2.4 Planetary migration

Planetary migration shapes the architecture of exoplanetary systems. This process, driven by gravitational interactions, explains the diverse orbital configurations we observe. Understanding migration mechanisms is crucial for unraveling how planets form and evolve over time.

From hot Jupiters to compact super-Earth systems, migration leaves its mark on planetary demographics. It influences water delivery to terrestrial worlds, affects orbital stability, and plays a key role in determining the habitability potential of planets across the galaxy.

Mechanisms of planetary migration

• Planetary migration describes the process of orbital changes in planetary systems due to gravitational interactions
• Understanding migration mechanisms provides crucial insights into the formation and evolution of exoplanetary systems
• Migration plays a significant role in shaping the final architecture of planetary systems, including our own solar system

Type I migration

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• Applies to low-mass planets embedded in a gaseous protoplanetary disk
• Driven by torques exerted on the planet by density waves in the disk
• Corotation torque and Lindblad torque contribute to the overall migration direction
• Migration rate depends on planet mass, disk properties, and local temperature gradient
• Typically results in inward migration on timescales shorter than disk lifetime

Type II migration

• Occurs when a massive planet opens a gap in the protoplanetary disk
• Planet becomes locked to the viscous evolution of the disk
• Migration rate is determined by the disk's viscous timescale
• Can result in both inward and outward migration depending on disk conditions
• Responsible for the formation of hot Jupiters and warm Jupiters in some systems

Type III migration

• Rapid form of migration applicable to intermediate-mass planets
• Driven by coorbital mass deficit in the planet's vicinity
• Can lead to very fast migration rates, potentially crossing the entire disk in a few orbits
• Highly non-linear process, sensitive to initial conditions and disk properties
• May explain the rapid formation of some close-in giant planets

Timescales of migration

Fast vs slow migration

• Fast migration occurs on timescales shorter than the disk lifetime (typically < 1 million years)
  • Can lead to significant orbital changes and planet-planet interactions
  • Examples include Type III migration and some cases of Type I migration
• Slow migration happens over timescales comparable to or longer than the disk lifetime
  • Allows for more gradual evolution of planetary systems
  • Type II migration often falls into this category
• Migration speed affects the final configuration of planetary systems and the likelihood of planet survival

Migration in protoplanetary disks

• Protoplanetary disks provide the environment for early stages of planetary migration
• Disk properties (mass, temperature profile, viscosity) strongly influence migration rates
• Migration can occur throughout the disk lifetime, typically 1-10 million years
• Disk evolution and dissipation can lead to changes in migration rates over time
• Interaction between multiple migrating planets can result in complex dynamical outcomes

Effects on planetary systems

Orbital resonances

• Migration can drive planets into mean motion resonances (MMRs)
• Common resonances include 2:1, 3:2, and 4:3 orbital period ratios
• Resonant configurations can stabilize planetary orbits and prevent further migration
• Examples of resonant systems include the Galilean moons of Jupiter and some exoplanet systems (GJ 876)
• Breaking of resonances can lead to instabilities and further orbital evolution

Hot Jupiters formation

• Migration explains the presence of gas giants very close to their host stars
• Type II migration can bring Jupiter-mass planets from beyond the snow line to short-period orbits
• Alternative formation mechanisms include in situ formation and high-eccentricity migration
• Hot Jupiters represent ~1% of known exoplanets, challenging our understanding of planet formation

Planetary system architecture

• Migration shapes the final orbital configuration of planetary systems
• Can lead to compact systems with multiple planets in close orbits
• Explains the diversity of observed exoplanetary system architectures
• Influences the distribution of planet masses and orbital periods in a system
• May result in the ejection of some planets, affecting the overall system stability

Observational evidence

Exoplanet population distribution

• Observed exoplanet demographics provide evidence for migration processes
• Pile-up of hot Jupiters at orbital periods of ~3 days suggests a migration origin
• Super-Earths and mini-Neptunes in compact systems indicate possible migration and orbital evolution
• Period ratio distribution of adjacent planets shows preference for near-resonant configurations
• Correlation between stellar metallicity and giant planet occurrence supports core accretion followed by migration

