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.     

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.     

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.     

From the Oort cloud to observable short-period comets – I. The initial stage of cometary capture

We investigate the first stage of the dynamical evolution of Oort cloud comets entering the planetary region for the first time. To this purpose, we integrate numerically the motions of a large number of fictitious comets pertaining to two samples, both with perihelion distances up to 5.7 au and random inclinations; the first sample is composed of comets whose orbits have at least one node close to 5.2 au, while the second is not subject to this constraint. We examine the orbits when the comets come to aphelion after their first perihelion passage within the planetary region, and find that there is a clear statistical dependence of the energy perturbations on the Tisserand parameter. There appear to be two main processes, of comparable importance, governing the shortening of semimajor axes to values of less than 1000 au, i.e. planetary close encounters, especially with Jupiter, and indirect perturbations due to the shifting of the motion from barycentric to heliocentric and back; the former process mostly affects comets crossing the ecliptic at about 5.2 au, or on low-inclination orbits, while the latter mostly affects comets of small perihelion distance. This last result may help to understand the relative paucity of Halley-type comets with perihelion distances larger than about 1.5 au.     

Capture of comets during the evolution of a star cluster and the origin of the Oort Cloud

It is generally assumed that the Solar System is surrounded by a swarm of comets, the so-called Oort Cloud, which contains approximately 10¹¹ members. The observed comets belong to a small subsection of the Cloud, and they have very elongated orbits. The origin of the Cloud is presently unclear. Here we consider the possibility that the comets were born in a star cluster together with the Sun. We follow the evolution of the star cluster with its embedded swarm of comets and calculate the rate at which stars accumulate stable comet companions. We conclude that if the Oort Cloud of comets was born in this process, then the present day density of comets in interstellar space has to be high, and that comets make a significant contribution to the overall mass density of the Galaxy.     

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.     

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.     

The variation of short-period comet size and decay rate with perihelion distance

Out of over 200 known short-period comets, we analyse a self-consistent list of 105 comets which have accurately estimated nuclei radii. It is found that both the median size and the size distribution index of these comets vary as a function of the perihelion distance, q , of the cometary orbit. A value of   q ≈ 2.7 au  divides the comets into an outer solar system group which are hardly affected by decay, and an inner solar system group which are decaying quickly. It is estimated that 10, 20 and 30 per cent of the 105 comets will have decayed away after 1000, 2000 and 3000 yr, respectively.     

Thermal destruction of cometary materials – application to activity of comets

Destruction mechanisms connected with thermodynamical behaviour of cometary material are reviewed with a special consideration of their effects on activity of comets. Consequences of thermal stresses which occur in the interior of a comet are discussed with reference to changes in the cometary brightness. Moreover, thermal destruction of grains placed in the head of the comet as well as on the surface of the nucleus is considered. It has been shown that the destruction of the cometary material can lead to an essential increase in the activity of the comet. Calculations have been carried out for a large assumed range of cometary parameters. The obtained simulated changes in the brightness of comets are consistent with the ones observed during the real variations and outbursts of brightness. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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)     

Dynamical capture and physical decay of short-period comets

The brightness evolution of short-period comets is discussed in connection with their physical lifetimes. It is shown that changes in the fraction of the free-subliming area of the nuclear surface may be more important than mass decrease in determining brightness variations. The decrease in the activity of short-period comets caused by the buildup of a dust mantle may be interrupted—and partially reversed—by dust blowoffs that leave exposed areas of fresh ices. Short-period comets may thus be subject to random brightness fluctuations that make quite uncertain any derivation of their physical lifetime based on comparisons of their absolute brightness at different apparitions. As an alternate procedure, the numerical integration of the whole sample of short-period comet orbits carried out by A. Carusi, L.Kresák, E. Perozzi and G. B. Valsecchi (1984, Long-Term Evolution of Short-Period Comets. Istituto Astrofisica Spaziale Internal Report 12, Rome) is used to draw conclusions about the transfer rate of their perihelia from Jupiter's region to the region of the terrestrial planets (heliocentric distances<1.5 AU). It is found that about one short-period comet per century reaches the region of the terrestrial planets. From this result and under the assumption of a steady-state comet population, an average lifetime of the order of 6 × 10³ years (～10³ revolutions) is derived for a typical kilometer-sized short-period comet of perihelion distance q ～ 1 AU. Such a rather long comet lifetime, as compared to some previous derivations, is consistent with the survival of some periodic comets on small-q orbits of long dynamical time scales.     

A survey of debris trails from short-period comets

We observed 34 comets using the 24 μm camera on the Spitzer Space Telescope. Each image contains the nucleus and covers at least ¹⁰⁶ km of each comet's orbit. Debris trails due to mm-sized or larger particles were found along the orbits of 27 comets; 4 comets had small-particle dust tails and a viewing geometry that made debris trails impossible to distinguish; and only 3 had no debris trail despite favorable observing conditions. There are now 30 Jupiter-family comets with known debris trails, of which 22 are reported in this paper for the first time. The detection rate is >80%, indicating that debris trails are a generic feature of short-period comets. By comparison to orbital calculations for particles of a range of sizes ejected over 2 yr prior to observation, we find that particles comprising 4 debris trails are typically mm-sized while the remainder of the debris trails require particles larger than this. The lower-limit masses of the debris trails are typically ¹⁰¹¹ g, and the median mass loss rate is 2 kg/s. The mass-loss rate in trail particles is comparable to that inferred from OH production rates and larger than that inferred from visible-light scattering in comae.     

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.     

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.     

A review of East Asian reports of aurorae and comets circa AD 775

Given that a strong ¹⁴C variation in AD 775 has recently been suggested to be due to the largest solar flare ever recorded in history, it is relevant to investigate whether celestial events observed around that time may have been aurorae, possibly even very strong aurorae, or otherwise related to the ¹⁴C variation (e.g. a suggested comet impact with Earth's atmosphere). We critically review several celestial observations from AD 757 to the end of the 770s, most of which were previously considered to be true, and in some cases, strong aurorae; we discuss in detail the East Asian records and their wording. We conclude that probably none among the events after AD 770 was actually an aurora, including the event in AD 776 Jan, which was misdated for AD 774 or 775; the observed white qi phenomenon that happened above the moon in the south‐east was most probably a halo effect near the full Moon – too late in any case to be related to the ¹⁴C variation in AD 774/5. There is another report of a similar (or identical) white qi phenomenon above the moon, reported just before a comet observation and dated to AD 776 Jan; the reported comet observed by the Chinese was misdated to AD 776, but actually sighted in AD 767. Our critical review of East Asian reports of aurorae circa AD 775 shows some very likely true Chinese auroral displays observed and reported for AD 762; there were also several events prior to AD 771 that may have been aurorae but are questionable. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.