Timing Of Millisecond Pulsars Research Articles

Discovery and Timing of Millisecond Pulsars in the Globular Cluster M5 with FAST and Arecibo

We report on a comprehensive multiwavelength study of the pulsars in the globular cluster (GC) M5, including the discovery of M5G, a new compact noneclipsing “black widow” pulsar. Thanks to the analysis of 34 yr of radio data taken with the Five-hundred-meter Aperture Spherical radio Telescope and Arecibo telescopes, we obtained new phase-connected timing solutions for four pulsars and improved those of the other three. These have resulted in, among other things, (a) much improved proper motions for five pulsars, with transverse velocities (relative to the cluster) that are smaller than their respective escape velocities; (b) 3σ and 1.5σ detections of Shapiro delays in M5F and M5D, respectively; and (c) greatly improved measurement of the periastron advance in M5B, whose value of implies that M5B is still likely to be a heavy () neutron star. The binary pulsars M5D, M5E, and M5F are confirmed to be in low-eccentricity binary systems, the low-mass companions of which are newly identified to be He white dwarfs using Hubble Space Telescope data. Four pulsars are also found to be associated with X-ray sources. Similarly to the eclipsing pulsar M5C, M5G shows little or no nonthermal X-ray emission, indicative of weak synchrotron radiation produced by intrabinary shocks. All seven pulsars known in M5 have short spin periods (<8 ms), and five are in binary systems with low orbital eccentricities. These characteristics differ from the overall GC pulsar population but confirm the expectations for the pulsar population in a cluster with a small rate of stellar encounters per binary system.

The Gravitational-wave Background Null Hypothesis: Characterizing Noise in Millisecond Pulsar Arrival Times with the Parkes Pulsar Timing Array

The noise in millisecond pulsar (MSP) timing data can include contributions from observing instruments, the interstellar medium, the solar wind, solar system ephemeris errors, and the pulsars themselves. The noise environment must be accurately characterized in order to form the null hypothesis from which signal models can be compared, including the signature induced by nanohertz-frequency gravitational waves (GWs). Here we describe the noise models developed for each of the MSPs in the Parkes Pulsar Timing Array (PPTA) third data release, which have been used as the basis of a search for the isotropic stochastic GW background. We model pulsar spin noise, dispersion measure variations, scattering variations, events in the pulsar magnetospheres, solar wind variability, and instrumental effects. We also search for new timing model parameters and detected Shapiro delays in PSR J0614−3329 and PSR J1902−5105. The noise and timing models are validated by testing the normalized and whitened timing residuals for Gaussianity and residual correlations with time. We demonstrate that the choice of noise models significantly affects the inferred properties of a common-spectrum process. Using our detailed models, the recovered common-spectrum noise in the PPTA is consistent with a power law with a spectral index of γ = 13/3, the value predicted for a stochastic GW background from a population of supermassive black hole binaries driven solely by GW emission.

Searches for Shapiro delay in seven binary pulsars using the MeerKAT telescope

ABSTRACT Precision timing of millisecond pulsars (MSPs) in binary systems enables observers to detect the relativistic Shapiro delay induced by space–time curvature. When favourably aligned, this enables constraints to be placed on the component masses and system orientation. Here, we present the results of timing campaigns on seven binary MSPs observed with the 64-antenna MeerKAT radio telescope that show evidence of Shapiro delay: PSRs J0101−6422, J1101−6424, J1125−6014, J1514−4946, J1614−2230, J1732−5049, and J1909−3744. Evidence for Shapiro delay was found in all of the systems, and for three the orientations and data quality enabled strong constraints on their orbital inclinations and component masses. For PSRs J1125−6014, J1614−2230, and J1909−3744, we determined pulsar masses to be $M_{\rm p} = 1.68\pm 0.17$, $1.94\pm 0.03$, and $1.45 \pm 0.03 \, {\rm M_{\odot }}$, and companion masses to be $M_{\rm c} = 0.33\pm 0.02$, $0.495\pm 0.005$, and $0.205 \pm 0.003 \, {\rm M_{\odot }}$, respectively. This provides the first independent confirmation of PSR J1614−2230’s mass, one of the highest known. The Shapiro delays measured for PSRs J0101−6422, J1101−6424, J1514−4946, and J1732−5049 were only weak, and could not provide interesting component mass limits. Despite a large number of MSPs being routinely timed, relatively few have accurate masses via Shapiro delays. We use simulations to show that this is expected, and provide a formula for observers to assess how accurately a pulsar mass can be determined. We also discuss the observed correlation between pulsar companion masses and spin period, and the anticorrelation between recycled pulsar mass and their companion masses.

