Bright Pulsars Research Articles

CHIME/FRB Outriggers: KKO Station System and Commissioning Results

Localizing fast radio bursts (FRBs) to their host galaxies is an essential step to better understanding their origins and using them as cosmic probes. The Canadian Hydrogen Intensity Mapping Experiment (CHIME)/FRB Outriggers program aims to add very long baseline interferometry localization capabilities to CHIME, such that FRBs may be localized to tens of milliarcsecond precision at the time of their discovery, more than sufficient for host galaxy identification. The first-built outrigger telescope is the Outrigger (KKO), located 66 km west of CHIME. Cross-correlating KKO with CHIME can achieve arcsecond precision along the baseline axis while avoiding the worst effects of the ionosphere. Since the CHIME–KKO baseline is mostly east/west, this improvement is mostly in right ascension. This paper presents measurements of KKO’s performance throughout its commissioning phase, as well as a summary of its design and function. We demonstrate KKO’s capabilities as a standalone instrument by producing full-sky images, mapping the angular and frequency structure of the primary beam, and measuring feed positions. To demonstrate the localization capabilities of the CHIME–KKO baseline, we collected five separate observations each, for a set of 20 bright pulsars, and aimed to measure their positions to within 5″. All of these pulses were successfully localized to within this specification. The next two outriggers are expected to be commissioned in 2024 and will enable subarcsecond localizations for approximately hundreds of FRBs each year.

Finding Candidate TeV Halos among Very-high-energy Sources

We search for possible pulsar TeV halos among the very-high-energy (VHE) sources reported in different VHE surveys, among which in particular we use the results from the first Large High Altitude Air Shower Observatory catalog of γ-ray sources. Six candidates are found. They share similar properties of containing a middle-aged, γ-ray–bright pulsar in their positional error circles (the respective pulsars are J0248+6021, J0359+5414, J0622+3749, J0633+0632, J2006+3102, and J2238+5903), being in a rather clean field without any common Galactic VHE-emitting supernova remnants or (bright) pulsar wind nebulae (PWNe), and showing an absence of any γ-ray emissions in 0.1–500 GeV after removing the pulsars’ emissions. Combining these candidates with several reported (candidate) TeV halos, we obtain relationships between their luminosity at 50 TeV (L 50TeV) and the corresponding pulsars’ spin-down energy ( Ė ), which are L50TeV∼Ė0.9 and L50TeV/Ė∼6.4×10−4 , respectively. The relationships are nearly identical to previously reported ones. We probe possible connections between the extent/sizes of the VHE sources and the pulsars’ ages, and find a weak older-and-smaller trend. By comparing to the VHE detection results for PWNe, it is clear that the (candidate) TeV halos have hard emissions by either having power-law indices smaller than 2 in 1–25 TeV or by only being detected in 25–100 TeV. In addition, we also consider seven other VHE sources as possible TeV halos based on the results from different studies of them, but they do not fit cleanly with the properties listed above, indicating their potentially complex nature.

Flickering pulsations in bright X-ray pulsars: the evidence of gravitationally lensed and eclipsed accretion column

ABSTRACT It is expected that the extreme mass accretion rate onto strongly magnetized neutron stars results in the appearance of accretion columns above the stellar surface. For a distant observer, rotation of a star results in periodic variations of X-ray flux. Because the mass accretion rate fluctuates around the average value, the pulse profiles are not stable and demonstrate fluctuations as well. In the case of bright X-ray pulsars, however, pulse fluctuations are not solely attributed to variations in the mass accretion rate. They are also influenced by the variable height of the columns, which is dependent on the mass accretion rate. This study delves into the process of pulse profile formation in bright X-ray pulsars, taking into account stochastic fluctuations in the mass accretion rate, the corresponding variations in accretion column geometry, and gravitational bending. Our analysis reveals that potential eclipses of accretion columns by a neutron star during their spin period should manifest specific features in pulse profile variability. Applying a novel pulse profile analysis technique, we successfully detect these features in the bright X-ray transient V 0332+53 at luminosities $\gtrsim 2\times 10^{38}\, {\rm erg\ \rm s^{-1}}$. This detection serves as compelling evidence for the eclipse of an accretion column by a neutron star. Detection of the eclipse places constraints on the relation between neutron star mass, radius, and accretion column height. Specifically, we can establish an upper limit on the accretion column height, which is crucial for refining theoretical models of extreme accretion.

