The magnitude distribution, perihelion distribution and flux of long-period comets

The mass distribution and perihelion distribution of long-period comets are re-assessed. The mass distribution index is found to be 1.598±0.016 , indicating that the distribution is somewhat steeper than was obtained by previous analyses of an amalgam of all the available historical data. The number of long-period comets that have orbital perihelion distances, q , that fall in a specific q to q +d q range is found to be independent of q . It is also noted that the flux of long-period comets to the inner Solar system has remained constant throughout recorded history.
The number of long-period comets, , per 1-au interval of perihelion distance, per year, brighter than H , entering the inner Solar system is found to be given by log₁₀ =−2.607+0.359 H . It is therefore estimated that, for example, about 0.5, 30 and 2000 long-period comets with absolute magnitudes brighter than 0, 5 and 10 respectively pass the Sun on orbits with perihelion distances less than 2.0 au, every century.     

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.     

Planetary impact probabilities for long-period comets

Planetary impact probabilities for long-period (near-parabolic) comets are determined by averaging Öpik's equations over inclination and perihelion distance for each planet. These averaged values compare well with the results of more elaborate Monte Carlo calculations. The impact probabilities are proportional to the square of the normalized capture radius of each planet, which in turn is a function of the planet's radius and mass, so that the major planets have the highest impact probabilities. Encounter velocities have an average value of $\text{3}\text{1}\text{2}$ times the planetary orbital velocity but the most probable encounter velocities are slightly higher than this for the terrestrial planets and slightly lower for the major planets. Comparison of the impact probabilities with the cratering record, corrected for gravity and velocity effects, indicates that long-period comets may account for 3 to 9% of the observed large crattes (diameter > 10 km) on the terrestrial planets. The inclination and perihelion properties of the impact probabilities obtained from numerical averaging provide a simple method for determining the impact probabilities for nonuniform distributions. The perihelion distribution of long period comets from J. A. Fernandez ((1981) Astron. Astrophys.96, 26–35) results in a crater production rate quite similar throughout the solar system, unlike that of a uniform perihelion distribution.     

Origin and evolution of the long-period comets

We consider the changes of cometary perihelion distances as a process of diffusion in the value of q, due to perturbations by stars. We find more comets at large q values than is observed. This suggests that a large number of long-period comets is not observed.     

Origin and evolution of the long-period comets

We consider the changes of cometary perihelion distances as a process of diffusion in the value of q, due to perturbations by stars. We find more comets at large q values than is observed. This suggests that a large number of long-period comets is not observed.     

Searches for transplutonian planets using long-period comets

We discuss the dynamical connection of long-period and nearly parabolic comets with hypothetical transplutonian planets. The statistics includes 792 comets with periods P > 200 years. The orbital plane of the parent planet can be determined from the observed distribution of the perihelia and poles of cometary orbits. The radius of a planetary orbit can be calculated using the Radzievsky-Tisseran criterion. We calculated the minimum distance of each of the 792 orbits to 11 hypothetical planetary orbits. Testing for the kinematic connection of comets with transplutonian planets yielded a negative result. The presence of the nodes of cometary orbits in the transplutonian region is shown to be the result of a geometric effect. We found a high concentration of the nodes and perihelia of cometary orbits in the zone of the terrestrial planets.     

The origin of the solar system: Implications for transneptunian planets and the nature of the long-period comets

