Capture into first-order resonances and long-term stability of pairs of equal-mass planets

Massive planets form within the lifetime of protoplanetary disks, and therefore, they are subject to orbital migration due to planet–disk interactions. When the first planet reaches the inner edge of the disk, its migration stops and consequently the second planet ends up locked in resonance with the first one. We detail how the resonant trapping works comparing semi-analytical formulae and numerical simulations. We restrict to the case of two equal-mass coplanar planets trapped in first-order resonances, but the method can be easily generalized. We first describe the family of resonant stable equilibrium points (zero-amplitude libration orbits) using series expansions up to different orders in eccentricity as well as a non-expanded Hamiltonian. Then we show that during convergent migration the planets evolve along these families of equilibrium points. Eccentricity damping from the disk leads to a final equilibrium configuration that we predict precisely analytically. The fact that observed multi-exoplanetary systems are rarely seen in resonances suggests that in most cases the resonant configurations achieved by migration become unstable after the removal of the protoplanetary disk. Here we probe the stability of the resonances as a function of planetary mass. For this purpose, we fictitiously increase the masses of resonant planets, adiabatically maintaining the low-amplitude libration regime until instability occurs. We discuss two hypotheses for the instability, that of a low-order secondary resonance of the libration frequency with a fast synodic frequency of the system, and that of minimal approach distance between planets. We show that secondary resonances do not seem to impact resonant systems at low amplitude of libration. Resonant systems are more stable than non-resonant ones for a given minimal distance at close encounters, but we show that the latter nevertheless play the decisive role in the destabilization of resonant pairs. We show evidence that as the planetary mass increases and the minimal distance between planets gets smaller in terms of mutual Hill radius, the region of stability around the resonance center shrinks, until the equilibrium point itself becomes unstable.     

Implications for behavior of volatile elements during impacts—Zinc and copper systematics in sediments from the Ries impact structure and central European tektites

Moldavites are tektites genetically related to the Ries impact structure, located in Central Europe, but the source materials and the processes related to the chemical fractionation of moldavites are not fully constrained. To further understand moldavite genesis, the Cu and Zn abundances and isotope compositions were measured in a suite of tektites from four different substrewn fields (South Bohemia, Moravia, Cheb Basin, Lusatia) and chemically diverse sediments from the surroundings of the Ries impact structure. Moldavites are slightly depleted in Zn (~10–20%) and distinctly depleted in Cu (>90%) relative to supposed sedimentary precursors. Moreover, the moldavites show a wide range in δ⁶⁶Zn values between 1.7 and 3.7‰ (relative to JMC 3‐0749 Lyon) and δ⁶⁵Cu values between 1.6 and 12.5‰ (relative to NIST SRM 976) and are thus enriched in heavy isotopes relative to their possible parent sedimentary sources (δ⁶⁶Zn = ?0.07 to +0.64‰; δ⁶⁵Cu = ?0.4 to +0.7‰). In particular, the Cheb Basin moldavites show some of the highest δ⁶⁵Cu values (up to 12.5‰) ever observed in natural samples. The relative magnitude of isotope fractionation for Cu and Zn seen here is opposite to oxygen‐poor environments such as the Moon where Zn is significantly more isotopically fractionated than Cu. One possibility is that monovalent Cu diffuses faster than divalent Zn in the reduced melt and diffusion will not affect the extent of Zn isotope fractionation. These observations imply that the capability of forming a redox environment may aid in volatilizing some elements, accompanied by isotope fractionation, during the impact process. The greater extent of elemental depletion, coupled with isotope fractionation of more refractory Cu relative to Zn, may also hinge on the presence of carbonyl species of transition metals and electromagnetic charge, which could exist in the impact‐induced high‐velocity jet of vapor and melts.     

