Dynamical evolution of comets and the problem of cometary fading

Possibilities to explain the observed 1/a-distribution are discussed in the light of improved understanding of the dynamical evolution of long-period comets. It appears that the fading problem applies both to single-injection and continuous-injection models. Although uncertainties due to nongravitational effects do not allow detailed results to be drawn from the observed 1/a-distribution at small perihelion distance q, that for q 1.5 AU shows that a constant fading probability cannot explain all the features of the observed distribution. Assuming that comets can reappear following a period of fading, values for the assumed constant fading and renewal probabilities, and the total cometary flux have been estimated for q > 1.5 AU.     

The provenance and evolution of comets

The process of comet formation through the hierarchical aggregation of originally submicron-sized interstellar grains to form micron-sized particles and then larger bodies in the protoplanetary disc, culminating in the formation of planetesimals in the disc extending from Jupiter to beyond Neptune, is briefly reviewed. The ‘planetesimal’ theory for the origin of comets implies the existence of distinct cometary reservoirs, with implications for the immediate provenance of observed comets (both long-period and short-period) and their evolution as a result of planetary perturbations and physical decay, for example splitting and sublimation. The principal mode of cometary decay and collisional interaction with the terrestrial planets is through the formation and evolution of streams of cometary debris and hitherto undiscovered ‘families’ of cometary asteroids. Recent dynamical results, in particular the sungrazing and sun-colliding end-state for short-period comet and asteroid orbits, are briefly discussed.     

Perihelion evolution of observed new comets implies the dominance of the galactic tide in making Oort cloud comets discernable

For an Oort cloud comet to be seen as a new comet, its perihelion must be moved from a point exterior to the loss cylinder boundary to a point interior to observable limits in a single orbit. The galactic tide can do this continuously, in a non-impulsive manner. Near-parabolic comets, with specific angular momentum , will most easily be made observable. Therefore, to reduce the perihelion distance H must decrease. Since weakly perturbed comets are, in general, more numerous than strongly perturbed comets, we can anticipate that new comets made observable by a weak tidal torque will more likely be first observed when their slowly changing perihelion distances are approaching their minimum osculating values under the action of the tide, rather than receding from their minimum values. That is, defining ΔH_tide as the vector change due to the galactic tidal torque during the prior orbit, and H_obs as the observed vector, the sign S≡Sign(H_obs·ΔH_tide) will more likely be −1 than +1 if a weak galactic tidal perturbation indeed dominates in making comets observable. Using comet data of the highest quality class (1A) for new comets (a>10,000 AU), we find that 49 comets have S=−1 and 22 have S=+1. The binomial probability that as many or more would exhibit this characteristic if in fact S=?1 were equally likely is only 0.0009. This characteristic also persists in other long-period comet populations, lending support to the notion that they are dominated by comets recently arrived from the outer Oort cloud. The preponderance of S=−1 also correlates with weakly perturbed (i.e., smaller semimajor axis) new comets in a statistically significant manner. This is strong evidence that the data are of sufficiently high quality and sufficiently free of observational selection effects to detect this unique imprint of the tide.     

The Shadow of Comet Hale–Bopp in Lyman-Alpha

For a few months around perihelion, thecentral part of the Hale–Bopp hydrogencloud has been optically thick to thesolar Lyα radiation, and hassignificantly reduced the solar flux availablefor the resonance glow of interstellarhydrogen beyond the comet. This shadowing effecton the interstellar gas is the first everobserved comet shadow. It is modeled andcompared with SWAN observations. Shadowmodelling will help to constrain the cometwater production and radiative transfer effectsin the interstellar ionisation cavity.     

Meteoroid streams that trace to candidate dormant comets

In an effort to identify space mission targets of interest, the association of known meteoroid streams with Near-Earth Objects (NEOs) was investigated. In addition to updating previous searches to include NEOs discovered up to January 1, 2007, a new dissimilarity criterion based on dynamical arguments was applied to evaluate the likelihood of each candidate association. The new criterion is based on the fact that the few established cases, such as 2003 EH1 and the Quadrantid stream, involve parent bodies that fragmented in the most recent nutation cycle of their secular orbital evolution. In established cases, the statistics speak strongly of an association due to the lack of NEOs in the a, e, i phase space occupied by these showers. The newly proposed associations are much more uncertain, because the odds of chance associations greatly increase as orbital inclination of the showers decreases. Forty-two plausible candidate dormant comets were identified, that deserve further scrutiny. Both comet and stream typically lack sufficient data to prove the association. Most candidate parent bodies pertain to NEOs with an aphelion distance just short of Jupiter's orbit, a perihelion distance near Earth orbit, and an eccentricity in the range 0.5-0.8. Surprisingly many have , which means that most candidate parent bodies are dormant Jupiter family comets that have not yet fully decoupled from Jupiter. Establishing these associations can provide further evidence that (mostly) dormant comets break frequently, making this the dominant mechanism for replenishing the zodiacal cloud.     

