High-Energy X-ray Imaging of the Pulsar Wind Nebula MSH~15-52: Constraints on Particle Acceleration and Transport
Hongjun An, Kristin K. Madsen, Stephen P. Reynolds, Victoria M. Kaspi, Fiona A. Harrison, Steven E. Boggs, Finn E. Christensen, William W. Craig, Chris L. Fryer, Brian W. Grefenstette, Charles J. Hailey, Kaya Mori, Daniel Stern, William W. Zhang
aa r X i v : . [ a s t r o - ph . H E ] A ug Draft version October 4, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
HIGH-ENERGY X-RAY IMAGING OF THE PULSAR WIND NEBULA MSH 15 − : CONSTRAINTS ONPARTICLE ACCELERATION AND TRANSPORT Hongjun An , Kristin K. Madsen , Stephen P. Reynolds , Victoria M. Kaspi , Fiona A. Harrison ,Steven E. Boggs , Finn E. Christensen , William W. Craig , Chris L. Fryer , Brian W. Grefenstette ,Charles J. Hailey , Kaya Mori , Daniel Stern , and William W. Zhang Department of Physics, McGill University, Montreal, Quebec, H3A 2T8, Canada Cahill Center for Astronomy and Astrophysics, California Institute of Technology, Pasadena, CA 91125, USA Physics Department, NC State University, Raleigh, NC 27695, USA Space Sciences Laboratory, University of California, Berkeley, CA 94720, USA DTU Space, National Space Institute, Technical University of Denmark, Elektrovej 327, DK-2800 Lyngby, Denmark Lawrence Livermore National Laboratory, Livermore, CA 94550, USA CCS-2, Los Alamos National Laboratory, Los Alamos, NM 87545, USA Columbia Astrophysics Laboratory, Columbia University, New York NY 10027, USA Jet Propulsion Laboratory, California Institute of Technology, Pasadena, CA 91109, USA Goddard Space Flight Center, Greenbelt, MD 20771, USA
Draft version October 4, 2018
ABSTRACTWe present the first images of the pulsar wind nebula (PWN) MSH 15 − in the hard X-rayband ( > ∼ Nuclear Spectroscopic Telescope Array (NuSTAR) . Overall,the morphology of the PWN as measured by
NuSTAR in the 3–7 keV band is similar to that seenin
Chandra high-resolution imaging. However, the spatial extent decreases with energy, which weattribute to synchrotron energy losses as the particles move away from the shock. The hard-bandmaps show a relative deficit of counts in the northern region towards the RCW 89 thermal remnant,with significant asymmetry. We find that the integrated PWN spectra measured with
NuSTAR and
Chandra suggest that there is a spectral break at 6 keV which may be explained by a break in thesynchrotron-emitting electron distribution at ∼
200 TeV and/or imperfect cross calibration. We alsomeasure spatially resolved spectra, showing that the spectrum of the PWN softens away from thecentral pulsar B1509 −
58, and that there exists a roughly sinusoidal variation of spectral hardness inthe azimuthal direction. We discuss the results using particle flow models. We find non-monotonicstructure in the variation with distance of spectral hardness within 50 ′′ of the pulsar moving in thejet direction, which may imply particle and magnetic-field compression by magnetic hoop stress aspreviously suggested for this source. We also present 2-D maps of spectral parameters and find aninteresting shell-like structure in the N H map. We discuss possible origins of the shell-like structureand their implications. Subject headings:
ISM: supernova remnants – ISM: individual (G320.4 − − INTRODUCTION
A pulsar wind nebula (PWN) is a region of particlesaccelerated in a shock formed by the interaction betweenthe pulsar’s particle/magnetic flux and ambient mattersuch as a supernova remnant (SNR) or the interstellarmedium (ISM). It has been theorized that the shock,called a termination shock, can accelerate particles to ∼ eV, which are believed to contribute to the cos-mic ray spectrum from low energies up to the ‘knee’at ∼ eV (e.g., de Jager et al. 1992; Atoyan et al.1996). In a PWN, the shock-accelerated particles prop-agate downstream and emit synchrotron photons underthe effects of the magnetic fields in that region (Wilson1972a,b; Rees & Gunn 1974). The electrons in the hardtail of the energy distribution produce X-rays, and thusthe detection of synchrotron X-rays indirectly proves theexistence of high energy electrons. Therefore, X-rayemitting PWNe are particularly interesting for studyingparticle shock acceleration, and for studying the inter- action of high energy particles with their environments(see Gaensler & Slane 2006, for a review).Since the accelerated particles in young PWNe losetheir energy primarily via synchrotron radiation at a rateproportional to E , the energy distribution of the parti-cles softens with distance from the shock, an effect called‘synchrotron burn-off’. As the particle spectrum soft-ens, the emitted photon spectrum is expected to softenas well. Details of the softening depend on the phys-ical environment and the particle flow in the PWNe;these have been modeled using particle advection (e.g.,Kennel & Coroniti 1984; Reynolds 2003, 2009) and/ordiffusion (e.g., Gratton 1972; Tang & Chevalier 2012). Inparticular, the advection models predict the radial pro-file of the photon index to be flat out to the PWN edgeand then to soften rapidly, while diffusion models predicta gradual spectral softening with radius. The particlespectrum can be inferred from the photon spectrum asthey are directly related. Therefore, spatially resolvedspectra or energy resolved images can be compared to Table 1
Summary of observations
Obs. No. Observatory Obs. ID Exposure Start Date(ks) (MJD)C1
Chandra
754 19 51770.6C2
Chandra
Chandra
Chandra
Chandra
NuSTAR
NuSTAR a
43 56451.8N3
NuSTAR
NuSTAR
Notes.
