Martian Thermosphere Research Articles

Solar Rotation Effects in Martian Thermospheric Density as Revealed by Five Years of MAVEN Observations

AbstractThe quasi‐periodic 27‐day solar rotation variation in extreme ultraviolet radiation represents the most prominent source of short‐term (40‐day) solar‐driven variability in Mars' thermosphere (ca. 125–250 km). Despite recent advances in our understanding of solar‐driven variations in Mars' thermosphere density and composition associated with solar flares, orbital eccentricity, and solar cycle afforded by new Mars Atmosphere and Volatile EvolutioN (MAVEN) observations, relatively little is known about this response to short‐term periodic solar flux variability. This work presents a detailed investigation of the solar rotation effects on the whole Martian thermosphere by applying correlation analysis techniques to over five years of coincident MAVEN Neutral Gas and Ion Spectrometer and Extreme Ultraviolet Monitor observations. Least squares methods are used to estimate the response of , Ar, and densities to the quasi‐27‐day solar rotation variability over the 0–7 nm, 17–22 nm, 0–45 nm, and 117–125 nm spectral bands. Results clearly reveal the presence of prominent solar rotation effects in the Martian thermosphere density for all species, irradiance bands, and altitudes. These effects are strongest at higher altitudes (200–250 km), while the dependence of the slope on solar zenith angle depends on the species, with having a higher slope on the nightside, Ar having a higher slope on the dayside, and having a different behavior depending on altitude.

Variability of temperatures and gravity wave activity in the Martian thermosphere during low solar irradiance

In this paper, we study the temperatures and gravity wave (GW) activity in the Martian thermosphere during low solar activity. For this purpose, we extracted the GW amplitudes and thermospheric temperatures from CO2 densities measured in situ by the Neutral Gas and Ion Mass Spectrometer (NGIMS) aboard the Mars Atmosphere and Volatile EvolutioN (MAVEN) mission. These observations were obtained during the declining phase of solar activity between solar longitude (Ls) =294° in Mars year (MY) 32 and Ls = 242° in MY 35. The observations of the present study show that the temperatures are lower and GW amplitudes are higher at low solar activity. The response of the thermospheric temperatures to solar irradiance is local time dependent such that the noontime and duskside temperatures show significant correlation (correlation coefficient, R > 0.8) with the solar irradiance whereas the temperatures on the dawnside show moderate correlation (R = 0.55). Furthermore, the nominal negative correlation between the gravity wave amplitudes and thermospheric temperatures, which was disturbed during the 2018 global dust event, was restored after the subsidence of the event. Interestingly, the correlation between the thermospheric temperatures and GW activity is also local time dependent with moderate correlation at noon (R = -0.65) and weak correlation at other local times. From the results of the present study, it is inferred that the variability of GW amplitudes in the Martian thermosphere are not necessarily controlled by the temperatures of the underlying atmosphere alone. Other factors, such as the variation of GW amplitudes at the source region and/or changes in the circulation of the underlying atmosphere, are also likely to play a significant role, particularly at the terminator and on the nightside.

Thermal structure of Mars’ middle and upper atmospheres: Understanding the impacts of dynamics and solar forcing

We report six years of observations of dayside temperatures of the middle and upper atmospheres of Mars made by the Imaging Ultraviolet Spectrograph instrument aboard the MAVEN spacecraft. Thermospheric temperatures show strong long-term variability associated with Martian season and solar cycle. Temperatures from both the Martian thermosphere and mesosphere show strong short-term variability indicating coupling from the lower atmosphere. The observed local time effect is strong in both upper and middle atmosphere temperatures. The thermosphere tends to be colder in the morning compared to the evening when temperatures are higher. Middle atmospheric temperatures show cooling during the dawn and dusk hours. Our analysis shows strong tidal activity during aphelion, whereas non-migrating tides are suppressed during perihelion, possibly due to increased dust activity. Observations during the deep minimum of solar cycle 24 reveal that thermospheric temperatures are highly variable with respect to local time if solar forcing, Mars–Sun distance, and spatial effects are removed.

