arXiv subjects

A. K. Harding

Publications and source records attributed to A. K. Harding.

At least 19 recordsLinked to original sources

arXiv2026

The Radius of the Neutron Star PSR J0614-3329 from NICER Data

Neutron star radius measurements, particularly using X-ray data collected with the Neutron star Interior Composition Explorer (NICER), have provided invaluable information for models of cold, catalyzed matter at densities above that of nuclear saturation. Here we present an analysis of NICER data on the 318-Hz pulsar PSR J0614-3329, which has a mass ~1.4-1.5 solar masses determined from radio observations. The best-fitting model we explore has three uniform-temperature circular hot spots and yields a symmetric 68% credible range for the equatorial circumferential radius of 9.88-12.77 km. We also explore joint fits to the NICER data and the X-ray Multi-Mirror (XMM-Newton) data on this pulsar, but find that the models that best fit both data sets systematically underpredict the XMM-Newton data when, as is standard, it is assumed that the XMM-Newton background is known from observations of surrounding fields. Finally, we discuss the implications of our results, combined with data on other neutron stars, for the properties of the dense matter in neutron star cores.

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arXiv2025

Timing and Spectral Evolution of the Magnetar 1E 1841-045 in Outburst

We present the timing and spectral analyses of the NICER, NuSTAR, and IXPE observations of the magnetar 1E 1841-045 covering 82 days following its August 2024 bursting activity as well as radio observations utilizing MeerKAT and Effelsberg. We supplement our study with a historical NuSTAR and all 2024 pre-outburst NICER observations. The outburst is marked by an X-ray flux enhancement of a factor 1.6 compared to the historical level, predominantly driven by a newly-formed non-thermal emitting component with a photon index $\Gamma=1.5$. This flux showed a 20% decay at the end of our monitoring campaign. The radio monitoring did not reveal any pulsed radio emission with an upper-limit of 20 mJy and 50 mJy ms on the mean flux density and single pulse fluence, respectively. We detect a spin-up glitch at outburst onset with a $\Delta\nu=6.1\times10^{-8}$ Hz and a $\Delta\dot{\nu}=-1.4\times10^{-14}$ Hz s$^{-1}$, consistent with the near-universality of this behavior among the continuously-monitored magnetars. Most intriguingly, the 1E 1841-045 2-10 keV pulse profile is markedly different compared to pre-outburst; it shows a new, narrow (0.1 cycles) peak that appears to shift towards merging with the main, persistently-present, pulse. This is the second case of pulse-peak migration observed in magnetars after SGR 1830$-$0645, and the two sources exhibit a similar rate of phase shift. This implies that this phenomenon is not unique and might present itself in the broader population. The newly-formed peak for 1E 1841-045 is non-thermal, with emission extending to $\gtrsim20$ keV, in contrast to the case of SGR 1830$-$0645. Our results are consistent with an untwisting magnetic field bundle with migration towards the magnetic pole, perhaps accompanied by plastic motion of the crust.

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arXiv2024

Towards Modelling AR Sco: Generalised Particle Dynamics and Strong Radiation-Reaction Regimes

Numerical simulations of relativistic plasmas have become more feasible, popular, and crucial for various astrophysical sources with the availability of computational resources. The necessity for high-accuracy particle dynamics is especially highlighted in pulsar modelling due to the extreme associated electromagnetic fields and particle Lorentz factors. Including the radiation-reaction force in the particle dynamics adds even more complexity to the problem, but is crucial for such extreme astrophysical sources. We have also realised the need for such modelling concerning magnetic mirroring and particle injection models proposed for AR Sco, the first white dwarf pulsar. This paper demonstrates the benefits of using higher-order explicit numerical integrators with adaptive time step methods to solve the full particle dynamics with radiation-reaction forces included. We show that for standard test scenarios, namely various combinations of uniform $E$- and $B$-fields and a static dipole $B$-field, the schemes we use are equivalent to and in extreme field cases outperform standard symplectic integrators in accuracy. We show that the higher-order schemes have massive computational time improvements due to the adaptive time steps we implement, especially in non-uniform field scenarios and included radiation reaction where the particle gyro-radius rapidly changes. When balancing accuracy and computational time, we identified the adaptive Dormand-Prince eighth-order scheme to be ideal for our use cases. The schemes we use maintain accuracy and stability in describing the particle dynamics and we indicate how a charged particle enters radiation-reaction equilibrium and conforms to the analytic Aristotelian Electrodynamics expectations.

