Light Cylinder Radius Research Articles

Peering at the outflow mechanisms in the transitional pulsar PSR J1023+0038: simultaneous VLT, XMM-Newton, and Swift high-time resolution observations

We report on a simultaneous near-infrared, optical, and X-ray campaign performed in 2017 with the XMM-Newton and Swift satellites and the HAWK-I instrument mounted on the Very Large Telescope (VLT) on the transitional millisecond pulsar PSR J1023+0038. Near-infrared observations were performed in fast-photometric mode (0.5 s exposure time) in order to detect any fast variation of the flux and correlate this with the optical and X-ray light curves. The optical light curve shows the typical sinusoidal modulation at the system orbital period (4.75 h). No significant flaring or flickering is found in the optical, nor any signs of transitions between active and passive states. On the contrary, the near-infrared light curve displays a bimodal behaviour, showing strong flares in the first part of the curve, and an almost flat trend in the rest. The X-ray light curves instead show a few low-high mode transitions, but no flaring activity is detected. Interestingly, one of the low-high mode transitions occurs at the same time as the emission of an infrared flare. This can be interpreted in terms of the emission of an outflow or a jet: the infrared flare could be due to the evolving spectrum of the jet, which possesses a break frequency that moves from higher (near-infrared) to lower (radio) frequencies after the launching, which has to occur at the low-high mode transition. We also present the cross-correlation function between the optical and near-infrared curves. The near.infrared curve is bimodal, therefore we divided it into two parts (flaring and quiet). While the cross-correlation function of the quiet part is found to be flat, the function that refers to the flaring part shows a narrow peak at ∼10 s, which indicates a delay of the near-infrared emission with respect to the optical. This lag can be interpreted as reprocessing of the optical emission at the light cylinder radius with a stream of matter spiraling around the system due to a phase of radio ejection. This strongly supports a different origin of the infrared flares that are observed for PSR J1023+0038 with respect to the optical and X-ray flaring activity that has been reported in other works on the same source.

On the beam properties of radio pulsars with interpulse emission

ABSTRACT In the canonical picture of pulsars, radio emission arises from a narrow cone centred on the star’s magnetic axis but many basic details remain unclear. We use high-quality polarization data taken with the Parkes radio telescope to constrain the geometry and emission heights of pulsars showing interpulse emission, and include the possibility that emission heights in the main and interpulse may be different. We show that emission heights are low in the centre of the beam, typically less than 3 per cent of the light cylinder radius. The emission beams are underfilled in longitude, with an average profile width only 60 per cent of the maximal beamwidth and there is a strong preference for the visible emission to be located on the trailing part of the beam. We show substantial evidence that the emission heights are larger at the beam edges than in the beam centre. There is some indication that a fan-like emission beam explains the data better than conal structures. Finally, there is a strong correlation between handedness of circular polarization in the main and interpulse profiles, which implies that the hand of circular polarization is determined by the hemisphere of the visible emission.

Pulsating in Unison at Optical and X-Ray Energies: Simultaneous High Time Resolution Observations of the Transitional Millisecond Pulsar PSR J1023+0038

PSR J1023+0038 is the first millisecond pulsar discovered to pulsate in the visible band; such a detection took place when the pulsar was surrounded by an accretion disk and also showed X-ray pulsations. We report on the first high time resolution observational campaign of this transitional pulsar in the disk state, using simultaneous observations in the optical (TNG, NOT, TJO), X-ray (XMM-Newton, NuSTAR, NICER), infrared (GTC) and UV (Swift) bands. Optical and X-ray pulsations were detected simultaneously in the X-ray high intensity mode in which the source spends $\sim$ 70% of the time, and both disappeared in the low mode, indicating a common underlying physical mechanism. In addition, optical and X-ray pulses were emitted within a few km, had similar pulse shape and distribution of the pulsed flux density compatible with a power-law relation $F_{\nu} \propto \nu^{-0.7}$ connecting the optical and the 0.3-45 keV X-ray band. Optical pulses were detected also during flares with a pulsed flux reduced by one third with respect to the high mode; the lack of a simultaneous detection of X-ray pulses is compatible with the lower photon statistics. We show that magnetically channeled accretion of plasma onto the surface of the neutron star cannot account for the optical pulsed luminosity ($\sim 10^{31}$ erg/s). On the other hand, magnetospheric rotation-powered pulsar emission would require an extremely efficient conversion of spin-down power into pulsed optical and X-ray emission. We then propose that optical and X-ray pulses are instead produced by synchrotron emission from the intrabinary shock that forms where a striped pulsar wind meets the accretion disk, within a few light cylinder radii away, $\sim$ 100 km, from the pulsar.

