Secular Timescales Research Articles

A detailed dynamical model for inclination-only dependent lunisolar resonances. Effect on the “eccentricity growth” mechanism

The focus of this paper is on inclination-only dependent lunisolar resonances, which shape the dynamics of a MEO (Medium Earth Orbit) object over secular time scales (i.e. several decades). Following the formalism of Daquin et al. (2022), we discuss an analytical model yielding the correct form of the separatrices of each one of the major lunisolar resonances in the “action” space (i,e) (inclination, eccentricity) for any given semi-major axis a. We then highlight how our method is able to predict and explain the main structures found numerically in Fast Lyapunov Indicator (FLI) cartography. We focus on explaining the dependence of the FLI maps from the initial phase of the argument of perigee ω and of the longitude of the ascending node Ω of the object and of the moon ΩL. In addition, on the basis of our model, we discuss the role played by the Ω-ΩL and the 2Ω-ΩL resonances, which overlap with the inclination-only dependent ones as they sweep the region for increasing values of a, generating large domains of chaotic motion. Our results provide a framework useful in designing low-cost satellite deployment or space debris mitigation strategies, exploiting the natural dynamics of lunisolar resonances that increase an object’s eccentricity up until it reaches a domain where friction leads to atmospheric re-entry.

Sulfur isotope fractionation derived from reaction-transport modelling in the Eastern Equatorial Pacific

Microbial sulfate reduction in subseafloor sediments regulates a significant portion of the marine organic matter burial flux. Over secular timescales, sulfate reduction is the fundamental process connecting the biogeochemical cycles of sulfur, carbon, oxygen and phosphorus. Similar to carbon reduction, sulfate reduction is associated with a strong isotope fractionation process that allows us to track this process through time. It depends on a variety of factors and it has been argued previously that systematic differences between shallow and deep-sea environments might explain secular changes in the marine S-isotope ratio. However, observational data of in situ fractionation from deep-sea areas are scarce. Here we use a reaction-transport model to analyse the S-isotope fractionation during microbial sulfate reduction in the interstitial water of Ocean Drilling Program (ODP) Site 1226 (Leg 201). We find that the upper 100 m below seafloor are best explained with fractionation around −76‰, whereas below this depth the degree of fractionation drops to around −42‰. We propose that this shift is caused by changes in the ratio of the rate of microbial sulfate reduction relative to the rate of abiotic sulfide oxidation. Because large parts of deep oceans are characterized by exceedingly low sulfate reduction rates, this process may be widespread and possibly explain why pyrite S-isotope data suggest that the average S-isotope fractionation is around −50‰, rather than the theoretically predicted value below −70‰. Supplementary material: Supplementary figures and model results are available at https://doi.org/10.6084/m9.figshare.c.5976772 Thematic collection: This article is part of the Sulfur in the Earth system collection available at: https://www.lyellcollection.org/cc/sulfur-in-the-earth-system

Plio-Pleistocene Perth Basin water temperatures and Leeuwin Current dynamics (Indian Ocean) derived from oxygen and clumped-isotope paleothermometry

