On the aging of comets

This study is based primarily on the calculations of comet orbits over ~ 10⁶ years for 160 short-period comets by Harold F. Levison and Martin J. Duncan from which there are calculated “ablation AGES”. There are positive statistical correlations (having many deviations) with radial nongravitational forces, comet activity measures, and dust-to-gas ratios in the spectra, in the sense that comets of greater “AGES” tend to be less active and to show less dust in their spectra than comets of lesser “AGES”.     

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.     

The restricted problem of n+ν bodies

The simplest, conventional, and original form of the circular restricted problem of three bodies is briefly described in sidereal and synodic systems using dimensional and non-dimensional variables. This dynamical system is generalized to n2 primary bodies (from n=2) with masses M_i, 1in, interacting with arbitrary force laws (instead of only gravitational forces). The number of bodies of small mass mM_i not perturbing the primaries is increased from =1 to 1 where 1 and the minor bodies are allowed to interact with one another under arbitrary force laws. While the minor bodies (m) do not affect the motions of the primaries (M_i), the primaries influence the motions of the minor bodies with arbitrary force laws.For the case where n=2, 1, and only gravitational forces act on the system, an integral of the system is derived. It is shown that the energy integral of the general problem of N bodies and the Jacobian integral of the classical restricted problem of three bodies are limiting cases of this integral. The role of the integral in bounding the motion of the minor bodies is discussed. Several applications of this system are given.     

Feedbacks between erosion and sediment transport in experimental bedrock channels

Natural bedrock rivers flow in self‐formed channels and form diverse erosional morphologies. The parameters that collectively define channel morphology (e.g. width, slope, bed roughness, bedrock exposure, sediment size distribution) all influence river incision rates and dynamically adjust in poorly understood ways to imposed fluid and sediment fluxes. To explore the mechanics of river incision, we conducted laboratory experiments in which the complexities of natural bedrock channels were reduced to a homogenous brittle substrate (sand and cement), a single sediment size primarily transported as bedload, a single erosion mechanism (abrasion) and sediment‐starved transport conditions. We find that patterns of erosion both create and are sensitive functions of the evolving bed topography because of feedbacks between the turbulent flow field, sediment transport and bottom roughness. Abrasion only occurs where sediment impacts the bed, and so positive feedback occurs between the sediment preferentially drawn to topographic lows by gravity and the further erosion of these lows. However, the spatial focusing of erosion results in tortuous flow paths and erosional forms (inner channels, scoops, potholes), which dissipate flow energy. This energy dissipation is a negative feedback that reduces sediment transport capacity, inhibiting further incision and ultimately leading to channel morphologies adjusted to just transport the imposed sediment load. Copyright © 2007 John Wiley & Sons, Ltd.     

Tectonic control of fan size: the importance of spatially variable subsidence rates

We study the geophysical controls on the size of alluvial fans. Simple relationships between catchment characteristics, sediment yield, subsidence patterns and fan size are developed. As predicting fan size is essentially a conservation of mass problem, our analysis is general, applying to all types of fan landform. The importance of spatially variable subsidence rates has gone largely unrecognized in previous studies of modern fans. Here we stress that the distribution of subsidence rates in the depositional basin is a primary control on relative fan size. Both free coefficients in the oft-cited power-law correlation of fan area and catchment area can be shown to be set primarily by the tectonic setting, taken to include source area uplift rate and the subsidence distribution in the depositional basin. In the case of a steady-state landscape, relative fan size is shown to be independent of both climate and source lithology; only during times of significant departure from steady state can relative fan size be expected to vary with either climate or source lithology. Transients associated with (1) a sudden increase in rock uplift rate, (2) a sudden change in climate and (3) the unroofing of strata with greatly differing erodibilities may produce variation of relative fan areas with both climate and source lithology. Variation of relative fan size with climate or lithology, however, requires that catchment–fan system response to perturbations away from steady state is sensitive to climate and lithology. Neither the strength of transient system responses nor their sensitivity to climate or lithology are known at present. Furthermore, internal feedbacks can significantly dampen any climatic or lithological effect. Thus theoretical considerations of the importance of climatic and lithological variables are inconclusive, but suggest that climatic and lithological effects are probably of secondary importance to tectonic effects. Field data from an unsteady landscape in Owens Valley, California, support and illustrate theoretical predictions regarding tectonic control of fan size. Field data from Owens Valley allow, but do not prove, a secondary dependence on source lithology. In addition, the Owens Valley field data indicate no relationship between relative fan size and climate. Headward catchment growth and enhanced sediment bypassing of fans during times of increased sediment yield (glacial) are put forward as plausible explanations.     

