Hydrodynamic study of condensation and sublimation of ice particles in cometary atmospheres

Condensation of ice particles in the vicinity of a cometary nucleus as pointed out by Yamamoto and Ashihara (1985, Astron. Astrophys. 152, L17–L20) is fully studied by solving the hydrodynamic equations for ice particles and H₂O gas. Formulation is presented for the hydrodynamics including condensation and sublimation of ice particles, and energy exchange between ice particles and the gas in a dustless comet. It is shown that sublimation of ice particles condensed leads to heating of the ambient gas, resulting in the higher gas temperature than those predicted by the models proposed so far. Compared with the previous calculation carried out under the conditions at the encounter of the spacecraft to Halley's Comet, the present results have revealed that the survival distance of ice particles against sublimation is longer, but that their size, which attains its maximum of 6.4 Å at 51 km from the center of the nucleus, is smaller, resulting in a larger fraction of uncondensed H₂O gas. Discussion is given on the physical conditions under which condensation of ice particles can take place in cometary comae.     

Saturn's rings: 3-mm low-inclination observations and derived properties

Recent 3-mm observations of Saturn at low ring inclinations are combined with previous observations of E. E. Epstein, M. A. Janssen, J. N. Cuzzi, W. G. Fogarty, and J. Mottmann (Icarus41, 103–118) to determine a much more precise brightness temperature for Saturn's rings. Allowing for uncertainties in the optical depth and uniformity of the A and B rings and for ambiguities due to the C ring, but assuming the ring brightness to remain approximately constant with inclination, a mean brightness temperature for the A and B rings of 17 ± 4°K was determined. The portion of this brightness attributed to ring particle thermal emission is 11 ± 5°K. The disk temperature of Saturn without the rings would be 156 ± 6°K, relative to B. L. Ulich, J. H. Davis, P. J. Rhodes, and J. M. Hollis' (1980, IEEE Trans. Antennas Propag.AP-28, 367–376) absolutely calibrated disk temperature for Jupiter. Assuming that the ring particles are pure water ice, a simple slab emission model leads to an estimate of typical particle sizes of ≈0.3 m. A multiple-scattering model gives a ring particle effective isotropic single-scattering albedo of 0.85 ± 0.05. This albedo has been compared with theoretical Mie calculations of average albedo for various combinations of particle size distribution and refractive indices. If the maximum particle radius (≈5 m) deduced from Voyager bistatic radar observations (E. A. Marouf, G. L. Tyler, H. A. Zebker, V. R. Eshleman, 1983, Icarus54, 189–211) is correct, our results indicate either (a) a particle distribution between 1 cm and several meters radius of the form r^?s with 3.3 ? s ? 3.6, or (b) a material absorption coefficient between 3 and 10 times lower than that of pure water ice Ih at 85°K, or both. Merely decreasing the density of the ice Ih particles by increasing their porosity will not produce the observed particle albedo. The low ring brightness temperature allows an upper limit on the ring particle silicate content of ≈10% by mass if the rocky material is uniformly distributed; however, there could be considerably more silicate material if it is segregated from the icy material.     

A redetermination of the ice/vapor ratio of Enceladus’ plumes: Implications for sublimation and the lack of a liquid water reservoir

