Modeling of cometary evolution by kinetic theory: Method and first results

Physical evolution of Jupiter family (JF) comets is considered as a simultaneous process of erosion and fading. Dynamical effects are limited to discrete changes of the perihelion distance, that result in changes of the evaporation rate. Assuming that the JF comet population is in a steady state, a distribution function of this population in the two dimensional phase space consisting of radius and active fraction of the nucleus surface is found as the solution of a set of kinetic equations, each one of them for a different perihelion distance. With use of the distribution function some statistical properties of the comet population, like the total number of comets in the considered region of the phase space, the number of objects that evaporate or get dormant per unit time, etc., are obtained. The cumulative distribution function with respect to the absolute brightness is calculated and compared with the observed one as a check on the considered models.     

Comets

Summary In Part II of this paper we comment on the modelling of the complex interactions which take place in cometary comae and tails between parent molecules, radicals, ions, dust grains and the solar electromagnetic and corpuscular radiation (Sect. 4), and we summarize some of the current thoughts about the nature of the elusive cometary nucleus (Sect. 5). Comets are ephemeral phenomena whose lifetimes are short on the cosmic scale; their evolution, statistically and as individual objects, is a main theme in contemporary research (Sect. 6). Although their origins are still not well known, comets undoubtedly carry important clues to the early history and evolution of the solar system (Sect. 7). Finally, we mention the main questions now being asked by cometary studies and illustrate some of the future observational possibilities which may provide crucial data for the next steps forward (Sect. 8).     

Injection of Oort Cloud comets: the fundamental role of stellar perturbations

We present Monte Carlo simulations of the dynamical evolution of the Oort cloud over the age of the Solar System, using an initial sample of one million test comets without any cloning. Our model includes perturbations due to the Galactic tide (radial and vertical) and passing stars. We present the first detailed analysis of the injection mechanism into observable orbits by comparing the complete model with separate models for tidal and stellar perturbations alone. We find that a fundamental role for injecting comets from the region outside the loss cone (perihelion distance q > 15 AU) into observable orbits (q < 5 AU) is played by stellar perturbations. These act in synergy with the tide such that the total injection rate is significantly larger than the sum of the two separate rates. This synergy is as important during comet showers as during quiescent periods and concerns comets with both small and large semi-major axes. We propose different dynamical mechanisms to explain the synergies in the inner and outer parts of the Oort Cloud. We find that the filling of the observable part of the loss cone under normal conditions in the present-day Solar System rises from <1% for a < 20 000 AU to about 100% for a ? 100 000 AU.     

Chaotic dynamics and Monte Carlo modelling

Practice, i.e., as long as the initial conditions cannot be specified exactlty, the outcome of a chaotic dynamical system can only be specified in statistical terms. Evolution equations (e.g., the Fokker-Planck equation) for a distribution of test particles can then be formulated, and as an alternative to analytical, mostly approximate or idealised solutions one may simulate the problem using Monte Carlo techniques. Such simulations are a well-known tool in the study of completely chaotic many-body systems such as star clusters or planetary rings, where the sample of test particles can indeed be taken to represent a random set of true solutions according to Bowen's shadowing lemma. In this sense the Monte Carlo modelling plays a role analogous to that of averaging or mapping in regular dynamics, i.e.: the exact dynamical system is replaced by a model overlooking the details of the short-term motion but yielding a good approximation to the long-term behaviour. By a further discretization of the problem the stochastic system can be modelled as a Markov chain. Both Monte Carlo simulations and Markov models have been used in cometary dynamics, and we review some examples from this work to illustrate the success as well as limitations of these stochastic modelling techniques. Lyapunov characteristic exponents and Kolmogorov entropy appear to be suitable tools for estimating the underlying stochasticity to which Monte Carlo simulations refer.     

The spin periods of masteroids

In an attempt to verify the suggestion by Harris and Burns (1979) that M-type asteroids in general have high spin rates we are currently involved in a programme of photoelectricUBV observations of M and CMEU asteroids. Recently we have thus determined rotation periods, light-curve amplitudes andUBV colour indices for the asteroids 201 Penelope and 250 Bettina, both of which are situated in the (C,M,E) domain of the two-colour diagram. The resulting periods are very short (cf., IAUC 3523 and 3527). In general, we find that both the M and CMEU asteroid groups appear to be characterized by fast rotations, large amplitudes and an avoidance of membership in Hirayama families.Based on observations partly obtained at the European Southern Observatory, La Silla, Chile.     

