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Recent pulsar timing data reported by the NANOGrav collaboration may indicatethe existence of a stochastic gravitational wave background around $f \sim10^{-8}$ Hz. We explore a possibility to generate such low-frequencygravitational waves from a dark sector phase transition. Assuming that the darksector is completely decoupled from the visible sector except via thegravitational interaction, we find that some amount of dark radiation shouldremain until present. The NANOGrav data implies that the amount of darkradiation is close to the current upper bound, which may help mitigate theso-called Hubble tension. If the existence of dark radiation is not confirmedin the future CMB-S4 experiment, it would imply the existence of new particlesfeebly interacting with the standard model sector at an energy scale ofO(1-100) MeV.

Gravitational Waves and Dark Radiation from Dark Phase Transition: Connecting NANOGrav Pulsar Timing Data and Hubble Tension