Eccentricity Damping Research Articles

Dynamic and Phase-Frequency Characteristics of Rotor Instability Induced by Steam Flow Excited Vibration in Seals

Steam flow excited vibration in seals seriously affects the seal-rotor stability. A mesh deformation based on user-defined functions was adopted to establish the multi-frequency whirl model, and the reliability of the simulation method was verified by experiments. The average effective damping and working ability of the fluid were proposed to analyse the stability of the seal. The mechanism of seal instability induced by steam flow excited vibration was revealed through the phase-frequency characteristics of exciting forces and displacements. The results show that direct damping decreases gradually with an increase in frequency, and the cross-coupling damping tends to be stable over 15 Hz. The average effective damping is more sensitive and accurate in predicting the seal stability. Effective damping decreases with increased frequency. Therefore, the rotor stability is decreased. Near the 12 Hz and 24 Hz frequencies, the average effective damping of eccentricity fluctuates, so the seal stability is poor. The negative effect of exciting forces increases, and the seal stability is improved when the eccentricity increases. When the phase difference between the excitation force and displacement changes, the seal stability decreases. The fundamental reason for rotor instability induced by steam flow excited vibration in seals is the sharp changes of phase difference caused by pressure fluctuations.

Repelling Planet Pairs by Ping-pong Scattering

The Kepler mission reveals a peculiar trough-peak feature in the orbital spacing of close-in planets near mean-motion resonances: a deficit and an excess that are, respectively, a couple of percent interior to and wide of the resonances. This feature has received two main classes of explanations: one involving eccentricity damping and the other scattering with small bodies. Here, we point out a few issues with the damping scenario and study the scattering scenario in more detail. We elucidate why scattering small bodies tends to repel two planets. As the small bodies random-walk in energy and angular momentum space, they tend to absorb fractionally more energy than angular momentum. This, which we call “ping-pong repulsion,” transports angular momentum from the inner to the outer planet and pushes the two planets apart. Such a process, even if ubiquitous, leaves identifiable marks only near first-order resonances: diverging pairs jump across the resonance quickly and produce the mean-motion resonance asymmetry. To explain the observed positions of the trough-peaks, a total scattering mass of order a few percent of the planet masses is required. Moreover, if this mass is dominated by a handful of Mercury-sized bodies, one can also explain the planet eccentricities as inferred from transit-time variations. Last, we suggest how these conditions may have naturally arisen during the late stages of planet formation.

A Recipe for Eccentricity and Inclination Damping for Partial-gap Opening Planets in 3D Disks

In a previous paper, we showed that, like the migration speed, the eccentricity damping efficiency is modulated linearly by the depth of the partial gap a planet carves in the disk surface density profile, resulting in less efficient e-damping compared to the prescription commonly used in population synthesis works. Here, we extend our analysis to 3D, refining our e-damping formula and studying how the inclination damping efficiency is also affected. We perform high-resolution 3D locally isothermal hydrodynamical simulations of planets with varying masses embedded in disks with varying aspect ratios and viscosities. We extract the gap profile and orbital damping timescales for fixed eccentricities and inclinations up to the disk scale height. The limit in gap depths below which vortices appear, in the low-viscosity case, happens roughly at the transition between classical type-I and type-II migration regimes. The orbital damping timescales can be described by two linear trends with a break around gap depths ∼80% and with slopes and intercepts depending on the eccentricity and inclination. These trends are understood on physical grounds and are reproduced by simple fitting formulas whose error is within the typical uncertainty of type-I torque formulas. Thus, our recipes for the gap depth and orbital damping efficiencies yield a simple description for planet–disk interactions to use in N-body codes in the case of partial-gap opening planets that is consistent with high-resolution 3D hydrosimulations. Finally, we show examples of how our novel orbital damping prescription can affect the outcome of population synthesis experiments.