Large polar caps for twisted magnetosphere of magnetars

Abstract The magnetic field of magnetars may be twisted compared with that of normal pulsars. Previous works mainly discussed magnetic energy release in the closed field line regions of magnetars. For a twisted magnetic field, the field lines will inflate in the radial direction. Similar to normal pulsars, the idea of light cylinder radius is introduced. More field lines will cross the light cylinder and become open for a twisted magnetic field. Therefore, magnetars may have a large polar cap, which may correspond to the hot spot during outburst. Particle flow in the open field line regions will result in the untwisting of the magnetic field. Magnetic energy release in the open field line regions can be calculated. The model calculations can catch the general trend of magnetar outburst: decreasing X-ray luminosity, shrinking hot spot etc. For magnetic energy release in the open field line regions, the geometry will be the same for different outburst in one magnetar.

Magnetic absorption of VHE photons in the magnetosphere of the Crab pulsar

The detection of the pulsed $\sim 1 $~TeV gamma-ray emission from the Crab pulsar reported by MAGIC and VERITAS collaborations demands a substantial revision of existing models of particle acceleration in the pulsar magnetosphere. In this regard model independent restrictions on the possible production site of the VHE photons become an important issue. In this paper, we consider limitations imposed by the process of conversion of VHE gamma rays into $e^{\pm}$ pairs in the magnetic field of the pulsar magnetosphere. Photons with energies exceeding 1~TeV are effectively absorbed even at large distances from the surface of the neutron star. Our calculations of magnetic absorption in the force-free magnetosphere show that the twisting of the magnetic field due to the pulsar rotation makes the magnetosphere more transparent compared to the dipole magnetosphere. The gamma-ray absorption appears stronger for photons emitted in the direction of rotation than in the opposite direction. There is a small angular cone inside which the magnetosphere is relatively transparent and photons with energy $1.5$~TeV can escape from distances beyond $0.1$~light cylinder radius ($R_{\rm{lc}}$). The emission surface from where photons can be emitted in the observer's direction further restricts the sites of VHE gamma-ray production. For the observation angle $57^{\circ}$ relative to the Crab pulsar axis of rotation and the orthogonal rotation, the emission surface in the open field line region is located as close as $0.4\,R_{\rm{lc}}$ from the stellar surface for a dipole magnetic field, and $0.1\,R_{\rm{lc}}$ for a force-free magnetic field.

Global Current Circuit Structure in a Resistive Pulsar Magnetosphere Model

Abstract Pulsar magnetospheres have strong magnetic fields and large amounts of plasma. The structures of these magnetospheres are studied using force-free electrodynamics. To understand pulsar magnetospheres, discussions must include their outer region. However, force-free electrodynamics is limited in it does not handle dissipation. Therefore, a resistive pulsar magnetic field model is needed. To break the ideal magnetohydrodynamic (MHD) condition , Ohm’s law is used. This work introduces resistivity depending upon the distance from the star and obtain a self-consistent steady state by time integration. Poloidal current circuits form in the magnetosphere while the toroidal magnetic field region expands beyond the light cylinder and the Poynting flux radiation appears. High electric resistivity causes a large space scale poloidal current circuit and the magnetosphere radiates a larger Poynting flux than the linear increase outside of the light cylinder radius. The formed poloidal-current circuit has width, which grows with the electric conductivity. This result contributes to a more concrete dissipative pulsar magnetosphere model.

