Rotation-powered Millisecond Pulsars Research Articles

Atmospheric Effects on Neutron Star Parameter Constraints with NICER

We present an analysis of the effects of uncertainties in the atmosphere models on the radius, mass, and other neutron star parameter constraints for the NICER observations of rotation-powered millisecond pulsars. To date, NICER has applied the X-ray pulse profile modeling technique to two millisecond-period pulsars: PSR J0030+0451 and the high-mass pulsar PSR J0740+6620. These studies have commonly assumed a deep-heated, fully ionized hydrogen atmosphere model, although they have explored the effects of partial ionization and helium composition in some cases. Here, we extend that exploration and also include new models with partially ionized carbon composition, externally heated hydrogen, and an empirical atmospheric beaming parameterization to explore deviations in the expected anisotropy of the emitted radiation. None of the studied atmosphere cases have any significant influence on the inferred radius of PSR J0740+6620, possibly due to its X-ray faintness, tighter external constraints, and/or viewing geometry. In the case of PSR J0030+0451, both the composition and ionization state could significantly alter the inferred radius. However, based on the evidence (prior predictive probability of the data), partially ionized hydrogen and carbon atmospheres are disfavored. The difference in the evidence for ionized hydrogen and helium atmospheres is too small to be decisive for most cases, but the inferred radius for helium models trends to larger sizes around or above 14–15 km. External heating or deviations in the beaming that are less than 5% at emission angles smaller than 60°, on the other hand, have no significant effect on the inferred radius.

Pulse profile modelling of thermonuclear burst oscillations − I. The effect of neglecting variability

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.

Relativistic force-free models of the thermal X-ray emission in millisecond pulsars observed by NICER

ABSTRACTJPSeveral important properties of rotation-powered millisecond pulsars (MSPs), such as their mass-radius ratio, equation of state and magnetic field topology, can be inferred from precise observations and modelling of their X-ray light curves. In the present study, we model the thermal X-ray signals originated in MSPs, all the way from numerically solving the surrounding magnetospheres up to the ray tracing of the emitted photons and the final computation of their light curves and spectra. The magnetosphere is solved by performing general relativistic force-free simulations of a rotating neutron star (NS) endowed with a simple centred dipolar magnetic field, for many different stellar compactness and pulsar misalignments. From these solutions, we derive an emissivity map over the surface of the star, based on the electric currents in the magnetosphere. In particular, the emission regions (ERs) are determined in this model by spacelike four-currents that reach the NS. We show that this assumption, together with the inclusion of the gravitational curvature on the force-free simulations, lead to non-standard ERs facing the closed-zone of the pulsar, in addition to other ERs within the polar caps. The combined X-ray signals from these two kinds of ERs (both antipodal) allow to approximate the non-trivial interpulses found in several MSPs light curves. Our modelled X-ray signals are compared against very accurate NICER observations of four target pulsars: PSR J043-4715, PSR J1231-1411, PSR J2124-3358, and PSR J0030 + 0451; achieving very good simultaneous fits for their light curves and spectral distributions.

GRMHD simulations of accreting neutron stars with non-dipole fields

ABSTRACT NASA’s NICER telescope has recently provided evidence for non-dipolar magnetic field structures in rotation-powered millisecond pulsars. These stars are assumed to have gone through a prolonged accretion spin-up phase, begging the question of what accretion flows on to stars with complex magnetic fields would look like. We present results from a suite of general relativistic magnetohydrodynamic simulations of accreting neutron stars for dipole, quadrupole, and quadrudipolar stellar field geometries. This is a first step towards simulating realistic hotspot shapes in a general relativistic framework to understand hotspot variability in accreting millisecond pulsars. We find that the location and size of the accretion columns resulting in hotspots changes significantly depending on initial stellar field strength and geometry. We also find that the strongest contributions to the stellar torque are from disc-connected field lines and the pulsar wind, leading to spin-down in almost the entire parameter regime explored here. We further analyse angular momentum transport in the accretion disc due to large-scale magnetic stresses, turbulent stresses, and wind and compressible effects which we identify with convective motions. The disc collimates the initial open stellar flux forming jets. For dipoles, the disc–magnetosphere interaction can either enhance or reduce jet power compared to the isolated case. However for quadrupoles, the disc always leads to an enhanced net open flux making the jet power comparable to the dipolar case. We discuss our results in the context of observed neutron star jets and provide a viable mechanism to explain radio power both in the low- and high-magnetic field case.

Constraining the Neutron Star Mass–Radius Relation and Dense Matter Equation of State with NICER. III. Model Description and Verification of Parameter Estimation Codes

Abstract 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.