Global N-body simulation of gap edge structures created by perturbations from a small satellite embedded in Saturn’s rings

Small satellites embedded in Saturn’s ring – Daphnis and Pan – open a clear gap. Observations by the Voyager and Cassini spacecrafts have revealed various striking features of the gap structure, such as the density waves, sharp edge, and vertical wall structure. In order to explain these features in a single simulation, we perform a high-resolution (N∼106−107) global full N-body simulation of gap formation by an embedded satellite considering gravitational interactions and inelastic collisions among all ring particles and the satellite, while these features have been mostly investigated separately with different theoretical approaches: the streamline models, 1D diffusion models, and local N-body simulation. As a first attempt of a series of papers, we here focus on the gap formation by separating satellite migration with fixing the satellite orbit in a Keplerian circular orbit. We reveal how the striking gap features – the density waves, sharp edge, and vertical wall structure – are simultaneously formed by an interplay of the satellite-ring and ring particle–particle interactions. In particular, we propose a new mechanism to quantitatively explain the creation of the vertical wall structure at the gap edge. Inelastic collisions between ring particles damp their eccentricity excited by the satellite’s perturbations to enhance the surface density at the gap edge, making its sharp edges more pronounced. We find the eccentricity damping process inevitably raises the vertical wall structures the most effectively in the second epicycle waves. Particle–particle collisions generally convert their lateral epicyclic motion into vertical motion. Because the excited epicyclic motion is the greatest near the ring edge and the epicycle motions are aligned in the first waves, the conversion is the most efficient in the gap edge of the second waves and the wall height is scaled by the satellite Hill radius, which are consistent with the observations.

Hydrodynamical evolution of black-hole binaries embedded in AGN discs – III. The effects of viscosity

ABSTRACT Stellar-mass binary black holes (BBHs) embedded in active galactic nucleus (AGN) discs offer a distinct dynamical channel to produce black hole mergers detected in gravitational waves by LIGO/Virgo. To understand their orbital evolution through interactions with the disc gas, we perform a suite of two-dimensional high-resolution, local shearing box, viscous hydrodynamical simulations of equal-mass binaries. We find that viscosity not only smooths the flow structure around prograde circular binaries,but also greatly raises their accretion rates. The torque associated with accretion may be overwhelmingly positive and dominate over the gravitational torque at a high accretion rate. However, the accreted angular momentum per unit mass decreases with increasing viscosity, making it easier to shrink the binary orbit. In addition, retrograde binaries still experience rapid orbital decay, and prograde eccentric binaries still experience eccentricity damping. Our numerical experiments further show that prograde binaries are more likely to be hardened if the physical sizes of the accretors are sufficiently small such that the accretion rate is reduced. The dependence of the binary accretion rate on the accretor size can be weaken through boosted accretion either due to a high viscosity or a more isothermal-like equation of state. Our results widen the explored parameter space for the hydrodynamics of embedded BBHs and demonstrate that their orbital evolution in AGN discs is a complex, multifaceted problem.

A recently formed ocean inside Saturn's moon Mimas.

Moons potentially harbouring a global ocean are tending to become relatively common objects in the Solar System1. The presence of these long-lived global oceans is generally betrayed by surface modification owing to internal dynamics2. Hence, Mimas would be the most unlikely place to look for the presence of a global ocean3. Here, from detailed analysis of Mimas's orbital motion based on Cassini data, with a particular focus on Mimas's periapsis drift, we show that its heavily cratered icy shell hides a global ocean, at a depth of 20-30 kilometres. Eccentricity damping implies that the ocean is likely to be less than 25 million years old and still evolving. Our simulations show that the ocean-ice interface reached a depth of less than 30 kilometres only recently (less than 2-3 million years ago), a time span too short for signs of activity at Mimas's surface to have appeared.