All
Chandra observations were made with the timed ex-posure mode (TE) on ACIS-I chips. a Only used for the spectral analysis along the jet and timing anal-ysis. model prediction to infer the particle flow properties andthe physical environments in PWNe.MSH 15 − (also known as “Hand of God”) is a largeTeV-detected PWN which is powered by the central 150-ms X-ray pulsar B1509 −
58 at a distance of ∼ ∼ ′ ( ∼ . XMM-Newton in the 0.5–10 keV band by Sch¨ock et al. (2010). Theymeasured the burn-off effect in that band by integrat-ing the spectrum azimuthally, however, given the highlyasymmetric morphology, a more in-depth analysis is war-ranted.In this paper, we report on the spatial and spectralproperties of the PWN MSH 15 − in a broad X-rayband measured with NuSTAR and
Chandra . We presenta two-dimensional synchrotron burn-off map for the firsttime using energy-resolved images and spatially resolvedspectra. We describe the observations and data reduc-tion in Section 2, and show the data analysis and resultsin Section 3. We discuss the implications of the analysisresults in Section 4 and present the summary in Sec-tion 5. OBSERVATIONS
The
NuSTAR instrument has two co-aligned hard X-ray optics and focal plane modules (modules A and Bwith each module having four detectors), and is themost sensitive satellite to date in the 3–79 keV band.The energy resolution is 400 eV at 10 keV (FWHM),and the temporal resolution is 2 µ s (see Harrison et al.2013, for more details), although the accuracy on or-bital timescales is ∼ NuSTAR has unparalleled angular resolution in the hardX-ray band (HPD=58 ′′ ). The fine broadband angu-lar response enables us to study detailed morphologicalchanges with energy for large PWNe such as MSH 15 − ,and NuSTAR ’s temporal resolution is sufficient to filter
Figure 1.
Normalized pulse profile for PSR B1509 −
58 in the3–79 keV band measured with
NuSTAR . Note that the off-pulsephases (0.7–1.0, dotted vertical lines) include DC emission of thepulsar as well as the nebula emission. out contamination from the bright central pulsar (e.g.,see Chevalier 2005; Kaspi, Roberts & Harding 2006, forpulsars in PWNe).MSH 15 − was observed with NuSTAR in 2013 Julywith a total net exposure of ∼
160 ks. Although the
NuS-TAR field of view (FoV) is large enough to observe thewhole PWN with a single pointing, we used four dif-ferent pointings in order to better sample different re-gions of the PWN. We also analyzed archival
Chandra
ACIS (Garmire et al. 2003) observations in order to ver-ify our spatial analysis technique, and to broaden the en-ergy range for spectroscopy (see also Gaensler et al. 2002;DeLaney et al. 2006; Yatsu et al. 2009). Table 1 summa-rizes the observations used in this paper. The
NuSTAR observation N2 was pointed to the jet, and most of thePWN fell outside the FoV. Therefore we used this obser-vation only for the timing analysis in Section 3.1 and thespectral analysis along the jet direction in Section 3.3.3.The
NuSTAR data were processed with nupipeline
Chandra data were reprocessed using the chandra repro tool of CIAO 4.5 along with CALDB 4.5.7. We furtherprocessed the cleaned event files for analyses as describedbelow. DATA ANALYSIS AND RESULTS
Timing Analysis
Since the pulsar B1509 −
58 is very bright, we neededto minimize its contamination in the PWN imaging andspectral analysis. For the
Chandra data, the pulsar con-tamination was removed by image filtering. However,we were not able to do the image filtering for
NuSTAR because its point spread function (PSF) is broad. There-fore, we selected the off-pulse interval in the
NuSTAR data for the image and spectral analyses below.We extracted the pulsar events in the
NuS-TAR observations in a 30 ′′ radius circle in the 3–79 keV band, barycenter-corrected the events us-ing R.A.=15 h m s .
