A Model of Polarized X-ray Emission from Twinkling Synchrotron Supernova Shells
A.M.Bykov, Yu.A.Uvarov, J.B.G.M.Bloemen, J.W. den Herder, J.S.Kaastra
aa r X i v : . [ a s t r o - ph . H E ] J u l Mon. Not. R. Astron. Soc. , 1– ?? (2002) Printed 26 October 2018 (MN L A TEX style file v2.2)
A Model of Polarized X-ray Emission from TwinklingSynchrotron Supernova Shells
A.M.Bykov ⋆ , Yu.A.Uvarov , J.B.G.M.Bloemen , J.W. den Herder and J.S.Kaastra Ioffe Institute for Physics and Technology, 194021 St.Petersburg, Russia SRON Netherlands Institute for Space Research, Utrecht, The Netherlands
Accepted 2 July 2009. Received 2009 July 2; in original form 2009 May 2.
ABSTRACT
Synchrotron X-ray emission components were recently detected in many young super-nova remnants (SNRs). There is even an emerging class - SN1006, RXJ1713.72-3946,Vela Jr, and others - that is dominated by non-thermal emission in X-rays, also prob-ably of synchrotron origin. Such emission results from electrons/positrons acceleratedwell above TeV energies in the spectral cut-off regime. In the case of diffusive shock ac-celeration, which is the most promising acceleration mechanism in SNRs, very strongmagnetic fluctuations with amplitudes well above the mean magnetic field must bepresent. Starting from such a fluctuating field, we have simulated images of polarized
X-ray emission of SNR shells and show that these are highly clumpy with high po-larizations up to 50%. Another distinct characteristic of this emission is the strongintermittency, resulting from the fluctuating field amplifications. The details of this”twinkling” polarized X-ray emission of SNRs depend strongly on the magnetic-fieldfluctuation spectra, providing a potentially sensitive diagnostic tool. We demonstratethat the predicted characteristics can be studied with instruments that are currentlybeing considered. These can give unique information on magnetic-field characteristicsand high-energy particle acceleration in SNRs.
Key words: radiation mechanisms: non-thermal—polarization—X-rays: ISM—(ISM:) supernova remnants—shock waves.
Electrons and positrons accelerated to TeV energies by dif-fusive shock acceleration (DSA) in SNR shells will effi-ciently radiate in X-rays in the associated magnetic fields(e.g., Reynolds & Chevalier 1981). A recent review on ‘SNRsat high energy’ is given by Reynolds (2008). In somesources (e.g. SN1006, RXJ1713.72-3946 and Vela Jr), thesynchrotron component is dominating the X-ray emission,whereas in others such as Cas A it is not easy to distinguishthe synchrotron component from the bremsstrahlung emis-sion. Mapping of the polarized
X-ray emission from SNRswould allow to separate out and study the synchrotron com-ponents.With the high-resolution imaging capability of
Chan-dra , likely synchrotron structures are already seen in theX-ray images of various SNRs (e.g., Vink & Laming 2003;Bamba et al. 2006; Patnaude & Fesen 2009). The observednon-thermal emission is concentrated in very thin (arc-seconds width) filaments and clumps and has typically arather steep spectrum with an exponential roll-off. In ad- ⋆ E-mail:[email protected]ffe.ru dition, Uchiyama et al. (2007) reported variability of suchX-ray hot spots in the shell of SNR RXJ1713.72-3946 onabout a one-year timescale. The thin filamentary structurescan be naturally explained in the DSA scenario: optionsare 1) a narrow spatial extend of the TeV-regime electronpopulation caused by efficient electron cooling due to syn-chrotron energy losses in the vicinity of the SNR shock withstrong magnetic-field amplification (e.g., Vink & Laming2003; Bamba et al. 2005; Vink 2008) and 2) the observednarrow filaments are limited by magnetic field damping andnot by the energy losses of the radiating electrons (e.g.,Pohl et al. 2005).Polarized X-ray emission - from any source - wasobserved so far only in very few cases. Observations ofthe Crab Nebula with X-ray polarimeters aboard
OSO-8 (Novick et al. 1972; Weisskopf et al. 1976) revealed a po-larized flux of about 15% at few keV energies (also de-tected with the
IBIS detector on
INTEGRAL by Forot et al.(2008)). Recently, G¨otz et al. (2009) reported variable polar-ized emission at 200-800 keV from GRB 041219A with
