Modelling pulsar emission in the high-energy and very-high-energy regimes
M. Barnard
备注：
PhD thesis supervised by C. Venter and A. K. Harding and accepted by the North-West University (Potchefstroom) South Africa in February 2021, 114 pages, 50 figures. Abstract abridged
The Fermi Large Area Telescope has revolutionised the $γ$-ray pulsar field, increasing the population to over 250 detected pulsars. The majority display spectra with exponential cutoffs in a narrow range around a few GeV. Models predicted cutoffs up to 100 GeV; it was therefore not expected that pulsars would be visible in the very-high-energy ($>$100 GeV) regime. Subsequent surprise discoveries by ground-based telescopes of pulsed emission from four pulsars above tens of GeV have marked the beginning of a new era, raising important questions about the electrodynamics and local environment of pulsar magnetospheres. Detection of the Vela pulsar by H.E.S.S. (20-120 GeV) and Fermi provides evidence for a curved spectrum. We posit this to result from curvature radiation via primary particles in the pulsar magnetosphere and current sheet. We present energy-dependent light curves using an extended slot gap and current sheet model and invoking a two-step accelerating $E$-field as motivated by kinetic simulations. I include a refined calculation of the curvature radius of particle trajectories, impacting the particle transport, predicted light curves, and spectra. The model reproduces the decrease of flux of the first light-curve peak relative to the second one, evolution of the bridge emission, near constant phase positions of peaks, and narrowing of pulses with increasing energy. We can fundamentally explain the first of these trends, since I found that the curvature radii of the particle trajectories in regions where the second $γ$-ray light curve peak originates are systematically larger than those associated with the first peak, implying a correspondingly larger cutoff for the second peak. An unknown azimuthal dependence of the $E$-field as well as uncertainty in the precise emission locale preclude a simplistic discrimination of emission mechanisms.
In recent years, surprise discoveries of pulsed emission from the Crab and Vela pulsars above 100 GeV have drawn renewed attention to this largely unexplored region of the energy range. In this paper, we discuss example light curves due to curvature emission, with good resolution in the different energy bands. Continued light curve modelling may help to discriminate between different emission mechanisms, as well as constrain the location where emission is produced within the pulsar magnetosphere, including regions beyond the light cylinder.
A spatially-independent model that can be used to calculate the temporal evolution of the electron/ positron spectrum in a spherically expanding pulsar wind nebula is presented. The model is applied to the young nebula G21.5-0.9, as well as to the unidentified TeV sources HESS J1427-608 and HESS J1507-622. The parameters derived from the model strengthens the idea that the unidentified sources can be identified as evolved pulsar wind nebulae.
The Fermi Large Area Telescope, in collaboration with several groups from the radio community, have had marvellous success at uncovering new gamma-ray millisecond pulsars (MSPs). In fact, MSPs now make up a sizable fraction of the total number of known gamma-ray pulsars. The MSP population is characterized by a variety of pulse profile shapes, peak separations, and radio-to-gamma phase lags, with some members exhibiting nearly phase-aligned radio and gamma-ray light curves (LCs). The MSPs' short spin periods underline the importance of including special relativistic effects in LC calculations,…
We present the results of modelling of the radio spectrum evolution and dispersion measure variations of PSR B1259-63, a pulsar in a binary system with Be star LS 2883. We base our model on a hypothesis that the observed variations of the spectrum are caused by thermal free-free absorption occurring in the pulsar surroundings. We reproduce the observed pulsar spectral shapes in order to examine the influence of the stellar wind of LS 2883 and the equatorial disc on the pulsar's radiation. The simulations of the pulsar's radio emission and its consequent free-free absorption give us an insight …
In the last decade, the relativistic magnetohydrodynamic (MHD) modelling of pulsar wind nebulae, and of the Crab nebula in particular, has been highly successful, with many of the observed dynamical and emission properties reproduced down to the finest detail. Here, we critically discuss the results of some of the most recent studies: namely the investigation of the origin of the radio emitting particles and the quest for the acceleration sites of particles of different energies along the termination shock, by using wisps motion as a diagnostic tool; the study of the magnetic dissipation proce…