52, Decl.= − ◦ ′ . ′′ H test (de Jager et al. 1989)on the event lists to measure the period for the subin-tervals and fit the period to a linear function to find thespin period and the spin-down rate. The pulsations weremeasured with very high significance in each subinter-val, and the measured period and the spin-down ratewere 0 . . × − s s − for56450 MJD, respectively. We folded the light curves us-ing the measured period, and show the resulting pulseprofile in Figure 1. We used phases 0.7–1.0 for the PWNto minimize the pulsar contamination in all the subse-quent NuSTAR data analyses in this paper. The otherphase interval was used for the pulsar analysis which willbe presented elsewhere. We note that there is contam-ination from the DC emission of the pulsar even in theoff-pulse interval. For example, ∼ R = 30 ′′ at a distance of 60 ′′ from the pulsar, but much less at larger distances. Image Analysis
In order to produce energy-resolved PWN images, wefirst produced a merged
Chandra image of the five obser-vations in Table 1 using the merge obs tool of CIAO 4.5in the 0.5–2 keV, 2–4 keV and 4–7 keV bands with binsize 4 pixels (Fig. 2). Note that the central 4 ′′ × ′′ cor-responding to the pulsar emission was removed in theseimages.For NuSTAR observations, we extracted events in theenergy bands 3–7 keV, 7–12 keV, 12–25 keV, and 25–40 keV for the off-pulse phase. After the phase selec-tion, the pulsar component is expected to be reducedsignificantly. The
NuSTAR absolute aspect reconstruc-tion accuracy on long timescales is ∼ ′′ (90% confidence),which can blur the resulting merged image obtained withthe three observations and two modules. Therefore, wealigned the images by registering the pulsar to the knownposition before phase filtering. Since only one pointsource (the pulsar) was significantly detected in each ob-servation, we were not able to fully correct the position(e.g., for translation, rotation and scale). We note thatthe rotational misalignments are measured and correctedwith high accuracy (Harp et al. 2010), and a small resid-ual change in scale is not a concern for the spatial scalesof our analyses. Therefore, we assumed that the positionoffsets were caused by pure translations.In order to produce deblurred images of the NuSTAR observations for comparison with the low-energy high-resolution
Chandra images, we corrected for the expo-sure and deconvolved the
NuSTAR images with the PSFusing the arestore tool of CIAO 4.5. We then mergedthe deconvolved images (see Fig. 2). The number of it-erations in the deconvolution process was determined bycomparing the deconvolved
NuSTAR image to the
Chan-dra image in a similar band. We chose the energy bandsso that the average photon energy weighted by the re-sponse and the spectrum in a
NuSTAR band is similarto that in a
Chandra band, and used the 3–7 keV and4–7 keV bands for
NuSTAR and
Chandra , respectively.Using the 2-D images, we produced projected profilesalong the jet axis (the south-east to north-west direction)in order to compare the deconvolved 3–7 keV
NuSTAR profile with the 4–7 keV
Chandra profile. Here, we filledthe pulsar region in the
Chandra data which were re-moved above with the average counts of the surrounding pixels. We rotated the images 60 ◦ clockwise with theorigin being the pulsar position, so that the jet structurelies in the horizontal direction (x-axis). We projected theimages in Figure 2 onto the axis along the jet, subtractedbackground, smoothed the profile over a 25 ′′ scale, andnormalized the scale with respect to the brightest pointat the center. The backgrounds were assumed to be flatover the detector chips. The background normalizationfactor was first determined by taking a box in a source-free region, and then further adjusted by matching they-projected profiles of the source and the backgroundat large distance from the center for each energy band.We found that the results presented below are not sen-sitive to the background subtraction since backgroundaccounts for only small fraction of the intensity. We findthat NuSTAR -measured profile in the 3–7 keV band issimilar to that measured with
Chandra in the 4–7 keVband (see dashed and dot-dashed curves in fig. 3), andthat the results of the deconvolution are not very sen-sitive to the number of iterations (e.g., 15–50), and weused 20 iterations.While the deconvolved
NuSTAR image (Fig. 2e) showssimilar overall morphology to the high-resolution
Chan-dra image in the similar band (Fig. 2d), there are dif-ferences. Most notably, the small arc-like structure andthe elongation in the central region ( R < ∼ ′′ ) are notresolved in the NuSTAR images. This is because thestructures are smaller than the FWHM ( ∼ ′′ ) of the NuSTAR
PSF. Also note that RCW 89, ∼ ′ north, isnot clearly visible in the NuSTAR data. This is mainlybecause the
NuSTAR observations did not have muchexposure in that region; most of RCW 89 fell outside theFoV during the observations.To measure the size of the narrow structures aroundthe pulsar, we projected events between − ′′ and 50 ′′ in the y-axis direction onto the x-axis in several energybands. The profile is very asymmetric and is not smoothon large scales ( R > ∼ ′′ ). Furthermore, the deconvo-lution produces artificial structures in the outer regionsdue to the paucity of counts. Therefore, defining a size(e.g., full width 1% maximum) is impractical on a largescale. However, the source images are smooth on smallerscales ( R < ∼ ′′ ), allowing us to measure the FWHM andHWHM in the northern and the southern directions ofthe projected profiles in several bands without smooth-ing the images. We measured the sizes by calculatingthe relative brightness with respect to the peak, andshow them in Figures 4a–c. Although there are differentstructures in the northern and the southern directions,the HWHM’s are similar to each other and to half theFWHM.We calculated the spectrum- and response-weightedaverage energy for each energy band, fit the widths toa power-law function R ( E ) = R E m as suggested byReynolds (2009), and measured the decay index m forvarious y-integration widths (e.g., ∼ ′′ ). The mea-sured decay index was stable over this range, as shownin Figure 4d. Note, however, that our measurement isbased on deconvolved images, and our uncertainties aretherefore approximate. Spectral Analysis
Figure 2.
