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Time synchronized measurements of electric grid parameters provide a basis for overall system operation optimization. An examination of the use of a millisecond rotation pulsar as a grid measurement timing source is presented
The Neutron star Interior Composition Explorer observed several rotation-powered millisecond pulsars (MSPs) to search for or confirm the presence of X-ray pulsations. When broad and sine-like, these pulsations may indicate thermal emission from hot polar caps at the magnetic poles on the neutron star surface. We report confident detections (≥4.7σ after background filtering) of X-ray pulsations for five of the seven pulsars in our target sample: PSR J0614−3329, PSR J0636+5129, PSR J0751+1807, PSR J1012+5307, and PSR J2241−5236, while PSR J1552+5437 and PSR J1744−1134 remain undetected. Of those, only PSR J0751+1807 and PSR J1012+5307 had pulsations previously detected at the 1.7σ and almost 3σ confidence levels, respectively, in XMM-Newton data. All detected sources exhibit broad sine-like pulses, which are indicative of surface thermal radiation. As such, these MSPs are promising targets for future X-ray observations aimed at constraining the neutron star mass–radius relation and the dense matter equation of state using detailed pulse profile modeling. Furthermore, we find that three of the detected MSPs exhibit a significant phase offset between their X-ray and radio pulses.
A number of rotation-powered millisecond pulsars are powerful sources of high-energy emission, detected so far at X-ray wavelengths. We present predictions for the spectral characteristics of these sources at gamma-ray energies, using a model for acceleration and pair cascades on open magnetic field lines above the polar caps. Although these pulsars have low surface magnetic fields, their short periods allow them to have large magnetospheric potential drops, but the majority do not produce sufficient pairs to completely screen the accelerating electric field. In these sources, the primary and secondary electrons continue to accelerate to high altitude and their Lorentz factors are limited by curvature and synchrotron radiation reaction. The resulting radiation above 1 GeV comes from curvature radiation by primary electrons with radiation-reaction-limited Lorentz factors. The spectra are very hard power-laws with exponential cutoffs between 1 and 50 GeV, and the spectral power peaks near the cutoff energy. Millisecond pulsars are thus ideal targets for air-Cherenkov detectors that are able to reach energy thresholds below 50 GeV.
The X-ray and gamma-ray spectrum of rotation-powered millisecond pulsars is investigated in a model for acceleration and pair cascades on open field lines above the polar caps. Although these pulsars have low surface magnetic fields, their short periods allow them to have large magnetospheric potential drops, but the majority do not produce sufficient pairs to completely screen the accelerating electric field. In these sources, the primary and secondary electrons continue to accelerate to high altitude and their Lorentz factors are limited by curvature and synchrotron radiation reaction. The accelerating particles maintain high Lorentz factors and undergo cyclotron resonant absorption of radio emission, that produces and maintains a large pitch angle, resulting in a strong synchrotron component. The resulting spectra consist of several distinct components: curvature radiation from primary electrons dominating from 1 - 100 GeV, synchrotron radiation from primary and secondary electrons dominating up to about 100 MeV, and much weaker inverse-Compton radiation from primary electrons a t 0.1 - 1 TeV. We find that the relative size of these components depends on pulsar period, period derivative, and neutron star mass and radius with the level of the synchrotron component also depending sensitively on the radio emission properties. This model is successful in describing the observed X-ray and gamma-ray spectrum of PSR J0218+4232 as synchrotron radiation, peaking around 100 MeV and extending up to a turnover around several GeV. The predicted curvature radiation components from a number of millisecond pulsars, as well as the collective emission from the millisecond pulsars in globular clusters, should be detectable with AGILE and GLAST. We also discuss a hidden population of X-ray-quiet and radio-quiet millisecond pulsars which have evolved below the pair death line, some of which may be detectable by telescopes sensitive above 1 GeV. Subject headings: pulsars: general - radiation mechanisms: nonthermal - stars: neutron - gamma rays: theory
We present two years of Neutron star Interior Composition Explorer (NICER) X-ray observations of three energetic rotation-powered millisecond pulsars (MSPs): PSRs B1937+21, B1821−24, and J0218+4232. We fit Gaussians and Lorentzians to the pulse profiles for different energy sub-bands of the soft X-ray regime to measure the energy dependence of pulse separation and width. We find that the separation between pulse components of PSR J0218+4232 decreases with increasing energy at >3σ confidence. The 95% upper limit on pulse separation evolution for PSRs B1937+21 and B1821−24 is less than 2 milliperiods per keV. Our phase-resolved spectral results provide updated constraints on the non-thermal X-ray emission of these three pulsars. The photon indices of the modeled X-ray emission spectra for each pulse component of PSR B1937+21 are inconsistent with each other at the 90% confidence level, suggesting different emission origins for each pulse. We find that the PSR B1821−24 and PSR J0218+4232 emission spectra are invariant with phase at the 90% confidence level. We describe the implications of our profile and spectral results in the context of equatorial current sheet emission models for these three MSPs with non-thermal, magnetospheric X-ray emission.
