Gravitational wave bursts from cosmic (super)strings: Quantitative analysis and constraints

We discuss data analysis techniques that can be used in the search for gravitational wave bursts from cosmic strings. When data from multiple interferometers are available, we describe consistency checks that can be used to greatly reduce the false alarm rates. We construct an expression for the rate of bursts for arbitrary cosmic string loop distributions and apply it to simple known solutions. The cosmology is solved exactly and includes the effects of a late-time acceleration. We find substantially lower burst rates than previous estimates suggest and explain the disagreement. Initial LIGO is unlikely to detect field-theoretic cosmic strings with the usual loop sizes, though it may detect cosmic superstrings as well as cosmic strings and superstrings with nonstandard loop sizes (which may be more realistic). In the absence of a detection, we show how to set upper limits based on the loudest event. Using Initial LIGO sensitivity curves, we show that these upper limits may result in interesting constraints on the parameter space of theories that lead to the production of cosmic strings.

Figure 1

Plot of the rate of gravitational wave bursts, $\gamma$ (top panel), and the probability $\eta$ of having at least least one event in our data set with amplitude larger than $A_{50\%}$ in a year of observation (bottom panel), as a function of $G\mu$. For all curves we have set $\alpha =\Gamma G\mu$, $\Gamma =50$, $f_{*}=75\mathrm{Hz}$, $c=p=1$, and the ignorance constants $g_1=g_2=1$. The dash-dot and dashed curves show $\gamma$ and $\eta$ computed with the Damour-Vilenkin cosmological functions Eqs. (62, 63, 64), with $A_{50\%}={10}^{-21}{\mathrm{s}}^{-1/3}$, and $A_{50\%}={10}^{-20}{\mathrm{s}}^{-1/3}$ respectively. The thick and thin solid curves show $\gamma$ and $\eta$ computed in a universe with a cosmological constant with amplitudes $A_{50\%}={10}^{-20}{\mathrm{s}}^{-1/3}$, and $A_{50\%}={10}^{-21}{\mathrm{s}}^{-1/3}$ respectively.

Figure 2

Comparison of $\gamma$ (top panel) and $\eta$ with a year of observation (bottom panel), as a function of $G\mu$ for several string models. For all three curves an Initial LIGO amplitude estimate of $A_{50\%}={10}^{-20}{\mathrm{s}}^{-1/3}$ has been used, and the cosmological functions have been evaluated in the $\Lambda$ universe. The model parameters are identical to those of Fig. 1 except where indicated. The solid curves show $\gamma$ and $\eta$ computed with a reconnection probability of $p={10}^{-3}$. The dashed curves show $\gamma$ and $\eta$ computed with a size of loops given by Eq. (57) with $\epsilon =1$, and $n=3/2$. The dashed-dot curves show the combined effect of a low reconnection probability, $p={10}^{-3}$, as well as a size of loops given by Eq. (57) with $\epsilon =1$, and $n=3/2$.

Figure 3

Same as Fig. 2 but with the Advanced LIGO amplitude estimate of $A_{50\%}={10}^{-21}{\mathrm{s}}^{-1/3}$.

Figure 4

Plot of the rate of bursts $\gamma$ (top panel), and $\eta$, the probability of having at least one event in our data set with amplitude larger than $A_{50\%}$ in a year of observation (bottom panel), as a function of $G\mu$ for various loops distributions. For all curves we have set $\Gamma =50$, $f_{*}=75\mathrm{Hz}$, $c=p=1$, and the ignorance constants $g_1=g_2=1$. As a reference we again show $\gamma$ and $\eta$ computed using the loop distribution from Eq. (56), according to Eq. (59), in the $\Lambda$-universe with $\alpha =\Gamma G\mu$ using the solid curve. The remaining curves have been computed through Eqs. (38, 55) with $A_{50\%}={10}^{-20}{\mathrm{s}}^{-1/3}$. The dashed curves show $\gamma$ and $\eta$ computed using the loop distribution of Eqs. (68, 69, 70). The dashed-dot curves show $\gamma$ and $\eta$ computed with Eq. (71).

Figure 5

Same as Fig. 4 but using our Advanced LIGO amplitude estimate $A_{50\%}={10}^{-21}{\mathrm{s}}^{-1/3}$.

Figure 6

Contour of excluded regions at various confidences. In the cosmic string model we have set $\tilde{\epsilon }=1$, and $n=3/2$, and allowed $X$ and $\beta$ to vary. For the loudest event we have used our Initial LIGO estimate for the amplitude $A_{50\%}={10}^{-20}{\mathrm{s}}^{-1/3}$.