The recent observations of the anomalous X-ray pulsars 4U 0142+61 and 1RXS J170849.0-400910 by the Imaging X-ray Polarimetry Explorer (IXPE) opened up a new avenue to study magnetars, neutron stars endowed with superstrong magnetic fields ($B\gtrsim 10^{14}$~G). The detected polarized X-rays from 4U 0142+61 exhibit a 90$^\circ$ linear polarization swing from low photon energies ($E\lesssim 4$~keV) to high energies ($E\gtrsim 5.5$~keV). We show that this swing can be explained by photon polarization mode conversion at the vacuum resonance in the magnetar atmosphere; the resonance arises from the combined effects of plasma-induced birefringence and QED-induced vacuum birefringence in strong magnetic fields. This explanation suggests that the atmosphere of 4U 0142 be composed of partially ionized heavy elements, and the surface magnetic field be comparable or less than $10^{14}$~G, consistent with the dipole field inferred from the measured spindown. It also implies that the spin axis of 4U 0142+61 is aligned with its velocity direction. The polarized X-rays from 1RXS J170849.0-400910 do not show such $90^\circ$ swing, consistent with magnetar atmospheric emission with $B\gtrsim 5\times 10^{14}$~G.
Phase-resolved spectral and spectropolarimetric X-ray observations of magnetars present us with the opportunity to test models of the origin of the X-ray emission from these objects, and to constrain the properties of the neutron star surface and atmosphere. We present a new X-ray fitting model for magnetars that accounts for four different emission models including a blackbody emission model, a magnetized atmosphere model, and fixed-ions and free-ions surface emission models. We use the new model for a phase resolved fit of archival XMM-Newton observations of the magnetar 1RXS J170849.0-40091…
Bayesian Geometrical Modeling of IXPE Polarization Angle Curves of the Magnetars 1E 2259+586 and 1E 1547.0-5408
State Key Laboratory of Radio Astronomy and Technology, Xinjiang Astronomical Observatory, Chinese Academy of Sciences（中国科学院新疆天文台射电天文与技术重点实验室）；University of Chinese Academy of Sciences（中国科学院大学）；Cosmology and Gravitation Group, Departamento de Física Teórica-IF-UERJ（里约热内卢州立大学理论物理系宇宙学与引力研究组）；Institute for Cosmology and Philosophy of Nature（自然哲学与宇宙学研究所）
IXPE observation of the new magnetar source EP J223759.5+531421
University of Padova（帕多瓦大学）；INAF - Istituto di Astrofisica e Planetologia Spaziali（意大利国家天体物理研究所空间天体物理学和行星科学研究所）；Mullard Space Science Laboratory, University College London（伦敦大学学院穆拉德空间科学实验室）；European Space Agency (ESA), European Space Astronomy Centre (ESAC)（欧洲航天局（ESA）欧洲空间天文中心（ESAC））；Institute of Space Sciences (ICE), CSIC（西班牙高等科学研究理事会空间科学研究所（ICE））；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚空间研究研究所（IEEC））；University School for Advanced Studies IUSS Pavia（帕维亚高等研究大学）
The long quest for vacuum birefringence in magnetars: 1E 1547.0-5408 and the elusive smoking gun
University of Padova（帕多瓦大学）；Mullard Space Science Laboratory, University College London（伦敦大学学院穆拉德空间科学实验室）；INAF - Istituto di Astrofisica e Planetologia Spaziali（意大利国家天体物理研究所空间天体物理学和行星学研究所）；European Space Agency (ESA), European Space Astronomy Centre (ESAC)（欧洲空间局（ESA）欧洲空间天文中心（ESAC））；INAF - Osservatorio Astronomico di Roma（意大利国家天体物理研究所罗马天文台）；INAF - Istituto di Astrofisica Spaziale e Fisica Cosmica di Milano（意大利国家天体物理研究所米兰空间天体物理学和宇宙物理学研究所）；INAF - Osservatorio Astronomico di Cagliari（意大利国家天体物理研究所卡利亚里天文台）
We report on the first detection of linearly polarized x-ray emission from an ultra-magnetized neutron star with the Imaging X-ray Polarimetry Explorer (IXPE). The IXPE 35 observations of the anomalous x-ray pulsar 4U 0142+61 reveal a linear polarization degree of $(12\pm 1)\%$ throughout the IXPE 2--8 keV band. We detect a substantial variation of the polarization with energy: the degree is $(14\pm 1)\%$ at 2--4 keV and $(41\pm 7)\%$ at 5.5--8 keV, while it drops below the instrumental sensitivity around 4--5 keV, where the polarization angle swings by $\sim 90^\circ$. The IXPE observations g…
