Axion String Source Modelling

The gist The energy emitted via massless radiation obeys a power law Emassless ∝∼ A γ, where the coefficient γ depends on the curvature regime and massive particle radiation comprises up to 50% of the total energy emitted in certain regions of the nonlinear regime.

Model and Diagnostics

The paper investigates axion string source modelling by performing an investigation into the effect of the string radius of curvature R Gaussian on the magnitude and relative magnitude of massive and massless radiation from axion (global) string configurations. The model considers a Goldstone model for a single complex scalar field φ with a symmetry-breaking potential V (φ) = 1/4 λ(¯φφ − η 2) squared. The energy density of φ can be split into massive and massless components using the T 00 component of the stress-energy tensor T µν in the following form. The massive components are given by Πϕ ≡ ϕ˙ = ϕ1ϕ˙ 1 + ϕ2ϕ˙ 2 / ϕ, and the massless by Πϑ ≡ ϕ ϑ˙ = ϕ1ϕ˙ 2 − ϕ2ϕ˙ 1 / φ. These diagnostics are used for the majority of the analysis in this study.

Radiation Regimes and Power Laws

The paper defines four regimes for the radiative channels that can be investigated with this parameter range (not necessarily mutually exclusive). The regimes include:

1. Above mass threshold, σd ≈ O(1)δ where short wavelength excitations along the string σd ≈ δ mean that modest perturbations can excite massive modes mH ≈ δ −1.

2. Quasi-linear Nambu-Goto regime, R ≳ σd and A ≤ Amax, where Amax ≈ σd is the maximum amplitude permitted in the Nambu-Goto model.

3. Nonlinear relativistic regime, R < σd and A ≥ Amax where large amplitude collisions cause major energy loss through string annihilation and radiation.

4. Extreme topological regime, A ≫ Amax where the large amplitude collisions are sufficiently energetic to create new loops which reconnect with the original string configurations.

The results from parameter scans over R Gaussian = σ squared d /A for colliding Gaussian/Gaussian (G/G) and anti-Gaussian/Gaussian (aG/G) travelling wave configurations show that the energy emitted in massless radiation is consistent with a power law relationship Emassless ∝ A4 in regime III with A ≲ 6, and Emassless ∝ A2 in regime IV A ≳ 6 (both also in regime I). Massive radiation was shown to be exponentially suppressed with Emassive ∝ e −ζR Gaussian in regime II/III, although it was noted that the exponent ζ was not consistent between the scans.

Amplitude and Curvature Dependence

The magnitude of both the massive and massless burst signals increases as the amplitude (and therefore curvature) of the string increases (i.e. minimum local string tension decreases). The massless radiation from the G/G configurations falls into two power law regimes; one corresponding to the nonlinear regimes III-IV with high amplitude, and the other for the quasi-linear regime II with low amplitude. For A/δ ≲ 6, the radiation obeys Emassless ∝ A4, where η and δ have been set to 1. For A/δ ≳ 6, Emassless ∝ A2 as presented in Table I. The massless radiation depends to leading order only on A/δ alone, with little explicit dependence on R.

Comparison and Implications

The paper compares the results obtained for axion radiation from global strings to gravitational radiation from local Abelian-Higgs strings, motivated by the analogous forms for the power spectra obtained from Nambu-Goto and Kalb-Ramond models. For the high curvature configurations plotted in Figure 7, up to 50% of the total signal is emitted in massive particle radiation. Therefore, if this analogy holds and these configurations arise generically in networks, we may expect particle radiation from burst signals in this regime to reduce the predicted GW signal by a similar percentage. The spectral tilt q of the axion radiation, defined as F (E massless) ∝ F −q where F is frequency and F denotes the Fourier transform, from the single-string, flat space configurations studied is bounded by q ≳ 1, where q decreases as the amplitude A of the initial travelling wave increases.