IBIS .Very little else can be reported thus far.Efficient DSA of protons and electrons in supernovashells requires turbulent magnetic fields, with energy den- c (cid:13) A.M.Bykov, Yu.A.Uvarov, J.B.G.M.Bloemen, J.W. den Herder, J.S.Kaastra sities that are a substantial fraction of the shock rampressure (e.g., Blandford & Eichler 1987; Malkov & Drury2001; Hillas 2005; Bell 2004; Amato & Blasi 2006;Vladimirov et al. 2006). Both regular and stochastic mag-netic fields determine the spectra and maps of synchrotronradiation of high-energy electrons and positrons from SNRs.A model of non-thermal radio emission from SNRs, ac-counting for the orientation of the regular ambient mag-netic field, was presented recently by Petruk et al. (2009).These authors synthesized radio maps of SNRs, making var-ious assumptions on the dependence of the electron injec-tion efficiency on the shock obliquity. Their method usesthe azimuthal profile of the radio surface brightness as aprobe of the orientation of the ambient magnetic field. Theeffect of random magnetic fields in supernova shells on ra-dio synchrotron emission was addressed by Stroman & Pohl(2009). They discussed the emission and transport of po-larized radio-band synchrotron radiation near the forwardshocks of young shell-type supernova remnants with a strongamplification of the turbulent magnetic field. Modeling themagnetic turbulence was done as a superposition of waves ata particular moment in time; no time evolution was consid-ered. They found that isotropic strong turbulence producesonly weakly polarized radio emission even in the absence ofinternal Faraday rotation. If anisotropy is imposed on themagnetic-field structure, then the degree of polarization canbe significantly increased, if the internal Faraday rotation isinefficient.It has long been known that random directions of mag-netic fields in addition to Faraday rotation may stronglyreduce the average polarization of synchrotron emissionsources (e.g., Westfold 1959; Crusius & Schlickeiser 1986;Stroman & Pohl 2009). This explains the relatively low po-larization frequently observed for radio synchrotron sources.However, as we will show below, the turbulent magneticfields that reduce the average polarization can result inhighly polarized patchy structures potentially observable inhigh resolution images at X-rays.Reynolds (1998) simulated X-ray synchrotron imagesassuming a regular magnetic field and distributions of ultra-relativistic electrons accelerated by a forward shock usingage-limited and loss-limited parameterizations.The effect of turbulent magnetic fluctuations (includ-ing field magnitude fluctuations) on synchrotron X-ray emis-sion images was recently addressed by Bykov et al. (2008).A system of finite size filled with a random magnetic fieldwas modeled and used to construct synchrotron emissionmaps of a source with kinetically simulated distributions ofultra-relativistic electrons. The random field was composedof a superposition of magnetic fluctuations (transverse planewaves propagating with some phase velocity) with randomphases and a given spectrum of amplitudes. Accounting forthe field magnitude fluctuations was especially important inview of the dependence of the emissivity on the local mag-netic field (further addressed below). A particulary strongdependence occurs in the cut-off regime of the synchrotronspectrum (also further addressed below). Bykov et al. (2008)found that non-steady structures (dots, clumps, and fila-ments) typically arise, in which the magnetic field reachesexceptionally high values. These magnetic-field concentra-tions dominate the synchrotron maps, with an evolving, in-termittent, and clumpy appearance. The modeling showed that the overall efficiency of synchrotron radiation from thecut-off regime of the electron spectrum can be strongly en-hanced in a turbulent field with some p h B i , compared toemission from a uniform field of the same magnitude p h B i ,but of just a random direction. Strong temporal variationsof the brightness of small structures were found, with timescales much shorter than variations in the underlying par-ticle distribution. The variability time scale depends on thephase velocity and the spectrum of magnetic fluctuations.The simulated structures indeed resemble the ’twinkling’structures that are observed in X-ray images of some su-pernova remnants.The same electrons that are producing X-ray syn-chrotron emission will emit TeV photons by inverse-Compton scattering. Both processes are of fundamental im-portance for our understanding of high-energy particle ac-celeration and the distinction between leptonic and nucle-onic contributions to the observed gamma-ray emission (e.g.,Aharonian et al. 2007, 2009). Gamma-ray images of a SNRwith efficient DSA in different circumstellar environmentswere constructed by Lee et al. (2008).In this paper we expand upon the work of Bykov et al.