State Switching of the X-Ray/Radio Transitional Millisecond Pulsar

Abstract PSR J1023+0038 is a known transitional pulsar, which switches between the accretion-powered X-ray pulsar state and the rotation-powered radio millisecond pulsar (MSP) state. Here, we study the conditions for its state transition by ascribing ∼GHz radio pulse emission to the plasma cutoff oscillation frequency at the magnetosphere, which depends on the plasma density or accretion rate. With the accretion X-ray luminosity declining fromhigh to low state (e.g., erg s−1 to erg s−1), the magnetosphere boundary expands to the light cylinder, where the plasma density is low enough to permit the emission of radio waves at the several-GHz frequency band. Thus, for a sufficiently low accretion-rate state ( erg s−1), the radio emission at the several-GHz band is not blocked by the plasma, and the radio pulsar can be detected in the favored “observational windows,” i.e., the L band (1–2 GHz), S band (2–4 GHz), and C band (4–8 GHz). Furthermore, to evaluate the penetration characteristics of the outgoing radio wave of low frequency, we calculate its skin depth, which is found to be a couple of centimeters for the low X-ray luminosity of erg s−1, a scale that is much shorter than the light cylinder radius of about 100 km for MSPs.

Nature of Coherent Radio Emission from Pulsars

The pulsar radio emission originates from regions below 10% of the light cylinder radius. This requires a mechanism where coherent emission is excited in relativistic pair plasma with frequency $\nu_{cr}$ which is below the plasma frequency $\nu_{\circ}$ i.e. $\nu_{cr} < \nu_{\circ}$. A possible model for the emission mechanism is charged bunches (charged solitons) moving relativistically along the curved open dipolar magnetic field lines capable of exciting coherent curvature radio emission. In this article we review the results from high quality observations in conjunction with theoretical models to unravel the nature of coherent curvature radio emission in pulsars.

Mapping the Emission Location of the Crab Pulsar’s Giant Pulses

AbstractThe Crab pulsar has a striking radio profile, dominated by two pulse components (the main pulse and interpulse) which are comprised of giant pulses. These pulses are randomly occurring, they extend to extremely high flux densities, and are closely aligned with emission across the entire electromagnetic spectrum. The Crab, like many pulsars, exhibits scintillation – a pattern in frequency and time arising from interfering scattered images. The pattern varies with location, with the physical scale over which it changes by order unity corresponding to the spatial resolution of the scattering surface. For the Crab, the scattering is in the nebula and the estimated spatial resolution is of order the light cylinder radius. Comparing scintillation spectra of the two components, we infer a difference in physical location of the same order.

The Crab pulsar at VHE

The last six years have witnessed major revisions of our knowledge about the Crab Pulsar. The consensus scenario for the origin of the high-energy pulsed emission has been challenged with the discovery of a very-high-energy power law tail extending up to 400 GeV, above the expected spectral cut off at a few GeV. Now, new measurements obtained by the MAGIC collaboration extend the energy spectrum of the Crab Pulsar even further, on the TeV regime. Above 400 GeV the pulsed emission comes mainly from the inter-pulse, which becomes more prominent with energy due to a harder spectral index. These findings require gamma-ray production via inverse Compton scattering close to or beyond the light cylinder radius by an underlying particle population with Lorentz factors greater than 5 times 106. We will present those new results and discuss the implications in our current knowledge concerning pulsar environments.

Quasi-periodicities in the anomalous emission events in pulsars B1859+07 and B0919+06

A quasi-periodicity has been identified in the strange emission shifts in pulsar B1859+07 and possibly B0919+06. These events, first investigated by Rankin, Rodriguez & Wright in 2006, originally appeared disordered or random, but further mapping as well as Fourier analysis has revealed that they occur on a fairly regular basis of approximately 150 rotation periods in B1859+07 and perhaps some 700 in B0919+06. The events-which we now refer to as "swooshes"-are not the result of any known type of mode-changing, but rather we find that they are a uniquely different effect, produced by some mechanism other than any known pulse-modulation phenomenon. Given that we have yet to find another explanation for the swooshes, we have appealed to a last resort for periodicities in astrophysics: orbital dynamics in a binary system. Such putative "companions" would then have semi-major axes comparable to the light cylinder radius for both pulsars. However, in order to resist tidal disruption their densities must be at least some 10$^5$ grams/cm$^3$-therefore white-dwarf cores or something even denser might be indicated.

