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 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 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.     

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.     

短周期彗星表面水冰升华分布研究

彗星是太阳系遗留的原始星子,研究彗星彗核的演化对理解太阳系其他天体的形成和演化历史具有重要意义.在太阳的辐射作用下,彗星携带的挥发性成分会发生升华,并带动尘埃运动,造成彗核物质的损失.因此,彗核的升华活动对其表面形貌甚至整体形状演化都会产生影响.从IAU (International Astronomical Union) MPC (Minor Planet Center)获取轨道数据,并考虑了彗核的自转以及进动,利用MONET (Mass lossdriven shape evolution model)形状演化模型对短周期彗星做数值模拟,计算得到了短周期彗星1P/Halley、9P/Tempel 1、 19P/Borrelly、 67P/C-G (Churyumov-Gerasimenko)、 81P/Wild 2和103P/Hartley 2在一个轨道周期内的太阳辐射能量以及表面侵蚀深度的分布,结合其动力学参数讨论了自转、进动和公转等特性对其表面水冰升华分布的影响以及造成南北侵蚀差异的可能性.     

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.     

Organic synthesis in the coma of Comet Hale–Bopp?

Several organic molecules have now been detected in the coma of Hale–Bopp. These species may either emanate from the nucleus, or, as has been suggested by Bockelée–Morvan et al., could be synthesized in the coma. We have modelled the gas phase chemistry which occurred in the coma of Hale–Bopp, concentrating on the observed organic molecules HCOOH, HCOOCH₃, HC₃N and CH₃CN. We find that gas phase chemical reactions are unable to synthesize the observed abundances of these molecules, so all these species are most probably present in the nuclear ice. We briefly discuss the implications of this result for the connection between cometary and interstellar ices.     

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.     

Light curves of the trans-Neptunian objects 1996 TP66 and 1994 VK8

We have obtained a number of CCD images of two trans-Neptunian objects, 1994 VK8 and 1996 TP66, over two nights. The changes in magnitude of these objects have been examined, in a search for periodic variation. In the case of 1996 TP66, nothing other than random noise can be found to within the errors of ∼0.04 mag. Although a periodic signal is found for 1994 VK8, it appears to be an artefact, as the same frequency appears in the variation of sky brightness and is probably due to the sampling of the data. However, 1994 VK8 does exhibit a variation of ∼0.5 mag. This would suggest either significant non-sphericity or a change in surface composition over a large area. In either case 1994 VK8 warrants further investigation.     

Local subgiants and time-scales of disc formation

This paper concentrates on the relationship between the rate of gas emission from the nucleus of Comet 9P/Tempel 1, the fraction f of the nucleus that is active, and the crater damage inflicted by the recent 2005 July 4 Deep Impact space mission. The cometary nucleus has a surface area of about  1.7 × 10⁸ m²  and a mean radius of about 3700 m. Before the impact it is estimated that only a fraction f = 0.0056 of the nucleus surface was actively producing gas and dust. The active area was about  9.4 × 10⁵ m²  . Absolute magnitudes obtained at recent perihelion passages of this comet indicate that variations in the 0.0074 > f > 0.0039 range can occur from apparition to apparition. Because of the low size of the original active area, the production of a new impact crater in the diameter range 40 to 300 m would lead to a long-term change in the cometary visual magnitude in the range 0.0018 to 0.098 respectively. This is below the limit of detectability. It has been suggested that the cometary dust is in the form of 'talcum powder' not 'beach sand'. We suggest that the dust ejected from the impact site has been broken up by the energetic impact process and thus has a different size distribution from dust locked in the snowy matrix of the nucleus and normally lifted off the nucleus by gentle sublimation processes.     

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.     

Orbit of periodic comet 153P/Ikeya–Zhang

The orbit of Comet C/2002C1 (Ikeya–Zhang) has a similarity to that of Comet C/1661C1 (Hevelius), and the numerical integration of the motion of C/2002C1 backward shows a possible linkage of those two comets. Thus, 153P/Ikeya–Zhang was designated a periodic comet. Historical records of comets in 877 and 1273 are also identified with Comet 153P/Ikeya–Zhang. The integrated orbital elements during 77 and 2362, and historical records of the comet are also presented and discussed.     

Computing secular motion under slowly rotating quadratic perturbation

We consider secular perturbations of nearly Keplerian two-body motion under a perturbing potential that can be approximated to sufficient accuracy by expanding it to second order in the coordinates. After averaging over time to obtain the secular Hamiltonian, we use angular momentum and eccentricity vectors as elements. The method of variation of constants then leads to a set of equations of motion that are simple and regular, thus allowing efficient numerical integration. Some possible applications are briefly described.     

The absolute magnitude distribution of trans-Neptunian objects

It is shown that the known trans-Neptunian objects (TNOs) have an absolute magnitude distribution index that increases as a function of orbital perihelion distance. In no perihelion range is the TNO index the same as that found for known short-period comets. However, the fact that the median diameters of the known members of these two populations (220 and 2.9 km respectively) differ by a factor of about 75 means that very small TNOs and short-period comets might still be related.