Relative motions of fragments of the split comets: II. Separation velocities and differential decelerations for extensively observed comets

A multiparameter model has been devised to discriminate the effects of the velocity of separation of two fragments of a split comet on their observed motions from the effects of the postsplit differential nongravitational forces. The iterative differential-correction procedure is applied to five extensively observed split comets: West 1975n, Ikeya-Seki 1965 VIII, Wirtanen 1957 VI, the Southern Comet 1947 XII, and Periodic Brooks 2 1889 V. The present model confirms that the major contribution to the observed rate of separation of the fragments comes from the postsplit forces. The model removes or substantially reduces the systematic trends in the residuals of comets West, Wirtanen, and P/Brooks 2, which could not be eliminated by a simple model that ignored the effects of the separation velocity. In particular, the results for Comet Wirtanen now indicate that the comet split at a heliocentric distance of more than 9 AU and that the initial rate of separation of the two fragments did not amount to more than 26 cm/sec. The separation velocities for the other comets range from 1 to 2 m/sec. Difficulties of the interpretation of the observed separation velocities are briefly discussed.     

That's the way the comet crumbles: Splitting Jupiter-family comets

Our current understanding of split, Jupiter-family comets is reviewed. The focus is on what recent studies of comets have told us about the nature of the splitting phenomenon. The goal is to not repeat the information given in recent reviews of split comets, but to build upon it. In particular, we discuss comets that have suffered splitting or fragmentation events in the past few years. These include comets (a) 57P/du Toit-Neujmin-Delporte, observed with a long train of fragments in 2002; (b) 73P/Schwassmann-Wachmann 3, which split in 1995 and was extensively studied during its relatively close passage to Earth in 2006, during which dozens of fragments were discovered and studied; and (c) 174P/Echeclus, a Centaur and potentially future JFC, which split in late 2005 and was the first such Centaur observed to do so. We also discuss recent observations by SOHO of split comets that are likely of short-period. The Spitzer Space Telescope has observed many JFCs and provided us with unprecedented detailed views of cometary debris trails, which may be thought of as a middle ground between “normal” ejection of micron-sized dust grains and the cleaving off of meter-to-kilometer sized fragments. We will also discuss potential breakthroughs in studying splitting JFCs that may come from future surveys.     

Specific features of orbits of Kreutz dwarf comets

Angular orbital parameters of Kreutz sungrazing comets are considered. Three groups of Kreutz dwarf comets are distinguished based on the positioning of orbit poles, and the motion of fragments from group A is modeled numerically. It is found that Kreutz dwarf comets have a very large parameter А ₃ of nongravitational acceleration. This may be associated with sublimation of substances more refractory than water ice at extremely short heliocentric distances. It is demonstrated that the nongravitational acceleration of Kreutz dwarf comets is asymmetric with respect to perihelion, and the perturbing function maximum is observed ~15 min after the perihelion passage.     

Asymmetric outgassing of short-periodic comets with respect to perihelion

The asymmetric model accounting for nongravitational effects is applied to improve orbits of a number of short-periodic comets that have shifts of maximum brightness with respect to their perihelions. Shifts of maximum gas productivity have been obtained for 20 short-periodic comets using photometric and dynamic methods. When using the photometric method, the maximum gas productivity is supposed to coincide with the maximum brightness of the comet, while, in the dynamic approach, it is believed to correspond to the maximum nongravitational acceleration. An analysis and evaluation of the results have been carried out.     

Collision with meteoroids as one of the possible mechanisms for the splitting of cometary nuclei

Results are presented of a statistical analysis of dynamic parameters for 114 comets with split nuclei. A list of the objects includes actually split comets, fragments of cometary pairs, lost comets with designation D, and comets with large-scale atmospheric features. Some aspects of the hypothesis that splitting is caused by collisions of cometary nuclei with meteoroid swarms are investigated. To verify the hypothesis, an analysis is conducted of the positions of split comets’ orbits relative to 58 meteor streams from Cook’s catalogue. The calculations give the number (N) of orbital nodes of split comets relative to the plane of each swarm within a distance of 0.001, 0.005, 0.01, 0.05, and 0.1 AU from each swarm. A special algorithm is proposed for determining the degree of redundancy of N by finding the expected value and dispersion for the number of the nodes. The comparison of N with the expected value, together with the consideration of the dispersion, reveals a redundancy of N in 29 cases. Therefore, collisions of comets with meteoroid swarms can be considered as one of the possible causes of comet splitting. A similar testing is conducted for the asteroid belt and Kuiper belt as potential sources of a vast number of sporadic meteoroids. Based on the results of the calculations, the former may be considered as the most effective region of splitting of periodic comets.     