General-relativistic force-free pulsar magnetospheres

Pulsar magnetospheres are shaped by ultra-relativistic electron/positron plasmas flowing in a strong magnetic field and subject to strong gravitational fields. The former induces magnetospheric currents and space charges responsible for the distortion of the electromagnetic field based on pure electrodynamics. The latter induces other perturbations in these fields based on space-time curvature. The force-free approximation describes the response of this magnetosphere to the presence of currents and charges and has been investigated by many authors. In this context, general relativity has been less discussed to quantify its influence on the neutron star electrodynamics. It is the purpose of this paper to compute general-relativistic force-free pulsar magnetospheres for realistic magnetic field configurations such as the inclined dipole. We performed time-dependent simulations of Maxwell equations in the 3+1 formalism of a stationary background metric in the slow-rotation approximation. We computed the resulting Poynting flux depending on the ratio~$R/\rlight$ and on frame-dragging through the spin parameter~$\as$, $R$ is the neutron star radius and $\rlight$ the light-cylinder radius. Both effects act together to increase the total Poynting flux seen by a distant observer by a factor up to~2 depending on the rotation rate. Moreover we retrieve the $\sin^2\chi$ dependence of this luminosity, $\chi$ being the obliquity of the pulsar, as well as a braking index close to $n=3$. We also show that the angular dependence of the Poynting flux scales like $\sin^2\vartheta$ for the aligned rotator but like $\sin^4\vartheta$ for the orthogonal rotator, $\vartheta$ being the colatitude.

Multipolar electromagnetic fields around neutron stars: exact vacuum solutions and related properties

The magnetic field topology in the surrounding of neutron stars is one of the key questions in pulsar magnetospheric physics. A very extensive literature exists about the assumption of a dipolar magnetic field but very little progress has been made in attempts to include multipolar components in a self-consistent way. In this paper, we study the effect of multipolar electromagnetic fields anchored in the star. We give exact analytical solutions in closed form for any order l and apply them to the retarded point quadrupole (l = 2), hexapole (l = 3) and octopole (l = 4), a generalization of the retarded point dipole (l = 1). We also compare the Poynting flux from each multipole and show that the spin-down luminosity depends on the ratio R/rL, R being the neutron star radius and rL the light-cylinder radius. Therefore the braking index also depends on R/rL. As such multipole fields possess very different topology, most importantly smaller length scales compared to the dipolar field, especially close to the neutron star, we investigate the deformation of the polar caps induced by these multipolar fields. Such fields could have a strong impact on the interpretation of the pulsed radio emission suspected to emanate from these polar caps as well as on the inferred geometry deduced from the high-energy light-curve fitting and on the magnetic field strength. Discrepancies between the two-pole caustic model and our new multipole caustic model are emphasized with the quadrupole field. To this respect, we demonstrate that working with only a dipole field can be very misleading.

Dissipation, energy transfer, and spin-down luminosity in 2.5D PIC simulations of the pulsar magnetosphere

We perform 2.5D axisymmetric simulations of the pulsar magnetosphere (aligned dipole rotator) using the charge conservative, relativistic, electromagnetic particle in cell code PICsar. Particle in cell codes are a powerful tool to use for studying the pulsar magnetosphere, because they can handle the force-free and vacuum limits and provide a self-consistent treatment of magnetic reconnection. In the limit of dense plasma throughout the magnetosphere, our solutions are everywhere in the force-free regime except for dissipative regions at the polar caps, in the current layers, and at the Y-point. These dissipative regions arise self-consistently, since we do not have any explicit dissipation in the code. A minimum of $ \approx 15-20\%$ of the electromagnetic spindown luminosity is transferred to the particles inside 5 light cylinder radii. However, the particles can carry as much as $\gtrsim 50 \%$ of the spindown luminosity if there is insufficient plasma in the outer magnetosphere to screen the component of electric field parallel to the magnetic field. In reality, the component of the spindown luminosity carried by the particles could be radiated as gamma rays, but high-frequency synchrotron emission would need to be implemented as a sub-grid process in our simulations and is not present for the current suite of runs. The value of the spindown luminosity in our simulations is within $\approx 10\%$ of the force-free value, and the structure of the electromagnetic fields in the magnetosphere is on the whole consistent with the force-free model.