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arXiv2024

A phase-resolved Fermi-LAT analysis of the mode-changing pulsar PSR J2021+4026 shows hints of a multipolar magnetosphere

The goal of our work is to study the mode changes of the radio-quiet gamma-ray pulsar PSR J2021+4026 with improved detail. By accurately characterizing variations in the gamma-ray spectrum and pulse profile, we aim to relate the Fermi-LAT observations to theoretical models and interpret the mode changes in terms of variations in the structure of a multipolar dissipative magnetosphere. We continually monitored the rotational evolution and the gamma-ray flux of PSR J2021+4026 using more than 13 years of Fermi-LAT data with a binned likelihood approach. We clearly detect the previous mode changes and confirm a more recent mode change that occurred around June 2020. We investigated the features of the phase-resolved spectrum and pulse profile, and we inferred the macroscopic conductivity, the electric field parallel to the magnetic field, and the curvature radiation cutoff energy. These physical quantities are related to the spin-down rate and the gamma-ray flux and therefore are relevant to the theoretical interpretation of the mode changes. We computed the relative variations in the best-fit parameters, finding typical flux changes between 13% and 20%. Correlations appear between the gamma-ray flux and the spectral parameters, as the peak of the spectrum shifts by about 10% toward lower energies when the flux decreases. The analysis of the pulse profile reveals that the pulsed fraction of the light curve is larger when the flux is low. We introduced a simple magnetosphere model that combines a dipole field with a strong quadrupole component. We simulated magnetic field configurations to determine the positions of the polar caps for different sets of parameters, and we conclude that some configurations could explain the observed multiwavelength variability.

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arXiv2023

Multiwavelength observations of PSR J2021+4026 across a mode change reveal a phase shift in its X-ray emission

Context. We have investigated the multiwavelength emission of PSR J2021+4026, the only isolated gamma-ray pulsar known to be variable, which in October 2011 underwent a simultaneous change in gamma-ray flux and spin-down rate, followed by a second mode change in February 2018. Multiwavelength monitoring is crucial to understand the physics behind these events and how they may have affected the structure of the magnetosphere. Aims.The monitoring of pulse profile alignment is a powerful diagnostic tool for constraining magnetospheric reconfiguration. We aim to investigate timing or flux changes related to the variability of PSR J2021+4026 via multiwavelength observations, including gamma-ray observations from Fermi-LAT, X-ray observations from XMM-Newton, and a deep optical observation with the Gran Telescopio Canarias.Methods. We performed a detailed comparison of the timing features of the pulsar in gamma and X-rays and searched for any change in phase lag between the phaseogram peaks in these two energy bands. Although previous observations did not detect a counterpart in visible light, we also searched for optical emission that might have increased due to the mode change, making this pulsar detectable in the optical. Results.We have found a change in the gamma-to X-ray pulse profile alignment by 0.21$\pm$0.02 in phase, which indicates that the first mode change affected different regions of the pulsar magnetosphere. No optical counterpart was detected down to g'=26.1 and r'=25.3. Conclusions.We suggest that the observed phase shift could be related to a reconfiguration of the connection between the quadrupole magnetic field near the stellar surface and the dipole field that dominates at larger distances. This is consistent with the picture of X-ray emission coming from the heated polar cap and with the simultaneous flux and frequency derivative change observed during the mode changes.