The upcoming IXPE (2-8 keV) and XL-Calibur (15-75 keV) missions will make it possible to measure the linear polarization of X-rays from mass accreting stellar mass black holes with unprecedented sensitivity, enabling the accurate measurement of percent-level and in some cases even sub-percent level polarization fractions. The measurements are expected to constrain the spins, inclinations, and the structure of the accretion flows of the observed black holes. The effects of Faraday rotation and birefringence of the Quantum Electrodynamics (QED) vacuum may impact the observable polarization fract…
The recent detection of a large polarization degree in the optical emission of an isolated neutron star led to the suggestion that this has been the first evidence of vacuum polarization in a strong magnetic field, an effect predicted by quantum electrodynamics but never observed before. This claim was challanged in a paper by Capparelli, Maiani & Polosa (2017), according to whom a much higher polarization degree would be necessary to positively identify vacuum polarization. Here we show that their conclusions are biased by several inadequate assumptions and have no impact on the original clai…
The photon spectrum emitted by a transrelativistic pair plasma is calculated in the presence of an ultrastrong magnetic field, and is shown to bear a remarkable resemblance to the rising hard X-ray spectra of quiescent magnetars. This emission is powered by pair annihilation which, in contrast with a weakly magnetized pair plasma, shows an extended low-frequency tail similar to bremsstrahlung. Cross sections for electron-positron annihilation/scattering, two-photon pair creation, and photon-$e^\pm$ scattering are adopted from our earlier ab initio QED calculations in the regime $10α_{\rm em}^{…
IXPE (Imaging X-ray Polarimetry Explorer) is a Small Explorer mission by NASA and ASI, launched on December 9$^{th}$ 2021, dedicated to investigating X-ray polarimetry allowing angular-, time- and energy-resolved observations in the 2--8 keV energy band. IXPE is in Science Observation phase since January 2022; it comprises of three identical telescopes with grazing-incidence mirrors, each one having in the focal plane a Gas Pixel Detector (GPD). In this paper, we present a possible guideline to obtain an optimal background selection in polarimetric analysis, and a rejection strategy to remove …
A strong electromagnetic field polarizes the vacuum and in the presence of an electric field creates pairs of a charged particle and its anti-particle. Magnetars, highly magnetized neutron stars with magnetic field comparable to or greater than the Schwinger field, give a significant amount of the vacuum polarization and vacuum birefringence and the induced electric field can create the electron-positron pairs, which are strong field quantum electrodynamics (QED) processes. In this paper, we use a closed formula for the one-loop effective action in the presence of a supercritical magnetic fiel…
Impact of Resonant Compton Scattering on Magnetar X-Ray Polarization with QED Vacuum Resonance
School of Physics and Astronomy, Shanghai Jiao Tong University（上海交通大学物理与天文学院）；Tsung-Dao Lee Institute, Shanghai Jiao Tong University（上海交大李政道研究所）；Center for Astrophysics and Planetary Science, Department of Astronomy, Cornell University（康奈尔大学天文学系天体物理学与行星科学中心）
Magnetars are believed to host the strongest magnetic fields in the present universe ($B\gtrsim10^{14}$ G) and the study of their persistent emission in the X-ray band offers an unprecendented opportunity to gain insight into physical processes in the presence of ultra-strong magnetic fields. Up to now, most of our knowledge about magnetar sources came from spectral analysis, which allowed to test the resonant Compton scattering scenario and to probe the structure of the star magnetosphere. On the other hand, radiation emitted from magnetar surface is expected to be strongly polarized and its …