Abstract. The Pliocene sedimentary record provides a window into Earth's climate dynamics under warmer-than-present boundary conditions. However, the Pliocene cannot be considered a stable warm climate that constitutes a solid baseline for middle-of-the-road future climate projections. The increasing availability of time-continuous sedimentary archives (e.g., marine sediment cores) reveals complex temporal and spatial patterns of Pliocene ocean and climate variability on astronomical timescales. The Perth Basin is particularly interesting in that respect because it remains unclear if and how the Leeuwin Current sustained the comparably wet Pliocene climate in Western Australia, as well as how it influenced Southern Hemisphere paleoclimate variability. To constrain Leeuwin Current dynamics in time and space, this project obtained eight clumped-isotope Δ47 paleotemperatures and constructed a new orbitally resolved planktonic foraminifera (Trilobatus sacculifer) stable isotope record (δ18O) for the Plio-Pleistocene (4–2 Ma) interval of International Ocean Discovery Program (IODP) Site U1459. These new data complement an existing TEX86 record from the same site and similar planktonic isotope records from the Northern Carnarvon Basin (Ocean Drilling Program (ODP) Site 763 and IODP Site U1463). The comparison of TEX86 and Δ47 paleothermometers reveals that TEX86 likely reflects sea surface temperatures (SSTs) with a seasonal warm bias (23.8–28.9 ∘C), whereas T. sacculifer Δ47 calcification temperatures probably echo mixed-layer temperatures at the studied Site U1459 (18.9–23.2 ∘C). The isotopic δ18O gradient along a 19–29∘ S latitudinal transect, between 3.9 and 2.2 Ma, displays large variability, ranging between 0.5 ‰ and 2.0 ‰. We use the latitudinal δ18O gradient as a proxy for Leeuwin Current strength, with an inverse relationship between both. The new results challenge the interpretation that suggested a tectonic event in the Indonesian Throughflow as the cause for the rapid steepening of the isotopic gradient (0.9 ‰ to 1.5 ‰) around 3.7 Ma. The tectonic interpretation appears obsolete as it is now clear that the 3.7 Ma steepening of the isotopic gradient is intermittent, with flat latitudinal gradients (∼0.5 ‰) restored in the latest Pliocene (2.9–2.6 Ma). Still, the new analysis affirms that a combination of astronomical forcing of wind patterns and eustatic sea level controlled Leeuwin Current intensity. On secular timescales, a period of relatively weak Leeuwin Current is observed between 3.7 and 3.1 Ma. Notably, this interval is marked by cooler conditions throughout the Southern Hemisphere. In conclusion, the intensity of the Leeuwin Current and the latitudinal position of the subtropical front are both long-range effects of the same forcing: heat transport through the Indonesian Throughflow (ITF) valve and its propagation through Indian Ocean poleward heat transport. The common ITF forcing explains the observed coherence of Southern Hemisphere ocean and climate records.

The dark mass signature in the orbit of S2

Context.The Schwarzschild precession of star S2, which orbits the massive black hole at the centre of the Milky Way, has recently been detected with the result of ∼12 arcmin per orbit. The same study also improved the 1σupper bound on a possibly present dark continuous extended mass distribution (e.g. faint stars, stellar remnants, stellar mass black holes, or dark matter) within the orbit of S2 to ∼4000 M⊙. The secular (i.e. net) effect of an extended mass onto a stellar orbit is known as mass precession, and it runs counter to the Schwarzschild precession.Aims.We explore a strategy for how the Schwarzschild and mass precessions can be separated from each other despite their secular interference, by pinpointing their signatures within a single orbit. From these insights, we then seek to assess the prospects for improving the dark mass constraints in the coming years.Methods.We analysed the dependence of the osculating orbital elements and of the observables on true anomaly, and we compared these functions for models with and without extended mass. We then translated the maximum astrometric impacts within one orbit to detection thresholds given hypothetical data of different accuracies. These theoretical investigations were then supported and complemented by an extensive mock-data fitting analysis.Results.We have four main results. 1. While the mass precession almost exclusively impacts the orbit in the apocentre half, the Schwarzschild precession almost exclusively impacts it in the pericentre half, allowing for a clear separation of the effects. 2. Data that are limited to the pericentre half are not sensitive to a dark mass, while data limited to the apocentre half are, but only to a limited extent. 3. A full orbit of data is required to substantially constrain a dark mass. 4. For a full orbit of astrometric and spectroscopic data, the astrometric component in the pericentre halff plays the stronger role in constraining the dark mass than the astrometric data in the apocentre half. Furthermore, we determine the 1σdark mass detection thresholds given different datasets on one full orbit. In particular, with a full orbit of data of 50 microarcsec (VLTI/GRAVITY) and 10 km s−1(VLT/SINFONI) precision, the 1σbound would improve to ∼1000 M⊙, for example.Conclusions.The current upper dark mass bound of ∼4000 M⊙has mainly been obtained from a combination of GRAVITY and VLT/NACO astrometric data, as well as from SINFONI spectroscopic data, where the GRAVITY data were limited to the pericentre half. From our results 3 and 4, we know that all components were thereby crucial, but also that the GRAVITY data were dominant in the astrometric components in constraining the dark mass. From results 1 and 2, we deduce that a future population of the apocentre half with GRAVITY data points will substantially further improve the dark mass sensitivity of the dataset, and we note that at the time of publication, we already entered this regime. In the context of the larger picture, our analysis demonstrates how precession effects that interfere on secular timescales can clearly be distinguished from each other based on their distinct astrometric signatures within a single orbit. The extension of our analysis to the Lense-Thirring precession should thus be of value in order to assess future spin detection prospects for the galactic centre massive black hole.