(2008), modeling the specific features of the polarized syn-chrotron emission arising from the stochastic nature of mag-netic fields of young SNR shells. In § § § In order to construct maps of polarized synchrotron emis-sion from SNR shells, it is convenient to use the local densi-ties of the Stokes parameters. Because of the additive prop-erty of the Stokes parameters ˜ I, ˜ Q, ˜ U, ˜ V for incoherent pho-tons, we can integrate these over the line of sight weightedwith the distribution function of radiating particles. Thedegree of polarization is determined in a standard way asΠ = p Q + U + V /I .The synchrotron emission is characterized by a coher-ence length l f that is of the order of a MeV electron gyro-radius (see e.g. Rybicki & Lightman 1979). In the simulationwe only consider the effects of magnetic fluctuations havingscales that are much larger than l f ∼ m e c /e p h B i . Thisis because in the nonlinear DSA modeling of non-relativisticSNR shocks the magnetic fluctuation spectra are expectedto fall down steeply at spatial scales below the gyro-radiusof a GeV proton (see for instance Fig.3 in Vladimirov et al.2006). That means that the fluctuation wavenumbers k sat-isfy k · l f ≪
1. Therefore, neglecting the magnetic fluctu-ations of the scale less or comparable to l f , we apply thestandard formulae (see e.g. Ginzburg & Syrovatskii 1965)for the synchrotron power of a single particle of Lorentz fac-tor γ ≫ c (cid:13) , 1– ?? Model of Polarized X-ray Emission from Twinkling Synchrotron Supernova Shells YY XZ X
Figure 1.
Geometry of the simulated supernova shell. The leftpanel shows half of the shell quarter with the boxes in whichthe random magnetic field was simulated. The local densities ofthe Stokes parameters were then integrated over the line of sightalong the axis −∞ < z < ∞ (i.e. the two half-quarters of thesphere). The right panel is the resulting projection that is shownin the simulated maps. from relativistic shocks of GRBs, pulsar wind nebulae andAGNs objects would likely require strong small scale mag-netic fluctuations of wavenumbers k · l f ∼ p (1) ν ( θ, γ ) and p (2) ν ( θ, γ ) with two principal directions of polarization ra-diated by a particle with Lorentz factor γ , as given byGinzburg & Syrovatskii (1965) [their Eqs.(2.20)]. Here θ isthe angle between the local magnetic field B ( r , t ) and thedirection to the observer. In the case of a random magneticfield it is convenient to use the local spectral densities of theStokes parameters expressed through p (1) ν and p (2) ν :ˆ˜ S = ˜ I ( r , t, ν )˜ Q ( r , t, ν )˜ U ( r , t, ν )˜ V ( r , t, ν ) = p (1) ν + p (2) ν ( p (1) ν − p (2) ν ) · cos 2 χ ( p (1) ν − p (2) ν ) · sin 2 χ ( p (1) ν − p (2) ν ) · tan 2 β where the angle χ is between the major axis of the po-larization ellipse and a coordinate in the plane perpen-dicular to the observer direction, and tan β is determinedby the ratio of the minor and major axes of the ellipse(Ginzburg & Syrovatskii 1965). Synchrotron X-ray emission is radiated by 10 TeVregime electrons since the magnetic field amplitude inSNR shells is typically below a mG. Efficient DSA of high-energy particles requires a substantial ampli-fication of magnetic field fluctuations in the vicinityof the shock; see e.g. Bell (1978); Blandford & Eichler(1987); Malkov & Drury (2001). Magnetic-field amplifica-tion mechanisms due to cosmic-ray instabilities in nonlinearDSA were proposed recently by Bell (2004); Amato & Blasi(2006); Vladimirov et al. (2006); Pelletier et al. (2006);Vladimirov et al. (2008); Zirakashvili & Ptuskin (2008).The models predict amplified magnetic-field amplitudes wellabove the interstellar field in the far upstream of the shock.These current models are suited to estimate the amplitudesand spectra of amplified magnetic fluctuations averaged oversome macroscopic spatial and temporal scales. The averagedmagnetic-field spectra available from the models are appro-priate to model energetic particle spectra, but do not allowto simulate the synchrotron images of SNR shells and tojudge about their temporal evolution.In reality the distribution of the emitting electrons isa random function of position and particle energy becauseof the stochastic nature of both the electromagnetic fieldsand the particle dynamics. However, no self-consistent treat-ment of such a particle distribution in strong magnetic tur-bulence is