Migration Of Low-mass Planets Research Articles

Pebble-driven migration of low-mass planets in the 2D regime of pebble accretion

Pebbles drifting past a disk-embedded low-mass planet develop asymmetries in their distribution and exert a substantial gravitational torque on the planet, thus modifying its migration rate. Our aim is to assess how the distribution of pebbles and the resulting torque change in the presence of pebble accretion, focusing on its 2D regime. First, we performed 2D high-resolution multi-fluid simulations with Fargo3D but found that they are impractical for resolving pebble accretion due to the smoothing of the planetary gravitational potential. To remove the smoothing and directly trace pebbles accreted by the planet, we developed a new code Deneb which evolves an ensemble of pebbles, represented by Lagrangian superparticles, in a steady-state gaseous background. For small and moderate Stokes numbers, $ St pebble accretion creates two underdense regions with a front-rear asymmetry with respect to the planet. The underdensity trailing the planet is more extended. The resulting excess of pebble mass in front of the planet then makes the pebble torque positive and capable of outperforming the negative gas torque. Pebble accretion thus enables outward migration (previously thought to occur mainly for $ St in a larger portion of the parameter space. It occurs for the planet mass pl oplus $ and for all the Stokes numbers considered in our study, $ St $, assuming a pebble-to-gas mass ratio of $Z=0.01$. If some of the observed planets underwent outward pebble-driven migration during their accretion, the formation sites of their progenitor embryos could have differed greatly from the usual predictions of planet formation models. To enable an update of the respective models, we provide a scaling law for the pebble torque that can be readily incorporated in N-body simulations.

Low-mass planets falling into gaps with cyclonic vortices

ABSTRACT We investigate the planetary migration of low-mass planets ($M_p\in [1,15]\, \mathrm{ M}_{\oplus }$, here $\mathrm{ M}_{\oplus }$ is the Earth mass) in a gaseous disc containing a previously formed gap. We perform high-resolution 3D simulations with the fargo3d code. To create the gap in the surface density of the disc, we use a radial viscosity profile with a bump, which is maintained during the entire simulation time. We find that when the gap is sufficiently deep, the spiral waves excited by the planet trigger the Rossby wave instability, forming cyclonic (underdense) vortices at the edges of the gap. When the planet approaches the gap, it interacts with the vortices, which produce a complex flow structure around the planet. Remarkably, we find a widening of the horseshoe region of the planet produced by the vortex at the outer edge of the gap, which depending on the mass of the planet differs by at least a factor of two with respect to the standard horseshoe width. This inevitably leads to an increase in the co-rotation torque on the planet and produces an efficient trap to halt its inward migration. In some cases, the planet becomes locked in co-rotation with the outer vortex. Under this scenario, our results could explain why low-mass planets do not fall towards the central star within the lifetime of the protoplanetary disc. Lastly, the development of these vortices produces an asymmetric temporal evolution of the gap, which could explain the structures observed in some protoplanetary discs.

Migration of low-mass planets in inviscid discs: the effect of radiation transport on the dynamical corotation torque

ABSTRACT Low-mass planets migrate in the type-I regime. In the inviscid limit, the contrast between the vortensity trapped inside the planet’s corotating region and the background disc vortensity leads to a dynamical corotation torque, which is thought to slow down inward migration. We investigate the effect of radiative cooling on low-mass planet migration using inviscid 2D hydrodynamical simulations. We find that cooling induces a baroclinic forcing on material U-turning near the planet, resulting in vortensity growth in the corotating region, which in turn weakens the dynamical corotation torque and leads to 2–3× faster inward migration. This mechanism is most efficient when cooling acts on a time-scale similar to the U-turn time of material inside the corotating region, but is none the less relevant for a substantial radial range in a typical disc (R ∼ 5–50 au). As the planet migrates inwards, the contrast between the vortensity inside and outside the corotating region increases and partially regulates the effect of baroclinic forcing. As a secondary effect, we show that radiative damping can further weaken the vortensity barrier created by the planet’s spiral shocks, supporting inward migration. Finally, we highlight that a self-consistent treatment of radiative diffusion as opposed to local cooling is critical in order to avoid overestimating the vortensity growth and the resulting migration rate.

