Numerical simulation of cometary nuclei: III. Internal temperatures of cometary nuclei

A one-dimensional heat-diffusion model was used to calculate internal temperatures in cometary nuclei composed of either crystalline or amorphous ice, and for a range of orbits. It was found that the final central temperature, T_c, was a complex function of the comet's orbital semimajor axis, a, and eccentricity, e, as well as the functional form of the thermal conductivity. For cometary nuclei with identical thermal properties, T_c was found to decrease with eccentricity for a short-period orbit with a = 3 AU. For an intermediate-period orbit with a = 20 AU, T_c initially increased with eccentricity but then declined at large values of e for a crystalline ice nucleus, while for amorphous ice T_c increased monotonically. In addition, it was found that for conductivities of similar magnitude, crystalline ice (for which the conductivity varies inversely proportional to temperature) reached the final central temperature twice as fast as amorphouslike ice (for which the conductivity is proportional to temperature). T_c also depended on the magnitude of the conductivity. A four- to fivefold decrease in the conductivity resulted in a 3–4°K decrease in T_c at large eccentricities, while at small eccentricities T_c was only weakly dependent on the conductivity. Finally, the numerical results are compared to the analytical solutions of J. Klinger (1981, Icarus 47, 320–324) and C. P. McKay, S. W. Squyres, and R. T. Reynolds (1986, Icarus, 66, 625–629), and a numerical correction factor is derived for the McKay et al. expression for the central temperature.     

New orbits for comets C/1843 J1 (Mauvais) and C/1853 W1 (van Arsdale)

New orbits for comet C/1843 J1 (Mauvais) and comet C/1853 W1 (van Arsdale) are calculated. Both orbits are hyperbolic, with e = 1.001145 and semi‐major axis a = –1412.18 AU for Mauvais and e = 1.000700 and a = –2919.24 AU for van Arsdale. Integrating the orbits backwards indicate that both comets were born in the far Oort cloud. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

A thermal modelling of cometary activity with a crystallized water ice nucleus

Arguments are presented to suggest that surface layers of the nuclei of periodic comets consist of crystallized rather than amorphous water ice and thermal modelling of such nuclei is presented. The rate of sublimation of water from a rotating nucleus is found to be greater than that from a uniformly heated nucleus. When the model is applied to P/Halley, the sublimation rate at perihelion is found to be 8.1 × 10²⁹ mol s⁻¹ for a nucleus rotating with a period of 50 hours and 7.6 × 10²⁹ for a uniformly heated nucleus on the premise that the effective radius of the nucleus is 2.5 km. The total sublimation of water per revolution is 5.38 × 10³⁶ molecules for P/Halley and 3.91 × 10³⁶ molecules per P/Crommelin. The result so obtained is discussed in relation to the observational data.     

Short-Period Comets with a High Tisserand Constant: III. Kinematics of Low-Velocity Encounters

Within the framework of a pair two-body problem (Sun–Jupiter, Sun–comet), the kinematics of the encounter of a minor body with a planet is investigated. The notion of points of low-velocity tangency of the orbits of the comet and Jupiter, as well as the point of Jovicentric velocity and the low-velocity tangent section of a cometary orbit, is introduced. The conditions and definitions of low-velocity and high-velocity encounters are proposed. The systems of inequalities relating the aand eparameters, which make it possible to single out those comets that are likely to be objects with low-velocity encounters, are presented. The regions of orbits that have low-velocity tangent sections, i.e., regions of low-velocity tangency of orbits, are singled out on the (a, e) plane. These regions agree well with the corresponding parameters of the orbits of real comets whose evolution contains low-velocity encounters with Jupiter.     

Long-period comet flux in the planetary region: Dynamical evolution from the Oort cloud

This study analyzes the evolution of 2 × 10⁵ orbits with initial parameters corresponding to the orbits of comets of the Oort cloud under the action of planetary, galactic, and stellar perturbations over 2 × 10⁹ years. The dynamical evolution of comets of the outer (orbital semimajor axes a > 10⁴ AU) and inner (5 × 10³ < a (AU) < 10⁴) parts of the comet cloud is analyzed separately. The estimates of the flux of “new” and long-period comets for all perihelion distances q in the planetary region are reported. The flux of comets with a > 10⁴ AU in the interval 15 AU < q < 31 AU is several times higher than the flux of comets in the region q < 15 AU. We point out the increased concentration of the perihelia of orbits of comets from the outer cloud, which have passed several times through the planetary system, in the Saturn-Uranus region. The maxima in the distribution of the perihelia of the orbits of comets of the inner Oort cloud are located in the Uranus-Neptune region. “New” comets moving in orbits with a < 2 × 10⁴ AU and arriving at the outside of the planetary system (q > 25 AU) subsequently have a greater number of returns to the region q < 35 AU. The perihelia of the orbits of these comets gradually drift toward the interior of the Solar System and accumulate beyond the orbit of Saturn. The distribution of the perihelia of long-period comets beyond the orbit of Saturn exhibits a peak. We discuss the problem of replenishing the outer Oort cloud by comets from the inner part and their subsequent dynamical evolution. The annual rate of passages of comets of the inner cloud, which replenish the outer cloud, in the region q < 1 AU in orbits with a > 10⁴ AU (～ 5.0 × 10^?14 yr^?1) is one order of magnitude lower than the rate of passage of comets from the outer Oort cloud (～ 9.1 × 10^?13 yr^?1).     

