An important next step for pulsar timing arrays (PTAs) is to measure anisotropies in the gravitational wave background (GWB) at $\sim$ nanohertz frequencies. We calculate the expected GWB anisotropies using empirically calibrated models for the merger rates of supermassive black hole binaries (SMBHBs). The anisotropies reflect both shot noise in the discrete SMBHB populations while also tracing, in part, the large-scale structure (LSS) of the universe. The shot-noise term is sensitive to the high-mass end of the merging SMBH mass function, depends somewhat on the low-redshift tail of the merger distribution, and is a strong function of observing frequency. The precise frequency dependence provides a test of SMBHB residence times. In our models, the mean shot-noise anisotropy typically lies close to or above the broad frequency-band NANOGrav upper limits. Consequently, near-future PTA data, and potentially, reanalyses of existing measurements using frequency-dependent shot-noise anisotropy templates, should be capable of detecting this signal or placing meaningful constraints on SMBHB merger models. A full interpretation, however, will require modeling the probability distribution of shot-noise amplitudes rather than relying solely on ensemble-averaged predictions. The LSS-induced anisotropies are at least 2 to 3 orders of magnitude smaller. Although the LSS contribution contains valuable information regarding the redshift distribution and clustering bias of the merging SMBHBs, detecting this component will be challenging.

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• Gravitational waves
• Astronomical black holes
• Large scale structure of the Universe
• Gravitational wave detectors