Diffusion Of Orbits Research Articles

Harnessing orbital Hall effect for efficient orbital torque in light metal vanadium

The orbital Hall effect depicts the conversion of charge current to orbital current in nonmagnetic materials without spin–orbit coupling. This absence of spin–orbit coupling enables the light metals serve as sources of orbital current exploited as the information carrier to be applied to the information technology. Here, we investigate current-induced torques in vanadium/ferromagnet (V/FM, FM = Fe, Co, Ni81Fe19) bilayers via spin-torque ferromagnetic resonance (ST-FMR) system. The sign reversal confirms that the orbital Hall effect exists in light metal V, and the orbital torque in V/Co and V/Ni81Fe19 bilayers is dominant. By performing the V thickness dependence of conversion efficiency, we determined the orbital diffusion length of 3.61 nm for V. Our experiment demonstrates that light metals can be used as novel materials in spin–orbit devices, and our research focuses on the orbital freedom of the electron and provides new content for the study of orbital dynamics.

The Contribution of Cornelian Cherry (Cornus mas L.) Alcoholic Beverages on the Sensory, Nutritional and Anti-Nutritional Characteristics—In Vitro and In Silico Approaches

Food producers have focused on novel and attractive raw materials with functional properties. Cornelian cherry (Cornus mas L.) fruits contain numerous compounds that may be beneficial for health. Objective: This study aimed to compare and assess the physicochemical properties and amygdalin levels in brandy and liquor prepared from frozen cornelian cherry fruits. Density functional theory-based B3LYP functionals were used to analyze the spectral and optical properties of amygdalin. The contents of the compounds and volatile products of amygdalin decay were found in two spirituose beverages of Cornus mas, using HPLC and GC-MS. Significant differences in their physicochemical properties were detected between the samples. Alcoholic beverages based on cornelian cherry fruits were rich in a wide range of functional ingredients with a low concentration of amygdalin. In silico analysis showed that orbital density diffusion has a major effect on the physical properties of amygdalin, while differences between the polarities of water and ethanol had no noticeable effect on the spectral properties of the compound. Cornelian cherry-based alcoholic drinks might be interesting functional products with rich aromatic bouquets. The amygdalin concentration is low enough to pose no toxicological threat, but rather shapes the tastory bouquet of the products. Levels of amygdalin may be controlled using the same analytical methods for solutions with different ethanol–water ratios.

Magneto-Optical Detection of the Orbital Hall Effect in Chromium.

The orbital Hall effect has been theoretically predicted but its direct observation is a challenge. Here, we report the magneto-optical detection of current-induced orbital accumulation at the surface of a light 3d transition metal, Cr. The orbital polarization is in-plane, transverse to the current direction, and scales linearly with current density, consistent with the orbital Hall effect. Comparing the thickness-dependent magneto-optical measurements with abinitio calculations, we estimate an orbital diffusion length in Cr of 6.6±0.6 nm.

Quasi-periodic eruptions from mildly eccentric unstable mass transfer in galactic nuclei

ABSTRACT We propose that the recently observed quasi-periodic eruptions (QPEs) in galactic nuclei are produced by unstable mass transfer due to Roche lobe overflow of a low-mass main-sequence star in a mildly eccentric (e ∼ 0.5) orbit. We argue that the QPE emission is powered by circularization shocks, but not directly by black hole (BH) accretion. Our model predicts the presence of a time-steady accretion disc that is bolometrically brighter than the time-averaged QPE luminosity, but primarily emits in the extreme-ultraviolet. This is consistent with the quiescent soft X-ray emission detected in between the eruptions in eROSITA QPE1, QPE2, and GSN 069. Such accretion discs have an unusual νLν ∝ ν12/7 optical spectrum. The lifetime of the bright QPE phase, 102–103 yr, is set by mass-loss triggered by ram-pressure interaction between the star and the accretion disc fed by the star itself. We show that the stellar orbits needed to explain QPEs can be efficiently created by the Hills breakup of tight stellar binaries provided that (i) the stellar binary orbit is tidally hardened before the breakup due to diffusive growth of the f-mode amplitude and (ii) the captured star’s orbit decays by gravitational wave emission without significant orbital angular momentum diffusion (which is the case for low-mass BHs, MBH ≲ 106 M⊙). We conclude by discussing the implications of our model for hyper-velocity stars, extreme mass ratio inspirals, repeating partial TDEs, and related stellar phenomena in galactic nuclei.

