Limits on Anisotropy in the Nanohertz Stochastic Gravitational Wave Background

The paucity of observed supermassive black hole binaries (SMBHBs) may imply that the gravitational wave background (GWB) from this population is anisotropic, rendering existing analyses suboptimal. We present the first constraints on the angular distribution of a nanohertz stochastic GWB from circular, inspiral-driven SMBHBs using the 2015 European Pulsar Timing Array data. Our analysis of the GWB in the $\sim 2–90\mathrm{nHz}$ band shows consistency with isotropy, with the strain amplitude in $l>0$ spherical harmonic multipoles $\lesssim 40\%$ of the monopole value. We expect that these more general techniques will become standard tools to probe the angular distribution of source populations.

Figure 1

95% upper limits on the strain amplitude, where $C_l=\sum _{m=-l}^l|c_{lm}{|}^2/(2l+1)$. Left: all-band anisotropy parametrization and frequency-dependent parametrization (ii). The right axis is the ratio of the upper limit to the monopole. The inset figure shows 95% upper limits on $(C_l/4\pi {)}^{1/4}$, which are marginalized over the strain amplitude for the all-band anisotropy parametrization and a constant likelihood analysis. Our limits reflect the constraints of the physical prior. Right: all-band anisotropy parametrization, where the $c_{lm}$ values are obtained by mapping cross-correlation values to the spherical harmonic basis, without physical prior rejection.

Figure 2

95% upper limits on the GW strain amplitude in each pixel. These limits are obtained by mapping from the Bayesian MCMC-sampled cross-correlation values to a pixelated ORF basis ($N_{\mathrm{pix}}=12288$). White stars show the pulsar locations.