Asteroids in cometary orbits

Orbital integrations are presented for a total of 14 asteroids with perihelia inside 1.7 AU and with aphelion distances in excess of 4 AU, 10 of which were discovered in 1979–1984. The integrations were normally extended over approximately ±1000 years in a three-body model (Sun-Jupiter-asteroid). The effects of uncertainties of starting orbits are not treated in this work, and as far as the real asteroids are concerned, the results should be regarded mostly as preliminary indications. A wide variety of orbital evolutions is found, and some of them evidently belong to the cometary, chaotic type. Three such cases are identified with certainty (1983 SA, 1983 XF, and 1984 BC) and two or three more with various degrees of likelihood. An asteroidal motion is found for the well-observed object 1979 VA. A stable libration around the $\text{2}\text{1}$ resonance is found for 1981 FD, which obviously adds to the Griqua group. A long-lasting libration around the $\text{5}\text{3}$ resonance performed by 1982 YA is probably unstable. Temporary librations are also found for 1983 SA ($\text{4}\text{3}$ resonance) and 1983 XF ($\text{2}\text{1}$ resonance), but these objects appear to transit into irregular motions with close approaches to Jupiter (less than 0.01 AU for 1983 XF). A very rapid large-amplitude ω libration around 90° is found in the future motion of 1983 VA. If this will indeed occur for the real asteroid, the object will oscillate with a period of only 750 years between a main-belt orbit of very high inclination and a low-inclination Apollo-type orbit.     

Comets

Summary The status of cometary astronomy and astrophysics as of mid-1992 is reviewed, i.e. at a time when the first in situ observations of comets in 1985–86 have been thoroughly discussed, interpreted and compared with ground-based investigations. Many earlier ideas about comets were vindicated and a plethora of new discoveries resulted which have now led to reformulation of certain observational strategies and, in particular, to greatly improved possibilities for the detailed physical/chemical modelling of many cometary phenomena.A main purpose of this paper is to assess the current situation and to provide a reasonably complete, yet concise and critical evaluation of the most important questions and promising lines of research in this field. After a short introduction which defines the overall subject and the framework of the present review (Sect. 1), we take a look at some of the major past developments of our concepts about comets, in particular the crucial new insights which were gained during the past four decades (Sect. 2). The rapid advances in observational technology have greatly extended the realm of accessible problems and we next discuss the present possibilities and restrictions of the various techniques employed (Sect. 3).Part II of this paper discusses the modelling of cometary comae and tails (Sect. 4), the cometary nucleus (Sect. 5), the evolution (Sect. 6) and origin (Sect. 7) of comets and ends with an overview of the main questions now being asked by cometary studies (Sect. 8).     

Photoelectric photometry of asteroids 33 Polyhymnia and 386 Siegena

Photometric parameters of the asteroids 33 Polyhymnia and 386 Siegena were obtained during an international campaign performed at three observatoroes: Table Mountain Observatory (A. W. Harris), European Southern Observatory (ESO; C.-I. Lagerkvist), and Catania Astrophysical Observatory (V. Zappalá and F. Scaltriti). The photoelectric observations were carried out in the period August 15–September 14, 1980.The rotational periods and amplitudes observed are: $\text{P}{}_{\mathrm{<mtext>syn</mtext>}}\text{= 9}{}^{\mathrm{<mtext>h</mtext><mtext>dot</mtext>}}\text{763 ± 0}{}^{\mathrm{<mtext>h</mtext><mtext>dot</mtext>}}\text{,}\text{Ampl.}\text{= 0}{}^{\mathrm{<mtext>m</mtext><mtext>dot</mtext>}}\text{11 ± 0}{}^{\mathrm{<mtext>m</mtext><mtext>dot</mtext>}}\text{01}$ for Siegena and $\text{P}{}_{\mathrm{<mtext>syn</mtext>}}\text{= 18}{}^{\mathrm{<mtext>h</mtext><mtext>dot</mtext>}}\text{601 ± 0}{}^{\mathrm{<mtext>h</mtext><mtext>dot</mtext>}}\text{004,}\text{Ampl.}\text{= 0}{}^{\mathrm{<mtext>m</mtext><mtext>dot</mtext>}}\text{14}\text{(near opposotion) and Ampl.}\text{= 0}{}^{\mathrm{<mtext>m</mtext><mtext>dot</mtext>}}\text{17 ± 0}{}^{\mathrm{<mtext>m</mtext><mtext>dot</mtext>}}\text{01}$ (at ～10° phase angle) for 33 Polyhymnia.The multiple-scattering factor Q [as defined by K. Lumme and E. Bowell, Astron. J.86, 1694–1704, 1705–1721 (1981a,b)] is found to be 0.15 ± 0.06 for 386 and 0.26 ± 0.03 for 33, implying higher albedos in each case than expected according to their taxonomic classes, C and S, respectively [E. Bowell, T. Gehrels, and B. Zellner, in Asteroids, pp. 1108–1129, Univ. of Arizona Press, Tucson (1979)].The color indices B - V and U - B, were measured and found to differ significantly from those given by Bowell et al.. Our values are, for 386, B - V = 0.71 and U - B = 0.36; and for 33, B - V = 0.81 and U - B = 0.39.     

