Origin of short period comets

Reasons for interest in the origin of short-period comets and the difficulties of computing their long-term dynamcal evolution are reviewed. The relative advantages of a source region in an extended inner core of the Oort cloud or a compact comet belt just beyond the planetary system are finely balanced, and it is premature to consider the problem solved. A complication is that some comets belonging to the Jupiter family may be part of a time-dependent system, possibly the remains of a giant comet such as Chiron which could have been part of the system 104 yr ago. The origin of short-period comets plays a pivotal role in many areas of solar system science: planet formation, the source of water (possibly life) on the terrestrial planets, the cratering record on the terrestrial planets and satellites of the outer planets, and the environmental impact posed by massive bodies and their decay products in the Earth's near-space environment.     

Origin of oort cloud comets in the interstellar space

Comets must form a major part of the interstellar medium. The solar system provides a flux of comets into the interstellar space and there is no reason to suspect that many other stars and their surrounding cometary systems would not make a similar contribution. Occasionally interstellar comets must pass through the inner solar system, but Whipple (1975) considers it unlikely that such a comet is among the known cases of apparently hyperbolic comets. Even so the upper limit for the density of unobserved interstellar comets is relatively high.In addition, we must consider the possibility that comets are a genuine component of interstellar medium, and that the Oort Cloud is merely a captured part of it (McCrea, 1975). Here we review various dynamical possibilities of two-way exchange of comet populations between the Solar System and the interstellar medium. We describe ways in which a traditional Oort Cloud (Oort, 1950) could be captured from the interstellar medium. However, we note that the so called Kuiper belt (Kuiper, 1951) of comets cannot arise through this process. Therefore we have to ask how necessary the concept of the yet unobserved Kuiper belt is for the theory of short period comets.There has been considerable debate about the question whether short period comets can be understood as a captured population of the Oort Cloud of comets or whether an additional source has to be postulated. The problem is made difficult by the long integration times of comet orbits through the age of the Solar System. It would be better to have an accurate treatment of comet-planet encounters in a statistical sense, in the form of cross sections, and to carry out Monte Carlo studies. Here we describe the plan of action and initial results of the work to derive cross sections by carrying out large numbers of comet — planet encounters and by deriving approximate analytic expressions for them. Initially comets follow parabolic orbits of arbitrary inclination and perihelion distance; cross sections are derived for obtaining orbits of given energy and inclination after the encounter. The results are used in subsequent work to make evolutionary models of the comet population.     

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.     

The activities of comets related to their aging and origin

Two indices have been developed for the purpose of comparing the natures of various classes of comets. The first is the Activity Index (AI), measuring the inherent magnitude increase in brightness from great solar distances to maximum near perihelion. The second, or Volatility Index (VI), measures the variation in magnitude near perihelion. Tentative determinations of these two indices are derived from observations by Max Beyer over more than 30 years for long-period (L-P) and short-period (S-P) comets near perihelion and from other homogeneous sources. AI determinations are made for 32 long-period (L-P) comets and for 14 short-period (S-P). The range of values of AI is of the order of 3 to 10 magnitudes with a median about 6. An expected strong correlation with perihelion distance q, is found to vary as q ^–2.3. Residuals from a least-square solution (AI) are used for comparing comets of different orbital classes, the standard deviation of a single value of AI is only ±1^m.1 for L-P comets and ±1^m.2 for S-P comets.Among the L-P comets, 19 of period P larger than 10⁴ years yield AI = 0^m.27 ± 0^m.25 compared to 0^m.39 ± 0^m.26 for 13 of period between 10² years and 10⁴ years. This denies any fading with aging among the L-P comets. Also no systematic change with period occurs for the VI index, leading to the same conclusions. Weak correlations are found with the Gas/Dust ratio of comets. No correlations are found between the two indices, nor of either index with near-perihelion magnitudes or orbital inclination.The various data are consistent with a uniform origin for all types of comets, the nuclei being homogeneous on the large scale but quite diverse on a small scale (the order of a fraction of kilometer in extent). Small comets thus may sublimate away entirely, leaving no solid core, while huge comets may develop a less volatile core by radioactive heating and possibly become inactive like asteroids after many S-P revolutions about the Sun. When relatively new, huge comets may be quite active at great solar distances because of volatiles from the core that have refrozen in the outer layers.     

