Gamma-ray Pulsars Research Articles

Effects of high temperatures on the splitting tensile strength and gamma ray shielding performance of radiation shielding concrete

The residual properties of radiation shielding concrete subjected to high temperatures require reassessment, considering that it may be exposed to high temperatures during service life. In this study, the effects of high temperatures on apparent characteristic, mass loss, splitting tensile strength, ultrasonic pulse velocity and gamma ray shielding performance of the more widely used barite concrete and magnetite concrete were investigated. The results showed that the relative velocity and damage index had a good correlation with the relative splitting tensile strength of radiation shielding concrete exposed to high temperatures, which could accurately reflect the failure of radiation shielding concrete subjected to high temperatures. Meanwhile, barite concrete appeared severe spalling phenomenon at 450 ℃, and magnetite concrete had better thermal stability, which had favorable physical, mechanical and shielding properties, thus it was more suitable for concrete under high temperature.

Distinct Thermal Emission from GRB 190109A

The gamma-ray bursts (GRBs) with distinct thermal components are rarely detected, especially in cases with thermal components throughout the prompt phase. Recently, Fermi/GBM, Swift/BAT, and Swift/XRT detected the special long-duration GRB 190109A, which has four pulses in the prompt gamma-ray emission, i.e, Pulse I (−4 to 20 s), Pulse II (20–50 s), Pulse III (50–90 s), and Pulse IV (90–120 s). GRB 190109A exhibits a very hard low-energy index (α ∼ 1) in the Band function relative to the typical GRBs (α ∼ − 1). In the whole burst prompt emission, we find distinct thermal emissions in the time-resolved spectra throughout four pulses. The blackbody (BB) temperature kT varies from 24.7 to 8.2 keV for Pulse I to Pulse IV. We also obtain the relation of F ∝ kT −0.40 for the early phase (Pulse I) and F ∝ kT 3.33±0.76 for the late phase (Pulses II–IV), respectively. The significant deviation of the kT − F relation in the early epochs from that in the late epochs likely suggests that the BB spectra origin of the early phase (Pulse I) may have disparate physical processes from those of the late phase (Pulses II–IV). For instance, it may be the transition from cocoon surroundings by a jet to the photosphere of the matter-dominated jet. A jet break is found in the late X-ray afterglow, which is in keeping with the standard external shock afterglow model in the interstellar medium circumburst.

Establishment of pulsed X-ray reference radiation field and measurement of related parameters

The international research on radiation protection dosimetry mainly focuses on continuous radiation. However, pulsed radiation has been widely used in the fields of new detector development, radiographic inspection, X-ray diagnosis, nuclear accident emergency and scientific research, the measurement of pulsed dose (rate) is very difficult. In order to solve the technical problem of pulse response test of active radiation dosimeter, the generation principle of pulsed X-ray and gamma ray radiation field is discussed, and the reference radiation field of pulsed X-ray is established based on three kinds of X-ray machines. Combined with the transfer ionization chamber and pulse width measurement system, the research of pulsed radiation dose (rate) measurement technology is carried out. The experimental results show that the pulse width of the established pulsed X-ray reference radiation field can be adjusted between 50 ns and 10 s, and the instantaneous dose rate range is 2.5 mSv/h-6.7 × 105 Sv/h, which can be widely used to study the pulsed X-ray response characteristics of active radiation dosimeter. This work can be widely used to study the pulsed X-ray response characteristics of active radiation dosimeter, which is of great significance to solve the calibration problem of pulsed radiation dose monitoring instrument.

Is the Black-widow Pulsar PSR J1555–2908 in a Hierarchical Triple System?

The 559 Hz black-widow pulsar PSR J1555−2908, originally discovered in radio, is also a bright gamma-ray pulsar. Timing its pulsations using 12 yr of Fermi-Large Area Telescope gamma-ray data reveals long-term variations in its spin frequency that are much larger than is observed from other millisecond pulsars. While this variability in the pulsar rotation rate could be intrinsic “timing noise,” here we consider an alternative explanation: the variations arise from the presence of a very-low-mass third object in a wide multiyear orbit around the neutron star and its low-mass companion. With current data, this hierarchical-triple-system model describes the pulsar’s rotation slightly more accurately than the best-fitting timing noise model. Future observations will show if this alternative explanation is correct.

