Mars high resolution gravity fields from MRO, Mars seasonal gravity, and other dynamical parameters

With 2 years of tracking data collection from the MRO spacecraft, there is noticeable improvement in the high frequency portion of the spherical harmonic Mars gravity field. The new JPL Mars gravity fields, MRO110B and MRO110B2, show resolution near degree 90. Additional years of MGS and Mars Odyssey tracking data result in improvement for the seasonal gravity changes which compares well to global circulation models and Odyssey neutron data and Mars rotation and precession (). Once atmospheric dust is accounted for in the spacecraft solar pressure model, solutions for Mars solar tide are consistent between data sets and show slightly larger values (k₂ = 0.164 ± 0.009, after correction for atmospheric tide) compared to previous results, further constraining core models. An additional 4 years of Mars range data improves the Mars ephemeris, determines 21 asteroid masses and bounds solar mass loss (dGM_Sun/dt < 1.6 × 10⁻¹³ GM_Sun year⁻¹).     

Loss of water from Mars:: Implications for the oxidation of the soil

The evolution of the martian atmosphere with regard to its H₂O inventory is influenced by thermal loss processes of H, H₂, nonthermal atmospheric loss processes of H⁺, H₂⁺, O, O⁺, CO₂, and O₂⁺ into space, as well as by chemical weathering of the surface soil. The evolution of thermal and nonthermal escape processes depend on the history of the intensity of the solar XUV radiation and the solar wind density. Thus, we use actual data from the observation of solar proxies with different ages from the Sun in Time program for reconstructing the Sun's radiation and particle environment from the present to 3.5 Gyr ago. The correlation between mass loss and X-ray surface flux of solar proxies follows a power law relationship, which indicates a solar wind density up to 1000 times higher at the beginning of the Sun's main sequence lifetime. For the study of various atmospheric escape processes we used a gas dynamic test particle model for the estimation of the pick up ion loss rates and considered pick up ion sputtering, as well as dissociative recombination. The loss of H₂O from Mars over the last 3.5 Gyr was estimated to be equivalent to a global martian H₂O ocean with a depth of about 12 m, which is smaller than the values reported by previous studies. If ion momentum transport, a process studied in detail by Mars Express is significant on Mars, the water loss may be enhanced by a factor of about 2. In our investigation we found that the sum of thermal and nonthermal atmospheric loss rates of H and all nonthermal escape processes of O to space are not compatible with a ratio of 2:1, and is currently close to about 20:1. Escape to space cannot therefore be the only sink for oxygen on Mars. Our results suggest that the missing oxygen (needed for the validation of the 2:1 ratio between H and O) can be explained by the incorporation into the martian surface by chemical weathering processes since the onset of intense oxidation about 2 Gyr ago. Based on the evolution of the atmosphere-surface-interaction on Mars, an overall global surface sink of about 2×10⁴² oxygen particles in the regolith can be expected. Because of the intense oxidation of inorganic matter, this process may have led to the formation of considerable amounts of sulfates and ferric oxides on Mars. To model this effect we consider several factors: (1) the amount of incorporated oxygen, (2) the inorganic composition of the martian soil and (3) meteoritic gardening. We show that the oxygen incorporation has also implications for the oxidant extinction depth, which is an important parameter to determine required sampling depths on Mars aimed at finding putative organic material. We found that the oxidant extinction depth is expected to lie in a range between 2 and 5 m for global mean values.     

Abundances of isotopes in planetary atmospheres

Carbon and oxygen isotopes show no large anomalies on Venus (10–15%) or Mars (<5%); the high value of¹⁵N/¹⁴N found on Mars is explained by non-thermal escape of nitrogen. The isotopes of non-radiogenic noble gases in the atmosphere of Mars exhibit abundance patterns similar to those in the primordial component of meteoritic gases and in the Earth's atmosphere. This implies that gas fractionation took place in the inner solar nebula prior to planet formation. The relatively high value of¹²⁹Xe on Mars emphasizes its deficiency on Earth, implying a difference in accretion histories of volatiles for the two planets. In the outer solar system, we find normal isotope ratios for nitrogen and carbon on Jupiter, and for carbon on Saturn, but precision is low (±15% at best). Controversy exists about the correct value of D/H, with current estimates ranging from 2.3±1.1 to 5.1±0.7×10^–5. Planetary missions planned for the next few years should add considerably to the quantity and quality of these data.Paper presented at the Conference on Protostars and Planets, held at the Planetary Science Institute, University of Arizona, Tucson, Arizona, between January 3 and 7, 1978.     