MSH 15 − images measured with NuSTAR and
Chandra in a 10 ′ × ′ rectangular region: ( a ) A NuSTAR and
Chandra b ) Chandra c ) Chandra d ) Chandra e ) NuSTAR f ) NuSTAR g ) NuSTAR h ) NuSTAR i ) NuSTAR exposure map and a box corresponding to the images. For the
NuSTAR data, we used off-pulsetime intervals only in order to minimize the effect of the central pulsar PSR B1509 −
58. Exposure and vignetting corrections are appliedto the images. A circle with radius 30 ′′ is shown in panels b–h in black for reference. Note that the images use a logarithmic scale, andeach image has a different background level. Figure 3.
Projected profiles at several energy bands. The profilesare obtained by projecting the images in Fig. 2 onto the jet axisand smoothing over 25 ′′ . The image analysis shows a spectral change with radiusin the PWN, and we therefore tried to see differences inspectra at different radii. We extracted spectra in variousregions as described, and backgrounds from source-freeregions, and fit them with an absorbed power-law model.Since spatial blurring due to the PSF size is much moresignificant for
NuSTAR than
Chandra , we did not at-tempt to fit the spectrum jointly except for one case ofusing a large aperture (Section 3.3.1), where PSF “blur-ring” is not a large effect. However, we jointly fit thespectra taken with single telescope at different epochs.We used the χ and the lstat statistics in XSPEC χ statistics. Sincethe NuSTAR data are not sensitive to the hydrogen col-umn density ( N H ) and the results are not affected bysmall change of N H , we froze it at a previously reportedvalue (0 . × cm − ; Gaensler et al. 2002). We useda cross-normalization factor to account for a slight dif-ference between NuSTAR module A and B, and betweenobservations. For the
Chandra data fitting, we let N H vary and introduced a cross-normalization factor betweenobservations. Spectrum of the Entire Nebula
We first measured the total spectrum of the PWN us-ing a source extraction aperture of R =5 ′ centered at thepulsar position for a phase interval 0.7–1.0 in the NuS-TAR data. Photons with energies up to ∼ NuSTAR observations, N1, N3 and N4 in Ta-ble 1, and jointly fit the spectra to a power law. Themeasured power-law index is 2.06 and the absorption-corrected 3–10 keV flux is 5.9 × − erg cm − s − (seeTable 2). For the Chandra data, we extracted sourcespectra using the same 5 ′ aperture, ignoring the cen-tral 5 ′′ in order to minimize the pulsar contamination,and jointly fit the five Chandra spectra of each regionto a power-law model in the 0.5–7 keV band becausebackground dominates above 7 keV. We note that the
Chandra data fits were not acceptable with χ /dof of2632/2214 ( p = 1 × − ), having large residuals in thelow energy band below 2 keV. This is perhaps becausethe large regions are a mixture of subregions with differ-ent spectra (e.g., see Section 3.3.4). We therefore fit thedata above 2 keV only with frozen N H . When remov-ing photons below 2 keV, the remaining data were fit toa single power-law model with a slightly smaller photonindex, having χ /dof=1757/1704 ( p = 0 . Chandra observationsare all within 1%. Note that letting N H vary also yieldsan acceptable fit ( χ /dof=1756/1703) with N H =0.91(4)and Γ = 1 . Chandra -measured spectrum in the 2–7 keV bandis significantly harder than that measured with
NuSTAR in the 3–20 keV band. We note that our results are con-sistent with the previous measurements made with
Bep-poSAX and
INTEGRAL (Mineo et al. 2001; Forot et al.2006). Mineo et al. (2001) reported a photon index of1.90(2) in the 1.6–10 keV band for a 4 ′ aperture, which isconsistent with our Chandra measurement in the 2–7 keVband. In the hard band, the reported photon indices were2.1(2) and 2.12(5) for
BeppoSAX (20–200 keV) and
IN-TEGRAL (15–100 keV), respectively. Note that the largeapertures used for
BeppoSAX and
INTEGRAL includethe RCW 89 region, but the effect of RCW 89 is negligiblebecause the emission is very soft (Yatsu et al. 2005) andthe telescopes operate only above 15 keV. The photonindex we measure with
NuSTAR in the 15–30 keV bandis 2.1(1) for the 5 ′ -aperture, which agrees with the previ-ous measurements. The results of our measurements aresummarized in Table 2.Since the large apertures include many subregions withdifferent spectral properties as we show below (see Sec-tions 3.3.1, 3.3.3, and 3.3.4), a single power law maynot properly represent the combined spectrum. In par-ticular, we find that the best-fit photon index for the Chandra data becomes smaller as we ignore lower en-ergy spectral channels, that is, the spectrum appears toharden (is concave up) as we move to higher energies.However, this is the opposite to what we see with
NuS-TAR (Table 2). While this may imply a spectral breakin the X-ray band, some other effects such as contamina-tion from the pulsar and/or RCW 89, or cross-calibrationsystematics between the two instruments may have someimpact. Therefore, we investigate some possibilities be-low in order to see if the discrepancy in the spectral indexmeasurements of
NuSTAR and
Chandra is caused by aspectral break.First, we note that the pulsar contamination was notcompletely removed in the
Chandra data. Excising 5 ′′ leaves 2–5% pulsar emission in the R = 5 ′ aperture,which may bias the PWN spectrum. In order to seethe effects quantitatively, we fit the pulsed spectrum ofthe pulsar in the NuSTAR data (total spectrum minusthe DC level in Fig. 1) with a power-law model and findthat the photon index is 1.36(1) and the 3–10 keV fluxis 2 . × − erg s − cm − which broadly agreewith the previous measurements (Cusumano et al. 2001;Ge et al. 2012). We added this pulsar component to the Chandra fit assuming 5% of the pulsar emission is inthe 5 ′ aperture after the 5 ′′ excision. Thus, the spec-tral model was a double power-law model, one for the Figure 4.