Detections of Gamma-Rays from Globular Clusters ESO 452-SC11, NGC 6380, Palomar 6 and UKS 1 with Fermi-LAT

The events from 157 globular clusters (GCs) are analyzed by using 12 yr long-term Pass 8 data from Fermi Large Area Telescope. Besides the 34 GCs reported in previous literatures, four additional GCs (ESO 452-SC11, NGC 6380, Palomar 6 and UKS 1) in the Milky Way are detected as gamma-ray GC candidates. Especially for UKS 1, these are known as the faintest GCs in long-wavelength bands. Further data analysis has been performed for the four GCs. While no pulsars are determined in radio and/or X-ray wavelengths so far, their gamma-ray pulsation emissions are not found, and no significant gamma-ray flux variability is detected. The numbers of MSPs within the four GCs are estimated based on the assumption that the MSPs within each GC emit similar amounts of gamma-rays. The gamma-ray results reported here could help us better understand the nature of gamma-ray emission origins for GCs.

Flares in gamma-ray burst X-ray afterglows as prompt emission from slightly misaligned structured jets

ABSTRACT We develop a model to explain the flaring activity in gamma-ray burst X-ray afterglows within the framework of slightly misaligned observers to structured jets. We suggest that flares could be the manifestation of prompt dissipation within the core of the jet, appearing to a misaligned observer in the X-ray band because of less favourable Doppler boosting. These flares appear during the afterglow phase because of core–observer light travel delays. In this picture, the prompt emission recorded by this observer comes from material along their line of sight, in the lateral structure of the jet, outside the jet’s core. We start by laying down the basic analytical framework to determine the flares characteristics as a function of those of the gamma-ray pulse an aligned observer would see. We show that there is viable parameter space to explain flares with typical observing times and luminosities. We then analytically explore this model, showing that it naturally produces flares with small aspect ratios, as observed. We perform fits of our model to two Swift/XRT flares representing two different types of morphology, to show that our model can capture both. The ejection time of the core jet material responsible of the flare is a critical parameter. While it always remains small compared to the observed time of the flare, confirming that our model does not require very late central engine activity, late ejection times are strongly favoured, sometimes larger than the observed duration of the parent gamma-ray burst’s prompt emission as measured by T90.

A gamma-ray pulsar timing array constrains the nanohertz gravitational wave background.

After large galaxies merge, their central supermassive black holes are expected to form binary systems. Their orbital motion should generate a gravitational wave background (GWB) at nanohertz frequencies. Searches for this background use pulsar timing arrays, which perform long-term monitoring of millisecond pulsars at radio wavelengths. We used 12.5 years of Fermi Large Area Telescope data to form a gamma-ray pulsar timing array. Results from 35 bright gamma-ray pulsars place a 95% credible limit on the GWB characteristic strain of 1.0 × 10-14 at a frequency of 1 year-1. The sensitivity is expected to scale with tobs, the observing time span, as [Formula: see text]. This direct measurement provides an independent probe of the GWB while offering a check on radio noise models.

Search for glitches in gamma-ray pulsars with deep learning

Pulsar glitches are generally assumed to be an apparent manifestation of the superfluid interior of neutron stars. Most of them have been discovered and extensively studied by continuous monitoring of radio emission. The Fermi-LAT space telescope has revolutionized the field by uncovering a large population of gamma-ray pulsars. In this paper we employ the observations of gamma-ray pulsars to search for new glitches. We developed a method capable of detecting step-like frequency changes associated with glitches in sparse gamma-ray data. The method is based on the calculation of the weighted H-test statistics and consequent glitch identification by a convolutional neural network. The method demonstrates the high accuracy of the Monte Carlo set and is applicable to searching for pulsar glitches in real gamma-ray data.

Discovery, Timing, and Multiwavelength Observations of the Black Widow Millisecond Pulsar PSR J1555–2908

Abstract We report the discovery of PSR J1555−2908, a 1.79 ms radio and gamma-ray pulsar in a 5.6 hr binary system with a minimum companion mass of 0.052 M ⊙. This fast and energetic ( E ̇ = 3 × 10 35 erg s−1) millisecond pulsar was first detected as a gamma-ray point source in Fermi Large Area Telescope (LAT) sky survey observations. Guided by a steep-spectrum radio point source in the Fermi error region, we performed a search at 820 MHz with the Green Bank Telescope that first discovered the pulsations. The initial radio pulse timing observations provided enough information to seed a search for gamma-ray pulsations in the LAT data, from which we derive a timing solution valid for the full Fermi mission. In addition to the discovery and timing of radio and gamma-ray pulsations, we searched for X-ray pulsations using NICER but no significant pulsations were detected. We also obtained time-series r-band photometry that indicates strong heating of the companion star by the pulsar wind. Material blown off the heated companion eclipses the 820 MHz radio pulse during inferior conjunction of the companion for ≈10% of the orbit, which is twice the angle subtended by its Roche lobe in an edge-on system.