New binary pulsar constraints on Einstein-æther theory after GW170817

The timing of millisecond pulsars has long been used as an exquisitely precise tool for testing the building blocks of general relativity, including the strong equivalence principle and Lorentz symmetry. Observations of binary systems involving at least 1 ms pulsar have been used to place bounds on the parameters of Einstein-æther theory, a gravitational theory that violates Lorentz symmetry at low energies via a preferred and dynamical time threading of the spacetime manifold. However, these studies did not cover the region of parameter space that is still viable after the recent bounds on the speed of gravitational waves from GW170817/GRB170817A. The restricted coverage was due to limitations in the methods used to compute the pulsar ‘sensitivities’, which parameterize violations of the strong-equivalence principle in these systems. We extend here the calculation of pulsar sensitivities to the parameter space of Einstein-æther theory that remains viable after GW170817/GRB170817A. We show that observations of the damping of the period of quasi-circular binary pulsars and of the triple system PSR J0337+1715 further constrain the viable parameter space by about an order of magnitude over previous constraints.

Galactic orbital effects on pulsar timing

ABSTRACTIn the currently accepted paradigm, dark matter is hypothesized as an explanation of the flat rotation curves of galaxies under the assumption of virialized orbits. The use of millisecond pulsar timing as a probe of Galactic dark matter content is explored as a means of relaxing this assumption. A method of inference of the Galactic potential using the frequency derivative $\dot{\nu }$ is produced, and an estimate for a virialized Galactic rotation curve is given through direct observation of acceleration. The data set used includes 210 pulsars with known $\dot{\nu }$ and astrometric properties, a subset of which also have measured $\ddot{\nu }$. In principle, this enables the exploration of kinematic effects, but in practice, $\ddot{\nu }$ values are found to be too imprecise at present to adequately constrain radial velocities of pulsars. Additionally, surface magnetic field strengths are inferred from $\dot{\nu }$ and the magnetic spin-down contribution to $\ddot{\nu }$ is estimated. For several pulsars, the radial velocity is known, and the kinematic contribution to $\ddot{\nu }$ is estimated accordingly. The binary orbital periods of PSR J1713+0747 and other binary pulsars are also used to constrain Galactic mass density models.

Space/ground based pulsar timescale for comprehensive PNT system

The comprehensive positioning navigation timing (PNT) system in China is a multi-source information fusion system with BeiDou navigation satellite system (BDS) as a core. The high-precision millisecond pulsar timing can enhance the long-term stability of the BDS time benchmark and maintain a space-time benchmark for future deep-space users. In this paper, a ground-based pulsar time service system is proposed for detecting and improving the time benchmark of BDS. The preliminary designs and functions of the system are outlined. At the same time, the method of establishing space and ground-based pulsar time is studied. The ground radio timing data from the international pulsar timing array (IPTA), the X-ray timing data from the neutron star interior composition explorer (NICER) in space, and the simulation data from the 500-meter spherical radio telescope (five-hundred-meter aperture spherical radio telescope, FAST) for three millisecond pulsars are used to analyze the stability of ground/space-based pulsar time. The research results are as follows. The annual stability of the PSR J0437-4715 ground-based pulsar time based on IPTA data is 3.30 × 10&lt;sup&gt;–14&lt;/sup&gt;, and the 10-year stability is 1.23 × 10&lt;sup&gt;–15&lt;/sup&gt;, respectively. The existence of pulsar red noise can reduce the time stability of the pulsar. The annual stability of the PSR J1939+2134 ground-based pulsar time is 6.51 × 10&lt;sup&gt;–12&lt;/sup&gt;. We find that the accuracy of the pulse time of Arrival(TOA) is an important factor that restricts the stability of space-based pulsar time. Based on NICER space X-ray timing data, the stability of the pulsar time for PSR J1824-2452A is 1.36 × 10&lt;sup&gt;–13&lt;/sup&gt; in one year. Finally, the simulation analysis of the FAST’s data without considering the influence of red noise is completed, and we find that the PSR J1939+2134 ground-based pulsar time based on the FAST has an annual stability of 2.55 × 10&lt;sup&gt;–15&lt;/sup&gt;, a 10-year stability of 1.39 × 10&lt;sup&gt;–16&lt;/sup&gt;, and a 20-year stability of 5.08 × 10&lt;sup&gt;–17&lt;/sup&gt;. It demonstrates that the powerful pulsar observation capability of FAST will help to improve the accuracy of ground-based pulsar time and enhance the long-term stability of the comprehensive PNT system time benchmark in China.