Coupling of radiation and magnetospheric accretion flow in ULX pulsars: radiation pressure and photon escape time

ABSTRACT The accretion flow within the magnetospheric radius of bright X-ray pulsars can form an optically thick envelope, concealing the central neutron star from the distant observer. Most photons are emitted at the surface of a neutron star and leave the system after multiple reflections by the accretion material covering the magnetosphere. Reflections cause momentum to be transferred between photons and the accretion flow, which contributes to the radiative force and should thus influence the dynamics of accretion. We employ Monte Carlo simulations and estimate the acceleration along magnetic field lines due to the radiative force as well as the radiation pressure across magnetic field lines. We demonstrate that the radiative acceleration can exceed gravitational acceleration along the field lines, and similarly, radiation pressure can exceed magnetic field pressure. Multiple reflections of X-ray photons back into the envelope tend to amplify both radiative force along the field lines and radiative pressure. We analyse the average photon escape time from the magnetosphere of a star and show that its absolute value is weakly dependent on the magnetic field strength of a star and roughly linearly dependent on the mass accretion rate being $\sim 0.1\, {\rm s}$ at $\dot{M}\sim 10^{20}\, {\rm g\, s^{-1}}$. At high mass accretion rates, the escape time can be longer than free-fall time from the inner disc radius.

Blind source separation for decomposing X-ray pulsar profiles

Accretion-powered X-ray pulsars offer a unique opportunity to study physics under extreme conditions. To fully exploit this potential, the interrelated problems of modelling radiative transport and the dynamical structure of the accretion flow must, however, be solved. This task is challenging both from a theoretical and observational point of view and is further complicated by a lack of direct correspondence between the properties of emission emerging from the neutron star and observed far away from it. In general, a mixture of emission from both poles of the neutron star viewed from different angles is indeed observed at some or even all phases of the pulse cycle. It is essential, therefore, to reconstruct the contributions of each pole to the observed flux in order to test and refine models describing the formation of the spectra and pulse profiles of X-ray pulsars. In this paper we propose a novel data-driven approach to address this problem using the pulse-to-pulse variability in the observed flux, and demonstrate its application to RXTE observations of the bright persistent X-ray pulsar Cen X-3. We then discuss the comparison of our results with previous work attempting to solve the same problem and how they can be qualitatively interpreted in the framework of a toy model describing emission from the poles of a neutron star.

Hitomi HXT deconvolution imaging of the Crab Nebula dazzled by the Crab pulsar

Abstract We develop a new deconvolution method to recover the precise Crab Nebula image taken by the Hitomi HXT, suppressing the artifact due to the bright Crab pulsar. We extend the Richardson–Lucy method, introducing two components corresponding to the nebula and pulsar with regularization for smoothness and flux, respectively, and performing simultaneous deconvolution of multi-pulse-phase images. The structures, including the torus and jets, seen in the deconvolved nebula image at the lowest energy band of 3.6–15 keV appear consistent with those identified in the high-resolution Chandra X-ray image. Above 15 keV, we confirm NuSTAR’s findings that the nebula size decreases in higher energy bands. We find that the north-east side of the nebula is fainter in higher energy bands. Our deconvolution method is applicable for any telescope images of faint diffuse objects containing a bright point source.

A Simultaneous Dual-frequency Scintillation Arc Survey of Six Bright Canonical Pulsars Using the Upgraded Giant Metrewave Radio Telescope

