arXiv subjects

J. Pétri

Publications and source records attributed to J. Pétri.

At least 19 recordsLinked to original sources

arXiv2026

Multi-wavelength emission modelling of PSR~J0437$-$4715

The diversity of pulsar light-curves and radio polarisation properties originates in the structure of the magnetic field close to the stellar surface. For millisecond pulsars, this complexity is particularly puzzling. Fortunately, some means exist to uncover the magnetic field topology which indeed impacts the emission within the magnetosphere but also on the surface through its hot spot thermal radiation. We aim at deducing a plausible magnetic field geometry for the millisecond pulsar J0437$-$4715 by using combined information from the soft X-ray hot spot geometry deduced from NICER observations by pulse profile modelling and from radio and $γ$-ray pulse profile fitting. We also check the consistency between the geometry obtained and the radio polarisation data. Our $γ$-ray light-curve shapes rely on the striped wind model, whereas the radio polarisation fits rely on the rotating vector model. The magnetosphere structure is obtained from dipolar force-free magnetosphere simulations. We demonstrate that a slightly off-centred dipole augmented by a small scale dipole located on one polar cap explains simultaneously the shape of the hot spot and the radio and $γ$-ray data with a magnetic obliquity of $α\approx (42\pm5) \degr$ and a line-of-sight inclination angle of $ζ\approx (136 \pm5) \degr$. Our simple dipole model reproduces all the radio and $γ$-ray characteristics of PSR~J0437$-$4715, including its radio polarisation data. It shows that the radio emission could be produced in regions where the magnetic field is mainly of dipolar nature.

astro-ph.HE↗

arXiv2025

A double dipole geometry for PSR~J0740+6620

Millisecond pulsars are known to show complex radio pulse profiles and polarisation position angle evolution with rotational phase. Small scale surface magnetic fields and multipolar components are believed to be responsible for this complexity due to the radiation mechanisms occurring close to the stellar surface but within the relatively small light-cylinder compared to the stellar radius. In this work, we use the latest NICER phase aligned thermal X-ray pulse profile of PSR~J0740+6620 combined with radio and $γ$-ray pulse profiles and radio polarisation to deduce the best magnetic field configuration that can simultaneously reproduce the light-curves in these respective bands. We assume a polar cap model for the radio emission and use the rotating vector model for the associated polarisation, a striped wind model for the $γ$-ray light-curves and rely on the NICER collaboration results for the hot spot geometry. We demonstrate that an almost centred dipole can account for the hot spot location with a magnetic obliquity of $α\approx 51 °$ and a line of sight inclination angle of $ζ\approx 82 °$. However, with this geometry, the hot spot areas are three times too large. We found a better solution consisting of two dipoles located just below the surface in approximately antipodal positions. Our double dipole model is able to reproduce all the salient radio and $γ$-ray characteristics of PSR~J0740+6620 including radio polarisation data. A double dipole solution is more flexible than an off-centred dipole because of two independent magnetic axes and could hint at a magnetic field mostly concentrated within the crust and not in the core.

astro-ph.HE↗

arXiv2024

Localisation of the non-thermal X-ray emission of PSR~J2229+6114 from its multi-wavelength pulse profiles

Pulsars are detected over the whole electromagnetic spectrum, from radio wavelengths up to very high energies, in the GeV-TeV range. Whereas the radio emission site for young pulsars is well constrained to occur at altitudes about several percent of the light-cylinder radius and $γ$-ray emission is believed to be produced in the striped wind, outside the light-cylinder, their non-thermal X-ray production site remains unknown. The aim of this letter is to localize the non-thermal X-ray emission region based on multi-wavelength pulse profile fitting for PSR J2229+6114, a particularly good candidate due to its high X-ray brightness. Based on the geometry deduced from the joint radio and $γ$-ray pulse profiles, we fix the magnetic axis inclination angle and the line of sight inclination angle but we leave the region of X-ray emission unlocalised, somewhere between the surface and the light-cylinder. We localize this region and its extension by fitting the X-ray pulse profile as observed by the NICER, NuSTAR and RXTE telescopes in the ranges 2-7 keV, 3-10 keV and 9.4-22.4 keV, respectively. We constrain the non-thermal X-ray emission to arise from altitudes between $0.2\,r_L$ and $0.55\,r_L$ where $r_L$ is the light cylinder radius. The magnetic obliquity is approximately $α\approx 45°-50°$ and the line of sight inclination angle $ζ\approx 32°-48°$. This letter is among the first works to tightly constrain the location of the non-thermal X-ray emission from pulsars. We plan to apply this procedure to several other good candidates to confirm this new result.