Effects of impacts on the atmospheric evolution: Comparison between Mars, Earth, and Venus

Classified as a terrestrial planet, Venus, Mars, and Earth are similar in several aspects such as bulk composition and density. Their atmospheres on the other hand have significant differences. Venus has the densest atmosphere, composed of CO₂ mainly, with atmospheric pressure at the planet's surface 92 times that of the Earth, while Mars has the thinnest atmosphere, composed also essentially of CO₂, with only several millibars of atmospheric surface pressure. In the past, both Mars and Venus could have possessed Earth-like climate permitting the presence of surface liquid water reservoirs. Impacts by asteroids and comets could have played a significant role in the evolution of the early atmospheres of the Earth, Mars, and Venus, not only by causing atmospheric erosion but also by delivering material and volatiles to the planets. Here we investigate the atmospheric loss and the delivery of volatiles for the three terrestrial planets using a parameterized model that takes into account the impact simulation results and the flux of impactors given in the literature. We show that the dimensions of the planets, the initial atmospheric surface pressures and the volatiles contents of the impactors are of high importance for the impact delivery and erosion, and that they might be responsible for the differences in the atmospheric evolution of Mars, Earth and Venus.     

Thermal conduction and modeling of static stellar coronal loops

We have modeled stellar coronal loops in static conditions for a wide range of loop length, plasma pressure at the base of the loop and stellar surface gravity, so as to describe physical conditions that can occur in coronae of stars ranging from low mass dwarfs to giants as well as on a significant fraction of the Main-Sequence stars.Three alternative formulations of heat conduction have been used in the energy balance equation, depending on the ratio ₀/L _Tbetween electron mean free path and temperature scale height: Spitzer's formulation for ₀/L _Tless than 2 × 10^–3, the Luciani, Mora, and Virmont non-local formulation for ₀/L _Tbetween 2 × 10^–3 and 6.67 × 10^–3 and the limited free-streaming formulation for ₀/L _Tlarger than 6.67 × 10^–3.We report the characteristics of all loop models studied, and present examples to illustrate how the temperature and density stratification can be drastically altered by the different conductivity regimes. Significant differences are evident in the differential emission measure distribution vs temperature, an important observable quantity. We also show how physical conditions of coronal plasma, and in particular thermal conduction, change with stellar surface gravity.We have found that, for fixed loop length and stellar gravity, a minimum of loop-top plasma temperature occurs, corresponding to the highest value of base plasma pressure for which the limited free-streaming conduction occurs. This value of temperature satisfies the appropriate scalingT 10^–9 L g, in cgs units.     

The case for a wet,warm climate on early Mars

Theoretical arguments are presented in support of the idea that Mars possessed a dense CO₂ atmosphere and a wet, warm climate early in its history. Calculations with a one-dimensional radiative-convective climate model indicate that CO₂ pressures between 1 and 5 bars would have been required to keep the surface temperature above the freezing point of water early in the planet's history. The higher value corresponds to globally and orbitally averaged conditions and a 30% reduction in solar luminosity; the lower value corresponds to conditions at the equator during perihelion at times of high orbital eccentricity and the same reduced solar luminosity.The plausibility of such a CO₂ greenhouse is tested by formulating a simple model of the CO₂ geochemical cycle on early Mars. By appropriately scaling the rate of silicate weathering on present Earth, we estimate a weathering time constant of the order of several times 10⁷ years for early Mars. Thus, a dense atmosphere could have persisted for a geologically significant time period (∼10⁹years) only if atmospheric CO₂ was being continuously resupplied. The most likely mechanism by which this might have been accomplished is the thermal decomposition of carbonate rocks induced directly and indirectly (through burial) by intense, global-scale volcanism. For plausible values of the early heat flux, the recycling time constant is also of the order of several times 10⁷ years. The amount of CO₂ dissolved in standing bodies of water was probably small; thus, the total surficial CO₂ inventory required to maintain these conditions was approximately 2 to 10 bars. The amount of CO₂ in Mars' atmosphere would eventually have dwindled, and the climate cooled, as the planet's internal heat engine ran down. A test for this theory will be provided by spectroscopic searches for carbonates in Mars' crust.     