Large damping-like torque and efficient current-induced magnetization reversal in Ti/Tb–Co/Cr structures

Seeking the magnetic heterostructures with large current-induced torque efficiency is currently one of the core hotspots in spintronics. In this work, we report the large and composition-dependent damping-like (DL) torque in the structure consisting of light metal Cr and Ti layers and a ferrimagnetic Tb–Co layer. The DL torque efficiency in the structures reaches a maximum (around −0.55) as the Tb content in the Tb–Co layer is in the range of 0.15–0.18. This composition-dependent behavior is different from that observed in the usual heavy-metal/ferrimagnetic structures. We also demonstrated the efficient current-induced magnetization reversal in these structures with a low threshold current density down to 8×1010 A/m2. In comparison, only very low efficiency values of −0.06 and −0.086 are obtained in the Ti/Co/Cr and Ti/Tb–Co/SiN control samples, respectively, suggesting that the large DL torque in the Ti/Tb–Co/Cr structures may originate from the orbital Hall effect in the Cr metal. By fitting the Cr layer thickness dependence of the torque efficiency with a simple orbital current diffusion model, we obtained an effective orbital Hall angle of −0.57±0.02 for the Ti/Tb0.85Co0.15/Cr samples. This work demonstrated the possibility to enhance the orbital torque effect by using the magnetic layer containing the element with strong spin–orbit coupling.

Giant efficiency of long-range orbital torque in Co/Nb bilayers

We report unambiguously experimental evidence of a strong orbital current in Nb films with weak spin-orbit coupling via the spin-torque ferromagnetic resonance (ST-FMR) spectrum for Fe/Nb and Co/Nb bilayers. The sign change of the damping-like torque in Co/Nb demonstrates a large spin-orbit correlation and thus great efficiency of orbital torque in Co/Nb. By studying the efficiency as a function of the thickness of Nb sublayer, we reveal a long orbital diffusion length (~3.1 nm) of Nb. Further planar Hall resistance (PHE) measurements at positive and negative applying current confirm the nonlocal orbital transport in ferromagnetic-metal/Nb heterostructures.

The phase space structure in the vicinity of vertical Lyapunov orbits around L1,2 in a barred galaxy model

ABSTRACT We study the phase space structure and the orbital diffusion from the vicinity of the vertical Lyapunov periodic orbits around the unstable Lagrangian points L1,2 in a 3D barred galaxy model. By perturbing the initial conditions of these periodic orbits, we detected the following five types of orbital structures in the 4D spaces of section: (i) Ring-like structures, sticky for large time intervals to the unstable invariant manifolds of the simple and double unstable vertical Lyapunov periodic orbits. (ii) 2D tori belonging to quasi-periodic orbits around stable periodic orbits existing in the region. They are associated either with vertical stable periodic orbits around L4,5 or with ‘stable anomalous’ periodic orbits. (iii) Orbits sticky for large time intervals to these tori, forming ‘sticky tori’, before they slowly depart from them. (iv) Clouds of points that have a strong chaotic behaviour. Such clouds of consequents have slow diffusion speeds, because they are hindered by the presence of the tori around the ‘stable anomalous’ periodic orbits. (v) Toroidal zones consisting of points that stick for long time on the unstable invariant manifolds of the ‘unstable anomalous’ periodic orbits. By continuing the integration, we find that eventually they become strongly chaotic, retaining however small diffusion speeds, due to the presence of the tori around the stable anomalous periodic orbits.

