Thermophysics of the planet Mercury

Recent observations of the thermal emission of Mercury at microwave and infrared frequencies now permit a determination of the thermal and electrical properties of the subsurface of the planet. Radar and optical measurements show that the rotation period is 58.65 days, 2/3 of the orbital period. Several negative spectrographic searches verify that the effects of an atmosphere need not be taken into account in computing surface and subsurface temperatures. The observed thermal emission from the planet can then be interpreted from models similar to those developed for study of the Moon but adapted to the peculiar diurnal insolation of Mercury. The observations of Epstein et al. (1970) at 3.3 mm and of Klein (1970a) at 3.75 cm, when interpreted together with recent laboratory measurements of thermal properties of terrestrial and lunar rock powders, indicate that the ratio of electrical to thermal skin depth is 0.9 ± 0.3 times the wavelength in centimeters. Further results of this analysis of the subsurface are: Density = 1.5 ± 0.4 g cm^-3; Electric loss tangent = 0.009 ± 0.004; Inverse thermal inertia = (15 ± 6) × 10^–6 erg^-1 cm² s^1/2 K; Equatorial midnight temperature = 100 ± 15K.The microwave data generally conform to the predictions of the thermophysical models of Mercury developed by Morrison and Sagan (1967), including a suggestion that variations having mean periods of 50 days and 35 days are present in addition to the classical phase effect with period about 116 days. The time-averaged microwave temperature of the planet appears to increase 25 % from millimeter to decimeter wavelengths; this increase suggests that radiation plays an important role in the transport of heat in the subsurface. All of the conclusions of this review indicate that the thermophysical behavior of Mercury closely approximates that expected for the Moon, were it placed in the orbit of Mercury.     

Missions to Mercury

Mercury is a very difficult planet to observe from the Earth, and space missions that target Mercury are essential for a comprehensive understanding of the planet. At the same time, it is also difficult to orbit because it is deep inside the Sun’s gravitational well. Only one mission has visited Mercury; that was Mariner 10 in the 1970s. This paper provides a brief history of Mariner 10 and the numerous imaginative but unsuccessful mission proposals since the 1970s for another Mercury mission. In the late 1990s, two missions—MESSENGER and BepiColombo—received the go-ahead; MESSENGER is on its way to its first encounter with Mercury in January 2008. The history, scientific objectives, mission designs, and payloads of both these missions are described in detail.     

MESSENGER and the Chemistry of Mercury’s Surface

The instrument suite on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft is well suited to address several of Mercury’s outstanding geochemical problems. A combination of data from the Gamma-Ray and Neutron Spectrometer (GRNS) and X-Ray Spectrometer (XRS) instruments will yield the surface abundances of both volatile (K) and refractory (Al, Ca, and Th) elements, which will test the three competing hypotheses for the origin of Mercury’s high bulk metal fraction: aerodynamic drag in the early solar nebula, preferential vaporization of silicates, or giant impact. These same elements, with the addition of Mg, Si, and Fe, will put significant constraints on geochemical processes that have formed the crust and produced any later volcanism. The Neutron Spectrometer sensor on the GRNS instrument will yield estimates of the amount of H in surface materials and may ascertain if the permanently shadowed polar craters have a significant excess of H due to water ice. A comparison of the FeO content of olivine and pyroxene determined by the Mercury Atmospheric and Surface Composition Spectrometer (MASCS) instrument with the total Fe determined through both GRNS and XRS will permit an estimate of the amount of Fe present in other forms, including metal and sulfides.     

飞向水星

人类数千年前就发现了水星,但至今对水星的了解却非常有限。为了研究水星表面的特征和环境,特别是水星表面的成分、水星内核和覆盖物、磁场和稀薄大气,搜索水冰和其他结冰的易挥发物,进而了解地球的起源、形成和演化过程,了解地磁场的演化和变化规律,揭示许多未知的领域,美国先后发射了2颗水星探测器,欧洲和日本也正在联合实施水星探测计划     

