An unified timing and spectral model for the Anomalous X-ray Pulsars XTE J1810-197 and CXOU J164710.2-455216
A. Albano, R. Turolla, G.L. Israel, S. Zane, L. Nobili, L. Stella
aa r X i v : . [ a s t r o - ph . H E ] J u l Draft version October 29, 2018
Preprint typeset using L A TEX style emulateapj v. 04/20/08
AN UNIFIED TIMING AND SPECTRAL MODEL FOR THE ANOMALOUS X-RAY PULSARSXTE J1810-197 AND CXOU J164710.2-455216
A. Albano , R. Turolla , G.L. Israel , S. Zane , L. Nobili and L. Stella Draft version October 29, 2018
ABSTRACTAnomalous X-ray pulsars (AXPs) and soft gamma repeaters (SGRs) are two small classes of X-ray sources strongly suspected to host a magnetar, i.e. an ultra-magnetized neutron star with B ≈ –10 G. Many SGRs/AXPs are known to be variable, and recently the existence of genuinely“transient” magnetars was discovered. Here we present a comprehensive study of the pulse profile andspectral evolution of the two transient AXPs (TAXPs) XTE J1810-197 and CXOU J164710.2-455216.Our analysis was carried out in the framework of the twisted magnetosphere model for magnetaremission. Starting from 3D Monte Carlo simulations of the emerging spectrum, we produced a largedatabase of synthetic pulse profiles which was fitted to observed lightcurves in different spectral bandsand at different epochs. This allowed us to derive the physical parameters of the model and theirevolution with time, together with the geometry of the two sources, i.e. the inclination of the line-of-sight and of the magnetic axis with respect to the rotation axis. We then fitted the (phase-averaged)spectra of the two TAXPs at different epochs using a model similar to that used to calculate the pulseprofiles ( ntzang in XSPEC) freezing all parameters to the values obtained from the timing analysis,and leaving only the normalization free to vary. This provided acceptable fits to
XMM-Newton data inall the observations we analyzed. Our results support a picture in which a limited portion of the starsurface close to one of the magnetic poles is heated at the outburst onset. The subsequent evolutionis driven both by the cooling/varying size of the heated cap and by a progressive untwisting of themagnetosphere.
Subject headings: radiation mechanisms: non-thermal — sources (individual): XTE J1810-197, CXOUJ164710.2-455216 — stars: magnetic fields — stars: neutron INTRODUCTION
In recent years an increasing number of high-resolutionspectral and timing observations of isolated neutron starshas become available. Many of these observations con-cern two peculiar classes of high-energy pulsars, theAnomalous X-Ray Pulsars (AXPs: 9 objects plus 1 can-didate) and the Soft Gamma-Ray Repeaters (SGRs: 6objects) . Historically these two classes of sources wereregarded as distinct. While SGRs were first discovered inlate 1978-early 1979, when SGR 1806-20 and SGR 0526-66 exhibited a bright burst of soft γ -rays (Mazets et al.1979; Laros et al. 1986), AXPs were observed for the firsttime in 1981, when Fahlman, & Gregory (1981) discov-ered pulsations in the EINSTEIN source 1E 2259+586.It was, however, not until the mid ’90s that AXPs wererecognized as a class of “anomalous” pulsars because oftheir luminosity substantially exceeding rotational en-ergy losses (Mereghetti, & Stella 1995).Although SGRs were mainly known as emitters ofshort, energetic bursts, they are also persistent X-raysources with properties quite similar to those of AXPs(see e.g. Woods & Thompson 2006; Mereghetti 2008, forreviews). They all are slow X-ray pulsars, with spin pe- Department of Physics, University of Padova, Via Marzolo 8,I-35131 Padova, Italy INAF-Astronomical Observatory of Rome, via Frascati 33, I-00040, Monte Porzio Catone, Italy Mullard Space Science Laboratory, University College London,Holmbury St. Mary, Dorking, Surrey, RH5 6NT, UK see for an updated catalogue ofSGRs/AXPs riods in a very narrow range ( P ∼ P ∼ − –10 − s s − ), spindown ages of 10 –10 yr, and stronger magnetic fieldscompared to those of rotation or accretion powered pul-sars ( B ∼ –10 G > B QED ≃ . × G). AXPsand SGRs have persistent X-ray luminosities L X ∼ –10 erg s − . Their spectra in the 0.1–10 keV band arerelatively soft and can be empirically fitted with a two-component model, an absorbed blackbody ( kT ∼ . ∼ INTEGRAL obser-vations revealed the presence of sizeable emission up to ∼
200 keV, which accounts for up to 50% of the total flux.Hard X-ray spectra are well represented by a power-law,which dominates above ∼
20 keV in AXPs.The large high-energy output can not be explainedin terms of rotational energy losses, as in conventionalmodels for radio-pulsars, while the lack of stellar com-panions argues against accretion. The powering mecha-nism of AXPs and SGRs, instead, is believed to residein the neutron star ultra-strong magnetic field (magne-tar; Duncan, & Thompson 1992, Thompson & Duncan1993). The magnetar scenario appears capable to explainthe properties of both the bursts (Thompson & Duncan1995) and the persistent emission (the twisted magne-tosphere model, Thompson, Lyutikov, & Kulkarni 2002;Zane et al. 2009, and references therein; see § ∼ ∼ ∼
10 with respect to the quiescentlevel, followed by the emission of ∼
80 short bursts withluminosity L X ∼ − erg s − (Kaspi et al. 2003).In early 2003 the 5.54 s AXP XTE J1810-197 was dis-covered at a luminosity ∼
100 greater than its quiescentvalue (10 erg s − ; Ibrahim et al. 2004). Analysis ofarchival data revealed that the outburst started betweenNovember 2002 and January 2003.On September 21st 2006 an outburst was ob-served from the AXP CXOU J164710.2-455216 ( P =10 .
61 s). The flux level was ∼
300 times higherthan that measured only 5 days earlier by
XMM-Newton (Muno et al. 2006b; Campana, & Israel 2006;Israel, & Campana 2006). This, much as in the caseof XTE J1810-197, indicates that some AXPs are tran-sient sources (dubbed Transient AXPs) and may becomevisible only when they enter an active state. Recentlyother AXPs and SGRs showed a series of short burstsof soft γ -rays which was detected by different satellites(Mereghetti et al. 2009).In this paper we present a comprehensive study ofthe pulse profile and spectral evolution of the TAXPsXTE J1810-197 and CXOU J164710.2-455216 through-out their outbursts of November 2002 and September2006, respectively. By confronting timing data with syn-thetic lightcurves obtained from the twisted magneto-sphere model (Nobili, Turolla, & Zane 2008), we wereable to estimate how the physical parameters of thesource (surface temperature and emitting area, electronenergy, twist angle) evolve in time. The fits of the pulseprofiles also allowed us to infer the geometry of the twosystems, i.e. the angles between the magnetic and ro-tational axes and the line of sight. Spectral models, ob-tained with the parameter values derived from the timinganalysis, provide acceptable fits to XMM-Newton data. TRANSIENT AXPS PROPERTIES
XTE J1810-107
The Transient AXP (TAXP) XTE J1810-197 wasserendipitously discovered in 2003 with the Rossi X-RayTiming Explorer (
RXTE ) while observing SGR 1806-20(Ibrahim et al. 2004). The source was readily identifiedas a X-ray pulsar, and soon after a search in archival
RXTE data showed that it produced an outburst around2002 November, followed by a monotonic decline of theX-ray flux. The X-ray pulsar spin period was foundto be 5.54 s, with a spin-down rate ∼ − s s − .Using the standard expression for magneto-rotationallosses, the inferred value of the (dipolar) magnetic fieldis B ∼ × G (Ibrahim et al. 2004). The source wasclassified as the first transient magnetar. The TAXPXTE J1810-197 was then studied with
Chandra and
XMM-Newton (Gotthelf et al. 2004; Israel et al. 2004; Gotthelf, & Halpern 2005, 2007), in order to monitor itsevolution in the post-outburst phase.By using archival Very Large Array (
VLA ) data a tran-sient radio emission with a flux of ∼ . . Chandra
X-ray position of XTEJ1810-197 (Halpern et al. 2005). Only later on it wasdiscovered that this radio emission was pulsed, highly po-larized and with large flux variability even on very shorttimescales (Camilo et al. 2006). The X-ray and the radiopulsations are at the same rotational phase. Since accre-tion is expected to quench radio emission, this is furtherevidence against the source being accretion-powered.Deep IR observations were performed for this source,revealing a weak ( K s = 20 . XMM-Newton , between September 2003 and September 2007,two times every year. The uninterrupted coverage of thesource during 4 years provides an unique opportunity tounderstand the phenomenology of TAXPs. Earlier obser-vations of XTE J1810-197 showed that the source spec-trum is well reproduced by a two blackbody model, likelyindicating that (thermal) emission occurs in two regionsof the star surface of different size and temperature: a hotone ( kT = 0 .
