Polynomial regression calculation of the Earth's position based on millisecond pulsar timing

Prior to achieving high precision navigation of a spacecraft using X-ray observations, a pulsar rotation model must be built and analysis of the precise posi- tion of the Earth should be performed using ground pulsar timing observations. We can simulate time-of-arrival ground observation data close to actual observed values before using pulsar timing observation data. Considering the correlation between the Earth＇s position and its short arc section of an orbit, we use polynomial regression to build the correlation. Regression coefficients can be calculated using the least square method, and a coordinate component series can also be obtained; that is, we can calcu- late Earth＇s position in the Barycentric Celestial Reference System according to pulse arrival time data and a precise pulsar rotation model. In order to set appropriate param- eters before the actual timing observations for Earth positioning, we can calculate the influence of the spatial distribution of pulsars on errors in the positioning result and the influence of error source variation on positioning by simulation. It is significant that the threshold values of the observation and systematic errors can be established before an actual observation occurs; namely, we can determine the observation mode with small errors and reject the observed data with big errors, thus improving the positioning result.

Constraints on the primordial curvature power spectrum by pulsar timing array data:a polynomial parameterization approach

The recent stochastic signal observed jointly by NANOGrav,parkes pulsar timing array,European pulsar timing array,and Chinese pulsar timing array can be accounted for by scalarinduced gravitational waves(SIGWs).The source of the SIGWs is from the primordial curvature perturbations,and the main contribution to the SIGWs is from the peak of the primordial curvature power spectrum.To effectively model this peak,we apply the Taylor expansion to parameterize it.With the Taylor expansion parameterization,we apply Bayesian methods to constrain the primordial curvature power spectrum based on the NANOGrav 15 year data set.The constraint on the primordial curvature power spectrum possesses a degree of generality,as the Taylor expansion can effectively approximate a wide range of function profiles.

Statistical analyses for NANOGrav 5-year timing residuals

In pulsar timing, timing residuals are the differences between the observed times of arrival and predictions from the timing model. A comprehensive timing model will produce featureless resid- uals, which are presumably composed of dominating noise and weak physical effects excluded from the timing model （e.g. gravitational waves）. In order to apply optimal statistical methods for detecting weak gravitational wave signals, we need to know the statistical properties of noise components in the residuals. In this paper we utilize a variety of non-parametric statistical tests to analyze the whiteness and Gaussianity of the North American Nanohertz Observatory for Gravitational Waves （NANOGrav） 5- year timing data, which are obtained from Arecibo Observatory and Green Bank Telescope from 2005 to 2010. We find that most of the data are consistent with white noise; many data deviate from Gaussianity at different levels, nevertheless, removing outliers in some pulsars will mitigate the deviations.

Searching for isotropic stochastic gravitational-wave background in the international pulsar timing array second data release

We search for isotropic stochastic gravitational-wave background(SGWB)in the International Pulsar Timing Array second data release.By modeling the SGWB as a power-law,we find very strong Bayesian evidence for a common-spectrum process,and further this process has scalar transverse(ST)correlations allowed in general metric theory of gravity as the Bayes factor in favor of the ST-correlated process versus the spatially uncorrelated common-spectrum process is 30±2.The median and the 90%equal-tail amplitudes of ST mode are A_(ST)=1.29^(+0.51)_(−0.44)×10^(−15),or equivalently the energy density parameter per logarithm frequency isΩSTGW=2.31^(+2.19)_(−1.30)×10^(−9),at frequency of 1 year−1.However,we do not find any statistically significant evidence for the tensor transverse(TT)mode and then place the 95%upper limits as A_(TT)<3.95×10^(−15),or equivalentlyΩ^(TT)_(GW)<2.16×10^(−9),at frequency of 1 year^(−1).

镜像量子色动力学相变解释纳赫兹随机引力波背景

Several Pulsar Timing Array(PTA)Collaborations have recently provided strong evidence for a n Hz Stochastic Gravitational-Wave Background(SGWB).Here we investigate the implications of a firstorder phase transition occurring within the early Universe's dark quantum chromodynamics epoch,specifically within the framework of the mirror twin Higgs dark sector model.Our analysis indicates a distinguishable SGWB signal originating from this phase transition,which can explain the measurements obtained by PTAs.Remarkably,a significant portion of the parameter space for the SGWB signal also effectively resolves the existing tensions in both the H_(0) and S_(8) measurements in Cosmology.This intriguing correlation suggests a possible common origin of these three phenomena for 0.2<ΔN_(eff)<0.5,where the mirror dark matter component constitutes less than 30% of the total dark matter abundance.Nextgeneration CMB experiments such as CMB-S4 can test this parameter region.