available. Rigorous modeling of the magnetic-fieldstructure and evolution should invoke simultaneously fullynonlinear PIC-type simulations of the collisionless shock,supersonic flow, and the effect of the high-energy parti-cles. A microscopic selfconsistent description of magnetic-field fluctuations that are strongly coupled with electric cur-rents of accelerated particles is not feasible yet for non-relativistic shock simulations in SNRs (see appendix inVladimirov et al. 2008, for a discussion).Therefore, to model the synchrotron SNR images wesimulated local statistically stationary random magneticfields of given spectra using the technique described inBykov et al. (2008). The statistically isotropic and homo-geneous random field was constructed as a sum over a largenumber of plane waves with wave vector, polarization, andphase chosen randomly. In the simulation presented belowwe assume a plane wave frequency ω n ( k n ) = v ph · k n pa-rameterized with a phase velocity v ph . The spectral energydensity of the magnetic-field fluctuations of wavenumber k is described as W ( k ) ∝ k − δ , where δ is the spectral index. h B i = Z k max k min dk W ( k ) , The average square magnetic field h B i , the spectral index δ , and the wavenumber range ( k min , k max ) are the input pa-rameters of the model. The spectral index δ in the standardDSA scenario is expected to be in the range 1 δ κ ( p ) ∝ p a , where a = 1 for TeV-regime electrons (the Bohmtype diffusion regime) and it has a flatter energy dependence c (cid:13) , 1– ?? A.M.Bykov, Yu.A.Uvarov, J.B.G.M.Bloemen, J.W. den Herder, J.S.Kaastra at MeV regime energies. The synchrotron losses of 10 TeVregime electrons in magnetic fields of √ < B > > − Gare faster than the inverse Compton losses that are domi-nated by CMB photon scattering.The scale sizes of the particle distributions of the shockupstream (both electrons and protons) for DSA is ∆ u ≈ κ ( p ) /u sh ∼ × · u sh8 · B − µ G · E TeV cm, where the r.m.s.magnetic field B µ G is in µ G units, u sh8 is the shock ve-locity in units of 1,000 km s − , and E TeV is the electronenergy in TeV units. In the shock upstream the width of thelayer where the highest energy electrons are stopped due tosynchrotron losses is about ∆ u . In the shock downstreamthe width of the ultra-relativistic electron/positron coolinglayer ∆ d s is about ∆ d ∼ × · u sh8 · B − µ G · E − TeV cm. Bothwidths ∆ u,d of the electron regions emitting X-rays are rel-atively narrow, typically below 0.3 pc for B µ G >
30 and E TeV ≫
1. Therefore, for large enough SNR shells of radii R SNR >> ∆ u,d the one dimensional approximation for thedetermination of the distribution function is well justified.It is also important that the wavelengths of magnetic fluc-tuations in the SNR shell are of the order of the gyroradii ofthe relativistic protons in DSA models, and therefore thatthese are below ∆ u,d justifying the use of a homogeneousr.m.s. field in the losses term of the kinetic equation. Wenumerically calculated the electron distribution function inthe vicinity of the SNR forward shock. The results were thenused in simulations of the maps of polarized synchrotronemission of the SNR. Figure 1 shows a 3-D sketch of the simulated SNR andits projection along the line of sight. To simulate the im-ages of the SNR shell we assumed that a quarter part of aspherical forward shock has a relativistic electron distribu-tion N ( z, γ, t ) that does not depend on the azimuthal andpolar angles, but is inhomogeneous in the radial directionwith a strong peak (of width ∆ s ) at the shock position at r = R SNR . The line of sight is along the z axis. The Stokesparameters ˜ I, ˜ Q, ˜ U, ˜ V for incoherent photons are additive, sowe can integrate these over the line of sight weighted withthe distribution function of emitting particles N ( z, γ, t ) toget the intensityˆ S ( R ⊥ , t, ν ) = Z dz dγ N ( z, γ, t ′ ) ˆ˜ S ( r , γ, t ′ ) . (1)To collect the photons reaching the observer at the same mo-ment t , we performed an integration over the source depthusing the retarded time t ′ = t − | r − R ⊥ | /c as argument in B ( r , t ′ ) and N ( r , E, t ′ ). The integration grid has a cell sizesmaller than L min . The result is a surface density of Stokesparameters of radiation from the volume along the line ofsite. The fourth Stokes parameter V is zero in the case of anisotropic electron velocity distribution. In order to achievea few percent accuracy we integrated over 8000 grid pointsalong the line of sight. The number