Porous,S‐bearing silica in metal‐sulfide nodules and in the interchondrule clastic matrix in two EH3 chondrites

Two new occurrences of porous, S‐bearing, amorphous silica are described within metal‐sulfide nodules (MSN) and as interchondrule patches in EH3 chondrites SAH 97072 and ALH 84170. This porous amorphous material, which was first reported from sulfide‐bearing chondrules, consists of sinewy SiO₂‐rich areas containing S with minor Na or Ca as well as Fe, Mg, and Al. Some pores contain minerals including pyrite, pyrrhotite, and anhydrite. Most pores appear vacant or contain unidentified material that is unstable under analytical conditions. Niningerite, olivine, enstatite, albite, and kumdykolite occur enclosed within porous silica patches. Porous silica is commonly interfingered with cristobalite suggesting its amorphous structure resulted from high‐temperature quenching. We interpret the S‐bearing porous silica to be a product of silicate sulfidation, and the Na, Ca, Fe, Mg, and Al detectable within this material are chemical residues of sulfidized silicates and metal. The occurrence of porous silica in the cores of MSN, which are considered to be pre‐accretionary objects, suggests the sulfidizing conditions occurred prior to final parent‐body solidification. Ubiquitous S‐bearing porous silica among sulfide‐bearing chondrules, MSN, and in the interchondrule clastic matrix, suggests that similar sulfidizing conditions affected all the constituents of these EH3 chondrites.     

Variation in Coronal Activity from Solar Cycle 24 Minimum to Maximum Using Three-Dimensional Reconstructions of the Coronal Electron Density from STEREO/COR1

Three-dimensional electron density distributions in the solar corona are reconstructed for 100 Carrington rotations (CR 2054?–?2153) during 2007/03?–?2014/08 using the spherically symmetric method from polarized white-light observations with the inner coronagraph (COR1) onboard the twin Solar Terrestrial Relations Observatory (STEREO). These three-dimensional electron density distributions are validated by comparison with similar density models derived using other methods such as tomography and a magnetohydrodynamics (MHD) model as well as using data from the Solar and Heliospheric Observatory (SOHO)/Large Angle and Spectrometric Coronagraph (LASCO)-C2. Uncertainties in the estimated total mass of the global corona are analyzed based on differences between the density distributions for COR1-A and -B. Long-term variations of coronal activity in terms of the global and hemispheric average electron densities (equivalent to the total coronal mass) reveal a hemispheric asymmetry during the rising phase of Solar Cycle 24, with the northern hemisphere leading the southern hemisphere by a phase shift of 7?–?9 months. Using 14 CR (\(\approx13\)-month) running averages, the amplitudes of the variation in average electron density between Cycle 24 maximum and Cycle 23/24 minimum (called the modulation factors) are found to be in the range of 1.6?–?4.3. These modulation factors are latitudinally dependent, being largest in polar regions and smallest in the equatorial region. These modulation factors also show a hemispheric asymmetry: they are somewhat larger in the southern hemisphere. The wavelet analysis shows that the short-term quasi-periodic oscillations during the rising and maximum phases of Cycle 24 have a dominant period of 7?–?8 months. In addition, it is found that the radial distribution of the mean electron density for streamers at Cycle 24 maximum is only slightly larger (by \(\approx30\%\)) than at cycle minimum.     

