Search for nontensorial gravitational-wave backgrounds in the NANOGrav 15-year dataset

The recent detection of a stochastic signal in the NANOGrav 15-year dataset has aroused great interest in uncovering its origin. However, the evidence for the Hellings-Downs correlations, a key signature of the gravitational-wave background (GWB) predicted by general relativity, remains inconclusive. In this paper, we search for an isotropic nontensorial GWB, allowed by general metric theories of gravity, in the NANOGrav 15-year dataset. Our analysis reveals a Bayes factor of approximately 2.5, comparing the quadrupolar (tensor transverse, TT) correlations to the scalar transverse (ST) correlations, suggesting that the ST correlations provide a comparable explanation for the observed stochastic signal in the NANOGrav data. We obtain the median and the 90% equal-tail amplitudes as ${\mathcal{A}}_{\mathrm{ST}}={7.8}_{-3.5}^{+5.1}\times {10}^{-15}$ at the frequency of $1/\mathrm{year}$. Furthermore, we find that the vector longitudinal (VL) and scalar longitudinal (SL) correlations are weakly and strongly disfavored by data, respectively, yielding upper limits on the amplitudes: ${\mathcal{A}}_{\mathrm{VL}}^{95\%}\lesssim 1.7\times {10}^{-15}$ and ${\mathcal{A}}_{\mathrm{SL}}^{95\%}\lesssim 7.4\times {10}^{-17}$. Lastly, we fit the NANOGrav data with the general transverse (GT) correlations parametrized by a free parameter $\alpha$. Our analysis yields $\alpha ={1.74}_{-1.41}^{+1.18}$, thus excluding both the TT ($\alpha =3$) and ST ($\alpha =0$) models at the 90% confidence level.

Figure 1

Various ORFs examined in this work. Here, the GTb model refers to the GT model with $\alpha =1.74$. The Bayesian reconstruction of normalized inter-pulsar correlations, as adapted from NANOGrav’s analysis [13], is depicted by the gray violins. It is important to emphasize that the longitudinal modes, VL and SL, depend on both pulsar distance and GW frequency. The illustration here specifically presents the scenario where $f{L}_a=f{L}_b=100$ for the VL and SL modes.

Figure 2

Bayesian posteriors for the amplitude, $A$, and power-law index parameter, $\gamma$, obtained in the ST, VL, and SL models. We show the $1\sigma$, $2\sigma$, and $3\sigma$ contours in the two-dimensional plot.

Figure 3

Same as Fig. 2 but for the $\mathrm{TT}+\mathrm{ST}$ model.

Figure 4

Bayesian posteriors for the $\alpha$ parameter in the GT model with a parameterized ORF as defined by Eq. (10). The two vertical dashed lines correspond to the ST ($\alpha =0$) and TT ($\alpha =3$) ORFs, respectively.