X-ray Perspective of the Twisted Magnetospheres of Magnetars
aa r X i v : . [ a s t r o - ph . H E ] M a y Draft version August 6, 2018
Preprint typeset using L A TEX style emulateapj v. 8/13/10
X-RAY PERSPECTIVE OF THE TWISTED MAGNETOSPHERES OF MAGNETARS
Shan-Shan Weng , Ersin G¨o˘g¨us¸ , Tolga G¨uver , & Lin Lin Sabancı University, Faculty of Engineering and Natural Sciences, Orhanlı Tuzla 34956 Istanbul Turkey Istanbul University, Science Faculty, Department of Astronomy and Space Sciences, Beyazıt, 34119, Istanbul, Turkey and Fran¸cois Arago Centre, APC, Universit´e Paris Diderot, CNRS/IN2P3 13 rue Watt, 75013 Paris, France
Draft version August 6, 2018
ABSTRACTAnomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) are recognized as the mostpromising magnetar candidates, as indicated by their energetic bursts and rapid spin-downs. It isexpected that the strong magnetic field leaves distinctive imprints on the emergent radiation both byaffecting the radiative processes in atmospheres of magnetars and by scattering in the upper magneto-spheres. We construct a self-consistent physical model that incorporates emission from the magnetarsurface and its reprocessing in the three-dimensional (3D) twisted magnetosphere using a Monte Carlotechnique. The synthetic spectra are characterized by four parameters: surface temperature kT, sur-face magnetic field strength B , magnetospheric twist angle ∆ φ , and the normalized electron velocity β . We also create a tabular model (STEMS3D) and apply it to a large sample of XMM-Newton spectraof magnetars. The model successfully fits nearly all spectra, and the obtained magnetic field for 7 outof the 11 sources are consistent with the values inferred from the spin-down rates. We conclude thatthe continuum-fitting by our model is a robust method to measure the magnetic field strength andmagnetospheric configuration of AXPs and SGRs. Investigating the multiple observations of variablesources, we also study the mechanism of their spectral evolution. Our results suggest that the magne-tospheres in these sources are highly twisted (∆ φ >
Subject headings: radiation mechanisms: nonthermal — stars: magnetic fields — stars: neutron —X-rays: stars INTRODUCTION
Anomalous X-ray pulsars (AXPs) and soft gamma-ray repeaters (SGRs) form an intriguing class of iso-lated neutron stars (NSs). They share the similar ob-servational properties: (1) relatively slow spin peri-ods ( P ∼ −
12 s); (2) large spin-down rates ( ˙ P ∼ − − − s s − ); (3) high persistent X-ray lumi-nosity ( L X ≈ − erg s − ), which significantlyexceeds their rotation power for most sources; and (4)different types of X-ray variability; i.e., long-term X-ray flux enhancements and short energetic bursts (seeMereghetti 2008, and Rea & Esposito 2011 for recent re-views). These behaviors can be understood within themagnetar scenario – extremely strong magnetic fieldsof some NSs giving rise to the observed exotic man-ifestations (Thompson & Duncan 1995, 1996). Thereare now 28 magnetars or magnetar candidates known (Olausen & Kaspi 2014; Zhou et al. 2014).Although recent multi-wavelength observations ofmagnetar activities significantly widened our views, themost essential knowledge on magnetars is provided bythe emission properties of their X-ray radiation. The X-ray spectra of SGRs and AXPs below 10 keV are soft andcan be empirically described by a power-law (PL) modelwith photon index Γ ∼ − kT ∼ . ∼
1) above 10keV (see, e.g., Kuiper et al. 2004, 2006; den Hartog et al. ν . With more accumulated data,Kaspi & Boydstun (2010) showed that the spectral in-dices in quiescence are not only correlated with ˙ ν butalso the magnetic field B inferred from timing analy-ses. Magnetars occasionally emit short ( ∼ . ∼ keV pho-tons, the resonant scattering occurs in the layer wherethe magnetic field decays to ∼ G regardless of theNS surface magnetic field. As a consequence, the es-sential information of SGRs/AXPs – the strength of themagnetic field—is not incorporated in both 1D and 3DRCS models since the scattering process is insensitive tothe magnetic field below its cyclotron frequency ( ≥ B ≥ G) NS atmospheres due to the effect of vacuumpolarization and proton cyclotron resonances, by af-fecting the interactions between the photons and theplasma (e.g., Ho & Lai 2003; ¨Ozel 2003). Thus, thespectral profile of surface emission strongly dependson the magnetic field. Taking into account the com-bined effects of the magnetar atmosphere and its mag-netosphere, G¨uver et al. (2007) developed the 1D sur-face thermal emission and magnetospheric scattering(STEMS) model, which can successfully fit the softX-ray spectra of both steady and variable magnetars(G¨uver et al. 2007, 2012; Ng et al. 2011; Lin et al. 2012).Additionally, the STEMS model uncovers the informa-tion concering the magnetic field. However, because theSTEMS model treats the scattering region as a plane-parallel slab, it cannot offer information about the ge-ometry of the magnetosphere.The long-term monitoring observations revealed thatthe X-ray emissions of most magnetars are variable(e.g., Rea 2014), in the extreme cases, namely the tran-sient magnetars (e.g., XTE J1810-197, and 1E 1547.0-5408), the overall flux can be enhanced up to threeorders of magnitude brighter than their quiescentlevel (e.g., Ibrahim et al. 2004; Mereghetti et al. 2009;Kaneko et al. 2010). Studying X-ray behaviors in dif-ferent flux levels would help us to explore the na-ture of magnetar, i.e., the evolution of magnetospheres(Beloborodov 2009) and the magneto-thermal evolutionof NSs (Pons & Rea 2012; Vigan`o et al. 2013). Basedon
XMM-Newton observations, Zhu et al. (2008) foundthat the afterglow of the 1E 2259+586’s 2002 outburstfollowed by a PL decay and the hardness is strongly cor-related with the flux. Alternatively, the flux relaxationof XTE J1810-197’s 2003 outburst is best described byan exponential decay and the surface temperature be-came cold in the meantime (Gotthelf & Halpern 2005).Diverse observational phenomena (see Rea & Esposito2011 and reference therein) suggest that X-ray activi- ties could be driven by different mechanisms, either thetwisted magnetospheres (Thompson et al. 2002) or thedeep crustal heating (Lyubarsky et al. 2002).In this work, we carry out 3D Monte Carlo simulationsof the emitted photons from the surface of a highly mag-netized NS propagation in a twisted magnetosphere. Thephysical bases of our model and the Monte Carlo methodare described in Section 2. The model properties are pre-sented in Section 3. We also numerically calculate modelspectra and create a tabular model, which is further ap-plied to the X-ray spectra of magnetars (Section 4). Theultimate goal of this paper is to better understand thesurface and magnetospheric properties of magnetars andtheir evolutions using our model. In Section 5, we discussthe spectral modeling results and their implications. MODELS
In this section, we first outline the physical processesin a strongly magnetized atmosphere, and then scatterthe surface emission in the 3D twisted magnetosphere.The gravitational redshift effect is also considered in ourmodel.