If the solar system origin is considered within the framework of the author's hypothesis on the binary stars formation as a result of rotational-exchange break-up of the rotating protostar, then difficulties involved in the usual nebular hypotheses are automatically removed (unclear aspects of the possibility of formation of the gas disc proper, the problems of the angular momentum including slow rotation of the Sun and coplanarity of the planetary orbits, of differences in planetary masses and composition, the need, for the disc remnants to be swept out, the long time of planetary formation as compared with the possible lifetime of a turbulized disc etc.).The major stages of division and evolution of the Jupiter-Sun system are described. Similarities between the massive rotating proto-Jupiter (PJ) and the classical protoplanetary discs are pointed out. The process of planetoid condensation inside PJ is discussed. The most probable site of the condensation is the region of the first Lagrangian point. The planetoids condensed were lost by PJ as a result of its fast mass decrease. A gas dynamic consideration of the motion of planetoids in PJ yields 1000–3000 yr as a time scale for the PJ's mass loss. The number of the moonlike bodies lost (the remaining Galilean satellites fixing their lower mass limit) could reach 10⁴.Evolution of such interacting bodies results in the formation beyond Neptune of a cloud (up to 10³) of moonlike (and more massive) planets.The excess concentration of the long-period comets aphelia in this area implies their genetic relation to the planets. A concept of a joint planeto-cometary cloud is introduced. A concrete hydrodynamic mechanism of ice ejection from planets into space, viz. the formation of cumulative (Monroe) jets, is pointed out.A program of further investigations is outlined and recommendations given for an experimental check on the implications of the new cosmogonic concepts.     

Re-ignition of dead pulsars by passages of interstellar comets through the magnetosphere: Possible nature of cosmic gamma-ray bursts

In a recent paper by Ruderman and Cheng (1988) a general scenario of radio pulsars evolution has been proposed, which explains jointly all galactical classes of neutron stars (NSs) radiating gamma-rays. This scheme associates cosmic gamma-ray bursts (GRBs) with electromagnetic cascades in magnetosphere of dead pulsars. Due to re-ignition processes in outer gaps, rotation energy of the NS was thought to convert to gamma-rays, but possible matches for re-ignition has not been pointed out. The passage of interstellar comet through the magnetosphere of dead pulsars is proposed below as a possible initiator of the GRBs. Values of the main parameters of the model (period of the NS rotation, concentration of interstellar comets and fraction of bursting NSs) are estimated, thus allowing to explain general characteristics of the phenomenon of the GRBs.     

Orbital evolution of long-period comets I. Trivariate Monte Carlo simulation

The mean orbital evolution of long-period comets for 16 representative initial orbits to short-period comets is calculated by a Monte Carlo method. First, trivariate perturbation distributions of barycentric Kepler energy, total angular momentum, and its z component in single encounters of comets with Jupiter are obtained numerically. Their characteristics are examined in detail and the distributions are found to be simple, symmetric, and easy to handle. Second, utilizing these distributions, we have done trivariate Monte Carlo simulations of the orbital evolution of long-period comets, with special emphasis on high-inclination orbits. About half of the 16 initial orbits are traced up to 5000 returns. For each of these orbits, the mean values of semimajor axis, perihelion distance, and inclination; their standard deviations, survival, and capture rates; as well as time scales of orbital evolution are calculated as functions of return number. Survival rates of the initial orbits with high inclination (～90°) and small perihelion distance (～1–2 AU) have been found to be only two or three times smaller than those of the main-source orbits of short-period comets established quantitatively by Everhart. The time scales of orbitsl evolution of the former, however, are nearly 10 times longer than the latter. There is a general trend that, for smaller perihelion distance, the survival efficiency becomes higher. The results of this paper should be considered a basis for a succeeding paper (Paper II) in which the physical lifetime of comets will be determined, and a comparison with the orbital data will be done.     

On the relationship of long-period comets to known and unknown planets

Statistical aspects of the question of the dynamical relationship of long-period comets to giant planets (Saturn, Uranus, Neptune), dwarf planets (Pluto, 2003 EL₆₁, 2003 UB₃₁₃), and five hypothetical planets are investigated. Data for 859 and 888 comets (2005, 2006) with periods P > 200 years are used in the statistics. No comets of the Kreutz, Marsden, Kracht, and Meyer groups are considered. The minimum interorbital distances of comets from the listed planetary bodies are mainly analyzed. Effects testifying to the kinematical relationship of some of the comets to planets have been established by testing the cometary data relative to 67 planes. The distribution of the perihelia of long-period comets is also discussed.     