Dust Storm‐Enhanced Gravity Wave Activity in the Martian Thermosphere Observed by MAVEN and Implication for Atmospheric Escape

AbstractLower atmospheric global dust storms affect the small‐ and large‐scale weather and variability of the whole Martian atmosphere. Analysis of the CO2 density data from the Neutral Gas and Ion Mass Spectrometer instrument on board NASA's Mars Atmosphere Volatile EvolutioN (MAVEN) spacecraft show a remarkable increase of gravity wave (GW)‐induced density fluctuations in the thermosphere during the 2018 major dust storm with distinct latitude and local time variability. The mean thermospheric GW activity increases by a factor of two during the storm event. The magnitude of relative density perturbations is around 20% on average and 40% locally. One and a half months later, the GW activity gradually decreases. Enhanced temperature disturbances in the Martian thermosphere can facilitate atmospheric escape. For the first time, we estimate observationally that, for a 20% and 40% GW‐induced disturbances, the net increase of Jeans escape flux of hydrogen is a factor of 1.3 and 2, respectively.

Species‐dependent Response of the Martian Ionosphere to the 2018 Global Dust Event

AbstractGlobal dust storms (GDS) are an important dynamical phenomenon of the Martian lower atmosphere but are known to have important impacts on the Martian middle/upper atmosphere and ionosphere. Despite extensive studies over the past several decades, how the composition of the Martian ionosphere is modified during the GDS has only been studied from a theoretical point of view. Here we present for the first time the observations of the compositional variation of the Martian ionosphere during the GDS in 2018, using the ion density measurements made by the Neutral Gas and Ion Mass Spectrometer onboard the Mars Atmosphere and Volatile Evolution. At a representative altitude of 170 km, the variations of ionospheric species during the GDS show either enhancement (, Ar+, , H2O+, , ArH+) or depletion (, O+, /CO+, OH+). Despite the apparent diversity, the observations are mostly understandable within the established framework of ionospheric chemistry on Mars, which further demonstrates that the variation of ion species during the GDS is a good diagnostic of the variation of relevant neutral species in the thermosphere. In particular, the observed ionospheric variation strongly supports a scenario that H2O is substantially enhanced in the Martian thermosphere during the GDS. However, the variations of and are inconsistent with predictions from ionospheric chemistry and require further investigation.

Tidal Effects on the Longitudinal Structures of the Martian Thermosphere and Topside Ionosphere Observed by MAVEN.

Longitudinal structures in the Martian thermosphere and topside ionosphere between 150 and 200 km altitudes are studied using in situ electron and neutral measurements from the NASA Mars Atmosphere and Volatile EvolutioN (MAVEN) mission. Four time intervals are selected for comparison, during which MAVEN sampled similar local time (9.3-10.3 h) and latitude (near 20°S) regions but at different solar longitude positions (two near northern summer solstice, one each at northern vernal and autumnal equinoxes). Persistent and pronounced tidal oscillations characterize the ionosphere and thermosphere, whose longitudinal variations in density are generally in-phase with each other. Our analysis of simultaneous and collocated neutral and electron data provides direct observational evidence for thermosphere-ionosphere coupling through atmospheric tides. We conclude that the ionosphere is subject to modulation by upward-propagating thermal tides, via both tide-induced vertical displacement and photochemical reactions. Atmospheric tides constitute a ubiquitous and significant perturbation source to the ionospheric electron density, up to ~15% near 200 km.

Interannual Variability of Atmospheric Gravity Waves in the Martian Thermosphere: Effects of the 2018 Planet‐Encircling Dust Event

AbstractWe study the interannual variability of atmospheric gravity waves (GWs) in the Martian thermosphere and their relation to the background temperatures using Ar densities measured by Neutral Gas and Ion Mass Spectrometer/Mars Atmosphere and Volatile Evolution (MAVEN). The amplitudes and wavelengths of the GWs are extracted from the neutral density perturbations in the inbound segment of the MAVEN orbit. The GW amplitudes predominantly lie between 5% and 10% and are mostly less than 30% of the background densities. The horizontal wavelengths are between 50 km and 300 km with peak wavelengths of 100–130 km. GW amplitudes show a significant diurnal variation with larger amplitudes during nighttime and smaller amplitudes during daytime. In addition, the GW amplitudes negatively correlate with the background temperatures indicating the role of convective instability in the saturation of the GWs. Most importantly, the GW amplitudes are larger and the wavelengths are smaller when there was a planet‐encircling dust event in the Mars’ lower atmosphere during 2018. As a result, the typical diurnal variation of GW amplitudes is not apparent. During the lower atmospheric dust event, the GW amplitudes do not show any significant correlation with the background temperatures. It is proposed that the PEDE‐2018 led to changes in the circulation of the mesosphere and lower thermosphere, so that the modified circulation enhanced the upward propagation/reduced the filtering of GWs leading to their enhancement in the upper thermosphere.

