Anomalous X-ray pulsars (AXPs) and Soft gamma repeaters (SGRs) form together a single class of astrophysical sources, commonly associated to magnetars. New-generation X-ray polarimeters will play a key role in assessing the nature of these sources by directly probing the star magnetic field. In the highly magnetized environment radiation is expected to be strongly polarized and such a measure will be easily within reach of IXPE and eXTP. Polarization measurements will eventually confirm the presence of ultra-strong magnetic fields, probing the magnetar scenario. In this work we will discuss theoretical expectations for the polarization signature of AXPs and SGRs and present numerical simulations for the detector response of the polarimeters currently under construction. We will also show how these sources can be used to test vacuum birefringence, a QED effect predicted by Heisemberg and Euler in the Thirties and not experimentally verified as yet

Potekhin, AY

Suleimanov, V

Taverna, R

Turolla, R

Zane, S

English

UCL Discovery

Neutron Star Astrophysics at the Crossroads: Magnetars and the Multimessenger RevolutionProceedings IAU Symposium No. 363, 2023E. Troja & M. G. Baring, eds.doi:10.1017/S174392132200028XPolarized emission from stronglymagnetized sourcesRoberto Taverna1 , Roberto Turolla1,2, Silvia Zane2,Valery Suleimanov3,4,5 and Alexander Y. Potekhin61Department of Physics and Astronomy, University of Padova, via Marzolo 8, Padova, Italyemail: taverna@pd.infn.it2Mullard Space Science Laboratory, University College London, Holmbury St. Mary, Surrey,RH5 6NT, UK3Institut für Astronomie und Astrophysik, Sand 1, D-72076 Tübingen, Germany4Kazan (Volga region) Federal University, Kremlevskaja str., 18, Kazan 420008, Russia5Space Research Institute of the Russian Academy of Sciences, Profsoyuznaya Str. 84/32,Moscow 117997, Russia6Ioffe Institute, Politekhnicheskaya 26, 194021, Saint Petersburg, RussiaAbstract. Anomalous X-ray pulsars (AXPs) and Soft gamma repeaters (SGRs) form together asingle class of astrophysical sources, commonly associated to magnetars. New-generation X-raypolarimeters will play a key role in assessing the nature of these sources by directly probing thestar magnetic field. In the highly magnetized environment radiation is expected to be stronglypolarized and such a measure will be easily within reach of IXPE and eXTP. Polarizationmeasurements will eventually confirm the presence of ultra-strong magnetic fields, probing themagnetar scenario. In this work we will discuss theoretical expectations for the polarizationsignature of AXPs and SGRs and present numerical simulations for the detector response of thepolarimeters currently under construction. We will also show how these sources can be used totest vacuum birefringence, a QED effect predicted by Heisemberg and Euler in the Thirties andnot experimentally verified as yet.Keywords. stars: magnetars, polarization, techniques: polarimetric1. IntroductionMagnetars form a particular group of isolated neutron stars (NSs) which are believedto host ultra-strong magnetic fields (≈ 1014–1015 G), observationally identified withAnomalous X-ray Pulsars (AXPs) and Soft Gamma Repeaters (SGRs). They are char-acterized by a peculiar persistent X-ray emission, with luminosity (between ≈ 1033 and1036 erg/s) tipically in excess of the rotational energy-loss rate. In the soft X-ray band(0.5–10 keV), spectra are characterized by the superposition of two components, a ther-mal one, fitted by a blackbody (BB) with temperature typically around 0.5 keV, and apower-law tail at higher energies. Magnetars are also known for their bursting activity,which is for sure their most distinguishing observational manifestation, divided into shortbursts, intermediate flares and giant flares, according to their duration and energy release(see Mereghetti 2008 and Turolla, Zane & Watts 2015 for reviews).The theoretical model which most successfully explains magnetar phenomenology isthe so-called twisted magnetosphere model (Thompson, Lyutikov & Kulkarni 2012).According to this, the internal magnetic field of magnetars is highly wound-up, with© The Author(s), 2023. Published by Cambridge University Press on behalf of International AstronomicalUnion. This is an Open Access article, distributed under the terms of the Creative Commons Attributionlicence (https://creativecommons.org/licenses/by/4.0/), which permits unrestricted re-use, distribution, andreproduction in any medium, provided the original work is properly cited.https://doi.org/10.1017/S174392132200028X Published online by Cambridge University PressPolarized emission from magnetars 277a strong toroidal component able to exert a magnetic stress on the conductive surface.For magnetars, this toroidal component is strong enough to deform the crust, makingthe external magnetic field “twisted”. Such a configuration is not potential, so chargedparticles must