Radiogenic heating of comets by 26Al and implications for their time of formation

The effect of radiogenic heating on the thermal evolution of spherical icy bodies with radii 1 km < R < 100 km was investigated. The radioisotopes considered were 26Al, 40K, 232Th, 235U, and 238U. Except for the 26Al abundance, which was varied, the other initial abundances were kept fixed, at values derived from those of chondritic meteorites and corresponding to a gas-to-dust ratio of 1. The initial models were homogeneous and isothermal (To = 10 K) amorphous ice spheres, in a circular orbit at 10(4) AU from the Sun. The main object of this study was to examine the conditions under which the transition temperature from amorphous into cubic ice (Ta = 137 K) would be reached. It was shown that the influence of the short-lived radionuclide 26Al dominates the effect of other radioactive species for bodies of radii up to approximately 50 km. Consequently, if we require comets to retain their ice in amorphous form, as suggested by observations, an upper limit of approximately 4 x 10(-9) is obtained for the initial 26Al abundance in comets, a factor of 100 lower than that of the inclusions in the Allende meteorite. A lower limit for the formation time of comets may thus be derived. The possibility of a coexistence of molten cometary cores and extended amorphous ice mantles is ruled out. Larger icy spheres (R > 100 km) reached Ta even in the absence of 26Al, due to the decay of the other radionuclides. As a result, a crystalline core formed whose relative size depended on the composition assumed. Thus the outermost icy satellites in the solar system, which might have been formed of ice in the amorphous state, have probably undergone crystallization and may have exhibited eruptive activity when the gas trapped in the amorphous ice was released (e.g., Miranda).     

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.     

Remote comets and related bodies: VJHK colorimetry and surface materials

Spectrophotometric data show that major compositional groups among outer solar system (OSS) surfaces include bright ices and at least two distinct classes of blackish carbonaceous-like materials, called C-type and RD-type. VJHK colorimetry of asteroids, satellites, and laboratory samples shows that these three classes can be distinguished by VJHK colors. We define an “α index” that denotes the position of objects in VJHK color - color diagrams; it empirically increases with albedo and ice/dirt ratio. We use the above data to define color fields that may be useful in interpreting our observations of eight comets (1980–1981). All eight comets have colors generally resembling RD asteroids and are inconsistent with reflection off clean ice surfaces. The observations suggest that these comets' halos contain RD dirt or dirty ice grains colored by RD dirt, supporting J. Gradie and J. Veverka's [Nature283, 840–842 (1980)] prediction of RD, rather than C, material in comets. Remote Comet P/Schwassmann-Wachmann 1 was observed both during outburst and quiescence and had the highest α index of any observed comet. Comet α indices appear to be correlated with solar distance. Further work will be needed to clarify possible coloring effects due to particle size, dispersal, and composition. We suggest a number of physical interpretations based on a single two-component mixing model, which assumes that all OSS planetesimals formed primarily from bright ices and dark carboneceous-like dirt, consistent with condensation theory. We discuss differentiation processes that concentrated one component or the other at the surface. All measured OSS interplanetary bodies have surfaces of dark dirt or dark dirty ice colored by the dirt component. Comets, consistent with the Whipple dirty iceberg model, are such objects close enough to the Sun for volatilization to throw dirty ice grains into the coma. In remote comets, the ice component of the grains remains stable, and we see dirty ice grains; in near comets, the ice component vaporizes, and we see dirt grains. A volatile-depleted dusty regolith on P/Schwassmann-Wachmann 1 and other remote comets could explain their eruptive behavior by means of gas pressure buildup in the porous, weakly bonded dust.     