Magnetars are surrounded by diffuse plasma in magnetic field strengths well above the quantum electrodynamic critical value. We derive equations of "quantum force-free electrodynamics" for this plasma using effective field theory arguments. We argue that quantum effects do not modify the large scale structure of the magnetosphere, and in particular that the spin-down rate does not deviate significantly from the classical result. We provide definite evolution equations that can be used to explore potentially important small-scale corrections, such as shock formation, which has been proposed as …
Plasma modes in QED super-strong magnetic fields of magnetars and laser plasmas
Institute for Advanced Study, School for Natural Sciences, Princeton（普林斯顿高等研究院自然科学学院）；Department of Astrophysical Sciences, Princeton University（普林斯顿大学天体物理科学系）；Department of Physics and Astronomy, University of Kansas（堪萨斯大学物理与天文系）；Laboratory for Nuclear Science, Massachusetts Institute of Technology（麻省理工学院核科学实验室）
Bursts and flares are among the distinctive observational manifestations of magnetars, isolated neutron stars endowed with an ultra-strong magnetic field ($B \approx 10^{14}$--$10^{15}$ G). It is believed that these events arise in a hot electron-positron plasma which remains trapped within the closed magnetic field lines. We developed a simple radiative transfer model to simulate magnetar flare emission in the case of a steady trapped fireball. After dividing the fireball surface in a number of plane-parallel slabs, the local spectral and polarization properties are obtained integrating the r…
Finite-Field QED Corrections to Vacuum Birefringence and Magnetar Polarization Transport
The University of Western Ontario（韦仕敦大学）；Peaceful Society, Science and Innovation Foundation（和平社会科学与创新基金会）；The University of British Columbia（不列颠哥伦比亚大学）
Magnetars are the most luminous compact objects in the stellar mass range observed in the Milky Way, with giant flares of hard X-ray power ~10^45 erg/sec being detected from three soft gamma repeaters in the Galactic neighborhood. Periodicity seen in magnetar persistent emission, and a distinctive "spin-down" lengthening of this period, have driven the paradigm that strongly-magnetized neutron stars constitute these fascinating sources. The steady X-ray emission includes both thermal atmospheric components, and magnetospheric contributions that are manifested as hard X-ray "tails." This paper …
Radiative corrections of quantum electrodynamics cause a vacuum threaded by magnetic field to be birefringent. This means that radiation of different polarizations travels at different speeds. Even in the strong magnetic fields of astrophysical sources the difference in speed is small; however, it has profound consequences for the extent of polarization expected from strongly magnetized sources. We demonstrate how the birefringence arises from first principles, show how birefringence affects the polarization state of radiation and present recent calculations for the expected polarization from …
Pulsed non-thermal quiescent emission between 10 keV and around 150 keV has been observed in $\sim10$ magnetars. For inner magnetospheric models of such hard X-ray signals, resonant Compton upscattering of soft thermal photons from the neutron star surface is the most efficient radiative process. We present angle-dependent hard X-ray upscattering model spectra for uncooled monoenergetic relativistic electrons. The spectral cut-off energies are critically dependent on the observer viewing angles and electron Lorentz factor. We find that electrons with energies less than around 15 MeV will emit …
Energy Loss of Newborn Magnetars by Schwinger Process
Institute for Basic Science（基础科学研究所）；Gwangju Institute of Science and Technology（光州科学技术院）；Kunsan National University（群山国立大学）；ICRANet（国际相对论天体物理中心网络）；Sapienza Università di Roma（罗马智慧大学）；INAF（意大利国家天体物理研究所）
