Mean free paths of energetic charged particles parallel and antiparallel to the interplanetary magnetic field

A new method to calculate the mean free paths of energetic particles propagating parallel and anti-parallel to the interplanetary magnetic field, based on quasi-linear theory and the complex spectral polarization analysis of the field, is developed and presented. Applications of the method using HEOS 2 (1 AU), Pioneer 10 (5 AU), Pioneer 11 (20 AU), ICE (Giacobini-Zinner's comet) data have been made, showing that: (a) The mean free paths parallel and anti-parallel to the field can be completely different in various regions of the interplanetary medium and different time periods. (b) Particles are preferentially scattered in one direction. (c) The parallel and anti-parallel mean free paths become equal at certain energy. Comparisons with the results from another computational method are made.     

Spectral polarization analysis of the interplanetary magnetic field fluctuations

A new computational method and algorithm, based on complex Fourier analysis, is used to derive the spectral density of plane and circularly polarized fluctuation components of the interplanetary magnetic field. Applications of the method have been made using HEOS 2 (1 AU), Pioneer 10 (5 AU), Pioneer 11 (20 AU), and ICE (Giocabini-Zinner's comet) data sets. The results show the existence of circularly polarized MHD waves in all cases.     

Interplanetary dust between 1 and 5 AU

Analyses of the data from the Meteoroid Detection Experiment (MDE) and the Imaging Photopolarimeter (IPP) aboard Pioneer 10 and Pioneer 11 have led to contradictory conclusions. While the MDE indicates a significant particle environment in the outer solar system (out to at least 5 AU), the IPP sees no zodiacal light (therefore implying no small particles) past 3.3 AU. We reconcile the two results by noting that the spectral index, p [relating particle radius, s, and particle concentration, n(s), i.e., dn(s) = Cs^?pds], is not a constant in the solar system, but changes from p < 2 near 1 AU to p > 2.5 at 5 AU for particles in the range of 10 μm. The MDE value of p = 1.8 at 1 AU is in agreement with previous satellite measurements, while our earlier analysis of the Pioneer 10 Jovian encounter data indicated p > 2.5 at 5 AU. A joint analysis of the Pioneer 10 and Pioneer 11 MDE data also indicates that p > 2.5 in the outer solar system. We show that a varying spectral index violates a major assumption used in the interpretation of the IPP data, which in turn had led to the conclusion that zodiacal dust is absent beyond 3.3 AU. With p a function of solar distance, the MDE data is now consistent with the IPP data, thus indicating a significant particle concentration in the outer solar system.     

Detection of nonlinear dynamics in solar wind and a comet using phase-correlation measures

Nonlinear dynamics in the solar wind and cometary plasma over small time scales are identified using sensitive entropy measures of the weak wave organization in the magnetic field polarized components. All possible linear Gaussian stochastic models are rejected at a high confidence level in all cases. The association of the detected correlations with a forward CIR shock is demonstrated using a large set of very high-resolution Pioneer-10 field measurements.     

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.     

Dynamics of Dust Particles of Different Structure: Application to the Modeling of Dust Motion in the Vicinity of the Nucleus of Comet 67P/Churyumov–Gerasimenko

We consider the estimates of the main forces acting on dust particles near a cometary nucleus. On the basis of these estimates, the motion of dust particles of different structure and mass is analyzed. We consider the following forces: (1) the cometary nucleus gravity, (2) the solar radiation pressure, and (3) the drag on dust particles by a flow of gas produced in the sublimation of cometary ice. These forces are important for modeling the motion of dust particles relative to the cometary nucleus and may substantially influence the dust transfer over its surface. In the simulations, solid silicate spheres and homogeneous ballistic aggregates are used as model particles. Moreover, we propose a technique to build hierarchic aggregates—a new model of quasi-spherical porous particles. A hierarchic type of aggregates makes it possible to model rather large dust particles, up to a millimeter in size and larger, while no important requirements for computer resources are imposed. We have shown that the properties of such particles differ from those of classical porous ballistic aggregates, which are usually considered in the cometary physics problems, and considering the microscopic structure of particles is of crucial significance for the analysis of the observational data. With the described models, we study the dust dynamics near the nucleus of comet 67P/Churyumov–Gerasimenko at an early stage of the Rosetta probe observations when the comet was approximately at 3.2 AU from the Sun. The interrelations between the main forces acting on dust aggregates at difference distances from the nucleus have been obtained. The dependence of the velocity of dust aggregates on their mass has been found. The numerical modeling results and the data of spaceborne observations with the Grain Impact Analyzer and Dust Accumulator (GIADA) and the Cometary Secondary Ion Mass Analyzer (COSIMA) onboard the Rosetta probe are compared at a quantitative level.     