Quantifying the Impact of the Dust Torque on the Migration of Low-mass Planets

Disk solids are critical in many planet formation processes; however, their effect on planet migration remains largely unexplored. Here we assess this important issue for the first time by building on the systematic measurements of dust torques on an embedded planet by Benitez-Llambay & Pessah. Adopting standard models for the gaseous disk and its solid content, we quantify the impact of the dust torque for a wide range of conditions describing the disk/planet system. We show that the total torque can be positive and reverse inward planet migration for planetary cores with M p ≲ 10 M ⊕. We compute formation tracks for low-mass embryos for conditions usually invoked when modeling planet formation processes. Our most important conclusion is that dust torques can have a significant impact on the migration and formation history of planetary embryos. The most important implications of our findings are as follows. (i) For nominal dust-to-gas mass ratios ϵ ≃ 0.01, low-mass planets migrate outwards beyond the water ice-line if most of the mass in the solids is in particles with Stokes numbers St ≃0.1. (ii) For ϵ ≳ 0.02–0.05, solids with small Stokes numbers, St ≃ 0.01, can play a dominant role if most of the mass is in those particles. (iii) Dust torques have the potential to enable low-mass planetary cores formed in the inner disk to migrate outwards and act as the seed for massive planets at distances of tens of au.

Effects of Radiative Diffusion on Dynamical Corotation Torque in Three-dimensional Protoplanetary Disks

The dynamical corotation torque arising from the deformation of horseshoe orbits, along with the vortensity gradient in the background disk, is important for determining the orbital migration rate and direction of low-mass planets. Previous two-dimensional studies have predicted that the dynamical corotation torque is positive, decelerating inward planet migration. In contrast, recent three-dimensional studies have shown that buoyancy resonance makes the dynamical corotation torque negative, accelerating inward migration. In this paper, we study the dependence of the dynamical corotation torque on thermal transport, using three-dimensional simulations. We first show that our results are consistent with previous three-dimensional studies when the disk is fully adiabatic. In more realistic radiative disks, however, radiative diffusion suppresses buoyancy resonance significantly, especially in high-altitude regions, and yields a positive dynamical corotation torque. This alleviates the issue of rapid migration being caused by the negative dynamical corotation torque in adiabatic disks. Our results suggest that radiative diffusion, together with stellar irradiation and accretion heating, are needed to accurately describe the migration of low-mass planets.

The importance of thermal torques on the migration of planets growing by pebble accretion

ABSTRACT A key process in planet formation is the exchange of angular momentum between a growing planet and the protoplanetary disc, which makes the planet migrate through the disc. Several works show that in general low-mass and intermediate-mass planets migrate towards the central star, unless corotation torques become dominant. Recently, a new kind of torque, called the thermal torque, was proposed as a new source that can generate outward migration of low-mass planets. While the Lindblad and corotation torques depend mostly on the properties of the protoplanetary disc and on the planet mass, the thermal torque depends also on the luminosity of the planet, arising mainly from the accretion of solids. Thus, the accretion of solids plays an important role not only in the formation of the planet but also in its migration process. In a previous work, we evaluated the thermal torque effects on planetary growth and migration mainly in the planetesimal accretion paradigm. In this new work, we study the role of the thermal torque within the pebble accretion paradigm. Computations are carried out consistently in the framework of a global model of planet formation that includes disc evolution, dust growth and evolution, and pebble formation. We also incorporate updated prescriptions of the thermal torque derived from high-resolution hydrodynamical simulations. Our simulations show that the thermal torque generates extended regions of outward migration in low-viscosity discs. This has a significant impact in the formation of the planets.

Migrating low-mass planets in inviscid dusty protoplanetary discs

ABSTRACT Disc-driven planet migration is integral to the formation of planetary systems. In standard, gas-dominated protoplanetary discs, low-mass planets or planetary cores undergo rapid inwards migration and are lost to the central star. However, several recent studies indicate that the solid component in protoplanetary discs can have a significant dynamical effect on disc–planet interaction, especially when the solid-to-gas mass ratio approaches unity or larger and the dust-on-gas drag forces become significant. As there are several ways to raise the solid abundance in protoplanetary discs, for example through disc winds and dust trapping in pressure bumps, it is important to understand how planets migrate through a dusty environment. To this end, we study planet migration in dust-rich discs via a systematic set of high-resolution, two-dimensional numerical simulations. We show that the inwards migration of low-mass planets can be slowed down by dusty dynamical corotation torques. We also identify a new regime of stochastic migration applicable to discs with dust-to-gas mass ratios of ≳0.3 and particle Stokes numbers ≳0.03. In these cases, disc–planet interaction leads to the continuous development of small-scale, intense dust vortices that scatter the planet, which can potentially halt or even reverse the inwards planet migration. We briefly discuss the observational implications of our results and highlight directions for future work.

