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The recent results from the Pulsar Timing Array (PTA) collaborations show thefirst evidence for the detection of a stochastic background of gravitationalwaves at the nHz frequencies. This discovery has profound implications for thephysics of both the late and the early Universe. In fact, together with thepossible interpretation in terms of super massive black hole binaries, manysources in the early Universe can provide viable explanations as well. In thispaper, we study the gravitational wave background sourced by a network ofaxion-like-particle (ALP) domain walls at temperatures around the QCDcrossover, where the QCD-induced potential provides the necessary bias toannihilate the network. Remarkably, this implies a peak amplitude atfrequencies around the sensitivity range of PTAs. We extend previous analysisby taking into account the unavoidable friction on the network stemming fromthe topological coupling of the ALP to QCD in terms of gluon and pionreflection off the domain walls at high and low temperatures, respectively. Weidentify the regions of parameter space where the network annihilates in thescaling regime ensuring compatibility with the PTA results, as well as thosewhere friction can be important and a more detailed study around the QCDcrossover is required.

Axionic domain walls at Pulsar Timing Arrays: QCD bias and particle friction