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arXiv2022

Magnetar spin-down glitch clearing the way for FRB-like bursts and a pulsed radio episode

Magnetars are a special subset of the isolated neutron star family, with X-ray and radio emission mainly powered by the decay of their immense magnetic fields. Many attributes of magnetars remain poorly understood: spin-down glitches or the sudden reductions in the star's angular momentum, radio bursts reminiscent of extra-galactic Fast Radio Bursts (FRBs), and transient pulsed radio emission lasting months to years. Here we unveil the detection of a large spin-down glitch event ($|\Delta\nu/\nu| = 5.8_{-1.6}^{+2.6}\times10^{-6}$) from the magnetar SGR~1935+2154 on 2020 October 5 (+/- 1 day). We find no change to the source persistent surface thermal or magnetospheric X-ray behavior, nor is there evidence of strong X-ray bursting activity. Yet, in the subsequent days, the magnetar emitted three FRB-like radio bursts followed by a month long episode of pulsed radio emission. Given the rarity of spin-down glitches and radio signals from magnetars, their approximate synchronicity suggests an association, providing pivotal clues to their origin and triggering mechanisms, with ramifications to the broader magnetar and FRB populations. We postulate that impulsive crustal plasma shedding close to the magnetic pole generates a wind that combs out magnetic field lines, rapidly reducing the star's angular momentum, while temporarily altering the magnetospheric field geometry to permit the pair creation needed to precipitate radio emission.

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arXiv2022

Search for new cosmic-ray acceleration sites within the 4FGL catalog Galactic plane sources

Cosmic rays are mostly composed of protons accelerated to relativistic speeds. When those protons encounter interstellar material, they produce neutral pions which in turn decay into gamma rays. This offers a compelling way to identify the acceleration sites of protons. A characteristic hadronic spectrum, with a low-energy break around 200 MeV, was detected in the gamma-ray spectra of four Supernova Remnants (SNRs), IC 443, W44, W49B and W51C, with the Fermi Large Area Telescope. This detection provided direct evidence that cosmic-ray protons are (re-)accelerated in SNRs. Here, we present a comprehensive search for low-energy spectral breaks among 311 4FGL catalog sources located within 5 degrees from the Galactic plane. Using 8 years of data from the Fermi Large Area Telescope between 50 MeV and 1 GeV, we find and present the spectral characteristics of 56 sources with a spectral break confirmed by a thorough study of systematic uncertainty. Our population of sources includes 13 SNRs for which the proton-proton interaction is enhanced by the dense target material; the high-mass gamma-ray binary LS~I +61 303; the colliding wind binary eta Carinae; and the Cygnus star-forming region. This analysis better constrains the origin of the gamma-ray emission and enlarges our view to potential new cosmic-ray acceleration sites.

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arXiv2022

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 whose orbital motion generates a gravitational wave background (GWB) at nanohertz frequencies. Searches for this background utilize pulsar timing arrays, which perform long-term monitoring of millisecond pulsars (MSPs) at radio wavelengths. We use 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 $1.0\times10^{-14}$ at 1 yr$^{-1}$, which scales as the observing time span $t_{\mathrm{obs}}^{-13/6}$. This direct measurement provides an independent probe of the GWB while offering a check on radio noise models.

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arXiv2022

X-ray burst and persistent emission properties of the magnetar SGR 1830-0645 in outburst

We report on NICER X-ray monitoring of the magnetar SGR 1830-0645 covering 223 days following its October 2020 outburst, as well as Chandra and radio observations. We present the most accurate spin ephemerides of the source so far: $\nu=0.096008680(2)$~Hz, $\dot{\nu}=-6.2(1)\times10^{-14}$~Hz~s$^{-1}$, and a significant second and third frequency derivative terms indicative of non-negligible timing noise. The phase-averaged 0.8--7~keV spectrum is well fit with a double-blackbody (BB) model throughout the campaign. The BB temperatures remain constant at 0.46 and 1.2 keV. The areas and flux of each component decreased by a factor of 6, initially through a steep decay trend lasting about 46 days followed by a shallow long-term one. The pulse shape in the same energy range is initially complex, exhibiting three distinct peaks, yet with clear continuous evolution throughout the outburst towards a simpler, single-pulse shape. The rms pulsed fraction is high and increases from about 40% to 50%. We find no dependence of pulse shape or fraction on energy. These results suggest that multiple hotspots, possibly possessing temperature gradients, emerged at outburst-onset, and shrank as the outburst decayed. We detect 84 faint bursts with \nicer, having a strong preference for occurring close to the surface emission pulse maximum the first time this phenomenon is detected in such a large burst sample. This likely implies a very low altitude for the burst emission region, and a triggering mechanism connected to the surface active zone. Finally, our radio observations at several epochs and multiple frequencies reveal no evidence of pulsed or burst-like radio emission.