astro-ph.HE↗

arXiv2023

Constraining the magnetic field geometry of the millisecond pulsar PSR~J0030+0451 from joint radio, thermal X-ray and $γ$-ray emission

With the advent of multi-wavelength electromagnetic observations of neutron stars, spanning many decades in photon energies, from radio wavelengths up to X-rays and $γ$-rays, it becomes possible to significantly constrain the geometry and the location of the associated emission regions. In this work, we use results from the modelling of thermal X-ray observations of PSR~J0030+0451 from the NICER mission and phase-aligned radio and $γ$-ray pulse profiles to constrain the geometry of an off-centred dipole able to reproduce the light-curves in these respective bands simultaneously. To this aim, we deduce a configuration with a simple dipole off-centred from the location of the centre of the thermal X-ray hot spots and show that the geometry is compatible with independent constraints from radio and $γ$-ray pulsations only, leading to a fixed magnetic obliquity of $α\approx 75°$ and a line of sight inclination angle of $ζ\approx 54°$. We demonstrate that an off-centred dipole cannot be rejected by accounting for the thermal X-ray pulse profiles. Moreover, the crescent shape of one spot is interpreted as the consequence of a small scale surface dipole on top of the large scale off-centred dipole.

astro-ph.HE↗

arXiv2021

Young radio-loud gamma-ray pulsar light-curve fitting

Observing simultaneously pulsed radio and gamma-ray emission from these stars helps to constrain the geometry and radiation mechanisms within their magnetosphere and to localize the multiple photon production sites. In this paper, we fit the time-aligned gamma-ray light-curves of young radio-loud gamma-ray pulsars. We assume a dipole force-free magnetosphere where radio photons emanate from high altitude above the polar caps and gamma-rays originate from outside the light-cylinder, within the striped wind current sheet. We compute a full atlas of radio and gamma-ray pulse profiles depending on the magnetic axis obliquity and line of sight inclination with respect to the neutron star rotation axis. By applying a $\rchi^2$ fitting technique, we are able to pin down accurately the magnetosphere geometry. Further constrains are obtained from radio polarization measurement following the rotating vector model, including aberration and retardation effects. We found a good agreement between our model and the time-aligned single or double peaked gamma-ray pulsar observations. We deduce the magnetic inclination angle and the observer line of sight with respect to the rotation axis within a small error bar. The distinction between radio-loud or radio-quiet gamma-ray pulsars or only radio pulsars can entirely be related to the geometry of the associated emitting regions. The high altitude polar cap model combined with the striped wind represents a minimalistic approach able to reproduce a wealth of gamma-ray pulse profiles for young radio pulsars. Based on self-consistent force-free simulations, it gives a full geometrical picture of the emission properties without resorting to detailed knowledge of the individual particle dynamics and energetics.

astro-ph.HE↗

arXiv2020

Magnetic quadri-dipolar stars rotating in vacuum

Main sequence stars and compact objects like white dwarfs and neutron stars are usually embedded in magnetic fields that strongly deviate from a pure dipole located right at the stellar centre. An off-centred dipole can sometimes better adjust existing data and offer a simple geometric picture to include multipolar fields. However, such configurations are usually to restrictive, limiting multipolar components to strength less than the underlying dipole. In this paper, we consider the most general lowest order multipolar combination given by a dipole and a quadrupole magnetic field association in vacuum. Following the general formalism for multipolar field computations, we derive the full electromagnetic field outside a rotating quadridipole. Exact analytical expressions for the Poynting flux and the electromagnetic kick are given. Such geometry is useful to study the magnetosphere of neutron stars for which more and more compelling observations reveals hints for at least quadridipolar fields. We also show that for sufficiently high quadrupole components at the stellar surface, the electromagnetic kick imprinted to a neutron star can reach thousands of km/s for a millisecond period at birth.