Galactic tidal perturbations of long-period comets and the distribution of the inclinations

Perturbation of the perihelion distance q of long-period comets by the galactic tidal force is calculated using Cowell's method. It is shown that the maximum perturbation is suffered by those with i (inclination) close to 50 ~ 60 and not by those with i close to 90 , contrary to the prediction of the first order perturbation theory. The dependence of the perturbation of q upon i is compared with the distribution of the inclinations of observed long-period comets and it is shown that the later is not consistent with an isotropic cloud of comets perturbed by the galactic tid alone. A close stellar encounter is unlikely to be an external disturbance. It is argued that giant molecular cloud is the most likely mechanism of the external disturbances.     

The Kozai resonance in the outer solar system and the dynamics of long-period comets

We consider the secular evolution of the orbits of bodies in the Outer Solar System under the perturbations of the jovian planets assumed on coplanar and circular orbits. Through the approach used for asteroidal belt by Yoshihide Kozai in 1962, we obtain that the Kozai resonance do not affect the behavior of bodies belonging to the Kuiper belt but concerns the long-timescale evolution of long-period comets. In particular this resonance appears as a process contributing to produce Sun-grazer comets.     

Analysis of the morphological structures of comet 1P/Halley in the perihelion passages in 1910 and 1986

This work is based on a systematic analysis of images of comet 1P/Halley collected during its penultimate and ultimate approaches, i.e., in 1910 and 1986. This research has identified, characterized, classified, and compared tail structures of comet 1P/Halley, namely disconnection events (DEs), wavy structures, and solitons. The images of the comet during its 1910 passage, as illustrated in the Atlas of Comet Halley 1910 II (Donn et al. 1986), were compared with those of its approach in 1986 as illustrated in The International Halley Watch Atlas of Large‐Scale Phenomena (Brandt et al. 1992). Two onsets of DEs were discovered after the perihelion passage in 1910 with an average value of the corrected cometocentric velocity (Vc) of 57 ± 15 km s^?1. Ten onsets of DEs were discovered after the perihelion passage in 1986 with an average Vc equal to 130 ± 37 km s^?1. The mean value of the corrected wavelength λc of wavy structures in 1910 is equal to 1.7 ± 0.1 × 10⁶ km, as compared to 2.2 ± 0.2 × 10⁶ km in 1986. The mean value of the amplitude A of the wave in 1910 is equal to 1.4 ± 0.1 × 10⁵ km and 2.8 ± 0.5 × 10⁵ km in 1986. The goals of this research were to report the results obtained from the analysis of the P/Halley's images from 1910 and 1986, to provide empirical data for comparison, and to form the input for future physical/theoretical work.     

On the nature and origin of comets and their contribution to planets

Observations of comets show that they were formed at extremely low temperatures and probably contain amorphous ices that give off exothermal energy on mild heating. The slow rotation period of 5^d.0 for the large comet P/Schwassmann-Wachmann 1 suggests that it was formed in a gravitationally undisturbed region of space. Many smaller typical comets appear to be rotating rapidly, indicating that encounters among them were frequent during formation. As a consequence, the product of the relaxation time for encounters and the mean space density near the end of comet formation was approximately 2×10² g s cm^–3. A time scale of 10⁶ yr for comet accumulation is suggested. Laboratory studies by Patashnick and Rupprecht support the probably amorphous nature of the ices. The evidence mildly favors Cameron's 1977 theory of the primitive accretion disk.Interstellar grains grown to large sizes in extremely cool clouds might pop on mild heating by supernovae or luminous young stars to increase the local opacity and scattering.Some probable and possible contribution of comets to the solar system are summarized.     

Have stellar and supernovae radiations altered the pristine nature of comets?

Effect of stellar and supernova radiations on cometary nuclei in the Oort cloud is investigated. Radiation dose received by a comet is calculated and compared with the one which Halley's comet receives by one perihelion passage. Stellar radiation provides 10 to 50% of Halley unit over 4 billion years. Inclusion of sublimation of volatile molecules such as CO or N₂ does not allow the temperature to rise to 30 K by irradiation of bright OB stars, contrary to the claim of Stern and Shull. A chance encounter with a SN provides radiation dose which is just sufficient to raise to 30 K the surface layer which is 1 m thick on the assumption that the radiation is wholly communicated to the interior. Thus, the comets remain pristine under the effect of stellar and SN radiations.     

