PSR J2021 Research Articles

Multiwavelength investigation of the candidate Galactic PeVatron MGRO J1908+06

ABSTRACT The candidate PeVatron MGRO J1908+06, which shows a hard spectrum beyond 100 TeV, is one of the most peculiar γ-ray sources in the Galactic plane. Its complex morphology and some possible counterparts spatially related with the very high energy (VHE) emission region, preclude to distinguish between a hadronic and leptonic nature of the γ-ray emission. In this paper, we illustrate a new multiwavelength analysis of MGRO J1908+06, with the aim to shed light on its nature and the origin of its ultra-high-energy emission. We performed an analysis of the 12CO and 13CO molecular line emission demonstrating the presence of dense molecular clouds spatially correlated with the source region. We also analysed 12 yr of Fermi-Large Area Telescope (LAT) data between 10 GeV and 1 TeV finding a counterpart with a hard spectrum (Γ ∼ 1.6). Our reanalysis of XMM–Newton data allowed us to put a more stringent constraint on the X-ray flux from this source. We demonstrate that a single accelerator cannot explain the whole set of multiwavelength data, regardless of whether it accelerates protons or electrons, but a two-zone model is needed to explain the emission from MGRO J1908+06. The VHE emission seems most likely the superposition of a TeV pulsar wind nebula powered by PSR J1907+0602, in the southern region, and of the interaction between the supernova remnant G40.5−0.5 and the molecular clouds, in the northern region.

Search for gamma rays from SNe with a variable-size sliding-time-window analysis of the Fermi-LAT data

ABSTRACT We present a systematic search for γ-ray emission from supernovae (SNe) in the Fermi Large Area Telescope (LAT) Pass 8 data. The sample of targets consists of 55,880 candidates from the Open Supernova Catalogue. We searched for γ rays from SNe by means of a variable-size sliding-time-window analysis. Our results confirm the presence of transient γ-ray emission from the sources of non-AGN classes, including transitional pulsars, solar flares, γ-ray bursts, novae, and the Crab Nebula, which are projected near some of these SN’s positions, and also strengthen support to the variable signal in the direction of SN iPTF14hls. The analysis is successful in finding both short (e.g. solar flares) and long (e.g. transitional pulsars) high flux states. Our search reveals two new γ-ray transient signals occurred in 2019 in the directions of optical transients that are SN candidates, AT2019bvr and AT2018iwp, with their flux increases within 6 months after the dates of SN’s discoveries. These signals are bright and their variability is at a higher statistical level than that of iPTF14hls. An exploration of archival multiwavelength observations towards their positions is necessary to establish their association with SNe or other classes of sources. Our analysis, in addition, shows a bright transient γ-ray signal at low Galactic latitudes in the direction of PSR J0205+6449. In addition, we report the results of an all-sky search for γ-ray transient sources. This provided two additional candidates to gamma-ray transient sources.

Evidence for three-dimensional spin–velocity alignment in a pulsar

More than 50 years after the discovery of pulsars1 and confirmation of their association with supernova explosions2–4, the origin of the initial spin and velocity of pulsars remains largely a mystery. The typical space velocities of several hundred km s−1 have been attributed to ‘kicks’ resulting from asymmetries either in the supernova ejecta or in the neutrino emission5–7. Observations have shown a strong tendency for alignment between the pulsar space velocity and the spin axis in young pulsars, but until now these comparisons have been restricted to two dimensions. Here, we report evidence for three-dimensional alignment between the spin and velocity vectors, largely based on observations made with the Five-hundred-meter Aperture Spherical Radio Telescope (FAST) of the pulsar PSR J0538+2817 and its associated supernova remnant S147. Analysis of these and related observations has enabled us to determine the location of the pulsar within the supernova remnant and hence its radial velocity. Current simulations of supernova explosions have difficulty producing such three-dimensional alignment7–9. Our results, which depend on the unprecedented sensitivity of the observations, add another dimension to the intriguing correlation between pulsar spin-axis and birth-kick directions, thereby deepening the mysteries surrounding the birth of neutron stars. Fast-moving pulsars and neutron stars in general may have received a kinetic ‘kick’ from an asymmetric element in the supernova explosion that formed them. Here, the spin axis of a pulsar is determined to lie along the three-dimensional direction of the pulsar’s motion, providing a challenging constraint on supernova explosion modelling.