Dynamical instability in multi-orbiter systems with gas friction

ABSTRACT Closely packed multiplanet systems are known to experience dynamical instability if the spacings between the planets are too small. Such instability can be tempered by the frictional forces acting on the planets from gaseous discs. A similar situation applies to stellar-mass black holes embedded in active galactic nuclei discs around supermassive black holes. We use N-body integrations to evaluate how the frictional damping of orbital eccentricity affects the growth of dynamical instability for a wide range of K (the difference in the planetary semimajor axes in units of the mutual Hill radius) and (unequal) planet masses. We find that, in general, the stable region (large K) and unstable region (small K) are separated by a “grey zone”, where the (in)stability is not guaranteed. We report the numerical values of the critical spacing for stability Kcrit and the “grey zone” range in different systems, and provide fitting formulae for arbitrary frictional forcing strength. We show that the stability of a system depends on the damping time-scale τ relative to the zero-friction instability growth time-scale tinst: two-planet systems are stable if tinst ≳ τ; three-planet systems require tinst ≳ 10τ−100τ. When K is sufficiently small, tinst can be less than the synodic period between the planets, which makes frictional stabilization unlikely to occur. As K increases, tinst tends to grow exponentially, but can also fluctuate by a few orders of magnitude. We also devise a linear map to analyse the dynamical instability of the “planet + test mass” system, and find qualitative agreement with N-body simulations.

Tidal dissipation of binaries in asteroid pairs

Tidal dissipation in a celestial body can be used to probe its internal structure. Tides govern the orbital evolution of binary systems and therefore constraints on the interior of binary system members can be derived by knowing the age and tidal state of the binary system. For asteroids, age estimates are challenging due to a lack of direct observation of their surface. However, the age of asteroid pairs formed by rotational fission of a parent body can be derived from dynamical modeling, and as such can be used to constrain the age of binary systems existing within asteroid pairs. We study 13 binary asteroid systems existing in asteroid pairs by modeling their tidal locking and eccentricity damping timescales from tidal dissipation in the primaries and secondaries. We consider the impact of thermal torques on these timescales from the YORP and BYORP effects. The resulting constraints on the tidal dissipation ratio Q/k2 are compared to monolithic and rubble pile asteroid theories, showing that all secondaries are consistent with rubble piles with regolith layers greater than 3 m and suggest that Q/k2 for rubble piles increases with radius. A particular case is the first bound secondary of asteroid (3749) Balam, whose Q/k2 is constrained to be between 2.7 ×104 and 1.4 ×106, consistent with a rubble-pile with a regolith thickness between 30 m and 100 m.

Do all gaps in protoplanetary discs host planets?

Following the assumption that the disc substructures observed in protoplanetary discs originate from the interaction between the disc and the forming planets embedded therein, we aim to test if these putative planets could represent the progenitors of the currently observed giant exoplanets. We performed N-body simulations initially assuming three, four, five, or seven planets. Our model includes pebble and gas accretion, migration, damping of eccentricities and inclinations, disc-planet interaction, and disc evolution. We located the planets in the positions where the gaps in protoplanetary discs have been observed and we evolved the systems for 100 Myr including a few million years of gas disc evolution, while also testing three values of α viscosity. For planetary systems with initially three and four planets, we find that most of the growing planets lie beyond the radial-velocity (RV) detection limit of 5AU and only a small fraction of them migrate into the inner region. We also find that these systems have final eccentricities that are too low to be in agreement with the observed giant planet population. Systems initially consisting of five or seven planets become unstable after ≈40 Kyr of integration time. This clearly shows that not every gap can host a planet. The general outcome of our simulations – eccentricities that are too low – is independent of the disc’s viscosity and surface density. Further observations could either confirm the existence of an undetected population of wide-orbit giants or exclude the presence of such an undetected population to constrain how many planets hide in gaps even further.