Historical geomorphological adjustments of an Upper Rhine sub-tributary over the two last centuries (

Reconstructing evolutionary trajectories of river systems gives valuable insights into the main drivers (i.e. hydro-climatic versus anthropogenic) of their historical morphodynamics. Understanding past and modern adjustments of hydrosystems is therefore a key for appropriate sustainable management schemes. In this respect, the historical evolution (~150 years) of a 6 km dynamic reach of an Upper Rhine sub-tributary, the Bruche River, is thoroughly studied using a wide array of planimetric and topographic data (ancient maps and longitudinal profile, orthophotos, LiDAR). The primary aim is to precisely quantify the lateral and vertical mobility, taking uncertainties into account. Lateral mobility is studied using a specifically designed indicator, the Aggregated Migration rate Index (AMI), which enables precise assessment of planform changes in m.yr-1 on elementary sub-reaches (~100 m). A twofold decrease in mean lateral mobility in the mid-20th century, most probably related to functional channel modifications associated with the installation of an underground pipeline, represents the most striking result. Vertical mobility is analysed through the comparison of diachronic LiDAR data (decadal timescale) and historical archive (secular timescale). From the mid-20th century onwards, an unexpected general aggradation of the riverbed (~0.6 m) has occurred, for which several explanations are discussed (i.e. bank erosion, deforestation, sediment release following weir lowering), though remaining speculative. Overall, our results show that historical geomorphological adjustments are primarily controlled by various anthropogenic factors. As the Bruche hosts one of the highest concentrations of spawning beds of emblematic fish species in the French Upper Rhine, this study lays the foundation for future restoration strategies.

Oscillating dynamical friction on galactic bars by trapped dark matter

ABSTRACT The dynamic evolution of galactic bars in standard ΛCDM models is dominated by angular momentum loss to the dark matter haloes via dynamical friction. Traditional approximations to dynamical friction are formulated using the linearized collisionless Boltzmann equation and have been shown to be valid in the fast limit, i.e. for rapidly slowing bars. However, the linear assumption breaks down within a few dynamical periods for typical slowly evolving bars, which trap a significant amount of disc stars and dark matter in resonances. Recent observations of the Galactic bar imply this slow regime at the main bar resonances. We formulate the time-dependent dynamical friction in the slow limit and explore its mechanism in the general slow regime with test-particle simulations. Here, angular momentum exchange is dominated by resonantly trapped orbits which slowly librate around the resonances. In typical equilibrium haloes, the initial phase-space density within the trapped zone is higher at lower angular momentum. Since the libration frequency falls towards the separatrix, this density contrast winds up into a phase-space spiral, resulting in a dynamical friction that oscillates with ∼Gyr periods and damps over secular time-scales. We quantify the long-term behaviour of this torque with secular perturbation theory, and predict two observable consequences: (i) The phase-space spirals may be detectable in the stellar disc where the number of windings encodes the age of the bar. (ii) The torque causes weak oscillations in the bar’s pattern speed, overlaying the overall slowdown – while not discussed, this feature is visible in previous simulations.

