Searching for Gravitational Waves from Cosmological Phase Transitions with the NANOGrav 12.5-Year Dataset

We search for a first-order phase transition gravitational wave signal in 45 pulsars from the NANOGrav 12.5-year dataset. We find that the data can be modeled in terms of a strong first order phase transition taking place at temperatures below the electroweak scale. However, we do not observe any strong preference for a phase-transition interpretation of the signal over the standard astrophysical interpretation in terms of supermassive black hole mergers; but we expect to gain additional discriminating power with future datasets, improving the signal to noise ratio and extending the sensitivity window to lower frequencies. An interesting open question is how well gravitational wave observatories could separate such signals.

Figure 1

In red (blue) the $1\text{−}\sigma$ (68% posterior credible level), and $2\text{−}\sigma$ (95% posterior credible level) contours for the two-dimensional posterior distributions in the $(T_{*},{\alpha }_{*})$ plane obtained in the BO (SWO). The BO analysis has been performed with the spectral shape computed by using the envelope approximation (left panel), semianalytic results (central panel), and numerical results (right panel). Specifically, we use $(a,b,c)=(1,2.61,1.5)$ for the semianalytic results, and $(a,b,c)=(0.7,2.3,1)$ for the numerical results.

Figure 2

Maximum likelihood GWB fractional energy-density spectrum for the BO (red) and SWO (blue) analyses compared with the marginalized posterior for the free power spectrum (independent per-frequency characterization; red violin plot) derived in NG12gwb For the BO analysis we show the results derived by using the envelope (solid line), semianalytic (dashed), and numerical (dot-dashed) spectral shapes. For the BO analyses the values of $({\alpha }_{*},T_{*})$ for these maximum likelihood spectra are (0.28,0.7 MeV) for the envelope results, (1.2,3.4 MeV) for the semianalytic results, and (0.13,14.1 MeV) for the numerical results. While for the SO analysis we get (6.0,0.32 MeV).

Figure 3

$1\text{−}\sigma$ (68% posterior credible level), and $2\text{−}\sigma$ (95% posterior credible level) contours for the parameters $A_{\mathrm{GWB}}$ and ${\alpha }_{*}$ in the $\mathrm{PT}+\mathrm{SMBHB}$ search. In red (blue) the results for the BO (SWO) analyses. In this figure we have used the semianalytic results for the bubble spectrum. The posteriors do not extend to lower values of ${\alpha }_{*}$ because of our choice for the ${\alpha }_{*}$ prior: log-uniform $[-1.3,1]$.

Figure 4

Corner plot showing the 1D and 2D posterior distributions for the parameters of the PT-only search. In red (blue) the results for the BO (SWO) analyses. In deriving these results we have used the semianalytic bubble spectral shape with $(a,b,c)=(1,2.61,1.5)$.