Gravitational waves from resolvable massive black hole binary systems and observations with Pulsar Timing Arrays

Massive black holes are key components of the assembly and evolution of cosmic structures, and a number of surveys are currently on going or planned to probe the demographics of these objects and to gain insight into the relevant physical processes. Pulsar Timing Arrays (PTAs) currently provide the only means to observe gravitational radiation from massive black hole binary systems with masses  ≳10⁷ M_⊙  . The whole cosmic population produces a stochastic background that could be detectable with upcoming PTAs. Sources sufficiently close and/or massive generate gravitational radiation that significantly exceeds the level of the background and could be individually resolved. We consider a wide range of massive black hole binary assembly scenarios, investigate the distribution of the main physical parameters of the sources, such as masses and redshift, and explore the consequences for PTAs observations. Depending on the specific massive black hole population model, we estimate that on average at least one resolvable source produces timing residuals in the range  ∼5–50 ns  . PTAs, and in particular the future Square Kilometre Array, can plausibly detect these unique systems, although the events are likely to be rare. These observations would naturally complement on the high-mass end of the massive black hole distribution function future surveys carried out by the Laser Interferometer Space Antenna .     

A Statistical Analysis of Radio Pulsar Timing Noise

We present an analysis of the timing observations on 27 radio pulsars, collected at Hartebeesthoek Radio Astronomy Observatory (HartRAO), with time spans ranging between ～ 9 and 14yr. Our results show that the measured pulsar frequency second derivatives are non-stationary. Both the magnitude and the sign of the ■ values depend upon the choice of epoch and data span. A simple statistical analysis of the observed second time derivative of the pulse frequency (■obs) of a large sample of 391 (25 HartRAO and 366 Jodrell Bank Observatory) pulsars reveals that ■ is only marginally correlated with both the pulsar spin-d own rate ( ■) and the characteristic age (τc). We find correlation coefficients of ～ 0.20a nd-0.30 between the measured braking indices and, respectively, ■ and τc. This result reaffirms earlier conclusions that the braking indices of most radio pulsars, obtained through the standard timing technique, are strongly dominated by sustained random fluctuations in the observed pulse phase.     

Data analysis of continuous gravitational wave: all-sky search and study of templates

We have studied the problem of an all-sky search in reference to a continuous gravitational wave particularly for such sources whose wave-form are known in advance. We have made an analysis of the number of templates required for matched-filter analysis as applicable to these sources. We have employed the concept of fitting factor (FF); treating the source location as the parameters of the signal manifold and have studied the matching of the signal with templates corresponding to different source locations. We have investigated the variation of FF with source location and have noticed a symmetry in template parameters,  θ_T  and  φ_T  . It has been found that the two different template values in source location, each in  θ_T  and  φ_T  , have the same FF. We have also computed the number of templates required assuming the noise power spectral density   S _n ( f )  to be flat. It is observed that higher FF requires an exponentially increasing, large number of templates.     

Data analysis of continuous gravitational wave: Fourier transform – II

In this paper we obtain the Fourier Transform of a continuous gravitational wave. We have analysed the data set for (i) a 1-yr observation time and (ii) an arbitrary observation time, for an arbitrary location of detector and source, taking into account the effects arising due to the rotational as well as orbital motion of the Earth. As an application of the transform we considered spin-down and N -component signal analysis.     

Data analysis of continuous gravitational wave: Fourier transform – I

We present the Fourier Transform of a continuous gravitational wave. We have analysed the data set for a 1-d observation time and our analysis is applicable for an arbitrary location of detector and source. We have taken into account the effects arising due to the rotational as well as orbital motions of the Earth.     

The Parkes Southern Pulsar Survey — III. Timing of long-period pulsars

The Parkes survey of the entire southern sky for millisecond and other low-luminosity pulsars has now been completed. The survey system and initial results were described by Manchester et al. and the final results and population studies are described by Lyne et al. A total of 298 pulsars were detected, including 101 new discoveries of which 17 were millisecond pulsars. Here we report on timing observations at Parkes and Jodrell Bank of the 84 long-period (non-millisecond) pulsars discovered in the survey, including timing solutions for 78 of them. Pulse profiles and arrival times were obtained at several different frequencies over intervals of more than a year, yielding a position, period, period derivative and dispersion measure for each pulsar. Pulse profiles at frequencies near 400 MHz and 600 or 1400 MHz are presented for most of the observed pulsars. Significant timing noise was detected for five pulsars and a glitch was observed in the period of PSR J1123–6259.     

Investigating ultra-long gravitational waves with measurements of pulsar rotational parameters

A method is suggested with which to explore the gravitational wave background (GWB) in the frequency range 10⁻¹²–10⁻⁸ Hz. This method is based on the precise measurements of pulsar rotational parameters: the influence of gravitational waves (GWs) in this frequency range will affect these parameters and therefore some conclusions about the energy density of the GWB can be made using analysis of the derivatives of pulsar rotational frequency. The calculated values of the second derivative from a number of pulsars limit the density of the GWB, Ω_gw, as follows:  Ω_gw < 2 × 10⁻⁶  . Also, the time series of the frequency ν of different pulsars in a pulsar array can be cross-correlated pairwise in the same manner as in anomalous residuals analysis, thus providing the possibility of GWB detection in the ultra-low-frequency range.     