Chaotic diffusion of asteroids in the exterior 1:2 mean motion resonance with Mars

ABSTRACT The inner asteroid belt between 2.1 and 2.5 au is of particular dynamical significance because it is the dominant source of both chondritic meteorites and near-Earth asteroids. This inner belt is bounded by an eccentricity-type secular resonance and by the 1:3 mean motion resonance with Jupiter. Unless asteroid perihelia are low enough to allow scattering by Mars, escape requires transport to one of the bounding resonances. In addition Yarkovsky forces are generally ineffective in changing either the eccentricity and/or inclination for asteroids with diameter ≳30 km. Thus, large asteroids with pericentres far from Mars may only escape from the inner belt through large changes in their eccentricities. In this paper, we study chaotic diffusion of orbits near the 1:2 mean motion resonance with Mars in a systematic way. We show that, while chaotic orbital evolution in both resonant and non-resonant orbits increase the dispersion of the inclinations and eccentricities, it does not significantly change their mean values. We show further that, while the dispersive growth is greatest for resonant orbits, at high e the resonance acts to mitigate asteroid scattering by Mars - making the asteroid lifetime in the belt longer than it would have been for a non-resonant orbit. For asteroids of all sizes in both resonant and non-resonant orbits, the changes in eccentricity needed to account for the observations cannot be achieved by gravitational forces alone. The role of resonant trapping in protecting asteroids from encounters with Mars is also analysed.

Non-resonant relaxation of anisotropic globular clusters

ABSTRACT Globular clusters are dense stellar systems whose core slowly contracts under the effect of self-gravity. The rate of this process was recently found to be directly linked to the initial amount of velocity anisotropy: tangentially anisotropic clusters contract faster than radially anisotropic ones. Furthermore, initially anisotropic clusters are found to generically tend towards more isotropic distributions during the onset of contraction. Chandrasekhar’s ‘non-resonant’ (NR) theory of diffusion describes this relaxation as being driven by a sequence of local two-body deflections along each star’s orbit. We explicitly tailor this NR prediction to anisotropic clusters, and compare it with N-body realizations of Plummer spheres with varying degrees of anisotropy. The NR theory is shown to recover remarkably well the detailed shape of the orbital diffusion and the associated initial isotropization, up to a global multiplicative prefactor which increases with anisotropy. Strikingly, a simple effective isotropic prescription provides almost as good a fit, as long as the cluster’s anisotropy is not too strong. For these more extreme clusters, accounting for long-range resonant relaxation may be necessary to capture these clusters’ long-term evolution.

Role of orbital magnetic resonance imaging in early detection of graves’ orbitopathy and disease activity

We aim to evaluate feasibility of using orbital diffusion tensor imaging (DTI) magnetic resonance imaging (MRI) of extraocular muscles (EOMs) in patients with Graves’ orbitopathy (GO) versus clinical activity score (CAS) in early detection of GO activity. This case control study was conducted on 20 consecutive patients (10 males, 10 females with a mean age of 35.50±13.65 years) with Graves’ orbitopathy and 10 age- and sex-matched volunteers without any thyroid abnormality as a health control (HC). The patients and HCs underwent DTI MRI of the orbit in the coronal plane. The mean diffusivity (MD) was calculated. Thyroid stimulating hormone receptor antibody (TRAb) was measured using third generation thyroid binding inhibiting immunoglobulin (TBII) with ELISA method. CAS score, according to the standardized criteria of the European Group on Graves Orbitopathy (EUGOGO), was calculated for the patients. GO patients’ EOMs showed significantly higher MD values and higher compared to HCs’ (P < 0.001). Median CAS score was 4. A statistically significant positive correlation was only detected between CAS score and inferior rectus (IR) MD (r=.360, p=.023).

