Gravitational radiation from cosmic (super)strings: Bursts, stochastic background, and observational windows

The gravitational wave (GW) signals emitted by a network of cosmic strings are reexamined in view of the possible formation of a network of cosmic superstrings at the end of brane inflation. The reconnection probability $p$ of intersecting fundamental or Dirichlet strings might be much smaller than 1, and the properties of the resulting string network may differ significantly from those of ordinary strings (which have $p=1$). In addition, it has been recently suggested that the typical length of newly formed loops may differ by a factor $ϵ\ll 1$ from its standard estimate. Here, we analyze the effects of the two parameters $p$ and $ϵ$ on the GW signatures of strings. We consider both the GW bursts emitted from cusps of oscillating string loops, which have been suggested as candidate sources for the LIGO/VIRGO and LISA interferometers, and the stochastic GW background, which may be detectable by pulsar-timing observations. In both cases we find that previously obtained results are quite robust, at least when the loop sizes are not suppressed by many orders of magnitude relative to the standard scenario. We urge pulsar observers to reanalyze a recently obtained 17-yr combined data set to see whether the large scatter exhibited by a fraction of the data might be due to a transient GW burst activity of some sort, e.g., to a near cusp event.

Figure 1

Effect of a reconnection probability ${10}^{-3}\le p\le 1$ on the gravitational wave amplitude of bursts emitted by cosmic string cusps in the LIGO/VIRGO frequency band ($f_{\mathrm{L}\mathrm{I}\mathrm{G}\mathrm{O}}=150\mathrm{H}\mathrm{z}$) as a function of the string tension parameter $G\mu$ (in a base-10 log-log plot). Here, as in the following figures, the average number of cusps per loop oscillation is assumed to be $c=1$. The horizontal dashed lines indicate the one sigma noise levels (after optimal filtering) of LIGO 1 (initial detector) and LIGO 2 (advanced configuration).

Figure 2

Effect of a reconnection probability ${10}^{-3}\le p\le 1$ on the gravitational wave amplitude of bursts emitted by cosmic string cusps in the LISA frequency band ($f_{\mathrm{LISA}}=3.88\times {10}^{-3}\mathrm{Hz}$) as a function of the string tension parameter $G\mu$ (in a base-10 log-log plot). The horizontal dashed line indicates the one sigma noise level (after optimal filtering) of the LISA detector.

Figure 3

Effect of a smaller fractional loop-length parameter ${10}^{-12}\le ϵ\equiv \alpha /(50G\mu )\le 1$ on the gravitational wave amplitude of bursts emitted by cosmic string cusps in the LIGO/VIRGO frequency band ($f_{\mathrm{L}\mathrm{I}\mathrm{G}\mathrm{O}}=150\mathrm{H}\mathrm{z}$) as a function of the string tension parameter $G\mu$ (in a base-10 log-log plot). The horizontal dashed lines indicate the one sigma noise levels (after optimal filtering) of LIGO 1 (initial detector) and LIGO 2 (advanced configuration).

Figure 4

Effect of a smaller fractional loop-length parameter ${10}^{-12}\le ϵ\equiv \alpha /(50G\mu )\le 1$ on the gravitational wave amplitude of bursts emitted by cosmic string cusps in the LISA frequency band ($f_{\mathrm{LISA}}=3.88\times {10}^{-3}\mathrm{Hz}$) as a function of the string tension parameter $G\mu$ (in a base-10 log-log plot). The horizontal dashed line indicates the one sigma noise level (after optimal filtering) of the LISA detector.

Figure 5

Effect of a reconnection probability ${10}^{-3}\le p\le 1$ on the fractional contribution ${\Omega }_g(f_{\mathrm{p}\mathrm{s}\mathrm{r}})$ [around the frequency $f_{\mathrm{psr}}\sim 1/(10\mathrm{yr})$] to the cosmological closure density of the stochastic GW noise due to overlapping GW bursts emitted by a network of strings (base-10 log-log plot). The upper (solid) horizontal line indicates the upper limit ${\Omega }_g<6h^{-2}\times {10}^{-8}$ derived from 8 yr of high-precision timing of two millisecond pulsars: PSR $1855+09$ and PSR $1937+21$. The middle (dashed) horizontal line indicates the potential sensitivity of 17 years of high-precision timing of PSR $1855+09$ (see text). The lower (dashed) horizontal line indicates the expected sensitivity from the timing of the set of pulsars to be hopefully detected by a square kilometer array of radio telescopes.

Figure 6

Effect of a smaller fractional loop-length parameter ${10}^{-3}\le ϵ\equiv \alpha /(50G\mu )\le 1$ on the fractional contribution ${\Omega }_g(f_{\mathrm{p}\mathrm{s}\mathrm{r}})$ [around the frequency $f_{\mathrm{psr}}\sim 1/(10\mathrm{yr})$] to the cosmological closure density of the stochastic GW noise due to overlapping GW bursts emitted by a network of strings (base-10 log-log plot). The upper (solid) horizontal line indicates the upper limit ${\Omega }_g<6h^{-2}\times {10}^{-8}$ derived from 8 yr of high-precision timing of two millisecond pulsars: PSR $1855+09$ and PSR $1937+21$. The middle (dashed) horizontal line indicates the potential sensitivity of 17 yr of high-precision timing of PSR $1855+09$ (see text). The lower (dashed) horizontal line indicates the expected sensitivity from the timing of the set of pulsars to be hopefully detected by a square kilometer array of radio telescopes.