Numerical renormalization-group-based approach to secular perturbation theory.

Perturbation theory is a crucial tool for many physical systems, when exact solutions are not available, or nonperturbative numerical solutions are intractable. Naive perturbation theory often fails on long timescales, leading to secularly growing solutions. These divergences have been treated with a variety of techniques, including the powerful dynamical renormalization group (DRG). Most of the existing DRG approaches rely on having analytic solutions up to some order in perturbation theory. However, sometimes the equations can only be solved numerically. We reformulate the DRG in the language of differential geometry, which allows us to apply it to numerical solutions of the background and perturbation equations. This formulation also enables us to use the DRG in systems with background parameter flows and, therefore, extend our results to any order in perturbation theory. As an example, we apply this method to calculate the soliton-like solutions of the Korteweg-de Vries equation deformed by adding a small damping term. We numerically construct DRG solutions which are valid on secular timescales, long after naive perturbation theory has broken down.

In-depth analysis of evolving binary systems that produce nova eruptions

ABSTRACT This study is the direct continuation of a previous work performed by Hillman et al., where they used their feedback dominated numerical simulations to model the evolution of four initial models with white dwarf (WD) masses of 0.7 and $1.0\, \mathrm{M}_\odot$ and red dwarf (RD) masses of 0.45 and $0.7\, \mathrm{M}_\odot$ from first Roche lobe contact of the donor RD, over a few times 109 yr, until the RD was eroded down to below $0.1\, \mathrm{M}_\odot$. This study presents an in-depth analysis of their four models complimented by three models with a higher WD mass of $1.25\, \mathrm{M}_\odot$, one of which comprises an oxygen-neon (ONe) core. Common features were found for all seven models on a secular time-scale as well as on a cyclic time-scale. On the other hand, certain features were found that are strongly dependent either on the WD or the RD mass but are indifferent to the other of the two. Additionally, a model with a WD composed of an ONe core was compared with its corresponding carbon oxygen (CO) core WD model and found to have a significant impact on the heavy element abundances in the ejecta composition.

The Influence of the Secular Perturbation of an Intermediate-mass Companion. II. Ejection of Hypervelocity Stars from the Galactic Center

Abstract There is a population of stars with velocities in excess of 500 km s−1 relative to the Galactic center. Many, perhaps most, of these hypervelocity stars (HVSs) are B stars similar to the disk and S stars in a nuclear cluster around a supermassive black hole (SMBH) near Sgr A⋆. In Paper I of this series, we showed that the eccentricity of the stars emerged from a hypothetical disk around the SMBH that can be rapidly excited by the secular perturbation of its intermediate-mass companion (IMC), and we suggested IRS 13E as a potential candidate for the IMC. Here we show that this process leads to an influx of stars on parabolic orbits to the proximity of Sgr A⋆ on a secular timescale of a few megayears. This timescale is much shorter than the diffusion timescale into the lost cone through either the classical or the resonant relaxation. Precession of the highly eccentric stars’ longitude of periastron, relative to that of the IMC, brings them to its proximity within a few megayears. The IMC’s gravitational perturbation scatters a fraction of the stars from nearly parabolic to hyperbolic orbits with respect to the SMBH. Their follow-up close encounters with the SMBH induce them to escape with hypervelocity. This scenario is a variant of the hypothesis proposed by Hills based on the anticipated breakup of some progenitor binary stars in the proximity of the SMBH, and its main objective is to account for the limited life span of the known HVSs. We generalize our previous numerical simulations of this process with a much wider range of orbital configurations. We demonstrate the robustness and evaluate the efficiency of this channel of HVS formation. From these numerical simulations, we infer observable kinematic properties for the HVSs.