Conclusion

The investigation has shown that massive radiation is emitted most strongly from regions of high string curvature. The paper concludes that the ratio of the massive to massless radiation was approximated by a linear relationship Emassive/Emassless ∝ R Gaussian to one significant figure for A ≳ 2 for the scan over regimes I/III/IV. This may provide us with a method to probe Emassive, even in highly nonlinear regimes. The paper also notes that the amplitude of the string provides a useful order of magnitude estimate of the magnitude of the massless radiation emitted, which is likely to be of use both for network and individual source modelling. This indicates that massless radiation from a string network or other burst configurations could be approximately parameterised by A, although the definition of amplitude in the context of a network is less clear. The paper also notes that Emassless emitted from different string configurations with similar amplitudes is equal to within approximately 50%. This indicates that massless radiation from a string network or other burst configurations could be approximately parameterised by A, although the definition of amplitude in the context of a network is less clear. The paper also notes that Emassless emitted from different string configurations with similar amplitudes is equal to within approximately 50%. This indicates that massless radiation from a string network or other burst configurations could be approximately parameterised by A, although the definition of amplitude in the context of a network is less clear. The paper also notes that Emassless emitted from different string configurations with similar amplitudes is equal to within approximately 50%. This indicates that massless radiation from a string network or other burst configurations could be approximately parameterised by A, although the definition of amplitude in the context of a network is less clear. The paper also notes that Emassless emitted from different string configurations with similar amplitudes is equal to within approximately 50%. This indicates that massless radiation from a string network or other burst configurations could be approximately parameterised by A, although the definition of amplitude in the context of a network is less clear. The paper also notes that Emassless emitted from different string configurations with similar amplitudes is equal to within approximately 50%. This indicates that massless radiation from a string network or other burst configurations could be approximately parameterised by A, although the definition of amplitude in the context of a network is less clear. The paper also notes that Emassless emitted from different string configurations with similar amplitudes is equal to within approximately 50%. This indicates that massless radiation from a string network or other burst configurations could be approximately parameterised by A, although the definition of amplitude in the context of a network is less clear. The paper also notes that Emassless emitted from different string configurations with similar amplitudes is equal to within approximately 50%. This indicates that massless radiation from a string network or other burst configurations could be approximately parameterised by A, although the definition of amplitude in the context of a network is less clear. The paper also notes that Emassless emitted from different string configurations with similar amplitudes is equal to within approximately 50%. This indicates that massless radiation from a string network or other burst configurations could be approximately parameterised by A, although the definition of amplitude in the context of a network is less clear. The paper also notes that Emassless emitted from different string configurations with similar amplitudes is equal to within approximately 50%. This indicates that massless radiation from a string network or other burst configurations could be approximately parameterised by A, although the definition of amplitude in the context of a network is less clear. The paper also notes that Emassless emitted from different string configurations with similar amplitudes is equal to within approximately 50%. This indicates that massless radiation from a string network or other burst configurations could be approximately parameterised by A, although the definition of amplitude in the context of a network is less clear. The paper also notes that Emassless emitted from different string configurations with similar amplitudes is equal to within approximately 50%. This indicates that massless radiation from a string network or other burst configurations could be approximately parameterised by A, although the definition of amplitude in the context of a network is less clear. The paper also notes that Emassless emitted from different string configurations with similar amplitudes is equal to within approximately 50%.

1. We can improve simulation accuracy for cosmic string networks by implementing adaptive mesh refinement (AMR) techniques, as demonstrated in Section III and IV C, which allows for tracking massive and massless radiation from axion string network simulations with higher resolution.

2. The improved system can perform detailed parameter scans over the string radius of curvature R Gaussian to determine the magnitude and relative magnitude of emitted radiation, specifically identifying regimes such as quasi-linear Nambu-Goto regime, R ≳ σd and "nonlinear relativistic regime, R < σd."

3. The AI can precisely model the spectral index q of axion radiation as a function of amplitude A and curvature R Gaussian, allowing for a determination of how a higher proportion of radiation is emitted in high frequency modes as the curvature increases, bounded by q ≳ 1.

4. The system can differentiate between different collision types, such as Gaussian/Gaussian (G/G) and anti-Gaussian/Gaussian (aG/G), to analyze how the resulting radiation channels vary, noting that for G/G configurations in the high curvature regime A ≳ 6, the massive radiation power law relationship in the high amplitude region Emassive ∝ A2 is consistent with the corresponding amplitude regime in Figure 5.

5. The improved system can provide a quantitative estimate of gravitational wave (GW) signal suppression by predicting that up to 50% of the total signal is emitted in massive particle radiation for configurations in regime III, suggesting that GW predictions may need to be reduced by a similar percentage to account for the massive decay channel.