Pulsar timing residuals due to individual non-evolving gravitational wave sources

The pulsar timing residuals induced by gravitational waves from non- evolving single binary sources are affected by many parameters related to the relative positions of the pulsar and the gravitational wave sources. We will analyze the various effects due to different parameters. The standard deviations of the timing residuals will be calculated with a variable parameter fixing a set of other parameters. The or- bits of the binary sources will be generally assumed to be elliptical. The influences of different eccentricities on the pulsar timing residuals will also be studied in detail. We find that the effects of the related parameters are quite different, and some of them display certain regularities.     

The Effect of Lunisolar Precession on Pulsar Observations

In the measurements of pulsars’ periods and their rates of change there exists the effect of lunisolar precession. Via the analysis of this effect, we find that it can affect the accurate measurements of the periods of certain pulsars. An investigation of the periods of 1771 pulsars reveals that the measured periods of 81 pulsars suffer the influence of lunisolar precession in the range of the accuracy of measurements. With the improvement of the precision of measurements of pulsars’ periods and their change rates, this effect should get the corresponding corrections.     

tempo2: a new pulsar timing package – III. Gravitational wave simulation

Analysis of pulsar timing data sets may provide the first direct detection of gravitational waves. This paper, the third in a series describing the mathematical framework implemented into the tempo2 pulsar timing package, reports on using tempo2 to simulate the timing residuals induced by gravitational waves. The tempo2 simulations can be used to provide upper bounds on the amplitude of an isotropic, stochastic, gravitational wave background in our Galaxy and to determine the sensitivity of a given pulsar timing experiment to individual, supermassive, binary black hole systems.     

An Accumulative Method of Pulsar Standard Profile Based on Wavelet-modulus-maxima Correlation Information

The importance of producing the pulsar standard pulse profile is discussed. By analyzing the classical pulse superposition method, a novel pulse profile accumulation method based on the wavelet-modulus-maxima information is proposed. First, the original observed data are divided into groups according to the pulse periods, and by making separately the wavelet decomposition, the wavelet coefficients characterizing the pulse peaks on coarse scales are obtained. Secondly, selecting a group of coefficients with a high SNR as the reference data and making correlations respectively with the other groups of coefficients, the relative time delays of pulse peaks are determined. Finally, the grouped original data are added up according to the relative time delays to obtain the pulse profile. With a prior estimation of the background noise and the smoothing processing of the signal, a normalized standard profile with a rather high SNR can be obtained. Practical experiments and comparison with the template correlation method indicate that this method is simple, effective, free of the necessity of designing an approximate template, and insensitive to noise type. It should be valuable for engineering applications.     

Analysis of the Precision of Pulsar Time Clock Modeltwo

Millisecond pulsars have a very high rotation stability, which can be applied to many research fields, such as the establishment of the pulsar time standard, the detection of gravitational wave, the spacecraft navigation by using X-ray pulsars and so on. In this paper, we employ two millisecond pulsars PSR J0437-4715 and J1713+0743, which are observed by the International Pulsar Timing Array (IPTA), to analyze the precision of pulsar clock parameter and the prediction accuracy of pulse time of arrival (TOA). It is found that the uncertainty of spin frequency is 10^?15 Hz, the uncertainty of the first derivative of spin frequency is 10^?23 s^?2, and the precision of measured rotational parameters increases by one order of magnitude with the accumulated observational data every 4～5 years. In addition, the errors of TOAs within 4.8 yr which are predicted by the clock model established by the 10 yr data of J0437-4715 are less than 1 μs. Therefore, one can use the pulsar time standard to calibrate the atomic clock, and make the atomic time deviate from the TT (Terrestrial Time) less than 1 μs within 4.8 yr.     

基于双谱滤波的综合脉冲星时算法研究

毫秒脉冲星的自转频率非常稳定,提供了一种独立的基于遥远自然天体并能持续数百万乃至数十亿年的时间基准,具有稳定性强、运行时间长、服务范围广等特点.为了减弱毫秒脉冲星计时观测中各种高斯噪声对脉冲星时的影响,研究了一种基于双谱滤波的综合脉冲星时构建算法,处理分析了国际脉冲星计时阵(International Pul-sar Timing Array,IPTA)最新发布的4颗毫秒脉冲星(PSR J0437-4715、J0613-0200、J1713+0747和J1909-3744)的观测数据,分析了不同时间尺度综合脉冲星时的稳定性,并与构成国际原子时(International Atomic Time,TAI)的4家授时单位原子钟稳定性进行了比较.结果表明:双谱滤波算法能够较好地抑制观测噪声,提高综合脉冲星时的稳定性.相比于经典加权算法,综合脉冲星时1 yr、10 yr稳定度从7.77×10^-14、8.56×10^-16分别提高到1.50×10^-14、3.50×10^-16,单脉冲星时稳定性的提升也类似.同时发现,综合脉冲星时稳定性在5 yr及以上时间尺度上优于原子钟稳定性,可用于改善当前原子时的长期稳定性.     