Pulsar Timing Signatures of Circumbinary Asteroid Belts

Abstract The gravitational pull of a large number of asteroids perturbs a pulsar’s motion to a degree that is detectable through precision timing of millisecond pulsars. The result is a low-frequency, correlated noise process, similar in form to the red timing noise known to affect canonical pulsars, or to the signal expected from a stochastic gravitational-wave background. Motivated by the observed fact that many millisecond pulsars are in binary systems, we describe the ways in which the presence of a binary companion to the pulsar would affect the signal produced by an asteroid belt. The primary effect of the companion is to destabilize the shortest-period orbits, cutting off the high-frequency component of the signal from the asteroid belt. We also discuss the implications of asteroid belts for gravitational-wave search efforts. Compared to the signal from a stochastic gravitational-wave background, asteroid-belt noise has a similar frequency and amplitude, and is similarly independent of radio frequency, but is not correlated between different pulsars, which should allow the two kinds of signal to be distinguished.

Designing miniature x-ray optics for the SmallSat lunar science mission concept CubeX

Planetary remote-sensing instruments are often required to cover a relatively large field of view, ideally with a uniform angular resolution over the field, due to relatively large apparent sizes of planetary targets at close proximities. They also have to comply with relatively tight mass and volume constraints. For these reasons, planetary x-ray telescopes in the past were mainly collimation-based x-ray spectrometers without focusing optics. Recent advances in x-ray optics technology now enable compact focusing x-ray telescopes suitable for planetary science (e.g., BepiColombo). We present two design options for compact Wolter-I x-ray optics for a SmallSat lunar mission concept—the CubeSat X-ray telescope (CubeX). The primary objectives of CubeX are to map surface elemental abundances of selected lunar impact craters and to assess the feasibility of millisecond x-ray pulsar timing navigation in realistic deep space navigation environments. The Miniature X-ray Optics (MiXO) in CubeX utilizes electroformed NiCo alloy replication (ENR) technology, which provides many advantages over micro-pore optics (MPO) employed in BepiColombo. We carry out extensive ray traces over a grid of mirror parameters and explore a novel tapered shaped design of tightly nested shells, where both shell length and focal-plane offsets vary with shell diameter. One of the two configurations is optimized for large effective areas at low energies, while the other for lower mass and high-energy response. We compare their performances with those of conventional designs through the spatial resolution and effective area estimated by ray traces.

High-precision X-Ray Timing of Three Millisecond Pulsars with NICER: Stability Estimates and Comparison with Radio