Surface emission of magnetars
In strong magnetic fields ( B ≥ G), the vacuum po-larization, a quantum electrodynamics phenomenon, canaffect radiative transfer in magnetized plasmas by mod-ifying polarization modes and the opacities of the nor-mal modes (e.g., Zane et al. 2001; Ho & Lai 2003; ¨Ozel2003). The proton cyclotron resonance is another phe-nomenon that affects the propagation of photons in amagnetized plasma. Following the methods discussed in¨Ozel (2001, 2003), the radiative equilibrium models areconstructed for the fully ionized hydrogen plasmas, tak-ing into account the effects of vacuum polarization andion cyclotron lines. We use a modified Feautrier methodfor the solution of the angle- and polarization-mode de-pendent radiative transfer problem and ensure radiativeequilibrium with a temperature correction scheme basedon the Lucy–Uns¨old algorithm. The surface emissionspectrum can be defined by just two parameters: theeffective temperature of atmosphere kT and the surfacemagnetic field strength B . Resonant cyclotron scattering in 3D twistedmagnetosphere
The Monte Carlo techniques are quite suitable to han-dle photon scattering in complicated 3D configurationsand the 3D RCS Monte Carlo code has already beenbuilt by Fern´andez & Thompson (2007) and Nobili et al.(2008). Both of these works considered axisymmetricglobally twisted magnetospheres and seed photons as be-ing the canonical blackbody (BB) emissions. Neverthe-less, these codes allow for an arbitrary distribution ofseed photons, velocity distribution of the charged parti-cles, and magnetic field geometry.We build our Monte Carlo code following an approachthat is similar to the one discussed in Nobili et al. (2008).The fundamental difference is the description of seed pho-tons. (1) The original BB emissions are distorted af-ter travelling through strongly magnetized atmospheres,mostly carried by extraordinary mode photons ( ¨Ozel2003). In our work, this surface emission is adopted asTEMS3D 3the seed photons, which are homogeneously injected fromthe stellar surface with a wavevector pointing in the ra-dial direction. Note that under the influence of an ultra-strong magnetic field, the surface emissions are expectedto be anisotropic and their temperature varies withlatitude (e.g., Heyl & Hernquist 1998; Bernardini et al.2011). However, the study on the anisotropic surfaceemissions is beyond the scope of this paper and willbe reported elsewhere. (2) The globally twisted mag-netosphere has a self-similar and force-free construction( j × B = 0), which is uniquely characterized by the nettwist angle of the field lines anchored close to the twomagnetic poles, ∆ φ . (3) The current density j is deducedfrom the Ampere’s law ( ▽ × B = (4 π/c ) j ) under theforce-free assumption. Following the work in Nobili et al.(2008), we consider the effects of bulk velocity and alsothermal velocity distribution of charge carriers, assuminga 1D Maxwellian distribution at a given temperature su-perimposed to a bulk motion. In order to reduce parame-ters in the model, the electron temperature kT e is derivedfrom the bulk velocity (and further halved) by assumingthe equipartition between thermal and bulk kinetic en-ergy. As a result, the number density of electrons ( n e )is a function of the twist angle and the average electronvelocity. (4) We neglect both the non-resonant scatter-ing and electron recoil effects, which are not importantin the soft X-ray band. The spectrum is calculated inthe non-relativistic regime with the simplified resonantcross-section (Equation (10) in Nobili et al. 2008), whichis independent of magnetic field and frequency.As photons propagate in the 3D twisted mag-netosphere, we check whether they can freelyescape out of the magnetosphere in every step(Fern´andez & Thompson 2007; Nobili et al. 2008).If the photon frequency together with moving directionstill allow resonant scattering, as soon as the integratedscattering depth τ s satisfies τ s ≥ − lnU , where U isa random number in the range [0,1], a scattering istriggered, and the photon frequency, direction, andpolarization are updated. Then, the photon continuesto travel in the magnetosphere until another scatteringoccurs or it escapes to infinity (observers). We alsorefer to Nobili et al. (2008) for more details on thescattering process. The spectra are calculated byevolving 5,000,000 photons and characterized by fourparameters: surface temperatures kT , magnetic fieldstrength at the poles B , magnetospheric twist angles∆ φ , and the normalized electron velocity β = v/c , where c is the speed of light. An example spectrum (kT = 0 . B = 10 G, ∆ φ = 1 .
0, and β = 0 .
3) is shown inFigure 1.
Gravitational redshift effect
Because of the strong gravitational field of NSs, thegravitational redshift effect is important and should becorrected for the photons close to NSs, but is negligiblefor the photons that are far away from NSs ( > severaltimes of the NSs radii). According to General Relativity,the photons experience a redshift in gravitational fieldsby a factor of 1 + z = q − GMRc assuming Schwarzschildgeometry. In principle, the gravitational redshift shouldbe corrected for the surface emission, before the magne-tospheric scattering. Since the scattering optical depth -5 -4 -3 -2 -1 I n t e n s i t y ( A r b i t r ay ) BBMS3D RCSSTEMS3D
Figure 1.
The BB (kT = 0 . kT = 0 . B = 10 G, red dotted line)emissions are scattered in a 3D twisted magnetosphere (∆ φ = 1 . β = 0 . -5 -4 -3 -2 -1 I n t e n s i t y ( A r b i t r ay ) BeforeAfter
Figure 2.
Example spectrum (kT = 0 . B = 10 G, ∆ φ =1 .
0, and β = 0 .
3) with the gravitational redshift correction ( z =0 . is independent of frequency in a self-similar magneto-sphere (Thompson et al. 2002; Fern´andez & Thompson2007), it allows us to correct the spectra after the mag-netospheric scattering. In order to test this hypothesis,we calculated the spectra for kT = 0 . B = 10 G, ∆ φ = 1 .
0, and β = 0 . z = 0 .
306 (corresponding to an NSwith mass 1.4 M ⊙ and R NS = 10 km) performed before(red line in Figure 2) and after (blue line) the magneto-spheric scattering, and find that both spectra are identi-cal. Therefore, it becomes feasible and convenient to dothe correction in XSPEC (after scattering, § MODEL PROPERTIES
The emerging radiation from the surface of a highlymagnetized NS is expected to be modified by both vac-uum polarization and proton cyclotron resonance. Atmagnetar-type field strengths, the resulting spectrum isspectrally harder than a Planckian and would exhibitproton line features in the soft-X-ray band (Figure 1). ∆φ τ β =0.2 β =0.3 β =0.5 β =0.8 Figure 3.
Angle-averaged optical depth ( τ ) vs. ∆ φ and differentvalues of β : 0.2 (solid), 0.3 (dotted), 0.5 (dashed), and 0.8 (dashed-dotted). The emerging photons further gain energy by multi-ple scattering in the twisted magnetosphere, manifest-ing themselves as the high energy tail. To illustrate thispoint, we performed the scattering of a BB ( kT = 0 . kT = 0 . B = 10 G) in a 3D twisted magnetosphere(∆ φ = 1 . β = 0 . τ ) with respectto ∆ φ and β . Figure 4 illustrates the effects on the spec-tral shape of varying twist angle and electron velocity.It is clearly seen that the level of upscattering of emer-gent thermal photons increases with ∆ φ and in particularwith β .Lyutikov & Gavriil (2006) pointed out that the deepline features present in the surface spectra can besmoothed out with a large scattering optical depth. How-ever, investigating the spectra obtained with a narrowvelocity distribution ( ¯ β = 0 .
5, ∆ β = 0 .
1) and large twist(∆ φ = 1 . ∼
2; how-ever, a significant line feature remained as a result of anoptical depth in the 3D twisted magnetosphere that wasnot very large. As already mentioned, the optical depthin 3D twisted magnetosphere depends not only on ∆ φ but increases sharply with decreasing β (Figure 3). Aswe show in Figure 4, we find that the STEMS3D modelcan indeed wash out the line features if the twist angle islarge (∆ φ ≥
1) and the electron speed is slow ( β ≤ . APPLICATION TO SOFT X-RAY SPECTRA OFMAGNETARS
We generated model X-ray spectra in the 0.01–10.0keV range using the numerical model described in §
3. We used the following parameter space for our numer-ical grid: the surface temperature kT = 0 . − . B =10 − G (step 10 G), magnetospheric twist an-gle ∆ φ = 0 . − . β = 0 . − . wftbmd , , to create a tab-ular model (named STEMS3D.mod) which can be im-plemented into the standard package for X-ray spectralanalysis, XSPEC . This tabular model is further appliedto the observational data of magnetars.