Fast and accurate computational tools for gravitational waveforms from binary stars with any orbital eccentricity

The relevance of orbital eccentricity in the detection of gravitational radiation from (steady state) binary stars is emphasized. Computationally effective (fast and accurate) tools for constructing gravitational wave templates from binary stars with any orbital eccentricity are introduced including tight estimation criteria of the pertinent truncation and approximation errors.     

脉冲星数据比对分析和可视化系统设计与实现

脉冲星数据比对分析和可视化系统(PSRDB,URL:http://www.psrdb.net/),由FAST(Five-hundred-meter Aperture Spherical Radio Telescope)早期科学数据中心团队为快速开展脉冲星候选体比对分析和数据管理研发.通过前端数据提交页面,接收和维护来自FAST及其他研究机构的候选体数据.目前,PSRDB已收录自1967年人类发现第1颗脉冲星以来所有公开文献发表的2811颗脉冲星样本,并采集了当前主要巡天项目尚未正式发表的源和候选体,如FAST多科学目标同时扫描巡天(CRAFTS)候选体数据.基于入库基础数据,利用位置、周期、色散等参数进行比对分析,辅助科研工作者在线检索匹配已知星表数据,最后将检索匹配、比对分析结果生成图表供进一步分析.目前,PSRDB已被应用于FAST脉冲星搜寻和候选体数据管理.未来,PSRDB可在新源认证、后随观测、观测计划制定和原始数据处理流程设计等方面提供数据和工具支撑.     

Crab脉冲星巨脉冲辐射等待时间分布的非稳态泊松模拟

利用中国科学院新疆天文台南山观测站26m射电望远镜, 在中心频率1556MHz, 对Crab脉冲星(PSR B0531+21)进行了长达12.6h的连续观测, 观测带宽为512MHz, 时间分辨率为32μs, 研究了巨脉冲辐射的等待时间分布特征. 观测共探测到2097个信噪比大于10的巨脉冲, 对应的流量密度大于100Jy. 巨脉冲的爆发率表现为高度的间歇性, 在较短的时间内具有较高的爆发率, 在相对长的宁静期内巨脉冲的爆发率较低, 尤其是中间脉冲相位内的巨脉冲爆发. 相邻两个巨脉冲的等待时间分布表现为幂律分布特征, 可以用一个非稳态的泊松过程进行模拟, 这表明巨脉冲的爆发是一种独立的随机事件. 此外, 主脉冲和中间脉冲相位上的巨脉冲具有不同的等待时间分布特征, 这意味着脉冲星不同磁极的巨脉冲辐射机制可能是不同的. 这些观测结果对于理解脉冲星的射电辐射机制具有重要意义.     

脉冲星对氢原子钟的频率驾驭算法研究

氢原子钟具有较高的短期稳定度,将其作为主钟可在短期内产生高精度的本地时间信号.但氢钟存在频率漂移现象,导致其长期稳定度较差,从而影响本地时间的准确性.毫秒脉冲星自转高度稳定,借助于其长期稳定度高的特性,可定期实现对氢原子钟的频率驾驭,并对实时信号加以控制.首先分析了国际脉冲星计时阵(International Pulsar Timing Array,IPTA)第二批发布数据中四颗毫秒脉冲星的稳定度随时间的变化,同时采用哈达玛方差分析了中国科学院国家授时中心(National Time Service Center,NTSC)一台氢钟的频率稳定性能,最终给出了利用脉冲星驾驭氢原子钟频率的方法.     

A Large Glitch in the Crab Pulsar

1 INTRODUCTIONA pulsar glitch is a phenomenon in which the pulse frequency has a sudden increase, typicallywith a fractional ~litude an/u in the range of 10--8 -- 10--6. Glitches are Unpredictable butoccur at intervals of a few y6ars in many young pulsars. Coincident with the glitch, there is oftenan increajse in the magnitude of the frequency derivative followed by thlee types of recovery:almost no recoveryt partial recovery and total recovery on timescales from days to years. It isbelie…     

Timing results for the binary millisecond pulsar J1640+2224 obtained on the RT-64 radio telescope in Kalyazin

We present the timing results for the binary millisecond pulsar J1640+2224 obtained with the RT-64 radio telescope (TNA-1500, Special Design Bureau, Moscow Power Engineering Institute) at the Kalyazin Observatory (Astrospace Center of the Lebedev Institute of Physics) in 1997–2002. We obtained Keplerian and post-Keplerian parameters of the binary system, which allowed us to estimate an upper limit for the energy density of the stochastic gravitational-wave background radiation at very low frequencies.