Spectral Trends of Solar Bursts at Sub-THz Frequencies

Previous sub-THz studies were derived from single-event observations. We here analyze for the first time spectral trends for a larger collection of sub-THz bursts. The collection consists of a set of 16 moderate to small impulsive solar radio bursts observed at 0.2 and 0.4 THz by the Solar Submillimeter-wave Telescope (SST) in 2012?–?2014 at El Leoncito, in the Argentinean Andes. The peak burst spectra included data from new solar patrol radio telescopes (45 and 90 GHz), and were completed with microwave data obtained by the Radio Solar Telescope Network, when available. We critically evaluate errors and uncertainties in sub-THz flux estimates caused by calibration techniques and the corrections for atmospheric transmission, and introduce a new method to obtain a uniform flux scale criterion for all events. The sub-THz bursts were searched during reported GOES soft X-ray events of class C or larger, for periods common to SST observations. Seven out of 16 events exhibit spectral maxima in the range 5?–?40 GHz with fluxes decaying at sub-THz frequencies (three of them associated to GOES class X, and four to class M). Nine out of 16 events exhibited the sub-THz spectral component. In five of these events, the sub-THz emission fluxes increased with a separate frequency from that of the microwave spectral component (two classified as X and three as M), and four events have only been detected at sub-THz frequencies (three classified as M and one as C). The results suggest that the THz component might be present throughout, with the minimum turnover frequency increasing as a function of the energy of the emitting electrons. The peculiar nature of many sub-THz burst events requires further investigations of bursts that are examined from SST observations alone to better understand these phenomena.     

Effects of Steady Flow on Magnetoacoustic-Gravity Surface Waves: I. The Weak Field Case

Magnetoacoustic gravity (MAG) waves have been studied for some time. In this article, we investigate the effect that a shear flow at a tangential discontinuity embedded in a gravitationally stratified and magnetised plasma has on MAG surface waves. The dispersion relation found is algebraically analogous to the relation of the non-flow cases obtained by Miles and Roberts (Solar Phys. 141, 205, 1992), except for the introduction of a Doppler-shifted frequency for the eigenvalue. This feature, however, introduces rather interesting physics, including the asymmetric presence of forward- and backward-propagating surface waves. We find that increasing the equilibrium flow speed leads to a shift in the permitted regions of propagation for surface waves. For most wave number combinations this leads to the fast mode being completely removed, as well as more limited phase speed regimes for slow-mode propagation. We also find that upon increasing the flow, the phase speeds of the backward propagating waves are increased. Eventually, at high enough flow speeds, the wave’s direction of propagation is reversed and is in the positive direction. However, the phase speed of the forward-propagating wave remains mainly the same. For strong enough flows we find that the Kelvin–Helmholtz instability can also occur when the forward- and backward-propagating modes couple.     

The Interaction of Successive Coronal Mass Ejections: A Review

We present a review of the different aspects associated with the interaction of successive coronal mass ejections (CMEs) in the corona and inner heliosphere, focusing on the initiation of series of CMEs, their interaction in the heliosphere, the particle acceleration associated with successive CMEs, and the effect of compound events on Earth’s magnetosphere. The two main mechanisms resulting in the eruption of series of CMEs are sympathetic eruptions, when one eruption triggers another, and homologous eruptions, when a series of similar eruptions originates from one active region. CME?–?CME interaction may also be associated with two unrelated eruptions. The interaction of successive CMEs has been observed remotely in coronagraphs (with the Large Angle and Spectrometric Coronagraph Experiment – LASCO – since the early 2000s) and heliospheric imagers (since the late 2000s), and inferred from in situ measurements, starting with early measurements in the 1970s. The interaction of two or more CMEs is associated with complex phenomena, including magnetic reconnection, momentum exchange, the propagation of a fast magnetosonic shock through a magnetic ejecta, and changes in the CME expansion. The presence of a preceding CME a few hours before a fast eruption has been found to be connected with higher fluxes of solar energetic particles (SEPs), while CME?–?CME interaction occurring in the corona is often associated with unusual radio bursts, indicating electron acceleration. Higher suprathermal population, enhanced turbulence and wave activity, stronger shocks, and shock?–?shock or shock?–?CME interaction have been proposed as potential physical mechanisms to explain the observed associated SEP events. When measured in situ, CME?–?CME interaction may be associated with relatively well organized multiple-magnetic cloud events, instances of shocks propagating through a previous magnetic ejecta or more complex ejecta, when the characteristics of the individual eruptions cannot be easily distinguished. CME?–?CME interaction is associated with some of the most intense recorded geomagnetic storms. The compression of a CME by another and the propagation of a shock inside a magnetic ejecta can lead to extreme values of the southward magnetic field component, sometimes associated with high values of the dynamic pressure. This can result in intense geomagnetic storms, but can also trigger substorms and large earthward motions of the magnetopause, potentially associated with changes in the outer radiation belts. Future in situ measurements in the inner heliosphere by Solar Probe+ and Solar Orbiter may shed light on the evolution of CMEs as they interact, by providing opportunities for conjunction and evolutionary studies.     

