Axion string source modeling

In this paper, we investigate the effect of the string radius of curvature <a:math xmlns:a="http://www.w3.org/1998/Math/MathML" display="inline"><a:mrow><a:msub><a:mrow><a:mi>R</a:mi></a:mrow><a:mrow><a:mtext>Gaussian</a:mtext></a:mrow></a:msub></a:mrow></a:math> on the massive and massless scalar radiation emitted from collisions of traveling waves propagating along an axion (global cosmic) string. We construct initial conditions for two colliding Gaussians and perform parameter scans over their amplitude <c:math xmlns:c="http://www.w3.org/1998/Math/MathML" display="inline"><c:mi>A</c:mi></c:math> and standard deviation <e:math xmlns:e="http://www.w3.org/1998/Math/MathML" display="inline"><e:msub><e:mi>σ</e:mi><e:mi mathvariant="normal">d</e:mi></e:msub></e:math>. We show that these collisions emit isotropic bursts of massless radiation and that the energy emitted via this channel obeys a power law <h:math xmlns:h="http://www.w3.org/1998/Math/MathML" display="inline"><h:mrow><h:mrow><h:mover><h:mrow><h:mo stretchy="false">∼</h:mo></h:mrow><h:mrow><h:mo>∝</h:mo></h:mrow></h:mover></h:mrow><h:msup><h:mrow><h:mi>A</h:mi></h:mrow><h:mrow><h:mi>γ</h:mi></h:mrow></h:msup></h:mrow></h:math>, where the coefficient <k:math xmlns:k="http://www.w3.org/1998/Math/MathML" display="inline"><k:mi>γ</k:mi></k:math> depends on the regime of <m:math xmlns:m="http://www.w3.org/1998/Math/MathML" display="inline"><m:mi>A</m:mi><m:mo>/</m:mo><m:mi>δ</m:mi></m:math> and <o:math xmlns:o="http://www.w3.org/1998/Math/MathML" display="inline"><o:mi>δ</o:mi></o:math> is the string width. Massive radiation is exponentially suppressed <q:math xmlns:q="http://www.w3.org/1998/Math/MathML" display="inline"><q:mrow><q:mover><q:mrow><q:mo stretchy="false">∼</q:mo></q:mrow><q:mrow><q:mo>∝</q:mo></q:mrow></q:mover><q:msup><q:mrow><q:mi>e</q:mi></q:mrow><q:mrow><q:mo>−</q:mo><q:mi>ζ</q:mi><q:msub><q:mrow><q:mi>R</q:mi></q:mrow><q:mrow><q:mtext>Gaussian</q:mtext></q:mrow></q:msub></q:mrow></q:msup></q:mrow></q:math> in the quasilinear regime <t:math xmlns:t="http://www.w3.org/1998/Math/MathML" display="inline"><t:msub><t:mi>σ</t:mi><t:mi mathvariant="normal">d</t:mi></t:msub><t:mo>≫</t:mo><t:mi>δ</t:mi></t:math> and exhibits power-law decay <w:math xmlns:w="http://www.w3.org/1998/Math/MathML" display="inline"><w:mrow><w:mover><w:mrow><w:mo stretchy="false">∼</w:mo></w:mrow><w:mrow><w:mo>∝</w:mo></w:mrow></w:mover><w:msubsup><w:mrow><w:mi>R</w:mi></w:mrow><w:mrow><w:mtext>Gaussian</w:mtext></w:mrow><w:mrow><w:mo>−</w:mo><w:msup><w:mrow><w:mi>γ</w:mi></w:mrow><w:mrow><w:mo>′</w:mo></w:mrow></w:msup></w:mrow></w:msubsup></w:mrow></w:math> in the nonlinear regime <z:math xmlns:z="http://www.w3.org/1998/Math/MathML" display="inline"><z:mrow><z:msub><z:mrow><z:mi>σ</z:mi></z:mrow><z:mrow><z:mi mathvariant="normal">d</z:mi></z:mrow></z:msub><z:mo>≲</z:mo><z:mn>2</z:mn><z:mi>δ</z:mi></z:mrow></z:math>, with different <cb:math xmlns:cb="http://www.w3.org/1998/Math/MathML" display="inline"><cb:mi>ζ</cb:mi></cb:math> and <eb:math xmlns:eb="http://www.w3.org/1998/Math/MathML" display="inline"><eb:msup><eb:mi>γ</eb:mi><eb:mo>′</eb:mo></eb:msup></eb:math> in different regimes of <gb:math xmlns:gb="http://www.w3.org/1998/Math/MathML" display="inline"><gb:msub><gb:mi>R</gb:mi><gb:mtext>Gaussian</gb:mtext></gb:msub></gb:math>. In this nonlinear regime, massive particle radiation can comprise 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 may become significant with respect to the massless (gravitational) channel for such nonlinear burst signals. For all configurations studied, we obtain a spectral index <ib:math xmlns:ib="http://www.w3.org/1998/Math/MathML" display="inline"><ib:mi>q</ib:mi><ib:mo>≳</ib:mo><ib:mn>1</ib:mn></ib:math> for the axion radiation, where <kb:math xmlns:kb="http://www.w3.org/1998/Math/MathML" display="inline"><kb:mi>q</kb:mi><kb:mo stretchy="false">→</kb:mo><kb:mn>1</kb:mn></kb:math> as <nb:math xmlns:nb="http://www.w3.org/1998/Math/MathML" display="inline"><nb:mi>A</nb:mi></nb:math> increases; i.e., a higher proportion of radiation is emitted in high-frequency modes. Published by the American Physical Society 2024