of pixels in the sky pro-jection is 100 × − propagating in a fully ion-ized plasma of number density 0.03 cm − . The kinetic model used to simulate the electron distribution was described indetail by Bykov et al. (2000). The magnetic field in the far-upstream region was fixed at 3 µ G and it was assumed thatthe magnetic-field amplification produces a random field of p h B i = 3 × − G in the shock vicinity. In the ran-dom magnetic field simulations we used a wavenumber range k min < k < k max , where L min = 2 π/k max = 2 × − π · D for δ = 1 . L min = 2 π/k max = 2 × − π · D for δ = 2 . L max = 2 π/k min = 0 . π · D for both δ values. Here D is the size of a unit cubic box, as shown in Figure 1. Therandom magnetic field in the simulated SNR shell quarterwas divided into 8 such boxes. This number of boxes waschosen to achieve the required accuracy of the integrationof the random field along the line of sight. The field in theboxes was simulated as a function of global SNR coordinatesas it is shown in Figure 1 (i.e., not just locally in each box).Note that the field was actually simulated in a region largerthan the SNR shell and that the box sizes are larger thanthe sizes of the random filamentary structures that appear. Figures 2-4 show examples of the resulting maps at differ-ent X-ray energies. The left panels show the synchrotronintensity, the right panels the polarization degree, and thecentral panels the product of the two. The latter is a mea-sure of the polarized flux and is meant to illustrate thatpeaks in the polarization-degree map do not necessarily cor-respond to peak intensities. The images clearly demonstrate1) the presence of detailed structures - clumps and filaments- produced by the stochastic field topology (for details seeBykov et al. 2008) and 2) that some of these structures emithighly polarized emission ( > δ = 2 . δ = 2 . p h B i = 3 × − G ).Irrespective of the precise value of δ , it is clear from Fig-ures 2-5 that the degree of polarization is higher at higherX-ray energies. The physical reason is best illustrated incase of a power-law electron distribution (with spectral indexΓ). Namely, the degree of polarization ˜Π and the local syn-chrotron emissivity ˜ I ( r , t, ν ) have the following dependencieson Γ: ˜Π ≈ (Γ+1) / (Γ+7 /
3) (i.e. the degree of of polarization˜Π is increasing with Γ) and ˜ I ( r , t, ν ) ∝ B / (i.e. the lo-cal emissivity is relatively very high for large B and large Γ)(see e.g., Ginzburg & Syrovatskii 1965; Rybicki & Lightman1979). In the high-energy cut-off regime the electron spec-trum is typically exponential, but the effective index Γ islarge indeed and the value increases for electrons emittingat higher frequency ν . This explains the increase of the po-larization degree with ν . In addition, the dependency of theemissivity ˜ I on B and Γ can lead to a highly polarized brightfeature that stands out in the map for even a single strong lo-cal field maximum. In lower-energy maps, for which Γ on av-erage is smaller (i.e. well below the cut-off regime), high po-larization of a single maximum can be smoothed or washed c (cid:13) , 1– ?? Model of Polarized X-ray Emission from Twinkling Synchrotron Supernova Shells Figure 2.
Simulated maps of polarized synchrotron emission ina random magnetic field at 0.5 keV. Intensity, ν · I ( R ⊥ , t, ν ), isshown with a linear color scale in the left panel. The central panelshows the product of intensity and polarization degree. The rightpanel shows the degree of polarization indicated by the colorbar.The stochastic magnetic field sample has p h B i = 3 × − Gand spectral index δ = 1 . Figure 3.
The same maps as in Figure 2, but at 5.0 keV. out by contributions from a number of weaker field maximaintegrated over the line of sight. This effect can be seen inFigures 2-4. The high-energy maps are ’twinkling’ because ofthe finite life-time of the magnetic-field amplifications. Thetimescale for variations in the polarization (and the energydependence) is similar to that of the time variability of theintensity maps (studied in § ′′ , 18 ′′ ,and 36 ′′ ) at 5 keV. In Figures 7 and 8 the polarization mapsare presented at 20 keV for larger pixel sizes of 3 ′ and 7.5 ′ (close to the INTEGRAL ISGRI pixel size) and δ = 1 and2. Comparison of Figures 7 and 8 shows again the strong de-pendence on the spectral index δ of the stochastic magneticfield. This work was stimulated by the fact that a number of X-raypolarimeter instruments is being considered currently. The
Figure 4.