Abstract The Neutron Star Interior Composition Explorer (NICER) is an X-ray astrophysics payload on the International Space Station. It enables unprecedented high-precision timing of millisecond pulsars (MSPs) without the pulse broadening and delays due to dispersion and scattering within the interstellar medium that plague radio timing. We present initial timing results from a year of data on the MSPs PSR B1937+21 and PSR J0218+4232, and nine months of data on PSR B1821−24. NICER time-of-arrival uncertainties for the three pulsars are consistent with theoretical lower bounds and simulations based on their pulse shape templates and average source and background photon count rates. To estimate timing stability, we use the σ z measure, which is based on the average of the cubic coefficients of polynomial fits to subsets of timing residuals. So far we are achieving timing stabilities σ z ≈ 3 × 10−14 for PSR B1937+21 and on the order of 10−12 for PSRs B1821−24 and J0218+4232. Within the span of our NICER data we do not yet see the characteristic break point in the slope of σ z ; detection of such a break would indicate that further improvement in the cumulative root-mean-square timing residual is limited by timing noise. We see this break point in our comparison radio data sets for PSR B1821−24 and PSR B1937+21 on timescales of &gt;2 yr.

Using Long-term Millisecond Pulsar Timing to Obtain Physical Characteristics of the Bulge Globular Cluster Terzan 5

Abstract Over the past decade, the discovery of three unique stellar populations and a large number of confirmed pulsars within the globular cluster Terzan 5 has raised questions over its classification. Using the long-term radio pulsar timing of ms pulsars in the cluster core, we provide new measurements of key physical properties of the system. As Terzan 5 is located within the galactic bulge, stellar crowding and reddening make optical and near-infrared observations difficult. Pulsar accelerations, however, allow us to study the intrinsic characteristics of the cluster independent of reddening and stellar crowding and probe the mass density profile without needing to quantify the mass-to-light ratio. Relating the spin and orbital periods of each pulsar to the acceleration predicted by a King model, we find a core density of × 106 pc−3, a core radius of pc, a pulsar density profile of , and a total mass of ( pc) ≃ 3.0 × 105 , assuming a cluster distance of 5.9 kpc. Using this information, we argue against Terzan 5 being a disrupted dwarf galaxy and discuss the possibility of it being a fragment of the Milky Way’s proto-bulge. We also discuss whether low-mass pulsars were formed via electron-capture supernovae or exist in a core full of heavy white dwarfs and hard binaries. Finally, we provide an upper limit for the mass of a possible black hole at the core of the cluster of .

Numerical simulations of necklaces in SU(2) gauge-Higgs field theory

We perform the first numerical simulations of necklaces in a non-Abelian gauge theory. Necklaces are composite classical solutions which can be interpreted as monopoles trapped on strings, rather generic structures in a Grand Unified Theory. We generate necklaces from random initial conditions, modelling a phase transition in the early Universe, and study the evolution. For all cases, we find that the necklace system shows scaling behaviour similar to that of a network of ordinary cosmic strings. Furthermore, our simulations indicate that comoving distance between the monopoles or semipoles along the string asymptotes to a constant value at late times. This means that while the monopole-to-string energy density ratio decreases as the inverse of the scale factor, a horizon-size length of string has a large number of monopoles, significantly affecting the dynamics of string loops. We argue that gravitational wave bounds from millisecond pulsar timing on the string tension in the Nambu-Goto scenario are greatly relaxed.

R modes and neutron star recycling scenario

To put new constraints on the r-mode instability window, we analyse the formation of millisecond pulsars (MSPs) within the recycling scenario, making use of three sets of observations: (a) X-ray observations of neutron stars (NSs) in low-mass X-ray binaries; (b) timing of millisecond pulsars; and (c) X-ray and UV observations of MSPs. As shown in previous works, r-mode dissipation by shear viscosity is not sufficient to explain observational set (a), and enhanced r-mode dissipation at the red-shifted internal temperatures $T^\infty\sim 10^8$ K is required to stabilize the observed NSs. Here, we argue that models with enhanced bulk viscosity can hardly lead to a self-consistent explanation of observational set (a) due to strong neutrino emission, which is typical for these models (unrealistically powerful energy source is required to keep NSs at the observed temperatures). We also demonstrate that the observational set (b), combined with the theory of internal heating and NS cooling, provides evidence of enhanced r-mode dissipation at low temperatures, $T^\infty\sim 2\times 10^7$ K. Observational set (c) allows us to set an upper limit on the internal temperatures of MSPs, $T^\infty<2\times 10^7$ K (assuming a canonical NS with the accreted crust). Recycling scenario can produce MSPs at these temperatures only if r-mode instability is suppressed in the whole MSP spin frequency range ($\nu\lesssim 750$ Hz) at temperatures $2\times 10^7\lesssim T^\infty\lesssim 3 \times 10^7$ K, providing thus a new constraint on the r-mode instability window. These observational constraints are analysed in more details in application to the resonance uplift scenario of Gusakov et al. [Phys. Rev. Lett., 112 (2014), 151101].