Widths of projected profiles in several energy bands and the best-fit power-law functions, R ( E ) = R E m , for the FWHM (a),HWHM of the northern (b) and the southern (c) nebulae for a width of 100 ′′ , and the decay indices m vs integration widths (d). pulsar emission and the other for the PWN emission.We froze the pulsar component, fit the PWN spectrum,and find that the spectral index of the PWN does notchange. Since the spectral index of the pulsed spectrummay be different in the soft band, we changed the spec-tral index of the pulsar component to 1.19 as reported byCusumano et al. (2001) in the 1.6–10 keV band, and findthat the photon index of the entire PWN softens only by∆Γ = 0 .
01. We further increased the pulsar flux by 10%and find no change in the spectral index of the PWN.We verified the results by increasing the excision regionto 10 ′′ . Note that the DC component of the pulsar isnot included in this study. However, the unmodeled DCcomponent is much smaller than the pulsed componentas seen in Figure 1, so the effect would be negligible inthe Chandra data fit.Second, we consider the effect of the pulsar DC com-ponent in the
NuSTAR data. Although the DC com-ponent is negligible in the
Chandra data due to the im-age filtering, the DC component presents in the
NuS-TAR data because time filtering does not remove theDC emission. Although it is not possible to measurethe DC spectrum accurately, we estimated 3–10 keVDC flux using a 30 ′′ aperture as follows. With NuS- TAR , we measure the total (pulsed+DC+nebula) andthe pulsed flux to be 3 . × − erg s − cm − and2 . × − erg s − cm − , respectively. The nebula fluxis measured to be 7 . × − erg s − cm − with Chandra (Section 3.3.3). By subtracting the pulsed and the neb-ula flux from the total flux, the 3–10 keV DC flux is esti-mated to be 3 . × − erg s − cm − . We assumed thatthe photon index is 1.7, similar to the NuSTAR -measuredvalue for the 30 ′′ aperture (Section 3.3.3). We includedthe DC emission in the NuSTAR fit of the 5 ′ -aperturespectrum, and followed the procedure described abovefor the pulsar contamination estimation in the Chandra data. This procedure effectively removes the DC com-ponent from the PWN spectrum. However, note thatremoving such a hard spectrum only softens the spec-trum of the entire PWN, making the discrepancy larger.We therefore arbitrarily changed the photon index of theDC component to 2.5 to mitigate the possibility of hav-ing very soft DC emission and find that the photon indexof the entire PWN hardens only by ∆Γ = 0 . ± Chandra and
NuSTAR , respectively. We also useddifferent background regions and found that the spectral
Table 2
Best-fit parameters for the total PWN emission spectrum
Data a Model b Radius Energy N Hc Γ s F PLd E break Γ h χ /dof ′ (keV) (10 cm − ) (keV)C PL 5 2–7 0.95 1.912(5) 5.98(2) · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · · Notes. σ uncertainties are given in parentheses at the same decimal place as the last digit. a N: NuSTAR , C:
Chandra . b PL: powerlaw model, and BPL: bknpower model in
XSPEC . c Frozen. d Absorption corrected 3–10 keV flux in units of 10 − erg s − cm − . Figure 5.
