Relative motions of fragments of the split comets.: I. A new approach

A new approach is formulated for the study of motions of the split comets. It is based on the assumption that two fragments of a comet separate at a rate that is determined primarily by a slight difference between their effective solar attractions rather than by the impulse imparted on them at the time of splitting. The net dynamical effect is interpreted as due to differential nongravitational forces, which depend on the size, density, structure, composition, and spin rate of the fragments. Since at least at smaller distances from the Sun these forces vary inversely as roughly the square of heliocentric distance, their dynamical effect resembles that of radiation pressure, so that the formalism developed for the motion of a dust particle in a cometary tail is applicable in principle. The calculations show that this approach provides reasonably good to excellent fits of the observed separations for a great majority of the split comets, and that it fails only in the case of Comet 1957 VI. The correlation between the differential nongravitational forces and the endurance of the fragment is investigated in terms of the physical behavior of the fragments, with the emphasis on the short-lived objects. Some of the unusual phenomena accompanying the split comets are discussed, and comments are also offered on the sequence of splitting for comets with multiple nuclei and on the distribution of the points of splitting in space.     

SOHO/SWAN observations of comets with small perihelia: C/2002 V1 (NEAT), C/2002 X5 (Kudo–Fujikawa), 2006 P1 (McNaught) and 96P/Machholz 1

SWAN, the all-sky hydrogen Lyman-alpha camera on the SOHO spacecraft, designed primarily to image the interplanetary neutral hydrogen around the Sun, also observes comets continuously over large portions of their apparitions to the north and south of the ecliptic and at small solar elongation angles. Because of SOHO’s location at the L1 Lagrange point, analysis of SWAN images provides excellent temporal coverage of water production. We report here our results of observations of some interesting target comets selected from the extensive SWAN archive. These include three Oort Cloud Comets C/2002 V1 (NEAT), C/2002 X5 (Kudo–Fujikawa), C/2006 P1 (McNaught) and three apparitions of atypical short-period Comet 96P/Machholz 1. The common aspect of these four comets is their small perihelion distances, which are 0.19, 0.09, 0.17, and 0.12 AU, respectively. Their water production rates over their whole apparitions can be approximated by power laws in heliocentric distance (r in AU) as follows: 1.3 × 10²⁹ r^−2.1 s⁻¹ for C/2002 V1 (NEAT), 7.5 × 10²⁸ r^−2.0 s⁻¹ for C/2002 X5 (Kudo–Fujikawa), 5.4 × 10²⁹ r^−2.4 s⁻¹ for C/2006 (P1 McNaught) and 4.6 × 10²⁷ r^−2.1 s⁻¹ for 96P/Machholz 1. We also present daily-average water production rates for the long-period comets over long continuous time periods. We examine these results in light of our growing survey of comets that is yielding some interesting comparisons of water production rate variations with heliocentric distance and taxonomic classes.     

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.     

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.     

Secular light curve of Comet 28P/Neujmin 1 and of spacecraft target Comets 1P/Halley, 9P/Tempel 1, 19P/Borrelly, 21P/Giacobinni-Zinner, 26P/Grigg-Skjellerup, 67P/Churyumov-Gerasimenko, and 81P/Wild 2

We present the secular light curves of eight comets listed in the title. Two plots per comet are needed to study these objects: a reduced magnitude (to Δ=1 AU = geocentric distance) vs time, and a reduced magnitude vs LogR (R=heliocentric distance). A total of over 16 new parameters, are measured from both plots, and give an unprecedented amount of information to characterize these objects: the onset of sublimation (RON), the offset of sublimation (ROFF), the time lag at perihelion (LAG), the absolute magnitude (m(1,1)), the maximum magnitude at perihelion (mMAX(1,LAG)), the nuclear magnitudes (VN), the amplitude of the secular light curve (ASEC), plus several others, and the photometric functions needed to describe the envelope. The most significant findings of this investigation are: (a) The envelope of the observations is the best representation of the secular light curve. (b) The H10 photometric system is unable to explain the curves and a new set of photometric rules and functions is used. (c) Only four comets exhibit power laws in their secular light curves, and only partially: 1P, 19P, 21P, and 81P. All others have to be described by more complex functions. Of the four, three exhibit a break of the power law, requiring two laws pre-perihelion and one post-perihelion. The reason for this behavior is not understood. (d) We predict the existence of a photometric anomaly in the secular light curve of 67P/Churyumov-Gerasimenko, evidenced by a region of diminished activity from −119 to −6 days before perihelion, that might be interpreted as a topographic effect or the turn off of an active region. (e) We define a photometric parameter (P-AGE) that attempts to measure the relative age of a comet through the activity exhibited in the secular light curve. 81P/Wild 2 (a comet that has recently entered the inner Solar System) is confirmed as a young object, while 28P/Neujmin 1 is confirmed as a very old comet. (f) Arranging the comets by P-AGE also classifies them by shape. A preliminary classification is achieved. (g) The old controversy of what is a nuclear magnitude is clearly resolved.     