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arXiv2022

Pulse Peak Migration during the Outburst Decay of the Magnetar SGR 1830-0645: Crustal Motion and Magnetospheric Untwisting

Magnetars, isolated neutron stars with magnetic field strengths typically $\gtrsim10^{14}$~G, exhibit distinctive months-long outburst epochs during which strong evolution of soft X-ray pulse profiles, along with nonthermal magnetospheric emission components, is often observed. Using near-daily NICER observations of the magnetar SGR 1830-0645 during the first 37 days of a recent outburst decay, a pulse peak migration in phase is clearly observed, transforming the pulse shape from an initially triple-peaked to a single-peaked profile. Such peak merging has not been seen before for a magnetar. Our high-resolution phase-resolved spectroscopic analysis reveals no significant evolution of temperature despite the complex initial pulse shape. Yet the inferred surface hot spots shrink during the peak migration and outburst decay. We suggest two possible origins for this evolution. For internal heating of the surface, tectonic motion of the crust may be its underlying cause. The inferred speed of this crustal motion is $\lesssim100$~m~day$^{-1}$, constraining the density of the driving region to $\rho\sim10^{10}$~g~cm$^{-3}$, at a depth of $\sim200$~m. Alternatively, the hot spots could be heated by particle bombardment from a twisted magnetosphere possessing flux tubes or ropes, somewhat resembling solar coronal loops, that untwist and dissipate on the 30-40~day timescale. The peak migration may then be due to a combination of field-line footpoint motion (necessarily driven by crustal motion) and evolving surface radiation beaming. These novel dataset paints a vivid picture of the dynamics associated with magnetar outbursts, yet it also highlights the need for a more generic theoretical picture where magnetosphere and crust are considered in tandem.

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arXiv2020

Einstein@Home Discovery of the Gamma-ray Millisecond Pulsar PSR J2039-5617 Confirms Its Predicted Redback Nature

The Fermi Large Area Telescope gamma-ray source 3FGL J2039.6$-$5618 contains a periodic optical and X-ray source that was predicted to be a "redback" millisecond pulsar (MSP) binary system. However, the conclusive identification required the detection of pulsations from the putative MSP. To better constrain the orbital parameters for a directed search for gamma-ray pulsations, we obtained new optical light curves in 2017 and 2018, which revealed long-term variability from the companion star. The resulting orbital parameter constraints were used to perform a targeted gamma-ray pulsation search using the Einstein@Home distributed volunteer computing system. This search discovered pulsations with a period of 2.65 ms, confirming the source as a binary MSP now known as PSR J2039$-$5617. Optical light curve modelling is complicated, and likely biased, by asymmetric heating on the companion star and long-term variability, but we find an inclination $i > 60{\deg}$, for a low pulsar mass between $1.1 M_{\odot} < M_{\rm psr} < 1.6 M_{\odot}$ and a companion mass of 0.15--0.22 $M_{\odot}$, confirming the redback classification. Timing the gamma-ray pulsations also revealed significant variability in the orbital period, which we find to be consistent with quadrupole moment variations in the companion star, suggestive of convective activity. We also find that the pulsed flux is modulated at the orbital period, potentially due to inverse Compton scattering between high-energy leptons in the pulsar wind and the companion star's optical photon field.