70 keV) and a warm one ( kT = 0 .
30 keV;Gotthelf, & Halpern 2005).
XMM-Newton observationsalso showed that the pulsed fraction decreases in time.Perna & Gotthelf (2008) discussed the post-outburstspectral evolution of XTE J1810-197 from 2003 to 2005in terms of two blackbody components, one arising froma hot spot and the other from a warm concentric ring.By varying the area and temperature of the two regions,this (geometric) model can reproduce the observed spec-tra, account for the decline of the pulsed fraction withtime and place a strong constrain on the geometry of thesource, i.e. the angles between the line of sight and thehot spot axis with respect to the spin axis.Recently, Bernardini et al. (2009) by re-examining allavailable
XMM-Newton data found that inclusion of athird spectral component, a blackbody at ∼ .
15 keV,improved the fits. When this component is added boththe area and temperature of the hot component wasfound to monotonically decrease in time, while the warmcomponent decreased in area but stayed at constant tem-perature. The coolest blackbody, which appeared notto change in time, is associated to emission from the(large) part of the surface which was not affected by theevent which triggered the outburst, and is consistent withthe spectral properties of the source as derived from a
ROSAT detection before the outburst onset. Finally, aninterpretation of XTE J1810-197 spectra in terms of aresonant compton scattering model (RCS, see §
3) waspresented by Rea et al. (2008).
CXOU J164710.2-455216
The TAXP CXOU J164710.2-455216 was discovered intwo
Chandra pointings of the young Galactic star clusterWesterlund 1 in May/June 2005. The period of the X-raypulsar was found to be P = 10 .
61 s (Muno et al. 2006), timing and spectral model for the AXPs XTE J1810 and CXOU J1647 3with a period derivative ˙ P = 9 × − s s − (Israel et al.2007). The implied magnetic field is B ∼ G.In November 2006, an intense burst was detected bythe
Swift
Burst Alert Telescope (BAT) in Westerlund 1(Krimm et al. 2006; Muno et al. 2006). Its short dura-tion (20 ms) suggested that its origin was the candidateAXP. However the event was initially attributed to anearby Galactic source, so the AXP was not promptlyre-observed by
Swift . A ToO observation program with
Swift was started 13 hrs after the burst, displaying apersistent flux level 300 times higher than the quiescentone. CXOU J164710.2-455216 was observed in radio,with the Parkes Telescope. The observation was car-ried out a week after the outburst onset, with the intentof searching for pulsed emission similar to that of XTEJ1810. In this case, however, only a (tight) upper limit tothe radio flux (40 µ Jy) was placed (Burgay et al. 2006).
XMM-Newton observations carried out across the out-burst onset show a complex pulse profile evolution. Justbefore the event the pulsed fraction was ∼ ∼
11% (Muno et al. 2007). More-over, the pulse profile changed from being single-peakedjust before the burst, to showing three peaks soon af-ter it. CXOU J164710.2-455216 spectra in the outburststate were fitted either with a two blackbody model( kT ∼ . kT ∼ . kT ∼ .
65 keV, Γ ∼ . THE MODEL
It is now widely accepted that AXPs and SGRsare magnetars, and that their burst/outburst activ-ity, together with the persistent emission, are pow-ered by their huge magnetic field. In particular, thesoft X-ray spectrum ( ∼ ∇ × B = 0;Thompson, Lyutikov, & Kulkarni 2002), where the cur-rents needed to support the field provide a large enoughoptical depth to resonant Compton scattering of ther-mal photons emitted by the star surface. Since chargesare expected to flow along the closed field lines at rela-tivistic velocities, photons gain energy in the (resonant)scatterings and ultimately fill a hard tail.Most studies on spectral formation in atwisted magnetosphere (Lyutikov, & Gavriil 2006;Fernandez, & Thompson 2007; Nobili, Turolla, & Zane2008) are based on the axially symmetric, force-free solution for a twisted dipolar field presented byThompson, Lyutikov, & Kulkarni (2002). This corre-sponds to a sequence of magnetostatic equilibria which,once the polar strength of the magnetic field B p is fixed,depends only on a single parameter: the radial indexof the magnetic field p ( B ∝ r − p − , 0 ≤ p ≤
1) or,equivalently, the twist angle∆ φ N − S = lim θ → Z π/ θ B φ B θ dθ sin θ , (1)where B r , B θ and B φ are the spherical components ofthe field, which depend only on r and θ because of axialsymmetry. Knowledge of B fixes the current density j =( c/ π ) ∇ × B , and, if the particle velocity is known, also the electron density in the magnetosphere n e ( r, θ ) = p + 14 πe (cid:16) B φ B θ (cid:17) Br |h β i| (2)where e is the electron charge and h β i is the averagecharge velocity (in units of c ). The charge density of thespace charge-limited flow of ions and electrons movingalong the closed field lines is orders of magnitude largerthan the Goldreich-Julian density, n GJ , associated to thecharge flow along the open field lines in radio-pulsars.In our investigation we make use of the spectral mod-els presented by Nobili, Turolla, & Zane (2008, NTZ inthe folowing), who studied radiative transfer in a glob-ally twisted magnetosphere by means of a 3D MonteCarlo code. Each model is characterized by the mag-netospheric twist ∆ φ N − S , the electron (constant) bulkvelocity β , and the seed photon temperature kT . Thepolar field was fixed at B p = 10 G. In the applica-tions presented by NTZ, it was assumed that the starsurface emits unpolarized, blackbody radiation and is atuniform temperature. Concerning the present investiga-tion, the most critical assumption is that of a globallytwisted magnetosphere, as discussed in some more detailin §
5. Taking a constant value for the electrons bulk ve-locity is certainly an oversimplification and reflects thelack of a detailed model for the magnetospheric currents.In a realistic case one would expect that β is a functionof position. However, resonant scattering is possible onlywhere the bulk velocity is mildly relativistic. If along aflux tube there are large variations of the Lorentz factor,only the region where β ≈ . β is indeed fairly con-stant along the central part of a flux tube (Beloborodov,private communication). The assumption of unpolarizedthermal radiation is not cogent either, since we are notinterested in the polarization of the escaping radiationand the emergent spectrum is quite insensitive to thepolarization fraction of the seed photons (see, e.g., Fig.4 of NTZ).The code works by dividing the stellar surface into N Θ × N Φ zones of equal area by means of a (cos Θ, Φ)grid, where Θ is the magnetic colatitude and Φ the lon-gitude. After a few scatterings photons escape from theneutron star magnetosphere and are collected on a spher-ical surface (the “sky”) which is divided into N Θ s × N Φ s patches, similarly to what is done for the star surface.The key point is that the evolution of seed photons fromeach patch is followed separately. This allows us to treatan arbitrary surface temperature distribution withoutthe need to perform new Monte Carlo runs, by simplycombining together models from runs with different tem-peratures at the post-production level (the geometry isshown in Fig. 1)Monte Carlo models are computed (and stored) for thesimplest geometrical case, in which the spin and the mag-netic axes are aligned. As discussed in NTZ, the mostgeneral situation in which the spin and magnetic axesare at an arbitrary angle ξ can be treated at the post-production level. If χ is the inclination of the line-of-sight (LOS) with respect to the star spin axis and α is Albano et al. Fig. 1.—