The Fermi Large Area Telescope (LAT) has recently reported the detection of pulsed gamma-rays from 6 young pulsars (J0631+1036, J0659+1414, J0742-2822, J1420-6048, J1509-5850, and J1718-3825), all exhibiting single-peaked pulse profiles (Weltevrede et al., 2010). High-quality radio polarization data are also available for 5 of these pulsars, allowing derivation of constraints on their viewing geometries. We obtain independent constraints on the viewing geometries of these pulsars by using a geometric pulsar emission code to model the Fermi LAT and radio light curves. We find fits for the magne…
We modelled the radio and gamma-ray light curves of millisecond pulsars using outer gap, two-pole caustic, low-altitude slot gap, and pair-starved polar cap geometric models, combined with a semi-empirical conal radio model. We find that no model fits all cases, with the outer gap and two-pole caustic models providing best fits for comparable numbers of millisecond pulsar light curves. We find a broad distribution of best-fit inclination angles as well as a clustering at large observer angles. The outer gap model furthermore seems to require relatively larger inclination angles, while the two-…
Guillemot et al. recently reported the discovery of $γ$-ray pulsations from the 22.7ms pulsar (pulsar A) in the famous double pulsar system J0737-3039A/B. The $γ$-ray light curve (LC) of pulsar A has two peaks separated by approximately half a rotation, and these are non-coincident with the observed radio and X-ray peaks. This suggests that the $γ$-ray emission originates in a part of the magnetosphere distinct from where the radio and X-ray radiation is generated. Thus far, three different methods have been applied to constrain the viewing geometry of pulsar A (its inclination and observer an…
We present a numerical study of the properties of the flow produced by the collision of a magnetized anisotropic pulsar wind with the circumbinary environment. We focus on studying the impact of the high wind magnetization on the geometrical structure of the shocked flow. This work is an extension of our earlier studies that focused on a purely hydrodynamic interaction and weak wind magnetization. We consider the collision in the axisymmetric approximation, that is, the pulsar rotation axis is assumed to be oriented along the line between the pulsar and the optical star. The increase of the ma…
In this paper, we present a numerical study of the properties of the flow produced by the collision of a magnetized anisotropic pulsar wind with its environment in binary system. We compare the impact of both the magnetic field and the wind anisotropy to the benchmark case of a purely hydrodynamical (HD) interaction of isotropic winds, which has been studied in detail by Bogovalov et al. (2008). We consider the interaction in axisymmetric approximation, i.e. the pulsar rotation axis is assumed to be oriented along the line between the pulsar and the optical star and the effects related to the …
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 ele…
We present the first detailed joint modelling of both the timing and spectral properties during the outburst decay of transient anomalous X-ray pulsars. We consider the two sources XTE J1810-197 and CXOU J164710.2-455216, and describe the source decline in the framework of a twisted magnetosphere model, using Monte Carlo simulations of magnetospheric scattering and mimicking localized heat deposition at the NS surface following the activity. Our results support a picture in which a limited portion of the star surface close to one of the magnetic poles is heated at the outburst onset. The subse…
Globular clusters are source of gamma-ray radiation. At GeV energies, their emission is attributed to magnetospheric activity of millisecond pulsars residing in the clusters. Inverse Compton scattering of ambient photon fields on relativistic particles diffusing through cluster environment is thought to be the source of GeV-TeV emission of globular clusters. Using pair starved polar cap model gamma-ray emission from synthetic millisecond pulsar was modelled. In addition to pulsar emission characteristics, the synthetic pulsar model yielded spectra of electrons escaping pulsar magnetosphere. To…