Low-mass planet migration in three-dimensional wind-driven inviscid discs: a negative corotation torque

ABSTRACT We present simulations of low-mass planet–disc interactions in inviscid three-dimensional discs. We show that a wind-driven laminar accretion flow through the surface layers of the disc does not significantly modify the migration torque experienced by embedded planets. More importantly, we find that 3D effects lead to a dramatic change in the behaviour of the dynamical corotation torque compared to earlier 2D theory and simulations. Although it was previously shown that the dynamical corotation torque could act to slow and essentially stall the inward migration of a low-mass planet, our results in 3D show that the dynamical corotation torque has the complete opposite effect and speeds up inward migration. Our numerical experiments implicate buoyancy resonances as the cause. These have two effects: (i) they exert a direct torque on the planet, whose magnitude relative to the Lindblad torque is measured in our simulations to be small; (ii) they torque the gas librating on horseshoe orbits in the corotation region and drive evolution of its vortensity, leading to the negative dynamical corotation torque. This indicates that at low turbulent viscosity, the detailed vertical thermal structure of the protoplanetary disc plays an important role in determining the migration behaviour of embedded planets. If this result holds up under a more refined treatment of disc thermal evolution, then it has important implications for understanding the formation and early evolution of planetary systems.

Vortex instabilities triggered by low-mass planets in pebble-rich, inviscid protoplanetary discs

Abstract In the innermost regions of protoplanerary discs, the solid-to-gas ratio can be increased considerably by a number of processes, including photoevaporative and particle drift. Magnetohydrodynamic disc models also suggest the existence of a dead zone at R ≲ 10 au, where the regions close to the mid-plane remain laminar. In this context, we use two-fluid hydrodynamical simulations to study the interaction between a low-mass planet (∼1.7 M⊕) on a fixed orbit and an inviscid pebble-rich disc with solid-to-gas ratio ϵ ≥ 0.5. For pebbles with Stokes numbers St = 0.1, 0.5, multiple dusty vortices are formed through the Rossby wave instability at the planet separatrix. Effects due to gas drag then lead to a strong enhancement in the solid-to-gas ratio, which can increase by a factor of ∼103 for marginally coupled particles with St = 0.5. As in streaming instabilities, pebble clumps reorganize into filaments that may plausibly collapse to form planetesimals. When the planet is allowed to migrate in an Minimum Mass Solar Nebula (MMSN) disc, the vortex instability is delayed due to migration but sets in once inward migration stops due a strong positive pebble torque. Again, particle filaments evolving in a gap are formed in the disc while the planet undergoes an episode of outward migration. Our results suggest that vortex instabilities triggered by low-mass planets could play an important role in forming planetesimals in pebble-rich, inviscid discs, and may significantly modify the migration of low-mass planets. They also imply that planetary dust gaps may not necessarily contain planets if these migrated away.

3D simulations of planet trapping at disc–cavity boundaries

Abstract Inward migration of low-mass planets and embryos of giant planets can be stopped at the disc–cavity boundaries due to co-orbital corotation torque. We performed the first global three-dimensional (3D) simulations of planet migration at the disc–cavity boundary, and have shown that the boundary is a robust trap for low-mass planets and embryos. A protoplanetary disc may have several such trapping regions at various distances from the star, such as at the edge of the stellar magnetosphere, the inner edge of the dead zone, the dust-sublimation radius and the snow lines. Corotation traps located at different distances from a star, and moving outward during the disc dispersal phase, may possibly explain the observed homogeneous distribution of low-mass planets with distance from their host stars.

Low mass planet migration in Hall-affected disks

Recent developments in non-ideal magnetohydrodynamic simulations of protoplanetary disks suggest that instead of being traditional turbulent (viscous) accretion disks, they have a largely laminar flow with accretion driven by large-scale wind torques. These disks are possibly threaded by Hall-effect generated large-scale horizontal magnetic fields. We have examined the dynamics of the corotation region of a low mass planet embedded in such a disk and the evolution of the associated migration torque. These disks lack strong turbulence and associated turbulent diffusion, and the presence of a magnetic field and radial gas flow presents a situation outside the applicability of previous corotation torque theory. We summarize the analytical analysis of the corotation torque, give details on the numerical methods used, and in particular the relative merits of different numerical schemes for the inviscid problem.