Circular polarization in comets: Observations of Comet C/1999 S4 (LINEAR) and tentative interpretation

Comet C/1999 S4 (LINEAR) was exceptional in many respects. Its nucleus underwent multiple fragmentations culminating in the complete disruption around July 20, 2000. We present circular polarization measurements along the cuts through the coma and nucleus of the comet during three separate observing runs, in June 28-July 2, July 8-9, and July 21-22, 2000. The circular polarization was detected at a rather high level, up to 0.8%. The left-handed as well as right-handed polarization was observed over the coma with the left circularly polarized light systematically observed in the sunward part of the coma. During our observations the phase angle of the comet varied from 61 up to 122°, which allowed us to reveal variations of circular polarization with the phase angle. Correlation between the degree of circular polarization, visual magnitude, water production rate, and linear polarization of Comet C/1999 S4 (LINEAR) during its final fragmentation in July 2000 was found. The mechanisms that may produce circular polarization in comets and specifically in Comet C/1999 S4 (LINEAR) are discussed and some tentative interpretation is presented.     

A survey of debris trails from short-period comets

We observed 34 comets using the 24 μm camera on the Spitzer Space Telescope. Each image contains the nucleus and covers at least ¹⁰⁶ km of each comet's orbit. Debris trails due to mm-sized or larger particles were found along the orbits of 27 comets; 4 comets had small-particle dust tails and a viewing geometry that made debris trails impossible to distinguish; and only 3 had no debris trail despite favorable observing conditions. There are now 30 Jupiter-family comets with known debris trails, of which 22 are reported in this paper for the first time. The detection rate is >80%, indicating that debris trails are a generic feature of short-period comets. By comparison to orbital calculations for particles of a range of sizes ejected over 2 yr prior to observation, we find that particles comprising 4 debris trails are typically mm-sized while the remainder of the debris trails require particles larger than this. The lower-limit masses of the debris trails are typically ¹⁰¹¹ g, and the median mass loss rate is 2 kg/s. The mass-loss rate in trail particles is comparable to that inferred from OH production rates and larger than that inferred from visible-light scattering in comae.     

On the population, physical decay and orbital distribution of Jupiter family comets: Numerical simulations

We study the Jupiter family comet (JFC) population assumed to come from the Scattered Disk and transferred to the Jupiter’s zone through gravitational interactions with the Jovian planets. We shall define as JFCs those with orbital periods and Tisserand parameters in the range 2<T?3.1, while those comets coming from the same source, but that do not fulfill the previous criteria (mainly because they have periods ) will be called ‘non-JFCs’. We performed a series of numerical simulations of fictitious comets with a purely dynamical model and also with a more complete dynamical-physical model that includes besides nongravitational forces, sublimation and splitting mechanisms. With the dynamical model, we obtain a poor match between the computed distributions of orbital elements and the observed ones. However with the inclusion of physical effects in the complete model we are able to obtain good fits to observations. The best fits are attained with four splitting models with a relative weak dependence on q, and a mass loss in every splitting event that is less when the frequency is high and vice versa. The mean lifetime of JFCs with radii and is found to be of about 150-200 revolutions (∼. The total population of JFCs with radii within Jupiter’s zone is found to be of 450±50. Yet, the population of non-JFCs with radii in Jupiter-crossing orbits may be ∼4 times greater, thus leading to a whole population of JFCs + non-JFCs of ∼2250±250. Most of these comets have perihelia close to Jupiter’s orbit. On the other hand, very few non-JFCs reach the Earth’s vicinity (perihelion distances ) which gives additional support to the idea that JFCs and Halley-type comets have different dynamical origins. Our model allows us to define the zones of the orbital element space in which we would expect to find a large number of JFCs. This is the first time, to our knowledge, that a physico-dynamical model is presented that includes sublimation and different splitting laws. Our work helps to understand the role played by these erosion effects in the distribution of the orbital elements and lifetimes of JFCs.     