Processes that Promote and Deplete the Exosphere of Mercury

It has been speculated that the composition of the exosphere is related to the composition of Mercury’s crustal materials. If this relationship is true, then inferences regarding the bulk chemistry of the planet might be made from a thorough exospheric study. The most vexing of all unsolved problems is the uncertainty in the source of each component. Historically, it has been believed that H and He come primarily from the solar wind (Goldstein, B.E., et al. in J. Geophys. Res. 86:5485–5499, 1981), Na and K come from volatilized materials partitioned between Mercury’s crust and meteoritic impactors (Hunten, D.M., et al. in Mercury, pp. 562–612, 1988; Morgan, T.H., et al. in Icarus 74:156–170, 1988; Killen, R.M., et al. in Icarus 171:1–19, 2004b). The processes that eject atoms and molecules into the exosphere of Mercury are generally considered to be thermal vaporization, photon-stimulated desorption (PSD), impact vaporization, and ion sputtering. Each of these processes has its own temporal and spatial dependence. The exosphere is strongly influenced by Mercury’s highly elliptical orbit and rapid orbital speed. As a consequence the surface undergoes large fluctuations in temperature and experiences differences of insolation with longitude. Because there is no inclination of the orbital axis, there are regions at extreme northern and southern latitudes that are never exposed to direct sunlight. These cold regions may serve as traps for exospheric constituents or for material that is brought in by exogenic sources such as comets, interplanetary dust, or solar wind, etc. The source rates are dependent not only on temperature and composition of the surface, but also on such factors as porosity, mineralogy, and space weathering. They are not independent of each other. For instance, ion impact may create crystal defects which enhance diffusion of atoms through the grain, and in turn enhance the efficiency of PSD. The impact flux and the size distribution of impactors affects regolith turnover rates (gardening) and the depth dependence of vaporization rates. Gardening serves both as a sink for material and as a source for fresh material. This is extremely important in bounding the rates of the other processes. Space weathering effects, such as the creation of needle-like structures in the regolith, will limit the ejection of atoms by such processes as PSD and ion-sputtering. Therefore, the use of laboratory rates in estimates of exospheric source rates can be helpful but also are often inaccurate if not modified appropriately. Porosity effects may reduce yields by a factor of three (Cassidy, T.A., and Johnson, R.E. in Icarus 176:499–507, 2005). The loss of all atomic species from Mercury’s exosphere other than H and He must be by non-thermal escape. The relative rates of photo-ionization, loss of photo-ions to the solar wind, entrainment of ions in the magnetosphere and direct impact of photo-ions to the surface are an area of active research. These source and loss processes will be discussed in this chapter.     

The Origin of Mercury

Mercury’s unusually high mean density has always been attributed to special circumstances that occurred during the formation of the planet or shortly thereafter, and due to the planet’s close proximity to the Sun. The nature of these special circumstances is still being debated and several scenarios, all proposed more than 20 years ago, have been suggested. In all scenarios, the high mean density is the result of severe fractionation occurring between silicates and iron. It is the origin of this fractionation that is at the centre of the debate: is it due to differences in condensation temperature and/or in material characteristics (e.g. density, strength)? Is it because of mantle evaporation due to the close proximity to the Sun? Or is it due to the blasting off of the mantle during a giant impact? In this paper we investigate, in some detail, the fractionation induced by a giant impact on a proto-Mercury having roughly chondritic elemental abundances. We have extended the previous work on this hypothesis in two significant directions. First, we have considerably increased the resolution of the simulation of the collision itself. Second, we have addressed the fate of the ejecta following the impact by computing the expected reaccretion timescale and comparing it to the removal timescale from gravitational interactions with other planets (essentially Venus) and the Poynting–Robertson effect. To compute the latter, we have determined the expected size distribution of the condensates formed during the cooling of the expanding vapor cloud generated by the impact. We find that, even though some ejected material will be reaccreted, the removal of the mantle of proto-Mercury following a giant impact can indeed lead to the required long-term fractionation between silicates and iron and therefore account for the anomalously high mean density of the planet. Detailed coupled dynamical–chemical modeling of this formation mechanism should be carried out in such a way as to allow explicit testing of the giant impact hypothesis by forthcoming space missions (e.g. MESSENGER and BepiColombo).     

