Models that produce Axion-Like-Particles (ALP) after cosmological inflation
due to spontaneous U(1) symmetry breaking also produce cosmic string
networks. Those axionic strings lose energy through gravitational wave emission
during the whole cosmological history, generating a stochastic background of
gravitational waves that spans many decades in frequency. We can therefore
constrain the axion decay constant and axion mass from limits on the
gravitational wave spectrum and compatibility with dark matter abundance as
well as dark radiation. We derive such limits from analyzing the most recent
NANOGrav data from Pulsar Timing Arrays (PTA). The limits are compatible with
the slightly stronger Neff bounds on dark radiation for ALP masses
ma≲10−10 eV. On the other hand, for heavy ALPs with ma≳0.1 GeV and NDW=1, new regions of parameter space can be probed
by PTA data due to the dominant Domain-Wall contribution to the gravitational
wave background.Comment: 8 pages, 4 figures + supplemental material (2 pages, 2 figures