Glitches in four gamma-ray pulsars and inferences on the neutron star structure

ABSTRACT We present timing solutions from the Fermi-LAT observations of gamma-ray pulsars PSR J0835 − 4510 (Vela), PSR J1023−5746, PSR J2111+4606, and PSR J2229+6114. Data ranges for each pulsar extend over a decade. From data analysis, we have identified a total of 20 glitches, 11 of which are new discoveries. Among them, 15 glitches are large ones with Δν/ν ≳ 10−6. PSR J1023−5746 is the most active pulsar with glitch activity parameter being Ag = 14.5 × 10−7 yr−1 in the considered data span and should be a target for frequently glitching Vela-like pulsars in future observations. We have done fits within the framework of the vortex creep model for 16 glitches with Δν/ν ≳ 10−7. By theoretical analysis of these glitches, we are able to obtain important information on the structure of neutron star, including moments of inertia of the superfluid regions participated in glitches and coupling time-scales between various stellar components. The theoretical prediction for the time to the next glitch from the parameters of the previous one is found to be in qualitative agreement with the observed inter-glitch time-scales for the considered sample. Recoupling time-scales of the crustal superfluid are within the range of theoretical expectations and scale inversely with the spin-down rate of a pulsar. We also determined a braking index n = 2.63(30) for PSR J2229+6114 after glitch-induced contributions have been removed.

On-ground and on-orbit time calibrations of GECAM

ABSTRACT High time resolution and accuracy are of critical importance in the studies of timing analysis and time delay localization of gamma-ray bursts (GRBs), soft gamma-ray repeaters (SGRs) and pulsars. The Gravitational wave high-energy Electromagnetic Counterpart All-sky Monitor (GECAM) consisting of two micro-satellites, GECAM-A and GECAM-B, launched on 2020 December 10, is aimed at monitoring and locating X-ray and GRBs all over the sky. To achieve its scientific goals, GECAM is designed to have the highest time resolution (0.1 $\mu {\rm s}$) among all GRB detectors ever flown. Here, we make a comprehensive time calibration campaign including both on-ground and on-orbit tests to derive not only the relative time accuracy of GECAM satellites and detectors, but also the absolute time accuracy of GECAM-B. Using the on-ground calibration with a $\rm ^{22}Na$ radioactive source, we find that the relative time accuracy between GECAM-A and GECAM-B is about 0.15 $\mu {\rm s}$ (1σ). To measure the relative time accuracy between all detectors of a single GECAM satellite, cosmic-ray events detected on orbit are utilized since they could produce many secondary particles simultaneously record by multiple detectors. We find that the relative time accuracy among all detectors onboard GECAM-B is about 0.12 $\mu {\rm s}$ (1σ). Finally, we use the novel Li-CCF method to perform the absolute time calibration with Crab pulsar and SGR J1935+2154, both of which were jointly observed by GECAM-B and Fermi/GBM, and obtain that the time difference between GECAM-B and Fermi/GBM is 3.06 ± 6.04 $\mu {\rm s}$ (1σ).

Multiwavelength Spectral Analysis and Neural Network Classification of Counterparts to 4FGL Unassociated Sources

Abstract The Fermi-LAT unassociated sources represent some of the most enigmatic gamma-ray sources in the sky. Observations with the Swift-XRT and -UVOT telescopes have identified hundreds of likely X-ray and UV/optical counterparts in the uncertainty ellipses of the unassociated sources. In this work we present spectral fitting results for 205 possible X-ray/UV/optical counterparts to 4FGL unassociated targets. Assuming that the unassociated sources contain mostly pulsars and blazars, we develop a neural network classifier approach that applies gamma-ray, X-ray, and UV/optical spectral parameters to yield a descriptive classification of unassociated spectra into pulsars and blazars. From our primary sample of 174 Fermi sources with a single X-ray/UV/optical counterpart, we present 132 P bzr > 0.99 likely blazars and 14 P bzr < 0.01 likely pulsars, with 28 remaining ambiguous. These subsets of the unassociated sources suggest a systematic expansion to catalogs of gamma-ray pulsars and blazars. Compared to previous classification approaches our neural network classifier achieves significantly higher validation accuracy and returns more bifurcated P bzr values, suggesting that multiwavelength analysis is a valuable tool for confident classification of Fermi unassociated sources.

