Gap formation driven by planets in invisicd discs

This repository implements the methods of Cimerman & Rafikov (2021), Cimerman & Rafikov (2023) and Cordwell & Rafikov (2024) to generate synthetic surface densities of gap formed by a planet in a protoplanetary discs. The 1D axisymmetric surface density of the protoplanetary disk can be generated within seconds and provides a good fit (especially in the outer disk) to the evolution of the disk.

We provide implementations of the vortensity reconstruction methods in both python and matlab, however the linear analytic solution is only provided in python.

Please see the associated notebooks for examples of function calls and output.

Running the python implementation requires matplotlib, numpy and scipy to be installed. The matlab implementation works with base matlab.

Please note that the python and Matlab implementationa have similar looking but different commands to call (and a slightly different implementation of the r to $\tau$ transformation).

Example Output

Implementation Description

CR21 generated a semi-analytical formula for the size of the shock generated by a sub thermal mass planet in a globally isothermal disk. They then used this to describe the linear evolution in vortensity $\zeta$. CR23 extended this to reconstruct the surface density of a disk from its vortensity.

CR24

Changes from the published papers

This repository includes an adjustment of $2 \pi$ multiplied to $\Delta \zeta$. This was an error in the original paper due to a mistaken normalisation, the evidence for this shift is shown in the python notebook example and a correction from the original authors is forthcoming.

Use in further work

These codes may be freely distributed and modified as long as credit to the author (Amelia J. Cordwell) remains. Any use in a scientific publication should cite both this repository, and the relevant papers.

Referenced papers

Cimerman & Rafikov, 2021 - https://arxiv.org/abs/2108.01423 Cimerman & Rafikov, 2023 - https://arxiv.org/abs/2212.03062 Cordwell & Rafikov, 2024 - In prep.