Stable Biological Production in the Eastern Equatorial Pacific Across the Plio‐Pleistocene Transition (∼3.35–2.0 Ma)

AbstractUpwelling within the Eastern Equatorial Pacific (EEP) Ocean is a key factor for the Earth's climate because it supports >10% of the present‐day biological production. The dynamics of upwelling in the EEP across the Plio‐Pleistocene transition—an interval particularly relevant for understanding near‐future warming due to Anthropocene‐like atmospheric carbon‐dioxide levels—have been intensively studied for the region east of the East Pacific Rise. In contrast, changes of the equatorial upwelling regime in the open Pacific Ocean west of this oceanographic barrier have received markedly less attention. We therefore provide new proxy records from Ocean Drilling Program Site 849 located within the EEP open‐ocean upwelling regime. Our target interval (∼3.35–2.0 Ma) covers the Plio‐Pleistocene transition characterized by the intensification of Northern Hemisphere Glaciation (iNHG). We use benthic δ18O values to generate a new, high‐resolution age model for Site 849, and sand‐accumulation rates together with benthic δ13C values to evaluate net export production. Although showing temporary substantial glacial‐interglacial variations, our records indicate stability in net export production on secular timescales across the iNHG. We suggest the following processes to have controlled the long‐term evolution of primary productivity at Site 849. First, nutrient export from the high latitudes to the EEP; second, a successive shoaling of the Pacific nutricline during the studied interval; and third, a simultaneous reduction in dust‐borne iron input.

The JADE code: Coupling secular exoplanetary dynamics and photo-evaporation

Close-in planets evolve under extreme conditions, which raises questions about their origins and current nature. Two evolutionary mechanisms thought to play a predominant role are orbital migration, which brings them close to their star, and atmospheric escape under the resulting increased irradiation. Yet their relative roles remain poorly understood, in part because we lack numerical models that couple the two mechanisms with high precision and on secular timescales. To address this need, we developed the Joining Atmosphere and Dynamics for Exoplanets (JADE) code, which simulates the secular atmospheric and dynamical evolution of a specific planet around its star, and can include the perturbation induced by a distant third body. On the dynamical side, the three dimensional evolution of the orbit is modeled under stellar and planetary tidal forces, a relativistic correction, and the action of the distant perturber. On the atmospheric side, the vertical structure of the atmosphere is integrated over time based on its thermodynamical properties, inner heating, and the evolving stellar irradiation, which results, in particular, in extreme ultraviolet induced photo-evaporation. The JADE code is benchmarked on GJ436 b, which is a prototype of the evaporating giants on eccentric, misaligned orbits at the edge of the hot Neptunes desert. We confirm previous results that the orbital architecture of GJ436 b is well explained by Kozai migration and bring to light a strong interplay between its atmospheric and orbital evolution. During the resonance phase, the atmosphere pulsates in tune with the Kozai cycles, which leads to stronger tides and an earlier migration. This triggers a strong atmospheric evaporation several billion years after the planet formed, refining the paradigm that mass loss is dominant in the early age of close-in planets. These results suggest that the edge of the desert could be formed of warm Neptunes whose evaporation was delayed by Kozai migration. They strengthen the importance of coupling atmospheric and dynamical evolution over secular timescales, which the JADE code will allow for one to simulate for a wide range of systems.

Analysis of 20th century surface air temperature using linear dynamical modes.

