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.

• The paper demonstrates that massive close-in planets can shield white dwarfs by ejecting or capturing over 80% of high-eccentricity asteroids before they pollute the star.
• It employs high-precision N-body simulations to analyze the effect of planetary mass, orbital distance, and fragmentation on asteroid removal efficiency.
• Results reveal that protection improves with increasing planet mass and tighter orbital separations, reconciling differences in observed pollution levels.

Dynamical Shielding of White Dwarfs: The Role of Close-in Planets in Suppressing Metal Pollution

Introduction

A significant fraction of white dwarfs exhibit signatures of ongoing accretion from remnant planetary systems, manifested as metal absorption lines in their atmospheres. These features—known as "white dwarf pollution"—trace the accretion of planetary debris, predominantly from tidal disruption of planetary bodies that are dynamically transported into the stellar Roche sphere. The presence of pollution requires an efficient delivery mechanism for debris. It has long been hypothesized that surviving planets in white dwarf systems are critical actors in facilitating this transport, via gravitational scattering of asteroids and minor bodies onto star-grazing orbits.

However, a subset of white dwarfs with detected planetary companions, notably WD 1856+534 with its tightly bound giant planet, do not exhibit detectable metal pollution. This challenges the paradigm of canonical planetary-driven pollution and raises the possibility that massive close-in planets may instead serve as dynamical barriers, ejecting or capturing incoming debris before it contaminates the stellar atmosphere.

This paper presents an ensemble of high-precision, short-term N-body simulations to systematically quantify the efficacy of close-in planets as "protectors" against asteroid-driven pollution. It evaluates the dynamical pathways for asteroid scattering, disruption, and ejection, and establishes parameter regimes (mass, semi-major axis) where planetary shielding is operative. The work directly addresses whether planets of varying properties are capable of suppressing the dominant pollution channel: dynamically-driven, high-eccentricity asteroid delivery.

Physical Model and Simulation Framework

The modeled system consists of a white dwarf, a close-in giant planet on a circular orbit, and a population of asteroids initialized on highly eccentric orbits with pericenters near or within the Roche radius of the star.

Figure 1: Schematic representation of the simulated white dwarf system, showing a planet on a circular orbit and an asteroid on a highly eccentric trajectory. The asteroid's periapsis is close to or inside the stellar Roche limit.

White dwarf and planet parameters were benchmarked to the observed WD 1856+534b system: $M_\mathrm{WD}=0.518\,M_\odot$, $R_\mathrm{WD}=0.0131\,R_\odot$, $a_p=0.02$ au, with the planet's mass primarily set to 13.8 $M_\mathrm{Jup}$ (theoretical upper limit) but varied across a wide range to probe mass dependence. The planet's physical radius across different masses uses updated empirical mass-radius relations [muller_mass-radius_2024].

Asteroids are treated as massless test particles and drawn from semi-major axes $a_\mathrm{ast}\in[1,10]$ au to represent an inner-system reservoir. Initial asteroid pericenters $q_\mathrm{ast}$ are uniformly sampled within (0.5, 1.0) $r_\mathrm{Roche}$, ensuring trajectories that would lead to near-disruptive passages in the absence of a planet. Both coplanar and three-dimensional initial configurations are considered, enabling assessment of inclination effects.

Integration is performed over $10T_\mathrm{ast}$, where $T_\mathrm{ast}$ is the asteroid's initial orbital period, with the duration motivated by tidal disruption timescales and capture/ejection efficiencies.

Dynamical Outcome Classification and Metrics

Each simulation tracks the fate of the asteroid, assigning it to one of five exclusive classes:

• Ejected-OutRoche: Ejected before entering the Roche radius.
• Ejected-InRoche: Ejected after passing through the Roche zone, pre-accretion.
• Collide: Collision with the planet.
• Crash: Collision with the white dwarf.
• Bound: Remains bound without colliding or being ejected by the end of the simulation.

This outcome structure enables robust calculation of the "protection fraction" $F_\mathrm{Protection}$—the proportion of asteroids removed from polluting the white dwarf (via ejection or planetary collision):

Figure 2: Representative asteroid trajectories for each classification. Asteroids can be ejected prior to entering the Roche zone, post-entry, collide with the planet, directly impact the white dwarf, or remain bound for extended periods.

The fate space is further analysed in terms of final orbital energy and closest approach to the white dwarf.

Figure 3: Distribution of asteroids in final energy-minimum distance space. Dots denote the fate classification: ejection (bound/unbound), collisions with the white dwarf or planet, and the initial state (red dots) are indicated.

Numerical Results

Protection Efficiency for Benchmark Case

For a WD1856+534b-like system ($a_p=0.02$ au, $M_p\gtrsim0.5\,M_\mathrm{Jup}$), the simulations yield the following core results:

• Ejection and planetary collision clear $>$80% of highly eccentric asteroids before they can accrete onto the white dwarf.
• For the fiducial maximum mass (13.8 $M_\mathrm{Jup}$), the overall protective fraction reaches $\sim$92%.
• Protection is dominated by post-Roche ejection ("Ejected-InRoche"), implying extensive phase space for dynamical removal even after tidal entry.