A Deep Chandra X-Ray Observatory Study of the Millisecond Pulsar Population in the Globular Cluster Terzan 5

Abstract We present an analysis of 745.8 ks of archival Chandra X-Ray Observatory Advanced CCD Imaging Spectrometer data accumulated between 2000 and 2016 of the millisecond pulsar (MSP) population in the rich Galactic globular cluster Terzan 5. Eight of the 38 MSPs with precise positions are found to have plausible X-ray source matches. Despite the deep exposure, the remaining MSPs are either marginally detected or have no obvious X-ray counterparts, which can be attributed to the typically soft thermal spectra of rotation-powered MSPs, which are strongly attenuated by the high intervening absorbing column (∼1022 cm−2) toward the cluster, and in some instances to severe source crowding/blending. For the “redback” MSP binaries PSR J1748−2446P and PSR J1748−2446ad and the “black widow” binary system PSR J1748−2446O, we find clear evidence for large-amplitude X-ray variability at the orbital period consistent with an intrabinary shock origin. The third redback MSP in the cluster, PSR J1748−2446A, shows order-of-magnitude variations in flux on timescales of years, possibly due to state transitions or intense flaring episodes from a magnetically active secondary star.

Magnetospheric return-current-heated atmospheres of rotation-powered millisecond pulsars

We computed accurate atmosphere models of rotation-powered millisecond pulsars in which the polar caps of a neutron star (NS) are externally heated by magnetospheric return currents. The external ram pressure, energy losses, and stopping depth of the penetrating charged particles were computed self-consistently with the atmosphere model, instead of assuming a simplified deep-heated atmosphere in radiative equilibrium. We used exact Compton scattering formalism to model the properties of the emergent X-ray radiation. The deep-heating approximation was found to be valid only if most of the heat originates from ultra-relativistic bombarding particles with Lorentz factors ofγ ≳ 100. In the opposite regime, the atmosphere attains a distinct two-layer structure with an overheated optically thin skin on top of an optically thick cool plasma. The overheated skin strongly modifies the emergent radiation: It produces a Compton-upscattered high-energy tail in the spectrum and alters the radiation beaming pattern from limb darkening to limb brightening for emitted hard X-rays. This kind of drastic change in the emission properties can have a significant impact on the inferred NS pulse profile parameters as performed, for example, by Neutron star Interior Composition ExploreR. Finally, the connection between the energy distribution of the return current particles and the atmosphere emission properties offers a new tool to probe the exact physics of pulsar magnetospheres.

A NICER View of Spectral and Profile Evolution for Three X-Ray-emitting Millisecond Pulsars

Abstract 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.

NICER X-Ray Observations of Seven Nearby Rotation-powered Millisecond Pulsars

Abstract 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.

Constraining the Neutron Star Mass–Radius Relation and Dense Matter Equation of State with NICER. I. The Millisecond Pulsar X-Ray Data Set

Abstract 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.

Effects of Compton scattering on the neutron star radius constraints in rotation-powered millisecond pulsars

The aim of this work is to study the possible effects and biases on the radius constraints for rotation-powered millisecond pulsars when using Thomson approximation to describe electron scattering in the atmosphere models, instead of using exact formulation for Compton scattering. We compare the differences between the two models in the energy spectrum and angular distribution of the emitted radiation. We also analyse a self-generated, synthetic, phase-resolved energy spectrum, based on Compton atmosphere and the most X-ray luminous, rotation-powered millisecond pulsars observed by the Neutron star Interior Composition ExploreR (NICER). We derive constraints for the neutron star parameters using both the Compton and Thomson models. The results show that the method works by reproducing the correct parameters with the Compton model. However, biases are found in both the size and the temperature of the emitting hotspot, when using the Thomson model. The constraints on the radius are still not significantly changed, and therefore the Thomson model seems to be adequate if we are interested only in the radius measurements using NICER.

Investigation of the Millisecond Pulsar Origins by their Spin Periods at the Wavebands of Radio, X-Ray, and γ-Ray

To track the formation and evolution links of the millisecond pulsars (MSPs) powered by accretion and rotation in the Galactic field, we investigate the spin period (P) and spin-down power () distributions of the MSPs observed at the wavebands of radio, X-ray, and γ-ray. We find that all but one (119/120) of the γ-ray MSPs have been detected with the radio signals (radio+γ MSPs); on the contrary, nearly half of the radio MSPs (118/237) have not been detected with γ-rays (radio-only MSPs). In addition, the radio+γ MSPs are shown to be the relative faster and more energetic objects ( and ) compared with the radio-only MSPs ( and ), while the spin periods of these two MSP populations are compatible with the log-normal distributions by the statistical tests. Most rotation-powered MSPs (RMSPs) with the radio eclipsing (31/34) exhibit the radio+γ signals, which share the faster spin () and larger spin-down power () distributions than the non-eclipsing ones (, ), implying the radio+γ MSPs to be younger than the radio-only MSPs. It is noticed that the spin distribution of the accretion-powered X-ray MSPs shows a clustering phenomenon around ∼1.6–2.0 ms, which is not observed in RMSPs, hinting that the RMSPs may experience the multiple possible origins. Particularly, all the three super-fast spinning RMSPs with P ∼ 1.4–1.6 ms exhibit the non-eclipsing, and we argue that they may be the distinctive sources formed by the accretion induced collapse (AIC) of white dwarfs.

