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.     

A timing formula for main-sequence star binary pulsars

In binary radio pulsars with a main-sequence star companion, the spin-induced quadrupole moment of the companion gives rise to a precession of the binary orbit. As a first approximation one can model the secular evolution caused by this classical spin-orbit coupling by linear-in-time changes of the longitude of periastron and the projected semi-major axis of the pulsar orbit. This simple representation of the precession of the orbit neglects two important aspects of the orbital dynamics of a binary pulsar with an oblate companion. First, the quasiperiodic effects along the orbit, owing to the anisotropic 1/ r ³ nature of the quadrupole potential. Secondly, the long-term secular evolution of the binary orbit, which leads to an evolution of the longitude of periastron and the projected semi-major axis, which is non-linear in time.   In this paper a simple timing formula for binary radio pulsars with a main-sequence star companion is presented which models the short-term secular and most of the short-term periodic effects caused by the classical spin-orbit coupling. I also give extensions of the timing formula that account for long-term secular changes in the binary pulsar motion. It is shown that the short-term periodic effects are important for the timing observations of the binary pulsar PSR B1259–63. The long-term secular effects are likely to become important in the next few years of timing observations of the binary pulsar PSR J0045–7319. They could help to restrict or even determine the moments of inertia of the companion star and thus probe its internal structure.   Finally, I reinvestigate the spin-orbit precession of the binary pulsar PSR J0045–7319 since the analysis given in the literature is based on an incorrect expression for the precession of the longitude of periastron. A lower limit of 20° for the inclination of the B star with respect to the orbital plane is derived.     

Precision timing measurements of PSR J1012+5307

We present results and applications of high-precision timing measurements of the binary millisecond pulsar J1012+5307. Combining our radio timing measurements with results based on optical observations, we derive complete 3D velocity information for this system. Correcting for Doppler effects, we derive the intrinsic spin parameters of this pulsar and a characteristic age of 8.6±1.9 Gyr . Our upper limit for the orbital eccentricity of only 8×10⁻⁷ (68 per cent confidence level) is the smallest ever measured for a binary system. We demonstrate that this makes the pulsar an ideal laboratory in which to test certain aspects of alternative theories of gravitation. Our precision measurements suggest deviations from a simple pulsar spin-down timing model, which are consistent with timing noise and the extrapolation of the known behaviour of slowly rotating pulsars.     

High-precision timing of PSR J1600−3053

We present the results of a high-precision timing campaign directed at the binary millisecond pulsar J1600−3053. Submicrosecond pulsar timing has long been the domain of bright, low dispersion measure millisecond pulsars or large diameter telescopes. This experiment, conducted using the Parkes radio telescope in New South Wales, Australia, and utilizing the latest baseband recording hardware, has allowed this pulsar, although distant and faint, to present residuals to a model of its spin behaviour of 650 ns over a period of more than 2 yr. We have also constrained the orbital inclination via Shapiro delay to be between 59° and 70° to 95 per cent confidence and obtained a scintillation velocity measurement indicating a transverse velocity less than 84 km s⁻¹. This pulsar is demonstrating remarkable stability comparable to, and in most cases improving upon, the very best long-term pulsar timing experiments. If this stability is maintained, the current limits on the energy density of the stochastic gravitational wave background will be reached in four more years.     

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.     

Precession of the Orbital Plane of Binary Pulsars and Significant Variabilities

There are two ways of expressing the precession of orbital plane of a binary pulsar system, given by Barker & O'Connell, Apostolatos et al. and Kidder, respectively. We point out that these two ways actually come from the same Lagrangian under different degrees of freedom. Damour & Schafer and Wex & Kopeikin applied Barker & O'Connell's orbital precession velocity in pulsar timing measurement. This paper applies Apostolatos et al.'s and Kidder's orbital precession velocity. We show that Damour & Schafer's treatment corresponds to negligible Spin-Orbit induced precession of periastron, while Wex & Kopeikin and this paper both found significant (but not equivalent) effects. The observational data of two typical binary pulsars, PSR J2051-0827 and PSR J1713+0747, apparently support a significant Spin-Orbit coupling effect. Specific binary pulsars with orbital plane nearly edge on could discriminate between Wex & Kopeikin and this paper: if the orbital period derivative of the double-pulsar system PSRs J0737-3039 A and B, with orbital inclination angle i = 87.7129 deg, is much larger than that of the gravitational radiation induced one, then the expression in this paper is supported, otherwise Wex & Kopeikin's is supported.     