Evidence of intra-binary shock emission from the redback pulsar PSR J1048+2339

We present simultaneous multiwavelength observations of the 4.66 ms redback pulsar PSR J1048+2339. We performed phase-resolved spectroscopy with the Very Large Telescope (VLT) searching for signatures of a residual accretion disk or intra-binary shock emission, constraining the companion radial velocity semi-amplitude (K2), and estimating the neutron star mass (MNS). Using the FORS2-VLT intermediate-resolution spectra, we measured a companion velocity of 291 < K2 < 348 km s−1 and a binary mass ratio of 0.209 < q < 0.250. Combining our results for K2 and q, we constrained the mass of the neutron star and the companion to (1.0 < MNS < 1.6) sin−3 i M⊙ and (0.24 < M2 < 0.33) sin−3i M⊙, respectively, where i is the system inclination. The Doppler map of the Hα emission line exhibits a spot feature at the expected position of the companion star and an extended bright spot close to the inner Lagrangian point. We interpret this extended emission as the effect of an intra-binary shock originating from the interaction between the pulsar relativistic wind and the matter leaving the companion star. The mass loss from the secondary star could be either due to Roche-lobe overflow or to the ablation of its outer layer by the energetic pulsar wind. Contrastingly, we find no evidence for an accretion disk. We report on the results of the Sardinia Radio Telescope (SRT) and the Low-Frequency Array (LOFAR) telescope simultaneous radio observations at three different frequencies (150 MHz, 336 MHz, and 1400 MHz). No pulsed radio signal is found in our search. This is probably due to both scintillation and the presence of material expelled from the system which can cause the absorption of the radio signal at low frequencies. The confirmation of this hypothesis is given by another SRT observation (L-band) taken in 2019, in which a pulsed signal is detected. Finally, we report on an attempt to search for optical pulsations using IFI+Iqueye mounted at the 1.2 m Galileo telescope at the Asiago Observatory.

Spectrum and Morphology of the Very-high-energy Source HAWC J2019+368

Abstract The MGRO J2019+37 region is one of the brightest sources in the sky at TeV energies. It was detected in the second HAWC catalog as 2HWC J2019+367 and here we present a detailed study of this region using data from HAWC. This analysis resolves the region into two sources: HAWC J2019+368 and HAWC J2016+371. We associate HAWC J2016+371 with the evolved supernova remnant CTB 87, although its low significance in this analysis prevents a detailed study at this time. An investigation of the morphology (including possible energy-dependent morphology) and spectrum for HAWC J2019+368 is the focus of this work. We associate HAWC J2019+368 with PSR J2021+3651 and its X-ray pulsar wind nebula, the Dragonfly nebula. Modeling the spectrum measured by HAWC and Suzaku reveals a ∼7 kyr pulsar and nebula system producing the observed emission at X-ray and γ-ray energies.

Reactivation of the High Magnetic Field Pulsar PSR J1846–0258 with Magnetar-like Bursts

Abstract We report on the 2020 reactivation of the energetic high magnetic field pulsar PSR J1846–0258 and its pulsar wind nebula (PWN) after 14 yr of quiescence with new Chandra and Green Bank Telescope observations. The emission of short-duration bursts from J1846–0258 was accompanied by an enhancement of X-ray persistent flux and significant spectral softening, similar to those observed during its first bursting episode in 2006. The 2020 pulsar spectrum is described by a power-law model with a photon index Γ = 1.7 ± 0.3 in comparison to a Γ = 1.2 ± 0.1 before outburst, and shows evidence of an emerging thermal component with blackbody temperature kT = 0.7 ± 0.1 keV. The 0.5–10 keV unabsorbed flux increased from × 10−12 erg cm−2 s−1 in quiescence to × 10−11 erg cm−2 s−1 following the outburst. We did not detect any radio pulsations from the pulsar at 2 GHz, and we place an upper limit of 7.1 μJy and 55 mJy for the coherent pulsed emission and single pulses, respectively. The 2020 PWN spectrum, characterized by a photon index of 1.92 ± 0.04 and X-ray luminosity of (1.2 ± 0.1) × 1035 erg s−1 at a distance of 5.8 kpc, is consistent with those observed before the outburst. An analysis of regions closer to the pulsar shows small-scale time variabilities and brightness changes over the 20 yr period from 2000 to 2020, while the photon indices did not change. We conclude that the outburst in PSR J1846–0258 is a combination of crustal and magnetospheric effects, with no significant burst-induced variability in its PWN based on the current observations.