We use the upgraded Giant Metrewave Radio Telescope (uGMRT) to measure scintillation arc properties in six bright canonical pulsars with simultaneous dual-frequency coverage. These observations, at frequencies from 300 to 750 MHz, allowed for detailed analysis of arc evolution across frequency and epoch. We perform more robust determinations of frequency dependence for arc curvature, scintillation bandwidth, and scintillation timescale, and comparison between arc curvature and pseudo-curvature than allowed by single-frequency-band-per-epoch measurements, which we find to agree with theory and previous literature. We find a strong correlation between arc asymmetry and arc curvature, which we have replicated using simulations, and attribute to a bias in the Hough transform approach to scintillation arc analysis. Possible evidence for an approximately week-long timescale over which a given scattering screen dominates signal propagation was found by tracking visible scintillation arcs in each epoch in PSR J1136+1551. The inclusion of a 155-minute observation allowed us to resolve the scale of scintillation variations on short timescales, which we find to be directly tied to the amount of interstellar medium sampled over the observation. Some of our pulsars showed either consistent or emerging asymmetries in arc curvature, indicating instances of refraction across their lines of sight. Significant features in various pulsars, such as multiple scintillation arcs in PSR J1136+1551 and flat arclets in PSR J1509+5531, that have been found in previous works, were also detected. The simultaneous multiple-band observing capability of the upgraded GMRT shows excellent promise for future pulsar scintillation work.

An investigation of the state changes of PSR J2021+4026 and the Vela pulsar

ABSTRACT We report on long-term evolution of gamma-ray flux and spin-down rate of two bright gamma-ray pulsars, PSR J2021+4026 and Vela (PSR J0835−4510). PSR J2021+4026 shows repeated state changes in gamma-ray flux and spin-down rate. We report two new state changes, a first one from a low gamma-ray flux to a high flux that occurred around MJD 58910, and a second one from high to low flux that occurred around MJD 59510. We find that the flux changes associated with these two state changes are smaller than those determined in the previous events, and the waiting time of the new state change from the high gamma-ray flux to low gamma-ray flux is significantly shorter than previous events. Since the waiting time-scale of the quasi-periodic state changes of PSR J2021+4026 is similar to the waiting time-scale of the glitch events of the Vela pulsar, we search for the state change of the gamma-ray emission of the Vela pulsar to investigate the possibility that the glitching process is the trigger of the state change of PSR J2021+4026. For the Vela pulsar, the flux of the radio pulses briefly decreased around the 2016 glitch, suggesting that the glitch may have affected the structure of the magnetosphere. Nevertheless, we could not find any significant change of the gamma-ray emission properties using 15 yr of Fermi-LAT data. Overall, it seems inconclusive that a glitch-like process similar to that occurred to the Vela pulsar triggers the structure change of the global magnetosphere and causes state changes of PSR J2021+4026. Further and deep investigations to clarify the mechanism of the mode change for PSR J2021+4026 are required.

Apparent luminosity and pulsed fraction affected by gravitational lensing of accretion columns in bright X-ray pulsars

ABSTRACT The luminosity of X-ray pulsars is their key parameter determining the geometry and physical conditions of the accretion flow both on the spatial scales of a binary system and on much smaller scales of emitting regions located close to the stellar surface. Traditionally, the luminosity of X-ray pulsars is estimated out of the X-ray energy flux averaged over the pulsed period and the estimated distance to the source. Due to the anisotropy of X-ray emission, the luminosity estimated on the base of the observed pulse profile can differ from the actual one. Super-cw2ritical X-ray pulsars with accretion columns are of particular interest because the X-ray flux from columns is a matter of strong gravitational lensing by a neutron star. Using toy model of an accretion column, we simulate beam patterns in super-critical X-ray pulsars, construct theoretical pulse profiles for different geometries and mutual orientations of pulsars and distant observers and show that despite strong light bending, the typical deviation of the apparent luminosity from the actual one is $\sim 20~{{\ \rm per \, cent}}$ only, and in $\sim 90~{{\ \rm per \, cent}}$ of cases, the apparent luminosity 0.8L ≲ Lapp ≲ 1.25L. However, the shape of the pulse profiles is strongly affected by the geometry of the emitting region. We show that the appearance and growth of accretion columns tend to be accompanied by an increase of observed pulsed fraction, which is in agreement with the recent observations of bright X-ray transients.

