Higher order intercommutations in Cosmic String Collisions

We report the first observation of multiple intercommutation (more than two successive reconnections) of cosmic strings at ultra-high collision speeds, and the formation of kink trains'' with up to four closely spaced left- or right-moving kinks. We performed a flat space numerical study of abelian Higgs cosmic string intercommutation in the type-II regime $\beta > 1$ (where $\beta = m^2_{scalar} / m^2_{gauge}$) up to $\beta = 64$, the highest value investigated to date. Our results confirm earlier claims that the minimum critical speed for double reconnection goes down with increasing $\beta$, from $\sim 0.98 c$ at $\beta = 1$ to $\sim 0.86 c$ for $\beta = 64$. Furthermore, we observe a qualitative change in the process leading to the second intercommutation: if $\beta \geq 16$ it is mediated by a loop expanding from the collision point whereas if $1 < \beta \leq 8 $ the previously reported loop’’ is just an expanding blob of radiation which has no topological features and is absorbed by the strings. The multiple reconnections are observed in the loop-mediated, deep type-II regime $\beta \geq 16$. Triple reconnections appear to be quite generic for collision parameters on the boundary between single and double reconnection. For $\beta = 16$ we observe quadruple events. They result in clustering of small scale structure in the form of ``kink trains’’. Our findings suggest that, due to the core interactions, the small scale structure and stochastic gravitational wave background of abelian Higgs strings in the strongly type-II regime may be quite different from what would be expected from studies of Nambu-Goto strings or of abelian Higgs strings in the $\beta \approx 1$ regime.

💡 Research Summary

The paper presents a comprehensive numerical investigation of intercommutation (reconnection) processes in Abelian‑Higgs cosmic strings, focusing on the strongly type‑II regime where the scalar‑to‑gauge mass ratio β = m²_scalar / m²_gauge exceeds unity. Using high‑resolution three‑dimensional lattice simulations in flat spacetime, the authors explore collisions over a wide range of β values (1 ≤ β ≤ 64), varying the impact angle and the relative velocity of the strings. Their primary goal is to determine how core interactions, which become increasingly important for larger β, affect the critical velocity for multiple reconnections and the resulting small‑scale structure on the strings.

Key findings are as follows:

1. Critical velocity decreases with β – The minimum speed required for a second reconnection drops from about 0.98 c at β = 1 to roughly 0.86 c at β = 64. This trend reflects the growth of the string core radius, which facilitates the formation of a topological loop after the first crossing.

2. Two distinct mechanisms for the second reconnection – For β ≥ 16 the post‑collision configuration includes a genuine topological loop that expands outward and triggers a second intercommutation. In contrast, for 1 < β ≤ 8 the “loop” observed in earlier work is merely an expanding blob of radiation lacking any winding number; it is eventually absorbed by the strings and does not lead to a second reconnection.

3. Multiple (triple and quadruple) reconnections – In the loop‑mediated, deep type‑II regime (β ≥ 16) the authors observe that collision parameters lying near the boundary between single and double reconnection frequently produce a third reconnection. At β = 16 they even record quadruple reconnection events. Each successive reconnection generates a kink (a discontinuity in the string’s tangent vector), and the rapid succession of kinks creates tightly spaced “kink trains” moving coherently left‑ or right‑ward.

4. Implications for small‑scale structure and gravitational‑wave background – The formation of kink trains clusters small‑scale excitations on the string, deviating markedly from the random kink distribution predicted by Nambu‑Goto simulations or by Abelian‑Higgs studies confined to β ≈ 1. Since kinks are efficient emitters of high‑frequency gravitational radiation, a network populated by kink trains is expected to produce a stochastic gravitational‑wave background with enhanced power at higher frequencies. Consequently, the standard predictions for the gravitational‑wave spectrum of cosmic‑string networks may need substantial revision in the strongly type‑II regime.

5. Broader significance – By extending the parameter space to β = 64, the work demonstrates that core‑level physics can qualitatively change reconnection dynamics, a factor that has been largely ignored in most large‑scale network simulations. The clear distinction between a true topological loop and a non‑topological radiation blob provides a concrete diagnostic for future studies. Moreover, the observation that multiple reconnections are not rare but rather generic near the critical velocity boundary suggests that network scaling solutions could be altered, potentially affecting string density, loop production rates, and the overall energy loss mechanisms.

In summary, the authors show that in the strongly type‑II Abelian‑Higgs model, ultra‑relativistic collisions can undergo more than two successive reconnections, leading to the creation of kink trains and a markedly different small‑scale structure than previously assumed. These results have important ramifications for the cosmological signatures of cosmic strings, especially the stochastic gravitational‑wave background that upcoming detectors such as LISA, PTA arrays, and ground‑based interferometers aim to measure. Future work should incorporate these core‑interaction effects into large‑scale network simulations to assess their impact on observable quantities.