We discuss the role of particle-in-cell (PIC) simulations in unveiling the origin of the emitting particles in PWNe. After describing the basics of the PIC technique, we summarize its implications for the quiescent and the flaring emission of the Crab Nebula, as a prototype of PWNe. A consensus seems to be emerging that, in addition to the standard scenario of particle acceleration via the Fermi process at the termination shock of the pulsar wind, magnetic reconnection in the wind, at the termination shock and in the Nebula plays a major role in powering the multi-wavelength signatures of PWNe…
Pulse profile modelling of accreting millisecond pulsars with disc occultation and its impact on parameter inference
Nanjing University（南京大学）；Key Laboratory of Modern Astronomy and Astrophysics (Nanjing University), Ministry of Education（南京大学现代天文与天体物理教育部重点实验室）；Anton Pannekoek Institute for Astronomy, University of Amsterdam（阿姆斯特丹大学安东·潘内克天文研究所）；Gravitation and Astroparticle Physics Amsterdam (GRAPPA), University of Amsterdam（阿姆斯特丹大学引力与天体粒子物理学阿姆斯特丹中心）；University of Helsinki（赫尔辛基大学）；University of Turku（图尔库大学）
Pulsars emit pulsed emission across the entire electromagnetic spectrum and their light curve phenomenology is strongly dependent on energy. This is also true for the gamma-ray waveband. Continued detections by Fermi Large Area Telescope in the GeV band and ground-based Cherenkov telescopes in the TeV band (e.g., Crab and Vela above 1 TeV) raise important questions about our understanding of the electrodynamics and local environment of pulsar magnetospheres. We model energy-dependent light curves (as a function of geometry, e.g., pulsar inclination and observer angle) in the curvature radiatio…
We present results from a leptonic emission code that models the spectral energy distribution of a pulsar wind nebula by solving a Fokker-Planck-type transport equation and calculating inverse Compton and synchrotron emissivities. We have created this time-dependent, multi-zone model to investigate changes in the particle spectrum as they traverse the pulsar wind nebula, by considering a time and spatially-dependent B-field, spatially-dependent bulk particle speed implying convection and adiabatic losses, diffusion, as well as radiative losses. Our code predicts the radiation spectrum at diffe…
In the last decade ground-based Imaging Atmospheric Cherenkov Telescopes have discovered roughly 30 pulsar wind nebulae at energies above 100 GeV. We present first results from a leptonic emission code that models the spectral energy density of a pulsar wind nebula by solving the Fokker-Planck transport equation and calculating inverse Compton and synchrotron emissivities. Although models such as these have been developed before, most of them model the geometry of a pulsar wind nebula as that of a single sphere. We have created a time-dependent, multi-zone model to investigate changes in the p…
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 sig…
We investigate broadband emission properties of the pulsar wind nebula (PWN) 3C 58 using a spectral energy distribution (SED) model. We attempt to match simultaneously the broadband SED and spatial variations of X-ray emission in the PWN. We further the model to explain a possible far-IR feature of which a hint is recently suggested in 3C 58: a small bump at $\sim$$10^{11}$ GHz in the PLANCK and Herschel band. While external dust emission may easily explain the observed bump, it may be internal emission of the source implying an additional population of particles. Although significance for the…
An isolated pulsar is a rotating neutron star possessing a high magnetic dipole moment that generally makes a finite angle with its rotation axis. As a consequence, the emission of magnetic dipole radiation (MDR) continuously takes away its rotational energy. This process leads to a time decreasing angular velocity of the star that is usually quantified in terms of its braking index. While this simple mechanism is indeed the main reason for the spin evolution of isolated pulsars, it may not be the only cause of this effect. Most of young isolated pulsars present braking index values that are c…
We model the morphology and spectrum of a pulsar wind nebula using a leptonic emission code. This code is a time-dependent, multi-zone model that investigates the changes in the particle spectrum as they traverse the nebula. We calculate the synchrotron and inverse Compton emissivities at different positions in the nebula, obtaining the surface brightness versus the radius, and also the size of the nebula as a function of energy. We incorporate a time and spatially-dependent $B$-field, spatially-dependent bulk particle speed implying convection and adiabatic losses, diffusion, as well as radia…
Emission spectrum is calculated for a weak axisymmetric pulsar. Also calculated are the observed spectrum, efficiency, and the observed efficiency. The underlying flow of electrons and positrons turns out to be curiously intricate.