Observations and data analysis
The main objective of our efforts here is to better un-derstand the surface and magnetospheric properties ofmagnetars using the STEMS3D model. For this investi-gation, we selected the sources that were bright enough( f . − ≥ − erg cm − s − ) to allow statisticallysignificant spectral results and were located in relativelylow interstellar absorption ( nH ≤ × cm − ) regionsof our Galaxy. When nH > × cm − , X-ray emis-sions below 2 keV are strongly absorbed, making the pa-rameters of the STEMS3D model unconstrained, even forthe bright source SGR 1806-20. The flux of the serendip-itously discovered magnetar, 3XMM J185246.6+003317,during its active phase is a few times of 10 − erg cm − s − . However, it was only detected with EPIC-MOS(Zhou et al. 2014), which has a smaller effective area.We do not include these spectra owing to the low signal-to-noise ratio (S/N).Our sample includes bright persistent magnetarsthat exhibited only subtle long-term flux varia-tions even when they experienced glitches or emit-ted energetic X-ray bursts 4U 0142+61 (Gavriil et al.2011); 1RXS J170849.0-400910 (S¸a¸smaz Mu¸s & G¨o˘g¨u¸s2013); 1E 1841-045 (S¸a¸smaz Mu¸s et al. 2014); andSGR 1900+14 (Israel et al. 2008). On the otherhand, two bright persistent sources: 1E 2259+586 and1E 1048.1-5937 showed long-term X-ray flux enhance-ments in connection with X-ray bursts and glitches(Kaspi et al. 2003; Dib et al. 2009). Over the lastdecade, transient magnetars have emerged as a sub-group. In quiescence, these sources emit X-rays at levelsnear or below our detection capabilities. Their X-rayfluxes are enhanced by a factor of 100 or more at theonset of their outburst episodes (Rea 2014). We selected1E 1547.0-5408 (Israel et al. 2008), Swift
J1822.3-1606(Scholz et al. 2014), SGR 0501+456 (G¨o˘g¨u¸s et al. 2010;Lin et al. 2012), and XTE J1810-197 (G¨uver et al. 2007)to investigate the spectral behavior of transient magne-tars. Note that the quiescent spectra of transient mag-netars are excluded even when their fluxes exceed thecritical flux level. We discuss the implications of thesespectra and limitations of our model for sources in qui-escence in §
5. We also include in our sample the longest
XMM-Newton observation of CXOU J171405.7-381031in 2010. The observational details of the X-ray dataused in this paper are listed in Table 1. Note that thetwo short observations of 1E 1841-045 in 2002 Octoberwere performed just two days apart. To improve count-ing statistics, we combine these two short observationsto one spectrum. http://heasarc.gsfc.nasa.gov/docs/heasarc/ofwg/docs/general/\modelfiles_memo/modelfiles_memo.html. TEMS3D 5 -5 -4 -3 -2 -1 I n t e n s i t y ( A r b i t r ay ) ∆φ =0.0 (Seed photons) ∆φ =0.5 ∆φ =1.0 ∆φ =2.0 -5 -4 -3 -2 -1 I n t e n s i t y ( A r b i t r ay ) Seed Photons β =0.2 β =0.5 Figure 4.
Left: model spectra (without gravitational redshift correction) for B = 10 G, kT = 0 . β = 0 . φ . Right: computed spectra for B = 10 G, kT = 0 . φ = 1 . β . The data collected with the
XMM-Newton
EPIC-pninstrument are reduced using the Science Analysis Sys-tem software (SAS) version 12.0.1, and filtered with thestandard criteria: cleaning for background areas, settingFLAG=0 and PATTERN ≤
4. We use the SAS task epat-plot to evaluate the pile-up fraction. For observationsshowing severe problems with pile-up (Table 1), spectraare extracted within annulus regions with the inner ra-dius ∼ ′′ and ARF files are calculated to correctthe missing part of the point-spread function, thus thecorrect flux level could still be measured through spec-tral fitting. The spectral response files are created usingthe SAS tasks rmfgen and arfgen . All spectra are re-binned with the task specgroup to have at least 20 countsper bin to enable the use of chi-square statistics and notto oversample the instrument energy resolution by morethan a factor of three. A 2% systematic error is addedto the data to account for uncertainties in instrumen-tal calibrations. The spectral analysis is performed inthe 0.5–7.0 keV energy range for the spectra having alow absorption, while in the 1.0–7.0 keV for those beinghighly absorbed. We note that the model-independentresiduals are detected in the spectra of 1E 1547.0-5408and CXOU J171405.7-381031 below 1.2 keV; therefore,only the spectra in the energy 1.2–7.0 keV are used (Ta-ble 1). All spectra are fitted with XSPEC
XMM-Newton observation executed on 2009 February 3, and we useda PL index Γ of 1.41 according to the Suzaku HXD-PINdata on 2009 January 28 (Enoto et al. 2010b).
Spectral analysis, spectral evolution, andcorrelations
Persistent Magnetars
4U 0142+61 is the brightest magnetar and hasbeen one of the most stable X-ray emitters in X-rays(Gonzalez et al. 2010; Wang et al. 2014). Its longest
XMM-Newton spectra in the 0.5 − kT = 0 .
33 keV, andsurface magnetic field, B = 5 . × G (see Table 2 forall other fit details and Figure 6 for the unfolded spec-trum and best-fit model curve). Note that these surfaceparameters are consistent with those that were obtainedusing STEMS (G¨uver et al. 2007). We find that themagnetospheric electrons are non-relativistic ( β =0.21),and that the magnetospheric twist angle, ∆ φ = 1.77,that is close to upper end of our parameter space. TheSTEMS3D component contributes more than 98% of thetotal flux below 7 keV.Since the first glitch activity detected in 1999(Kaspi et al. 2000), several glitches were unveiled in1RXS J170849.0-400910 (S¸a¸smaz Mu¸s & G¨o˘g¨u¸s 2013).The source emits persistent radiation in both soft- andhard-X-rays. Fitting the 0.5 − kT =0 .
49 keV) and the other parameters are quite close tothose in 4U 0142+61, i.e., B = 6 . × G, ∆ φ = 1.82,and β = 0.20 (Table 2). The STEMS3D component con-tributes about 88% of the total soft-X-ray flux (Figure6).The AXP 1E 1841-045 is located at the center ofthe X-ray and radio supernova remnant (SNR) Kes 73 Table 1
Log of the
XMM-Newton observations used in this workSource Obs No. ObsID Obs Date Mode Net Exposure Energy band(ksec) (keV)4U 0142+61 ♯ Obs1 0206670101 2004 Mar 01 Timing 37 0.5-7.01RXS J170849.0-400910 ♯ Obs1 0148690101 2003 Aug 28 SW 31 0.5-7.01E 1841-045 ♯ Obs1 0013340101 2002 Oct 05 LW 2 1.0-7.0... ... 0013340201 2002 Oct 07 LW 4 ...SGR 1900+14 ♯ Obs1 0305580101 2005 Sep 20 FF 21 1.0-7.0... Obs2 0305580201 2005 Sep 22 FF 20 ...... Obs3 0410580101 2006 Apr 01 FF 14 ...... Obs4 0506430101 2008 Apr 08 FF 23 ...1E 1048.1-5937 Obs1 0112780401 2000 Dec 28 FF 4 0.5-7.0... Obs2 0147860101 † † † † † † † Swift
J1822.3-1606 Obs1 0672281801 † † ♯ Obs1 0560181101 † Note . — Mode: operating mode of the EPIC-pn including full-frame (FF), large-window (LW), small-window (SW), and timingmodes. Net exposure: clean exposure (in unit of kiloseconds) after background flares excluded. energy band: Energy band in whichspectra are fitted with
XSPEC . ♯ : Sources’ spectra are fitted by the absorbed (STEMS3D+PL) model with the PL index Γ fixed (see the text for more details), and theothers are fitted by a single absorbed STEMS3D model. † : Observations suffer problems with pile-up, and spectra are extracted from annular regions centered on the source position. (Vasisht & Gotthelf 1997) and has the slowest spin pe-riod of ∼ ∼
8% of thetotal flux below 7 keV; however, it starts to overcomethe STEMS3D component around 5 keV. The fitting re-sults indicate that the magnetosphere is modestly twisted(∆ φ = 0.31) and the electrons have the fastest velocity( β = 0 .