Particle acceleration in axisymmetric pulsar current sheets

The equatorial current sheet in pulsar magnetospheres is often regarded as an ideal site for particle acceleration via relativistic reconnection. Using 2D spherical particle-in-cell simulations, we investigate particle acceleration in the axisymmetric pulsar magnetosphere as a function of the injected plasma multiplicity and magnetization. We observe a clear transition from a highly charge-separated magnetosphere for low plasma injection with little current and spin-down power, to a nearly force-free solution for high plasma multiplicity characterized by a prominent equatorial current sheet and high spin-down power. We find significant magnetic dissipation in the current sheet, up to 30% within 5 light-cylinder radii in the high-multiplicity regime. The simulations unambiguously demonstrate that the dissipated Poynting flux is efficiently channeled to the particles in the sheet, close to the Y-point within about 1-2 light cylinder radii from the star. The mean particle energy in the sheet is given by the upstream plasma magnetization at the light cylinder. The study of particle orbits shows that all energetic particles originate from the boundary layer between the open and the closed field lines. Energetic positrons always stream outward, while high-energy electrons precipitate back towards the star through the sheet and along the separatrices, which may result in auroral-like emission. Our results suggest that the current sheet and the separatrices may be the main source of high-energy radiation in young pulsars.

General relativistic monopole magnetosphere of neutron stars: a pseudo-spectral discontinuous Galerkin approach

The close vicinity of neutron stars remains poorly constrained by observations. Although plenty of data are available for the peculiar class of pulsars we are still unable to deduce the underlying plasma distribution in their magnetosphere. In the present paper, we try to unravel the magnetospheric structure starting from basic physics principles and reasonable assumptions about the magnetosphere. Beginning with the monopole force-free case, we compute accurate general-relativistic solutions for the electromagnetic field around a slowly rotating magnetized neutron star. Moreover, here we address this problem by including the important effect of plasma screening. This is achieved by solving the time-dependent Maxwell equations in a curved space-time following the 3+1~formalism. We improved our previous numerical code based on pseudo-spectral methods in order to allow for possible discontinuities in the solution. Our algorithm based on a multi-domain decomposition of the simulation box belongs to the discontinuous Galerkin finite element methods. We performed several sets of simulations to look for the general-relativistic force-free monopole and split monopole solutions. Results show that our code is extremely powerful in handling extended domains of hundredth of light-cylinder radii~$\rlight$. The code has been validated against known exact analytical monopole solutions in flat space-time. We also present semi-analytical calculations for the general-relativistic vacuum monopole.

Explosive reconnection of the double tearing mode in relativistic plasmas with application to the Crab nebula

The Crab pulsar and its surrounding nebula is a well-known relic of a massive star that exploded in 1054 AD. The Crab nebula was generally believed to be a good standard candle in gamma rays. Recently, this view has been challenged by sudden increases in the gamma-ray flux in a narrow spectral band within a few hundred MeV. These flares are short but powerful; their duration is between a few hours and up to several days with a rising/falling time of a few hours/days. To date it is neither clear what mechanism powers these flares nor where exactly in the nebula they should be located. However, recent models seem to favor emission sites inside the nebula. In the present work, we study the magneto-hydrodynamic tearing instability occurring in a double current sheet configuration with application to the Crab flares. This is investigated by means of resistive relativistic magneto-hydrodynamic simulations. These put some constraints on the maximum Lorentz factor of the striped wind, Γ≲150 and on the localization of the emission region, r ≈ 50 rL where rL = c/Ω is the light-cylinder radius, c is the speed of light and Ω is the rotation speed of the pulsar. Sites close to but outside the light-cylinder are favored in our model.