Construction of Martian Interior Model

We present the results of extensive numerical modeling of the Martian interior. Yoder et al. in 2003 reported a mean moment of inertia of Mars that was somewhat smaller than the previously used value and the Love number k₂ obtained from observations of solar tides on Mars. These values of k₂ and the mean moment of inertia impose a strong new constraint on the model of the planet. The models of the Martian interior are elastic, while k₂ contains both elastic and inelastic components. We thoroughly examined the problem of partitioning the Love number k₂ into elastic and inelastic components. The information necessary to construct models of the planet (observation data, choice of a chemical model, and the cosmogonic aspect of the problem) are discussed in the introduction. The model of the planet comprises four submodels—a model of the outer porous layer, a model of the consolidated crust, a model of the silicate mantle, and a core model. We estimated the possible content of hydrogen in the core of Mars. The following parameters were varied while constructing the models: the ferric number of the mantle (Fe#) and the sulfur and hydrogen content in the core. We used experimental data concerning the pressure and temperature dependence of elastic properties of minerals and the information about the behavior of Fe(γ-Fe ), FeS, FeH, and their mixtures at high P and T. The model density, pressure, temperature, and compressional and shear velocities are given as functions of the planetary radius. The trial model M13 has the following parameters: Fe#=0.20; 14 wt % of sulfur in the core; 50 mol % of hydrogen in the core; the core mass is 20.9 wt %; the core radius is 1699 km; the pressure at the mantle-core boundary is 20.4 GPa; the crust thickness is 50 km; Fe is 25.6 wt %; the Fe/Si weight ratio is 1.58, and there is no perovskite layer. The model gives a radius of the Martian core within 1600–1820 km while ≥30 mol % of hydrogen is incorporated into the core. When the inelasticity of the Martian interior is taken into account, the Love number k₂ increases by several thousandths; therefore, the model radius of the planetary core increases as well. The prognostic value of the Chandler period of Mars is 199.5 days, including one day due to inelasticity. Finally, we calculated parameters of the equilibrium figure of Mars for the M13 model: J ₂ ⁰ = 1.82 × 10^?3, J ₄ ⁰ = ?7.79 × 10^?6, e _c-m ^D = 1/242.3 (the dynamical flattening of the core-mantle boundary).     

The distribution of mass in the planetary system and solar nebula

A model solar nebula is constructed by adding the solar complement of light elements to each planet, using recent models of planetary compositions. Uncertainties in this approach are estimated. The computed surface density varies approximately asr ^–3/2. Mercury, Mars and the asteroid belt are anomalously low in mass, but processes exist which would preferentially remove matter from these regions. Planetary masses and compositions are generally consistent with a monotonic density distribution in the primordial solar nebula.     

The maximum and minimum masses of galaxies

Galaxies may have formed by fragmentation in a collapsing cloud of very large mass. The most massive galaxies were formed from fragments which were nearly but not quite opaque: the least massive galaxies were formed from fragments about as large as the Jeans mass. If the maximum mass of galaxies is 10¹³ M , then the minimum mass should be 10⁶ M .     

The nitrogen cycle on Mars: Impact decomposition of near-surface nitrates as a source for a nitrogen steady state

Nitrogen isotopes appear to be escaping from Mars at approximately the primordial ratio ¹⁴N/¹⁵N ≈ 275 and to have an atmospheric nitrogen depletion time scale of about 800 Myr. For the standard model of a progressive decline of an initial inventory of atmospheric nitrogen, having no source of N, the agreement of the isotopic ratio of escaping N with primitive nitrogen would be coincidental. Here we propose a steady state model in which nitrates, produced early in Mars' history, are later decomposed by the current impact flux. The detection of near-surface nitrates can discriminate between the standard and the steady state models. Based on current estimates of N loss to space, we predict a quantity of nitrates equivalent to 60 ± 30 mbars for a steady state, or a global layer of about 3 m of pure NaNO₃.     

Spectral reflectance properties of minerals exposed to simulated Mars surface conditions

A number of mineral species were exposed to martian surface conditions of atmospheric pressure and composition, temperature, and UV light regime, and their evolution was monitored using reflectance spectroscopy. The stabilities for different groups varied widely. Phyllosilicate spectra all showed measurable losses of interlayer H₂O, with some structural groups showing more rapid H₂O loss than others. Loss of OH from the phyllosilicates is not always accompanied by a change in metal-OH overtone absorption bands. OH-bearing sulfates, such as jarosite and alunite, show no measurable change in spectral properties, suggesting that they should be spectrally detectable on Mars on the basis of diagnostic absorption bands in the 0.4-2.5 μm region. Fe³⁺- and H₂O-bearing sulfates all showed changes in the appearance and/or reduction in depths of hydroxo-bridged Fe³⁺ absorption bands, particularly at 0.43 μm. The spectral changes were often accompanied by visible color changes, suggesting that subsurface sulfates exposed to the martian surface environment may undergo measurable changes in reflectance spectra and color over short periods of time (days to weeks). Organic-bearing geological materials showed no measurable change in CH related absorption bands, while carbonates and hydroxides also showed no systematic changes in spectral properties. The addition of ultraviolet irradiation did not seem to affect mineral stability or rate of spectral change, with one exception (hexahydrite). In some cases, spectral changes could be related to the formation of specific new phases. The data also suggest that hydrated minerals detected on Mars to date retain their diagnostic spectral properties that allow their unique identification.     