Secular light curves of comets, II: 133P/Elst-Pizarro, an asteroidal belt comet

We present the secular light curve (SLC) of 133P/Elst-Pizarro, and show ample and sufficient evidence to conclude that it is evolving into a dormant phase. The SLC provides a great deal of information to characterize the object, the most important being that it exhibits outburst-like activity without a corresponding detectable coma. 133P will return to perihelion in July of 2007 when some of our findings may be corroborated. The most significant findings of this investigation are: (1) We have compiled from 127 literature references, extensive databases of visual colors (37 comets), rotational periods and peak-to-valley amplitudes (64 comets). 2-Dimensional plots are created from these databases, which show that comets do not lie on a linear trend but in well defined areas of these phase spaces. When 133P is plotted in the above diagrams, its location is entirely compatible with those of comets. (2) A positive correlation is found between cometary rotational periods and diameters. One possible interpretation suggest the existence of rotational evolution predicted by several theoretical models. (3) A plot of the historical evolution of cometary nuclei density estimates shows no trend with time, suggesting that perhaps a consensus is being reached. We also find a mean bulk density for comets of 〈ρ〉=0.52±0.06 g/cm³. This value includes the recently determined spacecraft density of Comet 9P/Tempel 1, derived by the Deep Impact team. (4) We have derived values for over 18 physical parameters, listed in the SLC plots, Figs. 6-9. (5) The secular light curve of 133P/Elst-Pizarro exhibits a single outburst starting at +42±4 d (after perihelion), peaking at LAG=+155±10 d, duration 191±11 d, and amplitude 2.3±0.2 mag. These properties are compatible with those of other low activity comets. (6) To explain the large time delay in maximum brightness, LAG, two hypothesis are advanced: (a) the existence of a deep ice layer that the thermal wave has to reach before sublimation is possible, or (b) the existence of a sharp polar active region pointing to the Sun at time = LAG, that may take the form of a polar ice cap, a polar fissure or even a polar crater. The diameter of this zone is calculated at ∼1.8 km. (7) A new time-age is defined and it its found that T-AGE = 80 cy for 133P, a moderately old comet. (8) We propose that the object has its origin in the main belt of asteroids, thus being an asteroid-comet hybrid transition object, an asteroidal belt comet (ABC), proven by its large density. (9) Concerning the final evolutionary state of this object, to be a truly extinct comet the radius must be less than the thermal wave depth, which at 1 AU is ∼250 m (at the perihelion distance of 133P the thermal wave penetrates only ∼130 m). Comets with radius larger than this value cannot become extinct but dormant. Thus we conclude that 133P cannot evolve into a truly extinct comet because it has too large a diameter. Instead it is shown to be entering a dormant phase. (10) We predict the existence of truly extinct comets in the main belt of asteroids (MBA) beginning at absolute magnitude ∼21.5 (diameter smaller than ∼190 m). (11) The object demonstrates that a comet may have an outburst of ∼2.3 mag, and not show any detectable coma. (12) Departure from a photometric R⁺² law is a more sensitive method (by a factor of 10) to detect activity than star profile fitting or spectroscopy. (13) Sufficient evidence is presented to conclude that 133P is the first member of a new class of objects, an old asteroidal belt comet, ABC, entering a dormant phase.     

The HNC/HCN Ratio in Comets

The abundance ratio of the isomers HCN and HNC has been investigated in comet Hale-Bopp (C/1995 O1) through observations of the J = 4−3 rotational transitions of both species for heliocentric distances 0.93 < r < 3 AU, both pre- and post-perihelion. After correcting for the optical depth of the stronger HCN line, we find that the column density ratio of HNC/HCN in our telescope beam increases significantly as the comet approaches the Sun. We compare this behavior to that predicted from an ion-molecule chemical model and conclude that the HNC is produced insignificant measure by chemical processes in the coma; i.e., for comet Hale-Bopp, HNC is not a parent molecule sublimating from the nucleus. This revised version was published online in July 2006 with corrections to the Cover Date.     

Crystalline silicates in comets: How did they form?