Role of sea surface temperature and rainfall in determining the stock and fishery of the common octopus (Octopus vulgaris,Mollusca, Cephalopoda) in Tunisia

Octopus (Octopus vulgaris, Mollusca, Cephalopoda) is an important and valuable fishery resource on the eastern and southern coasts of Tunisia, but its landings are highly variable. This paper explores the effect of environment on octopus catch per unit effort (CPUE) during a 12‐year period, through correlation analyses and the incorporation into surplus production models of sea surface temperature (SST) and rainfall data collected during cold (January–May) and hot (August–October) seasons. CLIMPROD software was used to select the appropriate model and fit it to the fishery and environment data. In both seasons, SST significantly contributed to CPUE variability; fishery production was influenced positively by cold season SST but negatively by hot season SST. Due to a poor fit with cold season data, the impact of rainfall was analysed only for the hot season, during which it has a positive effect on production. Results are discussed in view of the life‐cycle of octopus and the dynamics of the Tunisian fishery. This first study of octopus variability in Tunisia highlights the necessity to incorporate environmental influence into stock assessment and management advice.     

Chemical signature of intermediate water masses along western Portuguese margin

Although the circulation of intermediate water masses in the eastern North Atlantic remains poorly defined, the presence of fresher intermediate waters, the Sub-Artic (SAIW) and the Antarctic Intermediate Water (AAIW), as well the saline intermediate Mediterranean Water (MW), has been tracked using biogeochemical properties. Here we assess the hydrographic and chemical structures of intermediate waters along the western Portuguese margin by examining the vertical distributions and property-property plots of chemical tracers (oxygen and nutrients). AAIW was traced by low oxygen and high nutrients, while SAIW was recognized by low nutrients. The Mediterranean Water (MW) undercurrent is shown to spread towards the eastern flank of Gorringe bank. Concurrently, the fresher waters gained salt by direct incorporation of MW, while this water was enriched in nutrients on its way northward and westward owing, to a great extent, to the entrainment of an AAIW branch. The distributions of nutrients and apparent oxygen utilization are discussed in terms of regional ocean circulation. Our analysis suggests a circulation pattern of the various intermediate waters along the western Portuguese margin: MW extends all over the area, but its presence is more pronounced around cape St. Vincent; SAIW apparently moves southward, reaching the Gorringe bank region, and AAIW flows northward along the coast and around the bank.     

郯庐断裂带(安徽段)及邻区的动力学分析与区域构造演化

依据区域构造层次划分,采用构造筛分法,层层深入,层层筛分,确定发生于各个不同时代地层/岩层内的断裂活动的同期及叠加的应力场特征。综合所有的同期应力场特征及辅以叠加的应力场特征来验证,从而确定了一个连续的、完整的断裂活动的应力场演化序列;结合区域构造变形特征分析,阐明郯庐断裂带(安徽段)的构造演化。应力场分析显示:晚三叠-早侏罗世应力场为北北西—南南东或近南北向挤压,属古特提斯构造域,断裂发生同造山走滑;早白垩世早期,应力场为北西—南东向挤压,断裂发生左行走滑运动,中国东部处于西环太平洋构造域;早白垩世晚期—古新世(始新世),区域发生北西—南东向伸展作用,断裂处于伸展断陷作用阶段;新生代,受区域上近东西向的挤压作用影响,断裂发生挤压逆冲兼右行走滑作用。