We have examined the cyclotron resonance instability developing in the relativistic out-flowing plasma in the pulsar magnetosphere. The instability condition leads to radio emission in the sub-GHz frequency regime which is likely to be seen as off-pulse emission. Recent studies have shown the presence of off-pulse emission in long period pulsars, and we demonstrate this plasma process to be an energetically viable mechanism.
It is conjectured that coherent re-emission of cyclotron resonance absorption could result in pulsar giant pulses. This conjecture seems reasonable as it can naturally explain the distribution of pulsars with giant pulses on the $P$-$\dot{P}$ diagram.
We apply a synchro-curvature spectral emission model based on characterizing the dynamics of magnetospheric particles to fit the phase-average spectra of the most extended database for the non-thermal spectra of pulsars. We consider 36 pulsars with well-determined non-thermal spectra from X-rays to gamma-rays. The sample includes Crab and Crab twin, for which the spectra extends even to the optical/ultraviolet and infrared energies. We find that the model --with just three physical parameters and a global scaling-- can fit the observations well across eight orders of magnitude for 18 of the 36…
$γ$-ray radiation from pulsars is usually thought to be mostly produced by the synchro-curvature losses of accelerated particles. Here we present a systematic study of all currently reported, good-quality Fermi-LAT pulsar spectral data. We do so by applying a model which follows the particle dynamics and consistently computes the emission of synchro-curvature radiation. By fitting observational data on a case by case basis, we are able to obtain constraints about the parallel electric field, the typical lengthscale over which particles emit the bulk of the detected radiation, and the number of…
PSR B1259-63/LS 2883 is a binary system in which a 48-ms pulsar orbits around a Be star in a high eccentric orbit with a long orbital period of about 3.4 yr. It is special for having asymmetric two-peak profiles in both the X-ray and the TeV light curves. Recently, an unexpected GeV flare was detected by $Fermi$ gamma-ray observatory several weeks after the last periastron passage. In this paper, we show that this observed GeV flare could be produced by the Doppler-boosted synchrotron emission in the bow shock tail. An anisotropic pulsar wind model, which mainly affects the energy flux injecti…
Nearby pulsars have been suggested as sources of $\sim$TeV $e^+/e^-$ Cosmic Ray (CR) excess on Earth. The High-Altitude Water Cherenkov Observatory (HAWC) detected extended TeV emission regions in the direction of two nearby middle-aged pulsars, Geminga and PSR B0656+14. By modeling the TeV emission as inverse Compton emission from electron-positron pairs diffusing in the interstellar medium (ISM), the HAWC collaboration derives a diffusion coefficient much smaller than the standard value in the vicinity of the two pulsars, which make them unlikely the origin of the positron excess. We propose…
I. There is growing evidence that pulsars' high energy emission is generated via Inverse Compton mechanism. II. The particles producing Crab flares, and possibly most of the Crab Nebula's high energy emission, are accelerated via reconnection events, and not at shock via Fermi mechanisms.
It is now known that the emission from radio pulsars can vary over a wide range of timescales, from fractions of seconds to decades. However, it is not yet known if long- and short-term emission variability are caused by the same physical processes. It has been observed that long-term emission variability is often correlated with rotational changes in the pulsar. We do not yet know if the same is true of short-term emission variability, as the rotational changes involved cannot be directly measured over such short timescales. To remedy this, we propose a continuous pulsar monitoring technique …
Electrons/positrons produced in a pulsar magnetosphere emit synchrotron radiation, which is widely believed as the origin of the non-thermal X-ray emission detected from pulsars. Particles are produced by curvature photons emitted from accelerated particles in the magnetosphere. These curvature photons are detected as pulsed $γ$-ray emissions from pulsars with age $\lesssim10^6$ yr. Using $γ$-ray observations and analytical model, we impose severe constraints on the synchrotron radiation as a mechanism of the non-thermal X-ray emission. In most middle-aged pulsars ($\sim10^5-10^6$ yr) which ph…
The search for radio emission from the gamma pulsar J0357+3205 in the meter wavelength range was carried out. Periodic emission was found in one of the 1,700 observation sessions. The average pulsar profile is single-component with a half-width of 20-25 ms. Estimation of the pulsar flux density is 14 mJy.
