ChatGPT_AMUSEscript.md

Assignment for Simulation and Modeling in Astrophysics

For the upcoming session on Wednesday, September 18th, you have completed the installation of AMUSE and have conducted preliminary assignments using units and particles. However, at this stage, you haven't yet engaged in a fully rewarding numerical simulation.

To better prepare for our lecture on September 18th, we encourage you to utilize ChatGPT to enhance your understanding of AMUSE.

Please follow these steps:

Create an account on ChatGPT by visiting https://chat.openai.com/. Start a session and request ChatGPT to generate an AMUSE script for evolving a star cluster. The specifications for the star cluster are as follows:

Total mass: 300 solar masses (300 MSun) Stellar distribution: Plummer sphere Virial radius: 1 parsec (pc) Stellar masses: Ranging from 1 MSun to 100 MSun, following a Salpeter mass function. Ignore stellar evolution and the Galactic tidal field. ChatGPT should provide you with a script that you can attempt to run in AMUSE.

Initially, execute the script generated by ChatGPT for a duration of 100 million years (100 Myr). You can run it in an Xterm using the command:

%> python ChatGPT_Nbody.py

Alternatively, you can paste the script into a Python notebook for execution.

Evaluate the script's functionality and whether it achieves your intended objectives. If there are any errors, troubleshoot and rectify them until the script runs successfully with the desired parameters.

Next, extend the script to search for binaries every 1 million years (1 Myr). When the first 20 binaries are found, halt the code and save the last snapshot.

Write a new script that reads this final snapshot, identifies the binary (which you know should exist), and calculates its Keplerian (orbital) elements.

You can ask ChatGPT to assist in creating this script and then verify its correctness. If ChatGPT's script fails, ensure that it includes the routine get_orbital_elements_from_binary(). Correct the ChatGPT-generated script and independently assess whether the parameters of the first hard binary make logical sense.

Finally, run the initial script 20 times with identical initial conditions but different realizations. For each run, record the moment the first hard binary forms and its eccentricity.

Create histograms of these recorded values and overlay the distributions with a Kernel Density Estimator.

Reflect on the following questions based on your findings:

• What conclusions can you draw from the distribution of first-hard binary formation times?

• What insights can you gather from the distribution of eccentricities?

Now make a small change in the initial conditions. You could change the lower-limit of the stellar mass function, or it's slope. Of you can change the initial density profile of the cluster or the virial radius.

Now redo the 20 runs with this small change, and compare the distribution in binary formation time and eccentricity.

• Comment on the differences between the distributions taking the change you introduced into account.

Now you are ready to run the Python notebook from the AMUSE-Tutorial named: running_an_Nbody_code.ipynb

Run the script, perform the analysis, and comment on what differences and difficulties you encounter.

• Were ChaptGPT's script appropriate, and did you correct them satisfactorily?

Feel free to reach out if you encounter any challenges during this assignment. Your comprehensive analysis will greatly contribute to our lecture discussions.