The 1995–2002 Long-Term Monitoring of Comet C/1995 O1 (HALE–BOPP) at Radio Wavelength

The bright comet Hale–Bopp provided the first opportunity to follow the outgassing rates of a number of molecular species over a large range of heliocentric distances. We present the results of our observing campaign at radio wavelengths which began in August 1995 and ended in January 2002. The observations were carried out with the telescopes of Nançay, IRAM, JCMT, CSO and, since September 1997, SEST. The lines of nine molecules (OH, CO, HCN, CH₃OH, H₂CO, H₂S, CS, CH₃CN and HNC) were monitored. CS, H₂S, H₂CO, CH₃CN were detected up to r_h= 3–4 AU from the Sun, while HCN and CH₃OH were detected up to 6 AU. CO, which is the main driver of cometary activity at heliocentric distances larger than 3–4 AU, was last detected in August 2001, at r_h= 14 AU. The gas production rates obtained from this programme contain important information on the nature of cometary ices, their thermal properties and sublimation mechanisms.Line shapes allow to measure gas expansion velocities, which, at large heliocentric distances, might be directly connected to the temperature of the nucleus surface. Inferred expansion velocity of the gas varied as r_h ^-0.4 within 7 AU from the Sun, but remained close to 0.4 km s^-1 further away. The CO spectra obtained at large r_hare strongly blueshifted and indicative of an important day-to-night asymmetry in outgassing and expansion velocity. The kinetic temperature of the coma, estimated from the relative intensities of the CH₃OH and CO lines, increased with decreasing r_h, from about 10 K at 7 AU to 110 K around perihelion.     

Natural transfer of viable microbes in space.

The possibility and probability of natural transfer of viable microbes from Mars to Earth and Earth to Mars traveling in meteoroids during the first 0.5 Ga and the following 4 Ga are investigated, including: --radiation protection against the galactic cosmic ray nuclei and the solar rays, dose rates as a function of the meteorite's radial column mass (radius x density), combined with dose rates generated by natural radioactivity within the meteorite; and survival curves for some bacterial species using NASA's HZETRN transport code --other factors affecting microbe survival: vacuum; central meteorite temperatures at launch, orbiting, and arrival; pressure and acceleration at launch; spontaneous DNA decay; metal ion migration --mean sizes and numbers of unshocked meteorites ejected and percentage falling on Earth, using current semiempirical results --viable flight times for the microbe species Bacillus subtilis and Deinococcus radiodurans R1 --the approximate fraction of microbes (with properties like the two species studied) viably arriving on Earth out of those ejected from Mars during the period 4 Ga BP to the present time, and during the 700 Ma from 4.5 to 3.8 Ga. Similarly, from Earth to Mars. The conclusion is that if microbes existed or exist on Mars, viable transfer to Earth is not only possible but also highly probable, due to microbes' impressive resistance to the dangers of space transfer and to the dense traffic of billions of martian meteorites which have fallen on Earth since the dawn of our planetary system. Earth-to-Mars transfer is also possible but at a much lower frequency.