LinearResponse.jl

LinearResponse.jl is a package written in Julia to perform Linear Response calculations. The software is described in Petersen et al. (2024). To see an example of the results from the software, see this repository, which reproduces all the figures from Petersen et al. (2024).

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Installation

To fully use LinearResponse.jl, you will need OrbitalElements.jl, FiniteHilbertTransform.jl, and AstroBasis.jl. This installation assumes that you have not installed any of the four libraries; if you have already installed any of the others (globally, not locally) you may skip that portion of the installation.

The libraries under the JuliaStellarDynamics organisation are currently unregistered¹. To add them to your julia² registry, follow these steps:

You may add all the packages³ at once with this command: julia -e 'using Pkg; Pkg.add(url="https://github.com/JuliaStellarDynamics/FiniteHilbertTransform.jl.git"); Pkg.add(url="https://github.com/JuliaStellarDynamics/OrbitalElements.jl.git"); Pkg.add(url="https://github.com/JuliaStellarDynamics/AstroBasis.jl.git"); Pkg.add(url="https://github.com/JuliaStellarDynamics/LinearResponse.jl.git")'

You can confirm the current version with status LinearResponse in the julia package manager.

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Quickstart

To reproduce the Plummer radial orbit instability calculation, see the example script in examples/PlummerE/runExamplePlummer.jl. Download the file by running:

wget https://github.com/JuliaStellarDynamics/LinearResponse.jl/blob/main/examples/PlummerE/runExamplePlummer.jl

This script will compute the location of the unstable radial orbit instability mode, using a simplified version of the calculation from Petersen et al. (2024) (n1max=1 instead of n1max=10, which results in a factor of 10 speedup). The outputs will all be cached (appearing as several files with the .h5 extension in the folder where the script is run), so re-running the example is inexpensive. This script will take approximately one minute to run.

Run the first example code with the following command:

$ julia path/to/runExamplePlummer.jl

This example will first install some required libraries (Plots). These installations might take a few minutes when first called.

The resulting plot will be created with the name ROIdeterminant.png.

In this image and test, we are highlighting two key results:

1. Measurement of an unstable mode, which is the pole located at $\omega=0.0+0.043i$. This mode location is verified against $N$-body simulations in Petersen et al. (2024).

2. False poles in the lower half-plane. All poles in the lower half-plane for this model are false poles owing to approximation of the function for linear response. We include them in this example as a caution against interpreting poles without validating via convergence tests.

An extension of this script, where the growth rate is computed for a range of radial anisotropy parameters, is Figure 1 in Petersen et al. (2024).

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Other examples

The examples directory also includes several other basic calculations for the Isochrone, Plummer, and Zang disc models. For example, to (very nearly) reproduce the Isochrone damped dipole mode calculation from Fouvry & Prunet (2022), see the example driver script in examples/IsochroneE/runlinearresponseIsochroneISO.jl. Note that this mode is not converged: adjusting parameters (in particular n1max) will result in different pole locations. The example examples/IsochroneA/runlinearresponseIsochroneISO.jl is precisely the calculation performed by Fouvry & Prunet (2022) -- that is, with the analytic isochrone relations. This example will take substantially more computational effort, and can take up to twenty minutes to complete.

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Interactive notebook

If you prefer interactive Jupyter notebooks, you will need to install IJulia following these instructions.

The interactive introduction example is then given in examples/PlummerE/runExamplePlummer.ipynb.

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Uninstall

First start by removing the packages from the environment by running

julia -e 'using Pkg; Pkg.rm("OrbitalElements"); Pkg.rm("AstroBasis");Pkg.rm("FiniteHilbertTransform");Pkg.rm("LinearResponse");'

If you worked in a test environment (that you do not want to keep) you can also simply erase the folder using rm -r /path/to/my_env.

Then to fully erase the package (installed in ~/.julia), run

julia -e 'using Pkg; using Dates; Pkg.gc(collect_delay=Day(0));'

It will erase all the packages which are not known in any of your "active" (i.e., for which the Manifest.toml file is reachable) project/environments, in particular LinearResponse.

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Authors

Mike Petersen - @michael-petersen - michael.petersen@roe.ac.uk

Mathieu Roule - @MathieuRoule - roule@iap.fr

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Footnotes

1. For detailed instructions, check here. ↩

2. If you are new to julia, install by following the instructions at julialang.org/downloads/. To invoke Julia in the Terminal, you need to make sure that the julia command-line program is in your PATH. See here for detailed instructions. ↩

3. Note on working with environments. By default packages are added to the default environment at ~/.julia/environments/v1.#. It is however easy to create other, independent, projects. If you want to install the packages in a different/test environment, first create a folder to host the environment files (Project.toml and Manifest.toml which will be created later on). Then, for every command line invoking Julia, use julia --project=/path/to/my_env instead of julia alone. Note that packages will always be cloned in ~/.julia/packages but only accessible in your project's context. ↩