How Do The Angular Momentum Deficits Of Protoplanetary Disks, As Inferred From ALMA Observations Of HL Tau And Other Disk Systems, Impact The Long-term Orbital Stability Of Hot Jupiters That Undergo Disk-driven Migration, Particularly In The Context Of The Secular Gravitational Interactions With The Disk's Residual Mass Distribution?

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The angular momentum deficit in protoplanetary disks, such as that observed around HL Tau, plays a crucial role in the migration and long-term stability of hot Jupiters. Here's a structured summary of the key points:

  1. Angular Momentum Deficit and Disk-Driven Migration:

    • A disk with an angular momentum deficit may have a lower mass or different structural properties, potentially altering the efficiency of disk-driven migration. This could affect the rate at which hot Jupiters spiral inward, possibly slowing migration due to reduced torques from the disk.

  2. Impact on Migration Efficiency:

    • The structure of the disk, influenced by its angular momentum, affects Lindblad resonances, which in turn influence the torque exerted on the planet. This could lead to variations in migration rates or directions.

  3. Secular Gravitational Interactions Post-Migration:

    • After a hot Jupiter migrates close to the star, residual disk material can exert secular gravitational influences. These interactions might cause orbital precession or oscillations, potentially affecting long-term orbital stability.

  4. Timescale Considerations:

    • Disk-driven migration occurs on shorter timescales (millions of years), while secular effects from residual disk material act over longer periods (billions of years). These effects might lead to gradual orbital changes, such as eccentricity variations.

  5. Gap-Opening and Transition Disks:

    • A planet opening a gap in the disk might experience continued influence from material beyond the gap. The residual mass distribution in transition disks could exert gravitational torques, affecting the planet's orbit.

  6. Relative Importance of Factors:

    • While secular effects from the disk are significant, tidal interactions with the host star might dominate in shaping the close orbits of hot Jupiters. The influence of residual disk mass needs to be weighed against these tidal forces.

In conclusion, the angular momentum deficit in protoplanetary disks can influence both the migration process and the subsequent orbital stability of hot Jupiters. Further research into observational data and theoretical models is essential to fully understand these mechanisms.