Surface-Exosphere-Magnetosphere System Of Mercury

Mercury is a poorly known planet, since the only space-based information comes from the three fly-bys performed in 1974 by the Mariner 10 spacecraft. Ground-based observations also provided some interesting results, but they are particularly difficult to obtain due to the planet’s proximity to the Sun. Nevertheless, the fact that the planet’s orbit is so close to the Sun makes Mercury a particularly interesting subject for extreme environmental conditions. Among a number of crucial scientific topics to be addressed, Mercury’s exosphere, its interaction with the solar wind and its origin from the surface of the planet, can provide important clues about planetary evolution. In fact, the Hermean exosphere is continuously eroded and refilled by these interactions, so that it would be more proper to consider the Hermean environment as a single, unified system – surface-exosphere-magnetosphere. These three parts are indeed strongly linked to each other. In recent years, the two missions scheduled to explore the iron planet, the NASA MESSENGER mission (launched in March 2004) and the ESA cornerstone mission (jointly with JAXA) BepiColombo (to be launched in 2012), have stimulated new interest in the many unresolved mysteries related to it. New ground-based observations, made possible by new technologies, have been obtained, and new simulation studies have been performed. In this paper some old as well as the very latest observations and studies related to the surface-exosphere-magnetosphere system are reviewed, outlining the investigations achievable by the planned space-based observations. This review intends to support the studies, in preparation of future data, and the definition of specific instrumentation.     

Radar Imaging of Mercury

Earth-based radar has been one of the few, and one of the most important, sources of new information about Mercury during the three decades since the Mariner 10 encounters. The emphasis during the past 15 years has been on full-disk, dual-polarization imaging of the planet, an effort that has been facilitated by the development of novel radar techniques and by improvements in radar systems. Probably the most important result of the imaging work has been the discovery and mapping of radar-bright features at the poles. The radar scattering properties of these features, and their confinement to permanently shaded crater floors, is consistent with volume backscatter from a low-loss volatile such as clean water ice. Questions remain, however, regarding the source and long-term stability of the putative ice, which underscores the need for independent confirmation by other observational methods. Radar images of the non-polar regions have also revealed a plethora of bright features, most of which are associated with fresh craters and their ejecta. Several very large impact features, with rays and other bright ejecta spreading over distances of 1,000 km or more, have been traced to source craters with diameters of 80–125 km. Among these large rayed features are some whose relative faintness suggests that they are being observed in an intermediate stage of degradation. Less extended ray/ejecta features have been found for some of the freshest medium-size craters such as Kuiper and Degas. Much more common are smaller (<40 km diameter) fresh craters showing bright rim-rings but little or no ray structure. These smaller radar-bright craters are particularly common over the H-7 quadrangle. Diffuse areas of enhanced depolarized brightness have been found in the smooth plains, including the circum-Caloris planitiae and Tolstoj Basin. This is an interesting finding, as it is the reverse of the albedo contrast seen between the radar-dark maria and the radar-bright cratered highlands on the Moon.     

Interior Evolution of Mercury

The interior evolution of Mercury—the innermost planet in the solar system, with its exceptional high density—is poorly known. Our current knowledge of Mercury is based on observations from Mariner 10’s three flybys. That knowledge includes the important discoveries of a weak, active magnetic field and a system of lobate scarps that suggests limited radial contraction of the planet during the last 4 billion years. We review existing models of Mercury’s interior evolution and further present new 2D and 3D convection models that consider both a strongly temperature-dependent viscosity and core cooling. These studies provide a framework for understanding the basic characteristics of the planet’s internal evolution as well as the role of the amount and distribution of radiogenic heat production, mantle viscosity, and sulfur content of the core have had on the history of Mercury’s interior. The existence of a dynamo-generated magnetic field suggests a growing inner core, as model calculations show that a thermally driven dynamo for Mercury is unlikely. Thermal evolution models suggest a range of possible upper limits for the sulfur content in the core. For large sulfur contents the model cores would be entirely fluid. The observation of limited planetary contraction (∼1–2 km)—if confirmed by future missions—may provide a lower limit for the core sulfur content. For smaller sulfur contents, the planetary contraction obtained after the end of the heavy bombardment due to inner core growth is larger than the observed value. Due to the present poor knowledge of various parameters, for example, the mantle rheology, the thermal conductivity of mantle and crust, and the amount and distribution of radiogenic heat production, it is not possible to constrain the core sulfur content nor the present state of the mantle. Therefore, it is difficult to robustly predict whether or not the mantle is conductive or in the convective regime. For instance, in the case of very inefficient planetary cooling—for example, as a consequence of a strong thermal insulation by a low conductivity crust and a stiff Newtonian mantle rheology—the predicted sulfur content can be as low as 1 wt% to match current estimates of planetary contraction, making deep mantle convection likely. Efficient cooling—for example, caused by the growth of a crust strongly in enriched in radiogenic elements—requires more than 6.5 wt% S. These latter models also predict a transition from a convective to a conductive mantle during the planet’s history. Data from future missions to Mercury will aid considerably our understanding of the evolution of its interior.     