A schematic view of the neutron star. Ω and µ arethe star spin and magnetic axis, respectively. The dashed linecorresponds to the line-of-sight. The two angles χ and ξ are alsoshown. The star surface is divided into three regions: a hot polarcap (red), a warm corona (blue) and a colder zone (gray). the rotational phase angle, the co-ordinates of the pointswhere the LOS intersects the sky can be found in termsof ξ , χ and α . The pulse profile in any given energyband is then obtained by integrating over the selectedrange the energy-dependent counts at these positions asthe star rotates (see again NTZ for details). In orderto compare model lightcurves with observations, integra-tion over energy is performed by accounting for both in-terstellar absorption and the detector response function.Actually, the interstellar absorption cross-section σ andthe response function A depend on the photon energyat infinity ¯ E = E p − R S /R NS , where E is the en-ergy in the star frame (which is used in the Monte Carlocalculation) and R S is the Schwarzschild radius (we as-sume a Schwarzschild space-time and take R NS = 10 kmand M NS = 1 . M ⊙ ). Our model pulse profile in the[ ¯ E , ¯ E ] energy band is then proportional to Z ¯ E ¯ E d ¯ E exp [ − N H σ ( ¯ E )] A ( ¯ E ) N ( α, E ) (3)where N H is the hydrogen column density and N ( α, E ) isthe phase- and energy-dependent count rate. In the ap-plications below we used the Morrison, & McCammon(1983) model for interstellar absorption and, since wedeal with XMM-Newton observations, we adopted theEPIC-pn response function. We remark that the MonteCarlo spectral calculation is carried out assuming aflat space-time (i.e. photons propagate along straightlines), so that, apart from the gravitational redshift,no allowance is made for general-relativistic effects (seeZane, & Turolla 2006, for a more detailed discussion).In particular, no constraints on the star mass and radiuscan be derived in the present case from the comparison ofmodel and observed pulse profiles (see e.g. Leahy et al. 2008, 2009).Finally, phase-averaged spectra are computed by sum-ming over all phases the energy-dependent counts. Notethat 0 ≤ ξ ≤ π/
2, while χ is in the range [0 , π ] becauseof the asymmetry between the north and south magneticpoles introduced by the current flow. TAXP ANALYSIS
Our first step in the study of the two TAXPs XTEJ1810-197 and CXOU J164710.2-455216 was to repro-duce the pulse profiles (and their time evolution) withinthe RCS model discussed in §
3. The fit to the ob-served pulse profiles in different energy bands (total:0 . ≤ E ≤
10 keV, soft: 0 . ≤ E ≤ ≤ E ≤
10 keV) provides an estimate of thesource parameters, including the two geometrical angles ξ and χ . While the twist angle, electron velocity and sur-face temperature may vary in the different observations(although they must be the same in the different energybands for a given observation), the fits have to producevalues of ξ and χ which are at all epochs compatible withone another (to within the errors) in order to be satisfac-tory. We then computed the phase-averaged spectra forthe two sources at the various epochs for the same sets ofparameters and compared them with the observed ones.There are several reasons which led us to choose such anapproach. The main one is that, as discussed in NTZ(see also Zane et al. 2009), spectral fitting alone is un-able to constrain the two geometrical angles. Moreover,lightcurve fitting allows for a better control in the case inwhich the surface thermal map is complex and changesin time (see below).For the present investigation, a model archive was gen-erated beforehand. Each model was computed by evolv-ing N patch = 225 ,
000 photons for N Θ × N Φ = 8 × N tot = 7 , ,
000 photons). The pa-rameter grids are: 0 . ≤ kT ≤ . .
05 keV),0 . ≤ β ≤ . .
1) and 0 . ≤ ∆ φ N − S ≤ . . N Θ s × N Φ s =10 ×
10 = 100 angular grid on the sky, and in N E =50 energy bins, equally spaced in log E in the range0 . −
100 keV.The analysis proceeds as follows. We first used theprincipal component analysis (PCA) to explore the prop-erties of the lightcurves as a population and to select themodel within the archive that is closest to the observedone at a given epoch. This serves as the starting point forthe pulse profile fitting procedure, which we performedby assuming that the whole star surface is at the sametemperature. The fitting is then repeated first for thecase in which the surface thermal distribution consists ofa hot spot and a cooler region, and then by generating anew archive with a finer surface gridding, and applyingit in the case of a surface thermal map consisting of ahot spot, a warm corona and a cooler region (see againFig 1). Finally, the source parameters derived from thelightcurve fitting are used to confront the model and ob-served (phase-averaged) spectra. Phase-resolved spectralanalysis, although feasible in our model and potentiallyimportant, was not attempted because the decay in fluxof both sources makes the counting statistics rather poorafter the first one/two observations (see Bernardini et al.2009, for more details in the case of XTE J1810-197). timing and spectral model for the AXPs XTE J1810 and CXOU J1647 5
Fig. 2.—
Principal component representation of the simulatedlightcurves in our archive (black squares) together with the ob-served lightcurves of XTE J1810-197 (red dots) and of CXOUJ164710.2-455216 (green dots). All the pulse profiles refer to the0.5–10 keV band.
PCA
The principal component analysis is a method of mul-tivariate statistics that allows to reduce the number ofvariables X i needed to describe a data set by introducinga new set variables, the principal components (PCs) Z i .The PCs are linear combinations of the original variablesand are such that Z displays the largest variance, Z thesecond largest, and so on. By using the PCs it is possibleto describe the data set in terms of a limited number ofvariables, which however, carry most of the informationcontained in the original sample (see e.g. Zane, & Turolla2006, and references therein).Synthetic lightcurves were generated for 32 phases inthe range [0 , π ] and for a 9 × ◦ ≤ ξ ≤ ◦ (step 10 ◦ ), 0 ◦ ≤ χ ≤ ◦ (step 20 ◦ ); the archive con-tains a total of 136323 models. Once the PCA was ap-plied to the lightcurve set, we found that the first threePCs ( Z , Z , Z ) accounts for as much as ∼
90% of thesample variance. This means that the entire set is sat-isfactorily described in terms of just three variables in-stead of the original 32 (see Zane, & Turolla 2006, foran interpretation of Z , Z , Z ). A graphic representa-tion of the lightcurves in the archive in terms of the firstthree PCs is shown in Fig. 2. In the same plot we alsoshow the PC representation of the pulse profiles of XTEJ1810-197 and CXOU J164710.2-455216 at the variousepochs. The points corresponding to observations fallwithin the volume occupied by models and this guaran-tees that there is a combination of the parameters forwhich a synthetic pulse profile reproduces the data. ThePC representation is also used to find the model in thearchive which is closest to a given observed lightcurve,by looking for the minimum of the (squared) Euclideandistance P i =1 ( Z i − Z obsi ) between the model and theobserved pulse profile. XTE J1810-197
We considered eight
XMM-Newton observations, cov-ering the period September 2003-September 2007 for theTAXP prototype XTE J1810-197 (see Table 1 for theobservation log). Only EPIC-pn data were used, and werefer to Bernardini et al. (2009), who analyzed the same observations, for all details on data extraction and re-duction. All the EPIC-pn spectra were rebinned beforefitting, to have at least 40 counts per bin and preventoversampling the energy resolution by more than a fac-tor of three.