On the interaction of pebble accreting embryos with the gaseous disc: importance of thermal forces

ABSTRACT A planetary embryo embedded in a gaseous disc can grow by pebble accretion while subjected to a gravitational force from the disc that changes its orbital elements. Usually, that force is considered to arise from the Lindblad and corotation resonances with the embryo. However, more important contributions exist for low-mass planets. Radiative thermal diffusion in the vicinity of embryos yields an additional contribution to the disc’s force that damps the eccentricity and inclination much more vigorously than the resonant interaction with the disc, and that in general induces fast inward migration. In addition, the irradiation of the disc by a hot embryo gives rise to an additional contribution that excites eccentricity and inclination, and induces outward migration. Which of the two contributions dominates depends on the embryo’s luminosity. We assess the importance of these contributions (termed thermal forces) on the dynamics and growth of a set of pebble-accreting embryos initially of Martian mass, by means of N-body simulations that include analytic expressions for the disc’s force. We find very different outcomes for the embryos subjected to thermal forces and those subjected only to resonant forces. Importantly, we find that the median final mass of the embryos subjected to thermal forces is nearly independent of the metallicity, whereas this mass roughly scales with the metallicity when they are subjected only to resonant forces. These results can be explained by the strong damping of eccentricity and inclination at low metallicity, which enhances the embryos’ accretion efficiency.

Exciting the transit timing variation phases of resonant sub-Neptunes

ABSTRACT There are excesses of sub-Neptunes just wide of period commensurabilities like the 3:2 and 2:1, and corresponding deficits narrow of them. Any theory that explains this period ratio structure must also explain the strong transit timing variations (TTVs) observed near resonance. Besides an amplitude and a period, a sinusoidal TTV has a phase. Often overlooked, TTV phases are effectively integration constants, encoding information about initial conditions or the environment. Many TTVs near resonance exhibit non-zero phases. This observation is surprising because dissipative processes that capture planets into resonance also damp TTV phases to zero. We show how both the period ratio structure and the non-zero TTV phases can be reproduced if pairs of sub-Neptunes capture into resonance in a gas disc while accompanied by a third eccentric non-resonant body. Convergent migration and eccentricity damping by the disc drives pairs to orbital period ratios wide of commensurability; then, after the disc clears, secular forcing by the third body phase shifts the TTVs. The scenario predicts that resonant planets are apsidally aligned and possess eccentricities up to an order of magnitude larger than previously thought.

A recipe for orbital eccentricity damping in the type-I regime for low-viscosity 2D discs

Context. It is well known that partial and deep gap opening depends on a disc’s viscosity; however, damping formulas for orbital eccentricities have only been derived at high viscosities, ignoring partial gap opening. Aims. In this work, we aim to obtain a simple formula to model eccentricity damping of the type-I regime in low-viscosity discs, where even small planets of a few to a few tens of Earth masses may start opening partial gaps in the gas surface density around their orbit. Methods. We performed high-resolution, 2D, locally isothermal hydrodynamical simulations of planets with varying masses on fixed orbits in discs with varying aspect ratios and viscosities. We determined the torque and power felt by the planet to ultimately derive migration and eccentricity damping timescales. Results. We first find a lower limit to the gap depths below which vortices appear; this happens roughly at the transition between type-I and classical type-II migration regimes. For the simulations that remain stable, we obtain a fit to the observed gap depth in the limit of vanishing eccentricities that is similar to the one currently used in the literature but accurate down to α = 3.16 × 10−5. We then record the eccentricity damping efficiency as a function of the observed gap depth and the initial eccentricity. When the planet has opened a deep enough gap such that the surface density is less than ~80% of the unperturbed disc surface density, a clear linear trend is observed independently of the planet’s eccentricity; at shallower gaps, this linear trend is preserved at low eccentricities, while it deviates to more efficient damping when e is comparable to the disc’s scale height. Both trends can be understood on theoretical grounds and are reproduced by a simple fitting formula. Conclusions. Our combined fits for the gap depth and eccentricity damping efficiency yield a simple recipe to implement type-I eccentricity damping in N-body codes in the case of partial gap opening planets that is consistent with high-resolution 2D hydrodynamical simulations. The typical error of the final fit is of the order of a few percent, and at most ~20%, which is the error of type-I torque formulas widely used in the literature. This will allow a more self-consistent treatment of planet-disc interactions of the type-I regime for population synthesis models at low viscosities.