The destruction of cometary grains and changes in the luminosity of comets

One explanation of the sudden changes in the brightness of comets is proposed based on the author's earlier suggestions involving the fragmentation of cometary grains. Within the inner coma, a core‐mantle model of the structure of grains is assumed. The proposed mechanism is a combination of electrostatic stress and thermodynamical fragmentation of the cometary grains water‐ice mantle. It has been shown that the vapour pressure of volatile inclusions placed in the waterice mantle of grains can increase sufficiently to cause their fragmentation. It takes place before grains can completely sublime into the vacuum away. Numerical calculations have been carried out for a large range of values of probable physical characteristics of cometary material. The proposed approach yields increases in cometary brightness consistent with observations of typical cometary outbursts. It is concluded that this approach can provide an explanation of the sudden change in activity of comets for a wide range of heliocentric distances (© 2009 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

An exceptional cosmic influence and its bearing on the evolution of human culture as evident in the apparent early development of mathematics and astronomy

The proposal that cometary dust particles play a significant role in the emergence and evolution of both life and disease on suitable planets was first made some 25 years ago by Hoyle and Wickramasinghe. Fundamental to this proposal was a process of punctuated seeding by particular (bio)chemical species believed to originate naturally and predominantly in larger comets, say those with diameters greater than about 100 kilometres. Rather less well known is a parallel proposal likewise favoured by Hoyle that a particular giant comet, the most recent to settle in cis-Jovian space, accounting for the latest significant phase of evolution on Earth, also had a significant part to play in the cultivation by homo sapiens of its civilization and culture. Such proposals may be seen by many as examples of excessively lateral thinking but they by no means lack independent support and have important implications for the otherwise uncertain origin of the latest ice-age (basic to climatology) and for the otherwise uncertain generation of early calendars (basic to the management of society). Aspects of these proposals are considered here in relation to a much respected supposedly Chaldean calendar probably passed down by the dynastic Isins (also the Essenes?) which evidently bears witness to known early mathematical and astronomical skills but which largely ceased to be available to subsequent scholarship beyond the Early Christians (ca. 100 CE) pending its (recent) recovery through the medium of Dead Sea Scrolls.     

The electric potential on dust particles in comets and in interplanetary space

We calculate the electric surface potential reached by small dust particles in cometary atmospheres and in interplanetary space. Plasma temperature and density are varied over a wide range; a two component plasma of ions and electrons in thermodynamic equilibrium is assumed. The calculations are performed for three types of grains whose photoelectric and secondary electron emission yield are choosen to cover about the range expected for real dust. Results for vanishing secondary electron emission are given for comparison. At the beginning, a short review of the theoretical formulation and the main assumptions are presented. Wir berechnen das Oberflächenpotential kleiner Staubteilchen im Plasma einer Kometenatmosphäre und im interplanetaren Raum. Die Plasma-parameter Temperatur und Dichte werden in einem weiten Bereich variiert, es wird jedoch stets thermodynamisches Gleichgewicht zwischen Elektronen und Ionen eines Zweikomponentenplasmas angenommen. Die Rechnungen werden für drei Teilchenmaterialien ausgeführt, deren Photo-effekt und Sekundärelektronenausbeute etwa den an realen Staubteilchen vorkommenden Bereich überdecken dürften; zum Vergleich werden auch die Ergebnisse bei vernachlässigbarer Sekundärelektronenausbeute mitgeteilt. Eine kurze Zusammenfassung der theoretischen Grundlagen und der wesentlichen Voraussetzungen ist den Rechnungen vorangestellt.     

The orbit and size distribution of small Solar System objects orbiting the Sun interior to the Earth's orbit