Pulse profiles
We started our analysis by making the simplest as-sumption about the star surface thermal map, a uniformdistribution at temperature T . Lightcurves were thencomputed in the total, soft and hard energy band for allthe models in the archive. Once the model closest toeach observation (and in each band) was found throughthe PCA, we used it as the starting point for a fit per-formed using an IDL script based on the minimizationroutine mpcurvefit.pro . Our fitting function has sixfree parameters, because, in addition to the twist angle,the temperature, the electron velocity, the angles χ and ξ , we have to include an initial phase to account for theindetermination in the position of the pulse peak. Sinceit is not possible to compute “on the fly” the pulse profilefor a set of parameters different from those contained inthe archive, lightcurves during the minimization processwere obtained from those in the archive using a linearinterpolation in the parameter space.In this way we obtained a fair agreement with theobserved pulse profiles ( χ ≤ .
12 in five out of eightobservations; see Table 4), and the values of the physi-cal parameters (∆ φ N − S , β , T ) turn out to be the same(to within the errors) for a given epoch among the dif-ferent energy bands, as it needs to be. Moreover, theevolution of the twist angle and of the surface temper-ature follows a trend in which both quantities decreasein time as the outburst declines. This is expected if theoutburst results from a sudden change in the NS mag-netic structure, producing both a heating of the star sur-face layers and a twisting of the magnetosphere whichthen dies away (Thompson, Lyutikov, & Kulkarni 2002;Beloborodov 2009). However, the model is not accept-able since we found that the geometrical angles χ and ξ change significantly from one observation to another,and even for the same observation in the different en-ergy bands (see Fig. 3 where the parameter evolution isshown for the three energy bands). The analysis of thehard band was not carried out after September 2006, be-cause in both the 2007 observations photons with energy > TABLE 1XTE J1810-197
XMM-Newton observations a Label OBS ID Epoch Exposure time (s) total counts background countsSep03 0161360301 2003-09-08 5199 60136 2903Sep04 0164560601 2004-09-18 21306 89082 1574Mar05 0301270501 2005-03-18 24988 54279 1760Sep05 0301270401 2005-09-20 19787 21876 1311Mar06 0301270301 2006-03-12 15506 12296 1197Sep06 0406800601 2006-09-24 38505 23842 2974Mar07 0406800701 2007-03-06 37296 21903 2215Sep07 0504650201 2007-09-16 59014 34386 4117 a EPIC-pn
Fig. 3.—
Parameters evolution for XTE J1810-197, uniform sur-face temperature; results refer to the total (red dots), soft (bluedots) and hard (green dots) energy bands. Parameter errors arecalculated by the minimization routine mpcurvefit.pro , and areat 1 σ . Time is computed starting from the September 2003 obser-vation. temperature ∼ .
15 keV, comparable to the quiescentone (see also Bernardini et al. 2009). In order to checkif this fit can be further refined, we started from theSeptember 2007 observation, freezing the colder temper-ature at T c = 0 .
15 keV, and letting the hot cap tem-perature T h free to vary. Since the cap area A h is notknown a priori, nor it can be treated as a free parameterin our minimization scheme, we tried several values of A h , corresponding to one up to eight patches of our sur-face grid (this means that A h is n/
32 of the star surface,with n = 1 , . . . , χ forthe fit in the different trials. We verified that in all casesthe same value of the cap area produces the minimum χ in all energy bands. Independent of the emitting areachosen, we always found for T h a value compatible with ∼ .
15 keV for both the September and March 2007 ob-servations.One can then conclude that, for these two epochs, theentire star is radiating at the same temperature, or ifa hot cap exists, its area is smaller than ∼ T c .However, we verified that the χ steeply grows when T c increases above 0 . − .
16 keV. Although there is noguarantee that the same is true when T c decreases, in thefollowing we assume that T c ∼ .
15 keV is a satisfactoryestimate for the uniform temperature at these epochs.We then proceeded backwards in time, from Septem-ber 2006 till September 2003. Again, the cooler tem-perature is kept fixed while several values of A h aretried. However, to account for the possibility thatalso T c varies, we repeated the calculation for T c =0 . , . , . , .
30 keV, looking for the pair ( T c , A h )which gives the lowest χ . Results are summarized intable 2. Although the fits improve with respect to theone-temperature model (see table 4), the two geometri-cal angles still change from one observation to anotherand also across different bands at the same epoch.In order to reproduce more accurately the star thermalmap, we generated a new model archive, increasing thenumber of surface patches to N Θ × N Φ = 50 × .
15 keV ≤ T ≤ . . ≤ β ≤ . . ≤ ∆ φ N − S ≤ . T h , a concentric warm corona at T w and theremaining part of the neutron star surface at a coolertemperature, T c . Again, we began our analysis from the2007 observations, fixing T c = 0 .
15 keV, and search-ing for the value of the warm temperature T w . Everyfit was repeated for twelve values of the emitting area A w = 0 . , , , , . . . ,
20 % the total surface.We found that the reduced χ improves with the addi-tion of a warm cap at T w ∼ . . T c = 0 .
15 keVand T h ∼ . T h for the two-temperaturemodel corresponds to T w in the present case). For thesetwo observations we repeated the fit, fixing T c at 0 .
15 keVwhile leaving T w free to vary. The size of the emit-ting area was estimated by following the same procedurediscussed above. We found an almost constant value, T w ∼ . TABLE 2XTE J1810-197 parameters and thermal map (two-temperature model) a Epoch ∆ φ N − S β ξ ( ◦ ) χ ( ◦ ) T h (keV) A h (%) T c (keV) A c (%)Sep03 0 . ± .
01 0 . ± .
01 22 . ± . . ± . . ± .
01 25 . ± . .
30 75 . ± . . ± .
01 0 . ± .
02 20 . ± . . ± . . ± .
01 18 . ± . .
30 81 . ± . . ± .
01 0 . ± .
01 21 . ± . . ± . . ± .
01 12 . ± . .
25 87 . ± . . ± .
01 0 . ± .
05 23 . ± . . ± . . ± .
01 9 . ± . .
25 90 . ± . . ± .
01 0 . ± .
11 23 . ± . . ± . . ± .
01 6 . ± . .
15 93 . ± . . ± .
01 0 . ± .
16 21 . ± . . ± . . ± .
01 3 . ± . .
15 96 . ± . . ± .
01 0 . ± .
01 29 . ± . . ± . − − . ± .
01 100 . . ± .
01 0 . ± .
08 22 . ± . . ± . − − . ± .
01 100 . a Total energy band; parameters with no reported errors are fixed. Parameter errors are calculated by the min-imization routine mpcurvefit.pro , and are at 1 σ . Errors on the area correspond to the smallest patch of thegrid. no need for a further component at T h at these epochs.On the other hand, results for the two-temperature case(see table 2) show the presence of a component withtemperature higher than 0 . .