Are There Many Inactive Jupiter-Family Comets among the Near-Earth Asteroid Population?

We analyze the dynamical evolution of Jupiter-family (JF) comets and near-Earth asteroids (NEAs) with aphelion distances Q>3.5 AU, paying special attention to the problem of mixing of both populations, such that inactive comets may be disguised as NEAs. From numerical integrations for 2×10⁶ years we find that the half lifetime (where the lifetime is defined against hyperbolic ejection or collision with the Sun or the planets) of near-Earth JF comets (perihelion distances q<1.3 AU) is about 1.5×10⁵ years but that they spend only a small fraction of this time (∼ a few 10³ years) with q<1.3 AU. From numerical integrations for 5×10⁶ years we find that the half lifetime of NEAs in “cometary” orbits (defined as those with aphelion distances Q>4.5 AU, i.e., that approach or cross Jupiter's orbit) is 4.2×10⁵ years, i.e., about three times longer than that for near-Earth JF comets. We also analyze the problem of decoupling JF comets from Jupiter to produce Encke-type comets. To this end we simulate the dynamical evolution of the sample of observed JF comets with the inclusion of nongravitational forces. While decoupling occurs very seldom when a purely gravitational motion is considered, the action of nongravitational forces (as strong as or greater than those acting on Encke) can produce a few Enckes. Furthermore, a few JF comets are transferred to low-eccentricity orbits entirely within the main asteroid belt (Q<4 AU and q>2 AU). The population of NEAs in cometary orbits is found to be adequately replenished with NEAs of smaller Q's diffusing outward, from which we can set an upper limit of ∼20% for the putative component of deactivated JF comets needed to maintain such a population in steady state. From this analysis, the upper limit for the average time that a JF comet in near-Earth orbit can spend as a dormant, asteroid-looking body can be estimated to be about 40% of the time spent as an active comet. More likely, JF comets in near-Earth orbits will disintegrate once (or shortly after) they end their active phases.     

Determination of Non-gravitational Effects in the Motion of Near-Sun Objects 321P, 322P, 323P,and 342P

At the beginning of this century, the SOHO space observatory discovered near-Sun comets with perihelion distances q ≈ 0.05 AU, which remained observable over several close encounters with the Sun. This became one of the surprises in studying the small bodies of the Solar System. Currently, there are objects that have already been observed in four (342P) and five (321P, 322P, and 323P) apparitions. In the present work, the estimates of nongravitational effects are obtained for these objects based on the pair-wise linkage of the apparitions. The calculations show that the observations of these objects are poorly represented if solely the gravitational forces are considered. The magnitude of nongravitational effects in the semimajor axis noticeably changes with time. The motion of all comets is significantly affected by the components of nongravitational forces that are perpendicular to the orbital plane.     

On the aging of comets

This study is based primarily on the calculations of comet orbits over ~ 10⁶ years for 160 short-period comets by Harold F. Levison and Martin J. Duncan from which there are calculated “ablation AGES”. There are positive statistical correlations (having many deviations) with radial nongravitational forces, comet activity measures, and dust-to-gas ratios in the spectra, in the sense that comets of greater “AGES” tend to be less active and to show less dust in their spectra than comets of lesser “AGES”.     

Orbital properties of Jupiter-family comets

The history of “comet families”, in particular the Jupiter comet family, is reviewed, together with ways in which the Jupiter family has been defined. New criteria are proposed, particularly with regard to distinguishing Jupiter-family comets (JFCs) from centaurs. The effect of nongravitational forces on JFCs is also discussed.     

