Axion String Source Modelling

TL;DR

This study investigates how the curvature of axion strings influences the emission of massive and massless radiation, revealing regimes where massive radiation is significant and its spectral properties.

Contribution

It models the effect of string curvature on radiation emission, demonstrating different energy decay laws and the potential importance of massive radiation in nonlinear regimes.

Findings

Massless radiation energy follows a power law with amplitude.

Massive radiation is exponentially suppressed or follows a power law depending on regime.

Up to 50% of energy can be from massive radiation in nonlinear regimes.

Abstract

In this paper, we perform an investigation into the effect of the string radius of curvature $R_\mathrm{\,Gaussian}$ on the magnitude and relative magnitude of the massive and massless radiation from axion (global) string configurations, motivated by qualitative observations from string network simulations. We construct initial conditions from travelling wave solutions on a global string for two colliding Gaussians, performing parameter scans over amplitude $A$ and standard deviation $\sigma_\mathrm{d}$. We show that the energy emitted via massless radiation obeys a power law $E_\mathrm{massless} \propto A^{\gamma}$, where the coefficient $\gamma$ depends on the curvature regime. Massive radiation is exponentially suppressed approximately as $E_{\mathrm{massive}} \propto e^{-\zeta R_\mathrm{\,Gaussian}}$ in the quasi-linear regime $\sigma_\mathrm{d} \gg \delta$ and exhibits power-law decay $E_{\mathrm{massive}} \propto (R_\mathrm{\,Gaussian})^{-\gamma}$ in the nonlinear regime where $\sigma_\mathrm{d} \lesssim 2\delta$, with different $\gamma$ in different regimes of $R_\mathrm{\,Gaussian}$. In certain regions of the nonlinear regime, massive particle radiation comprises up to 50% of the total energy emitted. Drawing on a known parallel between axion radiation from global strings and gravitational radiation from Abelian-Higgs strings, this suggests that massive particle radiation channel may become of equal significance to the massless (gravitational) channel for nonlinear burst signals where $R < \sigma_\mathrm{d}$, unless we are in the regime where additional loops are generated. We also estimate the spectral index $q$ of the axion radiation for different amplitudes, showing that a higher proportion of radiation is emitted in high frequency modes as the curvature increases, bounded by $q \gtrsim 1$ for the configurations studied.