An investigation of the ‘10 keV feature’ in the spectra of accretion powered X-ray pulsars with NuSTAR

ABSTRACT Some of the accreting X-ray pulsars are reported to exhibit a peculiar spectral feature at ∼10 keV, known as the ‘10 keV feature’. The feature has been characterized as either an emission line or an absorption line, and its origin is unknown. It has been found in multiple observations of the same source by different observatories, but not all the observations of any particular source consistently showed the presence of it. In this work, we have carried out a systematic investigation for the presence of the ‘10 keV feature’ using data from NuSTAR, a low background spectroscopic observatory having uninterrupted wide band coverage on either side of 10 keV. We performed a systematic spectral analysis on 58 archival NuSTAR observations of 30 bright X-ray pulsars. The 3–79 keV spectral continua of these selected sources were fitted with a model chosen on the basis of its fitting quality in 3–15 keV and model simplicity, and then inspected for the presence of the ‘10 keV feature’. Our analysis indicates the presence of such a feature in 16 out of 58 the NuSTAR observations of 11 different sources and is fitted with a Gaussian absorption model centred around 10 keV. Our analysis also suggests that such a feature could be wrongly detected if flare data is not analysed separately from persistent emission.

Bright X-ray pulsars as sources of MeV neutrinos in the sky

ABSTRACT High-mass accretion rate on to strongly magnetized neutron stars results in the appearance of accretion columns supported by the radiation pressure and confined by the strong magnetic field of a star. At mass accretion rates above $\sim 10^{19}\, {\rm g\, s^{-1}}$ , accretion columns are expected to be advective. Under such conditions, a noticeable part of the total energy release can be carried away by neutrinos of a MeV energy range. Relying on a simple model of the neutrino luminosity of accreting strongly magnetized neutron stars, we estimate the neutrino energy fluxes expected from six ULX pulsars known up to date and three brightest Be X-ray transits hosting magnetized neutron stars. Despite the large neutrino luminosity expected in ULX pulsars, the neutrino energy flux from the Be X-ray transients of our Galaxy, Small Magellanic Cloud (SMC), and Large Magellanic Cloud is dominant. However, the neutrino flux from the brightest X-ray transients is estimated to be below the isotropic background by two orders of magnitude at least, which makes impossible direct registration of neutrino emission from accreting strongly magnetized neutron stars nowadays.

Beam Pattern Evolution of Accreting X-Ray Pulsar 1A 0535+262 during Its 2020 Giant Outburst

We report on pulse profile decomposition analysis of bright transient X-ray pulsar 1A 0535+262 using broadband Insight-HXMT observations during a giant outburst of the source in 2020. We show that the observed pulse profile shape can be described in terms of a combination of two symmetric single-pole contributions for a wide range of energies and luminosities for a fixed geometry defining the basic geometry of the pulsar. This corresponds to a slightly distorted dipole magnetic field, i.e., one pole has to be offset by ∼12° from the antipodal position of the other pole. We reconstruct the intrinsic beam patterns of the pulsar assuming that the geometry is recovered from the decomposition analysis, and we find evidence for a transition between “pencil” and “fan” beams in energy ranges above the cyclotron line energy, which can be interpreted as a transition from sub- to supercritical accretion regimes associated with the onset of an accretion column. At lower energies, however, the beam pattern appears to be more complex and contains a substantial “fan” beam and an additional “pencil” beam component at all luminosities. The latter is not related to the accretion rate and is stronger in the fading phase of the outburst. We finally discuss the results in the context of other observational and theoretical findings earlier reported for the source in the literature.

Single-pulse studies of three millisecond pulsars

Abstract Single-pulse studies are important to understand the pulsar emission mechanism and the noise floor in precision timing. We study total intensity and polarimetry properties of three bright millisecond pulsars – PSRs J1022+1001, J1713+0747, and B1855+09 – that have detectable single pulses at multiple frequencies. We report for the first time the detection of single pulses from PSRs J1022+1001 and J1713+0747 at 4.5 GHz. In addition, for those two pulsars, the fraction of linear polarization in the average profile is significantly reduced at 4.5 GHz, compared to 1.38 GHz, which could support the expected deviation from a dipolar field closer to the pulsar surface. There is a hint of orthogonal modes in the single pulses of PSR J1713+0747. More sensitive multifrequency observations may be useful to confirm these findings. The jitter noise contributions at 1.38 GHz, scaled to one hour, for PSRs J1022+1001, J1713+0747, and B1855+09 are ≈135, ≈45, and ≈60 ns, respectively and are consistent with previous studies. We also show that selective bright-pulse timing of PSR J1022+1001 yields improved root-mean-square residuals of ≈22 $\mu$s, which is a factor of ≈3 better than timing using single pulses alone.