28) among all sources studied here, i.e., the small-est optical depth in the magnetosphere (Figure 3). Themodel parameters, however, have relative large errors be- cause of the short effective exposure ( ∼ ∼
950 yr (Sato et al. 2010). Therehave been only modest flux variations (less than a fac-tor of two) reported with two Chandra and one
XMM-Newton observations during 2007 February and 2010March (Sato et al. 2010). Currently, no model providesa good fit to its X-ray spectra below ∼ -4-2024 χ a χ b -4-2024 χ c χ d Figure 5.
Spectra of 4U 0142+61 and 1RXS J170849.0-400910 are fitted with the single absorbed STEMS3D model, and the fit residualsare shown in panels (a), (b), respectively. Panels (c) and (d) plot the residuals when the same spectra are fitted with the absorbed(STEMS3D+PL) model.
Table 2
Spectral fit results of 4U 0142+61, 1RXS J170849.0-400910, and 1E 1841-045Source nH kT B ∆ φ β Flux χ /dof(10 cm − ) (keV) (10 G) (rad)4U 0142+61 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
26 85.2/1091E 1841-045 4 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
61 178.4/161
Note . — Flux: 0.5–7.0 keV absorbed flux in units of 10 −
11 erg cm − −
1. All errors are in the 90% confidence level. due to the contamination of diffuse nonthermal X-raysaround the source (in the SNR). We, therefore, investi-gate its 1.2–7.0 keV spectrum with a single STEMS3Dmodel, and obtain nH = 4 . +0 . − . × cm − , kT =0 . +0 . − . keV, B = 9 . − . × G, ∆ φ = 0 . +0 . − . , β = 0 . +0 . − . , absorbed flux in 0.5–7.0 keV of 1 . × − erg cm − s − , and χ /dof = 121 . /
98. Owing to thelowest flux and a large value of nH, we cannot obtain theupper error of B , which turns out to be the strongestsurface magnetic field estimate among all sources.SGR 1900+14 is another source whose broadbandspectra (1 −
200 keV) can be modeled with a BB plusa single PL component. Vrba et al. (2000) reported thatthis source is embedded in a cluster of high-mass stars, at ∼ −
15 kpc away. We fit the four
XMM-Newton spec-tra of SGR 1900+14 in the 1.0 − B in oursimultaneous fit so that our modeling would yield a com-mon value for these two surface parameters. We find that B = 8 . × G, kT = 0 .
54 keV, β ∼ .
11, and the twistangle is less constrained. If we further tie β and ∆ φ butallow the PL and STEMS3D normalizations to vary, weobtain the equivalently good fits ( χ /dof = 361 . / B = 7 . × G, kT = 0 . φ = 1 .
92, and the β hit the lower limit (0.1) of pa- rameter space (Table 3). These results suggest that thephysical parameters do not evolve and SGR 1900+14 isa stable emitter. The ratio between the PL flux and theSTEMS3D flux in 0.5–7.0 keV is ∼ /
70 (Figure 8).
Variable Magnetars
1E 1048.1-5937 and 1E 2259+586 are two bright mag-netar sources, whose persistent X-ray flux varied by a fac-tor of 10 or more over the timescale of months (Dib et al.2009; Zhu et al. 2008). Dib et al. (2009) performed acomprehensive timing analysis on ∼
10 yr RXTE data of1E 1048.1-5937, and showed that all three pulsed flareswere accompanied by temporal events, e.g., significantpulse profile changes and/or a glitch. The infrared en-hancement was also reported at the onset of the 2001flare (Wang & Chakrabarty 2002). We fit all spectra of1E 1048.1-5937 with the single STEMS3D model (Fig-ure 9) and find that the strength of the surface mag-netic field remains ∼ . × G (see Group 1 in Table4). By linking the B parameter for all observations, wefind that the kT varies in the range of 0.39 − B = 2 . × G, ∆ φ > .
0, and β in the range of0.12 − B , we link the kT,∆ φ , and β for Obs1 and Obs8, kT and β for Obs5 andObs7, and kT only for Obs3 and Obs4. This groupingimproves the fit quality slightly ( χ /dof = 1113 . / β , and 0.5–7.0 keV flux. We find that kT is cor-related with flux (the Spearman’s rank correlation co-efficient, ρ = 0.788, the probability of obtaining such a n o r m a li ze d c o un t s s - k e V -
4U 0142+61 χ -4 -3 -2 -1 k e V ( P h o t o n s c m - s - k e V - )
4U 0142+61 n o r m a li ze d c o un t s s - k e V - RXS J170849.0-400910 χ -3 -2 k e V ( P h o t o n s c m - s - k e V - ) RXS J170849.0-400910 n o r m a li ze d c o un t s s - k e V -
1E 1841-045 χ -4 -3 -2 k e V ( P h o t o n s c m - s - k e V - )
1E 1841-045
Figure 6.
Left panels: the X-ray count spectra of 4U 0142+61, 1RXS J170849.0-400910, and 1E 1841-045 are fitted by the STEMS3Dmodel (Table 2) and the residuals are shown below. Right panels: the corresponding unfolded spectra. The dotted, dashed, and solid linesin the right panels mark the STEMS3D, PL components, and the sum, respectively. -3 -2 n o r m a li ze d c o un t s s - k e V - CXOU J171405.7-381031 χ -5 -4 -3 k e V ( P h o t o n s c m - s - k e V - ) CXOU J171405.7-381031
Figure 7.
Same as Figure 6 but for CXOU J171405.7-381031.
TEMS3D 9 n o r m a li ze d c o un t s s - k e V - SGR 1900+14 χ -5 -4 -3 k e V ( P h o t o n s c m - s - k e V - ) SGR 1900+14
Figure 8.
Left panel: spectra of SGR 1900+14 are fitted with the STEMS3D model. Different colors correspond to the four differentepochs of observations and their fitting residuals are shown in the bottom panel (Table 3). Right panel: the corresponding unfolded spectra.
Table 3
Spectral parameters of SGR 1900+14Group Obs No. nH kT B ∆ φ β Flux χ /dof(10 cm − ) (keV) (10 G) (rad)Group1 Obs1 3 . +0 . − . . +0 . − . . − . . +0 . − . . +0 . − . .
07 340.7/380... Obs2 ... 0 . +0 . − . . +2 . − . . − . . +0 . − . .
08 ...... Obs3 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
69 ...... Obs4 ... 0 . +0 . − . . − . . − . . +0 . .
93 ...Group2 Obs1 3 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . .
07 350.3/386... Obs2 ... ... ... 1 . +0 . − . . +0 . .
09 ...... Obs3 ... ... ... 2 . − . . +0 . − . .
68 ...... Obs4 ... ... ... 1 . +0 . − . . +0 . .
93 ...Group3 Obs1 3 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . .
07 361.9/392... Obs2 ... ... ... ... ... 3 .
09 ...... Obs3 ... ... ... ... ... 3 .
68 ...... Obs4 ... ... ... ... ... 2 .
93 ...
Note . — Flux: 0.5–7.0 keV absorbed flux in units of 10 −
11 erg cm − −
1. All errors are in the 90% confidence level.Group1: the only parameter of nH is linked for different observations in the simultaneous fit. Group2: parameters of nH, kT,and B are linked. Group3: parameters of nH, kT, B , ∆ φ , and β are linked. P = 0 . β isanti-correlated with kT ( ρ/P = − . / . ρ/P = − . / . XMM-Newton fluxdecay is best described by the PL and is correlated withthe hardness. A simultaneous fit to all 10 observationsyields a rather constant surface magnetic field strength.By linking B and refitting, we obtain B ∼ . × G (Group 2 in Table 5). To better constrain themagnetospheric parameters, we also merged some suc-cessive observations (namely, Obs1/Obs2, Obs4/Obs5,Obs7/Obs8, and Obs9/Obs10), which have similar sur-face emission properties (kT) and are either before orafter the bursting episode. We find that the magneto-spheric twist angle rises to its maximum level follow-ing the bursting episode, and declines gradually over atimescale of two to three years. The particle velocity,on the other hand remains nearly constant around 0.2.Based on the results of Group 3 in Table 5, we find astrong correlation between ∆ φ and flux with the Spear-man’s rank correlation coefficient of ρ/P = 0 . / . Transient Magnetars
XTE J1810-197 was discovered in 2003 when itsuddenly brightened by about two orders of mag-nitude above its quiescent flux (Ibrahim et al. 2004;Halpern & Gotthelf 2005). As it is the first transientmagnetar, this source has been visited with
XMM-Newton more than 24 times and its spectra are well stud-ied, including investigations with STEMS (G¨uver et al.2007). Due to the fact that the source shows no clearnonthermal component in quiescence, we only consid-ered the observations during the outburst decay before2005 March 18. There are two observations performedon 2003 September 8, and their spectral fitting resultsare consistent with each other. However, the S/N ra-tio of the second one (ObsID = 0161360401) is relativelylow (due to its short exposure time of < . ± .