Joint fit results of the
NuSTAR and the
Chandra spectra for the single power-law (left) and the broken power-law (right)models. Spectra obtained with each telescope are merged for display purpose only. indices do not change significantly.Finally, we estimate the contamination of the RCW 89emission in the
NuSTAR data. Using the
NuSTAR
PSF,we estimated the contamination of a structure at ∼ ′ into the 5 ′ circle to be ∼ NuSTAR observation N1 which sam-pled the RCW 89 best among the
NuSTAR observations.We added the spectrum as additional background in thePWN spectral fit. Since the other observations N3 andN4 sampled only a small fraction of the RCW 89 region,we used the RCW 89 spectrum extracted from N1 forthese observations as well. We varied the normalizationof the RCW 89 background from 0.14 to 0.28 in orderto account for the fact that the actual RCW 89 regionmay be larger than what we sampled with
NuSTAR , andfound that the photon index changes by < ∼ NuSTAR and
Chandra cannot be ex-plained by a combination of the above effects. We there-fore consider alternatives below. We note that theremay be cross-calibration systematics between
NuSTAR and
Chandra . For example, Kirsch et al. (2005) showedthat systematic uncertainties between X-ray observato-ries caused by cross calibration are significant using ob-servations of the Crab nebula, for which the authorsfound that
Chandra and
BeppoSAX /LECS measuredsmaller spectral indices than
BeppoSAX /MECS and
IN- TEGRAL did. Since
NuSTAR is calibrated so that thespectrum of the Crab nebula is a simple power law witha photon index of 2.1, larger than the
Chandra -measuredvalue of 1.95 (Kirsch et al. 2005), the spectral break wesee for MSH 15 − could be explained by imperfectcross-calibration.However, the cross-calibration effects may be differentfrom source to source depending on the spectral shape,and the measurements made for the Crab nebula maynot be directly translated into the case of MSH 15 − .We therefore consider an alternative; the discrepancyof spectral indices between the Chandra and the
NuS-TAR measurements is caused by a spectral break. Wejointly fit the 2–7 keV
Chandra and the 3–20 keV
NuS-TAR data with a single power law and a broken powerlaw. We find that a single power law does not describethe data well having χ /dof=3878/3592 ( p = 5 × − ),but a broken power law with a break energy of 6.3 keVdoes ( χ /dof=3691/3590, p = 0 . NuSTAR and the
Chandra spectra inthe same energy range below the possible break at 6 keVin order to see if the break is a single sharp break. Ifso, we expect the
NuSTAR and the
Chandra spectra tobe same regardless of the difference in the effective areashape. We fit the
NuSTAR and the
Chandra spectrain the common energy band, defined as 3– E max , where Figure 6.
Azimuthal variation of spectral hardness and flux measured with
NuSTAR (triangles) and
Chandra (diamonds) at R = 60 ′′ (a), R = 120 ′′ (b), and R = 180 ′′ (c) from the pulsar. Sinusoidal trends for the photon index variation are shown in dotted lines, and solidlines connecting flux data points are shown for clarity. Flux is in units of 10 − erg s − cm − . N H values measured with Chandra for thesame regions are shown in (d)-(f). we vary E max from 4.5 keV to 7 keV. In the lowest en-ergy band (3–4.5 keV), the NuSTAR and
Chandra re-sults agreed with photon indices of 1.99(7) and 1.98(2).However, as the upper energy range increased to 5 keVand above, the
NuSTAR results were significantly softerthan that of
Chandra . For example, the photon indicesare 2.03(2) and 1.90(1) in the 3–7 keV band, for
NuS-TAR and
Chandra respectively, inconsistent with eachother with 90% confidence. This suggests that the spec-tral break is likely to be caused by the cross-calibrationeffect. However, if the spectral break is real, the obser-vational discrepancy in the common energy band mayimply that the broadband spectrum is not sharply bro-ken at 6.3 keV but slowly curves over a energy range (e.g.,4–7 keV) probably because different regions in the 300 ′′ aperture have different break energies. In this case, NuS-TAR collects relatively more photons above the breakthan
Chandra does since it has rising effective area inthat band, yielding a softer spectrum.
Azimuthal Variation of the Spectrum
In order to see if the PWN spectrum varies az-imuthally, we first extracted
NuSTAR events in 30 ′′ ra-dius circles for six, twelve, and eighteen azimuth anglesfor three radial distances, 60 ′′ , 120 ′′ , and 180 ′′ from thepulsar, respectively. The regions do not overlap. For eachregion, backgrounds were extracted from an aperture of R = 45 ′′ in a source-free region on the same detectorchip. We jointly fit the NuSTAR spectra for the threeobservations N1, N2 and N4. The energy ranges for thefit were 3–20 keV, where the source events were detectedabove the background. We performed these analysis forthe same regions with the
Chandra data in the 0.5–7 keVband. We show the results in Figure 6, where the azimuthangle φ is defined from east in a clockwise direction. Asinusoidal variation of the spectral hardness is clearlyvisible for each radial group, and the spectrum is hardestin the jet region ( φ ∼ ◦ ). The flux values also peakin the jet regions but do not seem to vary sinusoidally.Note there is a small discrepancy between the NuSTAR and
Chandra measurements in Figure 6; the
NuSTAR -measured spectral indices are larger than those measuredwith
Chandra in general. While this may suggest thespectral break we see in the spectrum of entire nebula(Section 3.3.1), it could be due to PSF mixing in the
NuSTAR data; when there is a sharp spatial contrastsuch as the jet or image edge, it is convolved with thePSF in the
NuSTAR data.It appears that the photon index covaries with N H inFigure 6. We checked if there is a correlation betweenthe two quantities using Pearson’s product moments, andfound no clear correlation in any radial group. Spectral Variation in the Northern Nebula and in theJet
Since we observe significant spectral variation in theazimuthal direction, we analyzed the northern nebulaand the jet separately. For the northern nebula we usedannular regions, ignoring the southern part. Hence, eachregion covers the upper > ∼ ◦ in azimuth angle. Theinnermost region was a circle with radius 30 ′′ centeredat the pulsar, and annuli with width 30 ′′ or 60 ′′ , andboxes were used for the outer regions (see Fig. 7a white).We used the off-pulse phase only for NuSTAR , and ig-nored the central pulsar using a circle with radius 5 ′′ for Chandra . Figure 7.
