Radiation from global topological strings using adaptive mesh refinement: Methodology and massless modes

Abstract

We implement adaptive mesh refinement (AMR) simulations of global topological strings using the public code, GRChombo. We perform a quantitative investigation of massive radiation from single sinusoidally displaced string configurations, studying a range of string widths defined by the coupling parameter λ over two orders of magnitude, effectively varying the mass of radiated particles mH ∼ √ λ. We perform an in-depth investigation into the effects of AMR on massive radiation emission, including radiation trapping and the refinement required to resolve high frequency modes. We use quantitative diagnostic tools to determine the eigenmode decomposition, showing a complex superposition of high frequency propagating modes with different phase and group velocities. We conclude that massive radiation is generally strongly suppressed relative to the preferred massless channel, with suppression increasing at lower amplitudes and higher λ. Only in extreme nonlinear regimes (e.g. with relative amplitude ε ∼ 1.5 and λ < 1) do we observe massive and massless radiation to be emitted at comparable magnitude. We find that massive radiation is emitted in distinct high harmonics of the fundamental frequency of the string, and we demonstrate that, for the sinusoidal configurations studied, massive radiation is exponentially suppressed with √ λ (i.e. the particle mass). Finally, we place these results in the context of axions and gravitational waves produced by cosmological cosmic string networks, and note that AMR provides a significant opportunity to explore higher λ (thin string) regimes whilst using fewer computational resources.

Aspects of Axions and ALPs Phenomenology

“…The calculation of the axion abundance from topological defects is extremely challenging, numerically, mainly because of the many orders of magnitude difference in the size of the strings core and their mutual distances. A significant progress was achieved recently through the use of the adaptive mesh refinement (AMR) technique [57], which led to the prediction of the mass window m a ∈ [40,180] µeV for the axion to be the totality of the CDM in the universe [37]. Nevertheless, more work is required for a complete confidence in these results.…”

Lessons for adaptive mesh refinement in numerical relativity

“…z-direction by symmetry-using v = −P rad z /M fin . Since the radiated momentum can be written in terms of a sum, with each term involving several multipolar amplitudes ψ m (equation (40) in [128]), analyzing this quantity has the benefit of additionally indirectly comparing the agreement of higher order multipoles (i.e. > 2) between the codes.…”

“…In contrast to the moving boxes approach, this approach allows for highly flexible 'manyboxes-in-many-boxes' mesh topologies, enabling the study of dynamical systems where the spacetime dynamics are not driven by localized compact systems e.g. in studying non spherical collapse scenarios [32,33], higher dimensional BHs/black string evolution [34][35][36][37][38][39], cosmic string evolution [40][41][42], and the behaviour of strongly inhomogeneous cosmological spacetimes [43][44][45][46][47][48][49][50][51].…”

Where is the ringdown? Reconstructing quasinormal modes from dispersive waves

“…arise after a phase transition in the early universe, when the symmetry of the vacuum is broken. There exists a plethora of models encompassing gauge and global strings, which have been studied analytically as well as numerically over many decades [83][84][85][86][87][88][89][90][91][92]. Only recently has the full gravitational behaviour of field theory cosmic strings been studied using numerical relativity [93,94] 2 , showing that gauge circular loops could collapse to black holes, emitting ∼ 2% of their initial mass in gravitational waves.…”