How a Close-in Planet Protects its White Dwarf Host from Pollution

Abstract

Approximately 25-50% of white dwarfs (WDs) exhibit metal absorption lines in their photospheres, which are attributed to accretion from their remnant planetary systems. Although white dwarfs with detected planetary systems are more likely to show photospheric pollution, one notable exception - WD 1856+534 - hosts a close-in giant planet yet exhibits no detectable photospheric metal pollution. Previous studies have proposed that massive, close-in planets can block inward transport of small particles driven by radiative forces (e.g., Poynting-Robertson drag and the Yarkovsky effect). However, it remains unclear whether the close-in planet can similarly prevent delivery of larger bodies via dynamical interactions. We aim to quantify the protective influence of close-in planets on white-dwarf pollution by asteroids approaching on near-parabolic orbits, and to explore the planetary masses and orbital separations required to provide effective protection. We perform ensembles of short-term N-body integrations, sampling a range of planet masses and orbital separations and initializing asteroids on highly eccentric orbits with periapses near the WD Roche radius, in order to measure scattering, capture, and ejection outcomes and quantify the planet's shielding efficiency. For WD1856+534b-like configurations (a_p = 0.02 au), giant planets with masses greater than 0.5 Jupiter masses are sufficient to clear over 80% of highly eccentric small-body contaminants. The effectiveness of the protective effect diminishes with decreasing planetary mass and increasing semi-major axis. These findings help explain why some white dwarfs that host close-in giant planets do not show the photospheric metal pollution commonly observed in other systems.

Figures (7)

• Figure 1: Simplified model of the white dwarf system used in our simulation. The planet orbits the central white dwarf on a circular path, while an asteroid initially follows a highly eccentric trajectory toward the white dwarf. Please note that the figure is not to scale.
• Figure 2: Typical asteroid trajectories of four classifications in section \ref{['subsec:define']} on a logarithmic scale, with units in au. Line colors denote classifications and the diamond markers indicate the starting points of the asteroids. (a) belong to "Ejected-OutRoche": The asteroid was ejected before entering into the roche limit; (b) and (c) are "Ejected-InRoche": They are both ejected after entering into the roche limit, the difference is the duration they spent within the Roche limit. (d) shows the "Collide" case: The asteroid collided with the planet when crossing the planetary orbit (We depict the planet at the moment of collision (navy circles); note that the planetary radii do not represent the planets' actual sizes.). (e) shows the "Crash" case: The asteroid was scattered directly to the WD. And (f) are still "Bound": They are still orbiting the white dwarf until the end of simulation.
• Figure 3: Distribution of asteroids' final energy and minimum distance to the WD during the entire simulation. The system parameters selected for this simulation are the benchmark parameters of WD1856+534b system given in Table. \ref{['tabel:parameter']}. The red dots in the figure represents the initial state of asteroids. black dots represent the final state of each asteroid group at the end of the simulation; the color of the region where they land denotes their ultimate fate. And the black inverted triangles indicate those that collided with planets.
• Figure 4: The proportion of bound asteroids to all simulated asteroids as a function of simulation time. The two different colors represent the trends under different time units.
• Figure 5: The evolution of the distance between the particles and the white dwarf over time. The top panel show the evolution of asteroid if tidal disruption is ignored. The middle and bottom panel show the evolution of the fragments considering the tidal disruption, with different line styles representing different fragments.