Stellar pulsation: (I) analysis of stability of envelope

The life-time of the star on AGB is approximately 6 × 10⁴ yr. We divide it into front half and back half of AGB (including to optical Mira variable and OH/IR star) according to their evolution character. The observations show that the star has non-pulsation, but constant mass loss rate ( 5 × 10^–7 M yr^–1) on front half of AGB. Its circumstellar envelope is formed. When the star has pulsation on back half of AGB, its mass loss rate is relative with time, and increases gradually. In this time the star is on the stage of optical Mira variable. When the mass loss rate reaches the value of 3 × 10^–6 M yr^–1, the star evoluted from the stage of optical variable into the stage of radio bright OH/IR star. On the end of AGB the mass loss rate reaches 10^–4 M yr^–1. (Band and Habing 1983, Hermen and Habing 1985).     

Anisotropic angular broadening in the solar wind

We present Very Large Array observations at wavelengths of 2, 3.5, 6, and 20 cm, of angular broadening of radio sources due to the solar wind in the region 2–16 solar radii. Angular broadening is anisotropic with axial ratios in the range 2–16. Larger axial ratios are observed preferentially at smaller solar distances. Assuming that anisotropy is due to scattering blobs elongated along magnetic field lines, the distribution of position angles of the elliptically broadened images indicates that the field lines are non-radial even at the largest heliocentric distances observed here. At 5R , the major axis scattering angle is 0.7 at =6 cm and it varies with heliocentric distance asR ^–1.6. The level of turbulence, characterized by the wave structure function at a scale of 10 km along the major axis, normalized to =20 cm, has a value 20±7 at 5R and varies with heliocentric distance asR ^–3. Comprison with earlier results suggest that the level of turbulence is higher during solar maximum. Assuming a power-law spectrum of electron density fluctuations, the fitted spectral exponents have values in the range 2.8–3.4 for scales sizes between 2–35 km. The data suggests temporal fluctuations (of up to 10%) in the spectral exponent on a time scale of a few tens of minutes. The observed structure functions at different solar distances do not show any evidence for an inner scale; the upper limits are 1 km at 2R and 4 km at 13R . These upper limits are in conflict with earlier determinations and may suggest a reduced inner scale during solar maximum.     

Oxygen and carbon isotope ratios in the martian atmosphere

Oxygen and carbon isotope ratios in the martian CO₂ are key values to study evolution of volatiles on Mars. The major problems in spectroscopic determinations of these ratios on Mars are uncertainties associated with: (1) equivalent widths of the observed absorption lines, (2) line strengths in spectroscopic databases, and (3) thermal structure of the martian atmosphere during the observation. We have made special efforts to reduce all these uncertainties. We observed Mars using the Fourier Transform Spectrometer at the Canada–France–Hawaii Telescope. While the oxygen and carbon isotope ratios on Mars were byproducts in the previous observations, our observation was specifically aimed at these isotope ratios. We covered a range of 6022 to 6308 cm⁻¹ with the highest resolving power of ν/δν=3.5×10⁵ and a signal-to-noise ratio of 180 in the middle of the spectrum. The chosen spectral range involves 475 lines of the main isotope, 184 lines of ¹³CO₂, 181 lines of CO¹⁸O, and 119 lines of CO¹⁷O. (Lines with strengths exceeding 10⁻²⁷ cm at 218 K are considered here.) Due to the high spectral resolution, most of the lines are not blended. Uncertainties of retrieved isotope abundances are in inverse proportion to resolving power, signal-to-noise ratio, and square root of the number of lines. Laboratory studies of the CO₂ isotope spectra in the range of our observation achieved an accuracy of 1% in the line strengths. Detailed observations of temperature profiles using MGS/TES and data on temperature variations with local time from two GCMs are used to simulate each absorption line at various heights in each part of the instrument field of view and then sum up the results. Thermal radiation of Mars' surface and atmosphere is negligible in the chosen spectral range, and this reduces errors associated with uncertainties in the thermal structure on Mars. Using a combination of all these factors, the highest accuracy has been achieved in measuring the CO₂ isotope ratios: ¹³C/¹²C = 0.978 ± 0.020 and ¹⁸O/¹⁶O = 1.018 ± 0.018 times the terrestrial standards. Heavy isotopes in the atmosphere are enriched by nonthermal escape and sputtering, and depleted by fractionation with solid-phase reservoirs. The retrieved ratios show that isotope fractionation between CO₂ and oxygen and carbon reservoirs in the solid phase is almost balanced by nonthermal escape and sputtering of O and C from Mars.     