Strong magnetic fields in magnetospheres of neutron stars (especially magnetars) and other astrophysical objects may release their energy in violent, intense episodes of magnetic reconnection. While reconnection has been studied extensively, the extreme field strength near neutron stars introduces new effects: synchrotron cooling and electron-positron pair production. Using massively parallel particle-in-cell simulations that self-consistently incorporate these new quantum-electrodynamic effects, we investigate relativistic magnetic reconnection in the strong-field regime. We show that reconne…
Magnetars are neutron stars characterized by strong surface magnetic fields generally exceeding the quantum critical value of 44.1 TeraGauss. High-energy photons propagating in their magnetospheres can be attenuated by QED processes like photon splitting and magnetic pair creation. In this paper, we compute the opacities due to photon splitting and pair creation by photons emitted anywhere in the magnetosphere of a magnetar. Axisymmetric, twisted dipole field configurations embedded in the Schwarzschild metric are treated. The paper computes the maximum energies for photon transparency that pe…
The energy loss of a rotationally powered pulsar is primarily carried away as electromagnetic radiation and a particle wind. Considering that the magnetic field strength of pulsars ranges from about $10^8$ to $10^{15}$ G, one could expect quantum electrodynamics (QED) to play a role in their spin-down, especially for strongly magnetized ones (magnetars). In fact several authors have argued that QED corrections will dominate the spin-down for slowly rotating stars. They called this effect quantum vacuum friction (QVF). However, QVF was originally derived using a problematic self-torque techniqu…
Non-thermal quiescent X-ray emission extending between 10 keV and around 150 keV has been seen in about 10 magnetars by RXTE, INTEGRAL, Suzaku, NuSTAR and Fermi-GBM. For inner magnetospheric models of such hard X-ray signals, inverse Compton scattering is anticipated to be the most efficient process for generating the continuum radiation, because the scattering cross section is resonant at the cyclotron frequency. We present hard X-ray upscattering spectra for uncooled monoenergetic relativistic electrons injected in inner regions of pulsar magnetospheres. These model spectra are integrated ov…
Magnetar Fireballs and Short Bursts: Curved Spacetime Lensing, QED Effects, Spectra, Polarization, and Impulse Responses
University of Maryland, College Park（马里兰大学帕克分校）；NASA Goddard Space Flight Center（美国宇航局戈达德太空飞行中心）；Center for Research and Exploration in Space Science and Technology, NASA/GSFC（NASA/GSFC空间科学与技术研究探索中心）；Rice University（莱斯大学）；Washington University in St. Louis（华盛顿大学圣路易斯分校）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；University of Maryland, Baltimore County（马里兰大学巴尔的摩县分校）；University of Toulouse（图卢兹大学）
Certain classes of astrophysical objects, namely magnetars and central engines of supernovae and gamma-ray bursts (GRBs), are characterized by extreme physical conditions not encountered elsewhere in the Universe. In particular, they possess magnetic fields that exceed the critical quantum field of 44 teragauss. Figuring out how these complex ultra-magnetized systems work requires understanding various plasma processes, both small-scale kinetic and large-scale magnetohydrodynamic (MHD). However, an ultra-strong magnetic field modifies the underlying physics to such an extent that many relevant…
Detailed Timing, Spectral, and Polarimetric Analysis of Magnetar 1RXS J170849.0-400910
George Washington University（乔治华盛顿大学）；University of Maryland, Baltimore County（马里兰大学巴尔的摩分校）；NASA Goddard Space Flight Center（美国宇航局戈达德太空飞行中心）；Los Alamos National Laboratory（洛斯阿拉莫斯国家实验室）；Rice University（莱斯大学）；University of Maryland, College Park（马里兰大学帕克分校）；Louisiana State University（路易斯安那州立大学）
Einstein Probe discovery of the magnetar EP J223759.5+531421
Institute of Space Sciences (ICE–CSIC)（空间科学研究所）；Institut d’Estudis Espacials de Catalunya (IEEC)（加泰罗尼亚太空研究学院）；INAF–Osservatorio Astronomico di Brera（意大利国家天体物理研究所布雷拉天文台）；European Space Astronomy Centre (ESAC), ESA（欧洲空间局太空飞行中心）；National Astronomical Observatories, Chinese Academy of Sciences（中国科学院国家天文台）；School of Astronomy and Space Science, University of Chinese Academy of Sciences（中国科学院大学天文与空间科学学院）；School of Astronomy and Space Science, Nanjing University（南京大学天文与空间科学学院）