flow along the closed field lines. The density of magnetospheric particlesturns out to be high enough to make the medium in which thermal, surface-emittedphotons propagate optically thick for resonant Compton scattering (RCS).In the presence of ultra-strong magnetic fields, photons turn out to be linearly polar-ized in two normal modes, called ordinary (O) and extraordinary (X), with the photonelectric field oscillating either in the kB plane (with k the photon wave vector and Bthe local magnetic field direction) or perpendicularly to this plane, respectively. Photonpolarization modes can change due to interactions with matter, like the magnetosphericcharged particles which flow along the closed field lines. On the other hand, for B in excessof the quantum critical field BQ  4.4× 1013 G, quantum electrodynamics (QED) effectscannot be neglected, in particular vacuum birefringence (Heisenberg & Euler 1936), forwhich the virtual e−-e+ pairs that populate the vacuum around the star are polarizedby the strong NS field, modifying the dielectric and magnetic permeability tensors of thevacuum. It can be shown (Fernández & Davis 2011; Taverna et al. 2015) that, due toQED effects, photons propagating in the magnetized vacuum are forced to maintain theiroriginal polarization mode up to large distances from the source, making it possible tostudy the processes which occur at the surface through X-ray polarimetric observations.X-ray polarimetry has attracted the interest of the scientific community particularlyin the last months, with the successful launch of the new-generation X-ray polarimeterIXPE (Weisskopf et al. 2016) on December 9, 2021, which will be followed by the Chinesemission eXTP (Zhang et al. 2019) in 2027.In this work we will present a numerical method to simulate the spectral and polariza-tion properties of the persistent X-ray emission from magnetars within the RCS scenario,considering different models for photon emission from the surface. We show that polar-ization measurements may be indeed used to extract information on the physical andgeometrical properties of the source, providing a tool to test for the first time the effectsof vacuum birefringence.2. Numerical implementationFor our simulations we used the Monte Carlo code originally developed by Nobili et al.(2008; see also Taverna et al. 2014). Although the twist of the external field is more likelylocalized into bundles of field lines, for the sake of simplicity we consider a globally-twisteddipole field. In this case the twist of the external field can be fully described by the twistangle,ΔφN−S =[C(p)p(1 + p)]1/2limθ→0∫ π/2θf1/psin θdθ , (2.1)where θ is the magnetic colatitude and the function f , the radial index p and the param-eter C can be computed numerically (see Pavan et al. 2009 for more details). As a furthersimplification, we consider the charge carriers along the close field lines as electrons (uni-directional flow approximation, see Nobili et al. 2008). Under this assumption, the densityof magnetospheric charges can be written asne =p+ 14πe(BφBθ)Br|〈β〉| , (2.2)with e the electron charge and r the radial distance. We assume electrons distributedaccording to a 1D relativistic Maxwellian at the temperature Tel = 10 keV, superimposedto a bulk motion at the velocity β (results do not depend much on the value of Tel).https://doi.org/10.1017/S174392132200028X Published online by Cambridge University Press278 R. Taverna et al.Photons are emitted from the star surface according to three different emission models(see Taverna et al. 2020 for further details). As a first-order approximation we considerphotons following an isotropic BB at a constant temperature T over the surface. Since instrong magnetic fields the opacity for X-mode photons turn out to be strongly reducedwith respect to that of O-mode ones (see e.g. Harding & Lai 2006), we assume in thiscase that photons are emitted 100% polarized in the X-mode. We then consider thecase of radiation reprocessed in a geometrically-thin/optically-thick, pure-H atmosphericlayer, properly accounting for the effects of strong magnetic fields on both spectra andpolarization properties (Suleimanov et al. 2009). Finally, we contemplate the possibil-ity that the star crust is composed by a magnetic condensate, which can be formedfor sufficiently high magnetic field strengths and sufficiently low temperatures (see e.g.Turolla, Zane & Drake 2004; see also Potekhin 2014 for a review). In this case, emission ismodeled in the free-ion and fixed-ion limits, both with proper spectral and polarimetricdistributions (see Potekhin et al. 2012).Once photons are launched from the surface (through a suitable acceptance-rejectionmethod), they are followed during their propagation in the magnetosphere, accountingfor both the effects of RCS and vacuum polarization. The latter are implemented bysolving the wave equation in terms of the Stokes parameters