A search for radio pulsars in five nearby supernova remnants

Context. Most neutron stars are expected to be born in supernovae, but only about half of supernova remnants (SNRs) are associated with a compact object. In many cases, a supernova progenitor may have resulted in a black hole. However, there are several possible reasons why true pulsar-SNR associations may have been missed in previous surveys: The pulsar’s radio beam may not be oriented towards us; the pulsar may be too faint to be detectable; or there may be an offset in the pulsar position caused by a kick. Aims. Our goal is to find new pulsars in SNRs and explore their possible association with the remnant. The search and selection of the remnants presented in this paper was inspired by the non-detection of any X-ray bright compact objects in these remnants when previously studied. Methods. Five SNRs were searched for radio pulsars with the Green Bank Telescope at 820 MHz with multiple pointings to cover the full spatial extent of the remnants. A periodicity search plus an acceleration search up to 500 m s−2 and a single pulse search were performed for each pointing in order to detect potential isolated binary pulsars and single pulses, respectively. Results. No new pulsars were detected in the survey. However, we were able to re-detect a known pulsar, PSR J2047+5029, near SNR G89.0+4.7. We were unable to detect the radio-quiet gamma-ray pulsar PSR J2021+4026, but we do find a flux density limit of 0.08 mJy. Our flux density limits make our survey two to 16 times more sensitive than previous surveys, while also covering the whole spatial extent of the same remnants. Conclusions. We discuss potential explanations for the non-detection of a pulsar in the studied SNRs and conclude that sensitivity is still the most likely factor responsible for the lack of pulsars in some remnants.

X-ray Properties of the Pulsar PSR J0205+6449 in 3C 58

X-ray Properties of the Pulsar PSR J0205+6449 in 3C 58

The relativistic binary programme on MeerKAT: science objectives and first results

ABSTRACT We describe the ongoing Relativistic Binary programme (RelBin), a part of the MeerTime large survey project with the MeerKAT radio telescope. RelBin is primarily focused on observations of relativistic effects in binary pulsars to enable measurements of neutron star masses and tests of theories of gravity. We selected 25 pulsars as an initial high priority list of targets based on their characteristics and observational history with other telescopes. In this paper, we provide an outline of the programme, and present polarization calibrated pulse profiles for all selected pulsars as a reference catalogue along with updated dispersion measures. We report Faraday rotation measures for 24 pulsars, twelve of which have been measured for the first time. More than a third of our selected pulsars show a flat position angle swing confirming earlier observations. We demonstrate the ability of the Rotating Vector Model, fitted here to seven binary pulsars, including the Double Pulsar (PSR J0737–3039A), to obtain information about the orbital inclination angle. We present a high time resolution light curve of the eclipse of PSR J0737–3039A by the companion’s magnetosphere, a high-phase-resolution position angle swing for PSR J1141–6545, an improved detection of the Shapiro delay of PSR J1811–2405, and pulse scattering measurements for PSRs J1227–6208, J1757–1854, and J1811–1736. Finally, we demonstrate that timing observations with MeerKAT improve on existing data sets by a factor of, typically, 2–3, sometimes by an order of magnitude.