We present the set of deep Neutron Star Interior Composition Explorer (NICER) X-ray timing observations of the nearby rotation-powered millisecond pulsars PSRs J0437−4715, J0030+0451, J1231−1411, and J2124−3358, selected as targets for constraining the mass–radius relation of neutron stars and the dense matter equation of state (EoS) via modeling of their pulsed thermal X-ray emission. We describe the instrument, observations, and data processing/reduction procedures, as well as the series of investigations conducted to ensure that the properties of the data sets are suitable for parameter estimation analyses to produce reliable constraints on the neutron star mass–radius relation and the dense matter EoS. We find that the long-term timing and flux behavior and the Fourier domain properties of the event data do not exhibit any anomalies that could adversely affect the intended measurements. From phase-selected spectroscopy, we find that emission from the individual pulse peaks is well described by a single-temperature hydrogen atmosphere spectrum, with the exception of PSR J0437−4715, for which multiple temperatures are required.
The regularity of the rotation rate of millisecond pulsars is the underlying hypothesis for using these neutron stars as 'celestial clocks'. Given their remote location in our galaxy and to our lack of precise knowledge on the galactic environment, a number of phenomena effect the apparent rotation rate observed on Earth. This paper reviews these phenomena and estimates the order of magnitude of their effect. It concludes that an ensemble pulsar time based on a number of selected millisecond pulsars should have a fractional frequency stability close to 2 x 10(sup -15) for an averaging time of a few years.
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ABSTRACT We study the effects of the time-variable properties of thermonuclear X-ray bursts on modelling their millisecond-period burst oscillations. We apply the pulse profile modelling technique that is being used in the analysis of rotation-powered millisecond pulsars by the Neutron Star Interior Composition Explorer to infer masses, radii, and geometric parameters of neutron stars. By simulating and analysing a large set of models, we show that overlooking burst time-scale variability in temperatures and sizes of the hot emitting regions can result in substantial bias in the inferred mass and radius. To adequately infer neutron star properties, it is essential to develop a model for the time-variable properties or invest a substantial amount of computational time in segmenting the data into non-varying pieces. We discuss prospects for constraints from proposed future X-ray telescopes.
We report on Bayesian estimation of the radius, mass, and hot surface regions of the massive millisecond pulsar PSR J0740+6620, conditional on pulse-profile modeling of Neutron Star Interior Composition Explorer X-ray Timing Instrument event data. We condition on informative pulsar mass, distance, and orbital inclination priors derived from the joint North American Nanohertz Observatory for Gravitational Waves and Canadian Hydrogen Intensity Mapping Experiment/Pulsar wideband radio timing measurements of Fonseca et al. We use XMM-Newton European Photon Imaging Camera spectroscopic event data to inform our X-ray likelihood function. The prior support of the pulsar radius is truncated at 16 km to ensure coverage of current dense matter models. We assume conservative priors on instrument calibration uncertainty. We constrain the equatorial radius and mass of PSR J0740+6620 to be-+12.390.981.30km and-+2.0720.0660.067Me respectively, each reported as the posterior credible interval bounded by the 16% and 84% quantiles, conditional on surface hot regions that are non-overlapping spherical caps of fully ionized hydrogen atmosphere with uniform effective temperature; a posteriori, the temperature is=-+TlogK5.99100.060.05([])for each hot region. All software for the X-ray modeling framework is open-source and all data, model, and sample information is publicly available, including analysis notebooks and model modules in the Python language. Our marginal likelihood function of mass and equatorial radius is proportional to the marginal joint posterior density of those parameters(within the prior support)and can thus be computed from the posterior samples.
We describe the X-ray pulse profile models we use and how we use them to analyze Neutron Star Interior Composition Explorer(NICER)observations of rotation-powered millisecond pulsars to obtain information about the mass–radius relation of neutron stars and the equation of state of the dense matter in their cores. Here we detail our modeling of the observed profile of PSR J0030+0451 that we analyzed in Miller et al. and Riley et al. and describe a cross-verification of computations of the pulse profiles of a star with R/M 3, in case stars this compact need to be considered in future analyses. We also present our early cross-verification efforts of the parameter estimation procedures used by Miller et al. and Riley et al. by analyzing two distinct synthetic data sets. Both codes yielded credible regions in the mass–radius plane that are statistically consistent with one another, and both gave posterior distributions for model parameter values consistent with the values that were used to generate the data. We also summarize the additional tests of the parameter estimation procedure of Miller et al. that used synthetic pulse profiles and the NICER pulse profile of PSR J0030+0451. We then illustrate how the precision of mass and radius estimates depends on the pulsar’s spin rate and the size of its hot spot by analyzing four different synthetic pulse profiles. Finally, we assess possible sources of systematic error in the estimates made using this technique, some of which may warrant further investigation.