Searching for γ-ray counterparts to very faint X-ray transient neutron star binaries

Very faint X-ray transients (VFXTs) are a group of X-ray binaries with low luminosities, displaying peak X-ray luminosities during their outbursts of only 1034–1036 erg s−1. Using γ-ray data obtained with the Large Area Telescope (LAT) onboard the Fermi Gamma-Ray Space Telescope (Fermi), we investigate their possible nature of containing rotation-powered pulsars, or more specifically being transitional millisecond pulsars (MSPs). Among more than 40 known VFXTs, we select 12 neutron star systems. We analyze the LAT data for the fields of 12 VFXTs in the energy range 0.2–300 GeV, but do not find any counterparts likely detected by Fermi. We obtain luminosity upper limits for the 12 sources. While the distances to the sources are largely uncertain, the upper limits are comparable to the luminosities of two transitional systems, PSR J1023−0038 and XSS J12270−4859. From our study, we conclude that no evidence is found at γ-rays for the suggestion that some VFXTs could contain rotation-powered MSPs (or be transitional MSP systems).

Advancing astronomy, one screen saver at a time

Astronomy One of the major challenges of modern astronomy is finding important results in the overwhelming volume of acquired data. Clark et al. used the computers of tens of thousands of volunteers participating in the Einstein@Home project to search Fermi Large Area Telescope data. Their goal was to discover radio-quiet gamma-ray millisecond pulsars (MSPs). More than 10,000 donated CPU years in this survey led to the discovery of two isolated MSPs, including a rotation-powered MSP that has remained undetected in radio observations. Sci. Adv. 10.1126/sciadv.aao7228 (2018).

Einstein@Home discovers a radio-quiet gamma-ray millisecond pulsar

Millisecond pulsars (MSPs) are old neutron stars that spin hundreds of times per second and appear to pulsate as their emission beams cross our line of sight. To date, radio pulsations have been detected from all rotation-powered MSPs. In an attempt to discover radio-quiet gamma-ray MSPs, we used the aggregated power from the computers of tens of thousands of volunteers participating in the Einstein@Home distributed computing project to search for pulsations from unidentified gamma-ray sources in Fermi Large Area Telescope data. This survey discovered two isolated MSPs, one of which is the only known rotation-powered MSP to remain undetected in radio observations. These gamma-ray MSPs were discovered in completely blind searches without prior constraints from other observations, raising hopes for detecting MSPs from a predicted Galactic bulge population.

A Multiwavelength Study of Nearby Millisecond Pulsar PSR J1400−1431: Improved Astrometry and an Optical Detection of Its Cool White Dwarf Companion

Abstract In 2012, five high-school students involved in the Pulsar Search Collaboratory discovered the millisecond pulsar (MSP) PSR J1400−1431, and initial timing parameters were published in Rosen et al. a year later. Since then, we have obtained a phase-connected timing solution spanning five years, resolving a significant position discrepancy and measuring , proper motion, parallax, and a monotonic slope in dispersion measure over time. Due to PSR J1400−1431’s proximity and significant proper motion, we use the Shklovskii effect and other priors to determine a 95% confidence interval for PSR J1400−1431’s distance, pc. With an improved timing position, we present the first detection of the pulsar’s low-mass white dwarf (WD) companion using the Goodman Spectrograph on the 4.1 m SOAR telescope. Deeper imaging suggests that it is a cool DA-type WD with K and . We show a convincing association between PSR J1400−1431 and a γ-ray point source, 3FGL J1400.5−1437, but only weak (3.3σ) evidence of pulsations after folding γ-ray photons using our radio timing model. We detect an X-ray counterpart with XMM-Newton, but the measured X-ray luminosity (1×1029 erg s−1) makes PSR J1400−1431 the least X-ray luminous rotation-powered MSP detected to date. Together, our findings present a consistent picture of a nearby ( pc) MSP in a 9.5-day orbit around a cool ∼0.3 M ⊙ WD companion, with orbital inclination .

X-rays from Radio Millisecond Pulsars

AbstractThe Galactic population of rotation-powered (aka radio) millisecond pulsars (MSPs) exhibits diverse X-ray properties. Energetic MSPs show pulsed non-thermal radiation from their magnetospheres. Eclipsing binary MSPs predominantly have X-ray emission from a pulsar wind driven intra-binary shock. Typical radio MSPs emit X-rays from their heated magnetic polar caps. These thermally emitting MSPs offer the opportunity to place interesting constraints on the long sought after dense matter equation of state, making them important targets of investigation of the recently deployed Neutron Star Interior Composition Explorer (NICER) X-ray mission.