Exploring the Origin of Thick Disks Using the NewHorizon and Galactica Simulations

Abstract Ever since a thick disk was proposed to explain the vertical distribution of the Milky Way disk stars, its origin has been a recurrent question. We aim to answer this question by inspecting 19 disk galaxies with stellar mass greater than 1010 M ⊙ in recent cosmological high-resolution zoom-in simulations: galactica and NewHorizon. The thin and thick disks are reasonably reproduced by the simulations with scale heights and luminosity ratios as observed. We then spatially classify the thin and thick disks and find that the thick disk stars are older, metal-poorer, kinematically hotter, and higher in accreted star fraction, while both disks are dominated by the stars formed in situ. Half of the in situ stars in the thick disks are formed before the galaxies develop their disks, and the rest are formed in spatially and kinematically thinner disks and then thickened with time by heating. However, the 19 galaxies have various properties and evolutionary routes, highlighting the need for statistically large samples to draw general conclusions. We conclude from our simulations that the thin and thick disk components are not entirely distinct in terms of formation processes but rather markers of the evolution of galactic disks. Moreover, as the combined result of the thickening of the existing disk stars and the continued formation of young thin disk stars, the vertical distribution of stars does not change much after the disks settle, pointing to the modulation of both orbital diffusion and star formation by the same confounding factor: the proximity of galaxies to marginal stability.

Strong chemical tagging with APOGEE: 21 candidate star clusters that have dissolved across the Milky Way disc

ABSTRACT Chemically tagging groups of stars born in the same birth cluster is a major goal of spectroscopic surveys. To investigate the feasibility of such strong chemical tagging, we perform a blind chemical tagging experiment on abundances measured from APOGEE survey spectra. We apply a density-based clustering algorithm to the 8D chemical space defined by [Mg/Fe], [Al/Fe], [Si/Fe], [K/Fe], [Ti/Fe], [Mn/Fe], [Fe/H], and [Ni/Fe], abundances ratios which together span multiple nucleosynthetic channels. In a high-quality sample of 182 538 giant stars, we detect 21 candidate clusters with more than 15 members. Our candidate clusters are more chemically homogeneous than a population of non-member stars with similar [Mg/Fe] and [Fe/H], even in abundances not used for tagging. Group members are consistent with having the same age and fall along a single stellar-population track in log g versus Teff space. Each group’s members are distributed over multiple kpc, and the spread in their radial and azimuthal actions increases with age. We qualitatively reproduce this increase using N-body simulations of cluster dissolution in Galactic potentials that include transient winding spiral arms. Observing our candidate birth clusters with high-resolution spectroscopy in other wavebands to investigate their chemical homogeneity in other nucleosynthetic groups will be essential to confirming the efficacy of strong chemical tagging. Our initially spatially compact but now widely dispersed candidate clusters will provide novel limits on chemical evolution and orbital diffusion in the Galactic disc, and constraints on star formation in loosely bound groups.

Nekhoroshev Estimates for the Survival Time of Tightly Packed Planetary Systems

Abstract N-body simulations of nonresonant, tightly packed planetary systems have found that their survival time (i.e., time to first close encounter) grows exponentially with their interplanetary spacing and planetary masses. Although this result has important consequences for the assembly of planetary systems by giant collisions and their long-term evolution, this underlying exponential dependence is not understood from first principles, and previous attempts based on orbital diffusion have only yielded power-law scalings. We propose a different picture, where large deviations of the system from its initial conditions is due to a few slowly developing high-order resonances. Thus, we show that the survival time of the system T can be estimated using a heuristic motivated by Nekhoroshev’s theorem, and obtain a formula for systems away from overlapping two-body mean-motion resonances as , where P is the average Keplerian period, a is the average semimajor axis, Δa ≪ a is the difference between the semimajor axes of neighboring planets, μ is the planet-to-star mass ratio, and c 1 and c 2 are dimensionless constants. We show that this formula is in good agreement with numerical N-body experiments for c 1 = 5 × 10−4 and c 2 = 8.

Assessment of optic nerve and optic tract alterations in patients with orbital space-occupying lesions using probabilistic diffusion tractography.

