LiRA

Linear Response of (galactic) Arms

Aim of the code

This code aims to compute the growth rate of the arms of a thin Kuzmin-Toomre galactic disc, influence by the presence of two Toomre sphere potential modeling a central bulge and a surrounding dark matter halo.

Used in Reddish et al. (2021) : arXiv:2106.02622.

Modeling

Following Aoki et al (1979), we consider thin disk made of polytropic gas with index 4/3, which gives analytical expression for the response matrix elements. The implementation of the bulge component and of the self-gravity parameter slightly modify those matrix elements, which we implement in this semi-analytical code.

Julia packages

Open the terminal in the folder packages and type

$ julia Install-pkg.jl

to install the following packages:

• HDF5
• ArgParse
• Plots
• LinearAlgebra
• StaticArrays
• SphericalHarmonics

!! WARNING !!

DO NOT INTERRUPT THE DOWNLOADING OF THE PACKAGES !!!!

Plot a growth rate map in (x,q) space

To compute a mapping of the system growth rate, one needs to open code/tests.

Then, run the command

$ julia MapGrowthRateAndPrecession.jl

within the folder code/tests. If one wants to run this with parallelization, one needs to run the following commands (supposing one is using bash)

$ export JULIA_NUM_THREADS=12
$ export JULIA_CPU_THREADS=12
$ julia -p 12 MapGrowthRateAndPrecession.jl --parallel yes --eps 0.1 --N 170 --m 2

where 12 is the number of parallelized threads. One can check the number of threads by opening the Julia terminal and by running the command

julia> Threads.nthreads()

The resulting file will be created in the folder code/data under the name Dump_Growth_Rate_Precession.hf5.

Go to the folder code/nb and open the Mathematica notebook GrowthRate.m. Use it to plot and save the map in (x,q) space in the folder code/graphs under the name GrowthRate.png (contour plot) and GrowthRate3D.png (3D plot).

One may also plot the precession frequency of the fastest growing mode using this notebook, and recover the plotd under the names PrecessionFrequency.png and PrecessionFrequency3D.png.

Plot the physical eigenvalues in a Nyquist diagram

To compute the physical eigenvalues of the system, one needs to open code/tests/ComputeEigenvalues.jl and specify the values of x - Mbulge/(Mbulge+Mdisk) - and q Mdisk/(Mhalo+Mdisk) in the file.

Then, run the command

$ julia ComputeEigenvalues.jl

within the folder code/tests. If one wants to run this with additional arguments, one needs to run the following command

$ julia ComputeEigenvalues.jl --eps 0.1 --N 170 --m 2

The resulting file will be created in the folder code/data under the name Dump_Eigenvalues.hf5.

Go to the folder code/nb and open the Mathematica notebook Eigenvalues.m. Use it to plot and save the Nyquist in the folder code/graphs under the name Eigenvalues.png (all eigenvalues of the truncated response matrix) and Physical_Eigenvalues.png (physical eigenvalues of the truncated response matrix).