We present the first observational measurement of the orbit and size distribution of small Solar System objects whose orbits are wholly interior to the Earth's (Inner Earth Objects, IEOs, with aphelion <0.983 AU). We show that we are able to model the detections of near-Earth objects (NEO) by the Catalina Sky Survey (CSS) using a detailed parameterization of the CSS survey cadence and detection efficiencies as implemented within the Jedicke et al. [Jedicke, R., Morbidelli, A., Spahr, T., Petit, J.M., Bottke, W.F., 2003. Icarus 161, 17-33] survey simulator and utilizing the Bottke et al. [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433] model of the NEO population's size and orbit distribution. We then show that the CSS detections of 4 IEOs are consistent with the Bottke et al. [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433] IEO model. Observational selection effects for the IEOs discovered by the CSS were then determined using the survey simulator in order to calculate the corrected number and H distribution of the IEOs. The actual number of IEOs with H<18 (21) is 36±26 (530±240) and the slope of the H magnitude distribution (∝¹⁰αH) for the IEOs is . The slope is consistent with previous measurements for the NEO population of αNEO=0.35±0.02 [Bottke, W.F., Morbidelli, A., Jedicke, R., Petit, J.-M., Levison, H.F., Michel, P., Metcalfe, T.S., 2002. Icarus 156, 399-433] and αNEO=0.39±0.013 [Stuart, J.S., Binzel, R.P., 2004. Icarus 170, 295-311]. Based on the agreement between the predicted and observed IEO orbit and absolute magnitude distributions there is no indication of any non-gravitational effects (e.g. Yarkovsky, tidal disruption) affecting the known IEO population.     

Collisions of comets and meteoroids: The post Stardust‐NExT discussion

The paper considers results of collisions between comets and meteoroids. We re‐discuss the five different approaches to estimate the sizes of holes created during such collisions. The results of the Deep Impact and the Stardust‐NExT missions to comet 9P/Temple 1 are applied to the estimation of these methods. We use the observed amount of ejected mass, the jump of brightness of the comet 9P/Tempel 1 as well as the diameter of the excavated crater. In the paper the simple way of estimation of impact consequences by use of the conception of the fragmentation energy of comet is also discussed. The numerical calculations were carried out for reasonable assumed values of a large range of cometary characteristics. The main conclusion of this paper confirms a general presumption that the main factor which determines the size of the impact crater on the comet 9P/Tempel 1 is the kinetic energy of impactor and strength or fragmentation energy of cometary material. In the considered case the gravitation of a comet has a minor meaning (© 2012 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Large cometary grains – their destruction and changes in the luminosity of comets

The catastrophic thermodynamic destruction of large cometary heterogeneous grains lying on the surface of a comet nucleus is examined. The core–mantle grain-structure model is assumed. Grain fragmentation as an explanation of sudden changes in cometary brightness is proposed. The approach presented to the problem of cometary outbursts is a development of a previous author's paper. The proposed mechanism is based on the idea of thermodynamical destruction of heterogeneous cometary grains. Numerical simulations have been carried out for a wide range of values of physical characteristics of cometary material. The results obtained are consistent with observational data. The main conclusion of this paper is that thermodynamical fragmentation of large grains can explain variations in brightness and also outbursts of comets.     

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.     

The striae in the dust tails of great comets — a comparison to various theories

We reanalyse positions and motion of the striae in the dust tails of the bright comets Mrkos 1957 V and West 1976 VI. Two theories are compared to the data: the high speed particle ejection theory of NOTNI (1964) and the two-step kinematical sequence proposed by SEKANINA and FARRELL (1980) in their particle fragmentation theory. The final decision is in favour of the two step sequence, though the real situation may be a mixtum compositum of both. The parent clouds (first step) are found to have low lateral velocity dispersion and higher than expected acceleration. The question how these clouds originate remains unsolved. It is suggested that they comprise particles which left the coma into a tailward region of high magnetic field and plasma density. Another possibility, additionally accounting for the sometimes apparent duplicity, is an origin out of an optically thick coma at angles orthogonal to the radius vector.     

The long-term evolution and initial size of comets 46P/Wirtanen and 67P/Churyumov–Gerasimenko

We present a new method to study the long-term evolution of cometary nuclei in order to estimate their original size, and we consider the case of comets 46P/Wirtanen (hereafter 46P) and 67P/Churyumov–Gerasimenko (hereafter 67P). We calculate the past evolution of the orbital elements of both comets over 100 000 yr using a Bulirsch–Stoer integrator and over 450 000 yr using a Radau integrator, and we incorporate a realistic model of the erosion of their nucleus. Their long-term orbital evolution is prominently chaotic, resulting from several close encounters with planets, and this result is independent of the choice of the integrator and of the presence or not of non-gravitational forces. The dynamical lifetime of comet 46P is estimated at ∼133 000 yr and that of comet 67P at ∼105 000 yr. Our erosion model assumes a spherical nucleus composed of a macroscopic mixture of two thermally decoupled components, dust and pure water ice. Erosion strongly depends upon the active fraction and the density of the nucleus. It mainly takes place at heliocentric distances <4 au and lasts for only ∼7 per cent of the lifetime. Assuming a density of 300 kg m⁻³ and an average active fraction over time of 10 per cent, we find an initial radius of ∼1.3 km for 46P and ∼2.8 km for 67P. Upper limit are obtained assuming a density of 100 kg m⁻³ and an active fraction of 100 per cent, and amounts to 21 km for 46P and 25 km for 67P. Erosion acts as a rejuvenating process of the surface so that exposed materials on the surface may only contain very little quantities of primordial materials. However, materials located just under it (a few centimetres to metres) may still be much less evolved. We will apply this method to several other comets in the future.     

