# Intro
This example consists of a homogeneous and periodic box filled with gas particles of equal mass. An individual star particle may be added after some time to first let the system rearrange.

This example tests the bubble propagation for different injection of stellar winds. 

# Configure
To run this example with the GEAR model,

```
CFLAGS="-DSWIFT_TEST_STELLAR_WIND" ./configure  --with-chemistry=GEAR_10 --with-cooling=grackle_0 --with-stars=GEAR --with-star-formation=GEAR --with-sink=GEAR --with-feedback=GEAR --with-kernel=wendland-C2
```

Then, type

```
make -j
```

# ICs
The run.sh script calls the `makeIC.py' script with default values. You can experiment by changing the ICs. Run `python3 makeIC.py --help` to get the list of parameters.
Don't hesitate to change the stellar mass, but also the density and the mass of the gas particle to see the differences.

# run 
To run the script, once you've changed the parameter you wanted, you can simply make a sbatch or srun on the `run.sh` script. It will automatically create a folder containing the IC and the simulation. Then, the script will call the `gas_profile_movie.py` that makes a gif of the bubble's quantities over time and log some parameters' information in a .txt file `radial_peak_position.txt`. Finally, the `bubble_evolution.py` will use the information in the .txt file to plot the evolution of the bubble alongside with some theoretical formulas.
(Exemple: ./run.sh)

# Theorethical formulas
The graphs plot different theoretical formulas coming from the book "Henny J. G. L. M. Lamers, Joseph P. Cassinelli - Introduction to Stellar Winds-Cambridge University Press (1999)" having the formulas for the energy conserving snowplow phase :
R(t) = 28 * (L_36 / (mu * n_0))^(1/5) * t_6^(3/5)                   (12.11)
v = 17 * (L_36 / (mu * n_0))^(1/5) * t_6^(-2/5)                     (12.12)
T2 = 1.6 * 10^6 * L_36^(8/35) * n_0^(2/35) * t_6^(-6/35)            (12.13)
n2 = 0.01 * L_36^(6/35) * n_0^(19/35) * t_6^(-22/35)                (12.14)

and for the momentum conserving snowplow phase :
R(t) = 16 * (L_36 / (v_3 * n_0))^(1/4) * t_6^(-1/2)                 (12.18)
v  =7.9 * (L_36 / (v_3 * n_0))^(1/4) * t_6^(-1/2)                   (12.19)

with some handsmade terms L_36 = L_w / 10^36 [erg / s], t_6 = t /10^6 [yrs] and v_3 = v_infty / 1000 [km / s]

For more information you can also see  "Interstellar bubble" by (castro et al, 1975) : https://ui.adsabs.harvard.edu/abs/1975ApJ...200L.107C/abstract

The two other fit for the radius come from the paper "Formation of star clusters and enrichment by massive stars in simulations of low-metallicity galaxies with a fully sampled initial stellar mass function" by (Lahén et al, 2023) : https://arxiv.org/abs/2211.15705
R = 0.88 * (L_w / rho_0)^(1/5) * t(3/5)                             (4)         for energy conserving snowplow phase
R = (3 * dot(M) * v_infty / (2 * pi * rho_0))^(1/4) * t^(1/2)       (6)         for momentum conserving snowplow phase 

The shockwae could be described by 5 different regions:
    1. The free wind regions, were the ejecta of the winds encounter nothing goes freely at the speed of the winds
    2. The "hot compressed wind" consisting of shocked stellar wind mixed with a small fraction of the swept-up ISM 
    3. The contact surface of the shockwave (the actual "shock" part of the shockwave)
    4. The hot swept-up ISm, the region preceding the shockwave
    5. The untouched ISM

Be aware that the theoretical formulas for the radius and velocity evolution is the same for both region 2 and 3. Whereas the formulas for the temperature and density correspond only to the region 2.