CORRECTING FOR INTERSTELLAR SCATTERING DELAY IN HIGH-PRECISION PULSAR TIMING: SIMULATION RESULTS

Light travel time changes due to gravitational waves may be detected within the next decade through precision timing of millisecond pulsars. Removal of frequency-dependent interstellar medium (ISM) delays due to dispersion and scattering is a key issue in the detection process. Current timing algorithms routinely correct pulse times of arrival (TOAs) for time-variable delays due to cold plasma dispersion. However, none of the major pulsar timing groups correct for delays due to scattering from multi-path propagation in the ISM. Scattering introduces a frequency-dependent phase change in the signal that results in pulse broadening and arrival time delays. Any method to correct the TOA for interstellar propagation effects must be based on multi-frequency measurements that can effectively separate dispersion and scattering delay terms from frequency-independent perturbations such as those due to a gravitational wave. Cyclic spectroscopy, first described in an astronomical context by Demorest (2011), is a potentially powerful tool to assist in this multi-frequency decomposition. As a step toward a more comprehensive ISM propagation delay correction, we demonstrate through a simulation that we can accurately recover impulse response functions (IRFs), such as those that would be introduced by multi-path scattering, with a realistic signal-to-noise ratio. We demonstrate that timing precision is improved when scatter-corrected TOAs are used, under the assumptions of a high signal-to-noise and highly scattered signal. We also show that the effect of pulse-to-pulse "jitter" is not a serious problem for IRF reconstruction, at least for jitter levels comparable to those observed in several bright pulsars.

The Future of Pulsar Timing Arrays

AbstractSignificant advances have been made in the sensitivity of pulsar timing arrays for the detection of gravitational waves in the last decade. This presentation looked forward to consider where the development of pulsar timing arrays might go as we head towards the Square Kilometre Array (SKA) and then beyond. I reviewed where progress needs to be made in terms of sensitivity to gravitational waves, including improvements to existing observing approaches and new telescopes such as MeerKAT and FAST and techniques like LEAP. The dramatic increase in the number of millisecond pulsars is presented and how that might affect progress towards a first detection is discussed. Developments in analytic techniques were also discussed, including the removal of interstellar medium effects, red noise and pulse profile variations. A summary of how the SKA can contribute through an increased millisecond pulsar population and pulsar timing sensitivity was presented. With the likelihood that the SKA will implement some form of Key Science Project approach, some ideas of how will this affect how the International Pulsar Timing Array effort and how it might evolve into a KSP were discussed.

What the timing of millisecond pulsars can teach us about their interior.

The cores of compact stars reach the highest densities in nature and therefore could consist of novel phases of matter. We demonstrate via a detailed analysis of pulsar evolution that precise pulsar timing data can constrain the star's composition, through unstable global oscillations (r modes) whose damping is determined by microscopic properties of the interior. If not efficiently damped, these modes emit gravitational waves that quickly spin down a millisecond pulsar. As a first application of this general method, we find that ungapped interacting quark matter is consistent with both the observed radio and x-ray data, whereas for ordinary nuclear matter some additional enhanced damping mechanism is required.