01 to 0 . ± .
01 keV) followingthe outburst of XTE J1810-197, while the magnetic fieldremains around (2 . − . × G, which is consistentwith those found using STEMS modeling (G¨uver et al.2007). In the meantime, the ∆ φ parameter typically re-mains around ∼ β reaches a lower limit of 0.1(Table 6). We also fit all four spectra with common val- ues of B and ∆ φ , which yields B = 2 . × G and∆ φ = 1 . XMM-Newton observationof this source took place while SGR 0501+456 was stillburst active; therefore, there were a few hundreds of shortbursts in about 45 ks of effective exposure. In order toexclude the times of these burst events, we constructedthe source light curve in a 0.1 s bin size, and then useda count rate cut-off criterion ( <
55 cts s − ) (Lin et al.2012). SGR 0501+456 has also been detected in hard-X-ray band (Enoto et al. 2010a), but the hard-X-ray taildoes not affect our fitting below 7 keV significantly. Thesoft-X-ray spectra are, therefore, fit with the STEMS3Dmodel alone. We find that the surface magnetic fieldstrength remains constant within errors (see Group 1 inTable 7). We refit all five spectra simultaneously to havea common value of B , and obtained it as B = 2 . × G. In this case, we obtain that the speed of magneto-spheric electrons declined from 0.2 to 0.15, while thetwist angle showed a marginal evidence of variation be-tween 1.5 and 1.7 (Group 2 in Table 7). Among all ofthe evolving parameters, we find a significant correlationbetween only β and the flux, with ρ/P = 1 / Swift
J1822.3-1606 underwent an outburst in 2011 July(Livingstone et al. 2011). The timing analysis revealeda spin period of P = 8 . P = 8 . × − s s − , which made this sourcethe second magnetar with a low dipole magnetic field, B timing ≃ . × G (Rea et al. 2012). Its spec-tral behavior during the flux decay resembles those ob-served from XTE J1810-197 in the 2003 outburst, whosedipole magnetic field inferred from spin parameters is B timing = 2 . × G (Camilo et al. 2007). The spec-tral evolution could be interpreted as the thermal relax-ation in the NS crust (Scholz et al. 2014). The long-term monitoring data suggest that the temperature ofthe thermal component decreases slowly. Alternatively,the decreasing normalization, which is not presented inTable 8, indicates that the emitting region shrinks duringthe outburst decay (Rea et al. 2012; Scholz et al. 2014).In our investigation of this source with the STEMS3Dmodel, we found that the surface temperature declinedslightly from 0 . ± .
02 to 0 . ± .
02 keV in the firstyear of the outburst, and the surface magnetic field( B ∼ . × G) and the electron velocity ( β ∼ . β for all yields a significant fluctuation of ∆ φ (see Group 2in Table 8). We also fit all spectra with the same valueof ∆ φ and the chi-square increases to 433 . / φ with an F-test valuelower than 0.005.1E 1547.0-5408 was discovered in 1980(Lamb & Markert 1981), but has shown repeatedX-ray flux enhancements in recent years: its flux wentup by a factor of >
50 with the 2008 October outburstand further increased to levels of ∼ Table 4
Spectral parameters of 1E 1048.1-5937.Group Obs No. nH kT B ∆ φ β Flux χ /dof(10 cm − ) (keV) (10 G) (rad)Group1 Obs1 1 . +0 . − . . +0 . − . . +0 . − . . − . . +0 . − . .
56 1060.6/902... Obs2 ... 0 . +0 . − . . +0 . − . . − . . +0 . − . .
39 ...... Obs3 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
96 ...... Obs4 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
80 ...... Obs5 ... 0 . +0 . − . . +0 . − . . − . . +0 . − . .
72 ...... Obs6 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
92 ...... Obs7 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
54 ...... Obs8 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
01 ...Group2 Obs1 1 . +0 . − . . +0 . − . . +0 . − . . − . . +0 . − . .
56 1108.3/909... Obs2 ... 0 . +0 . − . ... 1 . − . . +0 . − . .
39 ...... Obs3 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
96 ...... Obs4 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
80 ...... Obs5 ... 0 . +0 . − . ... 2 . − . . +0 . − . .
72 ...... Obs6 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
91 ...... Obs7 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
54 ...... Obs8 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
01 ...Group3 Obs1 1 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
56 1113.9/915... Obs2 ... 0 . +0 . − . ... 1 . − . . +0 . − . .
39 ...... Obs3 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
96 ...... Obs4 ... = obs . +0 . − . . +0 . − . .
80 ...... Obs5 ... 0 . +0 . − . ... 2 . − . . +0 . − . .
72 ...... Obs6 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
91 ...... Obs7 ... = obs . +0 . − . = obs .
54 ...... Obs8 ... = obs obs obs .
01 ...
Note . — Flux: 0.5–7.0 keV absorbed flux in units of 10 −
11 erg cm − −
1. All errors are in the 90% confidence level. Group1:the only parameter of nH is linked for different observations in the simultaneous fit. Group2: both parameters of nH, and B arelinked. Group3: β for Obs1 and Obs8, kT and β for Obs5 and Obs7, and kT only for Obs3 and Obs4 are further linked. (Enoto et al. 2010b) and INTEGRAL (Kuiper et al.2012) during the decay of the 2009 outburst. Thebroadband X-ray spectrum can be described with aBB component plus a single PL component, and itsspectrum evolved significantly in the soft-X-rays as wellas in the hard-X-ray data (Kuiper et al. 2012). Here,we only use the XMM-Newton observation executed on2009 February 3, which is one week after the Suzakuobservation (on 2009 January 28), and Γ of 1.41 isadopted based on the 15–70 keV Suzaku HXD-PIN data(Enoto et al. 2010b). The low energy portion of itsspectrum is contaminated because the source is locatedat the center of SNR G327.24-013 (Gelfand & Gaensler2007). Therefore, we again fit the 1.2–7.0 keV spectrumin order to eliminate large deviations owing to thecontamination of diffuse nonthermal X-rays at the lowenergy (Figure 11). We find the best-fit parametersnH = 4 . +0 . − . × cm − , kT = 0 . +0 . − . keV, B = 8 . +0 . − . × G, ∆ φ = 1 . +0 . − . , β = 0 . +0 . − . ,absorbed flux in 0.5–7.0 keV F = 5 . × − erg cm − s − , and χ /dof = 96 . / ∼ G based onthe STEMS fitting. The strong magnetic field case inthis source was later confirmed by Tiengo et al. (2013).Nevertheless, the STEMS3D model cannot provide anacceptable fit to the spectrum of SGR 0418+5729 (ObsID= 0610000601). The canonical (BB+PL) model resultsindicate that the overall flux is dominated by a very hotthermal component ( kT ∼ . β ∼ . τ ∼
9. However,as can be seen in the Figure 3, the optical depth in theSTEMS3D model is governed by both β and ∆ φ , andcannot be larger than two when the β is greater than0.3.The AXP CXOU J164710.2-455216 is located in theyoung massive stars cluster, Westerlund 1 (Muno et al.2006). The source underwent the first intense outburston 2006 September and the second one on 2011 Septem-ber (Rodr´ıguez Castillo et al. 2014). Measuring the spinperiod and period derivative, An et al. (2013) suggestedthat the spin-down inferred magnetic field strength is lessthan 7 × G. We attempted to fit six bright
XMM-Newton pointing data during 2006 and 2011, and ob-tained statistically acceptable fits with χ /dof ∼ . B in both STEMS and STEMS3Dmodeling peg at the low limit of 10 G; therefore, theobtained parameters are not reliable. We, therefore, donot include this source for further discussion. DISCUSSION Table 5
Spectral parameters of 1E 2259+586.Group Obs No. nH kT B ∆ φ β Flux χ /dof(10 cm − ) (keV) (10 G) (rad)Group1 Obs1 0 . +0 . − . . +0 . − . . +0 . − . . − . . +0 . − . .