NuSTAR Hard X-Ray Observations of the Energetic Millisecond Pulsars PSR B1821-24, PSR B1937+21, and PSR J0218+4232

Abstract We present Nuclear Spectroscopic Telescope Array (NuSTAR) hard X-ray timing and spectroscopy of the three exceptionally energetic rotation-powered millisecond pulsars PSRs B1821-24, B1937+21, and J0218+4232. By correcting for the frequency and phase drifts of the NuSTAR onboard clock, we are able to recover the intrinsic hard X-ray pulse profiles of all three pulsars with a resolution down to . The substantial reduction of background emission relative to previous broadband X-ray observations allows us to detect for the first time pulsed emission up to ∼50 keV, ∼20 keV, and ∼25 keV for the three pulsars, respectively. We conduct phase-resolved spectroscopy in the 0.5–79 keV range for all three objects, obtaining the best measurements yet of the broadband spectral shape and high-energy pulsed emission to date. We find extensions of the same power-law continua seen at lower energies, with no conclusive evidence for a spectral turnover or break. Extrapolation of the X-ray power-law spectrum to higher energies reveals that a turnover in the 100 keV to 100 MeV range is required to accommodate the high-energy γ-ray emission observed with Fermi-LAT, similar to the spectral energy distribution observed for the Crab pulsar.

Constraining Relativistic Bow Shock Properties in Rotation-powered Millisecond Pulsar Binaries

Multiwavelength followup of unidentified Fermi sources has vastly expanded the number of known galactic-field "black widow" and "redback" millisecond pulsar binaries. Focusing on their rotation-powered state, we interpret the radio to X-ray phenomenology in a consistent framework. We advocate the existence of two distinct modes differing in their intrabinary shock orientation, distinguished by the phase-centering of the double-peaked X-ray orbital modulation originating from mildly-relativistic Doppler boosting. By constructing a geometric model for radio eclipses, we constrain the shock geometry as functions of binary inclination and shock stand-off R0. We develop synthetic X-ray synchrotron orbital light curves and explore the model parameter space allowed by radio eclipse constraints applied on archetypal systems B1957+20 and J1023+0038. For B1957+20, from radio eclipses the stand-off is R0 ~ 0.15-0.3 fraction of binary separation from the companion center, depending on the orbit inclination. Constructed X-ray light curves for B1957+20 using these values are qualitatively consistent with those observed, and we find occultation of the shock by the companion as a minor influence, demanding significant Doppler factors to yield double peaks. For J1023+0038, radio eclipses imply R0 ≲ 0.4 while X-ray light curves suggest 0.1 ≲ R0 ≲ 0.3 (from the pulsar). Degeneracies in the model parameter space encourage further development to include transport considerations. Generically, the spatial variation along the shock of the underlying electron power-law index should yield energy-dependence in the shape of light curves motivating future X-ray phase-resolved spectroscopic studies to probe the unknown physics of pulsar winds and relativistic shock acceleration therein.

System mass constraints for the accreting millisecond pulsar XTE J1814-338 using Bowen fluorescence

We present phase-resolved spectroscopy of the millisecond X-ray pulsar XTE J1814-338 obtained during its 2003 outburst. The spectra are dominated by high-excitation emission lines of HeII $\lambda$4686, H$\beta$, and the Bowen blend CIII/NIII 4630-50\AA. We exploit the proven Bowen fluorescence technique to establish a complete set of dynamical system parameter constraints using bootstrap Doppler tomography, a first for an accreting millisecond X-ray pulsar binary. The reconstructed Doppler map of the NIII $\lambda$4640 Bowen transition exhibits a statistically significant (>4$\sigma$) spot feature at the expected position of the companion star. If this feature is driven by irradiation of the surface of the Roche lobe filling companion, we derive a strict lower limit to the true radial velocity semi-amplitude $K_2$. Combining our donor constraint with the well constrained orbit of the neutron star leads to a determination of the binary mass ratio: q = $0.123^{+0.012}_{-0.010}$. The component masses are not tightly constrained given our lack of knowledge of the binary inclination. We cannot rule out a canonical neutron star mass of 1.4 $M_{\odot}$ (1.1 $M_{\odot}$ < $M_1$ < 3.1 $M_{\odot}$; 95%). The 68/95% confidence limits of $M_2$ are consistent with the companion being a significantly bloated, M-type main sequence star. Our findings, combined with results from studies of the quiescent optical counterpart of XTE J1814-338, suggest the presence of a rotation-powered millisecond pulsar in XTE J1814-338 during an X-ray quiescent state. The companion mass is typical of the so-called 'redback' pulsar binary systems ($M_2$ ~ 0.2 $M_{\odot}$).