The discovery of plumes of H₂O vapor and ice particles erupting from the south pole of Enceladus, the tiny frigid satellite of Saturn, sparked controversy over whether these plumes are produced by boiling, or by sublimation with subsequent recondensation of the sublimated vapor [Porco, C.C., Helfenstein, P., Thomas, P.C., Ingersoll, A.P., Wisdom, J., West, R., Neukum, G., Denk, T., Wagner, R., Roatsch, T., Kieffer, S., Turtle, E., McEwen, A., Johnson, T.V., Rathbun, J., Veverka, J., Wilson, D., Perry, J., Spitale, J., Brahic, A., Burns, J.A., DelGenio, A.D., Dones, L., Murray, C.D., Squyres, S., 2006. Science 311, 1393-1401]. Porco et al.’s analysis that the masses of ice (I) and vapor (V) in the plume were comparable was taken to argue against the occurrence of sublimation and recondensation, leading to the hypothesis that the reservoir was boiling water, possibly as close as 7 m to the surface. Thus, it has been advocated that Enceladus should be a target for astrobiology exploration. Here we show, with recalculations using the original data and methodologies, as well as with new sensitivity studies, that the mass of ice in the column is significantly less than the mass of water vapor, and that by considering three additional effects, I/V is likely to be <0.2-0.1. This means that the plume is dominated by vapor that the thermodynamics permits to be easily produced by sublimation with recondensation. The low I/V ratio provides no compelling criterion for consideration of a liquid water reservoir. The uncertainties on the I/V ratio have not previously been discussed in the literature. Although the I/V ratio is sensitive to particle sizes and size distributions, the masses of ice (I) and vapor (V) are not comparable in any scenario constrained by available observations. We thus discuss the implications of sublimation from a thermodynamic point of view in a context that has not been presented previously. Constraints on I/V ratio from future spacecraft measurements of the plume, in conjunction with consideration of the total plume composition and multicomponent analysis, can help constrain source conditions for the plume.     

Orbital Evolution of Dust Particles in the Sublimation Zone near the Sun

We have performed the calculations of the orbital evolution of dust particles from volcanic glass (p-obsidian), basalt, astrosilicate, olivine, and pyroxene in the sublimation zone near the Sun. The sublimation (evaporation) rate is determined by the temperature of dust particles depending on their radius, material, and distance to the Sun. All practically important parameters that characterize the interaction of spherical dust particles with the radiation are calculated using the Mie theory. The influence of radiation and solar wind pressure, as well as the Poynting–Robertson drag force effects on the dust dynamics, are also taken into account. According to the observations (Shestakova and Demchenko, 2016), the boundary of the dust-free zone is 7.0–7.6 solar radii for standard particles of the zodiacal cloud and 9.1–9.2 solar radii for cometary particles. The closest agreement is obtained for basalt particles and certain kinds of olivine, pyroxene, and volcanic glass.     

On the sublimation of ice particles on the surface of Mars; with applications to the 2007/8 Phoenix Scout mission

Experimental studies related to the sublimation of ice, in bulk or as small particles, alone or mixed with dust similar to that expected on the surface of Mars, are reported. The experiments, a cloud physics particle sublimation model, and a convection model presented by Ingersoll, all indicate a strong dependence of sublimation rate on temperature, and this appears to be the dominant factor, assuming that the relative humidity of the air is fairly low. In addition the rate of loss of water vapour appears to depend primarily on exposed surface area and less on particle size and the total mass of the sample, or the mass of ice in the sample. The 2007/8 Phoenix Scout mission plans to obtain and analyse samples of sub-surface ice from about 70° N on Mars. A concern is that these samples, in the form of ice chips of size about 1 mm diameter, could be prone to sublimation when exposed for prolonged periods (many hours) to a relatively warm and dry atmosphere. Our laboratory simulations confirm that this could be a problem if particles are simply left lying on the surface, but also indicate that samples kept suitably cold and collected together in confined piles will survive long enough for the collection and delivery (to the analysis instruments) procedure to be completed.     