52 871.1/928... Obs2 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
60 ...... Obs3 ... 0 . +0 . − . . +0 . − . . − . . +0 . − . .
62 ...... Obs4 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
46 ...... Obs5 ... 0 . +0 . − . . +0 . − . . − . . +0 . − . .
59 ...... Obs6 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
03 ...... Obs7 ... 0 . +0 . − . . +1 . − . . +0 . − . . +0 . − . .
96 ...... Obs8 ... 0 . +0 . − . . +0 . − . . − . . +0 . − . .
96 ...... Obs9 ... 0 . +0 . − . . +0 . − . . − . . +0 . − . .
94 ...... Obs10 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
87 ...Group2 Obs1 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
52 930.0/937... Obs2 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
60 ...... Obs3 ... 0 . +0 . − . ... 2 . − . . +0 . − . .
63 ...... Obs4 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
46 ...... Obs5 ... 0 . +0 . − . ... 2 . − . . +0 . − . .
59 ...... Obs6 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
03 ...... Obs7 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
96 ...... Obs8 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
96 ...... Obs9 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
94 ...... Obs10 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
87 ...Group3 Obs1/Obs2 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . . / .
60 976.4/949... Obs3 ... 0 . +0 . − . ... 2 . − . . +0 . − . .
63 ...... Obs4/Obs5 ... 0 . +0 . − . ... 1 . − . . +0 . − . . / .
57 ...... Obs6 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
03 ...... Obs7/Obs8 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . . / .
97 ...... Obs9/Obs10 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . . / .
87 ...
Note . — Flux: 0.5–7.0 keV absorbed flux in units of 10 −
11 erg cm − −
1. All errors are in the 90% confidence level. Group1: the onlyparameter of nH is linked for different observations in the simultaneous fit. Group2: both parameters of nH, and B are linked. Group3:three pairs of successive observations (Obs1/Obs2, Obs7/Obs8, and Obs9/Obs10) are merged. Table 6
Spectral fit results of XTE J1810-197Group Obs No. nH kT B ∆ φ β Flux χ /dof(10 cm − ) (keV) (10 G) (rad)Group1 Obs1 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . .
76 559.7/442... Obs2 ... 0 . +0 . − . . +0 . − . . − . . +0 . .
19 ...... Obs3 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
32 ...... Obs4 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
55 ...Group2 Obs1 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . .
74 750.7/448... Obs2 ... 0 . +0 . − . ... ... 0 . +0 . .
19 ...... Obs3 ... 0 . +0 . − . ... ... 0 . +0 . − . .
32 ...... Obs4 ... 0 . +0 . − . ... ... 0 . +0 . .
55 ...
Note . — Flux: 0.5–7.0 keV absorbed flux in units of 10 −
11 erg cm − −
1. All errors are in the 90% confidence level.Group1: the only parameter of nH is linked for different observations in the simultaneous fit. Group2: parameters of nH, B ,and ∆ φ are linked. TEMS3D 13 -3 n o r m a li ze d c o un t s s - k e V -
1E 1048.1-5937 χ -6 -5 -4 -3 k e V ( P h o t o n s c m - s - k e V - )
1E 1048.1-5937 -3 -2 n o r m a li ze d c o un t s s - k e V -
1E 2259+586 χ -5 -4 -3 k e V ( P h o t o n s c m - s - k e V - )
1E 2259+586
Figure 9.
Same as Figure 6 but for 1E 1048.1-5937 and 1E 2259+586.
Table 7
Spectral fit results of SGR 0501+456Group Obs No. nH kT B ∆ φ β Flux χ /dof(10 cm − ) (keV) (10 G) (rad)Group1 Obs1 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
72 600.2/604... Obs2 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
13 ...... Obs3 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
94 ...... Obs4 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
65 ...... Obs5 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
44 ...Group2 Obs1 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
72 605.9/608... Obs2 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
13 ...... Obs3 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
94 ...... Obs4 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
65 ...... Obs5 ... 0 . +0 . − . ... 1 . +0 . − . . +0 . − . .
44 ...
Note . — Flux: 0.5–7.0 keV absorbed flux in units of 10 −
11 erg cm − −
1. All errors are in the 90% confidence level. Group1:the only parameter of nH is linked for different observations in the simultaneous fit. Group2: both parameters of nH, and B arelinked. -3 -2 n o r m a li ze d c o un t s s - k e V - XTE J1810-197 χ -5 -4 -3 k e V ( P h o t o n s c m - s - k e V - ) XTE J1810-197 -3 -2 n o r m a li ze d c o un t s s - k e V - SGR 0501+456 χ -5 -4 -3 k e V ( P h o t o n s c m - s - k e V - ) SGR 0501+456 -3 -2 n o r m a li ze d c o un t s s - k e V - Swift J1822.3-1606 χ -5 -4 -3 k e V ( P h o t o n s c m - s - k e V - ) Swift J1822.3-1606
Figure 10.
Same as Figure 6 but for transients XTE J1810-197, SGR 0501+456, and
Swift
J1822.3-1606.
Table 8
Spectral fit results of
Swift
J1822.3-1606Group Obs No. nH kT B ∆ φ β Flux χ /dof(10 cm − ) (keV) (10 G) (rad)Group1 Obs1 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . .
90 415.5/420... Obs2 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . .
31 ...... Obs3 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
43 ...... Obs4 ... 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
28 ...Group2 Obs1 0 . +0 . − . . +0 . − . . +0 . − . . +0 . − . . +0 . − . .
91 420.5/426... Obs2 ... 0 . +0 . − . ... 1 . +0 . − . ... 1 .
31 ...... Obs3 ... 0 . +0 . − . ... 1 . +0 . − . ... 0 .
44 ...... Obs4 ... 0 . +0 . − . ... 1 . +0 . − . ... 0 .
28 ...
Note . — Flux: 0.5–7.0 keV absorbed flux in units of 10 −
11 erg cm − −
1. All errors are in the 90% confidence level.Group1: the only parameter of nH is linked for different observations in the simultaneous fit. Group2: parameters of nH, B ,and β are linked. TEMS3D 15 -2 -1 n o r m a li ze d c o un t s s - k e V -
1E 1547.0-5408 χ -3 -2 k e V ( P h o t o n s c m - s - k e V - )
1E 1547.0-5408
Figure 11.
Same as Figure 6 but for the observation of 1E 1547.0-5408 taken on 2009 February 3. (BB+PL) (10 cm -2 )0123456 n H S TE M S D ( c m - ) STEMS (10 G)246810 B S TE M S D ( G ) Figure 12.
Upper panel: nH
STEMS3D vs. nH (BB+PL) . Bottompanel: B STEMS3D vs. B STEMS . Table 9
Log of the Magnetic FieldSource B timing B STEMS B STEMS3D (10 G) (10 G) (10 G)4U 0142+61 1.3 a . +0 . − . . +0 . − . b . +0 . − . . +0 . − .
1E 1841-045 6.9 b . +0 . − . . +0 . − . CXOU J171405.7-381031 5.0 c . +0 . − . . − . SGR 1900+14 7.0 d . +0 . − . . +0 . − .
1E 1048.1-5937 3.9 e . +0 . − . . +0 . − .
1E 2259+586 0.59 f . +0 . − . . +0 . − . XTE J1810-197 2.1 g . +0 . − . . +0 . − . SGR 0501+456 1.9 h . +0 . − . . +0 . − . Swift
J1822.3-1606 0.135 i . +0 . − . . +0 . − .