The same maps as in Figure 2, but at 50.0 keV.
Figure 5.
The 5.0 keV synchrotron map for a different magneticfield spectrum in the shell. The stochastic magnetic field samplehas p h B i = 3 × − G and δ = 2 . Figure 6.
The simulated 5.0 keV synchrotron polarization mapswith different pixel sizes. The left one has a pixel size of 9 ′′ , thecentral of 18 ′′ , and the right of 36 ′′ . The yellow frame of 2.6 ′ × ′ indicates the field of view of the XPOL polarimeter (see text). Thestochastic magnetic field sample has p h B i = 3 × − G and δ = 1 .
0. The simulated SNR shell has the radius of about 0.4 ◦ .c (cid:13) , 1– ?? A.M.Bykov, Yu.A.Uvarov, J.B.G.M.Bloemen, J.W. den Herder, J.S.Kaastra
Figure 7.
The simulated 20.0 keV synchrotron polarizationmaps with different pixel sizes. The left one has a pixel sizeof 3 ′ and the right of 7.5 ′ . The yellow line indicates the for-ward shock position. The stochastic magnetic field sample has p h B i = 3 × − G and δ = 1 .
0. The field was simulated in abox larger than the SNR shell, but the regions well outside theforward shock are dim as it is clearly seen in the left panels inFigures 2 - 5.
Figure 8.
The same maps as in Figure 7, but for magneticturbulence with δ = 2 . Imaging X-ray Polarimetry Explorer
IXPE was proposedby Weisskopf et al. (2008) as a dedicated X-ray-polarimetryobservatory to measure the X-ray linear polarization as afunction of energy, time, and position. Legere et al. (2005)is developing a Compton polarimeter to measure polariza-tion of hard X-rays in the 50-300 keV energy range. Aballoon-borne hard X-Ray polarimeter
HX-POL is proposedby Krawczynski et al. (2008). A Hard X-ray Telescope
HET aboard the Energetic X-ray Imaging Survey Telescope
EX-IST (Grindlay 2009), with a wide field of view for the codedaperture imaging, is being designed to study the polariza-tion at high energies and its temporal evolution. Polariza-tion detection of X-ray sources as faint as 1 milliCrab is anaim of the Gravity and Extreme Magnetism SMEX (GEMS) mission that uses foil mirrors and Time Projection Cham-ber detectors (Swank et al. 2008; Jahoda et al. 2008). Themissions listed above have good perspectives in this fieldof research. We address here the potentials of the
XPOL polarimeter as proposed for XEUS (Costa et al. 2008) - al- though evolved into International X-ray Observatory (
IXO )in the mean time - to illustrate the observational possibili-ties for synchrotron X-ray studies of SNR RXJ1713.72-3946as a generic example.RXJ1713.72-3946 has an extended shell of about onedegree angular diameter. A field of view of 1.5 ′ × ′ andan angular resolution of 5 ′′ was proposed by Costa et al.(2008), if XPOL was part of the
XEUS mission. A polarime-ter like
XPOL aboard the
IXO mission will have a some-what larger field of view. We illustrate that case in Figure 6where the field of view of 2.6 ′ × ′ is shown as a yellow boxin the polarization maps simulated with pixel sizes of 9 ′′ , of18 ′′ , and of 36 ′′ to illustrate the angular resolution effect.In the case of an extended source like RXJ1713.72-3946 first of all a wide field map of the source regionis needed to specify the XPOL pointing. Using
Chandra archive data, we estimate the 2-10 keV flux from a 2.6 ′ × ′ region in the shell of RXJ1713.72-3946 to be about4.5 × − erg cm − s − . From the minimum detectablepolarization as a function of observing time as presentedin Fig. 6 of Costa et al. (2008), corrected for the reducedeffective area of IXO , we estimated that a meaningful po-larization map can be constructed with XPOL within anexposure time of 100 ks. The polarization map of 2.6 ′ × ′ should likely reveal detailed highly-polarized structures withtypical scales of about 10 ′′ as it was discovered in Chandra images by Uchiyama et al. (2007). The degree of polariza-tion will increase with increasing X-ray energy as predictedfrom the modeling in this paper. The polarization will betime variable on a few year time scale (depending on thephoton energy) as it was found by Bykov et al. (2008) insimulated intensity maps. Mapping of the whole extendedshell of RXJ1713.72-3946 in polarized X-rays would be un-realistic with that set up, therefore the target must be firstidentified with a wide field X-ray imager.Another object of great interest is Cas A, that is of anangular size comparable with the field of view of
XPOL .We estimate that some thin peripheral polarized X-ray fil-aments of some ten arcsecond scale can be studied with
XPOL , also with an exposure of about 100 ks. In the DSAmodel the scale size L max of the magnetic fluctuations re-sponsible for the twinkling polarized structures is expectedto be connected to gyroradii of accelerated protons at max-imal energies. These can be roughly estimated to be about3 × · B − µ G · E TeV cm. Therefore, their angular sizesare expected to be above a few arcseconds for SNRs withina few kiloparsec distance.