A next generation of Compton and pair telescopes that improve MeV-band detection sensitivity by more than a decade beyond current instrumental capabilities will open up new insights into a variety of astrophysical source classes. Among these are magnetars, the most highly magnetic of the neutron star zoo, which will serve as a prime science target for a new mission surveying the MeV window. This paper outlines the core questions pertaining to magnetars that can be addressed by such a technology. These range from global magnetar geometry and population trends, to incisive probes of hard X-ray e…
Magnetars are the most strongly magnetized neutron stars, and one of the most promising targets for X-ray polarimetric measurements. We present here the first Imaging X-ray Polarimetry Explorer (IXPE) observation of the magnetar 1RXS J170849.0-400910, jointly analysed with a new Swift observation and archival NICER data. The total (energy and phase integrated) emission in the 2-8 keV energy range is linerarly polarized, at a ~35% level. The phase-averaged polarization signal shows a marked increase with energy, ranging from ~20% at 2-3 keV up to ~80% at 6-8 keV, while the polarization angle re…
The surfaces of neutron stars are likely sources of strongly polarized soft X rays due to the presence of strong magnetic fields. Scattering transport in the surface layers is critical to the determination of the emergent anisotropy of light intensity, and is strongly influenced by the complicated interplay between linear and circular polarization information. We have developed a magnetic Thomson scattering simulation to model the outer layers of fully-ionized atmospheres in such compact objects. Here we summarize emergent intensities and polarizations from extended atmospheric simulations, sp…
Over the last four decades, persistent and flaring emission of magnetars observed by various telescopes has provided us with a suite of light curves and spectra in soft and hard X-rays, with no emission yet detected above around 1 MeV. Attenuation of such high-energy photons by magnetic pair creation and photon splitting is expected to be active in the magnetospheres of magnetars, possibly accounting for the paucity of gamma-rays in their signals. This paper explores polarization-dependent opacities for these two QED processes in static vacuum dipole magnetospheres of highly-magnetized neutron…
Vacuum birefringence and the polarized X-ray emission from a radio magnetar
George Washington University（乔治华盛顿大学）；Rice University（莱斯大学）；NASA Goddard Space Flight Center（美国宇航局戈达德太空飞行中心）；University of Maryland Baltimore County（马里兰大学巴尔的摩县分校）；Swinburne University of Technology（斯威本科技大学）；Louisiana State University（路易斯安那州立大学）；South African Radio Astronomy Observatory（南非射电天文观测台）
We evaluate several basic electrodynamic processes as modified by the presence of a very strong magnetic field, exceeding $B_{\rm Q} \equiv m^2/e = 4.4\times 10^{13}$ G. These results are needed to build models of dissipative phenomena outside magnetars and some other neutron stars. Differential and total cross sections and rates are presented for electron-photon scattering, the annihilation of an electron-positron pair into two photons, the inverse process of two-photon pair creation, and single-photon pair creation into the lowest Landau state. The relative importance of these interactions c…
Based on our previous work, we deduce a general formula for pressure of degenerate and relativistic electrons,Pe, which is suitable for superhigh magnetic fields, discuss the quantization of Landau levels of electrons, and consider the quantum electrodynam-ic(QED) effects on the equations of states (EOSs) for different matter systems. The main conclusions are as follows:Pe is related to the magnetic field B, matter density ?, and electron fraction Ye ; the stronger the magnetic field, the higher the electron pressure becomes; the high electron pressure could be caused by high Fermi energy of e…
