densities and this affects the variation of N 2 /CO 2 . The seasonal N 2 /CO 2 variations, which in the local time bin of 12:00 -14:00 become ~0.063 on average during aphelion (between 50°

	and 90° in L s ) and ~0.031 on average during perihelion (between 230° and 270° in L s ), show
	an anti-correlation with the variations of CO 2 and N 2 densities. The other local time bins also
	demonstrate a clear seasonal variation.
	Higher number densities of CO 2 and N 2 appear around perihelion (L s ~ 250°). Lower number
	densities appear around aphelion (L s ~ 70°). This seasonal variation of CO 2 density obtained
	in this study agrees well with that found by Mars Express (MEx) Spectroscopy for
	Investigation of Characteristics of the Atmosphere Mars (SPICAM) observations of CO 2
	density in the lower thermosphere (Forget et al., 2009). Although each profile's density

depends on the combinations of local time, latitude, and local season, the variations in CO 2 and N 2 densities at 140 km observed by IUVS limb show predominately a seasonal sinusoidal trend.

Acknowledgments

This study was supported by Grant-in-Aids for Scientific Research (C) No. 19K03943 and No. 18H04453 and for Scientific Research (A) No. 19H00707 and No. 16H02229 from JSPS. The MAVEN project is supported by NASA through the Mars Exploration Program. This work was conducted under NASA's MAVEN Participating Scientist Program (proposal #12-MAVENPS12-0017, PI: K. Seki). YN is supported by The international Joint Graduate Program in Earth and Environmental Sciences, Tohoku University (GP-EES). YN would like to acknowledge F. González-Galindo, E. Millour, and F.

Forget for their assistance and fruitful comments with the results of the MCD in this paper.

YN highly appreciates constructive comments and feedback from anonymous reviewers and Editor, and B. Johnston's kind proofreading.

Data Availability Statement MAVEN/IUVS limb level 2 version 13 revision 1 data used in this study are available through the NASA Planetary Data System (PDS) at https://atmos.nmsu.edu/data_and_services/atmospheres_data/MAVEN/limb.html. (Schneider, N. et al., MAVEN IUVS Derived-level Data product Bundle, urn:nasa:pds:maven.iuvs.processed 2015). MAVEN/EUVM level 2 version 11 revision 4 data are available through the NASA PDS at https://pds-ppi.igpp.ucla.edu. (Eparvier, F. G., MAVEN EUV calibrated irradiances Data Collection, urn:nasa:pds:maven.euv.calibrated:data.bands 2020) The full version of MCD v5.3 was provided from E. Millour. The results retrieved from the IUVS limb observation and extracted from the MCD used in this article are available at https://scholar.colorado.edu/concern/datasets/q237ht027, [START_REF] Yoshida | MAVEN/IUVS interpolated Limb data and predicted MCD data for the derivation of homopause altitude[END_REF].