spiral structure Ghost matter astrophysics.6: Spiral structure. (p9)
8) Interaction regimes.
Our simulation program computes the momentum of the cluster at each step. As shown in figure 14, this momentum decreases during the first ten turns. We observed that a stable momentum plateau is established when dynamical friction becomes negligible and the tidal effect becomes predominant.
Fig.14 : Evolution of the momentum of the positive mass cluster, as a function of the number of turns. ** ** At the same time, the negative mass halo forms its own clusters by gravitational instability and resonance processes, and the central positive mass cluster forms arms due to tidal forces. These tidal effects tend to slow down the rotation of the central cluster, but with less efficiency than the close contact dynamical friction effect observed at the beginning of the process. On figure 13-f, we show the typical appearance of the negative mass clusterized halo (but, as mentioned above, this clusterization is not a relevant phenomenon). . Fig. 15 : Ten turns. The halo of negative mass with its clusters. ** **
- Fourier analysis
The previous results come from the experience. Our eyes are the best tools to identify spiral structures. However, F. Lansheat has computed a spatial Fourier transformation on the cluster, which clearly highlights a signal. The transformation is first applied on a radius of the cluster, then summed over 360 degrees. Three spatial spectra are presented in figure 16. The spatial frequency is expressed here as a function of the inverse of the number of pixels. A value of one pixel corresponds to the minimum distance in our calculation grid.
Figure 16 (top): The cluster at time 0 has been assigned to the positive mass population. The halo has the shape given by the two-dimensional Eddington equations. The peak corresponds to the average cluster radius, which is here 1/0.05 = 20 pixels.
Figure 16 (middle): After two turns, dynamical friction creates the first irregularities. Their size is quite small. The top of the peak is here at 0.2 pixel⁻¹. This corresponds to a width of about 5 pixels.
Figure 16 (bottom): The tidal effect is now mainly acting. The peak of the spatial spectrum is at 0.12. This corresponds to an approximate size of 8 pixels. This spectrum will remain constant for the rest of the calculation.
** ** Fig. 16 : Spatial Fourier transformation of the cluster. This clearly shows the appearance of arm structures. ** ** 