Seasonal and Latitudinal Variations of Dayside N2/CO2 Ratio in the Martian Thermosphere Derived From MAVEN IUVS Observations

AbstractThe dayside N2/CO2 at 140 km altitude in the Martian thermosphere has been investigated by the imaging ultraviolet spectrograph (IUVS) aboard the Mars atmosphere and volatile evolution spacecraft during the period from October 2014 to May 2018. We find that N2/CO2 at 140 km altitude varies significantly in the range of 0.02–0.20 and shows a seasonal sinusoidal trend. The higher value appears during aphelion and the lower value during perihelion. Variations of observed N2/CO2 ratio at 140 km are mainly associated with CO2 number density. Thus, while we found that N2/CO2 varies at a given altitude, we could not identify variations at a given pressure level. In order to reveal the drivers of N2/CO2 variations at 140 km, we examine the effects of surface N2/CO2, thermospheric temperature, and homopause altitude. The variations of homopause altitude could be the dominant driver of changes in N2/CO2. Inferred dayside homopause altitudes derived from IUVS observations show an anti‐correlation with the trend of N2/CO2 at 140 km. Distributions of CO2 density at the inferred homopause altitudes suggest that dayside homopause altitude is mainly controlled by inflation and contraction of the lower atmosphere. Additionally, N2/CO2 shows a clear latitudinal dependence for Ls = 80°–100°. Higher N2/CO2 values appear in the southern winter hemisphere, corresponding to lower homopause altitude by ∼30 km. Meanwhile, the latitudinal dependence of both N2/CO2 and homopause altitude disappears for Ls = 340°–360°.

First estimations of gravity wave potential energy in the Martian thermosphere: an analysis using MAVEN NGIMS data

ABSTRACT First estimations of Gravity Wave Potential Energy (GWPE) for Martian thermosphere are reported herein using the height profile of CO2 density derived temperature fluctuations for different Martian seasons during the 33rd Martian year. Explicit diurnal evolution of GWPE (52⁰ to 73⁰ latitude bin) with a post sunset maximum is delineated for summer. The higher values of GWPE are observed during morning, compared to post-midnight (35⁰ to 55⁰ latitude bin) for summer. As latitude increases from 16⁰ to 45⁰, GWPE (1-4 LT bin) is found to be nearly doubled for summer. Further, GWPE estimates in autumn are 6 times higher during night compared to day (-45⁰ to -72⁰ latitude bin) and day time (-53⁰ to -72⁰ latitude bin) GWPE is much lower in autumn compared to spring for all longitudes. Overall, from the available data, southern autumn daytime periods appear better suited for aero-braking operations of Martian landing missions.

Enhanced Densities in the Martian Thermosphere Associated With the 2018 Planet‐Encircling Dust Event: Results From MENCA/MOM and NGIMS/MAVEN

AbstractResponse of the Martian upper thermosphere to the lower atmospheric dust activity is studied using unique observations made together by the Mars Orbiter Mission (MOM) and the Mars Atmosphere and Volatile Evolution (MAVEN) spacecraft. The Mars Exospheric Neutral Composition Analyzer (MENCA)/MOM and the Neutral Gas and Ion Mass Spectrometer (NGIMS)/MAVEN have simultaneously (on the same day) measured the neutral densities in the Martian thermosphere on 5, 8, 10, 13, 16, and 29 June 2018. The measurement period falls in the onset and progression time of the planet‐encircling dust event (PEDE) in the Mars lower atmosphere. During this time, the inbound trajectories of MAVEN and MOM spacecraft occurred on the dawnside and duskside, respectively. Using these observations, we found that thermospheric densities both on the dawnside and duskside are enhanced associated with the onset and growth of PEDE‐2018. The enhancement, however, is more on the duskside than on the dawn, showing the dawn‐dusk asymmetry. The densities on the duskside reach their maximum on 29 June 2018, close to the time of peak dust activity. These results are explained by considering the local time asymmetries in radiative heating of the lower atmosphere and subsequent expansion of the thermosphere due to PEDE‐2018. Furthermore, O/CO2 ratios below 220‐km altitude become one on the dawnside, whereas they are always <0.2 at the dusk. This indicates that radiative cooling is more effective on the dawnside than the duskside.

