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arXiv · 1703.10617

Variations on Debris Disks IV. An Improved Analytical Model for Collisional Cascades

Scott J. Kenyon·Benjamin C. Bromley
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Abstract

We derive a new analytical model for the evolution of a collisional cascade in a thin annulus around a single central star. In this model, $r_{max}~$ the size of the largest object declines with time (t); $r_{max} \propto t^{-\gamma}$, with $\gamma$ = 0.1-0.2. Compared to standard models where $r_{max}~$ is constant in time, this evolution results in a more rapid decline of $M_d$, the total mass of solids in the annulus and $L_d$, the luminosity of small particles in the annulus: $M_d \propto t^{-(\gamma + 1)}~$ and $L_d \propto t^{-(\gamma/2 + 1)}~~$. We demonstrate that the analytical model provides an excellent match to a comprehensive suite of numerical coagulation simulations for annuli at 1 AU and at 25 AU. If the evolution of real debris disks follows the predictions of the analytical or numerical models, the observed luminosities for evolved stars require up to a factor of two more mass than predicted by previous analytical models.

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Scott J. Kenyon, Benjamin C. Bromley. 2017-03-30. Variations on Debris Disks IV. An Improved Analytical Model for Collisional Cascades. https://doi.org/10.3847/1538-4357%2Faa6982

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