Follow-up of 27 radio-quiet gamma-ray pulsars at 110–190 MHz using the international LOFAR station FR606

Context. The Fermi Large Area Telescope has detected over 260 gamma-ray pulsars. About one quarter of these are labeled as radio-quiet, that is they either have radio flux densities < 30 μJy at 1400 MHz, or they are not detected at all in the radio domain. In the population of nonrecycled gamma-ray pulsars, the fraction of radio-quiet pulsars is higher, about one half. Aims. Most radio observations of gamma-ray pulsars have been performed at frequencies between 300 MHz and 2 GHz. However, pulsar radio fluxes increase rapidly with decreasing frequency, and their radio beams often broaden at low frequencies. As a consequence, some of these pulsars might be detectable at low radio frequencies even when no radio flux is detected above 300 MHz. Our aim is to test this hypothesis with low-frequency radio observations. Methods. We have observed 27 Fermi-discovered gamma-ray pulsars with the international LOw Frequency ARray (LOFAR) station FR606 in single-station mode. We used the LOFAR high band antenna band (110−190 MHz), with an average observing time of 13 h per target. Part of the data had to be discarded due to radio frequency interference. On average, we kept 9 h of observation per target after the removal of affected datasets, resulting in a sensitivity for pulse-averaged flux on the order of 1−10 mJy. Results. We do not detect radio pulsations from any of the 27 sources, and we establish stringent upper limits on their low-frequency radio fluxes. These nondetections are compatible with the upper limits derived from radio observations at other frequencies. We also determine the pulsars’ geometry from the gamma-ray profiles to see for which pulsars the low-frequency radio beam is expected to cross Earth. Conclusions. This set of observations provides the most constraining upper limits on the flux density at 150 MHz for 27 radio-quiet gamma-ray pulsars. In spite of the beam-widening expected at low radio frequencies, most of our nondetections can be explained by an unfavorable viewing geometry; for the remaining observations, especially those of pulsars detected at higher frequencies, the nondetection is compatible with insufficient sensitivity.

Young radio-loud gamma-ray pulsar light curve fitting

Context. Since the launch of the Fermi gamma-ray telescope, several hundred radio-loud gamma-ray pulsars have been detected, many belonging to millisecond pulsars but some belonging to the young pulsar population with spin periods longer than 30 ms. Aims. Observing simultaneously pulsed radio and gamma-ray emission from these stars helps to constrain the geometry and radiation mechanisms within their magnetosphere and to localize the multiple photon production sites. In this paper we fit the time-aligned gamma-ray light curves of young radio-loud gamma-ray pulsars. We assume a dipole force-free magnetosphere where radio photons emanate from high altitudes above the polar caps and gamma rays originate from outside the light cylinder, within the striped wind current sheet. Methods. We computed a full atlas of radio and gamma-ray pulse profiles depending on the magnetic axis obliquity and line-of-sight inclination with respect to the neutron star rotation axis. By applying a χ2 fitting technique, we were able to pin down accurately the magnetosphere geometry. Further constraints were obtained from radio polarization measurement following the rotating vector model, including aberration and retardation effects. Results. We find a good agreement between our model and the time-aligned single- or double-peaked gamma-ray pulsar observations. We deduce the magnetic inclination angle and the observer line of sight with respect to the rotation axis within a small error bar. The distinction between radio-loud or radio-quiet gamma-ray pulsars or only radio pulsars can entirely be related to the geometry of the associated emitting regions. Conclusions. The high-altitude polar cap model combined with the striped wind represents a minimalistic approach able to reproduce a wealth of gamma-ray pulse profiles for young radio pulsars. Based on self-consistent force-free simulations, it gives a full geometrical picture of the emission properties without resorting to detailed knowledge of the individual particle dynamics and energetics.