A Bayesian Linear Dynamical Mode (LDM) decomposition method is applied to isolate robust modes of climate variability in the observed surface air temperature (SAT) field. This decomposition finds the optimal number of internal modes characterized by their own time scales, which enter the cost function through a specific choice of prior probabilities. The forced climate response, with time dependence estimated from state-of-the-art climate-model simulations, is also incorporated in the present LDM decomposition and shown to increase its optimality from a Bayesian standpoint. On top of the forced signal, the decomposition identifies five distinct LDMs of internal climate variability. The first three modes exhibit multidecadal scales, while the remaining two modes are attributable to interannual-to-decadal variability associated with El Niño-Southern oscillation; all of these modes contribute to the secular climate signal-the so-called global stadium wave-missing in the climate-model simulations. One of the multidecadal LDMs is associated with Atlantic multidecadal oscillation. The two remaining slow modes have secular time scales and patterns exhibiting regional-to-global similarities to the forced-signal pattern. These patterns have a global scale and contribute significantly to SAT variability over the Southern and Pacific Oceans. In combination with low-frequency modulation of the fast LDMs, they explain the vast majority of the variability associated with interdecadal Pacific oscillation. The global teleconnectivity of the secular climate modes and their possible crucial role in shaping the forced climate response are the two key dynamical questions brought about by the present analysis.

Axisymmetric hydrodynamics in numerical relativity using a multipatch method

We describe a method of implementing the axisymmetric evolution of general-relativistic hydrodynamics and magnetohydrodynamics through modification of a multipatch grid scheme. In order to ease the computational requirements required to evolve the post-merger phase of systems involving binary compact massive objects in numerical relativity, it is often beneficial to take advantage of these system’s tendency to rapidly settle into states that are nearly axisymmetric, allowing for 2D evolution of secular timescales. We implement this scheme in the spectral Einstein code and show the results of application of this method to four test systems including viscosity, magnetic fields, and neutrino radiation transport. Our results show that this method can be used to quickly allow already existing 3D infrastructure that makes use of local coordinate system transformations to be made to run in axisymmetric 2D with the flexible grid creation capabilities of multipatch methods. Our code tests include a simple model of a binary neutron star postmerger remnant, for which we confirm the formation of a massive torus which is a promising source of post-merger ejecta.

A candidate secular variation model for IGRF-13 based on MHD dynamo simulation and 4DEnVar data assimilation

We have submitted a secular variation (SV) candidate model for the thirteenth generation of International Geomagnetic Reference Field model (IGRF-13) using a data assimilation scheme and a magnetohydrodynamic (MHD) dynamo simulation code. This is the first contribution to the IGRF community from research groups in Japan. A geomagnetic field model derived from magnetic observatory hourly means, and CHAMP and Swarm-A satellite data, has been used as input data to the assimilation scheme. We adopt an ensemble-based assimilation scheme, called four-dimensional ensemble-based variational method (4DEnVar), which linearizes outputs of MHD dynamo simulation with respect to the deviation from a dynamo state vector at an initial condition. The data vector for the assimilation consists of the poloidal scalar potential of the geomagnetic field at the core surface and flow velocity field slightly below the core surface. Dimensionless time of numerical geodynamo is adjusted to the actual time by comparison of secular variation time scales. For SV prediction, we first generate an ensemble of dynamo simulation results from a free dynamo run. We then assimilate the ensemble to the data with a 10-year assimilation window through iterations, and finally forecast future SV by the weighted sum of the future extension parts of the ensemble members. Hindcast of the method for the assimilation window from 2004.50 to 2014.25 confirms that the linear approximation holds for 10-year assimilation window with our iterative ensemble renewal method. We demonstrate that the forecast performance of our data assimilation and forecast scheme is comparable with that of IGRF-12 by comparing data misfits 4.5 years after the release epoch. For estimation of our IGRF-13SV candidate model, we set assimilation window from 2009.50 to 2019.50. We generate our final SV candidate model by linear fitting for the weighted sum of the ensemble MHD dynamo simulation members from 2019.50 to 2025.00. We derive errors of our SV candidate model by one standard deviation of SV histograms based on all the ensemble members.