astro-ph.HE↗

arXiv2020

A relativistic particle pusher for ultra-strong electromagnetic fields

Abridged. Kinetic plasma simulations are nowadays commonly used to study a wealth of non-linear behaviours and properties in laboratory and space plasmas. In particular, in high-energy physics and astrophysics, the plasma usually evolves in ultra-strong electromagnetic fields produced by intense laser beams for the former or by rotating compact objects such as neutron stars and black holes for the latter. In these ultra-strong electromagnetic fields, the gyro-period is several orders of magnitude smaller than the timescale on which we desire to investigate the plasma evolution. Some approximations are required like for instance artificially decreasing the electromagnetic field strength which is certainly not satisfactory. The main flaw of this downscaling is that it cannot reproduce particle acceleration to ultra-relativistic speeds with Lorentz factor above $γ\approx 10^3-10^4$. In this paper, we design a new algorithm able to catch particle motion and acceleration to Lorentz factor up to $10^{15}$ or even higher by using Lorentz boosts to special frames where the electric and magnetic field are parallel. Assuming that these fields are locally uniform in space and constant in time, we solve analytically the equation of motion in a tiny region smaller than the length scale of the spatial and temporal gradient of the field.

physics.comp-ph↗

arXiv2017

An fully implicit scheme for numerical integration of the relativistic particle equation of motion

Relativistic strongly magnetized plasmas are produced in laboratories thanks to state-of-the-art laser technology but can naturally be found around compact objects such as neutron stars and black holes. Detailed studies of the behaviour of relativistic plasmas require accurate computations able to catch the full spatial and temporal dynamics of the system. Numerical simulations of ultra-relativistic plasmas face severe restrictions due to limitations in the maximum possible Lorentz factors that current algorithm can reproduce to good accuracy. In order to circumvent this flaw and repel the limit to $γ\approx10^9$, we design a new fully implicit scheme to solve the relativistic particle equation of motion in an external electromagnetic field using a three dimensional Cartesian geometry. We show some examples of numerical integrations in constant electromagnetic fields to prove the efficiency of our algorithm. The code is also able to follow the electric drift motion for high Lorentz factors. In the most general case of spatially and temporally varying electromagnetic fields, the code performs extremely well as shown by comparison with exact analytical solutions for the relativistic electrostatic Kepler problem as well as for linearly and circularly polarized plane waves.

physics.plasm-ph↗

arXiv2016

Polarized emission from of an off-centred dipole

Radio polarization measurements of pulsed emission from pulsars offer a valuable insight into the basic geometry of the neutron star: inclination angle between the magnetic and rotation axis and inclination of the line of sight. So far, all studies about radio polarization focused on the standard rotating vector model with the underlying assumption of a centred dipole. In this letter, we extend this model to the most general off-centred dipole configuration and give an exact closed analytic expression for the phase-resolved polarization angle. It is shown that contrary to the rotating vector model, for an off-centred dipole, the polarization angle also depends on the emission altitude. Although the fitting parameter space increases from two to six (position of the dipole, altitude and shift of the zero phase), statistical analysis should remain tractable. Observations revealing an evolution of the polarization angle with frequency would undeniably furnish a strong hint for the presence of a decentred magnetic dipole in neutron stars.

astro-ph.HE↗

arXiv2016

Theory of pulsar magnetosphere and wind

Neutron stars are fascinating astrophysical objects immersed in strong gravitational and electromagnetic fields, at the edge of our current theories. These stars manifest themselves mostly as pulsars, emitting a timely very stable and regular electromagnetic signal. Even though discovered almost fifty years ago, they still remain mysterious compact stellar objects. In this review, we summarize the most fundamental theoretical aspects of neutron star magnetospheres and winds. The main competing models susceptible to explain their radiative properties like multi-wavelength pulse shapes and spectra and the underlying physical processes such as pair creation and radiation mechanisms are scrutinized. A global but still rather qualitative picture emerges slowly thanks to recent advances in numerical simulations on the largest scales. However considerations about pulsar magnetospheres remain speculative. For instance the exact composition of the magnetospheric plasma is not yet known. Is it solely filled with a mixture of $e^\pm$~leptons, or does it contain a non negligible fraction of protons and/or ions? Actually, is it almost entirely filled or mostly empty except for some small anecdotal plasma filled regions? Answers to these questions will strongly direct the description of the magnetosphere to seemingly contradictory results leading sometimes to inconsistencies. Nevertheless, account are given to the latest developments in the theory of pulsar magnetospheres and winds, the existence of a possible electrosphere and physical insight obtained from related observational signatures of multi-wavelength pulsed emission.