1E 1547.0-5408 3.2 j . − . . +0 . − . Note . — Period derivatives of magnetars are highlyvariable, and the derived B timing could be significantly dif-ferent from the values listed here.(a) Dib et al. 2007; (b) Dib et al. 2008; (c) Sato et al.2010; (d) Mereghetti et al. 2006; (e) Dib et al. 2009;(f) Gavriil & Kaspi 2002; (g) Camilo et al. 2007; (h)G¨o˘g¨u¸s et al. 2010; (i) Scholz et al. 2014; (j) Dib et al. 2012. In this paper, we developed a physically motivated nu-merical model to account for the magnetar surface emis-sion and magnetospheric scattering in three dimensions.We applied our model to the X-ray spectra of 13 magne-tars, including persistent X-ray emitters as well as tran-sient sources. We find that most spectra analyzed herewere adequately described with the STEMS3D model,yielding important physical parameters, such as the sur-face magnetic field strengths and degree of twisting inthe magnetosphere. To compare with our results, we alsomodeled all magnetar spectra with the STEMS model,which employs the same atmospheric emission proper-ties, but incorporates an only 1D scattering scheme onthe emergent radiation (G¨uver et al. 2007). We find thatthe surface magnetic field strengths obtained by fittingthe STEMS3D model are generally slightly higher, butare still in agreement within errors with those obtainedwith the STEMS model (see the lower panel of Figure12).Dipole magnetic fields inferred from spin parameters( B timing ) in 7 out of the 11 sources are consistent withthe values obtained from the STEMS3D model fitting(Table 9). The STEMS3D model does not providean acceptable fit to the spectrum of the first low- B magnetar, SGR 0418+5729, for reasons as already dis-cussed in § B timing < G, 1E 2259+586 and
Swift
J1822.3-1606,the strengths of B given by the STEMS3D model areabout one order of magnitude higher than their dipolemagnetic fields. However, taking both twisted magneto-spheres (Thompson et al. 2002; Beloborodov 2009) andparticle outflows (Tong et al. 2013) into account, the ex-pected spin-down torque ( ˙ P ) will be larger than a puredipole case with the same poloidal magnetic field. Theconflict between larger values of B STEMS3D and timingresults could be reconciled by either a small magneticinclination angle (e.g., Tong & Xu 2012) and/or a morecomplex structure of magnetosphere (i.e., higher ordermultipoles). In a multipolar field, the strong surfacemagnetic field decays more rapidly with radius; thus, atoo fast spin-down rate can be avoided (Turolla et al.2011).On the other hand, an important caveat for the in-ferred dipole field is that, magnetars are very noisy andtheir period derivatives can vary significantly within ashort timescale (e.g., Archibald et al. 2015, and refer-ences therein,), leading to fluctuations in B timing , whichis unphysical. For example, Livingstone et al. (2011)measured a spin-down rate of ˙ P = 2 . × − ss − using data collected in the first four months fol-lowing the 2011 July outburst of Swift
J1822.3-1606.Rea et al. (2013) estimated ˙ P = 8 . × − s s − withthe data covering 2011 July – 2012 April, and recentlyScholz et al. (2014) took the new Swift data into accountand reported ˙ P = 2 . × − s s − . As a consequence,the corresponding B timing decreased from the previousvalue of 4 . × G to 1 . × G listed in Table 9.The decreasing spin-down rate can be interpreted as ei-ther a sign of wind braking (Tong & Xu 2013) or a glitchrecovery (Scholz et al. 2014). Our spectral investigationswith the STEMS3D, however, yields magnetar-like sur-face magnetic field strength (2 . × G), which is likelythe case given that, at the very least, the source exhibitedTEMS3D 17energetic bursts.We find that the temperatures of the magnetar surfacesvary between 0.24 and 0.56 keV, and the magnetosphericelectrons are non-relativistic ( β ≤ XMM-Newton observations typically spanningyears of five magnetars and find that the strength of thesurface magnetic fields remains nearly constant. We alsomodeled all magnetar spectra with the phenomenologi-cal (BB+PL) model to better establish the interstellarabsorbtion aspects toward magnetars studied here. Itis well known that the simple PL model increases veryrapidly at low energies, and as a consequence, a largerabsorption column density is required to account for theoverestimated PL flux, especially for the steep PL indices(Durant & van Kerkwijk 2006; G¨uver et al. 2008). In allsources except 1E 1841-045, the hydrogen column densityobtained from the STEMS3D model fits (nH
STEMS3D ) islower than the value derived from the (BB+PL) modelfits (nH (BB+PL) ; Figure 12). We argue that, given theempirical nature of the (BB+PL) model, the density ofinterstellar hydrogen obtained with the STEMS3D is amore reliable indicator.As already stated, the surface magnetic field valuesfrom the STEMS3D model mostly agree with those ob-tained with the STEMS model results (Table 9). How-ever, the STEMS model makes simplifying assumptionsabout the magnetic field geometry, i.e., treating the scat-tering region as a plane-parallel slab; therefore, it cannotoffer information about the geometry of the magneto-sphere. Alternatively, the 3D self-similar magnetic con-figuration is characterized by a free parameter, ∆ φ , inthe STEMS3D model. Our fitting results indicate thatthe magnetospheres in most magnetars are highly twisted(∆ φ ≥ .
32) component in the fitting for 1E 1841-045, which could be the reason why it has a large valueof nH STEMS3D . The derived small magnetospheric twistangle ∆ φ = 0 . +0 . − . and large β = 0 . +0 . − . should betreated with caution, and longer exposure observationsare required to check the magnetospheric parameters of1E 1841-045 in the future.Compared with the STEMS model, the STEMS3Dmodel embodies some other significant improvements:(1) in the 1D geometry, the magnetic field is fixed tofollow a B ∝ r − dependence, and the optical depth τ isindependent of the electron velocity β . In contrast, theradial dependence of the magnetic field is consistently ob-tained from ∆ φ , while the angle-averaged optical depth τ is determined by β and ∆ φ . (2) The charged particlesare assumed to have a top-hat velocity distribution in the1D model, while a more realistic distribution, involvingthe effects of bulk motion and also thermal velocity dis-tribution of electrons, is used in the STEMS3D model.Following the work in Nobili et al. (2008), we adopt the1D Maxwellian distribution at the electron temperature T e , which is further linked with β by assuming equipar-tition between thermal and bulk kinetic energy in orderto reduce the number of parameters in the model. (3)In the 3D configuration, the optical depth varies signifi-cantly with angles and vanishes at magnetic poles in thetwisted magnetosphere. Thus, it is possible to detect thesurface radiation which is mostly carried by extraordi-nary mode photons, if one of the magnetic poles is in our line of sight. The polarization and the proton cyclotronabsorption lines are expected to vary with the rotationalphase. Note that Tiengo et al. (2013) recently reporteda phase-variable absorption feature observed during theoutburst of SGR 0418+5729.We also aimed to understand the nature of variableand transient magnetars by investigating their spectralevolution. For this purpose, we analyzed multiple XMM-Newton observations of six magnetars. 1E 1048.1-5937has been quite active in the past 10 yr: three X-rayflares were recorded with RXTE in 2001, 2002, and 2007March (Dib et al. 2009). The eight
XMM-Newton ob-servations we used here are sampled before, after andin between these flares: Obs1 was performed before thefirst flare; Obs2-5 were executed between the second andthird flares; Obs6-7 were performed after the third flare;comparing with Obs7, the source brightened by a fac-tor of two in Obs8 (on 2013 July 22, after the end ofRXTE mission). We find that the surface temperaturemonotonically decreases with declining flux from Obs2 toObs5 and from Obs6 to Obs7 (see Group 1–3 in Table 4).This is likely due to cooling of the NS crust that is heatedby the mechanism leading to these flares. However, themagnetospheric twist angle cannot be constrained in thissource.In the magnetar framework, both the crustal cool-ing (e.g., Pons & Rea 2012) and the magnetosphericrelaxation (e.g., Bernardini et al. 2009) models are pro-posed for the flux relaxation in different sources. Thedense
XMM-Newton observations on 1E 2259+586 pro-vide a good opportunity to study this topic. The firsttwo data sets are observed before the burst event, andthe other eight observations monitored the flux relax-ation of the outburst in the following three years. TheSTEMS3D fitting results suggest a large magnetic field ∼ . × G for the source, and the ∆ φ suddenly in-creased to a maximum from Obs2 to Obs3 then decreasedfollowing the flux decays. The only exception, Obs4,which was executed ∼
20 days after the burst, has asmall ∆ φ = 1 .