Insights into the planetary dynamics of HD 206893 with ALMA

ABSTRACT Radial substructure in the form of rings and gaps has been shown to be ubiquitous among protoplanetary discs. This could be the case in exo-Kuiper belts as well, and evidence for this is emerging. In this paper, we present ALMA observations of the debris/planetesimal disc surrounding HD 206893, a system that also hosts two massive companions at 2 and 11 au. Our observations reveal a disc extending from 30 to 180 au, split by a 27 au wide gap centred at 74 au, and no dust surrounding the reddened brown dwarf (BD) at 11 au. The gap width suggests the presence of a 0.9MJup planet at 74 au, which would be the third companion in this system. Using previous astrometry of the BD, combined with our derived disc orientation as a prior, we were able to better constrain its orbit finding it is likely eccentric ($0.14^{+0.05}_{-0.04}$). For the innermost companion, we used radial velocity, proper motion anomaly, and stability considerations to show its mass and semimajor axis are likely in the ranges 4–100MJup and 1.4–4.5 au. These three companions will interact on secular time-scales and perturb the orbits of planetesimals, stirring the disc and potentially truncating it to its current extent via secular resonances. Finally, the presence of a gap in this system adds to the growing evidence that gaps could be common in wide exo-Kuiper belts. Out of six wide debris discs observed with ALMA with enough resolution, four to five show radial substructure in the form of gaps.

Global Hydromagnetic Simulations of Protoplanetary Disks with Stellar Irradiation and Simplified Thermochemistry

Abstract Outflows driven by large-scale magnetic fields likely play an important role in the evolution and dispersal of protoplanetary disks and in setting the conditions for planet formation. We extend our 2D-axisymmetric nonideal MHD model of these outflows by incorporating radiative transfer and simplified thermochemistry, with the dual aims of exploring how heating influences wind launching and illustrating how such models can be tested through observations of diagnostic spectral lines. Our model disks launch magnetocentrifugal outflows primarily through magnetic tension forces, so the mass-loss rate increases only moderately when thermochemical effects are switched on. For typical field strengths, thermochemical and irradiation heating are more important than magnetic dissipation. We furthermore find that the entrained vertical magnetic flux diffuses out of the disk on secular timescales as a result of nonideal MHD. Through postprocessing line radiative transfer, we demonstrate that spectral line intensities and moment-1 maps of atomic oxygen, the HCN molecule, and other species show potentially observable differences between a model with a magnetically driven outflow and one with a weaker, photoevaporative outflow. In particular, the line shapes and velocity asymmetries in the moment-1 maps could enable the identification of outflows emanating from the disk surface.

Compact-object Mergers in the Galactic Center: Evolution in Triaxial Clusters

Abstract There is significant observational evidence that a large fraction of galactic centers, including those in the Milky Way and M31, host a supermassive black hole (SMBH) embedded in a triaxial nuclear star cluster. In this work, we study the secular orbital evolution of binaries in these environments and characterize the regions and morphological properties of nuclear star clusters that lead to gravitational wave mergers and/or tidal captures. We show that even a modest level of triaxiality in the density distribution of a cluster (an ellipsoid with axis ratios of 0.7 and 0.95) dramatically enhances the merger rates in the central parsecs of the Galaxy by a factor of up to ∼10–30 relative to a spherical density distribution. Moreover, we show that the merger fraction of binaries with semimajor axes in the range 10–100 au remains above 10% for the entire central parsec of the cluster, reaching values close to unity at a distance of ∼0.2–0.4 pc from the SMBH. We understand this large merger efficiency in terms of two distinct mechanisms: (i) eccentricity oscillations driven by the dominant axisymmetric part of the cluster potential that are enhanced by the slow modulation of a binary’s angular momentum from the triaxial contribution, similar to the well-known octupole-level dynamics in three-body systems; and (ii) chaotic diffusion of eccentricities arising when the nodal precession timescale of a binary’s orbit about the SMBH becomes comparable to its characteristic secular timescale. Overall, our results indicate that galactic centers are significantly more collisional than previously thought, with mergers taking place up to the effective radii of their nuclear star clusters.