Sublimation coefficient of water ice under simulated cometary-like conditions

In papers dealing with evolution of cometary nuclei it is commonly assumed that the coefficients of sublimation _s and condensation _c of vapour are both equal to one. The experimental investigation of ice samples under simulated cometary-like conditions (Kossacki, K.J., Kömle, N.I., Leliwa-Kopysty ski, J., Kargl, G., 1997. Thermal and structural evolution of cometary subsurface layer: selfconsistent model and experimental verification. Icarus 128, 127–144) suggests, however, that the sublimation flux calculated with the Hertz–Knudsen formula and the above assumption is nearly an order of magnitude too high. This may imply that actual values of _s for the ice/dust sample used in these experiments are of the order of 0.1. A similar conclusion can be drawn for _c from the results of various experiments concerning growth of ice crystals from the vapour phase and their sublimation (Lamb, D., Scott, W.D., 1972. Linear growth rates of ice crystals grown from the vapor phase. Journal of Crystal Growth 12, 21–31; Beckmann, W., Lacmann, R., 1982. Interface kinetics of growth and evaporation of ice II. Journal of Crystal Growth 58, 433–442; Sei, T., Gonda, T., 1989. The growth mechanism and the habit change of ice crystals growing from the vapour phase. Journal of Crystal Growth 94, 697–707). The exact values of both of these coefficients depend on various parameters such as temperature, concentration of surface impurities and deviation of the vapour pressure from that of the phase equilibrium. In this work the temperature dependence of the sublimation and condensation coefficients is discussed and an appropriate formula is proposed to fit the experimental results. This new formulation is then used to analyse the implications for the thermal conductivity of a porous cometary-like ice and the rate of vapour flux from a cometary nucleus.     

Comet 17P/Holmes: Possibility of a CO driven explosion

This work is a continuation of our previous paper about brightening of Comet 17P/Holmes (Kossacki, K.J., Szutowicz, S. [2010]. Icarus 207, 320–340). In that paper we presented results of simulations indicating that the nonuniform crystallization of amorphous water ice itself is probably not sufficient for an explosion. In the present work we investigate the possibility that the explosion is caused by a rapid sublimation of the CO ice leading to the rise of gas pressure above the tensile strength of the nucleus. We simulated evolution of a model nucleus in the orbit of Comet 17P/Holmes. The nucleus is composed of water ice, carbon monoxide ice and dust and has the shape of an elongated ellipsoid. The simulations include crystallization of amorphous ice in the nucleus, changes of the dust mantle thickness, and sublimation of the CO ice. In our model CO is mantling grains composed of dust and amorphous water ice. Orientation of the nuclear spin axis in space is the same as derived in Moreno et al. (Moreno, F., Ortiz, J.L., Santos-Sanz, P., Morales, N., Vidal-Nunez, M.J., Lara, L.M., Gutierrez, P.J. [2008]. Astrophys. J. 677, L63–L66) for Comet Holmes during recent brightening event. Hence, the angle between the orbital and the equatorial planes of the comet is I = 95°, and the cometocentric solar longitude at perihelion is Φ = 210°. The calculations are performed for the south pole being the sub-solar point close to time of the outburst. Our computations indicate, that the CO pressure within the comet nucleus can rise to high values. When the layer between the dust mantle and the crystallization front of the amorphous water ice is very fine grained, few microns in radius, the CO pressure within the nucleus can exceed 10 kPa. This value is the lowest estimate for the tensile strength of the nucleus of Comet Holmes (Reach, W.T., Vaubaillon, J., Lisse, C.M., Holloway, M., Rho, J. [2010]. Icarus 208, 276–292). Hence, when the gas pressure reaches this value the nucleus may explode.     

Dust ring formation due to ice sublimation of radially drifting dust particles under the Poynting-Robertson effect in debris disks

In a disk with a low optical depth, dust particles drift radially inward by the Poynting-Robertson (P-R) drag rather than are blown out by stellar radiation pressure following destructive collisions. We investigate the radial distribution of icy dust composed of pure ice and refractory materials in dust-debris disks taking into account the P-R drag and ice sublimation. We find that icy dust particles form a dust ring by their pile-ups at the edge of their sublimation zone, where they sublime substantially at the temperature 100-110 K. The distance of the dust ring is 20-35 AU from the central star with its luminosity L_??30L_⊙ and 65(L_?/100L_⊙)^1/2 AU for L_??30L_⊙, where L_⊙ is the solar luminosity. The effective optical depth is enhanced by a factor of 2 for L_??100L_⊙ and more than 10 for L_??100L_⊙. The optical depth of the outer icy dust disk exceeds that of the inner disk filled with refractory particles, namely, the residue of ice sublimation, which are further subjected to the P-R effect. As a result, an inner hole is formed inside the sublimation zone together with a dust ring along the outer edge of the hole.     