Strongly pulsed thermal X-rays from a single extended hot spot on PSR J2021+4026

The radio-quiet pulsar PSR J2021+4026 is mostly known because it is the only rotation-powered pulsar that shows variability in its γ-ray emission. Using XMM-Newton archival data, we first confirmed that its flux is steady in the X-ray band, and then we showed that both the spectral and timing X-ray properties, that is to say the narrow pulse profile, the high pulsed fraction of 80–90%, and its dependence on the energy, can be better reproduced using a magnetized atmosphere model instead of simply a blackbody model. With a maximum likelihood analysis in the energy-phase space, we inferred that the pulsar has, in correspondence of one magnetic pole, a hot spot with a temperature of T ∼ 1 MK and colatitude extension of θ ∼ 20°. For the pulsar distance of 1.5 kpc, this corresponds to a cap of R ∼ 5 − 6 km, which is greater than the standard dimension of the dipolar polar caps. The large pulsed fraction further argues against emission from the entire star surface, as it would be expected in the case of secular cooling. An unpulsed (≲40% pulsed fraction), nonthermal component, probably originating in a wind nebula, is also detected. The pulsar geometry derived with our spectral fits in the X-ray is relatively well constrained (χ = 90° and ξ = 20°–25°) and consistent with what is deduced from γ-ray observations, provided that only one of the two hemispheres is active. The evidence for an extended hot spot in PSR J2021+4026, which was also found in other pulsars of a similar age but not in older objects, suggests a possible age dependence of the emitting size of thermal X-rays.

X-Ray Spectroscopy of the Highly Magnetized Pulsar PSR J1846-0258, Its Wind Nebula, and Hosting Supernova Remnant Kes 75

Abstract We present broadband X-ray spectroscopy of the energetic components that make up the supernova remnant (SNR) Kesteven 75 using concurrent 2017 August 17–20 XMM-Newton and NuSTAR observations, during which the pulsar PSR J1846−0258 is found to be in the quiescent state. The young remnant hosts a bright pulsar wind nebula powered by the highly energetic ( erg s−1) isolated, rotation-powered pulsar, with a spin-down age of only . Its inferred magnetic field (B s = 4.9 × 1013 G) is the largest known for these objects, and is likely responsible for intervals of flare and burst activity, suggesting a transition between/to a magnetar state. The pulsed emission from PSR J1846−0258 is well-characterized in the 2–50 keV range by a power-law model with photon index ΓPSR = 1.24 ± 0.09 and a 2–10 keV unabsorbed flux of (2.3 ± 0.4) × 10−12 erg s−1 cm−2. We find no evidence for an additional non-thermal component above 10 keV in the current state, as would be typical for a magnetar. Compared to the Chandra pulsar spectrum, the intrinsic pulsed fraction is 71 ± 16% in 2–10 keV band. A power-law spectrum for the pulsar wind nebulae (PWN) yields ΓPWN = 2.03 ± 0.02 in the 1–55 keV band, with no evidence of curvature in this range, and a 2–10 keV unabsorbed flux (2.13 ± 0.02) × 10−11 erg s−1 cm−2. The NuSTAR data reveal evidence for a hard X-ray component dominating the SNR spectrum above 10 keV that we attribute to a dust-scattered PWN component. We model the dynamical and radiative evolution of the Kes 75 system to estimate the birth properties of the neutron star, the energetics of its progenitor, and properties of the PWN. This suggests that the progenitor of Kes 75 was originally in a binary system which transferred most of its mass to a companion before exploding.

Rotating vector model for magnetars

ABSTRACT The modification of the rotating vector model in the case of magnetars are calculated. Magnetars may have twisted magnetic field compared with normal pulsars. The polarization position angle of magnetars will change in the case of a twisted magnetic field. For a twisted dipole field, we found that the position angle will change both vertically and horizontally. During the untwisting process of the magnetar magnetosphere, the modifications of the position angle will evolve with time monotonously. This may explain the evolution of the position angle in magnetar PSR J1622-4950 and XTE J1810-197. The relation between the emission point and the line of sight will also change. We suggest every magnetospheric models of magnetars also calculate the corresponding changes of position angle in their models. Order of magnitude estimation formula for doing this is given. This opens the possibility to extract the magnetic field geometry of magnetars from their radio polarization observations.

