Implications of Pulsar Timing Array Results for High Frequency Gravitational Waves

Several pulsar timing array (PTA) experiments such as NANOGrav and PPTA recently reported evidence of a gravitational wave (GW) background at nano-Hz frequency band. This signal can originate from scalar-induced gravitational waves (SIGW) generated by the enhanced curvature perturbation. Production of SIGW is expected to be accompanied by formation of primordial black holes (PBH), which can emit GW through binary mergers. Here we perform a joint likelihood inference on PTA datasets in combination with existing limits on PBH abundance and GW density, we derive full Bayesian posteriors for PBH distribution and relevant PBH merger signal. Our results show that analysis using PTA data alone implies significant overproduction of PBHs, and accounting for current PBH limits causes visible shifts in SIGW posterior. If PTA signals are indeed of SIGW origin, the required curvature perturbation amplitude produces PBHs in a narrow mass window of $[6 \times 10^{-2}, 2 \times 10^{-1}]\ m_\odot$. Mergers of these PBHs can leave a strong GW signature in $[10^{-3}, 10^5]$ Hz frequency range, to be detectable at upcoming interferometers such as LISA, aLIGO, Einstein Telescope, DECIGO and BBO, etc. This offers a multi-frequency opportunity to further scrutinize the source of the observed PTA signal and can potentially improve current PBH constraints by up to 5 orders of magnitudes.