Hard, non-thermal, persistent pulsed X-ray emission extending between 10 keV and $\sim 150$ keV has been observed in nearly ten magnetars. For inner-magnetospheric models of such emission, resonant inverse Compton scattering of soft thermal photons by ultra-relativistic charges is the most efficient production mechanism. We present angle-dependent upscattering spectra and pulsed intensity maps for uncooled, relativistic electrons injected in inner regions of magnetar magnetospheres, calculated using collisional integrals over field loops. Our computations employ a new formulation of the QED Co…
This paper continues the approach of Kostenko \& Thompson to calculating quantum electrodynamic processes in the ultrastrong magnetic field near some neutron stars, such as magnetars or merging binary neutron stars. Here we consider electron-positron scattering, the Coulomb scattering of electrons and positrons off ions, and relativistic $e^\pm$-ion bremsstrahlung. The evaluation of differential and total cross sections simplifies considerably when the magnetic field lies in the range $10^3B_{\rm Q} \gg B \gg B_{\rm Q}$, where $B_{\rm Q} \equiv m^2/e = 4.4\times 10^{13}$ G. Then, relativistic …
Energy losses from isolated neutron stars are commonly attributed to the emission of electromagnetic radiation from a rotating point-like magnetic dipole in vacuum. This emission mechanism predicts a braking index $n=3$, which is not observed in highly magnetized neutron stars. Despite this fact, the assumptions of a dipole field and rapid early rotation are often assumed a priori, typically causing a discrepancy between the characteristic age and the associated supernova remnant (SNR) age. We focus on neutron stars with `anomalous' magnetic fields that have established SNR associations and kn…
We consider the bending of light by nonlinear electrodynamics when the magnetic field $B$ exceeds the critical value $B_{\rm c}$. Using the index of refraction derived from the analytic series representation in one-loop effective action of QED, we found the trajectory and the bending angle of light in geometric optics. The angle bent by ultra-strong magnetic field of magnetar was estimated and compared with the gravitational bending. The result may be useful in studying the lensing, birefringence, and other nonlinear quantum electrodynamic effects above $B_{\rm c}$.
We show that photons may be redshifted or blueshifted when interacting with the field of an overcritical dipole, which incorporates the one-loop QED corrections coming from vacuum polarization. Using the effective metric, it follows that such effect depends on the polarization of the photon. The shifts, plotted against the azimuthal angle for various values of the magnetic field, may show an intensity comparable to the gravitational redshift for a magnetar. To obtain these results, we have corrected previous literature.
In this paper we present the science potential of the enhanced X-ray Timing and Polarimetry (eXTP) mission for studies of strongly magnetized objects. We will focus on the physics and astrophysics of strongly magnetized objects, namely magnetars, accreting X-ray pulsars, and rotation powered pulsars. We also discuss the science potential of eXTP for QED studies. Developed by an international Consortium led by the Institute of High Energy Physics of the Chinese Academy of Sciences, the eXTP mission is expected to be launched in the mid 2020s.
By introducing Dirac ?-function in superhigh magnetic field, we deduce a general formula for pressure of degenerate and relativistic electrons, Pe, which is suitable for superhigh magnetic fields, discuss the quantization of Landau levels of electrons, and consider the quantum electrodynamic(QED) effects on the equations of states (EOSs) for different matter systems. The main conclusions are as follows: the stronger the magnetic field strength, the higher the electron pressure becomes; compared with a common radio pulsar, a magnetar could be a more compact oblate spheroid-like deformed neutron…