  Figure 4: Time evolution of the fraction of bound asteroids. Most ejection/collision outcomes occur in the first few orbital periods.

Dependence on Planet Mass and Orbital Separation

The efficacy of dynamical protection is strongly sensitive to both planet mass and orbital distance:

• At fixed $a_p=0.02$ au, protection remains $>$80% for $M_p\gtrsim0.1\,M_\mathrm{Jup}$ and rises toward $\sim$95% at $M_p\sim5-13.8\,M_\mathrm{Jup}$.
• Increasing $a_p$ to 0.5–1.0 au reduces the protection fraction to $\lesssim70\%$ even for massive planets.

These trends are consistent with analytical scaling using a Safronov-like criterion, parameterized as the close-encounter ratio $\Lambda_c$.

Figure 5: (Left) Protection fraction as a function of planetary mass for different semi-major axes. (Right) Contours of the close-encounter ratio $\Lambda_c$ in the $(M_p,a_p)$ parameter plane.

Tidal Fragmentation and Debris Removal

A crucial extension evaluated the impact of asteroid fragmentation upon Roche passage. A parent asteroid, upon first entry into the Roche sphere, is instantaneously split into multiple fragments. Tracking individual fragment evolution, the simulations demonstrate:

• Even after fragmentation, most debris is dynamically removed (ejected or captured by the planet) before accretion.
• Protection fraction remains robust (within $\sim1\%$) over a broad spectrum of fragment sizes (10–500 km), confirming that planetary shielding remains effective post-disruption.

  Figure 6: Evolution of particle distances to the white dwarf, comparing intact (top panel) versus tidally disrupted fragments (middle and bottom panels). Many fragments are subsequently ejected by planetary interactions.

Three-Dimensional Effects

Isotropic inclination distributions (3D) further enhance planetary protection, yielding shielding fractions of $\sim$97% for fiducial planet parameters. However, for lower-mass or more distant planets, the efficiency degrades more quickly than in the coplanar case.

Figure 7: Fractional classification outcomes as a function of asteroid initial periapsis location, illustrating insensitivity of protection efficiency to initial perihelion parameters within studied ranges.

Implications and Context

Interpretation of Observations

The dynamical barrier produced by close-in giant planets reconciles the absence of pollution in WD 1856+534 and similar systems, despite the prevalence of high-pollution rates in other white dwarfs. The results demonstrate that the majority of potential asteroid polluters are either dynamically ejected or intercepted by the planet, with only a small residual contribution from orbiters that remain bound for many orbits.

These findings suggest that the mere presence of a massive close-in planet leads to a statistical suppression of white dwarf pollution by roughly an order of magnitude compared to systems lacking such protection. This offers an explanation for the decoherence between planetary presence and pollution fraction across the white dwarf population.

Consistency With and Advancement Over Previous Work

Prior studies focused on radiative drag-driven migration or on wide-orbit planetary perturbers [veras_white_2020, pham_polluting_2024], but did not systematically assess the direct dynamical barrier posed by close-in planets to highly eccentric asteroid influx [rogers_wd0141-675_2023]. The current work expands the theoretical framework and quantifies the planet mass–separation regime necessary for effective protection.

Theoretical and Practical Implications

• Planetary system architecture is a critical regulator of white dwarf pollution rates. Systems containing close-in gas giants (particularly with $a_p\lesssim0.1$ au and $M_p\gtrsim0.5\,M_\mathrm{Jup}$) should be characterized by significantly lower photospheric metal abundances.
• Distant and low-mass planets have dramatically reduced shielding capability, suggesting that in these systems, classical pollution mechanisms remain effective.
• The signature of planetary protection may manifest as enhanced compositional enrichment of the planet itself, particularly in the case of planetary interception and accretion of polluters—a potential target for infrared and high-resolution characterization.
• Future white dwarf planetary system surveys (notably with JWST and ground-based facilities) should test for anti-correlations between close-in planetary presence and white dwarf pollution signatures to further validate and refine these theoretical expectations.

Conclusion

This study provides a rigorous numerical demonstration that close-in (sub-au), massive planets can serve as efficient dynamical barriers, reducing the pollution of white dwarfs by highly eccentric asteroids to below 20% of the unfiltered rate, with effectiveness scaling positively with mass and inversely with orbital separation. The results explain the lack of metal pollution in planetary systems like WD 1856+534 and delineate a quantitative framework for predicting pollution rates as a function of system architecture. Non-detection of pollution in certain planetary systems, therefore, does not challenge the broader paradigm of planet-mediated pollution, but instead illuminates the distinct dynamical role played by close-in planetary companions.

Further systematic discoveries of white dwarf systems with varied planetary architectures will enable empirical discrimination between stochastic and planet-suppressed pollution scenarios, deepening our understanding of post-main-sequence planetary system evolution.