Cosmic rays from cosmic strings with condensates

We revisit the production of cosmic rays by cusps on cosmic strings. If a scalar field (“Higgs”) has a linear interaction with the string world sheet, such as would occur if there is a bosonic condensate on the string, cusps on string loops emit narrow beams of very high energy Higgses which then decay to give a flux of ultrahigh energy cosmic rays. The ultrahigh energy flux and the gamma to proton ratio agree with observations if the string scale is $\sim {10}^{13}\mathrm{GeV}$. The diffuse gamma ray and proton fluxes are well below current bounds. Strings that are lighter and have linear interactions with scalars produce an excess of direct and diffuse cosmic rays and are ruled out by observations, while heavier strings ($\sim {10}^{15}\mathrm{GeV}$) are constrained by their gravitational signatures. This leaves a narrow window of parameter space for the existence of cosmic strings with bosonic condensates.

Figure 1

String segment at 3 different times, with a cusp at O, with velocity along $z$. The size of the curved section of string is $L$. The observer is at an angle ${\theta }_0$ from the $z$ axis at a distance $d$. There is strong emission from the cusp in a beam along the $z$ axis.

Figure 2

Higgs emission with momentum $k$ occurs from a section of the string with length $\sim L/(kL{)}^{1/3}$. Cusp annihilation occurs over a length $\sim \sqrt{L/M}$ [12] and is smaller than the region for Higgs emission for $k<M\sqrt{ML}$.

Figure 3

The integration in $I(Y,x)$ is over $y$ (dashed vertical line) at a definite value of $x$ (say $x_0$). The different loop trajectories are labeled by the initial length, $y_i$, at $x=0$. The dotted line at $y=1$ is where the differential equation changes behavior [see Eq. (20)]. For small values of $y(x_0)$, $y_i\approx x$ up to factors of order 1. For large $y(x_0)$, $y_i\approx y$.

Figure 4

A cusp on a loop close to Earth emits particles that lose energy as they propagate and also spread out.

Figure 5

The integration region in (45) in the $ry$ plane falls in the region bounded by the $y_{\min }$ and $y_{\max }$ curves from $r=0$ to $r=r_4$, while the integrand depends on whether $y<x$ or $y>x$. The dominant contribution to the integral comes from the region $0<r<r_1$.