THE VELA PULSAR WITH AN ACTIVE FALLBACK DISK

Fallback disks are expected to form around young neutron stars. The presence of these disks can be revealed by their blackbody spectrum in the infrared, optical and UV bands. We present a re-reduction of the archival optical and infrared data of the Vela pulsar, together with the existing infrared and UV spectrum of Vela, and model their unpulsed components with the blackbody spectrum of a supernova debris disk. We invoke the quiescent disk solution of Sunyaev and Shakura for the description of the disk in the propeller stage and find the inner radius of the disk to be inside the light cylinder radius. We perform a high resolution X-ray analysis with XMM-Newton and find a narrow absorption feature at 0.57 keV which can be interpreted as K$_{\alpha}$ line of He-like oxygen (OVII). The strength of the line indicates an element over-abundance in our line of sight exceeding the amounts that would be expected from ISM. The spectral feature may originate from the pulsar wind nebula and may be partly caused by the reprocessed X-ray radiation by the fallback disk. We discuss the lower-than-3 braking index of Vela as partially due to the contribution of the propeller torques. Our results suggest that the pulsar mechanism can work simultaneously with the propeller processes and that the debris disks can survive the radiation pressure for at least $\sim 10^4$ years. As Vela is a relatively close object, and a prototypical pulsar, the presence of a disk, if confirmed, may indicate the ubiquity of debris disks around young neutron stars.

MAGNETIC PAIR CREATION TRANSPARENCY IN GAMMA-RAY PULSARS

Magnetic pair creation $\gamma \to e^+e^-$ has been at the core of radio pulsar paradigms and central to polar cap models of gamma-ray pulsars for over three decades. The Fermi gamma-ray pulsar population now exceeds 140 sources and has defined an important part of Fermi's science legacy. Among the population characteristics well established is the common occurrence of exponential turnovers in their spectra in the 1--10 GeV range. These turnovers are too gradual to arise from magnetic pair creation in the strong magnetic fields of pulsar inner magnetospheres. By demanding insignificant photon attenuation precipitated by such single-photon pair creation, the energies of these turnovers for Fermi pulsars can be used to compute lower bounds for the typical altitude of GeV band emission. This paper explores such pair transparency constraints below the turnover energy, and updates earlier altitude bound determinations of that have been deployed in various Fermi pulsar papers. For low altitude emission locales, general relativistic influences are found to be important. Rotational aberration influences are also explored, and are found to be small at low altitudes, except near the magnetic pole. The altitude bounds are typically in the range of 2-7 stellar radii for the young Fermi pulsar population, and provide key information on the emission altitude in radio quiet pulsars that do not possess double-peaked pulse profiles. The bound for the Crab pulsar is at a much higher altitude, with the putative detection by MAGIC out to 350-400 GeV implying a lower bound of 310km to the emission region, i.e., approximately 20% of the light cylinder radius. These results are also extended to the super-critical field domain, where it is found that emission in magnetars originating below around 10 stellar radii will not appear in the Fermi-LAT band.

Analysis of single pulse radio flux measurements of PSR B1133+16 at 4.85 and 8.35 GHz

We show the results of microsecond resolution radio data analysis focused on flux measurements of single pulses of PSR B1133+16. The data were recorded at 4.85 GHz and 8.35 GHz with 0.5 GHz and 1.1 GHz bandwidth, respectively, using Radio Telescope Effelsberg (MPIfR). The most important conclusion of the analysis is, that the strongest single pulse emission at 4.85 GHz and 8.35 GHz contributes almost exclusively to the trailing part of the leading component of the pulsar mean profile, whereas studies at lower frequencies report that the contribution is spread almost uniformly covering all phases of the pulsar mean profile. We also estimate the radio emission heights to be around 1%--2% of the light cylinder radius which is in agreement with previous studies. Additionally these observations allowed us to add two more measurements of the flux density to the PSR B1133+16 broadband radio spectrum covering frequencies from 16.7 MHz up to 32 GHz. We fit two different models to the spectrum: the broken power law and the spectrum based on flicker noise model, which represents the spectrum in a simpler but similarly accurate way.