Comet Splitting – Observations and Model Scenarios

Splitting events affect cometary nuclei to a different level of severity ranging from complete disruption of the nucleus (e.g., C/1999 S4 LINEAR) to separation of major fragments (e.g., 73P/Schwassmann-Wachmann 3) and spill-offs of smaller boulders (e.g., C/2001 A2 LINEAR).Fragmentation of comets produces secondary products over a wide range of sizes (from cometesimals to sub-micron dust). It is detectable through the presence of fragments (with own comae and tails) in the coma of the parent nucleus, through outbursts in its activity and through arc-lets (“coma wings”)associated with fragments. The secondaries have different life times and show different non-gravitational forces. Nucleus splitting is also considered to generate whole families of comets (Kreutz group) or — if gravitational bound — multiple nuclei (e.g., C/1995 O1 Hale-Bopp). It may explain the striae phenomena seen in dust tails of bright comets (C/1995 O1 Hale-Bopp) and the detection of chains of impact craters onother bodies in the solar system. As process of significant mass loss it is relevant for the scenario of nucleus extinction, at the same time it also plays a role for the number statistics of existing (observable) comets and for the size distribution of comet nuclei. Various model scenarios for nucleus splitting are proposed: tidal disruption, rotational splitting, break-up due to internal gas pressure, fragmentation due to collision with other bodies. Only in one case, Comet D/1993 F1Shoemaker-Levy 9, the physical process of fragmentation could be undoubtedly identified. In any case, comet splitting provides important insights inthe internal structure, surface layering and chemistry of comet nuclei.     

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.     

Chaotic motion of comets in near-parabolic orbit: Mapping approaches

There exist many comets with near-parabolic orbits in the Solar System. Among various theories proposed to explain their origin, the Oort cloud hypothesis seems to be the most reasonable (Oort, 1950). The theory assumes that there is a cometary cloud at a distance 10³ – 10⁵ AU from the Sun and that perturbing forces from planets or stars make orbits of some of these comets become of near-parabolic type. Concerning the evolution of these orbits under planetary perturbations, we can raise the question: Will they stay in the Solar System forever or will they escape from it? This is an attractive dynamical problem. If we go ahead by directly solving the dynamical differential equations, we may encounter the difficulty of long-time computation. For the orbits of these comets are near-parabolic and their periods are too long to study on their long-term evolution. With mapping approaches the difficulty will be overcome. In another aspect, the study of this model has special meaning for chaotic dynamics. We know that in the neighbourhood of any separatrix i.e. the trajectory with zero frequency of the unperturbed motion of an Hamiltonian system, some chaotic motions have to be expected. Actually, the simplest example of separatrix is the parabolic trajectory of the two body problem which separates the bounded and unbounded motion. From this point of view, the dynamical study on near-parabolic motion is very important. Petrosky's elegant but more abstract deduction gives a Kepler mapping which describes the dynamics of the cometary motion (Petrosky, 1988). In this paper we derive a similar mapping directly and discuss its dynamical characters.     

New edition of the catalogue of short-period comets

The Institute of Theoretical Astronomy in St. Petersburg and the Astronomical Institute in Bratislava are preparing a new edition of the Catalogue of short-period comets. This edition will be supplemented by short-period comets discovered after the year 1983 and comprises some new features, e. g. the evolution of orbital elements between the years 1750 and 2050, and the perihelion passages of comets within the 1994–2050 years. A new method has been employed for the determination of nongravitational parameters from the osculating elements of a comet based on all its observed returns.The method has been tested on the comets P/Comas Solá and P/Forbes with all returns, except the last one. The results have been compared with the osculating elements of the last return and those used in the old edition of the Catalogue of short-period comets. The new method enables a good prediction of osculating elements for the future, at least for the next return.     

Comparative Study Of The Dust Polarimetric Properties In Split And Normal Comets

Our polarimetric database contains six comets, C/1975 V1 (West), 16P/Brooks 2,C/1988 A1 (Liller), D/1996 Q1 (Tabur), C/1999 S4 (LINEAR), and C/2001 A2(LINEAR), which can be related to the group of split comets. Comets West, S4(LINEAR) and A2 (LINEAR) were observed during splitting. We compare thepolarimetric measurements of the dust particles in these comets, sometimes togetherwith available photometric and colorimetric data, with those in normal comets. Weconclude that there is no significant evidence for differences of polarization betweentidally split comets (e.g., Brooks 2), dissipating comets (e.g., Tabur), non-tidally splitcomets (e.g., West) and normal comets. The total disintegration of Comet S4 (LINEAR), however, did produce significant changes in the observed properties of dust.     