Mercury: Magnetic field and interior

Between 1965 and 1975, our knowledge of Mercury and its physical characteristics improved dramatically. Radar studies of the planetary orbit and rotation rate and Mariner 10 spacecraft studies of its surface, atmosphere, magnetic field and plasma environment provided startling new results on what had been the least understood member of the terrestrial planets. With a highly cratered surface and a modest magnetic field, Mercury is a differentiated planet with fractionally the largest iron core of all.     

Earth-Based Visible and Near-IR Imaging of Mercury

New planned orbiter missions to Mercury have prompted renewed efforts to investigate the surface of Mercury via ground-based remote sensing. While the highest resolution instrumentation optical telescopes (e.g., HST) cannot be used at angular distances close to the Sun, advanced ground-based astronomical techniques and modern analytical and software can be used to obtain the resolved images of the poorly known or unknown part of Mercury. Our observations of the planet presented here were carried out in many observatories at morning and evening elongation of the planet. Stacking the acquired images of the hemisphere of Mercury, which was not observed by the Mariner 10 mission (1974–1975), is presented. Huge features found there change radically the existing hypothesis that the “continental” character of a surface may be attributed to the whole planet. We present the observational method, the data analysis approach, the resulting images and obtained properties of the Mercury’s surface.     

The Mercury Atmospheric and Surface Composition Spectrometer for the MESSENGER Mission

The Mercury Atmospheric and Surface Composition Spectrometer (MASCS) is one of seven science instruments onboard the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) spacecraft en route to the planet Mercury. MASCS consists of a small Cassegrain telescope with 257-mm effective focal length and a 50-mm aperture that simultaneously feeds an UltraViolet and Visible Spectrometer (UVVS) and a Visible and InfraRed Spectrograph (VIRS). UVVS is a 125-mm focal length, scanning grating, Ebert-Fastie monochromator equipped with three photomultiplier tube detectors that cover far ultraviolet (115–180 nm), middle ultraviolet (160–320 nm), and visible (250–600 nm) wavelengths with an average 0.6-nm spectral resolution. It will measure altitude profiles of known species in order to determine the composition and structure of Mercury’s exosphere and its variability and will search for previously undetected exospheric species. VIRS is a 210-mm focal length, fixed concave grating spectrograph equipped with a beam splitter that simultaneously disperses the spectrum onto a 512-element silicon visible photodiode array (300–1050 nm) and a 256-element indium-gallium-arsenide infrared photodiode array 850–1,450 nm. It will obtain maps of surface reflectance spectra with a 5-nm resolution in the 300–1,450 nm wavelength range that will be used to investigate mineralogical composition on spatial scales of 5 km. UVVS will also observe the surface in the far and middle ultraviolet at a 10-km or smaller spatial scale. This paper summarizes the science rationale and measurement objectives for MASCS, discusses its detailed design and its calibration requirements, and briefly outlines observation strategies for its use during MESSENGER orbital operations around Mercury.     

