Running a head on collision

If your code compiles just fine and you are able to run one of the examples as described in the Running examples page without crashing the code, you should pat yourself on the shoulder. You now should be in the position to run your first binary BS head-on collision and analyse the results.

For simplicity, here we will quote all numerical values in code units.

Let us navigate to the BBSEqualMassFix example folder and run the params.txt file. This parameter file is for an equal-mass head-on collision consisting of two fairly compact BSs with $A(0) = 0.17$. Their individual masses are $m_{\rm{BS}} = 0.7134$ and they have compactness values of $C \sim 0.222$. We place them on the grid with the horizontal separation of $d=14$ and boost them towards each other with rapidities of 0.1. As the stars are quite compact, it is reasonable to expect that they should form a black hole post-merger. We monitor the dynamics and the outcome of the collision, using the following diagnostics: (i) the maximum of the scalar field profile located in the mod_phi_max.dat file, (ii) the stars' $x$-positions located in the StarCentres.dat file, and (iii) the mass of a black hole as found by the apparent horizon finder and located in the stats_AH1.dat file. Below we include the plot showing all of these quantities as functions of time (note that the positions have been scaled by a factor of 1/6 in order to fit all the data in one plot).

We see that the scalar field amplitude remains roughly constant up until merger (indicated by the black dashed line, where the two stars' positions start to overlap), indicating that the stars remain in equilibrium, as desired. After the merger, the scalar field starts to drop to zero, signalling the onset of black hole formation. Almost all of the scalar field ends up in the black hole. The black hole formation post-merger is further confirmed by the apparent horizon data, from which we extract the final mass of the black hole formed.

It is possible to have your stars initially out of the equilibrium and this is typically an artefact of poorly chosen initial data. Try running the same configuration using plain superposition (see BBSPlainSuperposition example) and compare your diagnostics. You should find that you form a black hole way sooner and before merger, leading to different binary dynamics and gravitational-wave generation.

To find out more about the role of initial data in evolutions of binary boson star systems, please have a look at the following references: https://arxiv.org/abs/2108.11995, https://arxiv.org/abs/2212.08023 and https://arxiv.org/abs/2311.16251.