Frequency steering of spaceborne clocks based on XPNAV-1 observations

Due to high stable rotations, timing of pulsars provides a natural tool to correct the frequency deviation of spaceborne atomic clocks. Based on processing the observational data about a year of Crab pulsar given by XPNAV-1 satellite, we study the possibility of correcting the frequency deviation of spaceborne atomic clocks using pulsar timing. According to the observational data in X-ray band and the timing model parameters from radio observations, the pre-fit timing residuals with a level of 67.66 μs are obtained. By fitting the slope of the timing residuals affected by the faked frequency-biased reference clock, we estimated successfully the relative frequency deviation of the reference clock. For a satellite clock with frequency deviation of the order about 10^(-12), a calibration accuracy with relative error of about 2% can be obtained from the Crab pulsar’s data for one year.The stability of the time scale based on Crab pulsar is about 10^(-12) for an interval of one year.

脉冲星计时阵列观测的随机背景信号对标量诱导引力波的限制

最近,NANOGrav、PPTA、EPTA和CPTA合作组各自独立报告了关于随机引力波背景的观测证据.尽管根据观测推断的引力波背景(幅度、频谱)与超大质量双黑洞并合的预言相一致,但这一观测也为搜寻宇宙早期的新物理现象提供了新的窗口.本文探讨了用早期宇宙中的标量诱导引力波来解释这一信号的可能性.作者采用参数化的拐折幂律谱作为随机引力波背景能谱的普适性描述,利用NANOGrav、PPTA和EPTA的新数据和贝叶斯推断的方法进行研究.本研究结果可以约束诱导引力波能谱的相关参数,并进一步对可能在早期宇宙中产生原初黑洞的各种暴胀模型给出限制,这些模型有望在未来的空间引力波观测实验中得到检验.

Implications for the supermassive black hole binaries from the NANOGrav 15-year data set

Several pulsar timing array(PTA)collaborations,including NANOGrav,EPTA,PPTA,and CPTA,have announced the evidence for a stochastic signal consistent with a stochastic gravitational wave background(SGWB).Supermassive black hole binaries(SMBHBs)are supposed to be the most promising gravitational-wave(GW)sources for this signal.In this paper,we use the NANOGrav 15-year data set to constrain the parameter space in an astro-informed formation model for SMBHBs.Our results prefer a large turn-over eccentricity of the SMBHB orbit when GWs begin to dominate the SMBHB evolution.Furthermore,the SGWB spectrum is extrapolated to the space-borne GW detector frequency band by including inspiral-merge-cutoff phases of SMBHBs,indicating that the SGWB from SMBHBs should be detected by LISA,Taiji and Tian Qin in the near future.

纳赫兹引力波对单态暗物质模型中电弱相变的影响

受脉冲星定时阵列合作组最近观测到的纳赫兹级随机引力波证据的启发,本文在标准模型的单态扩展中探讨了利用极端过冷的电弱相变解释这些观测结果的可能性,并考虑了相变对于暗物质的影响.研究结果表明,通过精细调节模型参数,相应的渗透温度可以连续降低到1 GeV甚至更低.在如此低的渗透温度下,单态暗物质可能在电弱相变之前就脱离热平衡,从而从热辐射中冻结出来.因此,相变期间产生的熵可以显著影响暗物质的残留密度.这减轻了单态扩展模型中同时解释重子生成和满足暗物质直接探测限制的压力,暗示着所考虑的新物理模型可能存在更广阔的参数空间,并可在未来的实验中得到验证.

Non-tensorial gravitational wave background in NANOGrav 12.5-year data set

We perform the first search for an isotropic non-tensorial gravitational-wave background(GWB) allowed in general metric theories of gravity in the North American Nanohertz Observatory for Gravitational Waves(NANOGrav) 12.5-year data set. By modeling the GWB as a power-law spectrum, we find strong Bayesian indication for a spatially correlated process with scalar transverse(ST) correlations whose Bayes factor versus the spatially uncorrelated common-spectrum process is 107 ± 7, but no statistically significant evidence for the tensor transverse, vector longitudinal, and scalar longitudinal polarization modes. The median and the 90% equal-tail amplitudes of ST mode are ■ , or equivalently the energy density parameter per logarithm frequency is ■, at frequency of 1/year.

NANOGrav hints on planet-mass primordial black holes

Recently, the North American Nanohertz Observatory for Gravitational Waves(NANOGrav) claimed the detection of a stochastic common-spectrum process of the pulsar timing array(PTA) time residuals from their 12.5 year data, which might be the first detection of the stochastic background of gravitational waves(GWs). We show that the amplitude and the power index of such waves imply that they could be the secondary GWs induced by the peaked curvature perturbation with a dust-like post inflationary era with-0.091 ≤ w ≤ 0.048. Such stochastic background of GWs naturally predicts substantial existence of planet-mass primordial black holes(PBHs), which can be the lensing objects for the ultrashort-timescale microlensing events observed by the Optical Gravitational Lensing Experiment(OGLE).