Packing effect of fluffy particles

Packing forces, produced by an anisotropic sublimation of mantle material of grains located at the surface layer of loosely conglomerated fluffy particles, move the grains towards the center of the fluffy particles. This leads to a reduction of the empty space inside the fluffy particle and consequently to an increase of the mass density of the fluffy particle with time.As observed by the Helios dust experiment, fluffy particles of low density are ejected by comets with high eccentricity e and large semimajor axis a Since e and a of fluffy particles decrease with time due to the Poynting-Robertson effect, the accompanying increase of the density of fluffy particles seems to explain the existence of normal dense particles in quasi-circular orbits as detected during in situ measurements. It also explains that the majority of lunar craters have been produced by normal dense particles rather than by low density particles.     

Orbits of short period comets captured from the Oort cloud

Oort cloud comets occasionally obtain orbits which take them through the planetary region. The perturbations by the planets are likely to change the orbit of the comet. We model this process by using a Monte Carlo method and cross sections for orbital changes, i.e. changes in energy, inclination and perihelion distance, in a single planet-comet encounter. The influence of all major planets is considered. We study the distributions of orbital parameters of observable comets, i.e. those which have perihelion distance smaller than a given value. We find that enough comets are captured from the Oort cloud in order to explain the present populations of short period comets. The median value of cos i for the Jupiter family is 0.985 while it is 0.27 for the Halley types. The results may explain the orbital features of short period comets, assuming that the active lifetime of a comet is not much greater than 400 orbital revolutions.     

Orbital evolution of giant comet-like objects

We investigated by numerical integrations the long-term orbital evolution of four giant comets or comet-like objects. They are Chiron, P/Schwassmann-Wachmann 1 (SW1), Hidalgo, and 1992AD (5145), and their orbits were traced for 100–200 thousand years (kyr) toward both the past and the future. For each object, 13 orbits were calculated, one for the nominal orbital elements and other 12 with slightly modified elements based on the rms residual of the orbit determination and on the number of observations. As past studies indicate, their orbital evolution is found to be very chaotic, and thus can be described only in terms of probability. Plots of the semi-major axis (a) and perihelion distance (q) of the objects treated here seem to cross each other frequently, suggesting a possibility of their common evolutionary paths. About a half of all the calculated orbits showedq- ora-decreasing evolution. This indicates that, at least on the time scale in question, the giant comet-like objects are possibly on a dynamical track that can lead to capture from the outer solar system. We could hardly find the orbits with perihelia far outside the orbit of Saturn (q>15 AU). This is perhaps because the evolution of the orbits beyond Saturn is so slow that substantial orbital changes do not take place within 100–200 kyr.     

Cometary dust properties retrieved from polarization observations: Application to C/1995 O1 Hale-Bopp and 1P/Halley

The analysis of the polarized light scattered by cometary dust particles provides information on the physical properties of the solid component of cometary comae for C/1995 O1 Hale-Bopp and 1P/Halley. A model of light scattering by a size distribution of aggregates of up to 256 submicron-sized grains (spherical or spheroidal) mixed with single spheroidal particles has been developed, with its parameters adjusted to fit the phase angle and wavelength dependence of the polarization observations. The particles are built of two materials: a non-absorbing silicates-type material and a more absorbing organic-type material. The model reproduces accurately the inversion angle and the positive branch of the polarization phase curves from the visible to the near-infrared spectral domains. A negative branch of the polarization phase curves appears in our model, although the negative branch is not deep enough to reproduce accurately the observations. Significant differences are shown between the two comets, with dominance of small grains in the coma of Comet C/1995 O1 Hale-Bopp, well fitted by a distribution of the volume-equivalent diameter, a, following a^−3.0 with a lower cutoff around 0.20 μm and an upper cutoff of at least 40 μm. For 1P/Halley, the size distribution follows a^−2.8 with a lower cutoff around 0.26 μm and an upper cutoff of about 38 μm. The relative amount of organic-type particles is larger for 1P/Halley while the amount of aggregates, significant for both comets, is larger for C/1995 O1 Hale-Bopp.     

All comets are born equal: infrared emission by dust as a key to comet nucleus composition

The infrared emission of various comets can be matched within the framework that all comets are made of aggregated interstellar dust. This is demonstrated by comparing results on Halley (a periodic comet), Borrelly (a Jupiter family short period comet), Hale-Bopp (a long period comet), and extra-solar comets in the β Pictoris disk. Attempts have been made to generalize the chemical composition of comet nuclei based on the observation of cometary dust and volatiles and the interstellar dust model. Finally, we deduce some of the expected dust and surface properties of comet Wirtanen from the interstellar dust model as applied to other comets.     