Nitric Oxide Abundance in the Martian Thermosphere and Its Diurnal Variation

AbstractAs an important species of the Martian thermosphere, NO is chemically and radiatively active. However, its abundance is poorly constrained due to difficulties in both remote sensing and in situ measurements. In this study, we use the Neutral Gas and Ion Mass Spectrometer measurements made onboard the Mars Atmosphere and Volatile Evolution to derive the N(4S), N(2D), and NO abundances in the Martian thermosphere based on time‐dependent odd N chemistry. At a reference altitude of 160 km, our calculations suggest that the NO abundance is maximized in the afternoon whereas the N(4S) and N(2D) abundances maximized in the morning, both driven by the variation of the ambient N2 mixing ratio. The difference in chemical loss time scale implies a strong diurnal variation for NO and N(2D) but a weak variation for N(4S).

Effect of the 2018 Martian Global Dust Storm on the CO2 Density in the Lower Nightside Thermosphere Observed From MAVEN/IUVS Lyman‐Alpha Absorption

AbstractThe MAVEN/Imaging Ultraviolet Spectrograph (IUVS) instrument measures Lyman‐α emissions from interplanetary and Martian hydrogen at the limb and through the extended corona of Mars. In June 2018, a global dust storm (GDS) surrounded Mars for a few months, heating the lower atmosphere and leading to an expansion of the Martian atmosphere. Nightside IUVS observations before and throughout this GDS showed the altitude of CO2 absorption of Lyman‐α photons in the thermosphere to increase by 4.5±1.0 km on 8 June 2018. This shift is attributed to an increase of the CO2 density by a factor 1.9±0.2 at 110 km due to the heating of the lower atmosphere. These nightside observations, not previously used to study dust storms, in an altitude range not sampled by other instruments, are consistent with dayside MAVEN observations and allow for more comprehensive determination of the global changes produced by the GDS on the Martian thermosphere.

Modeling Wind‐Driven Ionospheric Dynamo Currents at Mars: Expectations for InSight Magnetic Field Measurements

AbstractWe model expected dynamo currents above, and resulting magnetic field profiles at, InSight's landing site on Mars, including for the first time the effect of electron‐ion collisions. We calculate their diurnal and seasonal variability using inputs from global models of the Martian thermosphere, ionosphere, and magnetosphere. Modeled currents primarily depend on plasma densities and the strength of the neutral wind component perpendicular to the combined crustal and draped magnetic fields that thread the ionosphere. Negligible at night, currents are the strongest in the late morning and near solstices due to stronger winds and near perihelion due to both stronger winds and higher plasma densities from solar EUV photoionization. Resulting surface magnetic fields of tens of nanotesla and occasionally >100 nT may be expected at the InSight landing site. We expect currents and surface fields to vary significantly with changes in the draped magnetic field caused by Mars' dynamic solar wind environment.

Lyman-α emission in the Martian proton aurora: Line profile and role of horizontal induced magnetic field

Enhancements of the dayside Lyman-α emission by as much as ∼50% have been observed between 120 and 130 km in the lower Martian thermosphere from the Mars Express and MAVEN satellites, usually following solar events such as coronal mass ejections and corotating interaction regions. They have been assumed to be optical signatures of proton aurora related to an increase in the solar wind proton flux hitting Mars’ bow shock. We present model simulations of the Lyman-α line profiles at different altitudes. These are partly guided by in situ measurements of the energy spectrum of protons in the magnetosheath region by the SWIA instrument on board the MAVEN spacecraft. We show that the auroral Lyman-α line profile is significantly broader than the hydrogen core of the planetary thermal H atom. Consequently, most of the auroral emission is produced outside the optically thick hydrogen core and creates the observed intensity enhancement. Simulations with incident energetic hydrogen atoms (H ENAs) produce a somewhat broader line profile. Monte Carlo calculations are made separately for incident solar wind protons and H ENAs produced by charge exchange in the hydrogen corona. Absorption by CO2 along the line of sight significantly affects the intensity distribution in the lower thermosphere. The calculated altitude of the peak emission for both types of incident particles is consistent with the observed characteristics of the proton aurora. We show that the presence of a horizontal induced magnetic field somewhat increases the line width and decreases the altitude of the emission peak as a consequence of the magnetic barrier effect on proton precipitation. The brightness of the Lyman-α emission also drops as a result of increased magnetic shielding of the protons.