To investigate the diffusion changes in both the optic nerve and optic tract in orbital space-occupying lesion patients with decreased visual acuity, and its clinical significance using probabilistic diffusion tractography (PDT). Twenty patients with orbital space-occupying lesions and 25 age- and gender-matched healthy persons were included. All patients and controls underwent routine orbital magnetic resonance imaging and diffusion tensor imaging (DTI), using a 3.0T magnetic resonance scanner (Trio Tim Siemens). After the image data were preprocessed, each DTI parameters of the optic nerve and optic tract was obtained by PDT, including fractional anisotropy (FA), mean diffusivity (MD), axial diffusivity (AD) and radial diffusivity (RD). The asymmetry index (AI) of each parameter was calculated. Compared the parameters of the affected side optic nerve and ipsilateral optic tract with the contralateral side by paired sample t-test; compared AI of parameters of optic nerve and optic tract between the patient group and the control group by independent sample t-test. Patients were divided into three subgroups according to the low vision grade standard of WHO, compared the FA and AI of FA between the three subgroups by single factor variance analysis. The affected side optic nerve presented significantly decreased FA, increased MD, AD, and RD values compared to the unaffected side (P<0.05). The AI of FA, MD, AD, and RD of optic nerve in the patients was significantly higher than that of the controls (P<0.05). The comparison results of the optic tract showed that there was no significant difference between the patient group and control group in terms of the bilateral optic tracts in patients (P>0.05). The AIs of the FA value of the optic nerve in the eyesight <0.1 subgroup was significantly higher than that in the other groups (P<0.05). FA, MD, AD, and RD of the affected side optic nerve of the orbital space-occupying lesions have significantly changed, the FA value is the most sensitive. The PDT could be a useful tool to provide valid quantitative markers of optic nerve injuries and evaluate the severity of orbital diseases, which other examinations cannot be acquired.

The Galactic disc in action space as seen byGaiaDR2

The quality and quantity of 6D stellar position-velocity measurements in the second Gaia data release (DR2) allows to study small-scale structure in the orbit distribution of the Galactic disc beyond the immediate Solar neighborhood. We investigate the distribution of orbital actions $(J_R,J_\phi=L_z,J_z)$ of $\sim 3.5$ million stars within $1.5~\text{kpc}$ of the Sun, for which precise actions can be calculated from Gaia DR2 alone. This distribution $n(J_R,L_z)$ reveals a remarkable amount of sub-structure. The known moving groups in the $(U,V)$-plane of the Solar neighborhood correspond to overdensities in $(J_R,L_z)$, as expected. But $n(J_R,L_z)$ also exhibits a wealth of density clumps and ridges that extend towards higher $J_R$. These $n(J_R,L_z)$ features are most prominent among orbits that stay close to the Galactic plane and remain consistently visible out to $\sim1.5~\text{kpc}$, as opposed to the sub-structure in velocity space. Some of these $n(J_R,L_z)$ ridges resemble features expected from rapid orbit diffusion along particular ($J_R,L_z$)-directions in the presence of various resonances. Several of these $n(J_R,L_z)$ structures show a dramatic imbalance of stars moving in or out, suggesting that stars are not phase-mixed along orbits or on resonant orbits. Orbital action and angle space of stars in Gaia DR2 is therefore highly structured over kpc-scales, and appears to be very informative for modeling studies of non-axisymmetric structure and resonances in the Galactic disc.

Astronomical calibration of the Ypresian timescale: implications for seafloor spreading rates and the chaotic behavior of the solar system?

