On topological stability in the general three-body problem

The confining curves in the general three-body problem are studied; the role of the integralc ² h (angular momentum squared times energy) as bifurcation parameter is established in a very simple way by using symmetries and changes of scale. It is well known (Birkhoff, 1927) that the bifurcations of the level manifolds of the classical integrals occur at the Euler-Lagrange relative equilibrium configurations. For small values of the mass ratio ε=m ₃/m ₂ both the positions of the collinear equilibrium points and thec ² h integral are expanded in power series of ε. In this way the relationship is found between the confining curves resulting from thec ² h integral in the general problem, and the zero velocity curves given by the Jacobi integral in the corresponding restricted problem. For small values of ε the singular confining curves in the general and in the restricted problem are very similar, but they do not correspond to each other: the offset of the two bifurcation values is, in the usual, system of units of the restricted problem, about one half of the eccentricity squared of the orbits of the two larger bodies. This allows the definition of an approximate stability criterion, that applies to the systems with small ε, and quantifies the qualitatively well known destabilizing effect of the eccentricity of the binary on the third body. Because of this destabilizing effect the third body cannot be bounded by any topological criterion based on the classical integrals unless its mass is larger than a minimum value. As an example, the three-body systems formed by the Sun, Jupiter and one of the small planets Mercury, Mars, Pluto or anyone of the asteroids are found to be ‘unstable’, i.e. there is no way of proving, with the classical integrals, that they cannot cross the orbit of Jupiter. This can be reliably checked with the approximate stability criterion, that given for the most important three-body subsystems of the Solar System essentially the same information on ‘stability’ as the full computation of thec ² h integral and of the bifurcation values.     

Hyperion: Collisional disruption of a resonant satellite

Hyperion is an irregularly shaped object of about 285 km in mean diameter, which appears as the likely remmant of a catastrophic collisional evolution. Since the peculiar orbit of this satellite (in $\text{4}\text{3}$ resonance locking with Titan) provides an effective mechanism to prevent any reaccretion of secondary fragments originated in a breakup event, the present Hyperion is probably the “core” of a disrupted precursor. This contrasts with the other, regularly shaped small satellites of Saturn, which, according to B.A. Smith et al. [Science215, 504–537 (1982)], were disrupted several times but could reaccrete from narrow rings of collisional fragments. The numerical experiments performed to explore the region of the phase space surrounding the present orbit show that most fragments ejected with a relative velocity $\text{?0.1}\text{km}\text{/}\text{sec}$ rapidly attain chaotic-type orbits, having repeated close encounters with Titan. Ejection velocities of this order of magnitude are indeed expected for a collision at a velocity of ～ 10 km/sec with a projectile-to-target mass ratio of the order of 10^?3; similar effects could be produced by less energetic but nearly grazing collisions. Such events are not likely to displace the largest remnant (i.e., the present Hyperion) outside the stable region of the phase space associated with the resonance, but could be responsible for the large amplitude of the observed orbital libration.     

Late accretion and lithification of chondritic parent bodies: Mg isotope studies on fragments from primitive chondrites and chondritic breccias

Abstract— Recent results of isotopic dating studies (¹⁸²Hf‐¹⁸²W, ²⁶Al‐²⁶Mg) and the increasing number of observed igneous and metamorphosed fragments in (primitive) chondrites provide strong evidence that accretion of differentiated planetesimals predates that of primitive chondrite parent bodies. The primitive chondrites Adrar 003 and Acfer 094 contain some unusual fragments that seem to have undergone recrystallization. Magnesium isotope analyses reveal no detectable radiogenic ²⁶Mg in any of the studied fragments. The possibility that evidence for ²⁶Al was destroyed by parent body metamorphism after formation is not likely because several other constituents of these chondrites do not show any metamorphic features. Since final accretion of a planetesimal must have occurred after formation of its youngest components, formation of these parent bodies must thus have been relatively late (i.e., after most ²⁶Al had decayed). Al‐Mg isotope data for some igneous‐textured clasts (granitoids and andesitic fragments) within the two chondrite regolith breccias Adzhi‐Bogdo and Study Butte reveal also no evidence for radiogenic ²⁶Mg. As calculated from the upper limits, the formation of these igneous clasts, the incorporation into the parent body regolith, and the lithification must have occurred at least 3.8 Myr (andesite in Study Butte) and 4.7 Myr (granitoids in Adzhi‐Bogdo) after calcium‐aluminum‐rich inclusions (CAI) formation. The absence of ²⁶Mg excess in the igneous inclusions does not exclude ²⁶Al from being a heat source for planetary melting. In large, early formed planetesimals, cooling below the closure temperature of the Al‐Mg system may be too late for any evidence for live ²⁶Al (in the form of ²⁶Mg excess) to be preserved. Thus, growing evidence exists that chondritic meteorites represent the products of a complex, multi‐stage history of accretion, parent body modification, disruption and re‐accretion.     