Prospects for meteor shower activity in the venusian atmosphere

We investigate the possibility of detectable meteor shower activity in the atmosphere of Venus. We compare the Venus-approaching population of known periodic comets, suspected cometary asteroids and meteor streams with that of the Earth. We find that a similar number of Halley-type comets but a substantially lesser population of Jupiter family comets approach Venus. Parent bodies of prominent meteor showers that might occur at Venus have been determined based on minimum orbital distance. These are: Comets 1P/Halley, parent of the η Aquarid and Orionid streams at the Earth; 45P/Honda-Mrkos-Pajdusakova which currently approaches the venusian orbit to 0.0016 AU; three Halley-type comets (12P/Pons-Brooks, 27P/Crommelin and 122P/de Vico), all intercepting the planet's orbit within a 5-day arc in solar longitude; and Asteroid (3200) Phaethon, parent of the December Geminids at the Earth. In addition, several minor streams and a number of cometary asteroid orbits are found to approach the orbit of Venus sufficiently close to raise the possibility of some activity at that planet. Using an analytical approach described in Adolfsson et al. (Icarus 119 (1996) 144) we show that venusian meteors would be as bright or up to 2 magnitudes brighter than their Earth counterparts and reach maximum luminosity at an altitude range of 100-120, 20-30 km higher than at the Earth, in a predominantly clear region of the atmosphere. We discuss the feasibility of observing venusian showers based on current capabilities and conclude that a downward-looking Venus-orbiting meteor detector would be more suitable for these purposes than Earth-based monitoring. The former would detect a shower of an equivalent Zenithal Hourly Rate of at least several tens of meteors.     

Dust Grains in the Comae and Tails of Sungrazing Comets: Modeling of Their Mineralogical and Morphological Properties

Observations of sungrazing comets, all of which belong to the Kreutz family, provide the opportunity of studying the properties of dust in the comae and tails of the comets. On the basis of available information on cometary and interplanetary dust as well as observations of dust in the tails of sungrazers, we model dust in sungrazing comets as fluffy silicate aggregates of submicrometer sizes. To better interpret observational data, we numerically calculate the solar radiation pressure, the equilibrium temperature, and the sublimation and crystallization rates of silicate grains near the Sun. Our results show that the dust tails contain aggregates of submicrometer crystal grains, but not amorphous grains, since amorphous silicates mostly crystallize after release from the comets. The peak in the lightcurves of the dust comae observed either at 11.2 or 12.3 solar radii (R_⊙) seems to result from sublimation of fluffy aggregates consisting of crystalline or amorphous olivines, respectively. We attribute an additional enhancement in the lightcurves inside 7 R_⊙ to increasing out-flow of crystalline and amorphous pyroxenes composed fluffy aggregates. According to our model, the observed lightcurves indicate a high abundance of olivine and a low abundance of pyroxene in the comets, which may bear implications about the dynamical and thermal history of the sungrazers and their progenitor.     

Periodic orbits and bifurcations in the Sitnikov four-body problem when all primaries are oblate

We study the motions of an infinitesimal mass in the Sitnikov four-body problem in which three equal oblate spheroids (called primaries) symmetrical in all respect, are placed at the vertices of an equilateral triangle. These primaries are moving in circular orbits around their common center of mass. The fourth infinitesimal mass is moving along a line perpendicular to the plane of motion of the primaries and passing through the center of mass of the primaries. A relation between the oblateness-parameter ‘A’ and the increased sides ‘ε’ of the equilateral triangle during the motion is established. We confine our attention to one particular value of oblateness-parameter A=0.003. Only one stability region and 12 critical periodic orbits are found from which new three-dimensional families of symmetric periodic orbits bifurcate. 3-D families of symmetric periodic orbits, bifurcating from the 12 corresponding critical periodic orbits are determined. For A=0.005, observation shows that the stability region is wider than for A=0.003.     

Optical properties of dust from Jupiter family comets

To try to define specific physical properties of the dust of Jupiter-family comets (JFCs), we compare the light scattered by them. Amongst the more than 1000 JFCs, less than 200 are numbered, 40 of them being rather bright. In the present work we use data from the latter. In situ observations of three nuclei show low albedo surfaces. The albedo of the dust particles in the coma is low, with generally a red colour. The A(α)fρ product is a measure of cometary activity and secular changes. Images of different regions (jets and fans) give indications on the nucleus rotation and position of the emitting areas, as compared to the position of the rotation axis. Differences in physical properties between the particles in different regions are pointed out by differences in the linear polarization of the scattered light and by spectral variations in brightness and polarization. Jupiter family comets are considered as dust-poor comets. Tails and trails’ studies give an estimation of the size distribution of the particles. However the dust production rates depend on the largest particles (up to centimetre size), which are mainly observed in the trails where large dark compact particles are found. These dark particles are also responsible for the high polarization in the inner most coma of some comets. The meaning, in terms of physical properties, of the linear polarization is discussed through different examples such as 2P/Encke, 9P/Tempel 1 or the fragments of 73P/Schwassmann-Wachmann 3. Cometary outbursts and splitting events show that the properties of the dust ejected from the interior of the nucleus are similar to the ones of more active comets (new or with larger semi-major axis).     