MILLISECOND PULSAR SCINTILLATION STUDIES WITH LOFAR: INITIAL RESULTS

High-precision timing of millisecond pulsars (MSPs) over years to decades is a promising technique for direct detection of gravitational waves at nanohertz frequencies. Time-variable, multi-path scattering in the interstellar medium is a significant source of noise for this detector, particularly as timing precision approaches 10 ns or better for MSPs in the pulsar timing array. For many MSPs the scattering delay above 1 GHz is at the limit of detectability; therefore, we study it at lower frequencies. Using the LOFAR (LOw-Frequency ARray) radio telescope we have analyzed short (5-20 min) observations of three MSPs in order to estimate the scattering delay at 110-190 MHz, where the number of scintles is large and, hence, the statistical uncertainty in the scattering delay is small. We used cyclic spectroscopy, still relatively novel in radio astronomy, on baseband-sampled data to achieve unprecedented frequency resolution while retaining adequate pulse phase resolution. We detected scintillation structure in the spectra of the MSPs PSR B1257+12, PSR J1810+1744, and PSR J2317+1439 with diffractive bandwidths of $6\pm 3$, $2.0\pm 0.3$, and $\sim 7$ kHz, respectively, where the estimate for PSR J2317+1439 is reliable to about a factor of 2. For the brightest of the three pulsars, PSR J1810+1744, we found that the diffractive bandwidth has a power-law behavior $\Delta\nu_d \propto \nu^{\alpha}$, where $\nu$ is the observing frequency and $\alpha = 4.5\pm 0.5$, consistent with a Kolmogorov inhomogeneity spectrum. We conclude that this technique holds promise for monitoring the scattering delay of MSPs with LOFAR and other high-sensitivity, low-frequency arrays like SKA-Low.

Stochastic and continuous gravitational wave analysis pipelines for pulsar timing array data

AbstractThe Nanohertz Observatory for Gravitational Waves (NANOGrav) collaboration aims to detect gravitational waves (GWs) through the precise timing of millisecond pulsars. GWs will come in the form of a stochastic background, continuous sources and burst sources. Here we will review recent progress on the development of data analysis pipelines aimed at the detection of a stochastic background as well as continuous sources. We will introduce the Optimal Statistic and F-Statistic methods that are used in the stochastic and continuous pipelines, respectively. Both pipelines are fully functional on real pulsar timing data and take into account the timing models for each pulsar. Finally, we will present the efficacy of each pipeline on locally simulated data as well as data from the 2012 IPTA data challenge.

MINIMUM REQUIREMENTS FOR DETECTING A STOCHASTIC GRAVITATIONAL WAVE BACKGROUND USING PULSARS

We assess the detectability of a nanohertz gravitational wave (GW) background with respect to additive red and white noise in the timing of millisecond pulsars. We develop detection criteria based on the cross-correlation function summed over pulsar pairs in a pulsar timing array. The distribution of correlation amplitudes is found to be non-Gaussian and highly skewed, which significantly influences detection and false-alarm probabilities. When only white noise and GWs contribute, our detection results are consistent with those found by others. Red noise, however, drastically alters the results. We discuss methods to meet the challenge of GW detection ("climbing mount significance") by distinguishing between GW-dominated and red or white-noise limited regimes. We characterize detection regimes by evaluating the number of millisecond pulsars that must be monitored in a high-cadence, 5-year timing program for a GW background spectrum $h_c(f) = A f^{-2/3}$ with $A = 10^{-15}$ yr$^{-2/3}$. Unless a sample of 20 super-stable millisecond pulsars can be found --- those with timing residuals from red-noise contributions $\sigma_r \lesssim 20$ ns --- a much larger timing program on $\gtrsim 50 - 100$ MSPs will be needed. For other values of $A$, the constraint is $\sigma_r \lesssim 20 {\rm ns} (A/10^{-15} {\rm yr}^{-2/3})$. Identification of suitable MSPs itself requires an aggressive survey campaign followed by characterization of the level of spin noise in the timing residuals of each object. The search and timing programs will likely require substantial fractions of time on new array telescopes in the southern hemisphere as well as on existing ones.

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 position 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 calculate 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 parameters 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.

Status update of the Parkes pulsar timing array

The Parkes Pulsar Timing Array project aims to make a direct detection of a gravitational wave background through the timing of millisecond pulsars. In this paper, the main requirements for that endeavour are described and recent and ongoing progress is outlined. We demonstrate that the timing properties of millisecond pulsars are adequate and that technological progress is timely to expect a successful detection of gravitational waves within a decade, or alternatively to rule out all current predictions for gravitational wave backgrounds formed by supermassive black-hole mergers.