Low-mass planet migration in magnetically torqued dead zones – II. Flow-locked and runaway migration, and a torque prescription

We examine the migration of low mass planets in laminar protoplanetary discs, threaded by large scale magnetic fields in the dead zone that drive radial gas flows. As shown in Paper I, a dynamical corotation torque arises due to the flow-induced asymmetric distortion of the corotation region and the evolving vortensity contrast between the librating horseshoe material and background disc flow. Using simulations of laminar torqued discs containing migrating planets, we demonstrate the existence of the four distinct migration regimes predicted in Paper I. In two regimes, the migration is approximately locked to the inward or outward radial gas flow, and in the other regimes the planet undergoes outward runaway migration that eventually settles to fast steady migration. In addition, we demonstrate torque and migration reversals induced by midplane magnetic stresses, with a bifurcation dependent on the disc surface density. We develop a model for fast migration, and show why the outward runaway saturates to a steady speed, and examine phenomenologically its termination due to changing local disc conditions. We also develop an analytical model for the corotation torque at late times that includes viscosity, for application to discs that sustain modest turbulence. Finally, we use the simulation results to develop torque prescriptions for inclusion in population synthesis models of planet formation.

The effects of a magnetic field on planetary migration in laminar and turbulent discs

We investigate the migration of low-mass planets ($5 M_{\oplus}$ and $20 M_{\oplus}$) in accretion discs threaded with a magnetic field using 2D MHD code in polar coordinates. We observed that, in the case of a strong azimuthal magnetic field where the plasma parameter is $\beta\sim 1-2$, density waves at the magnetic resonances exert a positive torque on the planet and may slow down or reverse its migration. However, when the magnetic field is weaker (i.e., the plasma parameter $\beta$ is relatively large), then non-axisymmetric density waves excited by the planet lead to growth of the radial component of the field and, subsequently, to development of the magneto-rotational instability, such that the disc becomes turbulent. Migration in a turbulent disc is stochastic, and the migration direction may change as such. To understand migration in a turbulent disc, both the interaction between a planet and individual turbulent cells, as well as the interaction between a planet and ordered density waves, have been investigated.

Fast migration of low-mass planets in radiative discs

Low-mass planets are known to undergo Type I migration and this process must have played a key role during the evolution of planetary systems. Analytical formulae for the disc torque have been derived assuming that the planet evolves on a fixed circular orbit. However, recent work has shown that in isothermal discs, a migrating protoplanet may also experience dynamical corotation torques that scale with the planet drift rate. The aim of this study is to examine whether dynamical corotation torques can also affect the migration of low-mass planets in non-isothermal discs. We performed 2D radiative hydrodynamical simulations to examine the orbital evolution outcome of migrating protoplanets as a function of disc mass. We find that a protoplanet can enter a fast migration regime when it migrates in the direction set by the entropy-related horseshoe drag and when the Toomre stability parameter is less than a threshold value below which the horseshoe region contracts into a tadpole-like region. In that case, an underdense trapped region appears near the planet, with an entropy excess compared to the ambient disc. If the viscosity and thermal diffusivity are small enough so that the entropy excess is conserved during migration, the planet then experiences strong corotation torques arising from the material flowing across the planet orbit. During fast migration, we observe that a protoplanet can pass through the zero-torque line predicted by static torques. We also find that fast migration may help in disrupting the mean-motion resonances that are formed by convergent migration of embryos.

The Effect of Convective Overstability on Planet Disk Interactions

AbstractWe run global two dimensional hydrodynamical simulations, using the PLUTO code and the planet-disk model of Uribe et al. 2011, to investigate the effect of the convective overstability (CO) on planet-disk interactions. First, we study the long-term evolution of planet-induced vortices. We found that the CO leads to smoother planetary gap edges, thus weaker planet-induced vortices. The main result was the observation of two generation of vortices, which can pose an explanation for the location of the vortex in the Oph IRS48 system. The lifetime of the primary vortices, as well as the birth time of the secondary vortices are shown to be highly dependent on the thermal relaxation timescale. Second, we study the long-term evolution of the migration of low mass planets and assess whether the CO can prevent the saturation of the horseshoe drag. We found that the disk parameters that favour slow inward or outward migration oppose the amplification of vortices, meaning that the CO does not seem to be a good mechanism to prevent the saturation of the horseshoe drag. On the other hand, we observed a planetary trap, caused by vortices formed in the horseshoe region. This trap may be an alternative mechanism to prevent the fast type I migration rates.