Fan-shaped coma,orientation of rotation axis,and surface structure of a cometary nucleus I. Test of a model on four comets

Conspicuous anisotropy in the outgassing from comets, especially from short-period ones, appears to be the factor responsible for a frequent occurrence of a fan-shaped coma, extending in the general direction of the Sun. It is proposed that the pattern of deviations from the sunward direction contains information on the orientation of the spin axis and on the time lag in the sublimation process, which in turn provides insight into the nature of the nuclear surface. A simple model of a spherical rotating nucleus is formulated and a trial-and-error technique devised to determine the axis-orientation constants and a lage angle, a meaasure of the time lag in units of the rotation period. The results of application of this method to periodic comets Encke, Tempel 2, Borrelly, and Schwassmann-Wachmann 3 are presented. It is shown that the sense of rotation determined in this fashion is consistent with the results established for three of the four comets from the transverse component of the nongravitational force affecting their orbital motions. It is found that in general the time lag is strongly time dependent and that lag angles approaching 90° are rather common near perihelion, suggesting a complex surface structure that involves an insulting crust of dust of variable thickness and strength. These results are compared with the observed lightcurves of the four comets and with the calculated distributions of integrated insolation at the nuclear surface as functions of the cometocentric latitude and time. Noticed is a tendency of the comets to turn their spin axes to the Sun near perihelion and to replace, on the outbound leg of orbit, the established fan-orientation pattern by a “late”-tail pattern indicative of old, slowly accelerated particles. It is suggested that the motion of P/Schwassmann-Wachmann 3, which is due for a favorable return in 1979, was affected by a secular deceleration in 1930.     

The effect of non-gravitational forces on the median inclination of short-period comets

The numbered Jupiter family comets (orbital periods   P < 20 yr  ) have a median orbital inclination of about     . In this paper, we integrate the orbits of these comets into the future, under the influence of both typical non-gravitational forces and planetary perturbation, using a Bulirsch–Stoer integrator. In the case where non-gravitational forces were not acting, the median inclination of those comets that remained on   P < 20 yr  orbits increased at the rate of  (1.92 ± 0.12) × 10⁻³ deg yr⁻¹  for the first 3600 yr of the integration. During this time the population of the original family decreases, such that the half-life is about 13 200 ± 800 yr. The introduction of non-gravitational forces slows down the rate of increase in inclination to a value of around  (1.23 ± 0.16) × 10⁻³ deg yr⁻¹  . This rate of increase in inclination was found to be only weakly dependent on the non-gravitational parameters used during the integration. After a few thousand years, the rate of change in inclination decreases, and after 20 000 yr the inclinations of those initial Jupiter family members that still have orbits with   P < 20 yr  become constant at about     , independent of whether non-gravitational forces are acting or not. The presently known Jupiter family of comets is losing members at the rate of one in every 67 yr. To maintain the family in equilibrium, Jupiter has to capture comets at a similar rate, and these captured comets have to be of low inclination to compensate for the pumping up of inclinations by gravitational perturbation.     

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.     

Thermal modeling of cometary nuclei

A new model of the sublimation of volatile ices from a cometary nucleus has been developed which includes the effects of diurnal heating and cooling, rotation period and pole orientation, and thermal properties of the ice and subsurface layers. The model also includes the contribution from coma opacity, scattering, and thermal emission, where the properties of the coma are derived from the integrated rate of volatile production by the nucleus. The model is applied to the specific case of the 1986 apparition of Halley's comet. It is found that the generation of a cometary dust coma actually increases the total energy reaching the Halley nucleus. This results because of the significantly greater geometrical cross section of the coma as compared with the bare nucleus, and because the coma provides an essentially isotropic source of multiply scattered sunlight and thermal emission over the entire nucleus surface. For Halley, the calculated coma opacity is approximately 0.2 at 1 AU from the Sun, and 1.2 at perihelion (0.587 AU). At 1 AU this has little effect on dayside temperatures (maximum ≈200°K) but raises nightside temperatures (minimum ≈150°K) by about 40°K. At perihelion the higher opacity results in a nearly isothermal nucleus with only small diurnal and latitudinal temperature variations. The general surface temperature is 205°K with a maximum of 209°K at local noon on the equator. Some possible consequences of the results with respect to the generation of nongravitational forces, observed volatile production rates for comets, and cometary lifetimes against sublimation are discussed.