Modeling pulsed radio and gamma-ray emissions from PSRs J2302+4442 and J0659+1414

The multi-band observation, from radio to gamma-ray, plays a crucial role in constraining the emission physics and geometrical magnetospheric models of the pulsars. In this paper, We use three-dimensional magnetospheric model, with the joint of the annular gap (AG) and core gap (CG) model, to simulate the radio and gamma-ray light curves for two representative pulsars, a millisecond pulsar J2302+4442 and a young pulsar J0659+1414. It is found that for PSR J2302 + 4442, the simulated magnetic inclination angle α and viewing angle ζ are 34∘ and 46∘, and for PSR J0659 + 1414 are 45∘ and 33∘. This implies that the radio and gamma-ray pulse emission originates from different magnetospheric regions and the radiation geometry for millisecond and young pulsar is different. The studies show that the joint of the AG and CG model can describe the light curves not only for millisecond pulsars but also for young pulsars, and hence it can be used to explain the multi-wavelength observations of pulsars.

Organic glass scintillator (OGS) property comparisons to Stilbene, EJ-276 and BC-404

A new fast organic glass scintillator (OGS), recently developed at Sandia National Laboratories, has been proposed as a lower cost alternative to stilbene for detecting fast neutrons in intense gamma-ray fields, where excellent pulse-shape analysis (PSA) is required. In this paper we evaluate this proposition by measuring OGS’s scintillation properties and comparing them to three well known materials: stilbene, EJ-276, and BC-404. The measured properties were single photon light emission curves, coincidence time resolution (CTR), luminosity (photons/MeV), and figure of merit (FOM) for neutron/gamma PSA. From the light emission curves, we found that OGS has an 0.82 ns 10–90 risetime, close to EJ-276’s value of 0.81 ns and 25% faster than BC-404 and stilbene’s values at 0.96 and 1.01 ns, respectively. CTR values were measured from 75 to 325 keV, with OGS approaching 200 ps at 325 keV, compared to 250, 325 and 325 ps for BC-404, stilbene, and EJ-276, respectively. OGS had the highest luminosity, at 15,821 photons/MeV, compared to stilbene (13,054), BC-404 (8410), and EJ-276 (5522). For PSA, we studied neutron and gamma-ray pulse shapes as a function of energy and investigated various PSA algorithms, finding a properly selected tail/peak ratio to be generally best. OGS PSA FOM values were found to be twice as large as for EJ-276 and almost as good as stilbene’s – reaching 2.9, 1.5, and 3.2 at 1 MeVee respectively. Since OGS can be produced by lower cost casting techniques, this work supports further OGS development efforts.

Search for Periodic Emission from Five Gamma-Ray Pulsars at the Frequency of 111 MHz

The search for pulsar (periodic) emission of five gamma-ray pulsars was carried out using the summed power spectra and the summed periodograms. No harmonics corresponding to the known pulsar periods were found. The upper estimations of the integral flux density of the pulsars J0357+3205 (<0.5 mJy), J0554+3107 (<0.5 mJy), J1958+2846 (<0.5 mJy), J2021+4026 (<0.4 mJy), and J2055+2539 (<0.55 mJy) is obtained.

Nearby SN-associated GRB 190829A: Environment, Jet Structure, and VHE Gamma-Ray Afterglows

Abstract We present a self-consistent paradigm to interpret the striking features of nearby low-luminosity GRB 190829A. Its prompt gamma-ray lightcurve has two separated pulses. We propose that the interaction of the hard prompt gamma-ray photons ( E p = 624 − 303 + 2432 keV) of its initial pulse with the dusty medium (A V = 2.33) not only results in the second soft gamma-ray pulse (E p ∼ 12 keV) but also makes a pre-accelerated e ± -rich medium shell via the γγ annihilation. In this paradigm, we show that the observed radio, optical, and X-ray afterglow lightcurves are well-fitted with the forward shock model. Its jet is almost isotropic (θ j &gt; 1.0 rad) with a Lorentz factor of ∼35, and the electron density of the e ± -rich medium shell is ∼15 cm−3, which is about seven times higher than the electron density of its normal surrounding medium. The GRB ejecta catches up with and propagates into the e ± -rich medium shell at a region of R = (4.07–6.46) × 1016 cm. This results in a bright afterglow bump at ∼103 seconds after the GRB trigger. The predicted very high energy (VHE) gamma-ray emission from the synchrotron self-Compton process agrees with the H.E.S.S. observation. The derived broadband spectral energy distribution shows that GRB 190829A like nearby GRBs would be promising targets of the VHE gamma-ray telescopes, such as H.E.S.S., MAGIC, and CTA (Cerenkov Telescope Arrays).