Noble gases in planetary atmospheres: Implications for the origin and evolution of atmospheres

The radiogenic and primordial noble gas content of the atmospheres of Venus, Earth, and Mars are compared with one another and with the noble gas content of other extraterrestial samples, especially meteorites. The fourfold depletion of ⁴⁰Ar for Venus relative to the Earth is attributed to the outgassing rates and associated tectonics and volcanic styles for the two planets diverging significantly within the first billion or so years of their history, with the outgassing rate for Venus becoming much less than that for the Earth at subsequent times. This early divergence in the tectonic style of the two planets may be due to a corresponding early onset of the runaway greenhouse on Venus. The 16-fold depletion of ⁴⁰Ar for Mars relative to the Earth may be due to a combination of a mild K depletion for Mars, a smaller fraction of its interior being outgassed, and to an early reduction in its outgassing rate. Venus has lost virtually all of its primordial He and some of its radiogenic He. The escape flux of He may have been quite substantial in Venus' early history, but much diminished at later times, with this time variation being perhaps strongly influenced by massive losses of H₂ resulting from efficient H₂O loss processes.Key trends in the primordial noble gas content of terrestial planetary atmospheres include (1) a several orders of magnitude decrease in ²⁰Ne and ³⁶Ar from Venus to Earth to Mars; (2) a nearly constant ²⁰Ne/³⁶Ar ratio which is comparable to that found in the more primitive carbonaceous chondrites and which is two orders of magnitude smaller than the solar ratio; (3) a sizable fractionation of Ar, Kr, and Xe from their solar ratios, although the degree of fractionation, especially for ³⁶Ar/¹³²Xe, seems to decrease systematically from carbonaceous chondrites to Mars to Earth to Venus; and (4) large differences in Ne and Xe isotopic ratios among Earth, meteorites, and the Sun. Explaining trends (2), (2) and (4), and (1) pose the biggest problems for the solar-wind implantation, primitive atmosphere, and late veneer hypotheses, respectively. It is suggested that the grain-accretion hypothesis can explain all four trends, although the assumptions needed to achieve this agreement are far from proven. In particular, trends (1), (2), (3), and (4) are attributed to large pressure but small temperature differences in various regions of the inner solar system at the times of noble gas incorporation by host phases; similar proportions of the host phases that incorporated most of the He and Ne on the one hand (X) and Ar, Kr, and Xe on the other hand (Q); a decrease in the degree of fractionation with increasing noble-gas partial pressure; and the presence of interstellar carriers containing isotopically anomalous noble gases.Our analysis also suggests that primordial noble gases were incorporated throughout the interior of the outer terrestial planets, i.e., homogeneous accretion is favored over inhomogeneous accretion. In accord with meteorite data, we propose that carbonaceous materials were key hosts for the primordial noble gases incorporated into planets and that they provided a major source of the planets' CO₂ and N₂.     

