What Are The Potential Effects Of Tidal Heating On The Orbital Decay Rates Of Planetary Bodies Composed Of Silicate-rich Materials In The Circumstellar Environment Of A 0.6 M⊙ White Dwarf With A Metal Pollution Level Of [Fe/H] = +2, Given The Presence Of A Close-in, Highly Eccentric Jupiter-mass Planet That Is Likely To Have Undergone Significant Orbital Migration During The Asymptotic Giant Branch Phase Of The Progenitor Star?

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The potential effects of tidal heating on the orbital decay rates of silicate-rich planetary bodies in the described system can be summarized as follows:

  1. Tidal Heating Mechanism: The gravitational pull of the 0.6 M⊙ white dwarf on the close-in, eccentric Jupiter-mass planet generates significant tidal forces. These forces cause internal friction and heat within the planet, leading to energy dissipation.

  2. Impact on Orbital Decay: The energy dissipated through tidal heating results in a loss of angular momentum for the planet. This loss accelerates the orbital decay, causing the planet's orbit to shrink and spiral inward toward the white dwarf.

  3. Role of Silicate Composition: Silicate-rich materials, common in rocky planets, may have lower rigidity compared to other compositions. This could enhance tidal dissipation, making the planet more susceptible to orbital decay as internal heat generation is more efficient.

  4. Influence of High Eccentricity: The planet's highly eccentric orbit amplifies tidal effects, especially during periastron, where the proximity to the white dwarf intensifies gravitational interactions, further contributing to orbital decay.

  5. System History and Metal Content: The white dwarf's high metal content ([Fe/H] = +2) suggests past accretion of planetary material, indicating a dynamically active system. This history supports the likelihood of ongoing orbital instability and decay for the remaining planets.

  6. Orbital Evolution: While tidal forces might tend to circularize orbits over time, the significant orbital migration during the AGB phase and the planet's current eccentric orbit suggest that decay is a dominant process, driven by the efficient energy dissipation in silicate-rich materials.

In conclusion, tidal heating significantly contributes to the orbital decay of the silicate-rich planet due to strong tidal forces, enhanced by the planet's close, eccentric orbit and material properties, leading to a faster spiral toward the white dwarf.