Imprints of relic gravitational waves on pulsar timing

Relic gravitational waves(RGWs), a background originating during inflation, would leave imprints on pulsar timing residuals. This makes RGWs an important source for detection of RGWs using the method of pulsar timing. In this paper, we discuss the effects of RGWs on single pulsar timing, and quantitatively analyze the timing residuals caused by RGWs with different model parameters. In principle, if the RGWs are strong enough today, they can be detected by timing a single millisecond pulsar with high precision after the intrinsic red noises in pulsar timing residuals are understood, even though simultaneously observing multiple millisecond pulsars is a more powerful technique for extracting gravitational wave signals. We correct the normalization of RGWs using observations of the cosmic microwave background(CMB), which leads to the amplitudes of RGWs being reduced by two orders of magnitude or so compared to our previous works. We obtained new constraints on RGWs using recent observations from the Parkes Pulsar Timing Array, employing the tensor-to-scalar ratio r = 0.2 due to the tensor-type polarization observations of CMB by BICEP2 as a reference value, even though its reliability has been brought into question. Moreover, the constraints on RGWs from CMB and Big Bang nucleosynthesis will also be discussed for comparison.     

The accretion powered spin-up of GRO J1750−27

The timing properties of the 4.45 s pulsar in the Be X-ray binary system GRO J1750−27 are examined using hard X-ray data from INTEGRAL and Swift during a type II outburst observed during 2008. The orbital parameters of the system are measured and agree well with those found during the last known outburst of the system in 1995. Correcting the effects of the Doppler shifting of the period, due to the orbital motion of the pulsar, leads to the detection of an intrinsic spin-up that is well described by a simple model including     and     terms of  −7.5 × 10⁻¹⁰ s s⁻¹  and  1 × 10⁻¹⁶ s s⁻²  , respectively. The model is then used to compare the time-resolved variation of the X-ray flux and intrinsic spin-up against the accretion torque model of Ghosh & Lamb; this finds that GRO J1750−27 is likely located 12–22 kpc distant and that the surface magnetic field of the neutron star is  ∼2 × 10¹²  G. The shape of the pulse and the pulsed fraction shows different behaviour above and below 20 keV, indicating that the observed pulsations are the convolution of many complex components.     

Determination of the orbital parameters of binary pulsars

We present a simple method for determination of the orbital parameters of binary pulsars, using data on the pulsar period at multiple observing epochs. This method uses the circular nature of the velocity space orbit of Keplerian motion and produces preliminary values based on two one-dimensional searches. Preliminary orbital parameter values are then refined using a computationally efficient linear least-squares fit. This method works for random and sparse sampling of the binary orbit. We demonstrate the technique on (i) the highly eccentric binary pulsar PSR J0514−4002 (the first known pulsar in the globular cluster NGC 1851) and (ii) 47 Tuc T, a binary pulsar with a nearly circular orbit.     

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 residuals, 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 to2010. 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.     

Dispersion measure variations and their effect on precision pulsar timing

We present an analysis of the variations seen in the dispersion measures (DMs) of 20-ms pulsars observed as part of the Parkes Pulsar Timing Array project. We carry out a statistically rigorous structure function analysis for each pulsar and show that the variations seen for most pulsars are consistent with those expected for an interstellar medium characterized by a Kolmogorov turbulence spectrum. The structure functions for PSRs J1045−4509 and J1909−3744 provide the first clear evidence for a large inner scale, possibly due to ion–neutral damping. We also show the effect of the solar wind on the DMs and show that the simple models presently implemented into pulsar timing packages cannot reliably correct for this effect. For the first time we clearly show how DM variations affect pulsar timing residuals and how they can be corrected in order to obtain the highest possible timing precision. Even with our presently limited data span, the residuals (and all parameters derived from the timing) for six of our pulsars have been significantly improved by correcting for the DM variations.     