Debris disk structures

• Asymmetries and gaps in debris disks can indicate the presence of migrating planets
• Warps and spiral structures in disks may be caused by planet-disk interactions
• Examples of systems with disk features attributed to planets include Beta Pictoris and HD 100546
• Observations of transition disks provide insights into ongoing planet formation and migration processes
• ALMA observations have revealed detailed disk structures consistent with planet-disk interactions

Migration in our solar system

Nice model

• Proposes a scenario for the late-stage migration of giant planets in our solar system
• Suggests that Jupiter, Saturn, Uranus, and Neptune formed in a more compact configuration
• Outward migration of Saturn, Uranus, and Neptune led to the current orbital architecture
• Explains the Late Heavy Bombardment and the formation of the Kuiper Belt
• Accounts for the capture of Jupiter's Trojan asteroids during the migration process

Grand Tack hypothesis

• Describes an early inward then outward migration of Jupiter and Saturn
• Jupiter's initial inward migration halted and reversed by Saturn's growth and migration
• Explains the relatively small size of Mars and the low mass of the asteroid belt
• Accounts for the delivery of water-rich material to the inner solar system
• Provides a mechanism for shaping the early solar system's planetary architecture

Numerical simulations

N-body simulations

• Model the gravitational interactions between multiple bodies in a planetary system
• Used to study long-term stability and evolution of planetary systems
• Can incorporate simplified models of gas drag and disk torques
• Allow for the investigation of planet-planet scattering and resonance capture
• Examples include the MERCURY and REBOUND codes widely used in planetary dynamics studies

Hydrodynamic simulations

• Model the interaction between planets and the gas disk in detail
• Solve fluid dynamics equations to capture disk structure and evolution
• Can resolve gap opening, spiral density waves, and gas accretion onto planets
• Used to study migration rates, gap profiles, and disk instabilities
• Examples include FARGO, PLUTO, and ATHENA codes used for protoplanetary disk simulations

Consequences for habitability

Water delivery to terrestrial planets

• Migration of ice-rich bodies from beyond the snow line can deliver water to inner planets
• Jupiter's migration may have influenced the water content of Earth and other terrestrial planets
• Affects the potential for life on exoplanets by determining their water inventory
• Simulations suggest that migration can lead to a wide range of water content in terrestrial planets
• Implications for the frequency of habitable worlds in different planetary system architectures

Orbital stability of habitable zones

• Migration can alter the long-term stability of planets in the habitable zone
• Giant planet migration may eject or destabilize potentially habitable planets
• Resonant configurations resulting from migration can enhance the stability of habitable planets
• The final architecture of a system post-migration determines the width of the stable habitable zone
• Studies show that systems with migrated giant planets can still maintain stable habitable planets

Challenges in migration theory

Disk lifetime vs migration time

• Classical migration theories often predict migration timescales shorter than observed disk lifetimes
• Rapid migration could lead to planet loss, contradicting the observed abundance of planets
• Proposed solutions include magnetic fields, disk winds, and planet traps
• Understanding this discrepancy is crucial for developing accurate planet formation models
• Ongoing research focuses on identifying mechanisms that can slow down or halt migration

Stopping mechanisms

• Various processes have been proposed to halt or slow down planetary migration
• Include disk edges, planet traps at opacity transitions, and multi-planet resonant chains
• Magnetospheric cavities around young stars may provide a natural inner boundary for migration
• Photoevaporation of the disk can create an inner cavity, potentially stopping inward migration
• Understanding these mechanisms is essential for explaining the observed diversity of exoplanet systems

Future research directions

Improved disk models

• Development of more realistic protoplanetary disk models incorporating detailed physics
• Inclusion of non-ideal MHD effects, dust evolution, and radiative transfer in migration simulations
• Investigation of 3D effects and vertical structure on migration rates
• Study of disk substructures (rings, gaps) and their impact on planet formation and migration
• Integration of disk chemistry models to understand the compositional evolution during migration

Multi-planet migration scenarios

• Exploration of migration in systems with multiple forming and evolving planets
• Investigation of resonance capture and breaking in multi-planet systems
• Study of the interplay between migration and planet-planet scattering
• Examination of how migration affects the final mass distribution in planetary systems
• Development of population synthesis models incorporating realistic multi-planet migration