Dynamics,interrelations and evolution of the systems of asteroids and comets

The dynamics of larger interplanetary bodies is reviewed, with emphasis on evolutionary problems, interrelations, and open questions. Observational biases distinguishing the sample of known objects from the whole population are briefly discussed. A schematic division of the solar system into zones with different regimes of motion, and a rough taxonomy of orbit types are attempted. The role of individual major planets in controlling the dynamical evolution of interplanetary objects, in particular by stabilizing resonances and destabilizing close encounters, is compared. There are significant evolution asymmetries due to boundary conditions and preferential evolutionary paths; individual major displacements in the phase space of orbital elements conserve the Tisserand invariant with respect to the planet responsible, thus favouring certain evolutionary sequences against others. Very limited lifetimes of some orbit types imply a long-term balance between source and sink, and require a continuous supply of objects from other types of orbits. In this respect, the ultimate fate of extinct comets is of particular interest. Under very specific conditions, nongravitational effects of mass loss can result in stabilization of a formerly unstable orbit. Since the dividing line between the two basic interplanetary populations distinguished by origin and composition — the asteroids and the comets — is essentially that between stable and unstable motion, orbital data can be used to specify which of the known asteroid-like objects may be devolatilized cometary nuclei.Paper presented at the European Workshop on Planetary Sciences, organised by the Laboratorio di Astrofisica Spaziale di Frascati, and held between April 23–27, 1979, at the Accademia Nazionale del Lincei in Rome, Italy.     

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.     

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.     

A model of cometary gas and dust production and nongravitational forces with application to P/Halley

A program that computes gas and dust production rates and idealized nongravitational force components has been developed and applied to the case of Comet Halley. We use a modified form of our earlier comet model (F.P. Fanale and J.R. Salvali[(1984) Icarus 60, 476–511] to which coma effects and a section on nongravitational forces have been added. The possibility of grain cohesion is also included. These models are used together with observations from 1910 and semiempirically derived data to investigate the effects of obliquity and thermal conductivity of the near thermal conductivity of the nucleus on gas and dust production. The results indicate that the thermal conductivity of the nucleus is of the order of 10⁵ ergs/cm-s-°K, which implies that the ice near the surface is in the crystalline form. A general method is presented for calculating the radii of cometary nuclei using theoretically derived and semiempirically derived nongravitational force components. This method is used to calculate possible radii for Comet Halley that depend on the model variation chosen. The method used and the results presented herein should have greater significance and value when the observational data from Halley's current perihelion passage become available.     

On the observability of radiation forces acting on near-Earth asteroids

We consider the perturbations on near-earth asteroid orbits due to various forces stemming from solar radiation. We find that the existence of precise radar astrometric observations at multiple apparitions, spanning periods on the order of 10 years, allows the detection of such forces on bodies as large as kilometer across. Indeed, the perturbations are so substantial that certain of the forces can be essential to fit an orbit to the observations. In particular, we show that the recoil force of thermal radiation from the asteroid, known as the Yarkovsky effect, is the most important of these unmodeled perturbations. We also show that the effect of reflected light can be important if even moderate albedo variations are present, while moderate changes in oblateness appear to have a far smaller effect. An unexpected result is that the Poynting–Robertson effect, typically only considered for submillimeter dust particles, could be observable on smaller asteroids with high eccentricity, such as 1566 Icarus. Finally, we also study the possibility of improving the orbit uncertainty through well-timed optical observations which might help in better detection of these nongravitational perturbations.     

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.     

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 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.     