Abstract. To fully understand the global climate dynamics of the warm early Eocene with its reoccurring hyperthermal events, an accurate high-fidelity age model is required. The Ypresian stage (56–47.8 Ma) covers a key interval within the Eocene as it ranges from the warmest marine temperatures in the early Eocene to the long-term cooling trends in the middle Eocene. Despite the recent development of detailed marine isotope records spanning portions of the Ypresian stage, key records to establish a complete astronomically calibrated age model for the Ypresian are still missing. Here we present new high-resolution X-ray fluorescence (XRF) core scanning iron intensity, bulk stable isotope, calcareous nannofossil, and magnetostratigraphic data generated on core material from ODP Sites 1258 (Leg 207, Demerara Rise), 1262, 1263, 1265, and 1267 (Leg 208, Walvis Ridge) recovered in the equatorial and South Atlantic Ocean. By combining new data with published records, a 405 kyr eccentricity cyclostratigraphic framework was established, revealing a 300–400 kyr long condensed interval for magnetochron C22n in the Leg 208 succession. Because the amplitudes are dominated by eccentricity, the XRF data help to identify the most suitable orbital solution for astronomical tuning of the Ypresian. Our new records fit best with the La2010b numerical solution for eccentricity, which was used as a target curve for compiling the Ypresian astronomical timescale (YATS). The consistent positions of the very long eccentricity minima in the geological data and the La2010b solution suggest that the macroscopic feature displaying the chaotic diffusion of the planetary orbits, the transition from libration to circulation in the combination of angles in the precession motion of the orbits of Earth and Mars, occurred ∼ 52 Ma. This adds to the geological evidence for the chaotic behavior of the solar system. Additionally, the new astrochronology and revised magnetostratigraphy provide robust ages and durations for Chrons C21n to C24n (47–54 Ma), revealing a major change in spreading rates in the interval from 51.0 to 52.5 Ma. This major change in spreading rates is synchronous with a global reorganization of the plate–mantle system and the chaotic diffusion of the planetary orbits. The newly provided YATS also includes new absolute ages for biostratigraphic events, magnetic polarity reversals, and early Eocene hyperthermal events. Our new bio- and magnetostratigraphically calibrated stable isotope compilation may act as a reference for further paleoclimate studies of the Ypresian, which is of special interest because of the outgoing warming and increasingly cooling phase. Finally, our approach of integrating the complex comprehensive data sets unearths some challenges and uncertainties but also validates the high potential of chemostratigraphy, magnetostratigraphy, and biostratigraphy in unprecedented detail being most significant for an accurate chronostratigraphy.

The destruction of an Oort Cloud in a rich stellar cluster

It is possible that the formation of the Oort Cloud dates back to the earliest epochs of solar system history. At that time, the Sun was almost certainly a member of the stellar cluster, where it was born. Since the solar birth cluster is likely to have been massive (1000--10 000 Msol), and therefore long-lived, an issue concerns the survival of such a primordial Oort Cloud. We have investigated this issue by simulating the orbital evolution of Oort Cloud comets for several hundred Myr, assuming the Sun to start its life as a typical member of such a massive cluster. We have devised a synthetic representation of the relevant dynamics, where the cluster potential is represented by a King model, and about 20 close encounters with individual cluster stars are selected and integrated based on the solar orbit and the cluster structure. Thousands of individual simulations are made, each including 3 000 comets with orbits with three different initial semi-major axes. Practically the entire initial Oort Cloud is found to be lost for our choice of semi-major axes (5 000--20 000 au), independent of the cluster mass, although the chance of survival is better for the smaller cluster, since in a certain fraction of the simulations the Sun orbits at relatively safe distances from the dense cluster centre. For the range of birth cluster sizes that we investigate, a primordial Oort Cloud will likely survive only as a small inner core with semi-major axes < 3 000 au. Such a population of comets would be inert to orbital diffusion into an outer halo and subsequent injection into observable orbits. Some mechanism is therefore needed to accomplish this transfer, in case the Oort Cloud is primordial and the birth cluster did not have a low mass. From this point of view, our results lend some support to a delayed formation of the Oort Cloud, that occurred after the Sun had left its birth cluster.

