Numerical Simulations of Gaseous Disks Generated from Collisional Cascades at the Roche Limits of White Dwarf Stars

TL;DR

This paper uses numerical simulations to study how gaseous disks form and evolve from collisional cascades of small particles near white dwarf stars, revealing two distinct accretion regimes depending on particle input rate.

Contribution

It introduces a model for long-term evolution of vaporized debris disks around white dwarfs, identifying critical mass transfer rates and different accretion behaviors.

Findings

Steady accretion disks form when input rate exceeds critical value.

System alternates between high and low accretion states below critical rate.

Models suggest significant metal accretion but no thin solid ensemble inside Roche limit.

Abstract

We consider the long-term evolution of gaseous disks fed by the vaporization of small particles produced in a collisional cascade inside the Roche limit of a 0.6 Msun white dwarf. Adding solids with radius \r0\ at a constant rate $\dot{M}_0$ into a narrow annulus leads to two distinct types of evolution. When $\dot{M}_0 > \dot{M}_{0,crit}$ = $3 \times 10^4 ~ (r_0 / {\rm 1~km})^{3.92}$~g s$^{-1}$, the cascade generates a fairly steady accretion disk where the mass transfer rate of gas onto the white dwarf is roughly $\dot{M}_0$ and the mass in gas is $M_g \approx 2.3 \times 10^{22} ~ (\dot{M}_0 / 10^{10}~g~s^{-1}) ~ ({\rm 1500~K} / T_0) ~ (10^{-3} / \alpha)$~g, where $T_0$ is the temperature of the gas near the Roche limit and $\alpha$ is the dimensionless viscosity parameter. If $ \dot{M}_0 < \dot{M}_{0,crit}$, the system alternates between high states with large mass transfer rates and low states with negligible accretion. Although either mode of evolution adds significant amounts of metals to the white dwarf photosphere, none of our calculations yield a vertically thin ensemble of solids inside the Roche limit. X-ray observations can place limits on the mass transfer rate and test this model for metallic line white dwarfs.