Are the cometary outbursts caused by impacts with interplanetary vagabonds probable?

The possibility of impacts and their results in relation to the cometary outbursts between comets and other small bodies in the solar system has been investigated. Taking into consideration certain physical features of cometary nuclei and impacting bodies, the probability of impacts of small bodies moving in the main asteroid belt with hypothetical comets which represent three types: Jupiter family comets, Halley family comets and long period comets has been computed. The probability of impacts between comets and meteoroids at large heliocentric distances has also been estimated. Potential consequences of these events in relation to outbursts of the cometary brightness have been discussed. (© 2004 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

The search for a cometary outbursts mechanism: a comparison of various theories

In the paper the potential sources of energy of cometary outbursts have been reviewed. Considerations focus on four probable sources of the outbursts' energy. These are the polymerization of hydrogen cyanide HCN, impacts with the meteoroids, destruction of cometary grains in the field of strong solar wind and the transformation of amorphous water Ice into the crystalline one. The values of released energy and jumps of cometary brightness caused by these mechanisms have been discussed. A modern approach to the problem of the thermodynamical evolution of the comet nucleus which includes amorphous water ice is considered as the starting point in the discussion presented in the paper. The main characteristics of an outburst of a hypothetical comet belonging to the Jupiter family comet are calculated. The obtained results are in a good agreement with the characteristics observed during the real outbursts of comets. The main conclusion of this paper confirms a general presumption that the cometary outbursts can have different causes. However, the hypothesis concerning the amorphous water ice transformation appears to be the most probable one. (© 2007 WILEY-VCH Verlag GmbH & Co. KGaA, Weinheim)     

Periodic variation of Oort Cloud flux and cometary impacts on the Earth and Jupiter

Time variation in impact probability is studied by assuming that the periodic flux of the Oort Cloud comets within 15 au arises from the motion of the Sun with respect to the Galactic mid-plane. The periodic flux clearly shows up in the impact rate of the captured Oort Cloud cometary population, with a phase shift caused by the orbital evolution. Depending on the assumed flux of comets and the size distribution of comets, the impact rate of the Oort Cloud comets of 1 km in diameter or greater is from 5 to 700 impacts Myr⁻¹ on the Earth and from 0.5 to 70 impacts per 1000 yr on Jupiter. The relative fractions of impacts are 0.09, 0.11, 0.26 and 0.54 for long-period comets, Halley type comets, Jupiter family comets and near-Earth objects, respectively. For Jupiter, the corresponding fractions in the first three categories are 0.18, 0.31 and 0.51. If we consider physical fading of comet activity that is compatible with the observations, then the impact rates of active comets are two orders of magnitude smaller than the total impact rates by all kinds of comets and cometary asteroids of size 1 km or greater.     

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)     

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.     

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)     

The influence of the nucleus shape on the maximum size of grains ejected from a comet by gentle sublimation and jet‐like features

This paper deals with obtaining the maximum size of cometary grains ejected from nuclei of different shapes. Two mechanisms in terms of grain ejection from comets are taken into consideration. The first one is dragging of particles by outflowing gas molecules released by gentle sublimation from the comets. The second one is related with gas jets from the cavities in a nucleus by cometary jet‐like phenomena. We focused on ellipsoidal shapes of cometary nuclei but with different flattening. Calculations have been carried out for a large range of cometary parameters. It has been shown that for fixed mass of the nucleus the maximum size of grains is an increasing function of the nucleus flattening. (© 2015 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.     

Dynamical evolution of cometary asteroids

We present results from long-term numerical integrations of hypothetical Jupiter-family comets (JFCs) over time-scales in excess of the estimated cometary active lifetime. During inactive periods these bodies could be considered as 'cometary' near-Earth objects (NEOs) or 'cometary asteroids'. The contribution of cometary asteroids to the NEO population has important implications not only for understanding the origin of inner Solar system bodies but also for a correct assessment of the impact hazard presented to the Earth by small bodies throughout the Solar system. We investigate the transfer probabilities on to 'decoupled' subJovian orbits by both gravitational and non-gravitational mechanisms, and estimate the overall inactive cometary contribution to the NEO population. Considering gravitational mechanisms alone, more than 90 per cent of decoupled NEOs are likely to have their origin in the main asteroid belt. When non-gravitational forces are included, in a simple model, the rate of production of decoupled NEOs from JFC orbits becomes comparable to the estimated injection rate of fragments from the main belt. The Jupiter-family (non-decoupled) cometary asteroid population is estimated to be of the order of a few hundred to a few thousand bodies, depending on the assumed cometary active lifetime and the adopted source region.     

