Cosmic String Interpretation of NANOGrav Pulsar Timing Data

Pulsar timing data used to provide upper limits on a possible stochastic gravitational wave background (SGWB). However, the NANOGrav Collaboration has recently reported strong evidence for a stochastic common-spectrum process, which we interpret as a SGWB in the framework of cosmic strings. The possible NANOGrav signal would correspond to a string tension $G\mu \in (4\times {10}^{-11},{10}^{-10})$ at the 68% confidence level, with a different frequency dependence from supermassive black hole mergers. The SGWB produced by cosmic strings with such values of $G\mu$ would be beyond the reach of LIGO, but could be measured by other planned and proposed detectors such as SKA, LISA, TianQin, AION-1 km, AEDGE, Einstein Telescope, and Cosmic Explorer.

Figure 1

Cosmic string spectra (solid blue curves) together with our fitted power laws for $G\mu =4\times {10}^{-11}$. The green-dashed lines show the results of numerically fitting the curves, while the orange lines result from the simple logarithmic derivative in Eq. (8). The thin gray lines indicate the frequency range of interest that was used in the NANOGrav linear fit.

Figure 2

The curve shows the slope $\gamma$ and amplitude $A$ of a power-law signal approximating the calculated cosmic string spectra, see Eqs. (6) and (8), with $G\mu$ values indicated by the indicated rainbow colors in the indicated frequency range. The solid and dashed black lines indicate the 68% and 95% ranges of $(\gamma ,A)$ fitted to their 12.5 yr data by the NANOGrav Collaboration [12]. The gray vertical line at $\gamma =13/3$ represents the slope expected for SMBH mergers [13], while the points on it mark the upper limits on the amplitude from previously reported pulsar timing data for that spectrum.

Figure 3

Cosmic string spectra calculated for $f\in 5\times {10}^{-10},6\times {10}^{-8}$) with $G\mu \in (4\times {10}^{-11},{10}^{-10})$ (between the solid black lines) and $G\mu \in (2\times {10}^{-11},3\times {10}^{-10})$ (between the dashed black lines) that fit the NANOGrav 12.5 yr data within the 68% and 95% confidence levels, respectively. We also show previously reported bounds from PPTA [10], EPTA [9], and NANOGrav 11 yr data [11].

Figure 4

Cosmic string spectra calculated for $f\in ({10}^{-9},200)\mathrm{Hz}$ with $G\mu \in (4\times {10}^{-11},{10}^{-10})$ (between the solid black lines) and $G\mu \in (2\times {10}^{-11},3\times {10}^{-10})$ (between the dashed black lines) that fit the NANOGrav 12.5 yr data at the 68% and 95% confidence levels, respectively. We also show the current sensitivity of LIGO O2 as well as its design sensitivity, as well as the estimated reaches of the other planned and proposed experiments SKA, LISA, TianQin, AEDGE, AION, ET, and CE.