Mean motion resonance capture in the context of type I migration

Capture into mean motion resonance (MMR) is an important dynamical mechanism because it shapes the final architecture of a planetary system. We simulate systems of two or three planets undergoing migration with varied initial parameters such as planetary mass and disk surface density and analyse the resulting resonant chains. In contrast to previous studies, our results show that the disk properties are the dominant impact on capture into MMR, while the total planetary mass barely affects the final system configuration as long as the planet does not open a gap in the disk. We confirm that adiabatic resonant capture is the correct framework for understanding the conditions leading to MMR formation because its predictions are qualitatively similar to the numerical results. However, we find that eccentricity damping can facilitate the capture in a given resonance. We find that under typical disk conditions, planets tend to be captured into 2:1 or 3:2 MMRs, which agrees well with the observed exoplanet MMRs. Our results predict two categories of systems: those that have uniform chains of wide resonances (2:1 or 3:2 MMRs), and those whose inner pair is more compact than the outer pair, such as 4:3:2 chains. Both categories of resonant chains are present in observed exoplanet systems. On the other hand, chains whose inner pair is wider than the outer pair are very rare and emerge from stochastic capture. Our work here can be used to link the current configuration of exoplanetary systems to the formation conditions within protoplanetary disks.

Energy dissipation in synchronous binary asteroids

Synchronous binary asteroids can experience libration about their tidally-locked equilibrium, which will result in energy dissipation. This is an important topic to the Asteroid Impact and Deflection Assessment, where excitation caused by the DART kinetic impact in the Didymos binary asteroid system may be reduced through dissipation before Hera arrives to survey the effects of the impact. We develop a numeric model for energy dissipation in binary asteroids to explore how different system configurations affect the rate of energy dissipation. We find tumbling within the synchronous state eliminates a systematic trend in libration damping on short timescales (several years), but not over long times (hundreds of years) depending on the material conditions. Furthermore, damping of libration, eccentricity, and fluctuations in the semimajor axis are primarily dependent on the stiffness of the secondary, whereas the semimajor axis secular expansion rate is dictated by the stiffness of the primary, as expected. Systems experiencing stable planar libration in the secondary can see a noticeable reduction in libration amplitude after only a few years depending on the stiffness of the secondary, and thus dissipation should be considered during Hera’s survey of Didymos. For a very dissipative secondary undergoing stable libration, Hera may be able to calculate the rate of libration damping in Dimorphos and therefore constrain its tidal parameters.

Hydrodynamical evolution of black-hole binaries embedded in AGN discs

ABSTRACT Stellar-mass binary black holes (BBHs) embedded in active galactic nucleus (AGN) discs are possible progenitors of black hole mergers detected in gravitational waves by LIGO/VIRGO. To better understand the hydrodynamical evolution of BBHs interacting with the disc gas, we perform a suite of high-resolution 2D simulations of binaries in local disc (shearing-box) models, considering various binary mass ratios, eccentricities and background disc properties. We use the γ-law equation of state and adopt a robust post-processing treatment to evaluate the mass accretion rate, torque and energy transfer rate on the binary to determine its long-term orbital evolution. We find that circular comparable-mass binaries contract, with an orbital decay rate of a few times the mass doubling rate. Eccentric binaries always experience eccentricity damping. Prograde binaries with higher eccentricities or smaller mass ratios generally have slower orbital decay rates, with some extreme cases exhibiting orbital expansion. The averaged binary mass accretion rate depends on the physical size of the accretor. The accretion flows are highly variable, and the dominant variability frequency is the apparent binary orbital frequency (in the rotating frame around the central massive BH) for circular binaries but gradually shifts to the radial epicyclic frequency as the binary eccentricity increases. Our findings demonstrate that the dynamics of BBHs embedded in AGN discs is quite different from that of isolated binaries in their own circumbinary discs. Furthermore, our results suggest that the hardening time-scales of the binaries are much shorter than their migration time-scales in the disc, for all reasonable binary and disc parameters.