Orbital period modulation and magnetic cycles in close binaries

We discuss the observed orbital period modulations in close binaries, and focus on the mechanism proposed by Applegate relating the changes of the stellar internal rotation associated with a magnetic activity cycle with the variation of the gravitational quadrupole moment of the active component; the variation of this quadrupole moment in turn forces the orbital motion of the binary stars to follow the activity level of the active star. We generalize this approach by considering the details of this interaction, and develop some illustrative examples in which the problem can be easily solved in analytical form. Starting from such results, we consider the interplay between rotation and magnetic field generation in the framework of different types of dynamo models, which have been proposed to explain solar and stellar activity. We show how the observed orbital period modulation in active binaries may provide new constraints for discriminating between such models. In particular, we study the case of the prototype active binary RS Canum Venaticorum, and suggest that torsional oscillations — driven by a stellar magnetic dynamo — may account for the observed behaviour of this star. Further possible applications of the relationship between magnetic activity and orbital period modulation, related to the recent discovery of binary systems containing a radio pulsar and a convecting upper main-sequence or a late-type low-mass companion, are discussed.     

Modelling interaction of relativistic and non-relativistic winds in binary system PSR B1259−63/SS2883 – I. Hydrodynamical limit

In this paper, we present a detailed hydrodynamical study of the properties of the flow produced by the collision of a pulsar wind with the surrounding in a binary system. This work is the first attempt to simulate interaction of the ultrarelativistic flow (pulsar wind) with the non-relativistic stellar wind. Obtained results show that the wind collision could result in the formation of an 'unclosed' (at spatial scales comparable to the binary system size) pulsar wind termination shock even when the stellar wind ram pressure exceeds significantly the pulsar wind kinetic pressure. Moreover, the post-shock flow propagates in a rather narrow region, with very high bulk Lorentz factor (γ∼ 100). This flow acceleration is related to adiabatic losses which are purely hydrodynamical effects. Interestingly, in this particular case, no magnetic field is required for formation of the ultrarelativistic bulk outflow. The obtained results provide a new interpretation for the orbital variability of radio, X-ray and gamma-ray signals detected from binary pulsar system PSR B1259−63/SS2883.     

Orbital evolution and orbital phase resolved spectroscopy of the HMXB pulsar 4U 1538-52 with RXTE-PCA and BeppoSAX

We report here results from detailed timing and spectral studies of the high mass X-ray binary pulsar 4U 1538-52 over several binary periods using observations made with the Rossi X-ray Timing Explorer (RXTE) and BeppoSAX satellites. Pulse timing analysis with the 2003 RXTE data over two binary orbits confirms an eccentric orbit of the system. Combining the orbitial parameters determined from this observation with the earlier measurements we did not find any evidence of orbital decay in this X-ray binary. We have carried out orbital phase resolved spectroscopy to measure changes in the spectral parameters with orbital phase, particularly the absorption column density and the iron line flux. The RXTE-PCA spectra in the 3–20 keV energy range were fitted ∼6.4 keV, whereas the BeppoSAX spectra needed only a power law and Gaussian emission line at ∼6.4 keV in the restricted energy range of 0.3–10.0 keV. An absorption along the line of sight was included for both the RXTE and BeppoSAX data. The variation of the free spectral parameters over the binary orbit was investigated and we found that the variation of the column density of absorbing material in the line of sight with orbital phase is in reasonable agreement with a simple model of a spherically symmetric stellar wind from the companion star.     

Gravitational radiation damping and the three-body problem

A model of three-body motion is developed which includes the effects of gravitational radiation reaction. The radiation reaction due to the emission of gravitational waves is the only post-Newtonian effect that is included here. For simplicity, all of the motion is taken to be planar. Two of the masses are viewed as a binary system, and the third mass, whose motion will be a fixed orbit around the centre-of-mass of the binary system, is viewed as a perturbation. This model aims to describe the motion of a relativistic binary pulsar that is perturbed by a third mass. Numerical integration of this simplified model reveals that, given the right initial conditions and parameters, one can see resonances. These ( m , n ) resonances are defined by the resonance condition,   mω =2 n Ω  , where m and n are relatively prime integers, and ω and Ω are the angular frequencies of the binary orbit and third mass orbit (around the centre-of-mass of the binary), respectively. The resonance condition consequently fixes a value for the semimajor axis of the binary orbit for the duration of the resonance; therefore the binary energy remains constant on average, while its angular momentum changes during the resonance.     