25 and 0 .
30 keV). It is tempting toassociate this to a transient hot cap that appears only inthe first period after the outburst, superimposed to theother, longer-lived emitting zones.To test this possibility, we re-fitted the first four ob-servations by fixing the coldest temperature at T c =0 .
15 keV, the warmer one at T w = 0 . A h and A w chosen among the twelvevalues in the range 0 . χ . Results ofthe lightcurve fitting at different epochs are listed in ta-ble 3 and shown in Fig. 4, while the reduced χ for thethree thermal distributions is reported in table 4.A worry may arise whether the best-fitting values ob-tained from the minimization routine correspond indeedto absolute minima of the reduced χ . In order to checkthis, and visually inspect the shape of the χ curve closeto the solution, we computed and plotted the reduced χ leaving, in turn, only one parameter free and freezing theremaining five at their best-fit values. This also allowedus to obtain a more reliable estimate of the parametererrors which were computed by looking, as usual, for theparameter change which corresponds to a 1 σ confidencelevel (and reported in table 3).We found that all values obtained with the mpcurvefit.pro routine indeed correspond to minimaof the reduced χ curve, with the exception of the tem-perature(s), for which there are observations (or energybands) with very flat χ curves (see Fig. 5). In par-ticular, for the September 2005 observation the curveobtained varying T h is flat in all the three energy bands.Also the curves relative to T w for the September 2006,March 2007 and September 2007 observations have thesame problem. This can be understood by noting thatin all these observations the size of the hot/warm regionaccounts for only < χ curve rel-ative to one of the temperatures is flat, but this occursonly for one of the three energy bands. The first case concerns the hot temperature and the soft band, the sec-ond the warm temperature and the hard band. As wediscussed above, when the hot (warm) area shrinks itaffects little the pulse profile; this shows up first in theenergy band in which its emission contributes less, i.e.the soft (hard) band.Given these findings, we concluded that lightcurveanalysis by itself is unable to yield an unique temperaturevalue for the September 2005, the September 2006, andboth the 2007 observations. On the other hand, spectralanalysis is more sensitive to temperature variations, sothat it is possible to infer a temperature value also inthese cases. As it will be discussed in the next section,by combining the two techniques we can remove mostof the uncertainties and validate the three temperaturemodel presented so far (see sec. 4.2.2 for details).There are several physical implications than can bedrawn from our model. The TAXP is seen at an angle χ = 148 ◦ +7 − with respect to the spin axis. The mis-alignment between the spin axis and the magnetic axisis ξ = 23 ◦ +15 − . These values of the two angles, and thecorresponding errors, are calculated from the weightedaverage in the three energy bands. To get a quantita-tive confirmation that χ and ξ do not change in time, wefitted a constant through the values of each angle as de-rived from the lightcurves fitting at the different epochsand found that the null hypothesis probability is < σ level. Low values of ξ produce, however, mod-els with pulsed fractions quite smaller than the observedones and, despite ξ ∼ § Z , is, in fact, directly related to theamplitude).It emerges a scenario in which, before the outburst,the NS surface radiates uniformly at a temperature T c ∼ .
15 keV. Soon after the burst the thermal map of XTEJ1810-197 substantially changes. The region around themagnetic north pole is heated, reaches a temperature of ∼ . ∼
8% of the total star sur-face. This hot spot is surrounded by a warmer corona at ∼ . ∼
16% of the surface.During the subsequent evolution, the hot cap decreases insize and temperature until the March 2006 observation,when it becomes too small and cold to be distinguished Albano et al.
TABLE 3XTE J1810-197 parameters and thermal map (three-temperature model) a Epoch ∆ φ N − S β ξ ( ◦ ) χ ( ◦ ) T h (keV) T w (keV) T c (keV) A h (%) A w (%)Sep 03 0 . +0 . − . . +0 . − . . +4 . − . . +4 . − . . +0 . − . .
30 0 .
15 8 . ± . . ± . . +0 . − . . +0 . − . . +4 . − . . +5 . − . . +0 . − . .
30 0 .
15 6 . ± . . ± . . +0 . − . . +0 . − . . +5 . − . . +7 . − . . +0 . − . .
30 0 .
15 4 . ± . . ± . . +0 . − . . +0 . − . . +10 . − . . +13 . − . . −− .
30 0 .
15 2 . ± . . ± . . +0 . − . . +0 . . . . − . . +7 . − . - 0 . +0 . − . .
15 - 6 . ± . . +0 . − . . +0 . − . . +12 . − . . +14 . − . - 0 . −− .
15 - 2 . ± . . +0 . − . . +0 . − . . +12 . − . . +19 . − . - 0 . −− .
15 - 0 . ± . . +0 . − . . +0 . − . . +16 . − . . +16 . − . - 0 . −− .
15 - 0 . ± . a Total energy band; parameters with no reported errors are fixed. Errors are computed from the χ curve (see textfor details) and are at 1 σ . No errors are reported when they could not be calculated (flat χ curves) and errors onthe area have the same meaning as in Tab. 2. Fig. 4.—
Parameters evolution for XTE J1810-197, three temperature model. Left (from top to bottom): twist angle (∆ φ ), bulk velocity( β ) and area of the different emitting regions. Right: the two geometrical angles, χ and ξ . Details as in fig. 3. TABLE 4Reduced χ for XTE J1810-197 a Epoch χ red χ red χ red χ red T (1T) (2T) (3T) (XSPEC) (keV)Sep 03 1.72 1.58 0.12 1.22 -Sep 04 0.66 0.42 0.36 1.93 -Mar 05 1.02 0.98 0.79 1.50 -Sep 05 1.06 0.40 0.39 1.52 0 . +0 . − . Mar 06 2.94 1.70 1.25 1.34 -Sep 06 0.94 0.38 0.35 1.36 0 . +0 . − . Mar 07 2.88 2.88 2.37 1.08 0 . +0 . − . Sep 07 1.12 1.12 0.96 1.29 0 . +0 . − . First three columns: reduced χ obtained from thelightcurves fitting for total the energy band (results forthe other two bands are similar). Last two columns:reduced χ obtained from the spectral fitting in XSPEC ,and corresponding temperatures. The temperature wasleft free to vary only at those epochs and for those com-ponents for which the lightcurve analysis did not pro-duce an unique value. Errors for the temperature areat 1 σ . from the surrounding warm corona. The warm regionremains almost constant until September 2005, then de-creases in size, and becomes a cap in March 2006, fol-lowing the hot spot disappearance. In September 2007(our last observation for XTE J1810-197) the warm capis still visible, even if its area is down to only ∼ . β ∼ . §
5, no further refinement of the surfacethermal map will be attempted here. Since XTE J1810- timing and spectral model for the AXPs XTE J1810 and CXOU J1647 9
Fig. 5.—
Two examples of the different behavior of the reduced χ for the warm temperature. The top curve refers to the March2006 observation (soft band) and exhibits a well-defined minimum.The bottom curve (September 2006 observation, total band) is soflat to make it impossible to gauge the best-fitting value and itserrors. Fig. 6.—
Synthetic (3T model) and observed pulse profiles forXTE J1810-197 in the total energy band. Solid lines represent thebest-fitting model, dots the observed lightcurves. Initial phases arearbitrary. The lower panel shows the residuals.
197 pulse profiles are fairly sinusoidal, we can computethe pulsed fraction and its evolution in time at differentenergies. The comparison of model results with data isshown in Fig. 7.