Resonance capture and long-term evolution of planets in binary star systems

Aims. The growing population of planets discovered in orbit around one stellar component of a binary star raises the question of the influence of the binary companion on the formation process of planetary systems. The aim of this work is to study the impact of a binary companion on the evolution of two-planet systems during both the Type-II migration phase and their long-term evolution after the dissipation of the protoplanetary disk. Methods. We used the symplectic integrator SyMBA, modified to include a wide binary companion. We also included the Type-II migration of giant planets during the protoplanetary disk phase with suitable eccentricity and inclination damping as well as the gravitational potential acting on the planets due to the disk and the nodal precession of the disk induced by the binary companion. We considered various inclinations, eccentricities, and separations of the binary companion. Results. Disk migration allows for the formation of planet pairs in mean-motion resonances despite the presence of the binary companion. When the binary separation is wide (1000 au), the timescale of the perturbations that it raises on the planets is longer than the disk’s lifetime and resonant pairs are routinely formed in the 2:1, 5:2, and 3:1 commensurabilities. Provided the planet-planet interaction timescale is smaller than the timescale of binary perturbations, these systems can remain in resonance long after the disk has dissipated. When the binary separation is smaller (250 au), only planets in the 2:1 resonance tend to remain in a resonant state and more chaotic evolutions are observed, as well as more ejections. After those ejections, the remaining planet can become eccentric due to the perturbations from the binary companion in addition, for strongly inclined binary companions, captures in the von Ziepel-Lidov-Kozai resonance can occur. Whereas in systems with two planets, this mechanism is quenched by planet-planet interactions. Our simulations reveal that the interplay between planet-disk, planet-planet, and planet-binary interactions can lead to the formation of resonant pairs of planets which remain stable over timescales much longer than the disk’s lifetime.

Dynamics of co-orbital exoplanets in a first-order resonance chain with tidal dissipation

Co-orbital planets (in a 1: 1 mean motion resonance) can be formed within a Laplace resonance chain. We develop a secular model tc study the dynamics of the resonance chain p: p : p + 1, where the co-orbital pair is in a first-order mean motion resonance with the outermost third planet. Our model takes into account tidal dissipation through the use of a Hamiltonian version of the constant time-lag model, which extends the Hamiltonian formalism of the point-mass case. We show the existence of several families of equilibria, anc how these equilibria extend to the complete system. In one family, which we call the main branch, a secular resonance between the libration frequency of the co-orbitals and the precession frequency of the pericentres has unexpected dynamical consequences when tidal dissipation is added. We report the existence of two distinct mechanisms that make co-orbital planets much more stable within the p : p : p + 1 resonance chain rather than outside it. The first is due to negative real parts of the eigenvalues of the linearised system with tides, in the region of the secular resonance mentioned above. The second comes from non-linear contributions of the vector fielt and is due to eccentricity damping. These two stabilising mechanisms increase the chances of a future detection of exoplanets in the co-orbital configuration.

Proximity of exoplanets to first-order mean-motion resonances

ABSTRACT Planetary formation theories and, more specifically, migration models predict that planets can be captured in mean-motion resonances (MMRs) during the disc phase. The distribution of period ratios between adjacent planets shows an accumulation in the vicinity of the resonance, which is not centred on the nominal resonance but instead presents an offset slightly exterior to it. Here, we extend on previous works by thoroughly exploring the effect of different disc and planet parameters on the resonance offset during the disc migration phase. The dynamical study is carried out for several first-order MMRs and for both low-mass Earth-like planets undergoing type-I migration and giant planets evolving under type-II migration. We find that the offset varies with time during the migration of the two-planet system along the apsidal corotation resonance family. The departure from the nominal resonance increases for higher planetary masses and stronger eccentricity damping. In the Earth to super-Earth regime, we find offset values in agreement with the observations when using a sophisticated modelling for the planet–disc interactions, where the damping time-scale depends on the eccentricity. This dependence causes a feedback that induces an increase of the resonance offsets. Regarding giant planets, the offsets of detected planet pairs are well reproduced with a classical K-factor prescription for the planet–disc interactions when the eccentricity damping rate remains low to moderate. In both regimes, eccentricities are in agreement with the observations too. As a result, planet–disc interactions provide a generic channel to generate the offsets found in the observations.