I, Q, U and V . Theseare eventually summed together, once referred to the fixed polarimeter frame at infinity,providing spectra and polarization properties of the radiation at the observer for differentviewing geometries and as functions of the star rotational phase.3. ResultsUsing the code described in the previous section, we produced an archive of differentsimulations for the bright AXP 1RXS J170849.0–400910, each one labelled with differentvalues of the twist angle ΔφN−S, the charge velocity β and the two angles χ and ξwhich give the inclinations of the observer’s line-of-sight and the star magnetic axiswith respect to the star spin axis. For simplicity, we considered a homogeneous surfacetemperature T = 0.5 keV, which is representative for magnetar sources. Each simulationis performed twice, either considering (QED-ON) or neglecting (QED-OFF) vacuumpolarization effects. In order to compare our numerical predictions with observations, weproduced a 1 Ms IXPE simulated observation, starting from a specific simulation of thearchive. Eventually, we fit the mock data obtained in this way with the entire archive oftheoretical models, to recover the values of χ, ξ, ΔφN−S and β and the emission modelused for the simulated observation (as we will do for a real observation).Figure 1 shows the mock data of the simulated IXPE measurement together with thebest fitting theoretical curves. The left panel shows the phase-dependent polarizationdegree, energy-integrated in the 2–8 keV range (blue circles with error bars), with super-imposed the best fitting QED-ON (orange-solid) and QED-OFF (orange-dashed) curvesobtained using the BB emission model (which returned the best reduced chi-squared).As it can be clearly seen, QED-OFF simulations fail in reproducing the phase-dependentbehavior of the polarization degree, providing, for all intents, an indirect proof of vac-uum birefringence effects. The phase-integrated, energy-dependent Stokes parameters forthe same simulated measurement are displayed in the right panel, with the solid curvesmarking the behaviors of I, Q and U again for the best fitting BB model QED-ON. Wecould check that all the other emission models (atmosphere and condensed surface) areexcluded at a high level of confidence, confirming that polarimetry is indeed sensitive tothe emission process which is at work at the surface. Finally, the input parameters werecovered joining together the results of the phase- and energy-dependent analyses do notdiffer much from the input ones (see Table 1), showing that polarization measurementswill provide information on both the physical and geometrical properties of the source.https://doi.org/10.1017/S174392132200028X Published online by Cambridge University PressPolarized emission from magnetars 279Figure 1. Best fit of the phase-dependent, energy-integrated polarization degree (left) and ofthe phase-integrated, energy-dependent Stokes parameters (right) obtained for a 1 Ms IXPEobservation of the AXP 1RXS J170849.0–400910 (see text for further details).Table 1. Best-fitting parameters obtained for the 1 Ms IXPE observation of the AXP 1RXSJ170849.0–400910 displayed in Figure 1 (errors are given at 1σ).Emission model QED effects χ (◦) ξ (◦) ΔφN−S (rad) βInput BB 100%-polarized QED-ON 85 55 0.35 0.39Best fit BB 100%-polarized QED-ON 82.68± 0.71 55.60± 0.41 0.300± 0.058 0.469± 0.008ReferencesFernández, R., & Davis, S.W. 2011, ApJ, 730, 131Harding, A.K., & Lai, D. 2006, Rep. Prog. Phys., 69, 2631Heisenberg, W., & Euler, H. 1936, Z. Phys., 98, 714Mereghetti 2008, A&AR, 15, 225Nobili, L., Turolla, R., & Zane, S. 2008, MNRAS, 386, 1527Pavan, L., Turolla, R., Zane, S. & Nobili, L. 2009, MNRAS, 395, 1527Potekhin, A.Y. 2014, Phys. Usp., 57, 735Potekhin, A.Y., Suleimanov, V., van Adelsberg M., & Werner K. 2012, A&A, 546, A121Suleimanov, V., Potekhin, A.Y., & Werner K. 2009, A&A, 500, 891Taverna, R., Muleri, F., Turolla, R., Soffitta, P., Fabiani, S., & Nobili, L. 2014, MNRAS, 438, 1686Taverna, R., Turolla, R., González Caniulef, D., Zane, S., Muleri, F., & Soffitta, P. 2015, MNRAS,454, 3254Taverna, R., Turolla, R., Suleimanov, V., Potekhin, A.Y., & Zane, S. 2020, MNRAS, 492, 5057Thompson, C., Lyutikov, M. & Kulkarni, S.R. 2002, ApJ, 574, 332Turolla, R., Zane, S. & Drake, J.J. 2004, ApJ, 603, 265Turolla, R., Zane, S. & Watts, A. 2015, Rep. Prog. Phys., 78, 11Weisskopf, M.C., et al. 2016, Proc. SPIE Conf. Ser., Space Telescopes and Instrumentation,Ultraviolet to Gamma Ray. SPIE, Bellingham, 9905, 990517Zhang, S., et al. 2019, Sci. China Phys. Mech. Astron., 62, 29502https://doi.org/10.1017/S174392132200028X Published online by Cambridge University Press

Polarized emission from strongly magnetized sources

https://discovery.ucl.ac.uk/10170915/1/polarized-emission-from-strongly-magnetized-sources.pdf

Polarized emission from strongly magnetized sources

Abstract

Similar works

Full text

Available Versions

UCL Discovery