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

Abstract

Abstract We investigate gravitational waves with sub-nHz frequencies (10−11 Hz ≲ fGW ≲ 10−9 Hz) from the spatial distribution of the spin-down rates of millisecond pulsars. As we suggested in Yonemaru et al. (2018, MNRAS, 478, 1670), gravitational waves from a single source induce a bias in the observed spin-down rates of pulsars depending on the relative direction between the source and the pulsar. To improve the constraints on the time derivative of gravitational wave amplitude obtained in our previous work (Kumamoto et al. 2019, MNRAS, 489, 3547), we adopt a more sophisticated statistical method called the Mann–Whitney U test. Applying our method to the ATNF pulsar catalogue, we first find that the current data set is consistent with no gravitational wave signal from any direction in the sky. Then, we estimate the effective angular resolution of our method to be 66 deg2 by studying the probability distribution of the test statistic. Finally, we investigate gravitational wave signals from the Galactic Center (GC) and M 87 and, comparing simulated mock data sets with the real pulsar data, we obtain upper bounds on the time derivative as $\dot{h}_{\rm GC} < 8.9 \times 10^{-19}$ s−1 for the GC and $\dot{h}_{\rm M87} < 3.3 \times 10^{-19}$ s−1 for M 87, which are stronger than those obtained in Kumamoto et al. (2019, MNRAS, 489, 3547) by factors of 7 and 25, respectively.