Fig. 7.—
The variation of XTE J1810-197 pulsed fraction withenergy at different epochs. The red line refers to the model, bluedots to observations (errors are at 1 σ ). Spectra
In order to verify if the thermal map inferred fromthe pulse profile fits is reasonable, and in order to re-move the uncertainties in the value of the temperatureat certain epochs (see § χ , ξ ) can also reproduce the spectral evolutionof XTE J1810-197 during the outburst decay. To thisend, we used the ntzang model that was implementedin XSPEC by Nobili, Turolla, & Zane (2008, the model isnot currently available in the public library, but it can beobtained from the authors upon request). The ntzangXSPEC model has the same free parameters as those usedin our fits of the pulse profiles. In addition it contains thenormalization and the column density. We caveat that,since this
XSPEC model was created by assuming that theentire star surface emits at uniform temperature, strictlyspeaking is not directly suited to the present case. As anapproximation, we fitted the spectra by adding togetherthree (absorbed) ntzang models, each associated to oneof the three thermal components, at temperatures T h , T w and T c , respectively. At each epoch the fit was per-formed by freezing ∆ φ N − S , β , T , χ and ξ at the valuesderived from the fit of the lightcurve in the total energyband (see § N H ,is the same for all the three spectral components and forall epochs. Since for the September 2005, the Septem-ber 2006 and both the 2007 observations the lightcurveanalysis did not return an unique value for the hotter0 Albano et al.temperature, we also left this parameter free to vary inthese four observations. In all these cases, we found thatthe fit converges to a value of the temperature close tothe best-fitting value obtained from the lightcurve anal-ysis (see table 4). Moreover, the reduced χ significantlyworsens by varying the temperature, meaning that thespectra are much more sensitive to the presence of thesecomponents. Results are shown in Fig. 8, while the re-duced χ for the fits at the various epochs are reportedin Tab. 4. The value of the column density is found to be N H = (7 . ± . × cm − , compatible at the 1 . σ level with the one obtained by Bernardini et al. (2009)with the 3 BB model, N H = (6 . ± . × cm − .We remark that, in assessing the goodness of the fits,only the normalizations of the three components (plus N H ) are free to vary; all the other model parameters arefrozen at the best values obtained from the pulse profileanalysis. Under these conditions, we regard the agree-ment of our model with observed spectra as quite satis-factory. We note that the presence of systematic residu-als at high energies (above 7–8 keV) may be hinted in thefits of the three earlier observations (see Fig. 8). As dis-cussed by Bernardini et al. (2009) they may be relatedto a harder spectral component which is however onlymarginally significant (3 . σ confidence level) and quiteunconstrained. Given that the high-energy residuals arecomparable to (or smaller than) those of the 3 BB modelused by Bernardini et al. (2009), we conclude that a hardtail is not significant also in our modelling and we did notattempt to include it in our fits.We checked how the reduced χ for the spectral fitchanges when the (frozen) parameters are varied within ∼ σ from their best-fit value (as from the pulse fitting).This has been done changing one parameter at a time.We found that indeed the χ increases quite smoothlyin response to the change of each parameter, with theexception of χ and ξ . This is not surprising, since weknew already that the spectrum is not much sensitive tothe geometry. We also tried a fit leaving all the param-eters free, apart from the two geometrical angles whichwere held fixed at their best-fit values. The fit returnsparameter values which are the same, within the errors,as those derived from the pulse fitting and comparablevalues of the reduced χ , implying that the solution wepresented is indeed a global χ minimum. The same pro-cedure and the same conclusions hold also in the case ofCXOU 164710.2-455216 (see § CXOU J164710.2-455216
Having verified that our model can provide a rea-sonable interpretation for the post-outburst timing andspectral evolution of TAXP prototype XTE J1810-197,we applied it to CXOU J164710.2-455216, the other tran-sient AXP for which a large enough number of
XMM-Newton observations covering the outburst decay areavailable (see table 5 for details). During September 2006the pn and MOS cameras were set in full window imagingmode with a thick filter (time resolution = 73 . × − s and 2.6 s for the pn and MOS, respectively), whileall other observations were in a large and small windowimaging mode with a medium filter (time resolution =4 . × − s and 0.3 s for the pn and MOS, respec-tively). To extract more than 90% of the source counts, Fig. 8.—
Spectral evolution in the eight
XMM-Newton obser-vations of XTE J1810-197. Solid lines represent the model, whiledotted lines refer to the single ntzang components (see text fordetails). Residuals are shown in the lower panel. we accumulated a one-dimensional image and fitted the1D photon distribution with a Gaussian. Then, we ex-tracted the source photons from a circular region of ra-dius 40 ′′ (smaller than the canonical 55 ′′ , correspondingto 90% of the source photons, in order to minimize thecontamination from nearby sources in the Westerlund1 cluster) centered at the Gaussian centroid. The back-ground for the spectral analysis was obtained (within thesame pn CCD where the source lies and a different CCDfor the MOS) from an annular region (inner and outerradii of 45 ′′ and 65 ′′ , respectively) centered at the bestsource position. In the timing analysis, the backgroundwas estimated from a circular region of the same size asthat of the source. EPIC-pn spectra were processed asin the case of XTE J1810-197 (see § Pulse profiles
The analysis of the pulse profiles of CXOU J164710.2-455216 follows closely that presented in § χ and ξ were not foundto vary in the same observation for the different energybands and for different epochs. We did not attempt tofit the pulse profiles in the hard band after the February2007 observation because of the very few counts at ener-gies > T h , a concentric warm coronaat T w and the rest of the neutron star at the colder tem-perature T c . Every fit was repeated for ten values ofthe hot cap area A h = 0 . , , , , . . . ,
16 % (ofthe total surface) and for 20 values of the warm coronaarea A w = 0 . , , , , . . . ,
30 %. Moreover,lightcurves fits were iterated for two values of the coldtemperature T c = 0 . , .
30 keV and also for two val-ues of the warm temperature T w = 0 . , .
45 keV. Thehotter temperature was left free to vary. We found thatin the last two observations, independent of the hot cap timing and spectral model for the AXPs XTE J1810 and CXOU J1647 11
TABLE 5CXOU J164710.2-455216
XMM-Newton observations a Label OBS ID Epoch Exposure time (s) total counts background countsSep 06 0311792001 2006-09-22 26780 56934 1709Feb 07 0410580601 2007-02-17 14740 18734 1264Aug 07 0505290201 2007-08-19 16020 11710 2384Feb 08 0505290301 2008-02-15 9080 4618 1131Aug 08 0555350101 2008-08-20 26360 7357 1689Aug 09 0604380101 2009-08-24 33030 4974 1959 a EPIC-pn size, T h is always ∼ .
45 keV, nearly indistinguishablefrom the temperature of the warm corona obtained fromthe fit. We concluded that, at least for our present sur-face grid resolution, in the last two observations thereare only two thermal components that contribute to theemission, the cold and warm ones, and repeated the fitleaving T w free to vary. Results are reported in table6 and plotted in Fig. 9, while a comparison of the re-duced χ for the three thermal distributions is given intable 7. Errors listed in the tables have the same mean-ing as in the case of XTE J1810-197. Again, when thespot at T h becomes very small its temperature can notbe determined unambiguously.According to our model, CXOU J164710.2-4552116 isviewed at an angle χ = 23 ◦ +4 − with respect to its spinaxis. The spin and the magnetic axes are almost orthog-onal, ξ = 84 ◦ +5 − . This is a quite peculiar condition, and itseems to be the only one capable of explaining the char-acteristic three-peaked shape of the observed lightcurveswithin the present model. As for XTE J1810-197 valuesand errors for both angles are calculated as the weightedaverage of parameters in the three energy bands. Also inthis case the probability that χ and ξ are not constantin time is < T h ∼ . ∼
8% of the total. This hot spot decreases in tem-perature and size as time elapses, until February 2008.In August 2008 the hot cap becomes so small in size andits temperature so close to that of the warm corona, thatit is impossible to distinguish between the two regions.The warm corona has a temperature of ∼ .
