Running a head‐on collision

If your code compiles and does not crash after the first few time steps, as described on Running examples page, you should pat yourself on the shoulder. You are now ready to evolve and analyse your first binary BS head-on collision simulation. Here we will describe how to analyse an equal-mass head-on collision using BSEqualMassFix example using params.txt file.

Here we will quote the numerical values in our code units.

In this parameter file we set-up a binary with horizontal separation of $d=14$ and consisting of two solitonic BSs ($\sigma_0 = 0.2$) with $A(0) = 0.17$. These stars have individual masses of $m_{\rm{BS}} = 0.7134$ and compactness of $C \sim 0.222$. They are then boosted towards each other along the $x$-axis with rapidities of 0.1, which correspond to a boost velocities of $v \sim 0.099668$.

As we are simulating fairy compact BSs (which are also stable), it is reasonable to expect that during the evolution after merger we will form a black hole. In order to understand what happens during the evolution, it is useful to monitor (i) the maximum of the scalar field modulus located in the mod_phi_max.dat file (ii) the stars' x-positions as functions of time located in StarCentres.dat file (iii) the mass of a black hole from apparent horizon finder. Below we include the plot of these diagnostics as functions of time. Note that the star positions have been rescaled by factors of 1/6 in order to fit all the data in one plot.

The tell-tales of a good evolution here are as follows: (i) the scalar field remains constant throughout the evolution up to close to merger, so our stars are in equilibrium, (ii) after the merger indicated by the dashed black line, the scalar field starts to drop to zero - we form a black hole and most of the scalar field falls into it, (iii) black hole formation is further confirmed by the apparent horizon finder, and we plot the final black hole mass it estimates as well.

For comparison as to how wrong things go in the case of plain superposition, try launching the same configuration but using plainly superposed initial data and looking at the diagnostics. You should find that with plain superposition you would form a black hole way sooner and before merger.

See the details on the role of initial data in these Refs: https://arxiv.org/abs/2108.11995, https://arxiv.org/abs/2212.08023, https://arxiv.org/abs/2311.16251