A survey of meteor spectra and orbits: evidence for three populations of Na-free meteoroids

We present a survey of 97 spectra of mainly sporadic meteors in the magnitude range +3 to −1, corresponding to meteoroid sizes 1-10 mm. For the majority of the meteors, heliocentric orbits are known as well. We classified the spectra according to relative intensities of the lines of Mg, Na, and Fe. Theoretical intensities of these lines for a chondritic composition of the meteoroid and a wide range of excitation and ionization conditions were computed. We found that only a minority of the meteoroids show chondritic composition. Three distinct populations of Na-free meteoroids, each comprising ∼10% of sporadic meteoroids in the studied size range, were identified. The first population are meteoroids on asteroidal orbits containing only Fe lines in their spectra and possibly related to iron-nickel meteorites. The second population are meteoroids on orbits with small perihelia (q?0.2 AU), where Na was lost by thermal desorption. The third population of Na-free meteoroids resides on Halley type cometary orbits. This material was possibly formed by irradiation of cometary surfaces by cosmic rays in the Oort cloud. The composition of meteoroids on Halley type orbits is diverse, probably reflecting internal inhomogeneity of comets. On average, cometary dust has lower than chondritic Fe/Mg ratio. Surprisingly, iron meteoroids prevail among millimeter-sized meteoroids on typical Apollo-asteroid orbits. We have also found varying content of Na in the members of the Geminid meteoroid stream, suggesting that Geminid meteoroids were not released from their parent body at the same time.     

Long-Period Comets and the Oort Cloud

Long-period (LP) comets, Halley-type (HT) comets, and even some comets of the Jupiter family, probably come from the Oort cloud, a huge reservoir of icy bodies that surrounds the solar system. Therefore, these comets become important probes to learn about the distant Oort cloud population. We review the fundamental dynamical properties of LP comets, and what is our current understanding of the dynamical mechanisms that bring these bodies from the distant Oort cloud region to the inner planetary region. Most new comets have original reciprocal semimajor axes in the range2 × 10^-5 < 1/a_orig < 5 × 10^-5AU^-1. Yet, this cannot be taken to represent the actual space distribution of Oort cloud comets, but only the region in the energy space in which external perturbers have the greatest efficiency in bringing comets to the inner planetary region. The flux of Oort cloud comets in the outer planetary region is found to be at least several tens times greater than the flux in the inner planetary region. The sharp decrease closer to the Sun is due to the powerful gravitational fields of Jupiter and Saturn that prevent most Oort cloud comets from reaching the Earth’s neighborhood (they act as a dynamical barrier). A small fraction of ～10^-2 Oort cloud comets become Halley type (orbital periods P < 200 yr), and some of them can reach short-period orbits with P < 20 yr. We analyze whether we can distinguish the latter, very ‘old” LP comets, from comets of the Jupier family coming from the Edgeworth-Kuiper belt.     

An interpretation of the nitrogen deficiency in comets

We propose an interpretation of the composition of volatiles observed in comets based on their trapping in the form of clathrate hydrates in the solar nebula. The formation of clathrates is calculated from the statistical thermodynamics of Lunine and Stevenson (1985, Astrophys. J. Suppl. 58, 493-531), and occurs in an evolutionary turbulent solar nebula described by the model of Hersant et al. (2001, Astrophys. J. 554, 391-407). It is assumed that clathrate hydrates were incorporated into the icy grains that formed cometesimals. The strong depletion of the N₂ molecule with respect to CO observed in some comets is explained by the fact that CO forms clathrate hydrates much more easily than does N₂. The efficiency of this depletion, as well as the amount of trapped CO, depends upon the amount of water ice available in the region where the clathration took place. This might explain the diversity of CO abundances observed in comets. The same theory, applied to the trapping of volatiles around 5 AU, explains the enrichments in Ar, Kr, Xe, C, and N with respect to the solar abundance measured in the deep troposphere of Jupiter [Gautier et al 2001a] and [Gautier et al 2001b].