Clustering of cosmic string loops within a Milky-way like halo

TL;DR

Cosmic string loops experience rocket recoil that affects their capture by galaxies; the authors test this with GADGET-4 DM-only zoom simulations by injecting non-backreacting tracer loops with a constant rocket acceleration. They find a pronounced peak in the captured-loop population at $ξ_{ m peak} ≈ 12.5$, giving roughly $O(10^6)$ bound loops for fiducial $Gμ ≈ 10^{-15}$, and show that smaller ξ are preferentially central while larger ξ trace the dark matter. These results imply a substantial local loop density, enhancing prospects for gravitational-wave and other signatures, and they highlight the importance of hierarchical structure formation over simplistic spherical-collapse models.

Abstract

Loops of cosmic string experience a recoil from anisotropic gravitational radiation, known as the rocket effect, which influences the extent to which they are captured by galaxies during structure formation. Analytical studies have reached different conclusions regarding loop capture in galaxies: early treatments argued for efficient capture, while later analyses incorporating the loop rocket force throughout halo formation found that capture efficiency is reduced and strongly dependent on loop size. In this work, we employ the N-body simulation code GADGET-4, introducing non-backreacting tracer particles subject to a constant recoil force to model cosmic string loops with the rocket effect. We simulate the formation of a Milky-Way-like halo from redshift $z=127$ to $z=0$, considering loop populations characterized by a range of length parameters $ξ$, inversely proportional to the rocket acceleration. We find that the number of captured loops exhibits a pronounced peak at $ξ_{\textrm{peak}}\simeq 12.5$, arising from the competition between rocket-driven ejection at small $ξ$ and the declining intrinsic loop abundance at large $ξ$. For fiducial string tensions, this corresponds to $\mathcal{O}(10^6)$ loops within the halo. We further find that loops with weak rocket forces closely trace the dark-matter distribution, while those subject to stronger recoil but still captured -- particularly the most abundant loops near $ξ_{\textrm{peak}}$ -- are preferentially concentrated toward the central regions of the halo.

Figures (5)

• Figure 1: The dark matter density in two dimensions (restricting to a $2 \hbox{Mpc}$ range for the third dimension) is shown for an example output of the N-body simulation. Mass density is indicated by color, given in $10^{16} M_{\text{sun}} / (\hbox{Mpc}/h)^3$. The white dashed (dotted) circle indicates the region within $r_{50}\approx 0.4 \hbox{Mpc}/h$ ($r_{200}\approx0.227 \hbox{Mpc}/h$) from the center of mass of the main halo.
• Figure 3: The fraction and number of loops captured within $r_{50} = 0.4 \hbox{Mpc}/h$ (black solid curves) and $r_{200}=0.227~\mathrm{Mpc}/h$ (orange dashed curves) are shown. The left panel presents the relationship between $\xi$ and the fraction of loops captured by the galaxy. The fraction is a monotonically increasing function of $\xi$, rising more steeply for $\xi < 10$. The right panel shows the simulated count of captured loops, computed using the predicted number density in \ref{['eq:number_density_actual']} and assuming $G\mu=10^{-15}$; for different values of $G\mu$, this result can be rescaled by $(G\mu/10^{-15})^{-3/2}$. A peak is observed at $\xi \sim 15$. The red curves show the expected number of loops found within $r_{50}$ (solid red) and $r_{200}$ (dashed red), assuming a uniform distribution of loops and no gravitational capture.
• Figure 4: String loop number density is shown as a function of distance from the center of mass of the main halo. The dashed lines show the would-be number density for $\xi=15$ (black), $\xi=12.5$ (blue), and $\xi=50$ (red) in the absence of the rocket effect. The solid curves show the resulting distribution with the rocket effect present, indicating that the distribution tends to be more concentrated near the center of the halo for smaller $\xi$. Dotted lines lines of each color show the corresponding uniform number density for each $\xi$ in the absence of any gravitational clustering.
• Figure 5: The energy spectrum of string loops in the final state at $z = 0$ is shown for the case with no rocket force. The mean loop energy (red dashed line) is below zero, with a distribution consisting mostly of negative energies but also including some positive-energy (black dashed lines indicate one standard deviation from the mean).
• Figure 6: Final-state energy spectra at $z = 0$ for two values of the loop-size parameter, $\xi = 10$ (blue shaded region) and $\xi = 50$ (orange shaded region). The left panel shows all loops in the simulation box. Loops with smaller $\xi$ generally have higher kinetic energies due to the stronger rocket force, and therefore exhibit energies well above zero. Loops with larger $\xi$ are more tightly bound, with energies concentrated around negative values. The right panel shows only loops located within $r_{50}$ of the central halo. In both cases, loops within this region tend to have negative energies, indicating that those which remain near the halo are gravitationally bound. Loops with larger $\xi$ constitute a larger fraction of this population.