Selected regions for studying the spectral variation in the northern nebula (white annuli and boxes) and in the jet (yellowcircles) (a), and spectral variation in the northern and the southern jet directions (b)–(e). Radial variation of the photon indices andsurface brightness in the northern nebula (b) and in the jet (c) measured with
NuSTAR (triangles) and
Chandra (diamonds). Also shownare the best-fit broken line (blue solid line) and the power law (magenta dotted line). Legends are same for (b) and (c). Brightness ismeasured in the 3–10 keV band in units of 10 − erg s − cm − arcsec − . Radial profiles of N H measured with Chandra are shown in (d)for the northern nebula and in (e) for the jet. Note that the range for the x-axis of (d) is different from that of (b) because N H was notmeasured for the last two data points in (b). We separately fit the
NuSTAR (N1, N2, and N4) andthe
Chandra (C1–C5) spectra of each region with an ab-sorbed power-law model. Since there is significant ther-mal contamination from RCW 89 in the
Chandra dataat large distances (see the two upper white box regionsin Fig. 7a), we ignore the low energy data below ∼ Chandra fits. Wealso tried to model the RCW 89 regions using the vnei plus a power law in
XSPEC , and fit the
Chandra data inthe 0.5–7 keV band. The result for the photon indexwas sensitive to the remnant model but broadly agreewith what we found by fitting data above 3 keV only(see also Yatsu et al. 2005). Our results for the
Chandra data are consistent with, but more accurate than thoseobtained by DeLaney et al. (2006) who used ∼
60 ks ofobservations taken from 2000 August to 2003 October.We present our measurements in Figure 7b and d.While our results show that N H increases with radius,we note that it is possible to force the N H to be constantand allow only the photon index to vary. For example,an N H value of 0 . ± . × cm − constant overthe field with photon indices of 1.58–2.16 fits the dataout to R = 200 ′′ in Figure 7 ( χ /dof=12289/12363),which implies no radial variation of N H and smaller vari-ation of the photon index with radius. However, the N H profile given in Figure 7d provides better fit with χ /dof=12223/12353 corresponding to F-test probabil-ity of 2 × − . We also verified that the results do notchange if we fit the spectra only in the 0.5–6 keV (belowthe spectral break, see section 3.3.1) in order to reducethe effect of the complex continuum. We note that bet-ter constraining Γ and N H by jointly fitting the NuSTAR data is not possible because of the PSF mixing in the
NuSTAR data and the spectral break (Section 3.3.1). There is a hint of a possible break in the linear slope ofthe radial profile of the photon index Γ( R ) (Fig. 7b). Wemeasured the location of the break in the northern nebulausing a broken line fit. We first fit the Chandra measuredphoton index profile, and found that the break occurs at R break = 71 ± ′′ . We note that using a constant N H overthe field changes Γ only slightly and gives a consistentresult ( R break = 68 ± ′′ ). The NuSTAR profile gives alarger R break = 150 ± ′′ because of the large photonindex at smaller radii which might be biased by mixingfrom outer regions. We also find that a single power-law model Γ( R ) = Γ R η with η = 0 . ± .
003 broadlyagrees with the data (see Fig. 7b).Since spectral softening is expected in the jet directionas well, we measured the spectral variation along thesouthern jet. To do this, we extracted source spectrausing non-overlapping circular apertures with radii 10 ′′ ,10 ′′ , 15 ′′ , 20 ′′ , 25 ′′ , 35 ′′ , and 25 ′′ along the jet (see yellowcircles in Fig. 7a), which we refer to as regions J1–J7.Note that the center of J1 is R ∼ ′′ from the pulsar,and all the NuSTAR observations (N1–N4) were used forthis analysis. We fit the spectra in each region with anabsorbed power law, and measured the photon index andflux. The results are presented in Figures 7c and e.The spectral indices of the J2 region measured with
Chandra and
NuSTAR are very different, which may sug-gest that there is a strong spectral break. However, wenote that measuring the spectral parameters with
NuS-TAR was difficult for regions with sharp spectral changesbecause the
NuSTAR
PSF changes from a circular shapeto an elliptical shape with off-axis angle (An et al. 2014),and thus regions with different off-axis angles have dif-ferent degrees of azimuthal mixing. The four
NuSTAR observations had different pointings and thus different0
Figure 8.
The spectral indices in the central regions, correspond-ing to the innermost two data points of Fig 7 (
R < ′′ ), with ahigher spatial resolution. off-axis and azimuthal angles. In particular, in the re-gions J1–J2 where we use small apertures and the sourcespectrum strongly varies, spatial mixing has significantimpact on the NuSTAR results. Therefore, the discrep-ancies in the spectral index between the
NuSTAR and
Chandra measurements, and even between the
NuSTAR observations are expected. The mixing was not a concernin the analysis of the northern nebula in which spectralvariation is not severe.We also measured the location of the break in the radialprofile of the photon index in the jet direction using the
Chandra measurement in Figure 7c. Here we ignored thefirst data point for the reason described below. A fit to abroken line gave a break location of R break = 110 ± ′′ .A single power-law model also fits the data with a powerindex η = 0 . ± .
