Constraints on ultra-low-frequency gravitational waves with statistics of pulsar spin-down rates. II. Mann–Whitney U test

We investigate gravitational waves with sub-nanoHz frequencies ($10^{-11}$ Hz $\lesssim f_{\rm GW} \lesssim 10^{-9}$ Hz) from the spatial distribution of spin-down rates milli-second pulsars. As we suggested in Yonemaru et al. 2018, a single source induces bias observed pulsars depending on relative direction between and pulsar. To improve constraints time derivative gravitational-wave amplitude obtained our previous work (Kumamoto 2019), adopt more sophisticated statistical method called Mann-Whitney U test. Applying to ATNF pulsar catalogue, first found that current data set is consistent no GW signal any sky. Then, estimate effective angular resolution be $(66~{\rm deg})^2$ by studying probability test statistic. Finally, Galactic Centre M87 and, comparing simulated mock sets real data, obtain upper bounds as $\dot{h}_{\rm GC} < 8.9 \times 10^{-19} {\rm s}^{-1}$ for M87} 3.3 M87, which are stronger than ones Kumamoto 2019 factors 7 25, respectively.