Ultra-light dark matter explanation of NANOGrav observations

The angular correlation of pulsar residuals observed by NANOGrav and other pulsar timing array (PTA) collaborations show evidence in support of the Hellings-Downs correlation expected from stochastic gravitational wave background (SGWB). In this paper, we offer a non-gravitational wave explanation of the observed pulsar timing correlations as caused by an ultra-light $L_{\mu} - L_{\tau}$ gauge boson dark matter (ULDM). ULDM can affect the pulsar correlations in two ways. The gravitational potential of vector ULDM gives rise to a Shapiro time delay of the pulsar signals and a non-trivial angular correlation (as compared to the scalar ULDM case). In addition, if the pulsars have a non-zero charge of the dark matter gauge group, then the electric field of the local dark matter causes an oscillation of the pulsar and a corresponding Doppler shift of the pulsar signal. We point out that pulsars carry a significant charge of muons, and thus the $L_{\mu} - L_{\tau}$ vector dark matter contributes to both the Doppler oscillations and the time delay of the pulsar signals. The synergy between these two effects provides a better fit to the shape of the angular correlation function, as observed by the NANOGrav collaboration, compared to the standard SGWB explanation or the SGWB combined with time delay explanations. Our analysis shows that in addition to the SGWB signal, there may potentially be excess timing residuals attributable to the $L_{\mu} - L_{\tau}$ ULDM.