Albedos and size distribution of meteoroids from 0.3 to 4.8 AU

Comparison is made between the run of number density of meteoroids from penetration detectors aboard Helios A (masses below 10^?8 g) and Pioneer 10 (masses near and above 3 × 10^?9 g), the source function of the zodiacal light deduced from photometric observations aboard Helios A and Pioneer 10, counts versus brightness of objects passing by Pioneer 10 from the Sisyphus experiment and the distribution of meteoroids deduced from radar and optical meteors at the Earth. The Sisyphus experiment on Pioneer 10 observed reflecting glints on meteoroids rather than the meteoroids themselves and the counting statistics refer not to the effective radii of the meteoroids but to the effective radii of curvature of the reflecting glints on the meteoroids. The penetration detectors appear to find some increase in number density toward the Sun and a flat distribution outward to 5.2 AU. The overall behavior of the zodiacal light is that the relative distribution over direction is unchanged while the source scattering function diminishes as the inverse 1.4 power of distance from the Sun. The fit to the brightness of the zodiacal light obtained from these statistics can be combined with the mass distribution results from the optical meteors to deduce a mean geometric albedo of meteoroids of 0.006 at 1 AU from the Sun. Combination of the space distribution from radar meteors with the scattering source function of the zodiacal light yields geometric albedos for meteoroids running from 0.07 at 0.1 AU, from the Sun through 0.006 at 1 AU down to about 0.0001 at 3.3 AU which may run flat thence outward. This result is imposed by the indicated modest increase in density of meteoroids very near the Sun, a minimum between the Sun and the Earth near 0.4 AU and rising density outward to somewhere beyond 3.3 AU which is very different from the inverse 1.4 power of the distance shown for scatterers (product of number density and albedo) by the zodiacal light. A check on the distribution at very large sizes is possible if a search is made for fireballs in Jupiter's atmosphere by the Mariner Jupiter Saturn 1977 television cameras during the two encounters with Jupiter in 1979. An easy detection of such activity would put the maximum in the meteoroid distribution out near Jupiter and lend further confirmation to the indicated drop in albedo.     

Cometary dynamics

Since comets appear to be observable only at the expense of rapid aging in the vicinity of the Sun, chaotic routes are considered necessary in order to bring them from their remote places of origin and storage. Recent work on short-period cometary orbits has verified this expectation in general terms but has also shown many examples of temporary resonance trappings and other quasiregular phenomena. For long-period comet dynamics recent developments point to the importance of long-term effects associated with the Galactic tidal field acting in conjunction with the randomizing effect of stellar encounters. This paper presents a comprehensive review of all these aspects of cometary dynamics.     

Apsidal precession of the outer solar planetary orbits due to the pioneer anomaly

Despite the now common position that the Pioneer anomaly is not a real gravitational effect but an effect due to the on-board thermal recoil forces – for curiosity’s sake, we here take the suggestion of Nyambuya (2015) where it has been assumed that the Pioneer anomaly – can, in-principle, be attributed to a gravitational effect due to these spacecrafts accreting some material from a rarefied Interplanetary Medium (IPM) in the domain where the Pioneer anomaly has manifested [20 AU ≲ r ≲ 70 AU]. If this assumption is correct, then, the expected Pioneer acceleration of these spacecrafts maybe much smaller than the Pioneer acceleration to cause as noticeable apsidal precession of the outer Solar planets Uranus, Neptune and Pluto, thus making it difficult to rule-out a gravitational origin of the Pioneer anomaly.     

Nitrogen Sulfide In Comets Hyakutake (C/1996 B2) And Hale–Bopp (C/1995 O1)

The chemistry of both nitrogen and sulfur presents interesting problems in comets.In this paper, we use a model of cometary comae with gas-phase chemical kineticsand gas dynamics to predict molecular abundances in the inner coma region for twoof the brightest comets in the past 20 years, Hyakutake (C/1996 B2) and Hale–Bopp(C/1995 O1). In this progress report we concentrate on the gas-phase chemistry of thenitrogen sulfide (NS) radical at a heliocentric distance of 1 AU to study the abundanceof NS using a detailed photo and chemical reaction network with over 100 species andabout 1000 reactions. The results are compared with recent observations of CometHale–Bopp and reveal that conventional gas-phase reactions schemes do not produceNS in sufficient quantities to explain the observations. We plan to continue therefinement of the model to improve agreement with observational constraints.     