The Correct Evaluation of the Sublimation Rate of Dusty Ices under Solar Illumination, and Its Implication on the Properties of P/Halley Nucleus

This note (1) provides a formal derivation of an algorithm proposed precedingly without proof for evaluating the sublimation rate of dusty ice under solar illumination, and (2) illustrates the importance of adopting a correct algorithm for such a purpose, by rediscussing the basic characteristics of P/Halley nucleus activity derived from the 1996 flyby data.     

Inhomogeneous models of the atmosphere of Saturn

Analyses of ultraviolet, visible, and near-infrared spectra of Saturn lead to an inhomogeneous atmospheric model, having a clear gas layer which lies above an absorbing particle layer which lies above an ammonia haze layer. The boundary between the clear layer and the absorbing particle layer is at a pressure of 0.2 atm in the equatorial region and 0.3 atm in the temperate region. The boundary between the absorbing particle layer and the haze layer is at the radiative-convective boundary. Observations of ammonia absorption lines indicate that sunlight penetrates the haze to the ammonia sublimation level at a depth of 1.1 atm. Absorbing particles cause the observed decrease in reflectivity from visible to ultraviolet wavelengths. Consideration of the wavelength variation of Mie scattering parameters leads to an upper limit of about 0.2 μm for the particle radii and a particle number density of 10³ cm^?3. Some possible particle compositions are discussed. Comparison of computed 3-0 and 4-0 band hydrogen quadropole line equivalent widths with observed values leads to a haze layer optical thickness above the ammonia sublimation level of approximately 10. Equivalent widths computed for an equilibrium distribution of states agree better with observed values than those computed for a normal distribution. Methane 3ν₃ band manifold equivalent widths are in best agreement with measured equivalent widths for a CH₄/H₂ abundance ratio of 2 × 10^?3, which is 4.5 times the solar C/H ratio.     

Total particulate mass in Enceladus plumes and mass of Saturn’s E ring inferred from Cassini ISS images

The eclipse mosaic (PIA08329) of the Saturn system, taken on September 15, 2006 when Cassini was in Saturn’s shadow, contains numerous color images of the Enceladus plume and the E ring at phase angles ranging from 173° to 179°. These forward-scattering observations sample the diffraction peak for particle radii in the 1–5 μm range. The phase angle dependence and total brightness are sensitive indicators of the total mass of solid material in the plume. We fit the data with a variety of particle shapes and size distributions, and find that the median radius of the equivalent-volume sphere is 3.1 μm, with an uncertainty of ±0.5 μm. The total mass of particles in the plume is (1.45 ± 0.5) × 10⁵ kg. We have not considered variations with altitude in the particle size and shape distribution, and we leave that for another paper. We find that the brightness of the E ring varies with position in the orbit, not only because of the viewing geometry, e.g., variations in phase angle, but also because of some unknown intrinsic variability. The total mass of solid material in the E ring is (12 ± 5.5) × 10⁸ kg. For the plume, the production rate of particles – the mass per unit time leaving the vents is 51 ± 18 kg s⁻¹. We estimate that 9% of these particles are escaping from Enceladus, implying lifetimes of ∼8 years for the E ring particles. Based on three comparisons with vapor amounts from ultraviolet spectroscopy, the ice/vapor ratio is in the range 0.35–0.70. This high ratio poses a problem for theories in which particles form by condensation from the gas phase, and could indicate that particles are formed as spray from a liquid reservoir.     

Possible nature of cometary atmosphere particles

The polarimetric and spectrophotometric data of observations, the results of laboratory simulations, and theoretical calculations are considered as evidence in favor of the presence of large irregular particles in cometary atmospheres. The attempt is made to define more precisely the particle parameters. In particular, observations of some comets at small phase angles can be interpreted by light scattering on large icy grains. The results of laboratory experiments with ice at low temperatures and pressures are adduced; this can be explain the formation of a large icy grain cloud near the cometary nucleus. Changes of these particles under the effects of solar radiation are considered.     