Type I planet migration in weakly magnetized laminar discs

The migration of low-mass planets, or type I planetary migration, has been studied in hydrodynamical disc models for more than three decades. For a long time, it was thought to be very rapid and directed inwards due to Lindblad torques. More recently, it has been shown that the corotation torque, linked to the horseshoe motion of the gas near the planet, may slow down or even reverse migration. How is this picture modified by the expected presence of a magnetic field in the protoplanetary disc? When the magnetic field is strong enough to prevent horseshoe motion, the corotation torque is replaced by a torque arising from magnetic resonances which may significantly alter the migration rate. In the case of a weaker magnetic field, the magnetic field is not strong enough to prevent horseshoe motion and a corotation torque then exists. In this regime, recent turbulent magnetohydrodynamical (MHD) simulations have reported the existence of an additional component of the corotation torque due to the presence of the magnetic field. The aim of this paper is to investigate the physical origin and the properties of this additional corotation torque. We performed MHD simulations of a low-mass planet embedded in a 2D laminar disc threaded by a weak toroidal magnetic field, where the effects of turbulence are modelled by a viscosity and a resistivity. We confirm that the interaction between the magnetic field and the horseshoe motion of the gas results in an additional corotation torque on the planet, which we dub the MHD torque excess. We demonstrate that it is caused by the accumulation of the magnetic field along the downstream separatrices of the horseshoe region, which gives rise to an azimuthally asymmetric underdense region at that location. The properties of the MHD torque excess are characterized by varying the slope of the density, temperature and magnetic field profiles, as well as the diffusion coefficients and the strength of the magnetic field. The sign of the torque excess and its radial distribution are found to be in agreement with the earlier full magnetorotational instability simulations. This sign depends on the density and temperature gradients only and is positive for profiles expected in protoplanetary discs. The magnitude of the torque excess is in turn mainly determined by the strength of the magnetic field and the turbulent resistivity. It can be strong enough to reverse migration even when the magnetic pressure is less than 1 per cent of the thermal pressure. The MHD torque excess can therefore lead to outward planetary migration in the radiatively efficient outer parts of protoplanetary discs, where the hydrodynamical corotation torque is too weak to prevent fast inward migration.

Stellar irradiated discs and implications on migration of embedded planets

The strength and direction of migration of low mass planets depends on the disc's thermodynamics. In discs where the viscous heating is balanced by radiative transport, the migration can be directed outwards, a process which extends the lifetime of growing planetary embryos. We investigate the influence of opacity and stellar irradiation on the disc thermodynamics. Utilizing the resulting disc structure, we determine the regions of outward migration. We perform two-dimensional numerical simulations of equilibrium discs with viscous heating, radiative cooling and stellar irradiation. We use the hydrodynamical code NIRVANA that includes a full tensor viscosity and stellar irradiation, as well as a two temperature solver that includes radiation transport in the flux-limited diffusion approximation. The migration is studied by using torque formulae. In the constant opacity case, we reproduce the analytical results of a black-body disc: the stellar irradiation dominates in the outer regions -- leading to flaring -- while the viscous heating dominates close to the star. We find that the inner edge of the disc should not be significantly puffed-up by the stellar irradiation. If the opacity depends on the local density and temperature, the structure of the disc is different, and several bumps in the aspect ratio H/r appear, due to transitions between different opacity regimes. The bumps in the disc can shield the outer disc from stellar irradiation. Stellar irradiation is an important factor for determining the disc structure and has dramatic consequences for the migration of embedded planets. Compared to discs with only viscous heating, a stellar irradiated disc features a much smaller region of outward migration for a range of planetary masses. This suggests that the region where the formation of giant planet cores takes place is smaller, which in turn might lead to a shorter growth phase.

