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The NANOGrav, Parkes, European, and International Pulsar Timing Array (PTA)Collaborations have reported evidence for a common-spectrum process that canpotentially correspond to a stochastic gravitational wave background (SGWB) inthe 1--100 nHz frequency range. We consider the scenario in which this signalis produced by magnetohydrodynamic (MHD) turbulence in the early Universe,induced by a nonhelical primordial magnetic field at the energy scalecorresponding to the quark confinement phase transition. We perform MHDsimulations to study the dynamical evolution of the magnetic field and computethe resulting SGWB. We show that the SGWB output from the simulations can bevery well approximated by assuming that the magnetic anisotropic stress isconstant in time, over a time interval related to the eddy turnover time. Theanalytical spectrum that we derive under this assumption features a change ofslope at a frequency corresponding to the GW source duration that we confirmwith the numerical simulations. We compare the SGWB signal with the PTA data toconstrain the temperature scale at which the SGWB is sourced, as well as theamplitude and characteristic scale of the initial magnetic field. We find thatthe generation temperature is constrained to be in the 1--200 MeV range, themagnetic field amplitude must be $>1$\% of the radiation energy density at thattime, and the magnetic field characteristic scale is constrained to be $>10$\%of the horizon scale. We show that the turbulent decay of this magnetic fieldwill lead to a field at recombination that can help to alleviate the Hubbletension and can be tested by measurements in the voids of the Large ScaleStructure with gamma-ray telescopes like the Cherenkov Telescope Array.

Gravitational wave signal from primordial magnetic fields in the Pulsar Timing Array frequency band