45 keV, whichremains about constant during the three years of obser-vations. In this case the corona area slightly increaseswith time, starting from ∼
20% and reaching ∼
30% ofthe NS surface. The third region has a lower temper-ature T c ∼ .
15 keV and its area remains constant at ∼
70% of the total. The twist angle is ∼ .
12 rad soonafter the burst, and it decreases with time. There arehints that its decay is slower until August 2007, thenproceeds faster. The electron velocity is about the sameat all epoch ( β ∼ . χ values not much higher than those of XTE J1810-197(compare Tab. 4 and 7) reflects the larger uncertaintiesin the phase-binned source counts. We also note that theerrors on the geometrical angles for CXOU J164710.2-455216 are smaller than those derived for XTE J1810-197, despite the worst agreement (see Tab. 3 and 6).This is most probably due to the different shapes of thepulses in the two sources. Because of the very peculiarlightcurve of CXOU J164710.2-455216, which can be re-produced by our model only invoking a nearly orthogonalrotator, even small depatures of ξ and χ from their best-fit values results in a rapid growth of the χ . This doesnot occur for the rather sinusoidal pulse of XTE J1810-197 since the model can produce lightcurves of more orless the right shape in a wider range of angles.Besides being of limited use because of the complexshape of the pulse, the pulsed fraction analysis was hin-dered by the lower count rate, especially at low energiesand was not pursued further for this source. As in XTEJ1810-197, we checked that the values obtained from theminimization routine indeed correspond to minima of thereduced χ s. Again we froze five of the six parameters tothe value obtained with the mpcurvefit.pro minimiza-tion routine, and calculated the reduced χ around itsminimum by varying the free parameter. The procedurewas repeated for all parameters and all observations inthe three energy bands. Again, for all parameters but thetemperature, results obtained with the mpcurvefit.pro routine indeed correspond to the minima of the reduced χ curve. There is one observation for which the χ curverelative to the hot temperature is very flat for all the en-ergy bands. This is the August 2008 observation, forwhich the size of the emitting area accounts for just 2%of the total neutron star surface. As in XTE J1810-197,we conclude that the fit is not very sensitive to the tem-perature variation for very small emitting areas. On theother hand, like in the previous case, it was possible toinfer a value for the August 2008 hot temperature usingthe spectral analysis (see sect. 4.3.2). Spectra
The spectral analysis for CXOU J164710.2-455216 wascarried out using the same approach discussed in § ntzang components, each representa-tive of an emitting region at different temperature, andfroze all parameters apart from the three normalizationsand N H (which were forced to be the same for all thecomponents and for all epochs). Moreover, since thelightcurve analysis the February 2008 observation failedto provide an unambiguous value for the hot tempera-2 Albano et al. TABLE 6CXOU J164710.2-455216 parameters and thermal map (three-temperature model) a Epoch ∆ φ N − S β ξ ( ◦ ) χ ( ◦ ) T h (keV) T w (keV) T c (keV) A h (%) A w (%)Sep 06 1 . +0 . − . . +0 . − . . +1 . − . . +0 . − . . +0 . − . .
45 0 .
15 8 . ± . . ± . . +0 . − . . +0 . − . . +2 . − . . +1 . − . . +0 . − . .
45 0 .
15 6 . ± . . ± . . +0 . − . . +0 . − . . +1 . − . . +2 . − . . +0 . − . .
45 0 .
15 4 . ± . . ± . . +0 . − . . +0 . − . . +2 . − . . +7 . − . . −− .
45 0 .
15 2 . ± . . ± . . +0 . − . . +0 . − . . +2 . − . . +4 . − . - 0 . +0 . − . .
15 - 30 . ± . . +0 . − . . +0 . − . . +9 . − . . +4 . − . - 0 . +0 . − . .
15 - 30 . ± . a Total energy band. Errors have the same meaning as in Tab. 3
Fig. 9.—
Same as in Fig. 4 for the TAXP CXOU J164710.2-455216; here time is computed starting from the September 2006 observation.
Fig. 10.—
Same as in Fig. 6 for CXOU J164710.2-455216; com-puted pulse profiles refer to the 3T model and initial phases arearbitrary. ture, also this parameter was left free to vary. Resultsare shown in Fig. 11. Given the approach we used forthe fit, the agreement is quite satisfactory (reduced χ TABLE 7Reduced χ for CXOU J164710.2-455216 a Epoch χ red χ red χ red χ red T (1T) (2T) (3T) (XSPEC) (keV)Sep 06 1.05 0.86 0.31 1.24 -Feb 07 1.32 0.76 0.65 0.83 -Aug 07 0.97 0.91 0.44 1.01 -Feb 08 1.45 1.12 0.63 1.08 0 . +0 . − . Aug 08 1.45 1.23 0.79 1.23 -Aug 09 2.03 1.97 1.52 1.36 - a Same as in tab. 4 are listed if Tab. 7). Systematic residuals at low (1–2 keV) energies are however present, especially in theSeptember 2006, August 2007 and August 2008 obser-vations. N H is found to be (2 . ± . × cm − ,somewhat higher than that derived by Naik et al. (2008), N H = (1 . ± . × cm − . DISCUSSION
The simultaneous study of the timing and spectralcharacteristics of the transient AXPs XTE J1810-197 andCXOU J164710.2-455216 presented in this paper showsthat the post-burst evolution of two sources share a num-ber of similar properties. In particular, the long-term timing and spectral model for the AXPs XTE J1810 and CXOU J1647 13
Fig. 11.—
Same as in Fig. 8 for the six
XMM-Newton observa-tions of CXOU J164710.2-455216. variability of the pulse profiles and spectra appears to be(semi)quantitatively consistent with a scenario in whichthe star surface thermal distribution and magnetosphericproperties progressively change in time. Our resultswere derived within the twisted magnetosphere modelfor magnetars and support a picture in which the twistaffects only a small bundle of closed field lines aroundone of the magnetic poles. As discussed by Beloborodov(2009), if the twist is initially confined along the mag-netic axis, the returning currents hit a limited portion ofthe star surface (typically a polar cap), which becomeshotter. In this scenario the post-outburst evolution is re-lated to the twist decay, during which the bundle shrinks,and the heated region decreases both in size and temper-ature. We found evidence for a cooling/shrinking of theheated polar cap in both sources, together with a de-crease of the twist angle. It should be noted that ourmagnetospheric model assumes a global twist, since nospectral calculations are currently available for a local-ized twist.Within this common framework, there are nonethelessdifferences between the two TAXPs. For XTE J1810-197we found that the star thermal map comprises three re-gions: a hot cap, a surrounding warm corona, and therest of the surface at a colder temperature. The hotcap decreases in size and temperature until it becomesindistinguishable from the corona around March 2006.Also the warm corona shrinks, although its temperaturestays about constant at ∼ . .
