Journal
MONTHLY NOTICES OF THE ROYAL ASTRONOMICAL SOCIETY
Volume 502, Issue 2, Pages 1579-1595Publisher
OXFORD UNIV PRESS
DOI: 10.1093/mnras/stab111
Keywords
hydrodynamics; instabilities; methods: numerical; planets and satellites: formation
Categories
Funding
- STFC Consolidated grants [2017-2020 ST/P000592/1, 2020-2023 ST/T000341/1]
- PRACE aisbl
- QMUL Research-IT
- Royal Society University Research Fellowship
- STFC [1949424, ST/T000341/1] Funding Source: UKRI
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The paper presents a new approach to streaming instabilities, allowing for more accurate solutions to linear stability problems with lower computational costs. It also demonstrates techniques for reducing integral equations to complex polynomials and counting roots of dispersion relations inside contours. The methods described can reproduce and surpass the accuracy of previous results in the literature.
Occurring in protoplanetary discs composed of dust and gas, streaming instabilities are a favoured mechanism to drive the formation of planetesimals. The polydispserse streaming instability is a generalization of the streaming instability to a continuum of dust sizes. This second paper in the series provides a more in-depth derivation of the governing equations and presents novel numerical methods for solving the associated linear stability problem. In addition to the direct discretization of the eigenproblem at second order introduced in the previous paper, a new technique based on numerically reducing the system of integral equations to a complex polynomial combined with root finding is found to yield accurate results at much lower computational cost. A related method for counting roots of the dispersion relation inside a contour without locating those roots is also demonstrated. Applications of these methods show they can reproduce and exceed the accuracy of previous results in the literature, and new benchmark results are provided. Implementations of the methods described are made available in an accompanying python package psitools.
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