Two processes have been proposed to explain observations of crystalline silicate minerals in comets and in protostellar sources, both of which rely on the thermal annealing of amorphous grains. First, high temperatures generated by nebular shock processes can rapidly produce crystalline magnesium silicate grains and will simultaneously produce a population of crystalline iron silicates whose average grain size is ∼10-15% that of the magnesium silicate minerals. Second, exposure of amorphous silicate grains to hot nebular environments can produce crystalline magnesium silicates that might then be transported outward to regions of comet formation. At the higher temperatures required for annealing amorphous iron silicates to crystallinity the evaporative lifetime of the grains is much shorter than a single orbital period where such temperatures are found in the nebula. Thermal annealing is therefore unable to produce crystalline iron silicate grains for inclusion into comets unless such grains are very quickly transported away from the hot inner nebula. It follows that observation of pure crystalline magnesium silicate minerals in comets or protostars is a direct measure of the importance of simple thermal annealing of grains in the innermost regions of protostellar nebulae followed by dust and gas transport to the outer nebula. The presence of crystalline iron silicates would signal the action of transient processes such as shock heating that can produce crystalline iron, magnesium and mixed iron-magnesium silicate minerals. These different scenarios result in very different predictions for the organic content of protostellar systems.     

A dynamical model with a new inversion technique applied to observations of Comet C/2000 WM1 (LINEAR)

Three continuum images of Comet C/2000 WM₁ (LINEAR) obtained on Nov 10, Nov 19, and Dec 03, 2001, are analyzed with the aid of a dynamical model, i.e. with a model that uses the size-dependent motion of dust grains under solar radiation pressure to determine the dust size distribution and its temporal change. The frames are photometrically calibrated in terms of the albedo filling factor product. On Nov 20.2 the Earth transited the orbital plane of the comet and an anti-tail was recognized in the image of Nov 19. For the determination of the particle fluxes describing the contribution of monodisperse particle shells to the cometary brightness the model uses a new regularization method employing Chebyshev polynomials of selected orders in emission time and particle size. It guarantees positiveness of the particle fluxes and imposes a varying degree of smoothness on their dependence on particle size and emission time. The particle emission velocities are still derived by trial and error. The dynamical model is described in detail. Results are presented for several low orders of the Chebyshev polynomials and are compared in order to understand the limitations imposed by the regularization process. The size distributions derived from the different observations do not always agree. This is particularly true for the earliest and most recent synchrones contributing to an image. In the observations of Nov 10 and Dec 03, i.e. excluding the anti-tail image, the integrated mass loss strongly decreases in the most recent time steps of the model although the comet is still approaching the Sun. This is interpreted as an artifact introduced by the overlap of the shells of large particle size emitted shortly before the observation. The model derives an increasing number of small particles released by the comet in the second half of November. This is at least in part considered as real and attributed to particle fragmentation occurring when the comet was at a heliocentric distance of about 1.4 AU.     

A simple mapping for comets in resonance

The dynamical evolution of a low inclination, intermediate period comet in mean-motion resonance with a giant planet can be described by a simple mapping giving the comet's heliocentric energy and ecliptic longitude at successive aphelia. Provided that the energy oscillations produced by the resonance are not too large, this mapping is linear. When the amplitude of the oscillations is close to the maximum possible within the resonance, the mapping can be improved by adding non-linear terms.     

The size-frequency distribution of dormant Jupiter family comets

We estimate the total number and the slope of the size-frequency distribution (SFD) of dormant Jupiter family comets (JFCs) by fitting a one-parameter model to the known population. We first select 61 near-Earth objects (NEOs) that are likely to be dormant JFCs because their orbits are dynamically coupled to Jupiter [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J., Levison, H.F., Michel, P., Metcalfe, T.S., 2002a. Icarus 156, 399-433]. Then, from the numerical simulations of Levison and Duncan [1997. Icarus 127, 13-32], we construct an orbit distribution model for JFCs in the NEO orbital element space. We assume an orbit-independent SFD for all JFCs, the slope of which is our unique free parameter. Finally, we compute observational biases for dormant JFCs using a calibrated NEO survey simulator [Jedicke, R., Morbidelli, A., Spahr, T., Petit, J., Bottke, W.F., 2003. Icarus 161, 17-33]. By fitting the biased model to the data, we estimate that there are ∼75 dormant JFCs with H<18 in the NEO region and that the slope of their cumulative SFD is −1.5±0.3. Our slope for the SFD of dormant JFCs is very close to that of active JFCs as determined by Weissman and Lowry [2003. Lunar Planet. Sci. 34. Abstract 2003]. Thus, we argue that when JFCs fade they are likely to become dormant rather than to disrupt and that the fate of faded comets is size-independent. Our results imply that the size distribution of the JFC progenitors—the scattered disk trans-neptunian population—either (i) has a similar and shallow SFD or (i^′) is slightly steeper and physical processes acting on the comets in a size-dependent manner creates the shallower active comet SFD. Our measured slope, typical of collisionally evolved populations with a size-dependent impact strength [Benz, W., Asphaug, E., 1999. Icarus 142, 5-20], suggests that scattered disk bodies reached collisional equilibrium inside the protoplanetary disk prior to their removal from the planetary region.     