astro-ph.HE↗

arXiv2016

Radiation from an off-centred rotating dipole in vacuum

When a neutron star forms, after the collapse of its progenitor, a strong magnetic field survives in its interior. This magnetic topology is usually assumed to be well approximated by a dipole located right at the centre of the star. However, there is no particular reason why this dipole should be attached to this very special point. A slight shift from the stellar centre could have strong implications for the surrounding electromagnetic field configuration leading to clear observational signatures. We study the effect of the most general off-centred dipole anchored in the neutron star interior. Exact analytical solutions are given in vacuum outside the star to any order of accuracy in the small parameter $ε= d/R$, where $d$ is the displacement of the dipole from the stellar centre and $R$ the neutron star radius. As a simple diagnostic of this decentred dipole, the spin-down luminosity and the torque exerted on its crust are computed to the lowest leading order in~$ε$. Results are compared to earlier works and a discussion on repercussions on pulsar braking index and multi-wavelength light curves is proposed.

astro-ph.HE↗

arXiv2015

Quantum electrodynamical corrections to a magnetic dipole in general relativity

Magnetized neutron stars are privileged places where strong electromagnetic fields as high as $\BQ=4.4\times10^9$~T exist, giving rise to non-linear corrections to Maxwell equations described by quantum electrodynamics (QED). These corrections need to be included to the general relativistic (GR) description of a magnetic dipole supposed to be anchored in the neutron star. In this paper, these QED and GR perturbations to the standard flat space-time dipole are calculated to the lowest order in the fine structure constant~$α_{\rm sf}$ and to any order in the ratio $\Rs/R$ where $R$ is the neutron star radius and $\Rs$ its Schwarzschild radius. Following our new 3+1~formalism developed in a previous work, we compute the multipolar non-linear corrections to this dipole and demonstrate the presence of a small dipolar~$\ell=1$ and hexapolar~$\ell=3$ component.

astro-ph.HE↗

arXiv2015

Thermal synchrotron radiation from RRMHD simulations of the double tearing mode reconnection - Application to the Crab flares

We study the magneto-hydrodynamic tearing instability occurring in a double current sheet configuration when a guide field is present. This is investigated by means of resistive relativistic magneto-hydrodynamic (RRMHD) simulations. Following the dynamics of the double tearing mode (DTM), we are able to compute synthetic synchrotron spectra in the explosive reconnection phase. The pulsar striped wind model represents a site where such current sheets are formed, including a guide field. The variability of the Crab nebula/pulsar system, seen as flares, can be therefore naturally explained by the DTM explosive phase in the striped wind. Our results indicate that the Crab GeV flare can be explained by the double tearing mode in the striped wind region if the magnetization parameter $σ$ is around $10^5$.

astro-ph.HE↗

arXiv2015

A 3+1 formalism for quantum electrodynamical corrections to Maxwell equations in general relativity

Magnetized neutron stars constitute a special class of compact objects harbouring gravitational fields that deviate strongly from the Newtonian weak field limit. Moreover strong electromagnetic fields anchored into the star give rise to non-linear corrections to Maxwell equations described by quantum electrodynamics (QED). Electromagnetic fields close to or above the critical value of $\BQ=4.4\times10^9$~T are probably present in some pulsars and for most of the magnetars. To account properly for emission emanating from the neutron star surface like for instance thermal radiation and its polarization properties, it is important to include general relativistic (GR) effects simultaneously with non-linear electrodynamics. This can be achieved through a 3+1 formalism known in general relativity and that incorporates QED perturbations to Maxwell equations. Starting from the lowest order corrections to the Lagrangian for the electromagnetic field, as given for instance by Born-Infeld or Euler-Heisenberg theory, we derive the non-linear Maxwell equations in general relativity including quantum vacuum effects. We also derive a prescription for the force-free limit and show that these equations can be solved with classical finite volume methods for hyperbolic conservation laws. It is therefore straightforward to include general relativity and quantum electrodynamics in the description of neutron star magnetospheres by using standard classical numerical techniques borrowed from Maxwell and Newton theory. As an application, we show that spin-down luminosity corrections associated to QED effects are negligible with respect to GR corrections.

astro-ph.HE↗

arXiv2014

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.

astro-ph.HE↗

arXiv2014

A spectral method in space and time to solve the advection-diffusion and wave equations in a bounded domain