Photochemistry of water in the martian thermosphere and its effect on hydrogen escape

Recent SPICAM IR solar occultations reveal significant abundances of water vapor up to ≈80 km near Mars perihelion. These abundances are stimulated by dust that heats the atmosphere and precludes condensation of water. This phenomenon correlates with detections of high escape of hydrogen near perihelion using the H Lyman-alpha in the SPICAM UV and HST observations. Here we present a self-consistent photochemical model of the martian neutral and ion composition at 80–300 km that accounts for variations of the atmospheric composition with solar activity and water abundance at 80 km. The model involves vertical transport by eddy, molecular, and ambipolar diffusion and both thermal and nonthermal escape of light species. The model predicts rather stable hydrogen escape of ≈1.9 × 108 cm−2 s−1 at 250 km during the most of the martian year beyond the perihelion period at LS = 200–330°. The reaction between H2 and CO2+ remains here the key process that determines the hydrogen escape. Therefore the HST observation of D and the FUSE observation of H2 at LS = 68 and 160°, respectively, do not need revision. Appearance of water in the thermosphere during the perihelion period results in significant increase in production of hydrogen by photolysis of water and reactions of its ions. Photolysis of H2O is the most effective at 160–180 nm and weakly depends on solar activity. Reactions of water ions start chiefly by charge exchange between CO2+ and H2O and end by recombination of H3O+. Both H2O photolysis and its ion reactions proceed near 100 km, and just a small part of the hydrogen production can escape. The calculated hydrogen escape at 250 km may be approximated by ΦH (cm−2 s−1) = 1.6 × 108 + 1.4 × 107fH2O (ppm). Here fH2O is the H2O mixing ratio at 80 km that is reduced to 150 km by a factor of 5 by the photolysis and ion reactions. Therefore the observed high hydrogen escape up to 109 cm−2 s−1 requires the dayside-mean water abundances up to 60 ppm at 80 km that are within those observed by the SPICAM IR solar occultations. The significant H2O abundances do not deplete densities of HCO+ and are compatible with the MAVEN/NGIMS ion composition. The H Lyman-alpha observations reflect mostly the dayside-mean photochemistry, and our one-dimensional model may adequately respond to the problem.

Martian Electron Temperatures in the Subsolar Region: MAVEN Observations Compared to a One‐Dimensional Model

AbstractPrior to the Mars Atmospheric Volatile EvolutioN (MAVEN) mission, altitude profiles of the electron temperature in the Martian thermosphere were measured only twice. Because the rates of several geophysically important processes depend strongly on the electron temperature, models of the Martian thermosphere and atmospheric escape rates have not been well constrained. In this paper, we use densities and temperatures measured by MAVEN instruments and the one‐dimensional model of Matta et al. (2014, https://doi.org/10.1016/j.icarus.2013.09.006) to test our understanding of the processes that determine the electron temperature. Our analysis is limited to inbound orbits where the magnetic field is within 30° of horizontal and the satellite is within 30° of the subsolar point at altitudes from 120 to 250 km. We introduce empirically adjusted electron temperatures below 180 km, where the MAVEN electron temperature measurements are known to be biased high. We introduce the concept of a local electron heating efficiency, which we define at a given altitude as the ratio of electron heating from photoionization to the total extreme ultraviolet energy deposited. Our analysis shows that MAVEN observations are consistent with the one‐dimensional model below ~210 km if the electron heating efficiency varies with altitude, and the electron temperature is within the empirical bounds below 180 km we introduced. It indicates that above ~210 km electron heat conduction dominates extreme ultraviolet heating in determining electron temperature. Our analysis also suggests that in the subsolar region electrons and neutrals are in thermal equilibrium below 120 km.