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)     

The source of energy of the comet 29P/Schwassmann-Wachmann 1 outburst activity: the test of the summary

The comet 29P/Schwassmann-Wachmann 1 is an exceptional comet as far as cometary outbursts are concerned. Despite its large distance from the Sun (about 6 au), it shows quasi-regular outburst activity, usually once or twice a year. Up to now there has not been a generally accepted model that explains this phenomenon. In the first part of this paper, the most well-known hypotheses that attempt to explain the outburst activity of this comet are presented and critically analysed. The main aim of this paper is to present a model for the outburst activity of this comet. The model is based on the global analysis of the internal structure and physical and chemical processes that take place in the cometary nucleus. Numerical calculations were carried out for reasonable assumed values of a large range of cometary characteristics. The obtained results are consistent with observational data.     

Near-Earth object velocity distributions and consequences for the Chicxulub impactor

An Öpik-based geometric algorithm is used to compute impact probabilities and velocity distributions for various near-Earth object (NEO) populations. The resulting crater size distributions for the Earth and Moon are calculated by combining these distributions with assumed NEO size distributions and a selection of crater scaling laws. This crater probability distribution indicates that the largest craters on both the Earth and the Moon are dominated by comets. However, from a calculation of the fractional probabilities of iridium deposition, and the velocity distributions at impact of each NEO population, the only realistic possibilities for the Chicxulub impactor are a short-period comet (possibly inactive) or a near-Earth asteroid. For these classes of object, sufficiently large impacts have mean intervals of 100 and 300 Myr respectively, slightly favouring the cometary hypothesis.     

Jupiter approaching asteroids and their possibilities for activity

Jupiter‐family comets (JFCs) may often, closely and/or slowly approach Jupiter. A list of their close approaches within 0.21 AU from Jupiter between 1970 and 2030 is presented to determine the typical changes in some of their orbital elements and their relation to any triggered activity. A few JFCs from the list were temporary satellites of Jupiter. There are also several JFCs which originally had asteroidal provisional designations due to their low activity at discovery. But Jupiter is also approached by asteroids. The presented list of their approaches within 0.60 AU from Jupiter between 1960 and 2040, together with their orbital changes can be compared with the list of comets. Some of the orbital changes are large enough to cause an extremely low or short‐lived activity. Usually, quick and dedicated observations by large‐aperture telescopes are missing to confirm or refute it. Currently, the most important cometary candidate among Jupiter approaching asteroids is 2004 FY140. (© 2005 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

Cometary masses derived from non-gravitational forces

We compute masses and densities for 10 periodic comets with known sizes: 1P/Halley, 2P/Encke, 6P/d'Arrest, 9P/Tempel 1, 10P/Tempel 2, 19P/Borrelly, 22P/Kopff, 46P/Wirtanen, 67P/Churyumov–Gerasimenko and 81P/Wild 2. The method follows the one developed by Rickman and colleagues, which is based on the gas production curve and on the change in the orbital period due to the non-gravitational force. The gas production curve is inferred from the visual light curve. We found that the computed masses cover more than three orders of magnitude:  ≃(0.3–400) × 10¹²  kg. The computed densities are in all cases very low (≲0.8 g cm⁻³), with an average value of 0.4 g cm⁻³, in agreement with previous results and models of the cometary nucleus depicting it as a very porous object. The computed comet densities turn out to be the lowest among the different populations of Solar system minor bodies, in particular as compared to those of near-Earth asteroids (NEAs). We conclude that the model applied in this paper, in spite of its simplicity (as compared to more sophisticated thermophysical models applied to very few comets), is useful for a statistical approach to the mean density of the cometary nuclei. However, we cannot assess from this simple model if there is a real dispersion among the bulk densities of comets that could tell us about differences in physical structure (porosity) and/or chemical composition.     