The advection-diffusion and wave equations are the fundamental equations governing any physical law and therefore arise in many areas of physics and astrophysics. For complex problems and geometries, only numerical simulations can give insight into quantitative and accurate behavior of the seeked solutions. The standard numerical algorithm to solve partial differential equations is to split the space and time discretisation separately into different uncorrelated methods. Time is usually advanced by explicit schemes, or, for too restrictive time steps, by implicit or semi-implicit algorithms. This separate time and space slicing is artificial and sometimes unpractical. Indeed, treating space and time directions symmetrically and simultaneously without splitting is highly recommended in some problems like diffusion. It is the purpose of this work to present a simple numerical algorithm to solve the standard linear scalar advection-diffusion and wave equations using a fully spectral method in a two-dimensional Cartesian $(x,t)$ bounded space-time domain. Generalization in three-dimensions $(x,y,t)$ is shown for the pure diffusion problem. The basic idea is to expand the unknown function in Chebyshev polynomials for the spatial variables $(x,y)$ as well as for the time variable $t$. We show typical examples and demonstrate the spectral accuracy of the method. The great advantage of fully spectral methods resides in their high-accuracy for a relatively small number of grid points (for sufficiently smooth solutions) compared to standard time-stepping techniques.

physics.comp-ph↗

arXiv2014

General-relativistic electromagnetic fields around a slowly rotating neutron star: time-dependent pseudo-spectral simulations

Pulsars are believed to loose their rotational kinetic energy primarily by a large amplitude low frequency electromagnetic wave which is eventually converted into particle creation, acceleration and followed by a broad band radiation spectrum. To date, there exist no detailed calculation of the exact spin-down luminosity with respect to the neutron star magnetic moment and spin frequency, including general-relativistic effects. Estimates are usually given according to the flat spacetime magnetodipole formula. The present paper pursue our effort to look for accurate solutions of the general-relativistic electromagnetic field around a slowly rotating magnetized neutron star. In a previous work, we already found approximate stationary solutions to this problem. Here we address again this problem but using a more general approach. We indeed solve the full set of time-dependent Maxwell equations in a curved vacuum space-time following the 3+1 formalism. The numerical code is based on our pseudo-spectral method exposed in a previous paper for flat space-time. We adapted it to an arbitrary fixed background metric. Stationary solutions are readily obtained and compared to semi-analytical calculations.

astro-ph.HE↗

arXiv2012

High-energy emission from the pulsar striped wind: a synchrotron model for gamma-ray pulsars

(abridged) Gamma-ray pulsars constitute a class of high and very high-energy emitters for which the known population is steadily increasing thanks to the Fermi/Large Area Telescope. In this paper, their gamma-ray luminosity and spectral features are explained in the framework of synchrotron radiation from particles located in the stripe of the pulsar wind. Apart from radiative losses, particles are also subject to a constant re-acceleration and reheating for instance by a magnetic reconnection induced electric field. The high-energy luminosity scales as $L_γ\approx 2\times10^{26} \textrm{W} \, (L_{\rm sd}/10^{28} \textrm{W})^{1/2} \, (P/1 \textrm{s})^{-1/2}$ where $L_{\rm sd}$ is the pulsar spindown luminosity and $P$ its period. From this relation, we derive important parameters of pulsar magnetosphere and wind theories. Indeed, we find bulk Lorentz factor of the wind scaling as $Γ_{\rm v} \approx 10 \, τ_{\rm rec}^{1/5} \, (L_{\rm sd}/10^{28} \textrm{W})^{1/2}$, pair multiplicity $κ$ related to the magnetization parameter $σ$ by $κ\,σ\, τ_{\rm rec}^{1/5} \approx 10^8$, and efficiency $η$ of spin-down luminosity conversion into particle kinetic energy according to the relation $η\,σ\approx1$. A good guess for the associated reconnection rate is then $τ_{\rm rec} \approx 0.5 \, (L_{\rm sd}/10^{28} \textrm{W})^{-5/12}$. Finally, pulses in gamma-rays are visible only if $L_{\rm sd}/P\gtrsim 10^{27} \textrm{W/s}$. This model differs from other high-energy emission mechanisms because it makes allowance not only for rotational kinetic energy release but also for an additional reservoir of energy anchored to the magnetic field of the stripe and released for instance by some magnetic reconnection processes.

astro-ph.HE↗