Tidal Disruption of Blanets by Supermassive Black Holes: From Test Particles to Planetary-Mass Bodies in Kerr Spacetime

Abstract

Planetary-mass bodies formed in active galactic nucleus (AGN) discs, termed "blanets", may undergo tidal disruption by the central supermassive black hole (SMBH). We analyse this process in Kerr spacetime using Mino-time geodesics and the Marck tidal tensor in a parallel-transported tetrad, treating the blanet as a test particle with finite size entering through the disruption criterion. For a blanet of $100M_{\oplus }$ and $6R_{\oplus }$ around a $10^7{M}_{\odot }$ SMBH, the tidal radius is 0.82 AU, or 8.3 gravitational radii, requiring a non-perturbative relativistic treatment. The Hills mass depends on bulk density as $M_{\mathrm{Hills}}\propto {\rho }_p^{-1/2}$ and is independent of blanet mass at fixed density. Rocky compositions yield a lower Hills mass than a Sun-like star, while volatile-rich compositions yield a higher value, suggesting a potential composition diagnostic. The frozen-in fallback model gives a peak time of about 15 yr and a peak luminosity of $3.7\times 10^{40}$ erg/s, about $3\times 10^{-5}$ of the Eddington luminosity, predicting a faint, ultraviolet-peaked transient lasting roughly a century. Scalar resonant relaxation in the surrounding nuclear star cluster may deliver blanets to disruptive orbits over $10^8$ to $10^9$ yr, implying an estimated per-AGN event rate of $10^{-7}$ to $10^{-6}$ per year. Gravitational waves from sub-Earth-mass debris fragments remain approximately nine orders of magnitude below Laser Interferometer Space Antenna sensitivity.

21 pages, 5 figures. Revised manuscript; corrected numerical estimates