On the Light-Absorbing Surface Layer of Cometary Nuclei: I. Radiative Transfer

A small but increasing volume of observations of cometary nuclei has accumulated during the past two decades. This development is accelerating with upcoming space missions such as Stardust, Contour, and Rosetta. In response to the growing need for a theoretical understanding of optical properties of cometary nuclei, we have calculated synthetic reflectance spectra in the wavelength region 0.2-2.0 μm, photometric colors in the Johnson-Kron-Cousins UBVRI system, and visual geometric albedos for a large number of porous ice-dust mixtures with differing composition, regolith grain sizes, and grain morphologies, such as core-mantle grains, dense clusters of such grains, and large irregular particles with internal scatterers. The calculations are based on Mie theory, the discrete dipole approximation, Hapke theory, and a numerical solution to the equation of radiative transfer in particulate media. In addition, wavelength-integrated directional-hemispherical albedos and flux attenuation profiles in the regolith as functions of depth have been calculated in order to improve the energy budget and treatment of energy boundary conditions in thermal models of cometary nuclei.Our results are compared with spectra and colors of observed cometary nuclei. Our main conclusions are that only regolith consisting of relatively large core-mantle grains, or clusters of smaller core-mantle grains, is capable of reproducing the red colors seen in comets; that ice-dust mixtures actually can be darker than ice-free regolith in certain circumstances; and that solar radiation sometimes penetrates to a depth that is comparable to the region in which diurnal temperature variations occur.     

On stellar encounters and their effect on cometary orbits in the Oort cloud

We systematically investigate the encounters between the Sun and neighbouring stars and their effects on cometary orbits in the Oort cloud, including the intrinsic one with the star Gl 710 (HIP 89 825), with some implications to stellar and cometary dynamics. Our approach is principally based on the combination of a Keplerian‐rectilinear model of stellar passages and the Hipparcos Catalogue (ESA 1997). Beyond the parameters of encounter, we pay particular attention to the observational errors in parallaxes and stellar velocities, and their propagation in time. Moreover, as a special case of this problem, we consider the collision probability of a star passing very closely to the Sun, taking also into account the mutual gravitational attraction between the stars. In the part dealing with the influence of stellar encounters on the orbital elements of Oort cloud comets, we derive new simple formulae calculating the changes in the cometary orbital elements, expressed as functions of the Jeans impulse formula. These expressions are then applied to calculate numerical values of the element changes caused by close encounters of neighbouring stars with some model comets in the Oort cloud. Moreover, the general condition for an ejection of comets from the cloud effected by a single encounter is derived and discussed.     

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 young long-period comet family of Saturn

The distributions of long-period comets with respect to the minimum distance Δ between their orbits and the orbit of Saturn or Jupiter, constructed by Konopleva using data up to 1972, exhibit a sharp peak at Δ<0.5 au for the Saturnian family, while being fairly monotonic for Jupiter. Hence, in view of the appreciable eccentricity of Saturn's orbit and the rotation of its perihelion longitude with a period of 47 kyr, the conclusion was drawn by Drobyshevski that the objects belonging to this peak are young (10 kyr).
Similar distributions constructed using more recent data show less pronounced differences between one another. Analysis of the distributions for various epochs shows that the initially noted difference is due to observational selection, being inherent to brighter comets. Since on average the cometary activity fades with age, the conclusion that the Saturnian family comets, forming the peak at Δ<0.5 au, are young is all the more substantiated. The question concerning the origin of these comets, which in all likelihood were ejected over a period of a decade from deep inside the Saturnian sphere of influence , is still open. The only self-consistent hypothesis that we see now is that of their appearance as a result of an explosion of the electrolysed ice envelope of Titan. We encourage the development of other explanations.     

Features of a comet nucleus: The case of 103P/Hartley 2

In the paper two chosen features of the comet 103P/Hartley 2 are studied. The first one are ‘cometary geysers’ which have been recorded by the camera on Deep Impact spacecraft. The numerical calculations related with this phenomenon have been carried out for large number of values of probable cometary characteristics. Our calculations confirm the assumption what also has been observed by NASA's scientists that the jets of carbon dioxide from the geysers are able to lift large chunks of water ice from the comet. The second discussed feature of the comet 103P/Hartley 2 is the lack of impact holes on the surface of its nucleus. The expected rate of impact holes on the surface of the nucleus of 103P/Hartley 2 is discussed. These holes could be the product of impacts between this comet and other small bodies orbiting in the main asteroid belt. The probability of such impacts, the total number of expected perceptible holes and changes in the luminosity of the comet caused by collisions are examined. We conclude that indeed the number of visible holes on its surface should be negligible (© 2011 WILEY‐VCH Verlag GmbH & Co. KGaA, Weinheim)     

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.