1. Note that, Obs4 and Obs5 were per-formed on the same day; however, the latter yields alarge ∆ φ ∼
2. Such a small discrepancy between Obs4and Obs5 was also seen in the (BB+PL) fitting results(Zhu et al. 2008), i.e., the flux ratio between PL and BBcomponents varied from 2.6 (Obs4) to 2.1 (Obs5). Itis not likely that the magnetosphere could untwist andretwist in a few days, and the small ∆ φ derived fromObs4 is dubious. Group 2 in Table 5 shows a strongcorrelation between ∆ φ and flux with the Spearman’srank correlation coefficient of ρ/P = 0 . / . φ and fluxbecomes more significant ( ρ/P = 0 . / . φ is linked, the χ increases by morethan 51.9, which suggests the significant variation of ∆ φ with an F-test probability lower than 2 × − . There-fore, our finding of an increased twist angle accompaniedwith the outburst (occurred between Obs2 and Obs3)8and then a decrease following the source decays, agreesperfectly with the twisted/untwisted magnetosphere sce-nario (Thompson et al. 2002).The STEMS3D fitting results of both XTE J1810-197and Swift
J1822.3-1606 show that the surface temper-ature monotonically declines with decreasing luminos-ity. The former source had been studied in detail withthe STEMS model (G¨uver et al. 2007). On the otherhand, it is the first time that we evaluated the sur-face magnetic field of
Swift
J1822.3-1606 via continuum-fitting, and obtained a significantly stronger magneticfield than the dipole magnetic field inferred from thespin-down rate (Scholz et al. 2014). It is interestingto note that XTE J1810-197 and
Swift
J1822.3-1606share the similar spectral sequences following their out-bursts (Rea et al. 2012; Scholz et al. 2014). Neverthe-less, the timing analyses infer a typical magnetar mag-netic field for XTE J1810-197 ( B timing ∼ . × G,Camilo et al. 2007) while a low value for the latter source( B timing ∼ . × G, Scholz et al. 2014). Our spec-troscopic measurements suggest a similar magnetic fieldstrength of B STEMS3D ∼ . × G for these two tran-sients. The monotonic decline of surface temperaturesduring the outburst decays in both XTE J1810-197 and
Swift
J1822.3-1606 are remarkable evidence of crustalcooling (G¨uver et al. 2007; Scholz et al. 2014). Addi-tionally, we also find a significant variation of ∆ φ in Swift
J1822.3-1606 (with a confidence of 99.5%). Wealso find a decline of the magnetospheric electron ve-locity β in the first ∼
40 days of the 2008 outburst ofSGR 0501+456 (Table 7), implying the energy dissipa-tion of charged particles, probably by the radiative drag.Different scenarios have been proposed to ac-count for the hard-X-ray emissions from magnetars.Thompson & Beloborodov (2005) put forward twomechanisms that soft- γ -rays either arise from the ther-mal bremsstrahlung emissions in a thin surface layerheated by a returning current or the synchrotron emis-sions from e ± pairs (see also Beloborodov & Thompson2007). Alternatively, Baring & Harding (2007) sug-gested that the high energy tail was produced by theresonant up-scattering in the magnetosphere. The 3DMonte Carlo simulations show that the soft-X-ray pho-tons can be up-scattered to ∼
100 keV if the scatteringparticles are energetic, i.e., β > . kT e >
100 keV (Nobili et al.2008; Zane et al. 2009). However, our spectral analysisshows that the ∆ φ > β ∼ . ± pairsdischarge near the neutron star and create the relativis-tic outflow that further scatters thermal photons to highenergies. This model provided a satisfactory explanationfor the hard-X-ray luminosity, spectral slopes, and pulsedprofiles (e.g., Hasco¨et et al. 2014; Vogel et al. 2014), andit may also contribute an non-negligible flux in the soft-X-ray band.It should be noted that the STEMS3D model stillhas some limitations, as other magnetospheric scatter-ing models do (see Zane et al. 2009 and Beloborodov2013). Both spectral and temporal analyses have demon-strated that the thermal emission is not uniformly dis- tributed on the surface of magnetars but are confinedin a small region (e.g., ¨Ozel 2002; Albano et al. 2010).However, because the uniform distribution is adoptedfor the seed photons, the STEMS3D model cannotprovide an acceptable fit to the spectra of magnetarsin quiescence, which lacks nonthermal emission. Asthe transients return to the quiescent state, the spec-tra of the three transients studied in our paper (i.e.,XTE J1810-197, SGR 0501+456, and Swift
J1822.3-1606) became significantly softer than those at outburstlevels, and the second or even third thermally emittingsurface regions were reported (Bernardini et al. 2009;Camero et al. 2014; Scholz et al. 2014). According to the(BB+BB) or (BB+PL) fits, it is found that the thermalemitting area decreases following the outburst decay. Inthese cases, the distinctive spectra would be formed forthe following reasons: (i) In the 3D twisted magneto-sphere, the optical depth and upscattering efficiency varywith latitude because the current density and direction(along the magnetic field line) depend on the position.The optical depth has a maximum and a minimum atthe equator and the poles (no current exists along themagnetic axis), respectively. Thus, a hot spot presentedat the pole would gain less energy from particles in themagnetosphere, resulting in a soft spectrum. (ii) Pho-tons would be scattered away from the initial propaga-tion directions and might move into or out of the sight ofview. The viewing effect should be taken into account.(iii) The superposition of two thermal components atdifferent temperatures modifies the spectral profile fur-ther. To date, however, it is impossible to incorporateall of these effects since it will involve too many parame-ters. We emphasize that those extremely soft spectra atvery low flux levels cannot be fitted by the STEMS3Dmodel nor the other normal Compton scattering models(e.g., 1D RCS, 3D RCS, STEMS models). Neverthe-less, Zane et al. (2009) claimed that a softer spectrumis caused by a non-homogeneous distribution of surfaceemission (effects (i) and (ii)). Meanwhile, Turolla et al.(2011) also suggested that a surface thermal componentdominated spectrum can be reproduced by consideringeffects (i) and (iii).Beloborodov (2009) argued that the puzzling behav-ior of XTE J1810-197 can be explained with a un-twisting magnetosphere, which is divided into a current-free (“cavity”) region and a current-carrying bundle (“j-bundle”) of field lines. The hot spot in the polar re-gion is interpreted as the footprint of the j-bundle, whichshrinks with time. As the magnetosphere untwists, thecavity expands and the j-bundle becomes so narrow thatonly a small fraction of the surface radiation can be scat-tered, producing very soft spectra in quiescence. How-ever, in this model it is difficult to explain that lack offlux enhancement when glitches occurred in the stablesources. Alternatively, Pons & Rea (2012) interpretedtransient behaviors as the magneto-thermal evolution,and suggested that short X-ray bursts and glitches mightalways be accompanied by a flux variation; neverthe-less, the long-term flux of bright/stable magnetars (e.g.,4U 0142+61) cannot be enhanced significantly.In some cases, magnetic configurations might be morecomplex than a dipole, and multipoles fields are re-quired to avoid too fast spin-down as we discussed above.TEMS3D 19In addition, the theoretical calculation indicates thatthe output luminosity from a globally twisted magne-tosphere with ∆ φ > ergs − , which is higher than the observed (Thompson et al.2002; Beloborodov 2009). There are now some observa-tional phenomena in favor of partially, instead of glob-ally, twisted magnetospheres (e.g., Woods et al. 2007;Pavan et al. 2009), which have been considered in the lit-erature (Beloborodov 2009). 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