ResNet and CycleGAN for pulse shape discrimination of He-4 detector pulses: Recovering pulses conventional algorithms fail to label unanimously

Pulse shape discrimination (PSD) capable detectors, such as He-4, that respond to neutron and gamma-ray interactions have a threshold deposited energy value below which n/γ discrimination vanishes when using conventional PSD algorithms. Recent attempts in applying supervised learning based artificial neural networks for PSD use the pulses in the separated regions to train the networks so they can be used to classify another set of separated pulses. In doing so, pulses previously indistinguishable are not recovered for classification, which would have increased the number of neutron and gamma-ray pulses that could be used for further analysis. Assuming the reason why conventional PSD algorithms have unseparated regions is because the parameter space of the algorithms fail to capture the intrinsic (but subtle) distinguishing behavior of some of the neutron and gamma-ray pulses, a cycle-consistent generative adversarial network (CycleGAN) was trained to amplify those differences and extract well separated neutron and gamma-ray clusters. Results show that, once the network is trained with pulses from separated and unseparated regions, it was able to transform the pulses in the unseparated region to improve the PSD. Subsequent n/γ classification was performed using deep residual network (ResNet) that takes pulses with 512 data points as an input. Two different ResNets were explored – simple ResNet and modified ResNet which takes segmented pulse inputs in the first layer and the corresponding time axis values in the last hidden layer. The later approach enables the network to extract time correlated pulse features to enhance its ability to capture the pulse behaviors relevant for PSD. Although it achieves slightly lower accuracy, 99.41% versus 99.89%, based on simply counting the number of correct n/γ labels assigned, compared to the simple ResNet, the modified ResNets architecture was able to decreases the cross-entropy loss function by half, which implies that the correct n/γ labels assigned are less likely to be accidental. PSD parameter distributions based on n/γ classification by ResNet before and after transforming unseparated pulses using CycleGAN show that by enhancing the separation between neutrons and gamma-rays, the transformation helps improve the performance of classifier networks that are trained using labeled dataset. The enhancement of neutron and gamma-ray separation by the CycleGAN increased the PSD figure of merit (FOM) by up to 70% in some regions. The results show that, if a given detector achieves clear separation between neutron and gamma-ray pulses in any energy region, such neural network approaches can help lower the energy threshold for the separation and increasing the number of neutron and gamma-ray pulses that can be used for further analysis.

Constraining millisecond pulsar geometry using time-aligned radio and gamma-ray pulse profile

Context. Since the launch of the Fermi Gamma-Ray Space Telescope, several hundred gamma-ray pulsars have been discovered, some being radio-loud and some radio-quiet with time-aligned radio and gamma-ray light curves. In the second Fermi Pulsar Catalogue, 117 new gamma-ray pulsars have been reported based on three years of data collected by the Large Area Telescope on the Fermi satellite, providing a wealth of information such as the peak separation Δ of the gamma-ray pulsations and the radio lag δ between the gamma-ray and radio pulses. Aim. We selected several radio-loud millisecond gamma-ray pulsars with period P in the range 2–6 ms and showing a double peak in their gamma-ray profiles. We attempted to constrain the geometry of their magnetosphere, namely the magnetic axis and line-of-sight inclination angles for each of these systems. Method. We applied a force-free dipole magnetosphere from the stellar surface up to the striped wind region – well outside the light cylinder – to fit the observed pulse profiles in gamma-rays, consistently with their phase alignment with the radio profile. In deciding whether a fitted curve is reasonable or not, we employed a least-square method to compare the observed gamma-ray intensity with that found from our model, emphasising the amplitude of the gamma-ray peaks, their separation, and the phase lag between radio and gamma-ray peaks. Results. We obtained the best fits and reasonable parameters in agreement with observations for ten millisecond pulsars. Eventually, we constrained the geometry of each pulsar described by the magnetic inclination α and the light-of-sight inclination ζ. We found that both angles are larger than approximately 45°.