Sublimation kinetics of CO2 ice on Mars

Dynamic models of the martian polar caps are in abundance, but most rely on the assumption that the rate of sublimation of CO₂ ice can be calculated from heat transfer and lack experimental verification. We experimentally measured the sublimation rate of pure CO₂ ice under simulated martian conditions as a test of this assumption, developed a model based on our experimental results, and compared our model's predictions with observations from several martian missions (MRO, MGS, Viking). We show that sun irradiance is the primary control for the sublimation of CO₂ ice on the martian poles with the amount of radiation penetrating the surface being controlled by variations in the optical depth, ensuring the formation and sublimation of the seasonal cap. Our model confirmed by comparison of MGS-MOC and MRO-HiRISE images, separated by 2-3 martian years, shows that ∼0.4 m are currently being lost from the south perennial cap per martian year. At this rate, the ∼2.4-m-thick south CO₂ perennial cap will disappear in about 6-7 martian years, unless a short-scale climatic cycle alters this rate of retreat.     

Motion of dust particles under the influence of a latitudinally dependent force

The Kelperian motion of dust particles in the solar system is mainly influenced by the electromagnetic and plasma Poynting-Robertson drag. The first force is isotropic while the second one shows latitudinal variations due to the observed differences of the solar wind parameters in the ecliptic plane and over the solar poles. Close to the Sun other effects become important, e.g. sublimation and sputtering, as well as for submicron particles Lorentz scattering has to be taken into account. These forces are very weak for dust grains of moderate size (10–100 µ) not too close (>0.03 AU) to the Sun and are neglected here. Assuming that the general form of the latidudinally dependent force is a series expansion in Legendre polynomials, we have studied the averaged equations of motion for the classical elements and found the first integral of them. The general character of motion is the same as for the classical Poynting-Robertson drag: particles spiral towards the Sun. The new features in the orbital evolution under the latitudinally dependent force as compared with the isotropic Poynting-Robertson drag are:

1. not only the semimajor axisa and the eccentricity ε but also the argument of the perihelion ω varies with time,
2. the rate of change ofa, ε, ω depends on the inclination.

An example of particle trajectories in the phase space of elements is presented.     

Interplanetary dust between 1 and 5 AU

Analyses of the data from the Meteoroid Detection Experiment (MDE) and the Imaging Photopolarimeter (IPP) aboard Pioneer 10 and Pioneer 11 have led to contradictory conclusions. While the MDE indicates a significant particle environment in the outer solar system (out to at least 5 AU), the IPP sees no zodiacal light (therefore implying no small particles) past 3.3 AU. We reconcile the two results by noting that the spectral index, p [relating particle radius, s, and particle concentration, n(s), i.e., dn(s) = Cs^?pds], is not a constant in the solar system, but changes from p < 2 near 1 AU to p > 2.5 at 5 AU for particles in the range of 10 μm. The MDE value of p = 1.8 at 1 AU is in agreement with previous satellite measurements, while our earlier analysis of the Pioneer 10 Jovian encounter data indicated p > 2.5 at 5 AU. A joint analysis of the Pioneer 10 and Pioneer 11 MDE data also indicates that p > 2.5 in the outer solar system. We show that a varying spectral index violates a major assumption used in the interpretation of the IPP data, which in turn had led to the conclusion that zodiacal dust is absent beyond 3.3 AU. With p a function of solar distance, the MDE data is now consistent with the IPP data, thus indicating a significant particle concentration in the outer solar system.     

A one-dimensional numerical model of H<Subscript>2</Subscript>O cloud formation in the Martian atmosphere

A one-dimensional numerical model with a size distribution of aerosol particles in Martian atmosphere is developed. The model incorporates detailed microphysics and turbulent transport. Dust particles suspended in the Martian atmosphere play a role of cloud condensation nuclei. Diurnal cycle of condensational processes is obtained on the basis of GCM temperature profiles. An effective radius of ice particles is 1–2 μm near the lower boundary of cloud layer and 0.2–0.3 μm at the altitude of 50–60 km. These results are consistent with solar infrared occultations by SPICAM experiment on Mars-Express. Near-surface fogs may form under specific conditions. The connections of condensational processes and cloud macroscopic parameters on microphysical properties of aerosol particles are main focus of this paper. In particular, the dependence on variations of cloud condensation nuclei contact parameter is analyzed, taking into account new experimental data of adsorption properties of minerals at low temperatures.     