This chapter provides a phenomenological appraisal of the high-energy emission of millisecond pulsars. We comment on some of their properties as a population, as well as consider the especial cases of transitional pulsars, other redbacks, and black widow systems.
The light curves of gamma-ray pulsars detected by the Fermi Large Area Telescope show great variety in profile shape and position relative to their radio profiles. Such diversity hints at distinct underlying magnetospheric and/or emission geometries for the individual pulsars. We implemented an offset-dipole magnetic field in an existing geometric pulsar modelling code which already includes static and retarded vacuum dipole fields. In our model, this offset is characterised by a parameter epsilon (with epsilon = 0 corresponding to the static dipole case). We constructed sky maps and light cur…
The recent detection of pulsed $γ$-ray emission from the Vela pulsar in the $\sim10$ to 100 GeV range by H.E.S.S. promises an important potential to probe into the very high energy (VHE) radiation mechanisms of pulsars. The recent detection of pulsed $γ$-ray emission from the Vela pulsar in the $\sim10$ to 100 GeV range by H.E.S.S. promises an important potential to probe into the very high energy (VHE) radiation mechanisms of pulsars. We analyze achievable particle energies in the magnetosphere of the Vela pulsar, and calculate the resultant emission properties. Inverse Compton up-scattering …
In this contribution we review the recent progress in the modeling of Pulsar Wind Nebulae (PWN). We start with a brief overview of the relevant physical processes in the magnetosphere, the wind-zone and the inflated nebula bubble. Radiative signatures and particle transport processes obtained from 3D simulations of PWN are discussed in the context of optical and X-ray observations. We then proceed to consider particle acceleration in PWN and elaborate on what can be learned about the particle acceleration from the dynamical structures called "wisps" observed in the Crab nebula. We also discuss…
It is generally accepted that the pulsar magnetic field converts most of its rotational energy losses into radiation. In this paper, we propose an alternative emission mechanism, in which neither the pulsar rotational energy nor its magnetic field is involved. The emission mechanism proposed here is based on the hypothesis that the pulsar matter is stable only when moving with respect to the ambient medium at a velocity exceeding some threshold value. A decrease in velocity below this threshold value leads to the decay of matter with the emission of electromagnetic radiation. It is shown that …
To look for possible phenomenological connections between pulsar's timing properties and emissions from pulsar wind nebulae and their pulsars, we studied the power-law component of the X-ray emissions from 35 pulsar wind nebulae which have a detected pulsar in X-rays. Our major results are in the following: (1) The power-law component of the X-ray luminosities, in the energy range from 0.5 keV to 8 keV, of the nebulae and of the pulsar both show a strong correlation with the pulsar spin-down power ($\dot{E}$), consistent with earlier studies. However, equally significant correlations with the …
The wealth of high-energy (E > 50 MeV) and very-high-energy (E > 100 GeV) data accumulated over the past few years have provided unprecedented opportunities to probe pulsar emission models. The Fermi Large Area Telescope (LAT) has now detected over 200 gamma-ray pulsars of vastly different ages, providing an extensive dataset of spectra and light curves compared to a mere decade ago. Ground-based Cherenkov telescopes deepened our appreciation of the mysterious richness of the pulsar mechanism by a surprise detection of pulsed emission up to 1 TeV from the Crab pulsar. These discoveries positio…
Binary pulsars are affected by general relativity (GR), causing the spin axes of each pulsar to precess. We present polarimetric radio observations of PSR J1906+0746 that demonstrate the validity of the geometrical model of pulsar polarisation. We reconstruct the (sky-projected) polarisation emission map over the pulsar's magnetic pole and predict the disappearance of the detectable emission by 2028. Two additional tests of GR are performed in this system, including the spin-precession for strongly self-gravitating bodies. We constrain the relativistic treatment of the pulsar polarisation mode…
We review a physical model where the high brightness temperature of 10$^{25}-10^{30}$ K observed in pulsar radio emission is explained by coherent curvature radiation excited in the relativistic electron-positron plasma in the pulsar magnetosphere.