Is the orbital distribution of multiplanet systems influenced by pure three-planet resonances?

ABSTRACT We analyse the distribution of known multiplanet systems (N ≥ 3) in the plane of mean-motion ratios, and compare it with the resonance web generated by two-planet mean-motion resonances (2P-MMR) and pure three-planet commensurabilities (pure 3P-MMR). We find intriguing evidence of a statistically significant correlation between the observed distribution of compact low-mass systems and the resonance structure, indicating a possible causal relation. While resonance chains, such as Kepler-60, Kepler-80, and TRAPPIST-1, are strong contributors, most of the correlation appears to be caused by systems not identified as resonance chains. Finally, we discuss their possible origin through planetary migration during the last stages of the primordial disc and/or an eccentricity damping process.

Migration of Jupiter-mass planets in low-viscosity discs

Context. Type-II migration of giant planets has a speed proportional to the disc’s viscosity for values of the α viscosity parameter larger than 10−4. Previous studies based on two-dimensional simulations, have shown that, at even lower viscosities, migration can be very chaotic and is often characterised by phases of fast migration. The reason is that vortices appear in low-viscosity discs due to the Rossby-wave instability at the edges of the gap opened by the planet. Migration is then determined by vortex-planet interactions. Aims. Our goal is to study giant planet migration in low-viscosity discs with 3D simulations. In 3D, vortices are more complex than the simple vertical extension of their 2D counterparts; their impact on planet migration is therefore not obvious. Methods. We performed numerical simulations using two grid-based codes: FARGOCA for three-dimensional simulations and FARGO-ADSG for the two dimensional case. Two-dimensional simulations were used mainly for preliminary tests to check the impact of self-gravity on vortex formation and on vortex-disc dynamics. After selecting disc masses for which self-gravity is not important at the planet location, three-dimensional simulations without self-gravity can be safely used. We have considered an adiabatic equation of state with exponential damping of temperature perturbations in order to avoid the development of the vertical shear instability. In our nominal simulation, we set α = 0 so that only numerical viscosity is present. We then performed simulations with non-zero α values to assess the threshold of prescribed viscosity below which the new migration processes appear. Results. We show that for α ≲ 10−5 two migration modes are possible, which differ from classical Type-II migration in the sense that they are not proportional to the disc’s viscosity. The first occurs when the gap opened by the planet is not very deep. This occurs in 3D simulations and/or when a big vortex forms at the outer edge of the planetary gap, diffusing material into the gap. The de-saturation of co-orbital and co-rotation resonances keeps the planet’s eccentricity low. Inward planet migration then occurs as long as the disc can refill the gap left behind by the migrating planet, either due to diffusion caused by the presence of the vortex or to the inward migration of the vortex itself due to its interaction with the disc. We call this type of migration ‘vortex-driven migration’, which differs from ‘vortex-induced’ migration described in Lin & Papaloizou (2010, MNRAS, 405, 1473, and 2011a, MNRAS, 415, 1445). This migration is very slow and cannot continue indefinitely because eventually the vortex dissolves. The second migration mode occurs when the gap is deep so that the planet’s eccentricity grows to a value e ~ 0.2 due to inefficient eccentricity damping by co-rotation resonances. Once the planet is on an eccentric orbit, gas can pass through the gap and planet migration unlocks from the disc’s viscous evolution. This second, faster migration mode appears to be typical of two-dimensional models in discs with slower damping of temperature perturbations. Conclusions. Vortex-driven migration in low-viscosity discs can be very slow and eventually reverses and stops, offering an interesting mechanism to explain the existence of the cold-Jupiter population, even if these planets originally started growing at the disc’s snowline.