We have studied the polarization of X-ray synchrotron emis-sion from SNRs addressing the significant effect of magnetic-field fluctuations on synchrotron emission in X-rays. Suchmagnetic fluctuations form a natural starting point becausethey must be present if diffusive shock acceleration is indeedthe basic mechanism for accelerating particles in SNRs. LikeBykov et al. (2008) we simulated random magnetics field toconstruct synchrotron emission maps, given a smooth and http://ixo.gsfc.nasa.gov/science/performanceRequirements.htmlc (cid:13) , 1– ?? Model of Polarized X-ray Emission from Twinkling Synchrotron Supernova Shells steady distribution of electrons, but now with special at-tention to the polarization of the resulting emission. Thesimulated random magnetic fields show non-steady local-ized structures with exceptionally high magnetic-field am-plitudes . These magnetic-field concentrations dominate thesynchrotron emission - integrated along the line of sight -from energetic > TeV electrons, i.e. in the cut-off regime. Interms of a power-law electron spectrum with spectral indexΓ, this can be understood since the synchrotron emissivity˜ I ( r , t, ν ) is proportional to B / (i.e. the local emis-sivity is relatively very high for large B and large Γ). Thepower-law approximation is only useful over a narrow elec-tron energy range in the cut-off regime, where the effectivespectral index Γ is increasing with the electron energy.Starting from the simulated magnetic-field simulations,we have constructed maps of polarized X-ray emission ofSNR shells. These are highly clumpy with high polarizationsup to 50%. This characteristic of high polarization again ap-plies to energetic > TeV electrons in the cut-off regime. Interms again of a power-law electron spectrum with spectralindex Γ, this can be understood since the degree of polariza-tion is given by ˜Π ≈ (Γ + 1) / (Γ + 7 /
3) (i.e. ˜Π is increasingwith Γ).The distinct characteristic of the modeled synchrotronemission is its strong intermittency, directly resulting fromthe exceptionally high magnetic-field amplifications ran-domly occurring as shown in the simulations. Also charac-teristic is the increase of the polarization degree with X-rayenergy addressed in §
3. Since this ”twinkling” polarized X-ray emission of SNRs depends strongly on the magnetic-fieldfluctuation spectra, it provides a potentially sensitive diag-nostic tool.The intermittent appearance of the polarized X-rayemission maps of young SNR shells can be studied in detailobservationally with imagers of a few arcsecond resolution,though even arcmin resolution images can provide impor-tant information as it is illustrated in Figures 6,7,8. Thepolarized emission clumps of arcsecond scales are time vari-able on a year or longer (depending on the observed photonenergy, magnetic field amplification factor and the plasmadensity in the shell) allowing for rather long exposures evenin the hard X-ray energy band. Hard X-ray observationsin the spectral cut-off regime are the most informative tostudy the magnetic fluctuation spectra and the accelerationmechanisms of ultra-relativistic particles.Altogether, the modeled appearance and its time vari-ability - on a timescale of typically a year - resembles closelywhat is observed already in X-ray images of some youngsupernova remnants. Observing the predicted high polar-ization in clumps and filaments, however, should proba-bly await future instruments that are currently being con-sidered. Such observations will provide unique informationon magnetic fields and high-energy particle acceleration inSNRs.
ACKNOWLEDGMENTS
We thank the anonymous referee for careful reading ofour paper and a useful comment. Some of the calculationswere performed at the Supercomputing Centre (SCC) of theA.F.Ioffe Institute, St.Petersburg. A.M.B. thanks R.Petre for a discussion of the
SMEX project perspective. A.M.B.and Yu.A.U were supported in part by RBRF grant 09-02-12080 and by the RAS Presidium Programm. SRON is sup-ported financially by NWO, the Netherlands Organisationfor Scientific Research.