The relationship between the rapid rotation of the millisecond pulsar and gravitational radiation is addressed. By balancing gravitational radiation against the rate of rotational energy loss, it is found that if the effective triaxiality exceeds about 10 to the -9th, gravitational radiation alone would spin a millisecond pulsar down at a faster rate than the observed period derivative. It is shown that the effective triaxiality is much less than the maximum triaxiality, so that gravitational radiation is not likely to play a major role in the evolution of millisecond pulsars even in the absence of damping. Damping times for precession of the solid crust are estimated to be less than 2000 years.
The interaction between the magnetospheres of accreting neutron stars and accretion disks plays at key role in determining the properties of many accretion-powered neutron star X-ray sources and the recycled binary and millisecond rotation-powered pulsars. Here we show that the behavior of the horizontal branch quasi-periodic intensity oscillations in low mass X-ray binaries and the correlation between the magnetic fields and periods of binary and millisecond pulsars are sensitive probes of the state of the inner disk.
The Station Explorer for X-ray Timing and Navigation Technology (SEXTANT) is a technology demonstration enhancement to the Neutron-star Interior Composition Explorer (NICER) mission, a NASA Astrophysics Explorer Mission of Opportunity to the International Space Station, launched in June of 2017. In late 2017, SEXTANT successfully completed a first demonstration of in-space and autonomous X-ray pulsar navigation (XNAV). This form of navigation relies on processing faint signals from millisecond pulsars-rapidly rotating neutron stars that appear to pulsate in the X-ray band-and could potentially provide a GPS-like navigation capability applicable throughout the solar-system and beyond. In this work, we briefly review prior SEXTANT results and then present new results focusing on: making use of the high- flux but rotationally unstable Crab pulsar, and using XNAV to estimate position, velocity, and time in the presence of an imperfect local clock.
As we prepare for extended missions on the Moon and in cislunar space, precise time synchronization between lunar and terrestrial clocks becomes increasingly critical for navigation, communication, and science measurements. One promising technique is the use of millisecond pulsars, which are highly magnetized, rapidly rotating neutron stars emitting beams of electromagnetic radiation. These celestial clocks offer extraordinary stability and precision, with rotational periods ranging from about 1 to 10 milliseconds and timing stability comparable to laboratory atomic clocks on Earth. Pulsars can provide a common time reference for clock comparisons, allowing time transfer independent of a communications link.
Millisecond pulsars (MSPs) are rapidly rotating neutron stars that appear to pulsate across the electromagnetic spectrum. Some MSPs have long-term timing stability that rivals that of atomic clocks. Pulse arrival phase can be predicted with great accuracy at any reference point in the Solar System through use of a pulsar timing model on a spacecraft. Comparing observed phase to predictions gives information that may be used in a navigation process. Why X-rays? Some stable MSPs have conveniently detectable X-ray emissions. X-rays are immune to interstellar dispersion effects thought to limit radio pulsar timing models. Highly directional compact detectors possible.
The Nuclear Spectroscopic Telescope Array (NuSTAR) mission is the first focusing X-ray telescope in the hard X-ray (3–79 keV) band. Among the phenomena that can be studied in this energy band, some require high time resolution and stability: rotation-powered and accreting millisecond pulsars, fast variability from black holes and neutron stars, X-ray bursts, and more. Moreover, a good alignment of the timestamps of X-ray photons to UTC is key for multi-instrument studies of fast astrophysical processes. In this paper, we describe the timing calibration of the NuSTAR mission. In particular, we present a method to correct the temperature-dependent frequency response of the on-board temperature-compensated crystal oscillator. Together with measurements of the spacecraft clock offsets obtained during downlinks passes, this allows a precise characterization of the behavior of the oscillator. The calibrated NuSTAR event timestamps for a typical observation are shown to be accurate to a precision of ∼65 μs.
Millisecond pulsars exhibit extremely stable rotational periods with negligible long-term variation, comparable to atomic clocks. Leveraging pulsar signal stability, this paper presents a hybrid Pulse Per Second (PPS) generation system for high-accuracy and GPS-independent timing. The system combines pulsar and GPS signals through a high-speed data acquisition platform featuring FPGA-driven processing and techniques. This design provides a reliable and precise timekeeping solution for energy systems, ensuring functionality when GPS signals are unavailable.