5% of theentire surface. The rest of the surface remains at a tem-perature comparable to the quiescent one (as measuredby
ROSAT ) during the entire evolution, indicating thatthe outburst likely involved only a fraction of the starsurface. Bernardini et al. (2009) obtained similar resultsusing a 3BB model, although they did not attempt tolocate the different emitting regions on the star surfacenor to fit the pulse profiles. In their (purely spectral)analysis the hot region is visible slightly longer (untilMarch 2006); the reason for the difference with respectto our results being most probably the resolution of oursurface grid. Moreover, in our case the hot temperaturedecrease is more pronounced. The twist angle decreases from ∼ . ∼ . ∼ .
45 keV andthe area increases. Actually, the area of the “hot+warm”region is constant and covers about ∼
30% of the surface,while the remaining ∼
70% is at a constant cooler tem-perature, ∼ .
15 keV. This is suggestive of a picturein which the ”quiescent” state of the source is charac-terized by a two-temperature map, with a warm polarregion superposed to the cooler surface. The outburstmight have heated a portion of the warm cap, produc-ing the hot zone which then cooled off. It is intriguingto notice that the disappearance of the hot spot occursat the same time (August 2008) at which the pulse pro-file dramatically changed, switching from a three-peakedto a single-peaked pattern. A quasi-sinusoidal shape ofthe lightcurve was observed when the source was in qui-escence (Israel et al. 2007). However, at that time thepulsed fraction was nearly 100% above 4 keV, likely in-dicating the presence of a small hot spot which is period-ically occulted as the star rotates. This is in agreementwith our finding that this TAXP is a nearly orthogonalrotator. Whether CXOU J164710.2-455216 is presentlyapproaching quiescence is unclear. If this is the case, itsquiescent state is different from that observed in 2005and also from that of XTE J1810-197.It is worth stressing that our claim that the temper-ature does not change spatially in each of the regionsshould not be taken literally. The assumption that thesurface can be divided in three (or two) thermal re-gions was mainly introduced to simplify the calculationswhile catching the essential features of the model. Asmooth temperature variation within a zone is likely tobe present. However, it is difficult to reconcile the ob-served pulsed fraction of XTE J1810-197 in the Septem-ber 2006 observation ( & × χ and ξ during the entire period covered by the4 Albano et al.observations.In their analysis of XTE J1810-197, Perna & Gotthelf(2008) assumed that the X-rays come from two concen-tric regions with varying temperatures and areas, eachemitting a blackbody spectrum; the rest of the surfacewas taken to be at zero temperature. They derived theangles χ and ξ , and, although their solution is not unique,they claim that the pair χ ∼ ◦ , ξ ∼ ◦ is favored.While this value of ξ coincides with our estimate, thetwo values of the inclination of the line-of-sight are insubstantial disagreement. Also the emitting areas of thehot/warm region and their temperatures turn out to bedifferent in the two cases. Their estimate of the hot tem-perature is always higher than ours and the size of thewarm corona is not monotonically decreasing. We re-mark that quantitative differences are to be expectedgiven the different assumed spectral models (blackbodyvs. RCS); moreover because Perna & Gotthelf (2008)did not include a colder region .Finally, we caveat that our analysis relies on a num-ber of simplifying assumptions. We already mentionedthat the synthetic spectra we used were obtained withthe Monte Carlo code by Nobili, Turolla, & Zane (2008),which was designed to solve radiation transport in aglobally twisted magnetosphere. Even though we tookthermal photons to originate mostly in a limited polarregion, this does not self-consistently describe resonantup-scattering in a magnetosphere where only a limitedbundle of field lines is actually twisted, as is probablythe case in AXPs (Beloborodov 2009). Moreover, as wediscussed in § ntzang XSPEC model is avail-able only in tabular form and it was created assumingemission at constant temperature from the entire starsurface. As such, it is not suited to be applied directlyto the present case. As a compromise, we decided tofit the spectra by adding together two/three (absorbed) ntzang components, each associated to one of the emit-ting regions, at temperatures T h , T w and T c , respectively.While this procedure works (and is routinely employed)in the case of blackbody spectra, it is expected to beonly approximately correct when different ntzang com-ponents are added together. The reason is that the ef-fects of resonant scattering on thermal photons dependson the location of the primary emission, since the mag-netospheric electron density is not isotropic. As a conse-quence, assuming thermal emission from a cap of limitedsize or from the entire star, even if the two are taken atthe same temperature, will give rise to different spectra.We checked this approximation for all the spectra we an-alyzed, finding that the maximum relative error is ∼ . CONCLUSIONS It was already noted by Bernardini et al. (2009) that the ad-dition of the colder component produces a monotonic decrease inboth the hot and warm areas
Fig. 12.—
Comparison between the spectrum obtained addingthree single ntzang model (red) and the spectrum of a neutron starwith a thermal map consisting of three regions at different temper-atures (black). The two spectra are relative to the September 2004observation of XTE J1810-197.
The monitoring of the two TAXPs XTE J1810-197and CXOU J164710.2-455216, carried out with
XMM-Newton in recent years, gave us the possibility to testthe twisted magnetosphere model and understand howthe physical parameters in the two sources change dur-ing the post-outburst evolution. We summarize our mainfindings below, remarking again that they were obtainedunder a number of assumptions (e.g. globally twistedfield, three temperature thermal map). • Soon after the outburst onset the surface ther-mal distribution in XTE J1810-197 and CXOUJ164710.2-455216 is well described by three com-ponents: a hot cap, a surrounding warm coronawhile the rest of the neutron star surface is at alower temperature. • The analysis of the pulse profile evolution for XTEJ1810-197 revealed that both the hot cap and thewarm corona decrease in size so that in the lastobservation (September 2007) virtually all the neu-tron star surface emits at a temperature compatiblewith the quiescent one. • The same analysis for CXOU J164710.2-455216showed that the hot cap decreases in temperatureand size, while the warm corona remains constantin temperature while it increases in size. In the lasttwo observations we examined (August 2008 andAugust 2009) the source thermal map comprises ahot cap covering ∼
30% of the neutron star sur-face, while the remaining surface is cooler. Thereare hints that this could be the quiescent state ofthe TAXP. • For both sources the twist angle is highest at theoutburst onset and then monotonically decreasesin time until it reaches a nearly constant, non-zerovalue. • The same model configuration which best-fits theobserved pulse profiles (thermal map, twist an-gle, electron bulk velocity, and geometrical angles)provides a reasonable description of
XMM-Newton spectra in the 0.1–10 keV band for both sources. timing and spectral model for the AXPs XTE J1810 and CXOU J1647 15To our knowledge this is the first time that a self-consistent spectral and timing analysis, based on a re-alistic modelling of resonant scattering, was carried outfor magnetar sources, considering simultaneously a largenumber of datasets over a baseline of years. Present re-sults support to a picture in which only a limited portionof the magnetosphere was affected by the twist. Futuredevelopments will require detailed spectral calculationsin a magnetosphere with a localized twist which decays in time.We are grateful to an anonymous referee for his/herconstructive criticism and helpful suggestions whichhelped in improving a previous version of this paper.Work partially supported by INAF-ASI through grantAAE I/088/06/0.spectra in the 0.1–10 keV band for both sources. timing and spectral model for the AXPs XTE J1810 and CXOU J1647 15To our knowledge this is the first time that a self-consistent spectral and timing analysis, based on a re-alistic modelling of resonant scattering, was carried outfor magnetar sources, considering simultaneously a largenumber of datasets over a baseline of years. Present re-sults support to a picture in which only a limited portionof the magnetosphere was affected by the twist. Futuredevelopments will require detailed spectral calculationsin a magnetosphere with a localized twist which decays in time.We are grateful to an anonymous referee for his/herconstructive criticism and helpful suggestions whichhelped in improving a previous version of this paper.Work partially supported by INAF-ASI through grantAAE I/088/06/0.