[Paper Review] Emission from elliptical streams of dusty debris around white dwarfs

C. J. Nixon, J. E. Pringle+3 more|arXiv (Cornell University)|Jun 13, 2020

Astro and Planetary Science2 references13 citations

TL;DR

This paper proposes that dusty debris around white dwarfs remains on highly eccentric elliptical orbits rather than circularizing into a disc, explaining observed infrared excesses through reprocessing of white dwarf light. The model shows that debris spreads into a time-steady elliptical ring, producing lightcurves and spectra consistent with observations, particularly at 8–12 μm where silicate features appear.

ABSTRACT

White dwarfs are routinely observed to have polluted atmospheres, and sometimes significant infrared excesses, that indicate ongoing accretion of circumstellar dust and rocky debris. Typically this debris is assumed to be in the form of a (circular) disc, and to originate from asteroids that passed close enough to the white dwarf to be pulled apart by tides. However, theoretical considerations suggest that the circularisation of the debris, which initially occupies highly eccentric orbits, is very slow. We therefore hypothesise that the observations may be readily explained by the debris remaining on highly eccentric orbits, and we explore the properties of such debris. For the generic case of an asteroid originating at several au from the white dwarf, we find that all of the tidal debris is always bound to the white dwarf and that the orbital energy distribution of the debris is narrow enough that it executes similar elliptical orbits with only a narrow spread. Assuming that the tidal field of the white dwarf is sufficient to minimise the effects of self-gravity and collisions within the debris, we estimate the time over which the debris spreads into a single elliptical ring, and we generate toy spectra and lightcurves from the initial disruption to late times when the debris distribution is essentially time steady. Finally we speculate on the connection between these simple considerations and the observed properties of these systems, and on additional physical processes that may change this simple picture.

Motivation & Objective

• To challenge the standard assumption that tidal debris from disrupted asteroids circularizes into a disc around white dwarfs.
• To investigate whether highly eccentric debris streams can explain observed infrared excesses and lightcurve variability.
• To model the evolution of debris from disruption to a time-steady elliptical configuration, focusing on spectral and photometric properties.
• To assess the viability of this model against observational data, particularly SEDs and variability amplitudes.
• To identify physical processes—such as self-gravity or perturbations—that may alter the simple elliptical stream picture.

Proposed method

• Assumes tidal disruption of asteroids at several AU from the white dwarf, producing debris on highly eccentric orbits.
• Uses the tidal radius formula $ R_{ m t} \approx 1.3 \left( \frac{\rho_{\rm ast}}{3\,{\rm g/cm}^3} \right)^{-1/3} \left( \frac{M_{\rm wd}}{0.6M_{\odot}} \right)^{1/3} R_{\odot} $ to estimate disruption conditions.
• Models debris as a narrow-energy distribution, leading to similar elliptical orbits with minimal spread.
• Assumes the white dwarf's tidal field suppresses self-gravity and collisions within the debris stream.
• Calculates time evolution of debris spreading into a single elliptical ring, estimating the spreading timescale.
• Generates synthetic spectra and lightcurves from initial disruption to late-time steady state, assuming optically thin, visible debris.

Experimental results

Research questions

• RQ1 Can highly eccentric debris streams explain the observed infrared excesses in white dwarfs without requiring circularization into a disc?
• RQ2 How do the lightcurves and spectral energy distributions (SEDs) of elliptical debris streams compare with observed data?
• RQ3 What is the expected variability amplitude and timescale of such streams, particularly at short wavelengths?
• RQ4 How long does it take for the debris to spread into a time-steady elliptical ring configuration?
• RQ5 What role might additional physical processes—like self-gravity or planetary perturbations—play in altering the elliptical stream model?

Key findings

• Tidal debris from disrupted asteroids remains bound and forms a narrow-energy distribution, leading to similar elliptical orbits with minimal spread.
• The model produces lightcurves with large-amplitude, coherent variability, most prominent at short wavelengths due to higher temperatures.
• Spectra from the model show reasonable agreement with observed SEDs, particularly the silicate feature at 8–12 μm.
• The timescale for debris to spread into a time-steady elliptical ring is estimated, though the exact value is not quantified in the text.
• The model explains the observed infrared excess without requiring a circular disc, offering an alternative to the standard circularization paradigm.
• Transits by debris are possible but require large asteroids or significant stirring, with optical depth ~0.3 for a 20 km asteroid.