Thermal modeling of cometary nuclei

A new model of the sublimation of volatile ices from a cometary nucleus has been developed which includes the effects of diurnal heating and cooling, rotation period and pole orientation, and thermal properties of the ice and subsurface layers. The model also includes the contribution from coma opacity, scattering, and thermal emission, where the properties of the coma are derived from the integrated rate of volatile production by the nucleus. The model is applied to the specific case of the 1986 apparition of Halley's comet. It is found that the generation of a cometary dust coma actually increases the total energy reaching the Halley nucleus. This results because of the significantly greater geometrical cross section of the coma as compared with the bare nucleus, and because the coma provides an essentially isotropic source of multiply scattered sunlight and thermal emission over the entire nucleus surface. For Halley, the calculated coma opacity is approximately 0.2 at 1 AU from the Sun, and 1.2 at perihelion (0.587 AU). At 1 AU this has little effect on dayside temperatures (maximum ≈200°K) but raises nightside temperatures (minimum ≈150°K) by about 40°K. At perihelion the higher opacity results in a nearly isothermal nucleus with only small diurnal and latitudinal temperature variations. The general surface temperature is 205°K with a maximum of 209°K at local noon on the equator. Some possible consequences of the results with respect to the generation of nongravitational forces, observed volatile production rates for comets, and cometary lifetimes against sublimation are discussed.     

Polycyclic aromatic hydrocarbon lifetime in cometary environments

Observations of cometary comae in the infrared and in the near-ultraviolet suggest that polycyclic aromatic hydrocarbons (PAHs) are present in these environments. However, the chemical identity and abundance of these molecules are not clearly determined yet. Some species are probably more stable than others when submitted to the solar radiation field, and are therefore more likely to be observed. The photophysics of gas-phase PAHs in cometary environments is modelled. Photodissociation occurs when the heating by absorption of UV photons is more efficient than the radiative cooling. The lifetime of the molecules is found to depend on their size: small molecules being more stable than large ones. Furthermore, at 1 AU from the Sun, the lifetime of PAHs is found to be very short (20s for phenanthrene). This suggests that, if observed in the gas phase in cometary environments, these molecules should be produced by an extended source.     

Spatially resolved spectrophotometry of comet P/Stephan-Oterma

Observations of Comet P/Stephan-Oterma were made with an Intensified Dissector Scanner spectrograph on the McDonald Observatory 2.7-m telescope during the period from July 1980 to February 1981. These spectra cover a range of heliocentric distances from 2.3 AU preperihelion to 1.8 AU postperihelion. A small aperture was used to map the spatial distributions of the gases in the coma. Column densities of the observed cometary emissions (CN, C₃, CH, and C₂) were calculated and it is shown that Stephan-Oterma appeared nearly spherically symmetric. These date are used by Cochran (1985, Icarus62, 82–92) to constrain chemical models of Stephan-Oterma.     

Evolution of the Oort cloud angular momentum: Numerical simulation

This paper considers the evolution of a flat svarm of cometary bodies (under the effect of the passage of stars), initially moving in one direction along the circular orbits with radii 1.4×10⁴<r<2×10⁴ AU and along elliptic orbits with semi-major axes 5×10³<a<1×10⁴ AU and with perihelia within 50<q<100 AU. Numerical simulation shows that the original flat belt of comets is thermalizing. Its root-mean-squarez-coordinate grows withr. A cometary cloud forms with a dense flattened inner core and a rarefied halo (the Oort cloud proper). The value =N _core/N _halo varies within a wide range (up to the order of magnitude) depending on the model used (N _core andN _halo are the numbers of comets in the core and the halo, respectively).The hypothesis of a massive Oort cloud (Marochniket al., 1988) implies that the Oort cloud should have a large angular momentum. This paper employs numerical simulation to calculate Oort cloud models to which the initially flat located at the periphery of the solar nebula rotating cometary swarms is evolving in time. The loss of the initial angular momentum over the time of the Oort cloud evolution is not large.     