Secular dynamics of hierarchical multiple systems composed of nested binaries, with an arbitrary number of bodies and arbitrary hierarchical structure – III. Suborbital effects: hybrid integration techniques and orbit-averaging corrections

ABSTRACT The secularmultiple code, presented in two previous papers of this series, integrates the long-term dynamical evolution of multiple systems with any number of bodies and hierarchical structure, provided that the system is composed of nested binaries. In the formalism underlying secularmultiple, we previously averaged over all orbits in the system. This approximation significantly speeds up numerical integration of the equations of motion, making large population synthesis studies possible. However, the orbit averaging approximation can break down when the secular evolution time-scale of the system is comparable to or shorter than any of the orbital periods in the system. Here, we present an update to secularmultiple in which we incorporate hybrid integration techniques, and orbit-averaging corrections. With this update, the user can specify which orbits should be integrated directly (without averaging), or assuming averaged orbits. For orbits that are integrated directly, we implemented two integration techniques, one which is based on the regularized Kustaanheimo–Stiefel equations of motion in element form. We also implemented analytical orbit-averaging corrections for pairwise interactions to quadrupole order. The updates presented here provide more flexibility for integrating the long-term dynamical evolution of hierarchical multiple systems. By effectively combining direct integration and orbit averaging the long-term evolution can be accurately computed, but with significantly lower computational cost compared to existing direct N-body codes. We give a number of examples in which the new features are beneficial. Our updated code, which is written in c++ supplemented with a user-friendly interface in python, is freely available.

Nodal Precession in Closely Spaced Planet Pairs

Abstract Planet–planet perturbations can cause planets’ orbital elements to change on secular timescales. Previous work has evaluated the nodal precession rate for planets in the limit of low α (semimajor axis ratio; 0 < α ≤ 1). Our simulations show that systems at high α (or low period ratio), similar to multiplanet systems found in the Kepler survey, have a nodal precession rate that is more strongly dependent on eccentricity and inclination. We present a complete expansion of the nodal precession rate to fourth order in the disturbing function and show that this analytical solution much better describes the simulated N-body behavior of high-α planet pairs; at α ≈ 0.5, the higher-order solution, on average, reduces the median analytical error by a factor of 7.5 from linear theory and 6.2 from a similar expansion assuming low α. We set limits on eccentricity and inclination where the theory is precisely validated by N-body integrations, which can be useful in future secular treatments of planetary systems.

Plio‐Pleistocene Hemispheric (A)Symmetries in the Northern and Southern Hemisphere Midlatitudes

AbstractThe transition from the warm, stable climate of the Pliocene to the progressively colder glaciations of the Pleistocene, as well as the climate system's evolving response to stationary orbital forcing over the Pleistocene, beg important questions about fundamental climate processes relevant to understanding the impacts of modern anthropogenic forcing of the Earth's energy budget. Here, we gain insight into the evolution of Plio‐Pleistocene climate by generating an alkenone‐derived, orbitally resolved sea surface temperature (SST) record from Ocean Drilling Program Site 1125 in the southwest Pacific. We compare our data set to midlatitude and equatorial SST records and to the benthic ∂18O signal in order to evaluate similarities and differences in climate response between the hemispheres and across latitudes over the Plio‐Pleistocene. Secular trends indicate first‐order symmetry between the Northern and Southern Hemispheres in the magnitude of mean, glacial, and interglacial cooling. However, the tight coupling that is observed on both secular and orbital timescales between Northern Hemisphere, high latitude, and tropical upwelling climate throughout the last 4 Ma does not extend to Southern Hemisphere climate records as Northern Hemisphere glaciation intensifies in the late Pliocene. The 41‐kyr signal remains weak at Site 1125 across the late Pliocene transition but strengthens in conjunction with a major increase in global climate system sensitivity to obliquity forcing beginning around 1.8 Ma. Our analysis points to regionally varied responses across the late Pliocene transition and the emergence of a global feedback mechanism and strengthened obliquity‐band climate sensitivity just prior to the mid‐Pleistocene transition.