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Register a new userConstraints on ultra-low-frequency gravitational waves with statistics of pulsar spin-down rates II: Mann-Whitney U test
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We investigate gravitational waves with sub-nanoHz frequencies ($10^{-11}$ Hz $lesssim f_{rm GW} lesssim 10^{-9}$ Hz) from the spatial distribution of the spin-down rates of milli-second pulsars. As we suggested in Yonemaru et al. 2018, gravitational waves from a single source induces the bias in the observed spin-down rates of pulsars depending on the relative direction between the source and pulsar. To improve the constraints on the time derivative of gravitational-wave amplitude obtained in our previous work (Kumamoto et al. 2019), we adopt a more sophisticated statistical method called the Mann-Whitney U test. Applying our method to the ATNF pulsar catalogue, we first found that the current data set is consistent with no GW signal from any direction in the sky. Then, we estimate the effective angular resolution of our method to be $(66~{rm deg})^2$ by studying the probability distribution of the test statistic. Finally, we investigate gravitational-wave signal from the Galactic Centre and M87 and, comparing simulated mock data sets with the real pulsar data, we obtain the upper bounds on the time derivative as $dot{h}_{rm GC} < 8.9 times 10^{-19} {rm s}^{-1}$ for the Galactic Centre and $dot{h}_{rm M87} < 3.3 times 10^{-19} {rm s}^{-1}$ for M87, which are stronger than the ones obtained in Kumamoto et al. 2019 by factors of 7 and 25, respectively.
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We probe ultra-low-frequency gravitational waves (GWs) with statistics of spin-down rates of milli-second pulsars (MSPs) by a method proposed in our prevous work (Yonemaru et al. 2016). The considered frequency range is $10^{-12}{rm Hz} lesssim f_{rm GW} lesssim 10^{-10}$Hz, which cannot be accessed by the conventional pulsar timing array. The effect of such low-frequency GWs appears as a bias to spin-down rates which has a quadrupole pattern in the sky. We use the skewness of the spin-down rate distribution and the number of MSPs with negative spin-down rates to search for the bias induced by GWs. Applying this method to 149 MSPs selected from the ATNF pulsar catalog, we derive upper bounds on the time derivative of the GW amplitudes of $dot{h} < 6.2 times 10^{-18}~{rm sec}^{-1}$ and $dot{h} < 8.1 times 10^{-18}~{rm sec}^{-1}$ in the directions of the Galactic Center and M87, respectively. Approximating the GW amplitude as $dot{h} sim 2 pi f_{rm GW} h$, the bounds translate into $h < 3 times 10^{-9}$ and $h < 4 times 10^{-9}$, respectively, for $f_{rm GW} = 1/(100~{rm yr})$. Finally, we give the implications to possible super-massive black hole binaries at these sites.
A new detection method for gravitational waves (GWs) with ultra-low frequencies ($f_{rm GW} lesssim 10^{-10}~{rm Hz}$), 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 $10^{-19}~{rm s}^{-1}$ 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 $< 10^{-12}~{rm Hz}$ compared to the previous estimates.
Milli-second pulsars with highly stable periods can be considered as very precise clocks and can be used for pulsar timing array (PTA) which attempts to detect nanoheltz gravitational waves (GWs) directly. Main sources of nanoheltz GWs are supermassive black hole (SMBH) binaries which have sub-pc-scale orbits. On the other hand, a SMBH binary which is in an earlier phase and has pc-scale orbit emits ultra-low-frequency ($lesssim 10^{-9},mathrm{Hz}$) GWs cannot be detected with the conventional methodology of PTA. Such binaries tend to obtain high eccentricity, possibly $sim 0.9$. In this paper, we develop a formalism for extending constraints on GW amplitudes from single sources obtained by PTA toward ultra-low frequencies considering the waveform expected from an eccentric SMBH binary. GWs from an eccentric binaries are contributed from higher harmonics and, therefore, have a different waveform those from a circular binary. Furthermore, we apply our formalism to several hypothetical SMBH binaries at the center of nearby galaxies, including M87, using the constraints from NANOGravs 11-year data set. For a hypothetical SMBH binary at the center of M87, the typical upper limit on the mass ratio is $0.16$ for eccentricity of $0.9$ and semi-major axis of $a=1~mathrm{pc}$, assuming the binary phase to be the pericenter.
We present a search for continuous gravitational-wave signals from the young, energetic X-ray pulsar PSR J0537-6910 using data from the second and third observing runs of LIGO and Virgo. The search is enabled by a contemporaneous timing ephemeris obtained using NICER data. The NICER ephemeris has also been extended through 2020 October and includes three new glitches. PSR J0537-6910 has the largest spin-down luminosity of any pulsar and is highly active with regards to glitches. Analyses of its long-term and inter-glitch braking indices provided intriguing evidence that its spin-down energy budget may include gravitational-wave emission from a time-varying mass quadrupole moment. Its 62 Hz rotation frequency also puts its possible gravitational-wave emission in the most sensitive band of LIGO/Virgo detectors. Motivated by these considerations, we search for gravitational-wave emission at both once and twice the rotation frequency. We find no signal, however, and report our upper limits. Assuming a rigidly rotating triaxial star, our constraints reach below the gravitational-wave spin-down limit for this star for the first time by more than a factor of two and limit gravitational waves from the $l=m=2$ mode to account for less than 14% of the spin-down energy budget. The fiducial equatorial ellipticity is limited to less than about 3e-5, which is the third best constraint for any young pulsar.
We give the asymptotic behavior of the Mann-Whitney U-statistic for two independent stationary sequences. The result applies to a large class of short-range dependent sequences, including many non-mixing processes in the sense of Rosenblatt. We also give some partial results in the long-range dependent case, and we investigate other related questions. Based on the theoretical results, we propose some simple corrections of the usual tests for stochastic domination; next we simulate different (non-mixing) stationary processes to see that the corrected tests perform well.
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