Comparison of Ground-Based and Space-Based Longitudinal Magnetograms

We compare photospheric line-of-sight magnetograms from the Synoptic Optical Long-term Investigations of the Sun (SOLIS) Vector Spectro-Magnetograph (VSM) instrument with observations from the 150-foot Solar Tower at Mt. Wilson Observatory (MWO), the Helioseismic and Magnetic Imager (HMI) on the Solar Dynamics Observatory (SDO), and the Michelson Doppler Imager (MDI) on the Solar and Heliospheric Observatory (SOHO). We find very good agreement between VSM and the other data sources for both disk-averaged flux densities and pixel-by-pixel measurements. We show that the VSM mean flux density time series is of consistently high signal-to-noise ratio with no significant zero offsets. We discuss in detail some of the factors ?C spatial resolution, flux dependence, and position on the solar disk ?C affecting the determination of scaling between VSM and SOHO/MDI or SDO/HMI magnetograms. The VSM flux densities agree well with spatially smoothed data from MDI and HMI, although the scaling factors show a clear dependence on flux density. The factor to convert VSM to HMI increases with increasing flux density (from ??1 to ??1.5). The nonlinearity is smaller for the VSM vs. SOHO/MDI scaling factor (from ??1 to ??1.2).     

Constraints on the formation environment of two chondrule‐like igneous particles from comet 81P/Wild 2

Using chemical and petrologic evidence and modeling, we deduce that two chondrule‐like particles named Iris and Callie, from Stardust cometary track C2052,12,74, formed in an environment very similar to that seen for type II chondrules in meteorites. Iris was heated near liquidus, equilibrated, and cooled at ≤100 °C h^‐1 and within ≈2 log units of the IW buffer with a high partial pressure of Na such as would be present with dust enrichments of ≈10³. There was no detectable metamorphic, nebular, or aqueous alteration. In previous work, Ogliore et al. (2012) reported that Iris formed late, >3 Myr after CAIs, assuming ²⁶Al was homogenously distributed, and was rich in heavy oxygen. Iris may be similar to assemblages found only in interplanetary dust particles and Stardust cometary samples called Kool particles. Callie is chemically and isotopically very similar, but not identical to Iris.     

Spectro-Polarimetric Observations and Non-Lte Modeling of Ellerman Bombs

Ellerman bombs are bright emission features observed in the wings of Hα, usually in the vicinity of magnetic concentrations. Here we show that they can also be detected in the Ca II infrared triplet lines, which are easier to interpret and therefore allow for more detailed diagnostics. We present full Stokes observations of the 849.8 and 854.2 nm lines acquired with the new spectro-polarimeter SPINOR. The data show no significant linear polarization at the level of 3 × 10⁻⁴. The circular polarization profiles exhibit measureable signals with a very intricate pattern of peaks. A non-LTE analysis of the spectral profiles emerging from these features reveals the presence of strong downflows (∼10 {km s⁻¹}) in a hot layer between the upper photosphere and the lower chromosphere. Visiting Astronomers, National Solar Observatory, operated by the Association of Universities for Research in Astronomy, Inc. (AURA), under cooperative agreement with the National Science Foundation. The National Center for Atmospheric Research (NCAR) is sponsored by the National Science Foundation, USA.     

Benthic Fluxes of Dissolved Inorganic Nitrogen in a Coastal Lagoon of the Northern Adriatic Sea: an Interpretation of Spatial Variability Based on Sediment Features and Infauna Activity

Abstract. Dark respiration rates, dissolved inorganic nitrogen (DIN) fluxes and nitrification rates were measured at two sites in the microtidal Sacca di Goro lagoon in September 2000. DIN fluxes correlated with the biomass of the dominant macrofauna species (the amphipod Corophium spp. at station Giralda and the polychaete Neanthes spp. at station Faro). Respiration (> 6 mmol O₂ m⁻²h⁻¹) and ammonium fluxes (> 80μmol N m⁻²h⁻¹) were higher at station Giralda despite the lower organic matter content (4.5 %) and lower macrofauna biomass (4 g AFDW m⁻²). At both sites ammonium fluxes were significantly correlated with the biomass of the benthic infauna, but Corophium stimulated ammonium NH₄⁺ fluxes 3-fold compared to Neanthes. The amphipod also enhanced nitrification rates (> 300 μmol N m⁻²h⁻¹) due to the high density of its burrows, the higher NH₄⁺ regeneration rates and the enhanced oxygen supply to the bacteria.     

Challenges for creating a site-specific groundwater-use record for the Ozark Plateaus aquifer system (central USA) from 1900 to 2010

Hydrologic budgets to determine groundwater availability are important tools for water-resource managers. One challenging component for developing hydrologic budgets is quantifying water use through time because historical and site-specific water-use data can be sparse or poorly documented. This research developed a groundwater-use record for the Ozark Plateaus aquifer system (central USA) from 1900 to 2010 that related county-level aggregated water-use data to site-specific well locations and aquifer units. A simple population-based linear model, constrained to 0 million liters per day in 1900, provided the best means to extrapolate groundwater-withdrawal rates pre-1950s when there was a paucity of water-use data. To disaggregate county-level data to individual wells across a regional aquifer system, a programmatic hierarchical process was developed, based on the level of confidence that a well pumped groundwater for a specific use during a specific year. Statistical models tested on a subset of the best-available site-specific water-use data provided a mechanism to bracket historic groundwater use, such that groundwater-withdrawal rates ranged, on average, plus or minus 38% from modeled values. Groundwater withdrawn for public supply and domestic use accounted for between 48 and 74% of total groundwater use since 1901, highlighting that groundwater provides an important drinking-water resource. The compilation, analysis, and spatial and temporal extrapolation of water-use data remain a challenging task for water scientists, but is of paramount importance to better quantify groundwater use and availability.