We present detailed optical photo-polarimetric observations of the recently-discovered white dwarf pulsar AR Scorpii. Our extensive dataset reveals that the polarized emission is remarkably stable and repeatable with spin, beat and orbital modulations. This has enabled us to construct a simple geometrical model which assumes that all of the optically polarized emission emanates from two diametrically opposed synchrotron emission regions on the white dwarf magnetosphere. We suggest that the observed polarimetric modulations occur as a result of an enhanced injection of relativistic electrons in…
We have revisited the problem of off-pulse emission in pulsars, where detailed search for the presence of low level radio emission outside the pulse window is carried out. The presence of off-pulse emission was earlier reported in two long period pulsars, PSR B0525+21 and B2046-16 at frequencies below 1 GHz using the Giant Meterwave Radio Telescope (GMRT). However, subsequent studies did not detect off-pulse emission from these pulsars at higher radio frequencies (> 1 GHz). We have carefully inspected the analysis scheme used in the earlier detections and found an anomaly with data editing rou…
I present a review of the main phenomenological properties at high energies related to massive gamma-ray binaries and I discuss some aspects of pulsar models for these objects.
Recent multi-frequency measurements of pulse widths W50 for the long-period pulsar J0250+5854 by Agar et al provide a unique insight to the emission process owing to its small polar-cap radius. The frequency-dependence of W50 can be simply understood as a consequence of the emitting plasma remaining under acceleration during the interval of radio emission. This is possible in a plasma of ions and protons but not in one of high-multiplicity electron-positron pairs. Extension of the model to the pulse profiles of the general pulsar population is considered briefly.
We perform spectral analyses of four bright $γ$-ray pulsars: PSR J0007+7303, Vela, Geminga and PSR J2021+3651 concentrating on the high-energy tails, defined as emission above 10\,GeV. The two competing models of pulsar $γ$-ray emission predict qualitatively different spectra well above the break energy: curvature emission predicts an exponential cut-off in the spectra, while the inverse-Compton scattering mechanism favors a power-law. We perform fits to the phase-averaged spectral energy distributions for each of the four pulsars. We find that in all cases both models fit the data equally wel…
Over the last fifty years since the discovery of pulsars, our understanding of where and how pulsars emit the radiation we observe has undergone significant revision. The location and mechanisms of high-energy radiation are intimately tied to the sites of particle acceleration. The evolution of emission models has paralleled the development of increasingly more sensitive telescopes, especially at high energies. I will review the history of pulsar emission modeling, from the early days of gaps at the polar caps, to outer gaps and slot gaps in the outer magnetosphere, to the present era of globa…
NASA's Fermi space telescope has provided us with a bountiful new population of gamma-ray sources following its discovery of 150 new gamma-ray pulsars. One common feature exhibited by all of these pulsars is the form of their spectral energy distribution, which can be described by a power law followed by a spectral break occurring between $\sim$1 and $\sim$8 GeV. The common wisdom is that the break is followed by an exponential cut-off driven by radiation/reaction-limited curvature emission. The discovery of pulsed gamma rays from the Crab pulsar, the only pulsar so far detected at very high e…
In this review paper we explain the following gamma-ray emission features from the millisecond pulsars. (1)Why is the dipolar field of millisecond pulsars so weak but the magnetic pair creation process may still be able to control the size of the outergap? (2)A sub-GeV pulse component could occur in the vicinity of the radio pulse of millisecond pulsars. (3)Orbital modulated gamma-rays should exist in the black widow systems for large viewing angle.
