Producing planetary debris exterior to white dwarf Roche radii through sublimative rotational fission

Technical Summary: Producing planetary debris exterior to white dwarf Roche radii through sublimative rotational fission

Problem Statement
Observations of white dwarf (WD) planetary systems reveal periodic transiting debris located at distances exceeding the canonical rubble-pile Roche limit (typically 1–5 Roche radii, $R_{Roche}$). This distribution contradicts standard formation models which posit that minor planets are tidally disrupted only within the Roche sphere. While mechanisms such as ejecta from impacts or internal spin-orbit angular momentum exchange have been proposed, they often struggle to explain debris at these larger distances or require specific physical conditions (e.g., extreme elongation). Furthermore, the radiative YORP (Yarkovsky-O'Keefe-Radzievskii-Paddack) effect, while capable of inducing rotational fission, is often inefficient for the relevant cooling ages and object sizes. The authors investigate whether sublimative outgassing, acting as a torque analogous to YORP (termed SYORP), can drive rotational fission of minor planets exterior to the Roche sphere.

Methodology
The study employs the Many Materials Orbital Sublimation (MaMOS) model to quantify the outgassing properties and resulting spin-up rates of minor planets. The approach involves:

1. Physical Modeling: The SYORP effect is modeled as the sublimative analogue to the YORP effect. The angular acceleration ($d\omega/dt$) is derived from the dynamic sublimation back-reaction pressure ($P_S$) and a dimensionless SYORP coefficient ($C_S$). The model solves energy balance equations incorporating stellar heating, radiative cooling, and sublimative cooling to determine surface temperature and mass flux.
2. Material Selection: Three representative planetary materials are analyzed: iron (core material), forsterite (mantle material), and water ice (cometary material). Parameters for these materials, including latent heat of sublimation, density, and sublimation coefficients, are drawn from observational and experimental data (e.g., Chang'e 6 lunar samples for forsterite).
3. Simulation Parameters: The authors simulate spin-up timescales for objects with radii of 0.1, 1.0, and 10 km orbiting a $0.6 M_\odot$ white dwarf. They vary the orbital distance (1–5 $R_{Roche}$) and the white dwarf cooling age (10 Myr to 10 Gyr).
4. Spin-Up Scenarios: The simulations test different spin-up regimes:
   • Uniform spin-up in a single direction.
   • Stochastic magnitude of spin kicks in a single direction.
   • Stochastic magnitude and direction of spin kicks.
   • Comparisons are made between objects with internal tensile strength ($\sigma = 1$ kPa) and strengthless rubble piles ($\sigma = 0$ Pa).
5. Comparison: SYORP timescales are directly compared against YORP fission timescales using established YORP coefficients ($\chi$).

Key Results

• Efficiency of Sublimative Fission: For white dwarfs with cooling ages up to $\sim 1$ Gyr, sublimative fission of planetesimals and fragments with radii $\lesssim 0.1$ km (driven primarily by water ice outgassing) occurs on observable timescales (within 10 years). This is true regardless of whether the spin-up is monotonic or stochastic.
• Comparison with YORP: Sublimative fission timescales are orders of magnitude shorter than corresponding YORP fission timescales, particularly for water ice outgassing across the 1–5 $R_{Roche}$ range. YORP and sublimation curves only begin to overlap at distances of $\approx 3-4 R_{Roche}$ and only for forsterite.
• Material Dependence:
  • Water Ice: Effective for young (10 Myr) to intermediate-age (1 Gyr) white dwarfs for small objects ($\lesssim 1$ km).
  • Iron and Forsterite: Effective for "drier" planetesimals around white dwarfs with cooling ages of 10–100 Myr.
• Object Size Limits: The results suggest that sublimative fission is primarily relevant for objects with radii $R < 10$ km. Objects larger than this are unlikely to undergo fission from a standing start within the observed timeframe, consistent with the lack of observed transiting debris larger than $\sim 10$ km.
• Strength Independence: The findings do not substantially differ between strengthless rubble piles and objects with 1 kPa of internal strength, as the reduction in destruction timescale due to decreasing radius dominates over the increase in strength for smaller fragments.
• Snowline Context: The study contextualizes these findings with sublimation radii ($r_{sub}$), noting that for young white dwarfs, the sublimation radius for iron and forsterite can extend well beyond the Roche limit, allowing these materials to sublimate and drive fission even in the absence of volatiles like water.

Significance and Claims
The paper claims to provide a viable mechanism for the production of planetary debris exterior to the white dwarf Roche sphere without requiring the parent body to be tidally disrupted within that sphere. The authors conclude that gravitationally scattered comets and asteroids do not need to adopt pericentres within the Roche radius to eventually enrich or pollute the star with metals. Instead, sublimative rotational fission (SYORP) can break apart minor planets at distances of 1–5 $R_{Roche}$, particularly for water-rich bodies around young to intermediate-age white dwarfs. This mechanism offers an explanation for the observed distribution of orbital periods (5–25 hours and beyond) in transiting debris systems, which cannot be easily explained by canonical tidal disruption models alone. The study suggests that this process may be a primary driver for the evolution of transiting debris around young white dwarfs, potentially explaining the rapid cessation of photometric activity observed in systems like WD 1145+017 and ZTF J1944+4557.