The population of faint Jupiter family comets near the Earth

We study the population of faint Jupiter family comets (JFCs) that approach the Earth (perihelion distances q<1.3 AU) by applying a debiasing technique to the observed sample. We found for the debiased cumulative luminosity function (CLF) of absolute total magnitudes H₁₀ a bimodal distribution in which brighter comets (H₁₀?9) follow a linear relation with a steep slope α=0.65±0.14, while fainter comets follow a much shallower slope α=0.25±0.06 down to H₁₀∼18. The slope can be pushed up to α=0.35±0.09 if a second break in the H₁₀ distribution to a much shallower slope is introduced at H₁₀∼16. We estimate a population of about 10³ faint JFCs with q<1.3 AU and 10<H₁₀<15 (radii ∼0.1-0.5 km). The shallowness of the CLF for faint near-Earth JFCs may be explained either as: (i) the source population (the scattered disk) has an equally very shallow distribution in the considered size range, or (ii) the distribution is flattened by the disintegration of small objects before that they have a chance of being observed. The fact that the slope of the magnitude distribution of the faint active JFCs is very similar to that found for a sample of dormant JFCs candidates suggests that for a surviving (i.e., not disintegrated) object, the probability of becoming dormant versus keeping some activity is roughly size independent.     

Dark red debris from three short-period comets: 2P/Encke, 22P/Kopff, and 65P/Gunn

We present observations of the extended dust structures near the orbits of three short-period comets: 2P/Encke, 22P/Kopff, and 65P/Gunn. The dust trails were originally discovered by the Infrared Astronomical Satellite (IRAS). Our observations were made using wide-field optical CCD cameras on the University of Hawaii 2.24-m telescope, the Canada-France-Hawaii 3.6-m telescope, and the Kiso 1.05-m Schmidt telescope. We compared the observed images with models and found that the extended structures seen around 2P/Encke and 22P/Kopff before perihelion passage were most likely “dust trails,” whereas images taken after perihelion passage show a high contamination by recently released particles (i.e., particles in Neck-Line structures are visible). We could not confirm the existence of a dust trail from 65P/Gunn within the field of view of the camera used. The effective sizes of the particles responsible for the scattered light were estimated at 1-100 mm (2P/Encke), 1-10 mm (22P/Kopff), and 100 μm-1 mm (65P/Gunn), respectively, which is consistent with previous studies of dust trails made with infrared space telescopes and optical telescopes. We evaluated the mass loss rates of these comets, averaged over their orbits, as reaching (2P/Encke), (22P/Kopff), and (65P/Gunn). These values are consistent with previous work. Therefore, the total amount of material ejected from these three comets is , which would contribute a considerable fraction of the lost within 1 AU that needs to be replaced if the zodiacal cloud is to be maintained in a steady state. We also found that the particles in the dust structures are significantly redder than the Sun and the zodiacal light, and might be redder than the average short-period comet nuclei. Specifically, the reflectivity gradients of 2P/Encke, 22P/Kopff, and 65P/Gunn are 13±7 (% ¹⁰³ Å⁻¹), 20±5 (% ¹⁰³ Å⁻¹), and 15±4 (% ¹⁰³ Å⁻¹), respectively. We examined the change in color with distance from the nucleus. No clear correlation was detected for 2P/Encke or 22P/Kopff to an accuracy of 3-11%, while the 65P/Gunn tail did show color variation, becoming redder with increasing distance from the nucleus. This dark red material, consisting of particles of sand-cobble size, has marginally escaped from the nuclei and will evolve into finer-grained interplanetary dust particles after subsequent collisions.     