The Magnetic Field of Mercury

The magnetic field strength of Mercury at the planet’s surface is approximately 1% that of Earth’s surface field. This comparatively low field strength presents a number of challenges, both theoretically to understand how it is generated and observationally to distinguish the internal field from that due to the solar wind interaction. Conversely, the small field also means that Mercury offers an important opportunity to advance our understanding both of planetary magnetic field generation and magnetosphere-solar wind interactions. The observations from the Mariner 10 magnetometer in 1974 and 1975, and the MESSENGER Magnetometer and plasma instruments during the probe’s first two flybys of Mercury on 14 January and 6 October 2008, provide the basis for our current knowledge of the internal field. The external field arising from the interaction of the magnetosphere with the solar wind is more prominent near Mercury than for any other magnetized planet in the Solar System, and particular attention is therefore paid to indications in the observations of deficiencies in our understanding of the external field. The second MESSENGER flyby occurred over the opposite hemisphere from the other flybys, and these newest data constrain the tilt of the planetary moment from the planet’s spin axis to be less than 5°. Considered as a dipole field, the moment is in the range 240 to 270 nT-R _M ³ , where R _M is Mercury’s radius. Multipole solutions for the planetary field yield a smaller dipole term, 180 to 220 nT-R _M ³ , and higher-order terms that together yield an equatorial surface field from 250 to 290 nT. From the spatial distribution of the fit residuals, the equatorial data are seen to reflect a weaker northward field and a strongly radial field, neither of which can be explained by a centered-dipole matched to the field measured near the pole by Mariner 10. This disparity is a major factor controlling the higher-order terms in the multipole solutions. The residuals are not largest close to the planet, and when considered in magnetospheric coordinates the residuals indicate the presence of a cross-tail current extending to within 0.5R _M altitude on the nightside. A near-tail current with a density of 0.1 μA/m² could account for the low field intensities recorded near the equator. In addition, the MESSENGER flybys include the first plasma observations from Mercury and demonstrate that solar wind plasma is present at low altitudes, below 500 km. Although we can be confident in the dipole-only moment estimates, the data in hand remain subject to ambiguities for distinguishing internal from external contributions. The anticipated observations from orbit at Mercury, first from MESSENGER beginning in March 2011 and later from the dual-spacecraft BepiColombo mission, will be essential to elucidate the higher-order structure in the magnetic field of Mercury that will reveal the telltale signatures of the physics responsible for its generation.     

Comparative Na and K Mercury and Moon Exospheres

Space Science Reviews - As a hyperspectral imager aboard the orbiter “HX-1” of China’s first Mars mission, the Mars Mineralogical Spectrometer (MMS) is designed with hyperspectral...     

The Mercury Laser Altimeter Instrument for the MESSENGER Mission

The Mercury Laser Altimeter (MLA) is one of the payload science instruments on the MErcury Surface, Space ENvironment, GEochemistry, and Ranging (MESSENGER) mission, which launched on August 3, 2004. The altimeter will measure the round-trip time of flight of transmitted laser pulses reflected from the surface of the planet that, in combination with the spacecraft orbit position and pointing data, gives a high-precision measurement of surface topography referenced to Mercury’s center of mass. MLA will sample the planet’s surface to within a 1-m range error when the line-of-sight range to Mercury is less than 1,200 km under spacecraft nadir pointing or the slant range is less than 800 km. The altimeter measurements will be used to determine the planet’s forced physical librations by tracking the motion of large-scale topographic features as a function of time. MLA’s laser pulse energy monitor and the echo pulse energy estimate will provide an active measurement of the surface reflectivity at 1,064 nm. This paper describes the instrument design, prelaunch testing, calibration, and results of postlaunch testing.     

The Mercury Dual Imaging System on the MESSENGER Spacecraft

The Mercury Dual Imaging System (MDIS) on the MESSENGER spacecraft will provide critical measurements tracing Mercury’s origin and evolution. MDIS consists of a monochrome narrow-angle camera (NAC) and a multispectral wide-angle camera (WAC). The NAC is a 1.5° field-of-view (FOV) off-axis reflector, coaligned with the WAC, a four-element refractor with a 10.5° FOV and 12-color filter wheel. The focal plane electronics of each camera are identical and use a 1,024×1,024 Atmel (Thomson) TH7888A charge-coupled device detector. Only one camera operates at a time, allowing them to share a common set of control electronics. The NAC and the WAC are mounted on a pivoting platform that provides a 90° field-of-regard, extending 40° sunward and 50° anti-sunward from the spacecraft +Z-axis—the boresight direction of most of MESSENGER’s instruments. Onboard data compression provides capabilities for pixel binning, remapping of 12-bit data into 8 bits, and lossless or lossy compression. MDIS will acquire four main data sets at Mercury during three flybys and the two-Mercury-solar-day nominal mission: a monochrome global image mosaic at near-zero emission angles and moderate incidence angles, a stereo-complement map at off-nadir geometry and near-identical lighting, multicolor images at low incidence angles, and targeted high-resolution images of key surface features. These data will be used to construct a global image base map, a digital terrain model, global maps of color properties, and mosaics of high-resolution image strips. Analysis of these data will provide information on Mercury’s impact history, tectonic processes, the composition and emplacement history of volcanic materials, and the thickness distribution and compositional variations of crustal materials. This paper summarizes MDIS’s science objectives and technical design, including the common payload design of the MDIS data processing units, as well as detailed results from ground and early flight calibrations and plans for Mercury image products to be generated from MDIS data.     

