Data analysis
The code used for this analysis can be viewed in the Jupyter Notebook since thats where you can "play" with the code the easiest in order to explore the data and make the graphs look good. The data analysis functions will get their own files as soon as possible.
Table of Contents
Initial galaxy
Since we didn't create the initial conditions, we first want to take a closer look at them. Specifically we will study different properties of the righthand galaxy. These properties are the density and the angular velocity of the different particles dependent on their distance from the center of mass.
Let's first take a look at the disk particles:
Figure 1: Logarithmic density distribution and mean angular velocity dependent on the radius of the disk particles of the right galaxy at t=0.
To confirm that this is what a real galaxy would look like, we compare these graphs to results from real world data. The density function indeed looks like it could come from an observable galaxy because it follows the typical Einasto profile. The angular velocity on the other hand looks in comparison a little bit more like the graph we would expect when there would be no dark matter, which is confusing since there is dark matter included in this simulation. But at least the magnitudes are correct. In both instances, simulation and real world data, we have velocities of around 100 km/s and size of the galaxy of a few 10 kpc.
Now let's compare that to the halo particles:
Figure 2: Logarithmic density distribution and mean angular velocity dependent on the radius of the halo particles of the right galaxy at t=0.
For the comparison we first inspect the center of the galaxy (r < 20kpc). There we see that the halo particles are less dense and have a higher velocity. Note that the velocity is nearly "immediately" (r ~ 0) at its highest value unlike the disk particles, which have their highest velocities at about r = 15kpc. This points to a more chaotic motion of the halo particles and can maybe be explained by the different shapes all particles of one type are forming. While the disk particles form the spiral galaxy we can see in the video of the simulation (or: a rotating disk), the halo particles have more of a spherical or elliptical shape (or: a halo around the galaxy).
Further away from the center of the galaxy (r > 20kpc) the picture begins to change. In terms of density the halo particles gain the upper hand, which again can be explained with their shape and, in addition, how we compute the density for a given radius r (mass/volume for spherical shell with radii [r, r+dr]), which of course "favors" a spherical shape over a disk. We also see that the halo (r ~ 100kpc) is larger than the disk (r ~ 60kpc). The angular velocities of disk particles on the other hand is now higher than that of the halo particles, as long as the disk hasn't faded out yet.
Resulting galaxy
Here we can see the result of the collision of the two galaxies. To make sure they merged "properly" and formed a new stable galaxy we let the simulation run until t=19.96. Again, as in the simulation, you can only see the disk particles, which is what you would also see when observing a real galaxy. And again let's split our observations and first take a look at the center of our new galaxy where most of the particles are. There we no longer have the shape of a disk and instead it looks more like a sphere or an ellipsoid. Further away we see the remains of our initial spiral galaxies. A kind of outer ring has formed around the galaxy and, perpendicular to the ring, two arms are spiraling into outer space.
These arms or tails really stand out, so maybe some real world examples can be found. And indeed, when we look for interacting galaxies captured by the Hubble Space Telescope, we find ESO 286-19 as an especially beautiful candidate. Like our simulation, this galaxy collision has also resulted in two arms, a long and a short one. Other honorable mentions include NGC 2623, which also has these spiraling arms, and ESO 77-14, which is still at the beginning of the collision, but already shows the same property of arms stretching into outer space.
Let's now turn to the more data driven analysis. Luckily we no longer have to split the particles into right or left galaxy, because there's only one galaxy left.
Figure 3: Logarithmic density distribution and mean angular velocity dependent on the radius of all disk particles at t=19.96.
By comparing these graphs to the graphs of our initial galaxy, we can see that they look a lot more like Figure 2 than Figure 1 despite being the graphs of the disk instead of the halo particles. This again can be explained by the different shape the galaxy now has. A closer look shows that the density near the center is about the same as in our initial galaxy, but is higher in comparison to it the further you get away from the center, which draws the obvious conclusion that the galaxy is now bigger.
Figure 4: Logarithmic density distribution and mean angular velocity dependent on the radius of all halo particles at t=19.96.
Unfortunately we can't derive much from these graphs. As we can see in the density distribution, the center of mass and the point of highest density are about 30kpc (10^1.5) apart. Normally we would expect them to be about the same. It is not clear where this anomaly comes from.
Conclusion
In conclusion I think we have some pretty amazing results here, especially if we keep in mind that this was a rather simple simulation that ran on a normal computer, not some high performance super computer. To give you an idea of the magnitudes between our simulation and reality, think of this: One initial galaxy in the simulation consists of 10.000 disk particles. Sounds like a lot of particles, but not if you know that in reality our milky way galaxy for example consists of about 250 billion stars. But our simulation still showed some fascinating similarities to what we know about galaxies.
The first similarity we want to appreciate are the graphs of Figure 1. Even though these are the (artificially created) initial conditons, it is still great to see how close two key properties of a galaxy, the density distribution and the angular velocity, are to reality.
It is even more amazing, to name a second similarity, to see our final result of the merging process of two spiral galaxies so closely match real observations, like the galaxies mentioned above with the same kind of "arms" that our simulation shows.