The NANOGrav, Parkes, European, and International Pulsar Timing Array (PTA) Collaborations have reported evidence for a common-spectrum process that can potentially correspond to a stochastic gravitational wave background (SGWB) in the 1--100 nHz frequency range. We consider the scenario in which this signal is produced by magnetohydrodynamic (MHD) turbulence in the early Universe, induced by a nonhelical primordial magnetic field at the energy scale corresponding to the quark confinement phase transition. We perform MHD simulations to study the dynamical evolution of the magnetic field and compute the resulting SGWB. We show that the SGWB output from the simulations can be very well approximated by assuming that the magnetic anisotropic stress is constant in time, over a time interval related to the eddy turnover time. The analytical spectrum that we derive under this assumption features a change of slope at a frequency corresponding to the GW source duration that we confirm with the numerical simulations. We compare the SGWB signal with the PTA data to constrain the temperature scale at which the SGWB is sourced, as well as the amplitude and characteristic scale of the initial magnetic field. We find that the generation temperature is constrained to be in the 1--200 MeV range, the magnetic field amplitude must be $>1$\% of the radiation energy density at that time, and the magnetic field characteristic scale is constrained to be $>10$\% of the horizon scale. We show that the turbulent decay of this magnetic field will lead to a field at recombination that can help to alleviate the Hubble tension and can be tested by measurements in the voids of the Large Scale Structure with gamma-ray telescopes like the Cherenkov Telescope Array.
Non-Gaussian timing residual skewness in pulsar timing arrays
Max Planck Institute for Gravitational Physics (Albert Einstein Institute), Leibnitz Universität Hannover（马克斯·普朗克引力物理研究所（爱因斯坦研究所），莱布尼茨汉诺威大学）；Department of Physics, National Central University（国立中央大学物理系）；Institute of Physics, Academia Sinica（台湾中央研究院物理研究所）；Institute of Astronomy and Astrophysics, Academia Sinica（台湾中央研究院天文及天文物理研究所）
Detecting Chiral Gravitational Wave Background with a Dipole Pulsar Timing Array
National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；Hangzhou Institute for Advanced Study, University of Chinese Academy of Sciences（中国科学院大学杭州高等研究院）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；Institute of Fundamental Physics and Quantum Technology, Ningbo University（宁波大学基础物理与量子技术研究所）；Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo（东京大学宇宙木理论研究所）；Asia Pacific Center for Theoretical Physics（亚太理论物理中心）；Leung Center for Cosmology and Particle Astrophysics, National Taiwan University（台湾大学梁氏宇宙学与粒子天体物理学研究中心）；Yukawa Institute for Theoretical Physics, Kyoto University（京都大学汤川理论物理研究所）