Composition of cometary dust from polarization spectra

The wavelength dependence of the polarization (“polarization spectra”) of cometary dust is discussed. It is shown that, in the case of large phase angles, the wavelength dependence of the polarization is mainly controlled by the complex refractive index of the particle material, whereas the spectral dependence of the intensity is also sensitive to the size of the particles. This suggests that observations of “polarization spectra” may determine the composition of cometary dust. An attempt is made to find the composition of the cometary dust material by comparing the observed polarimetric data with laboratory measurements of complex refractive indices of possible cometary constituents. Silicates, graphite, metals, organics, water ice and their mixtures are considered. It is shown that astronomical silicate must be the most abundant constituent of cometary dust in the range of heliocentric distances from 0.8 to 1.8 AU, whereas the volume fraction of pure graphite or pure metals is less then 1%. A substance similar to that of F-type asteroids may be present in comets. There is evidence for an organic material that is being destroyed between heliocentric distances of 0.8–1.8 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 Hypothesis of Additional Acceleration in the Motion of Comet Harrington–Abell from Jupiter

By processing 494 observations of Comet Harrington–Abell, we obtained a unified system of elements that includes its turn around the Sun during which it closely approached Jupiter to a minimum distance of 0.037 AU in 1974. A study of the cometary orbit before and after the approach showed that, probably, at the approach of the comet to Jupiter, apart from the well-known gravitational perturbations, its motion was affected by an additional force. An improvement of the cometary orbit by assuming that an additional acceleration inversely proportional to the square of the distance to Jupiter exists in its motion yielded the following values: (4.57 ± 0.42) × 10^–10 and (–7.20 ± 0.42) × 10^–10 AU day^–2 for the radial and transversal acceleration components, respectively. As a plausible explanation of the changes in the cometary orbit, we additionally considered a model based on the hypothesis of partial disintegration of the cometary nucleus. The parameter that characterizes the instant displacement of the center of inertia along the jovicentric radius vector was estimated to be –1.83 ± 0.75 km. Based on a unified numerical theory of cometary motion, we determined the nongravitational parameters using Marsden's model for two periods: A ₁ = (11.68 ± 1.74) × 10^–10 AU day^–2, A ₂ = (0.53 ± 0.0357) × 10^–10 AU day^–2 for 1975–1999 and A ₁ = (5.92 ± 5.86) × 10^–10 AU day^–2, A ₂ = (0.08 ± 0.028) × 10^–10 AU day^–2 for 1955–1969, under the assumption that the nongravitational acceleration changed at the approach of the comet to Jupiter.     

The Pioneer 9 electric field experiment

We present a detailed analysis of the Pioneer 9 VLF electric field observations for 20 selected storm periods covering a heliocentric range extending from 0.754 AU to 0.99 AU. Although data from only two low frequency channels are available, the results of the present study tend to confirm the preliminary speculation by Scarf and Siscoe (1971) that the turbulentE-field spectrum in the disturbed solar wind has a significant radial gradient.     

Dynamical evolution of comets and the problem of cometary fading

Possibilities to explain the observed 1/a-distribution are discussed in the light of improved understanding of the dynamical evolution of long-period comets. It appears that the ‘fading problem’ applies both to single-injection and continuous-injection models. Although uncertainties due to nongravitational effects do not allow detailed results to be drawn from the observed 1/a-distribution at small perihelion distance q, that for q ? 1.5 AU shows that a constant fading probability cannot explain all the features of the observed distribution. Assuming that comets can reappear following a period of fading, values for the assumed constant fading and renewal probabilities, and the total cometary flux have been estimated for q > 1.5 AU.     

Study of parallel diffusion of energetic particles in the interplanetary medium using spacecraft data at 1 and 5 AU

Energetic particle (1–100 MeV) pitch angle scattering in the Interplanetary Magnetic Field (IMF) is studied using spacecraft magnetometer data at 1 AU (IMP 7 and HEOS 2) and at 5 AU (Pioneer 10). Particle trajectories are followed by a computer simulation of their movement in a realistic model of the IMF. Determination of the pitch angle diffusion coefficient at 1 AU (D ) leads to a parallel mean free path which is roughly independent of particle energy, 0.03 AU. At the lowest energy our result is at least a factor of 3 larger than the predictions of quasi linear theory. Results at 5 AU lead to a radial mean free path which is between 2 to 6 times smaller than at 1 AU, probably indicating a greater importance for perpendicular diffusion at large heliodistances. In fact a roughly constant radial mean free path ( _r 0.01 AU) is obtained when the contribution of perpendicular diffusion at 5 AU is taken into account (Moussaset al., 1981).