CARP

Chandrasekhar Anisotropic Rotating Plummer.

Aim of the code

This repository allows for the computation of the diffusion coefficients and the diffusion rates of a rotating, anisotropic Plummer cluster using the orbit-averaged Chandrasekhar theory.

The parametrization of velocity anisotropy follows Dejonghe (1987), and is described by a parameter $q$.

The parametrization rotation follows the Lynden-Bell demon from Lynden-Bell (1960), and described by

$$F_{\mathrm{rot}}(J_{\mathrm{r}},L,L_{z}) = F_{\mathrm{tot}}(J_{\mathrm{r}},L) \big(1 + \alpha \ \mathrm{sgn}[L_{\mathrm{z}}/L] \big),$$

where $F_{\mathrm{rot}}(J_{\mathrm{r}},L,L_{z})$ is the distribution function in action space for the rotating cluster, $F_{\mathrm{tot}}(J_{\mathrm{r}},L)$ is the distribution function for the associated non-rotating cluster and $\alpha$ is the rotation parameter (between -1 and 1).

This repository makes use of the Julia Language (see Bezanson et al. (2017)), whose repository is located at JuliaLang.

A GPU-accelerated version of this code, making use of the CUDA.jl library, is available at the repository CARP_GPU.

Installation

Install Julia 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.

Packages

Open the terminal in the folder packages and type

$ julia Install-pkg.jl

to install the following packages:

• ArgParse
• HypergeometricFunctions
• SpecialFunctions
• StaticArrays
• Interpolations
• HDF5
• Plots
• LaTeXStrings

!! WARNING !!

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

Sampling the diffusion rate in action space

To compute a mapping of the diffusion rate $\partial F/\partial t$, one can use the Julia scripts located at code/compute/. These script will compute a 2D map in action space and store it in a .hf5 file in the folder code/data.

As an example, Compute_dFdt_JrL.jl will compute a 2D map in $(J_{\mathrm{r}},L)$ space.

This script is parallelized. The full list of arguments can be found in the file code/sources/julia/Args.jl.

Here is an example of a console command to launch the computation in $(J_{\mathrm{r}},L)$ space for 12 threads, for a Plummer cluster with anisotropy parameter $q=0.0$ and rotation parameter $\alpha=0.1$.

$ cd ./code/compute
$ julia -t 12 Compute_dFdt_JrL.jl --q 0.0 --a 0.1

The resulting file will be created in the folder code/data under the name Dump_dFdt_JrL_Map_q_0.0_a_0.1.hf5 in about 30 seconds for these parameters.

One may also be interested in samlping the $(J_{\mathrm{r}},\cos I)$ space. To that end, one should use the following command

$ cd ./code/compute
$ julia -t 12 Compute_dFdt_JrCosI.jl --q 0.0 --a 0.1 --nbw 20 --nbphi 200 --nbvartheta 50

The resulting file will be created in the folder code/data under the name Dump_dFdt_JrCosI_Map_q_0.0_a_0.1.hf5 in about 120 seconds for these parameters.

Plotting the diffusion rate in action space

After having sampled a 2D-slice of the action space, one may plot the data using the Julia scripts located at code/compute/.

As an example, PlotContour_JrL.jl will compute a 2D map in $(J_{\mathrm{r}},L)$ space for the data of the cluster $(q,\alpha)=(0.0,0.1)$ when typing the follow command in the console

$ cd ./code/compute
$ julia PlotContour_JrL.jl --q 0.0 --a 0.1

The resulting file will be created in the folder code/graphs under the name Map_dFdt_JrL_q_0.0_a_0.1.png.

Similarly, PlotContour_JrCosI.jl will compute a 2D map in $(J_{\mathrm{r}},\cos I)$ space for the data of the cluster $(q,\alpha)=(0.0,0.1)$ when typing the follow command in the console

$ cd ./code/compute
$ julia PlotContour_JrCosI.jl --q 0.0 --a 0.1

The resulting file will be created in the folder code/graphs under the name Map_dFdt_JrCosI_q_0.0_a_0.1.png.