Recently, Pulsar Timing Array (PTA) collaborations have detected a stochastic
gravitational wave background (SGWB) at nano-Hz frequencies, with Domain Wall
networks (DWs) proposed as potential sources. To be cosmologically viable, they
must annihilate before dominating the universe energy budget, thus generating a
SGWB. While sub-horizon DWs shrink and decay rapidly, causality requires DWs
with super-horizon size to continue growing until they reach the Hubble
horizon. Those entering the latest can be heavier than a Hubble patch and
collapse into Primordial Black Holes (PBHs). By applying percolation theory, we
pioneer an estimation of the PBH abundance originating from DW networks. We
conduct a Bayesian analysis of the PTA signal, interpreting it as an outcome of
SGWB from DW networks, accounting for PBH overproduction as a prior. We
included contributions from supermassive black hole binaries along with their
astrophysical priors. Our findings indicate that DWs, as the proposed source of
the PTA signal, result in the production of PBHs about ten times heavier than
the sun. The binary mergers occurring within these PBHs generate a second SGWB
in the kilo-Hz domain which could be observable in on-going or planned
Earth-based interferometers if the correlation length of the DW network is
greater than approximately 60% than the cosmic horizon, L≳0.6t.Comment: Major improvements of the PBH formation modeling, of the depth of the
Bayesian analysis and of the SMBH binary prior (5 pages, 4 figures +
appendix, 21 pages in total