Formation and Composition of Planetesimals

The composition of planetesimals depends upon the epoch and the location of their formation in the solar nebula. Meteorites produced in the hot inner nebula contain refractory compounds. Volatiles were present in icy planetesimals and cometesimals produced in the cold outer nebula. However, the mechanism responsible for their trapping is still controversial. We argue for a general scenario valid in all regions of the turbulent nebula where water condensed as a crystalline ice (Hersant et al., 2004). Volatiles were trapped in the form of clathrate hydrates in the continuously cooling nebula. The epoch of clathration of a given species depends upon the temperature and the pressure required for the stability of the clathrate hydrate. The efficiency of the mechanism depends upon the local amount of ice available. This scenario is the only one so far which proposes a quantitative interpretation of the non detection of N₂ in several comets of the Oort cloud (Iro et al., 2003). It may explain the large variation of the CO abundance observed in comets and predicts an Ar/O ratio much less than the upper limit of 0.1 times the solar ratio estimated on C/2001 A2 (Weaver et al., 2002). Under the assumption that the amount of water ice present at 5 AU was higher than the value corresponding to the solar O/H ratio by a factor 2.2 at least, the clathration scenario reproduces the quasi uniform enrichment with respect to solar of the Ar, Kr, Xe, C, N and S elements measured in Jupiter by the Galileo probe. The interpretation of the non-uniform enrichment in C, N and S in Saturn requires that ice was less abundant at 10 AU than at 5 AU so that CO and N₂ were not clathrated in the feeding zone of the planet while CH₄, NH₃ and H₂S were. As a result, the 14N/15N ratio in Saturn should be intermediate between that in Jupiter and the terrestrial ratio. Ar and Kr should be solar while Xe should be enriched by a factor 17. The enrichments in C, N and S in Uranus and Neptune suggest that available ice was able to form clathrates of CH₄, CO and the NH₃ hydrate, but not the clathrate of N₂. The enrichment of oxygen by a factor 440 in Neptune inferred by Lodders and Fegley (1994) from the detection of CO in the troposphere of the planet is higher by at least a factor 2.5 than the lower limit of O/H required for the clathration of CO and CH4 and for the hydration of NH₃. If CO detected by Encrenaz et al. (2004) in Uranus originates from the interior of the planet, the O/H ratio in the envelope must be around of order of 260 times the solar ratio, then also consistent with the trapping of detected volatiles by clathration. It is predicted that Ar and Kr are solar in the two planets while Xe would be enriched by a factor 30 to 70. Observational tests of the validity of the clathration scenario are proposed.     

Water and Volatile Inventories of Mercury,Venus, the Moon,and Mars

We review the geochemical observations of water, \(\mbox{D}/\mbox{H}\) and volatile element abundances of the inner Solar System bodies, Mercury, Venus, the Moon, and Mars. We focus primarily on the inventories of water in these bodies, but also consider other volatiles when they can inform us about water. For Mercury, we have no data for internal water, but the reducing nature of the surface of Mercury would suggest that some hydrogen may be retained in its core. We evaluate the current knowledge and understanding of venusian water and volatiles and conclude that the venusian mantle was likely endowed with as much water as Earth of which it retains a small but non-negligible fraction. Estimates of the abundance of the Moon’s internal water vary from Earth-like to one to two orders of magnitude more depleted. Cl, K, and Zn isotope anomalies for lunar samples argue that the giant impact left a unique geochemical fingerprint on the Moon, but not the Earth. For Mars, an early magma ocean likely generated a thick crust; this combined with a lack of crustal recycling mechanisms would have led to early isolation of the Martian mantle from later delivery of water and volatiles from surface reservoirs or late accretion. The abundance estimates of Martian mantle water are similar to those of the terrestrial mantle, suggesting some similarities in the water and volatile inventories for the terrestrial planets and the Moon.