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arXiv2020

Broadband X-ray Burst Spectroscopy of the FRB-Emitting Galactic Magnetar

Magnetars are young, magnetically-powered neutron stars possessing the strongest magnetic fields in the Universe. Fast Radio Bursts (FRBs) are extremely intense millisecond-long radio pulses of primarily extragalactic origin, and a leading attribution for their genesis focuses on magnetars. A hallmark signature of magnetars is their emission of bright, hard X-ray bursts of sub-second duration. On April 27th 2020, the Galactic magnetar SGR J1935+2154 emitted hundreds of X-ray bursts in a few hours. One of these temporally coincided with an FRB, the first detection of an FRB from the Milky Way. Here we present spectral and temporal analyses of 24 X-ray bursts emitted 13 hours prior to the FRB and seen simultaneously with the NASA NICER and Fermi/GBM missions in their combined energy range, 0.2 keV-30 MeV. These broadband spectra permit direct comparison with the spectrum of the FRB-associated X-ray burst (FRB-X). We demonstrate that all 24 NICER/GBM bursts are very similar temporally, albeit strikingly different spectrally, from FRB-X. The singularity of the FRB-X burst is perhaps indicative of an uncommon locale for its origin. We suggest that this event originated in quasi-polar open or closed magnetic field lines that extend to high altitudes.

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arXiv2020

A radiatively-quiet glitch and anti-glitch in the magnetar 1E 2259+586

We report on the timing and spectral properties of the soft X-ray emission from the magnetar 1E 2259+586 from January 2013, $\sim 8$ months after the detection of an anti-glitch, until September 2019, using the Neil Gehrels Swift and NICER observatories. During this time span, we detect two timing discontinuities. The first, occurring around 5 years after the April 2012 anti-glitch, is a relatively large spin-up glitch with a fractional amplitude $\Delta\nu/\nu=1.24(2)\times10^{-6}$. We find no evidence for flux enhancement or change in the spectral or pulse profile shape around the time of this glitch. This is consistent with the picture that a significant number of magnetar spin-up glitches are radiatively-quiet. Approximately 1.5 years later in April 2019, 1E 2259+586 exhibited an anti-glitch with spin-down of a fractional amplitude $\Delta\nu/\nu=-5.8(1)\times10^{-7}$; similar to the fractional change detected in 2012. We do not, however, detect any change to the pulse-profile shape or increase in the rms pulsed flux of the source, nor do we see any possible bursts from its direction around the time of the anti-glitch; all of which occurred during the 2012 event. Hence, similar to spin-up glitches, anti-glitches can occur silently. This may suggest that these phenomena originate in the neutron star interior, and that their locale and triggering mechanism do not necessarily have to be connected to the magnetosphere. Lastly, our observations suggest that the occurrence rate of spin-up and spin-down glitches is about the same in 1E 2259+586, with the former having a larger net fractional change.

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arXiv2019

PSR J0030+0451 Mass and Radius from NICER Data and Implications for the Properties of Neutron Star Matter

Neutron stars are not only of astrophysical interest, but are also of great interest to nuclear physicists, because their attributes can be used to determine the properties of the dense matter in their cores. One of the most informative approaches for determining the equation of state of this dense matter is to measure both a star's equatorial circumferential radius $R_e$ and its gravitational mass $M$. Here we report estimates of the mass and radius of the isolated 205.53 Hz millisecond pulsar PSR J0030+0451 obtained using a Bayesian inference approach to analyze its energy-dependent thermal X-ray waveform, which was observed using the Neutron Star Interior Composition Explorer (NICER). This approach is thought to be less subject to systematic errors than other approaches for estimating neutron star radii. We explored a variety of emission patterns on the stellar surface. Our best-fit model has three oval, uniform-temperature emitting spots and provides an excellent description of the pulse waveform observed using NICER. The radius and mass estimates given by this model are $R_e = 13.02^{+1.24}_{-1.06}$ km and $M = 1.44^{+0.15}_{-0.14}\ M_\odot$ (68%). The independent analysis reported in the companion paper by Riley et al. (2019) explores different emitting spot models, but finds spot shapes and locations and estimates of $R_e$ and $M$ that are consistent with those found in this work. We show that our measurements of $R_e$ and $M$ for PSR J0030$+$0451 improve the astrophysical constraints on the equation of state of cold, catalyzed matter above nuclear saturation density.