The nature of the solar wind interaction with CO2/CO-dominated comets

The varying overall nature of the solar wind interaction with the ionospheres of CO and CO₂-dominated comets is investigated and compared with previous results for H₂O-dominated comets. It is shown that as a comet approaches the sun, it may exhibit one of two types of ionospheric transitions. (In rare circumstances, the cometary ionosphere may display a third type of transition in addition to one of the first two). For both transitions, the ionosphere turns from being hard (in other words, the ionosphere is not susceptible to compression under sudden solar wind pressure increases) to soft. However, for one type of transition, the bow shock changes from being weak (M2) to being strong (M10), whereas for the other type of transition, the bow shock remains weak. The heliocentric distance at which these transitions may occur is found to be a function of the cometary nuclear radius, the latent heat of sublimation of the surface volatiles, the surface bolometric albedo and the following ionospheric properties: the optical depth, the average ionization time scale and the amount of heat addition. Two important consequences of the strong shocks are the large solar wind velocity modulation of the energization of electrons at the bow-shock and the relatively quick formation of cometary plasma tails.These results are applied to the case of comet Humason (1962 VIII). It is shown that either a CO or CO₂ dominated surface can explain not only the strong coma and tail activity of this comet at large heliocentric distances, but it can also explain the irregular activity of this comet at such distances.     

Invisible comets on evolutionary track of short-period comets

We systematically surveyed the orbits of short-period (SP) comets that show a large change of perihelion distance (q) between 1–2 AU (visible comets) and 4–5 AU (invisible comets) during 4400 years. The data are taken from Cosmo-DICE (Nakamura and Yoshikawa 1991a), which is a long-term orbital evolution project for SP comets. Recognizing that q is the most critical element for observability of comets, an invisibility factor (f), defined as the ratio of unobservable time span to observable span during 4400 years, is calculated for each of the large-q-change comets. A detection limit for each comet is obtained from the heliocentric distance at discovery and/or the absolute magnitude at recent apparitions. A mean f value for 35 SP comets with 2.9 J (J is the Tisserand's invariant) is found to be 19.8. This implies that for each visible SP comet of this J-range, at every epoch of time, there exist about 20 invisible comets near the capture orbits by Jupiter, under the assumptions of steady-state flux and ergodicity for the SP-comet population.     

Long-term evolution of Oort Cloud comets: capture of comets

We test different possibilities for the origin of short-period comets captured from the Oort Cloud. We use an efficient Monte Carlo simulation method that takes into account non-gravitational forces, Galactic perturbations, observational selection effects, physical evolution and tidal splittings of comets. We confirm previous results and conclude that the Jupiter family comets cannot originate in the spherically distributed Oort Cloud, since there is no physically possible model of how these comets can be captured from the Oort Cloud flux and produce the observed inclination and Tisserand constant distributions. The extended model of the Oort Cloud predicted by the planetesimal theory consisting of a non-randomly distributed inner core and a classical Oort Cloud also cannot explain the observed distributions of Jupiter family comets. The number of comets captured from the outer region of the Solar system are too high compared with the observations if the inclination distribution of Jupiter family comets is matched with the observed distribution. It is very likely that the Halley-type comets are captured mainly from the classical Oort Cloud, since the distributions in inclination and Tisserand value can be fitted to the observed distributions with very high confidence. Also the expected number of comets is in agreement with the observations when physical evolution of the comets is included. However, the solution is not unique, and other more complicated models can also explain the observed properties of Halley-type comets. The existence of Jupiter family comets can be explained only if they are captured from the extended disc of comets with semimajor axes of the comets   a <5000 au  . The original flattened distribution of comets is conserved as the cometary orbits evolve from the outer Solar system era to the observed region.     

The motion of the perihelion of Trojan asteroids

The problem is investigated by using the equations of Jupiter's main perturbations in the eccentricity and in the perihelion longitude of Trojan asteroids. The limits and the period of the variation of the eccentricity and of the perihelion longitude are calculated for 30 Trojans. The perihelion is shown to circulate in 20 cases and to librate for 10 asteroids.