Dynamics of Dust Particles of Different Structure: Application to the Modeling of Dust Motion in the Vicinity of the Nucleus of Comet 67P/Churyumov–Gerasimenko

We consider the estimates of the main forces acting on dust particles near a cometary nucleus. On the basis of these estimates, the motion of dust particles of different structure and mass is analyzed. We consider the following forces: (1) the cometary nucleus gravity, (2) the solar radiation pressure, and (3) the drag on dust particles by a flow of gas produced in the sublimation of cometary ice. These forces are important for modeling the motion of dust particles relative to the cometary nucleus and may substantially influence the dust transfer over its surface. In the simulations, solid silicate spheres and homogeneous ballistic aggregates are used as model particles. Moreover, we propose a technique to build hierarchic aggregates—a new model of quasi-spherical porous particles. A hierarchic type of aggregates makes it possible to model rather large dust particles, up to a millimeter in size and larger, while no important requirements for computer resources are imposed. We have shown that the properties of such particles differ from those of classical porous ballistic aggregates, which are usually considered in the cometary physics problems, and considering the microscopic structure of particles is of crucial significance for the analysis of the observational data. With the described models, we study the dust dynamics near the nucleus of comet 67P/Churyumov–Gerasimenko at an early stage of the Rosetta probe observations when the comet was approximately at 3.2 AU from the Sun. The interrelations between the main forces acting on dust aggregates at difference distances from the nucleus have been obtained. The dependence of the velocity of dust aggregates on their mass has been found. The numerical modeling results and the data of spaceborne observations with the Grain Impact Analyzer and Dust Accumulator (GIADA) and the Cometary Secondary Ion Mass Analyzer (COSIMA) onboard the Rosetta probe are compared at a quantitative level.     

Water distribution in Martian permafrost regions from joint analysis of HEND (Mars Odyssey) and MOLA (Mars Global Surveyor) data

We jointly analyze data from the High-Energy Neutron Detector (HEND) onboard the NASA Mars Odyssey spacecraft and data from the Mars Orbiter Laser Altimeter (MOLA) onboard the Mars Global Surveyor spacecraft. The former instrument measures the content of hydrogen (in the form of H₂O or OH) in the subsurface layer of soil and the latter instrument measures the surface albedo with respect to the flux of solar energy. We have checked the presence of a correlation between these two data sets in various Martian latitude bands. A significant correlation has been found between these data at latitudes poleward of 40° in the northern hemisphere and at latitudes 40°–60° in the southern hemisphere. This correlation is interpreted as evidence for the presence of stable water ice in these regions under a dry layer of soil whose thickness is determined by the condition for equilibrium between the condensation of water from the atmosphere and its sublimation when heated by solar radiation. For these regions, we have derived an empirical relation between the flux of absorbed solar radiation and the thickness of the top dry layer. It allows the burial depth of the water ice table to be predicted with a sub-kilometer resolution based on near-infrared albedo measurements. We have found no correlation in the southern hemisphere at latitudes >60°, although neutron data also suggest that water ice is present in this region under a layer of dry soil. We conclude that the thickness of the dry layer in this region does not correspond to the equilibrium condition between the water ice table and the atmosphere.     

Mass-radius relationships in icy satellites

Using published laboratory data for H₂O ice, we have developed a modeling technique by which the bulk density, density and temperature profile, rotational moment of inertia, central pressure, and location of the rock-ice interface can all be obtained as a function of the radius, the heliocentric distance, and the silicate composition. Models of the interiors of Callisto, Ganymede, Europa, Rhea, and Titan are given, consistent with present mass and radius data. The radius and mass of spheres of ice under self-gravitation for two different temperature classes are given (103 and 77°K). Measurements of mass, radius, and I/MR² by spacecraft can be interpreted by this model to yield substantial information about the internal structure and the ice: rock ratio of the icy satellites of Jupiter and Saturn.