REFERENCES
Aharonian F., Akhperjanian A. G., Bazer-Bachi A. R., etal. 2007, A&A, 464, 235Aharonian F., Akhperjanian A. G., de Almeida U. B., etal. 2009, ApJ, 692, 1500Amato E., Blasi P., 2006, MNRAS, 371, 1251Bamba A., Yamazaki R., Yoshida T., et al. 2005, ApJ, 621,793Bamba A., Yamazaki R., Yoshida T., et al. 2006, Advancesin Space Research, 37, 1439Bell A. R., 1978, MNRAS, 182, 147Bell A. R., 2004, MNRAS, 353, 550Blandford R., Eichler D., 1987, Phys. Rep., 154, 1Bykov A. M., Chevalier R. A., Ellison D. C., et al. 2000,ApJ, 538, 203Bykov A. M., Uvarov Y. A., Ellison D. C., 2008, ApJ, 689,L133Costa E., Bellazzini R., Bregeon J., et al. 2008, in Proc. ofSPIE Vol. 7011. pp 70110F–1Crusius A., Schlickeiser R., 1986, A&A, 164, L16Forot M., Laurent P., Grenier I. A., et al. 2008, ApJ, 688,L29Ginzburg V. L., Syrovatskii S. I., 1965, ARA&A, 3, 297G¨otz D., Laurent P., Lebrun F., et al. 2009, ApJ, 695, L208Grindlay J. E., 2009, in Bulletin of the American Astro-nomical Society Vol. 41. p. 388Hillas A. M., 2005, Journal of Physics G Nuclear Physics,31, 95Jahoda K., Black K., Deines-Jones P., et al. 2008, inAAS/High Energy Astrophysics Division p. 28.15Krawczynski H., Garson III A., Li Q., et al. 2008, ArXive-print 0812.1809Lee S.-H., Kamae T., Ellison D. C., 2008, ApJ, 686, 325Legere J., Bloser P. L., Macri J. R., et al. 2005, in Proc. ofSPIE Vol. 5898. p. 413Malkov M. A., Drury L., 2001, Reports on Progress inPhysics, 64, 429Novick R., Weisskopf M. C., Berthelsdorf R., et al. 1972,ApJ, 174, L1Patnaude D. J., Fesen R. A., 2009, ApJ, 697, 535Pelletier G., Lemoine M., Marcowith A., 2006, A&A, 453,181Petruk O., Dubner G., Castelletti G., et al. 2009, MNRAS,393, 1034Pohl M., Yan H., Lazarian A., 2005, ApJ, 626, L101Reynolds S. P., 1998, ApJ, 493, 375Reynolds S. P., 2008, ARA&A, 46, 89Reynolds S. P., Chevalier R. A., 1981, ApJ, 245, 912Rybicki G. B., Lightman A. P., 1979, Radiative processesin astrophysics, Wiley-Interscience, New YorkSpitkovsky A., 2008, ApJ, 682, L5Stroman W., Pohl M., 2009, ApJ, 696, 1864Swank J., Kallman T., Jahoda K., 2008, in 37th COSPARScientific Assembly Vol. 37. p. 3102 c (cid:13) , 1– ?? A.M.Bykov, Yu.A.Uvarov, J.B.G.M.Bloemen, J.W. den Herder, J.S.Kaastra
Uchiyama Y., Aharonian F. A., Tanaka T., et al. 2007, Nat,449, 576Vink J., 2008, in Aharonian F. A. e. a., ed., AIP Conf.Ser. Vol. 1085, Multiwavelength Signatures of Cosmic RayAcceleration by Young Supernova Remnants. p. 169Vink J., Laming J. M., 2003, ApJ, 584, 758Vladimirov A., Ellison D. C., Bykov A., 2006, ApJ, 652,1246Vladimirov A. E., Bykov A. M., Ellison D. C., 2008, ApJ,688, 1084Weisskopf M. C., Bellazzini R., Costa E., et al. 2008, inProc. of SPIE Vol. 7011. pp 70111I–1Weisskopf M. C., Cohen G. G., Kestenbaum H. L., et al.1976, ApJ, 208, L125Westfold K. C., 1959, ApJ, 130, 241Zirakashvili V. N., Ptuskin V. S., 2008, ApJ, 678, 939 c (cid:13) , 1–, 1–