Orbital linkages of Comet 6P/d'Arrest based on its asymmetric light curve

We present an investigation of different models of the nongravitational acceleration on Comet 6P/d'Arrest, as used in orbital linkages spanning 150 years from the discovery of the comet in 1851 until the recent observations made in 2001. Some of our models use the time-shifted g-like function to represent the variation of outgassing rate, but the main thrust is on models using instead a production curve that is fitted to recent light curve observations—mainly those in 1976. We pay special attention to the proper scaling of such a production curve, when applied to other apparitions with a different perihelion distance q, and we find a best fit with a q^−1.6 power-law. Generally, the best fit is found with models, in which the acceleration components are expressed in terms of the angular parameters of the rotating nucleus. We thus find the orientation of the spin axis, and using the orbital evolution we are able to predict a variable time shift of the outgassing curve. The very best results are found when applying this time shift to the light-curve based, angular models. The totality of the 1851-2001 observations can then be linked with a mean residual of less than 4″. This may be brought down to ∼^2″ by solving for individual ‘activity parameters’ of all apparitions, which are multiplicative factors applied to the acceleration amplitudes. These turn out to be within 10% of unity for the best fit. We have also performed a linkage to the observations of Comet 1678 (La Hire) using our models. We find an indication of a secular increase of the amount of asymmetry of the outgassing with respect to perihelion, part of which is due to the variable time shift caused by the orbital evolution.     

Migration of Trans-Neptunian Objects to the Terrestrial Planets

The orbital evolution of more than 22000 Jupiter-crossing objects under thegravitational influence of planets was investigated. We found that the meancollision probabilities of Jupiter-crossing objects (from initial orbits close tothe orbit of a comet) with the terrestrial planets can differ by more than twoorders of magnitude for different comets. For initial orbital elements close tothose of some comets (e.g., 2P and 10P), about 0.1% of objects got Earth-crossingorbits with semi-major axes a < 2 AU and moved in such orbits for more than a Myr (up to tens or even hundreds of Myrs).Results of our runs testify in favor of at least one of these conclusions: (1) the portionof 1-km former trans-Neptunian objects (TNOs) among near-Earth objects (NEOs)can exceed several tens of percent, (2) the number of TNOs migrating inside the solarsystem could be smaller by a factor of several than it was earlier considered, (3) mostof 1-km former TNOs that had got NEO orbits disintegrated into mini-comets and dustduring a smaller part of their dynamical lifetimes if these lifetimes are not small.     

Radio observations of Jupiter-family comets

Radio observations from decimetric to submillimetric wavelengths are now a basic tool for the investigation of comets. Spectroscopic observations allow us: (i) to monitor the gas production rate of the comets, by directly observing the water molecule, or by observing secondary products (e.g., the OH radical) or minor species (e.g., HCN); (ii) to investigate the chemical composition of comets; (iii) to probe the physical conditions of cometary atmospheres: kinetic temperature and expansion velocity. Continuum observations probe large-size dust particles and (for the largest objects) cometary nuclei.Comets are classified from their orbital characteristics into two separate classes: (i) nearly isotropic, mainly long-period comets and (ii) ecliptic, short-period comets, the so-called Jupiter-family comets (JFCs). These two classes apparently come from two different reservoirs, respectively, the Oort cloud and the trans-Neptunian scattered disc. Due to their different history and—possibly—their different origin, they may have different chemical and physical properties that are worth being investigated.The present article reviews the contribution of radio observations to our knowledge of the JFCs. The difficulty of such a study is the commonly low gas and dust productions of these comets. Long-period, nearly isotropic comets from the Oort cloud are better known from Earth-based observations. On the other hand, JFCs are more easily accessed by space missions. However, unique opportunities to observe JFCs are offered when these objects come by chance close to the Earth (like 73P/Schwassmann-Wachmann 3 in 2006), or when they exhibit unexpected outbursts (as did 17P/Holmes in 2007).About a dozen JFCs were successfully observed by radio techniques up to now. Four to ten molecules were detected in five of them. No obvious evidence for different properties between JFCs and other families of comets is found, as far as radio observations are concerned.     

Is Comet C/1853 E1 (Secchi) extrasolar?

Comet C/1853 E1 (Secchi) has a hyperbolic orbit with eccentricity 1.01060 and perihelion outside of the Earth's orbit. Integrating the orbit with barycentric coordinates backwards to 50000 AU, the approximate edge of the Oort cloud, shows that the orbit remains hyperbolic. This is still true even if plutoids additional to Pluto are included in the integration. Nor does including Galactic tidal and disc effects and possible nongravitational forces change the orbit to a high eccentricity ellipse. Although certain factors, such as unknown massive plutoids, gravitational effects by interstellar gas clouds, or unmodelled nongravitational forces operating on the comet, could change this situation, the tentative conclusion that the origin of this comet is extrasolar remains the one most consistent with the observations (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)