The Pioneer 10 anomalous acceleration and Oort cloud comets

Anderson et al. [Phys. Rev. D 65 (2002) 082004] recently reported new evidence that both Pioneer 10 and 11 are experiencing nearly the same unmodeled anomalous acceleration directed toward the Sun. Numerous mechanisms, both internal and external to the spacecraft, have been proposed to explain this unmodeled acceleration. If we assume that the cause of the anomalous acceleration is (1) external to the spacecraft, (2) isotropic, and (3) acts on bodies of cometary mass, then it would imply that new comets are more tightly bound to the Sun than previously believed. Here we show that the implied higher binding energy is incompatible with the established evidence that the galactic tide is dominant in making Oort cloud comets observable. We conclude that one or more of these assumptions must be invalid.     

Near-nucleus photometry of comets using archived NEAT data

Though optimized to discover and track fast moving Near-Earth Objects (NEOs), the Near-Earth Asteroid Tracking (NEAT) survey dataset can be mined to obtain information on the comet population observed serendipitously during the asteroid survey. We have completed analysis of over 400 CCD images of comets obtained during the autonomous operations of two 1.2-m telescopes: the first on the summit of Haleakala on the Hawaiian island of Maui and the second on Palomar Mountain in southern California. Photometric calibrations of each frame were derived using background catalog stars and the near-nucleus comet photometry measured. We measured dust production and normalized magnitudes for the coma and nucleus in order to explore cometary activity and comet size-frequency distributions. Our data over an approximately two-year time frame (2001 August-2003 February) include 52 comets: 12 periodic, 19 numbered, and 21 non-periodic, obtained over a wide range of viewing geometries and helio/geocentric distances. Nuclear magnitudes were estimated for a subset of comets observed. We found that for low-activity comets (Afρ<100 cm) our model gave reasonable estimates for nuclear size and magnitude. The slope of the cumulative luminosity function of our sample of low-activity comets was 0.33 ± 0.04, consistent with the slope we measured for the Jupiter-family cometary nuclei collected by Fernández et al. [Fernández, J.A., Tancredi, G., Rickman, H., Licandro, J., 1999. Astron. Astrophys. 392, 327-340] of 0.38 ± 0.02. Our slopes of the cumulative size distribution α=1.50±0.08 agree well with the slopes measured by Whitman et al. [Whitman, K., Morbidelli, A., Jedicke, R., 2006. Icarus 183, 101-114], Meech et al. [Meech, K.J., Hainaut, O.R., Marsden, B.G., 2004. Icarus 170, 463-491], Lowry et al. [Lowry, S.C., Fitzsimmons, A., Collander-Brown, S., 2003. Astron. Astrophys. 397, 329-343], and Weissman and Lowry [Weissman, P.R., Lowry, S.C., 2003. Lunar Planet. Sci. 34. Abstract 34].     

Activity of comets at large heliocentric distances pre-perihelion

We present observational data for two long-period and three dynamically new comets observed at heliocentric distances between 5.8 to 14.0 AU. All of the comets exhibited activity beyond the distance at which water ice sublimation can be significant. We have conducted experiments on gas-laden amorphous ice samples and show that considerable gas emission occurs when the ice is heated below the temperature of the amorphous-crystalline ice phase transition (T∼137 K). We propose that annealing of amorphous water ice is the driver of activity in comets as they first enter the inner Solar System. Experimental data show that large grains can be ejected at low velocity during annealing and that the rate of brightening of the comet should decrease as the heliocentric distance decreases. These results are consistent with both historical observations of distant comet activity and with the data presented here. If observations of the onset of activity in a dynamically new comet are ever made, the distance at which this occurs would be a sensitive indicator of the temperature at which the comet had formed or represents the maximum temperature that it has experienced. New surveys such as Pan STARRS, may be able to detect these comets while they are still inactive.     

Activity of comets: Gas transport in the near-surface porous layers of a cometary nucleus

The gas transport through non-volatile random porous media is investigated numerically. We extend our previous research of the transport of molecules inside the uppermost layer of a cometary surface ( [Skorov and Rickman, 1995] and [Skorov et al., 2001]). We assess the validity of the simplified capillary model and its assumptions to simulate the gas flux trough the porous dust mantle as it has been applied in cometary physics. A microphysical computational model for molecular transport in random porous media formed by packed spheres is presented. The main transport characteristics such as the mean free path distribution and the permeability are calculated for a wide range of model parameters and compared with those obtained by more idealized models. The focus in this comparison is on limitations inherent in the capillary model. Finally a practical way is suggested to adjust the algebraic Clausing formula taking into consideration the nonlinear dependence of permeability on layer porosity. The retrieved dependence allows us to accurately calculate the permeability of layers whose thickness and porosity vary in the range of values expected for the near-surface regions of a cometary nucleus.