Escape of O(3P), O(1D), and O(1S) from the Martian atmosphere

We have computed here the escape probabilities, fluxes and rates for hot O atoms that are initially produced in the ground state and the first two excited metastable states, O(1D)and O(1S), in the Martian thermosphere by dissociative recombination of O2+. In order to compare our results with those of our previous calculations and with those of others, we have employed here the pre-MAVEN models that we have used previously. To compute the escape probabilities, we have employed the Monte Carlo escape code that has been described previously, but we here use for the first time energy-dependent elastic cross sections for collisions of the energetic O atoms with each of the twelve background species in our model. We also incorporate three mechanisms that interchange identities of the O(3P) and O(1D) atoms, including collisional excitation of O(3P) to O(1D), quenching of O(1D) to O(3P), and excitation exchange of O(1D) with O(3P). We find that the escape probabilities of O atoms that are produced initially as O(1D) are reduced compared to those in which these processes are not included, but the escape probabilities of O atoms that are initially produced as O(3P) are not significantly reduced. As a guide for our future research and those of other investigators, we review here what is known about the interactions of O atoms with other species in which the energies of the O atoms are altered, and several other sources of hot and escaping O, many of which have been suggested by other investigators. We will incorporate these data in a future MAVEN-like model.

Sources of Ionospheric Variability at Mars

AbstractDuring the Mars Atmosphere and Volatile EvolutioN (MAVEN) mission's deep‐dip #2 campaign of 17–22 April 2015, spacecraft instruments observed all of the physical parameters needed to assess the photo‐chemical‐equilibrium (PCE) explanation for ionospheric variability at a fixed altitude (135 km) near the peak of the Martian ionosphere. MAVEN measurements of electron density, electron temperature, neutral CO2 density, and solar irradiance were collected during 28 orbits. When inserted into the PCE equation, the measurements of varying PCE drivers correlated with the observed electron density variations to within instrumental uncertainty levels. The dominant source of this positive correlation was the variability of CO2 densities associated with the longitudinal wave‐2 component of nonmigrating tides in the Martian thermosphere.

Photochemical determination of O densities in the Martian thermosphere: Effect of a revised rate coefficient

AbstractWe investigate the production and loss rates of in the photochemical equilibrium region of the Martian ionosphere near the subsolar point. We adopt neutral and ion densities measured by the Mars Atmosphere and Volatiles EvolutioN (MAVEN) Neutral Gas and Ion Mass Spectrometer (NGIMS), electron densities and temperatures measured by the Langmuir Probe and Waves, and ion temperatures measured by the Supra‐Thermal and Thermal Ion Composition instruments on the MAVEN spacecraft. Contrary to the conventional wisdom, we find that loss of by dissociative recombination is balanced mainly by production due to the reaction of O+ with CO2, with a smaller contribution due to the reaction of with O. We find that the O densities derived from this calculation are larger than those measured by the NGIMS instrument by a factor that averages about 4 over the range of 130–155 km. This general conclusion is supported by a newly measured rate coefficient for the reaction of O with , which is smaller by a factor of about 6 than the only value in the literature, which was measured 47 years ago.

MAVEN NGIMS observations of atmospheric gravity waves in the Martian thermosphere

AbstractGravity waves have a significant impact on both the dynamics and energy budget of the Martian thermosphere. Strong density variations of spatial scales indicative of gravity waves have previously been identified in this region by using in situ observations. Here we use observations from the Neutral Gas and Ion Mass Spectrometer (NGIMS) mass spectrometer on Mars Atmosphere and Volatile EvolutioN Mission to identify such waves in the observations of different atmospheric species. The wave signatures seen in CO2 and Ar are almost identical, whereas the wave signature seen in N2, which is lighter and has a larger scale height, is generally smaller in amplitude and slightly out of phase with those seen in CO2 and Ar. Examination of the observed wave properties in these three species suggests that relatively long vertical wavelength atmospheric gravity waves are the likely source of the waves seen by NGIMS in the upper thermosphere. A two‐fluid linear model of the wave perturbations in CO2 and N2 has been used to find the best fit intrinsic wave parameters that match the observed features in these two species. We report the first observationally based estimate of the heating and cooling rates of the Martian thermosphere created by the waves observed in this region. The observed wave density amplitudes are anticorrelated with the background atmospheric temperature. The estimated heating rates show a weak positive correlation with the wave amplitude, whereas the cooling rates show a clearer negative correlation with the wave amplitude. Our estimates support previous model‐based findings that atmospheric gravity waves are a significant source of both heating and cooling.