Modelling of particle acceleration in the pulsar wind nebulae with bow shocks

The observations of the pulsar wind nebulae (PWNe) indicate the presence of efficient acceleration of positrons and electrons in these sources. The Fermi acceleration in the colliding shock flows can explain the observed hard synchrotron emission spectra of PWNe with bow shocks (BSPWNe). This may result in their maximal luminosities in the far ultraviolet range (FUV; 1250 — 2000 Å, ∼ 6 — 10 eV) due to the synchrotron emission of pairs rather than due to the thermal emission of the shocked interstellar matter. Fine spectroscopic observations of sufficiently bright sources with Hubble Space Telescope could be applied to distinguish between these two scenarios. In this paper we simulate BSPWNe flows structure with the relativistic magnetohydrodynamic code PLUTO, consider particle transport and their synchrotron emission for a number of BSPWNe. We calculate the synchrotron FUV luminosities of these BSPWNe and discuss the prospective of their observation in FUV. We also consider possible contribution of PSR J1741-2054 to the positron excess detected by AMS-02 and PAMELA.

An extreme particle accelerator in the Galactic plane: HESS J1826−130

The unidentified very-high-energy (VHE;E> 0.1 TeV)γ-ray source, HESS J1826−130, was discovered with the High Energy Stereoscopic System (HESS) in the Galactic plane. The analysis of 215 h of HESS data has revealed a steadyγ-ray flux from HESS J1826−130, which appears extended with a half-width of 0.21° ± 0.02stat° ± 0.05sys°. The source spectrum is best fit with either a power-law function with a spectral index Γ = 1.78 ± 0.10stat± 0.20sysand an exponential cut-off at 15.2−3.2+5.5TeV, or a broken power-law with Γ1= 1.96 ± 0.06stat± 0.20sys, Γ2= 3.59 ± 0.69stat± 0.20sysfor energies below and aboveEbr= 11.2 ± 2.7 TeV, respectively. The VHE flux from HESS J1826−130 is contaminated by the extended emission of the bright, nearby pulsar wind nebula, HESS J1825−137, particularly at the low end of the energy spectrum. Leptonic scenarios for the origin of HESS J1826−130 VHE emission related to PSR J1826−1256 are confronted by our spectral and morphological analysis. In a hadronic framework, taking into account the properties of dense gas regions surrounding HESS J1826−130, the source spectrum would imply an astrophysical object capable of accelerating the parent particle population up to ≳200 TeV. Our results are also discussed in a multiwavelength context, accounting for both the presence of nearby supernova remnants, molecular clouds, and counterparts detected in radio, X-rays, and TeV energies.

Detection of the Geminga pulsar with MAGIC hints at a power-law tail emission beyond 15 GeV

We report the detection of pulsed gamma-ray emission from the Geminga pulsar (PSR J0633+1746) between 15 GeV and 75 GeV. This is the first time a middle-aged pulsar has been detected up to these energies. Observations were carried out with the MAGIC telescopes between 2017 and 2019 using the low-energy threshold Sum-Trigger-II system. After quality selection cuts, ∼80 h of observational data were used for this analysis. To compare with the emission at lower energies below the sensitivity range of MAGIC, 11 years of Fermi-LAT data above 100 MeV were also analysed. From the two pulses per rotation seen by Fermi-LAT, only the second one, P2, is detected in the MAGIC energy range, with a significance of 6.3σ. The spectrum measured by MAGIC is well-represented by a simple power law of spectral index Γ = 5.62 ± 0.54, which smoothly extends the Fermi-LAT spectrum. A joint fit to MAGIC and Fermi-LAT data rules out the existence of a sub-exponential cut-off in the combined energy range at the 3.6σ significance level. The power-law tail emission detected by MAGIC is interpreted as the transition from curvature radiation to Inverse Compton Scattering of particles accelerated in the northern outer gap.

Is PSR J0855−4644 responsible for the 1.4 TeV electron spectral bump hinted by DAMPE?