Global models of planetary system formation in radiatively-inefficient protoplanetary discs

We present the results of N-body simulations of planetary system formation in radiatively-inefficient disc models, where positive corotation torques may counter the rapid inward migration of low-mass planets driven by Lindblad torques. The aim of this work is to examine the nature of planetary systems that arise from oligarchic growth in such discs. We adapt the commonly used Mercury-6 symplectic integrator by including simple prescriptions for planetary migration (types I and II), planetary atmospheres that enhance the probability of planetesimal accretion by protoplanets, gas accretion on to forming planetary cores, and gas disc dispersal. We perform a suite of simulations for a variety of disc models with power-law surface density and temperature profiles, with a focus on models in which unsaturated corotation torques can drive outward migration of protoplanets. In some models, we account for the quenching of corotation torques which arises when planetary orbits become eccentric. Approximately half of our simulations lead to the successful formation of gas giant planets with a broad range of masses and semimajor-axes. Giant planetary masses range from being approximately equal to that of Saturn up to approximately twice that of Jupiter. The semimajor-axes of these range from being ∼0.2 au up to ∼75 au, with disc models that drive stronger outward migration favouring the formation of longer period giant planets. Out of a total of 20 giant planets being formed in our simulation suite, we obtain three systems that contain two giants. No super-Earth or Neptune-mass planets were present in the final stages of our simulations, in contrast to the large abundance of such objects being discovered in observation surveys. This result arises because of rapid inward migration suffered by massive planetary cores that form early in the disc lifetime (for which the corotation torques saturate), combined with gas accretion on to massive cores which leads them to become gas giants. Numerous low-mass planets are formed and survive in the simulations, with masses ranging from a few tenths of an Earth mass up to ∼3 Earth masses. Simulations in which the quenching of corotation torques for planets on modestly eccentric orbits was included failed to produce any giant planets, apparently because Lindblad torques induce rapid inward migration of planetary cores in these systems. We conclude that convergent migration induced by corotation torques operating during planetary formation can enhance the growth rate of planetary cores, but these often migrate into the central star because corotation torques saturate. Outward migration of planetary cores of modest mass can lead to the formation of gas giant planets at large distances from the central star, similar to those observed recently through direct imaging surveys. The excitation of planetary eccentricities through planet–planet scattering during oligarchic growth may quench the effects of corotation torques, however, such that inward migration is driven by Lindblad torques.

Corotation torques experienced by planets embedded in weakly magnetized turbulent discs

The migration of low-mass planets is driven by the differential Lindblad torque and the corotation torque in non-magnetic viscous models of protoplanetary discs. The corotation torque has recently received detailed attention as it may slow down, stall, or reverse migration. In laminar viscous disc models, the long-term evolution of the corotation torque is intimately related to viscous and thermal diffusion processes in the planet's horseshoe region. This paper examines the properties of the corotation torque in discs where MHD turbulence develops as a result of the magnetorotational instability, considering a weak initial toroidal magnetic field. We present results of 3D MHD simulations carried out with two different codes. Non-ideal MHD effects and the disc's vertical stratification are neglected, and locally isothermal disc models are considered. The running time-averaged torque exerted by the disc on a fixed planet is evaluated in three disc models. We first present results with an inner disc cavity (planet trap). As in viscous disc models, the planet is found to experience a positive running time-averaged torque over several hundred orbits, which highlights the existence of an unsaturated corotation torque maintained in the long term in MHD turbulent discs. Two disc models with initial power-law density and temperature profiles are also adopted, in which the time-averaged torque is found to be in decent agreement with its counterpart in laminar viscous disc models with similar viscosity at the planet location. Detailed analysis of the averaged torque density distributions indicates that the differential Lindblad torque takes very similar values in MHD turbulent and laminar viscous discs, and there exists an unsaturated corotation torque in MHD turbulent discs. This analysis also reveals the existence of an additional corotation torque in weakly magnetized discs.

Dust settling and rapid planetary migration

Planetary migration is essential to explain the observed mass-period relation for exoplanets. Without some stopping mechanism, the tidal, resonant interaction between planets and their gaseous disc generally causes the planets to migrate inward so efficiently that they plunge into the host star within the gaseous disc lifetime ($\sim $ 1-3 Myrs). We investigate planetary migration by analytically calculating the migration rate and time within self-consistently computed, radiatively heated discs around M stars in which the effects of dust settling are included. We show that dust settling lowers the disc temperature and raises the gas density in the mid-plane. This inescapable evolution of disc structure speeds up type I planetary migration for lower mass bodies by up to a factor of about 2. We also examine the effects of dust settling on the gap-opening mass and type II migration, and find that the gap-opening mass is reduced by a factor of 2 and type II migration becomes slower by a factor of 2. While dust settling can somewhat alleviate the problem of planetary migration for more massive planets, the more rapid migration of low mass planets and planetary cores requires a robust slowing mechanism.