Vertical motions in an intense magnetic flux tube

The recent discovery of localised intense magnetic fields in the solar photosphere is one of the major surprises of the past few years. Here we consider the theoretical nature of small amplitude motions in such an intense magnetic flux tube, within which the field strength may reach 2 kG. We give a systematic derivation of the governing expansion equations for a vertical, slender tube, taking into account the dependence upon height of the buoyancy, compressibility and magnetic forces. Several special cases (e.g., the isothermal atmosphere) are considered as well as a more realistic, non-isothermal, solar atmosphere. The expansion procedure is shown to give good results in the special case of a uniform basic-state (in which gravity is negligible) and for which a more exact treatment is possible.The form of both pressure and velocity perturbations within the tube is discussed. The nature of pressure perturbations depends upon a critical transition frequency, _p , which in turn is dependent upon depth, field strength, pressure and density in the basic (unperturbed) state of the tube. At a given depth in the tube pressure oscillations are possible only for frequencies greater than _p for frequencies below _p exponentially decaying (evanescent) pressure modes occur. In a similar fashion the nature of motions within the flux tube depends upon a transition frequency, _v . At a given depth within the tube vertically propagating waves are possible only for frequencies greater than _v ; for frequencies below _v exponentially decaying (evanscent) motions occur.The dependence of both _v and _p on depth is determined for each of the special cases, and for a realistic solar atmosphere. It is found that the use of an isothermal atmosphere, instead of a more realistic temperature profile, may well give misleading results.For the solar atmosphere it is found that _v is zero at about 12 km above optical depth ₅₀₀₀= 1, thereafter rising to a maximum of 0.04 s^–1 at some 600 km above ₅₀₀₀ = 1. Below ₅₀₀₀ = 1, in the convection zone, _v has a maximum of 0.013 s^–1. The transition frequency, _p , for the pressure perturbations, is peaked at 0.1 s^–1 just below ₅₀₀₀ = 1, falling to a minimum of 0.02 s^–1 at about one scale-height deeper in the tube     

Ion escape from Mars as a function of solar wind conditions: A statistical study

The influence of solar EUV and solar wind conditions on ion escape at Mars is investigated using ion data from the Aspera-3 instrument on Mars Express, combined with solar wind proxy data obtained from the Mars Global Surveyor (MGS) spacecraft. A solar EUV flux proxy based on data from the Earth position, scaled and shifted in time for Mars, is used to study relatively long time scale changes related to solar EUV variability. Data from May 2004 until November 2005 has been used. A clear dependence on the strength of the subsolar magnetic field as inferred from MGS measurements is seen in the ion data. The region of significant heavy ion flows is compressed and the heavy ion flux density is higher for high subsolar magnetic field strength. Because of the difference in outflow area, the difference in estimated total outflow is somewhat less than the difference in average flux density. We confirm previous findings that escaping planetary ions are mainly seen in the hemisphere into which the solar wind electric field is pointed. The effect is more pronounced for the high subsolar magnetic field case.The average ion motion has a consistent bias towards the direction of the solar wind electric field, but the main motion is in the antisunward direction. The antisunward flow velocity increases with tailward distance, reaching above at 2 to 3 martian radii downtail from Mars for O⁺ ions. Different ion species reach approximately the same bulk flow energy. We did not find any clear correlation between the solar EUV flux and the ion escape distribution or rate, probably because the variation of the solar EUV flux over our study interval was too small. The results indicate that the solar wind and its magnetic field directly interacts with the ionosphere of Mars, removing more ions for high subsolar magnetic field strength. The interaction region and the tail heavy ion flow region are not perfectly shielded from the solar wind electric field, which accelerates particles over relatively large tail distances.     

Evolution of the north-polar cap of Mars: a modelling study

Celestial-mechanical computations show that, even stronger than for Earth, Mars is subject to Milankovi? cycles, that is, quasi-periodic variations of the orbital parameters obliquity, eccentricity and precession. Consequently, solar insolation varies on time-scales of 10⁴-10⁵ years. It has long been supposed that this entails climatic cycles like the terrestrial glacial-interglacial cycles. This hypothesis is supported by the light-dark layered deposits of the north- and south-polar caps indicating a strongly varying dust content of the ice due to varying climate conditions in the past. This study aims at simulating the dynamic and thermodynamic evolution of the north-polar cap (NPC) of Mars with the ice-sheet model SICOPOLIS. The boundary conditions of surface accumulation, ablation and temperature are derived directly from the solar-insolation history by applying the newly developed model MAIC. We consider steady-state scenarios under present climate conditions as well as transient scenarios over climatic cycles. It is found that the NPC is most likely not in steady state with the present climate. The topography of the NPC is mainly controlled by the history of the surface mass balance. Ice flow, which is of the order of , plays only a minor role. In order to build up the present cap during the last five million years of relatively low obliquities, a present accumulation rate of water equiv a⁻¹ is required. Computed basal temperatures are far below pressure melting for all simulations and all times.     

Hidden mass in the solar neighborhood

It is suggested that the minimum mass of a star at the time of its formation is approximately 0.01M . Making use of this fact and the stellar mass functionF(M) M ^–, it is found that the hidden mass (or the missing mass) in the solar neighborhood may be explained by the presence of a large number of invisible stars of very low mass (0.01M M<0.07M ).