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.     

Trapping and dynamical evolution of interplanetary dust particles in Earth’s quasi-satellite resonance

We used numerical simulations to model the orbital evolution of interplanetary dust particles (IDPs) evolving inward past Earth’s orbit under the influence of radiation pressure, Poynting–Robertson light drag (PR drag), solar wind drag, and gravitational perturbations from the planets. A series of β values (where β is the ratio of the force from radiation pressure to that of central gravity) were used ranging from 0.0025 up to 0.02. Assuming a composition consistent with astronomical silicate and a particle density of 2.5 g cm⁻³ these β values correspond to dust particle diameters ranging from 200 μm down to 25 μm. As the dust particle orbits decay past 1 AU between 4% (for β = 0.02, or 25 μm) and 40% (for β = 0.0025, or 200 μm) of the population became trapped in 1:1 co-orbital resonance with Earth. In addition to traditional horseshoe type co-orbitals, we found about a quarter of the co-orbital IDPs became trapped as so-called quasi-satellites. Quasi-satellite IDPs always remain relatively near to Earth (within 0.1–0.3 AU, or 10–30 Hill radii, R_H) and undergo two close-encounters with Earth each year. While resonant perturbations from Earth halt the decay in semi-major axis of quasi-satellite IDPs their orbital eccentricities continue to decrease under the influence of PR drag and solar wind drag, forcing the IDPs onto more Earth-like orbits. This has dramatic consequences for the relative velocity and distance of closest approach between Earth and the quasi-satellite IDPs. After 10⁴–10⁵ years in the quasi-satellite resonance dust particles are typically less than 10R_H from Earth and consistently coming within about 3R_H. In the late stages of evolution, as the dust particles are escaping the 1:1 resonance, quasi-satellite IDPs can have deep close-encounters with Earth significantly below R_H. Removing the effects of Earth’s gravitational acceleration reveals that encounter velocities (i.e., velocities “at infinity”) between quasi-satellite IDPs and Earth during these close-encounters are just a few hundred meters per second or slower, well below the average values of 2–4 km s⁻¹ for non-resonant Earth-crossing IDPs with similar initial orbits. These low encounter velocities lead to a factor of 10–100 increase in Earth’s gravitationally enhanced impact cross-section (σ_grav) for quasi-satellite IDPs compared to similar non-resonant IDPs. The enhancement in σ_grav between quasi-satellite IDPs and cometary Earth-crossing IDPs is even more pronounced, favoring accretion of quasi-satellite dust particles by a factor of 100–3000 over the cometary IDPs. This suggests that quasi-satellite dust particles may dominate the flux of large (25–200 μm) IDPs entering Earth’s atmosphere. Furthermore, because quasi-satellite trapping is known to be directly correlated with the host planet’s orbital eccentricity the accretion of quasi-satellite dust likely ebbs and flows on 10⁵ year time scales synchronized with Earth’s orbital evolution.     

Atlas of the mean motion resonances in the Solar System

The aim of this work is to present a systematic survey of the strength of the mean motion resonances (MMRs) in the Solar System. We know by applying simple formulas where the resonances with the planets are located but there is no indication of the strength that these resonances have. We propose a numerical method for the calculation of this strength and we present an atlas of the MMRs constructed with this method. We found there exist several resonances unexpectedly strong and we look and find in the small bodies population several bodies captured in these resonances. In particular in the inner Solar System we find one asteroid in the resonance 6:5 with Venus, five asteroids in resonance 1:2 with Venus, three asteroids in resonance 1:2 with Earth and six asteroids in resonance 2:5 with Earth. We find some new possible co-orbitals of Earth, Mars, Saturn, Uranus and Neptune. We also present a discussion about the behavior of the resonant disturbing function and where the stable equilibrium points can be found at low and high inclination resonant orbits.