Epigenetic gorges in fluvial landscapes

Epigenetic gorges form when channels that have been laterally displaced during episodes of river blockage or aggradation incise down into bedrock spurs or side‐walls of the former valley rather than excavating unconsolidated fills and reinhabiting the buried paleovalley. Valley‐filling events that promote epigenetic gorges can be localized, such as a landslide dam or an alluvial/debris flow fan deposit at a tributary junction, or widespread, such as fluvial aggradation in response to climate change or fluctuating base‐level. The formation of epigenetic gorges depends upon the competition between the resistance to transport, strength and roughness of valley‐filling sediments and a river's ability to sculpt and incise bedrock. The former affects the location and lateral mobility of a channel incising into valley‐filling deposits; the latter determines rates of bedrock incision should the path of the incising channel intersect with bedrock that is not the paleovalley bottom. Epigenetic gorge incision, by definition, post‐dates the incision that originally cut the valley. Strath terraces and sculpted bedrock walls that form in relation to epigenetic gorges should not be used to directly infer river incision induced by tectonic activity or climate variability. Rather, they are indicative of the variability of short‐term bedrock river incision and autogenic dynamics of actively incising fluvial landscapes. The rate of bedrock incision associated with an epigenetic gorge can be very high (>1 cm/yr), typically orders of magnitude higher than both short‐ and long‐term landscape denudation rates. In the context of bedrock river incision and landscape evolution, epigenetic gorges force rivers to incise more bedrock, slowing long‐term incision and delaying the adjustment of rivers to regional tectonic and climatic forcing. Copyright © 2008 John Wiley & Sons, Ltd.     

Equilibrium solutions of the restricted problem of 2+2 bodies

Fourteen equilibrium solutions of the restricted problem of 2+2 bodies are shown to exist. Six of these solutions are located about the collinear Lagrangian points of the classical restricted problem of three bodies. Eight solutions are found in the neighborhood of the triangular Lagrangian points. Linear stability analysis reveals that all of the equilibrium solutions are unstable with the exception of four solutions; two in the vicinity of each of the triangular Lagrangian points. These four solutions are found to be stable provided the mass parameter of the primary masses is less than a critical value which depends also on the mass of the minor bodies.     

Comet P/Holmes, 1892III: A case of duplicity?

The observations of comet P/Holmes 1892III, exhibiting two 8- to 10-mag bursts, have been carefully analyzed. The phenomena are consistent with the grazing encounter of a small satellite with the nucleus on November 4.6, 1892, and the final encounter on January 16.3, 1893. The grazing encounter produced, besides the first great burst, an active area on the nucleus, which was rotating retrograde with a period of 16.3 hr and inclination of nearly 180°. After the final encounter, the spin period was essentially unchanged, but two areas became active, separated some 164° in longitude on the nucleus. After the first burst the total magnitude fell less than 2 mag from November 7 to 30 (barely naked eye) while the nuclear region remained diffuse or complex, rarely of ever showing a stellar appearance. The fading was much more rapid after the second burst (barely naked eye at maximum) while the nucleus frequently appeared stellar after the first day. It seems reasonable to conclude that the grazing encounter distributed a volume of large chunks in the neighborhood of the nucleus, maintaining activity for weeks. The final encounter activated a new area on the nucleus, the shock and fall back disturbing the area already exposed by the grazing encounter. Several details of this scenario are fitted rather well.     

A study of Wilson's determination of ferrous iron in silicates

The chemical factors affecting the accuracy of Wilson's procedure for determination of ferrous iron in silicates have been investigated. This procedure utilizes pentavalent vanadium to oxidize ferrous iron as it is set free from the silicate by hydrofluoric acid. The quadrivalent vanadium produced is more resistant to oxidation by oxygen than ferrous iron, and conserves the reducing power of the silicate. The procedure is done at room temperature.Recovery of ferrous iron under various conditions has been studied to elucidate the chemical mechanisms of loss in the procedure. Some improvements have been made. The studies indicate that the procedure is of high accuracy.An effect resulting in loss of ferrous iron titre has been found, involving the chemical attack of solids by solutions containing oxygen and pentavalent vanadium. This loss does not appear to take place if all ion species are in solution.     

Strength matters: Resisting erosion across upland landscapes

Soil-covered upland landscapes comprise a critical part of the habitable world and our understanding of their evolution as a function of different climatic, tectonic, and geologic regimes is important across a wide range of disciplines. Soil production and transport play essential roles in controlling the spatial variation of soil depth and therefore hillslope hydrological processes, distribution of vegetation, and soil biological activity. Field-based confirmation of the hypothesized relationship between soil thickness and soil production is relatively recent, however, and here we quantify a direct, material strength-based influence on variable soil production across landscapes. We report clear empirical linkages between the shear strength of the parent material (its erodibility) and the overlying soil thickness. Specifically, we use a cone penetrometer and a shear vane to determine saprolite resistance to shear. We find that saprolite shear strength increases systematically with overlying soil thickness across three very different field sites where we previously quantified soil production rates. At these sites, soil production rates, determined from in situ produced beryllium-10 (¹⁰Be) and aluminum-26 (²⁶Al), decrease with overlying soil thickness and we therefore infer that the efficiency of soil production must decrease with increasing parent material shear strength. We use our field-based data to help explain the linkages between biogenic processes, chemical weathering, hillslope hydrology, and the evolution of the Earth's surface. © 2019 John Wiley & Sons, Ltd.