Electron Density Variations in the Interstellar Medium and the Average Frequency Profile of a Scintle from Pulsar Scintillation Spectra

We observed the scintillation pattern of nine bright pulsars at 324 MHz and three at 1.68 GHz and analyzed the wavenumber spectrum, which is related to electron density variations of the plasma turbulence of the interstellar medium (ISM). For all pulsars the frequency section of the autocorrelation function (ACF) of the dynamic spectra to at least 45% of the maximum corresponds to predictions of scattering theories with a range of power-law exponents of the wavenumber spectrum of 3.56 ≤ α ≤ 3.97 with errors ≤0.05 and a mean with standard deviation of 3.76 ± 0.13. The range includes α = 3.67 for the Kolmogorov spectrum. Similar results, although with larger errors, were found from the Fourier transform of the ACFs down to ∼10−3 of the maximum. No clear case of a distinction between thin-screen and extended-medium scattering models was found. The average frequency profile of the scintles can be characterized for steep wavenumber spectra with α ≲ 4 by a cusp with a somewhat rounded peak. For flatter spectra, down to at least α ∼ 3.56 the cusp with its peak becomes more pronounced and its decay steepens. We discuss our findings in the context of the scattering characteristics of the ISM.

Bright X-ray pulsars: how outflows influence beaming, pulsations and pulse phase lags

ABSTRACT Extreme accretion in X-ray pulsars (XRPs) results in radiation-driven outflows launched from the inner parts of the accretion disc. The outflows affect the apparent luminosity of the XRPs and their pulsations through the geometrical beaming. We model processes of geometrical beaming and pulse formation using Monte Carlo simulations. We confirm our earlier statement that strong amplification of luminosity due to the collimation of X-ray photons is inconsistent with a large pulsed fraction. Accounting for relativistic aberration due to possibly high outflow velocity (∼0.2c) does not affect this conclusion. We demonstrate that the beaming causes phase lags of pulsations. Within the opening angle of the accretion cavity formed by the outflows, phase lags tend to be sensitive to observers viewing angles. Variations in outflow geometry and corresponding changes of the phase lags might influence the detectability of pulsation in bright X-ray pulsars and ULXs. We speculate that the strong geometrical beaming is associated with large radiation pressure on the walls of accretion cavity due to multiple photons reflections. We expect that the mass-loss rate limits geometrical beaming: strong beaming becomes possible only under sufficiently large fractional mass-loss rate from the disc.

Upgraded GMRT survey for pulsars in globular clusters

Context. Globular clusters (GCs) contain a unique pulsar population, with many exotic systems that can form only in their dense stellar environments. Such systems are potentially very interesting for new tests of gravity theories and neutron-star mass measurements. Aims. The leap in sensitivity of the upgraded Giant Metrewave Radio Telescope (uGMRT) in India, especially at low radio frequencies (< 1 GHz), motivated a new search for radio pulsars in a group of eight southern GCs. We aim to image these clusters in order to have independent measurements of the radio fluxes of known pulsars and the identification of bright radio sources that could be pulsars missed by pulsation search pipelines due to their inherent limitations. Methods. The observations were conducted at 650 MHz (Band 4 receivers) on Terzan 5, NGC 6441, NGC 6440, and NGC 6544, and at 400 MHz (Band 3 receivers) on NGC 6652, NGC 6539, NGC 1851, and M 30. Segmented acceleration and jerk searches were performed on the data. Simultaneously, we obtained interferometric data on these clusters, which were later converted into radio images. Results. We discovered PSR J1835−3259B, a 1.83-ms pulsar in NGC 6652; this is in a near-circular wide orbit of 28.7-h with an unidentified low-mass (∼0.2 M⊙) companion, likely a helium white dwarf. We derived a ten-year timing solution for this system. We also present measurements of scattering, flux densities, and spectral indices for some of the previously known pulsars in these GCs. Conclusions. A significant fraction of the pulsars in these clusters have steep spectral indices. Additionally, we detected eight radio point sources not associated with any known pulsar positions in the radio images. There are four newly identified sources, three in NGC 6652 and one in NGC 6539, as well as one previously identified source in NGC 1851, NGC 6440, NGC 6544, and Terzan 5. Surprisingly, our images show that our newly discovered pulsar, PSR J1835−3259B, is the brightest pulsar in all GCs we have imaged; like other pulsars with broad profiles (Terzan 5 C and O), its flux density in the radio images is much larger than in its pulsations. This indicates that their pulsed emission is only a fraction of their total emission. The detection of radio sources outside the core radii but well within the tidal radii of these clusters show that future GC surveys should complement the search analysis by using the imaging capability of interferometers, and preferentially synthesise large number of search beams in order to obtain a larger field of view.