Resonant thickening of self-gravitating discs: imposed or self-induced orbital diffusion in the tightly wound limit

The secular thickening of a self-gravitating stellar galactic disc is investigated using the dressed collisionless Fokker–Planck equation and the inhomogeneous multicomponent Balescu–Lenard equation. The thick WKB limits for the diffusion fluxes are found using the epicyclic approximation, while assuming that only radially tightly wound transient spirals are sustained by the disc. This yields simple quadratures for the drift and diffusion coefficients, providing a clear understanding of the positions of maximum vertical orbital diffusion within the disc, induced by fluctuations either external or due to the finite number of particles. These thick limits also offer a consistent derivation of a thick disc Toomre parameter, which is shown to be exponentially boosted by the ratio of the vertical to radial scaleheights. Dressed potential fluctuations within the disc statistically induce a vertical bending of a subset of resonant orbits, triggering the corresponding increase in vertical velocity dispersion. When applied to a tepid stable tapered disc perturbed by shot noise, these two frameworks reproduce qualitatively the formation of ridges of resonant orbits towards larger vertical actions, as found in direct numerical simulations, but overestimates the time-scale involved in their appearance. Swing amplification is likely needed to resolve this discrepancy, as demonstrated in the case of razor-thin discs. Other sources of thickening are also investigated, such as fading sequences of slowing bars, or the joint evolution of a population of giant molecular clouds within the disc.

Collisionless loss-cone refilling: there is no final parsec problem

Coalescing massive black hole binaries, formed during galaxy mergers, are expected to be a primary source of low frequency gravitational waves. Yet in isolated gas-free spherical stellar systems, the hardening of the binary stalls at parsec-scale separations owing to the inefficiency of relaxation-driven loss-cone refilling. Repopulation via collisionless orbit diffusion in triaxial systems is more efficient, but published simulation results are contradictory. While sustained hardening has been reported in simulations of galaxy mergers with $N \sim 10^6$ stars and in early simulations of rotating models, in isolated non-rotating triaxial models the hardening rate continues to fall with increasing N, a signature of spurious two-body relaxation. We present a novel approach for studying loss cone repopulation in galactic nuclei. Since loss cone repopulation in triaxial systems owes to orbit diffusion, it is a purely collisionless phenomenon and can be studied with an approximated force calculation technique, provided the force errors are well behaved and sufficiently small. We achieve this using an accurate fast multipole method and define a proxy for the hardening rate that depends only on stellar angular momenta. We find that the loss cone is efficiently replenished even in very mildly triaxial models (with axis ratios 1 : 0.9 : 0.8). Such triaxiality is unavoidable following galactic mergers and can drive binaries into the gravitational wave regime. We conclude that there is no final parsec problem.

Stability of multiplanet systems in binaries

When exploring the stability of multiplanet systems in binaries, two parameters are normally exploited: the critical semimajor axis ac computed by Holman and Wiegert (1999) within which planets are stable against the binary perturbations, and the Hill stability limit Delta determining the minimum separation beyond which two planets will avoid mutual close encounters. Our aim is to test whether these two parameters can be safely applied in multiplanet systems in binaries or if their predictions fail for particular binary orbital configurations. We have used the frequency map analysis (FMA) to measure the diffusion of orbits in the phase space as an indicator of chaotic behaviour. First we revisited the reliability of the empirical formula computing ac in the case of single planets in binaries and we find that, in some cases, it underestimates by 10-20% the real outer limit of stability. For two planet systems, the value of Delta is close to that computed for planets around single stars, but the level of chaoticity close to it substantially increases for smaller semimajor axes and higher eccentricities of the binary orbit. In these configurations ac also begins to be unreliable and non linear secular resonances with the stellar companion lead to chaotic behaviour well within ac, even for single planet systems. For two planet systems, the superposition of mean motion resonances, either mutual or with the binary companion, and non linear secular resonances may lead to chaotic behaviour in all cases. We have developed a parametric semiempirical formula determining the minimum value of the binary semimajor axis, for a given eccentricity of the binary orbit, below which stable two planet systems cannot exist.