Detailed study of detection method for ultralow frequency gravitational waves with pulsar spin-down rate statistics

Abstract

A new detection method for gravitational waves (GWs) with ultra-low frequencies ( f GW 10 −10 Hz), which is much lower than the range of pulsar timing arrays (PTAs), was proposed in Yonemaru et al. (2016). This method utilizes the statistical properties of spin-down rates of milli-second pulsars (MSPs) and the sensitivity was evaluated in Yonemaru et al. (2018). There, some simplifying assumptions, such as neglect of the "pulsar term" and spatially uniform distribution of MSPs, were adopted and the sensitivity on the time derivative of GW amplitude was estimated to be 10 −19 s −1 independent of the direction, polarization and frequency of GWs. In this paper, extending the previous analysis, realistic simulations are performed to evaluate the sensitivity more reasonably. We adopt a model of 3-dimensional pulsar distribution in our Galaxy and take the pulsar term into account. As a result, we obtain expected sensitivity as a function of the direction, polarization and frequency of GWs. The dependence on GW frequency is particularly significant and the sensitivity becomes worse by a few orders for < 10 −12 Hz compared to the previous estimates.

Constraints on ultra-low-frequency gravitational waves with statistics of pulsar spin-down rates

“…In the SKA era, we will have 3,000 MSPs (Keane et al 2015;Kramer & Stappers 2015) and the constraint on ultra-low-frequency GWs considered here will improve accordingly. In fact, we estimated the future constraints with the skewness difference in Hisano et al (2019) and h < 2 × 10 −19 s −1 at f GW = 10 −11 Hz was obtained for the GC, which is stronger than the constraint obtained in Kumamoto et al (2019) by a factor of 30. It is possible that a future constraint based on the Mann-Whitney U test statistics will improve by a similar factor.…”

“…As we suggested in Yonemaru et al (2018), the GW from a single source induce the bias in the observed spin-down rates of pulsars depending on the relative direction between the GW source and pulsar. Compared with our previous studies (Yonemaru et al 2018;Hisano et al 2019;Kumamoto et al 2019), where the skewness difference in the spin-down rate distribution was considered to detect the bias, we adopted a more sophisticated statistical method called the Mann-Whitney U test.…”

“…Then the effect of GWs with much longer periods can be approximated to be linear function in time-domain. While the pulsar term has been often neglected in the literature, we investigated its importance quantitatively through Monte Carlo simulations in Hisano et al (2019). It was found that the pulsar term behaves as a random noise with zero average when the GW wavelength is shorter than or comparable to the typical pulsar distance (∼ 1 kpc), in other words, the GW period is smaller than O(1, 000) years.…”

“…Here, we used the skewness as a statistical quantity to characterize the distribution of spin-down rates and the skewness difference between the two groups was considered to be a measure of GW signals. In Hisano et al (2019), we adopted a realistic model of the pulsar spatial distribution within Galaxy to improve the prediction of the sensitivity. Then, in Kumamoto et al (2019), we derived upper bounds on the time derivative of the GW amplitudes from two possible GW sources, the Galactic Centre and M87.…”

Constraints on ultra-low-frequency gravitational waves from an eccentric supermassive black hole binary

“…The method utilizes the fact that the spin-down rate of MSPs is biased by ultra-low-frequency GWs and it was shown that the time derivative of GW amplitude is constrained from the statistics of spatial pattern of pulsar spin-down rates in the sky. Then we evaluated the sensitivity with Monte-Carlo simulations (Yonemaru et al 2018;Hisano et al 2019) and put constraints on GWs from the Galactic Center and M87 as ℎ < 6.2 × 10 −18 sec −1 and ℎ < 8.1 × 10 −18 sec −1 , respectively, for GW = 1/(1000 year) (Kumamoto et al 2019), where ℎ is the GW amplitude and the dot represents the time derivative.…”