ABSTRACT DAMPE observation on the cosmic ray electron spectrum hints a narrow excess at ∼1.4 TeV. Although the excess can be ascribed to dark matter particles, pulsars and pulsar wind nebulae are believed to be more natural astrophysical origins: electrons injected from nearby pulsars at their early ages can form a bump-like feature in the spectrum due to radiative energy losses. In this paper, with a survey of nearby pulsars, we filter out four pulsars that may have notable contributions to ∼1.4 TeV cosmic ray electrons. Among them, PSR J0855−4644 has a spin-down luminosity more than 50 times higher than others and presumably dominates the electron fluxes from them. X-ray observations on the inner compact part (which may represent a tunnel for the transport of electrons from the pulsar) of PWN G267.0−01.0 are then used to constrain the spectral index of high-energy electrons injected by the pulsar. We show that high-energy electrons released by PSR J0855−4644 could indeed reproduce the 1.4 TeV spectral feature hinted by the DAMPE with reasonable parameters.

Chandra Monitoring of the J1809–1917 Pulsar Wind Nebula and Its Field

Abstract PSR J1809–1917 is a young (τ = 51 kyr) and energetic ( erg s−1) radio pulsar powering an X-ray pulsar wind nebula (PWN) that exhibits morphological variability. We report on the results of a new monitoring campaign by the Chandra X-ray Observatory (Chandra), carried out across six epochs with a ∼7 week cadence. The compact nebula can be interpreted as a jet-dominated outflow along the pulsar’s spin axis. Its variability can be the result of Doppler boosting in the kinked jet, whose shape changes with time (akin to the Vela pulsar jet). The deep X-ray image, composed of 405 ks of new and 131 ks of archival Chandra data, reveals an arcminute-scale extended nebula (EN) whose axis of symmetry aligns with both the axis of the compact nebula and the direction toward the peak of the nearby TeV source HESS J1809–193. The EN’s morphology and extent suggest that the pulsar is likely moving through the ambient medium at a transonic velocity. We also resolved a faint 7′ long nonthermal collimated structure protruding from the PWN. It is possibly another instance of a “misaligned outflow” (also known as a “kinetic jet”) produced by high-energy particles escaping the PWN’s confinement and tracing the interstellar magnetic field lines. Finally, taking advantage of the 536 ks exposure, we analyzed the point sources in the J1809 field and classified them using multiwavelength data. None of the classified sources in the field can reasonably be expected to produce the extended TeV flux in the region, suggesting that PSR J1809–1917 is indeed the counterpart to HESS/eHWC J1809–193.

Investigating the multiband non-thermal emission of the 100 TeV source eHWC J2019+368 with a pulsar wind nebula scenario

ABSTRACT eHWC J2019+368 is one of the sources emitting γ-rays with energies higher than 100 TeV based on the recent measurement with the High Altitude Water Cherenkov Observatory (HAWC), and the origin is still in debate. The pulsar PSR J2021+3651 is spatially coincident with the TeV source. We investigate theoretically whether the multiband non-thermal emission of eHWC J2019+368 can originate from the pulsar wind nebula (PWN) G75.2+0.1 powered by PSR J2021+3651. In the model, the spin-down power of the pulsar is transferred to high-energy particles and magnetic field in the nebula. As the particles with an energy distribution of either a broken power law or a power law continually injected into the nebula, the multiband non-thermal emission is produced via synchrotron radiation and inverse Compton scattering. The spectral energy distribution of the nebula from the model with the reasonable parameters is generally consistent with the detected radio, X-ray, and TeV γ-ray fluxes. Our study supports that the PWN has the ability to produce the TeV γ-rays of eHWC J2019+368, and the most energetic particles in the nebula have energies up to about 0.4 PeV.

Multiwavelength observations of PSR J2032+4127 during the 2017 periastron passage

ABSTRACT PSR J2032+4127 is only the second known gamma-ray binary where it is confirmed that a young radio pulsar is in orbit around a Be-star. The interaction of the pulsar wind with the mass outflow from the companion leads to broad-band emission from radio up to TeV energies. In this paper we present results of optical monitoring of the 2017 periastron passage with the Nordic Optical Telescope. These observations are complemented by X-ray (Swift/XRT, NuSTAR) and GeV (Fermi/LAT) monitoring. Joint analysis of the evolution of the parameters of the H α line and the broad-band (X-ray to TeV) spectral shape allows us to propose a model linking the observed emission to the interaction of the pulsar and Be-star winds under the assumption of the inclined disc geometry. Our model allows the observed flux and spectral evolution of the system to be explained in a self-consistent way.

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.