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arXiv2019

Modelling the polarisation signatures detected from the first white dwarf pulsar AR Sco

Marsh et al. detected radio and optical pulsations from the binary system AR Scorpii (AR Sco). This system, with an orbital period of 3.56 h, is composed of a cool, low-mass star and a white dwarf with a spin period of 1.95 min. Optical observations by Buckley et al. showed that the polarimetric emission from the white dwarf is strongly linearly polarised ( up to $\sim40\%$) with periodically changing intensities. This periodic non-thermal emission is thought to be powered by the highly magnetised ($ 5 \times 10^{8} $ G) white dwarf that is spinning down. The morphology of the polarisation signal, namely the position angle plotted against the phase angle, is similar to that seen in many radio pulsars. In this paper, we demonstrate that we can fit the traditional pulsar rotating vector model to the optical position angle. We used a Markov-chain-Monte-Carlo technique to find the best fit for the model yielding a magnetic inclination angle of $\alpha = (86.6^{+3.0}_{-2.8})^{\circ}$ and an observer angle of $\zeta = (60.5^{+5.3}_{-6.1})^{\circ}$. This modelling supports the scenario that the synchrotron emission originates above the polar caps of the white dwarf pulsar and that the latter is an orthogonal rotator.

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arXiv2018

Assessment of a statistical approach that facilitates the constraint of pulsar geometry via dualband light curve fitting

The Large Area Telescope aboard the Fermi spacecraft has detected more than 200 $\gamma$-ray pulsars since its launch in 2008. By concurrently fitting standard geometric model light curves onto Fermi and radio data, researchers have constrained the inclination and observer angles of a number of pulsars. At first this was done by comparing observed and modelled light curves by eye, and later via statistical approaches. We fit modelled light curves of 16 pulsars to radio and $\gamma$-ray data by optimising a custom test statistic that we have developed for combining light curves across the two wavebands, taking their disparate errors into account. We present geometrical constraints found using this process, and compare them with results found by eye or using other statistical methods.

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arXiv2018

On the maximum pair multiplicity of pulsar cascades

We study electron-positron pair production in polar caps of energetic pulsars to determine the maximum multiplicity of pair plasma a pulsar can produce under the most favorable conditions. This paper complements and updates our study of pair cascades presented in Timokhin & Harding (2015) with more accurate treatment of the effects of ultra strong B>3x10^{12}G magnetic fields and emission processes of primary and secondary particles. We include pairs produced by curvature and synchrotron radiation photons as well as resonant Compton scattered photons. We develop a semi-analytical model of electron-positrons cascades which can efficiently simulate pair cascades with an arbitrary number of microphysical processes and use it to explore cascade properties for a wide range of pulsar parameters. We argue that the maximum cascade multiplicity can not exceed ~ a few x 10^5 and the multiplicity has a rather weak dependence on pulsar period on pulsar period. The highest multiplicity is achieved in pulsars with magnetic field 4x10^{12} 10^6K. We also derive analytical expressions for several physical quantities relevant for electromagnetic cascade in pulsars which may be useful in future works on pulsar cascades, including the upper limit on cascade multiplicity and various approximations for the parameter \chi, the exponential factor in the expression for photon attenuation in strong magnetic field.

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arXiv2017

Calibration of statistical methods used to constrain pulsar geometries via multiband light curve modelling

Since its launch in 2008, the Fermi Large Area Telescope (LAT) has detected over 200 -ray pulsars above 100 MeV. This population of pulsars is characterised by a rich diversity of light curve morphologies. Researchers have been using both the radio and -ray light curves to constrain the inclination and observer angles for each of these pulsars. At first, this was done using a by-eye technique and later via statistical approaches. We have also developed two novel statistical approaches that place the radio and -ray data on equal footing despite their disparate relative flux errors. We chose eleven pulsars from the Second Fermi Pulsar Catalog, both old and young, and applied these new techniques as well as the by-eye technique to constrain their geometric parameters using standard pulsar models. We present first results on our comparison of the best-fit parameters yielded by each of the aforementioned techniques. This will assist us in determining the utility of our new statistical approaches, and gauge the overlap of the best-fit parameters (plus errors) from each of the different methods. Such a statistical fitting approach will provide the means for further pulsar magnetospheric model development using light curve data.

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