Single-pulse Variability in Gamma-Ray Pulsars

The Fermi Large Area Telescope receives ≪1 photon per rotation from any γ-ray pulsar. However, out of the billions of monitored rotations of the bright pulsars Vela (PSR J0835−4510) and Geminga (PSR J0633+1746), a few thousand have ≥2 pulsed photons. These rare pairs encode information about the variability of pulse amplitude and shape. We have cataloged such pairs and find the observed number to be in good agreement with simple Poisson statistics, limiting any amplitude variations to <19% (Vela) and <22% (Geminga) at 2σ confidence. Using an array of basis functions to model pulse-shape variability, the observed pulse phase distribution of the pairs limits the scale of pulse-shape variations of Vela to <13%, while for Geminga we find a hint of ∼20% single-pulse-shape variability most associated with the pulse peaks. If variations last longer than a single rotation, more pairs can be collected, and we have calculated upper limits on amplitude and shape variations for assumed coherence times up to 100 rotations, finding limits of ∼1% (amplitude) and ∼3% (shape) for both pulsars. Because a large volume of the pulsar magnetosphere contributes to γ-ray pulse production, we conclude that the magnetospheres of these two energetic pulsars are stable over one rotation and very stable on longer timescales. All other γ-ray pulsars are too faint for similar analyses. These results provide useful constraints on rapidly improving simulations of pulsar magnetospheres, which have revealed a variety of large-scale instabilities in the thin equatorial current sheets where the bulk of GeV γ-ray emission is thought to originate.

Single Pulse Variability in Gamma-ray Pulsars

The Fermi Large Area Telescope receives $\ll$1 photon per rotation from any $\gamma$-ray pulsar. However, out of the billions of monitored rotations of the bright pulsars Vela (PSR~J0835$-$4510) and Geminga (PSR~J0633$+$1746), a few thousand have $\geq$2 pulsed photons. These rare pairs encode information about the variability of pulse amplitude and shape. We have cataloged such pairs and find the observed number to be in good agreement with simple Poisson statistics, limiting any amplitude variations to $<$19% (Vela) and $<$22% (Geminga) at 2$\sigma$ confidence. Using an array of basis functions to model pulse shape variability, the observed pulse phase distribution of the pairs limits the scale of pulse shape variations of Vela to $<$13% while for Geminga we find a hint of $\sim$20% single-pulse shape variability most associated with the pulse peaks. If variations last longer than a single rotation, more pairs can be collected, and we have calculated upper limits on amplitude and shape variations for assumed coherence times up to 100 rotations, finding limits of $\sim$1% (amplitude) and $\sim$3% (shape) for both pulsars. Because a large volume of the pulsar magnetosphere contributes to $\gamma$-ray pulse production, we conclude that the magnetospheres of these two energetic pulsars are stable over one rotation and very stable on longer time scales. All other $\gamma$-ray pulsars are too faint for similar analyses. These results provide useful constraints on rapidly-improving simulations of pulsar magnetospheres, which have revealed a variety of large-scale instabilities in the thin equatorial current sheets where the bulk of GeV $\gamma$-ray emission is thought to originate.

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.

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.