Correcting for the solar wind in pulsar timing observations: the role of simultaneous and low-frequency observations

The primary goal of pulsar timing array projects is to detect ultra-low-frequency gravitational waves. Pulsar data sets are affected by numerous noise processes including varying dispersive delays in the interstellar medium and from the solar wind. The solar wind can lead to rapidly changing variations that, with existing telescopes, can be hard to measure and then remove. In this paper we study the possibility of using a low frequency telescope to aid in such correction for the Parkes Pulsar Timing Array(PPTA) and also discuss whether the ultra-wide-bandwidth receiver for the FAST telescope is sufficient to model solar wind variations. Our key result is that a single wide-bandwidth receiver can be used to model and remove the effect of the solar wind. However, for pulsars that pass close to the Sun such as PSR J1022+1022, the solar wind is so variable that observations at two telescopes separated by a day are insufficient to correct the solar wind effect.     

OJ287双黑洞轨道计算:3.5阶后牛顿近似

大质量双黑洞OJ287是一个强引力辐射源.为了探测其引力波信号,需要知道波形,而这主要是由轨道运动所决定.为此,从广义相对论3.5阶后牛顿近似的运动方程出发对OJ287的轨道进行仔细研究,取大黑洞位置固定作为近似,给出了后牛顿近似下3.5阶的次黑洞轨道解,比他人2.5阶的工作高了一阶.次黑洞撞击吸积盘面到光学爆发存在时间延迟,这对于确定轨道参数有很大影响.利用径向距离与爆发时间关系的线性模型,对最近7次爆发时刻的观测值拟合,给出了更精确的OJ287双黑洞的轨道参数及其运动轨道.分析了计算结果,研究运动特征,并且发现了两个新性质:次黑洞进动在初期增加,在晚期接近并和时,进动达到最大值,然后减小并越过0而趋于负值.尚不能确定晚期的这个行为是否由3.5阶近似不够准确所造成.运动方程中耗散性的辐射项,后牛顿2.5阶和3.5阶的系数具有相反的符号.这意味着3.5阶项反而是从外界吸收能量.但2.5阶与3.5阶之和仍然是向外辐射引力波的,体系能量变化率为负.这个工作的计算结果可以用来更精确地计算OJ287的引力辐射.     

tempo2, a new pulsar-timing package – I. An overview

Contemporary pulsar-timing experiments have reached a sensitivity level where systematic errors introduced by existing analysis procedures are limiting the achievable science. We have developed tempo2 , a new pulsar-timing package that contains propagation and other relevant effects implemented at the 1-ns level of precision (a factor of ∼100 more precise than previously obtainable). In contrast with earlier timing packages, tempo2 is compliant with the general relativistic framework of the IAU 1991 and 2000 resolutions and hence uses the International Celestial Reference System, Barycentric Coordinate Time and up-to-date precession, nutation and polar motion models. tempo2 provides a generic and extensible set of tools to aid in the analysis and visualization of pulsar-timing data. We provide an overview of the timing model, its accuracy and differences relative to earlier work. We also present a new scheme for predictive use of the timing model that removes existing processing artefacts by properly modelling the frequency dependence of pulse phase.     

黑洞的搜寻和证认(II):脉冲星-黑洞(PSR-BH)双星系统的研究和搜寻

综述了脉冲星-黑洞（PSR－BH）系统的诞生率理论并指出近期发现该系统的可能性。通过综述和分析脉冲星-中子星（PSR－NS）系统的观测特性,特别是脉冲星精确守时性对精确确定双星轨道参量和验证引力理论的重要意义,推测了PSR－BH系统的可能性质,指出发现PSR-BH系统对黑洞的搜寻和最终证认的重要意义。最后简介目前搜寻PSR-BH系统的现状和我们搜寻短轨道周期脉冲双星的计划。     

The mass of the neutron star in the binary millisecond pulsar PSR J 1012 + 5307

We have measured the radial velocity variation of the white dwarf secondary in the binary system containing the millisecond pulsar PSR J 1012 + 5307. Combined with the orbital parameters of the radio pulsar, we infer a mass ratio q (≡ M ₁/ M ₂) = 10.5 ± 0.5. Our optical spectroscopy has also allowed us to determine the mass of the white dwarf companion by fitting the spectrum to a grid of DA model atmospheres: we estimate M ₂ = 0.16 ± 0.02 M⊙, and hence the mass of the neutron star is 1.64 ± 0.22 M⊙, where the error is dominated by that of M ₂. The orbital inclination is 52 ± 4°. For an initial neutron star mass of ∼ 1.4 M⊙, only a few tenths of a solar mass at most has been successfully accreted over the lifetime of the progenitor low-mass X-ray binary. If the initial mass of the secondary was ∼ 1 M⊙, our result suggests that the mass transfer may have been non-conservative.