01 (Fig. 7c).We note that the first
Chandra data point, correspond-ing to region J1, shows a very soft spectrum comparedto the next one in J2, unexpected in synchrotron coolingmodels (e.g., Reynolds 2003; Tang & Chevalier 2012).The steady-state solutions may not be applicable to theinner region within ∼ ′ of the pulsar for this source,as DeLaney et al. (2006) found strong variability in thebrightness and morphology in that region.We tried to see if the spectral hardness in J1 variedover time. We first jointly fit the Chandra spectra ofthe region taken from the five observations C1–C5 witha common N H , but separate photon index and cross nor-malization for each observation, and found that the pho-ton indices are all within the 1 σ uncertainty of the valuein Figure 7. We carried out the same analysis for the J2region, and found that the spectrum of one observation(C1, Obs. ID 754) was slightly softer than the others(Γ = 1 . ± .
12) but not significantly. It is probably be-cause the region in this observation fell on the detectorchip gap. Therefore, we conclude that the spectral indexdid not change significantly over time in this region.Since spectral hardness covaries with N H , the spec-tral difference between the J1 and J2 regions may beless significant if we consider the covariance. In orderto investigate the effect of covariance, we ignored Obs.ID 754 because the J2 region in this observation was onthe chip gap. We then jointly fit the spectra of each re-gion, varied both N H and Γ using the steppar tool in XSPEC and found that the 99% contours do not overlap,which suggests that the difference is significant with thecovariance as well, and the spectrum of the J1 region issignificantly softer than that of the J2 region. If we takethe best-fit values, the N H variations of ∼ × cm − imply extremely high densities of n ∼ − foran assumed line-of-sight distance of 0.5 pc (similar tothe transverse distance for the assumed distance to thesource of 5.2 kpc) in the regions with high N H .We further spatially resolved the J1–J2 regions usingoverlapping circular regions with radius 5 ′′ . We fit thespectrum of each region with a power-law model, andfound spectral softening in the innermost regions ( R < ∼ ′′ ). We show the photon indices in Figure 8.Note that N H increases with radius in the northernnebula. In the jet direction, we used finer spatial res-olution, and see a more complicated change; there is adip at R =30–70 ′′ . At large distances, we find that N H islarge. This structure is visible in the 2-D N H map as well(see Fig. 9). Note also that the power-law index ( η ) ofthe photon index profile is larger in the northern nebulathan in the jet, that is, the spectral steepening is morerapid, which was also implied by the imaging analysisabove (e.g., Fig. 3). We produced 2-D maps of the spectral parameters forthe ∼ ′ × ′ field containing the PWN. We used a 1 ′ × ′ square region, sliding it over the field with a step of 0.5 ′ .Thus, two adjacent regions overlap by 50%. Backgroundswere extracted from far outer regions. In order to min-imize the pulsar contamination, we excluded a circularregion with radius 5 ′′ for the Chandra data, and used thepulse phase 0.7–1.0 only for the
NuSTAR data.After extracting 0.5–7 keV spectra in each region forthe five
Chandra observations, we jointly fit the spec-tra with a common absorbed power-law model havingdifferent cross normalization factors between observa-tions and allowing all the parameters to vary through-out. The same procedure was applied to the
NuS-TAR data in the 3–20 keV band with N H frozen tothe Chandra -measured value in each region. After pro-ducing the 2-D maps, we select regions with positiveflux with 3 σ confidence and show the results in Fig-ure 9. The average (median) of the 1 σ uncertaintiesfor the parameters obtained with the Chandra data were1 . × − erg cm − s − (1 . × − erg cm − s − ),0.07 (0.05), and 5 . × cm − (3 . × cm − ),for flux, photon index, and N H , respectively. For NuS-TAR , the uncertainties were 6 . × − erg cm − s − (5 . × − erg cm − s − ) and 0.15 (0.12) for flux andphoton index, respectively. The flux map shows thestructures seen in the count map (Fig. 2). We also notethat the photon index map shows the same structure seenin the radial and the azimuthal profiles (Figs. 6 and 7);the photon index increases radially outwards.We find an interesting shell-like structure in the N H map (top right panel of Fig. 9). Since it is possiblethat the structure is produced by a correlation betweenΓ and N H , we calculated the correlation coefficient be-tween pairs of parameters using Pearson’s product mo-ments. The coefficients were transformed into Fisher co-efficients to calculate the significance. In this study, we1 Figure 9.
Top: − erg cm − s − arcmin − , power-law photon index, and N H (from leftto right) measured with Chandra by fitting the spectra in the 0.5–7 keV band.
Bottom left and middle:
Brightness and photon indexmeasured with
NuSTAR by fitting the spectra in the 3–20 keV band.
Bottom right: Chandra counts map and the field for the 2-D maps(white dashed box). The location of the pulsar, PSR B1509 −
58, is noted with a star except for in the bottom right plot. We arbitrarilyassigned zero values to the spectral parameters in regions where the parameters are unconstrained due to paucity of source counts (darkblue regions). found that the correlation between flux and photon in-dex is − .
58, and the significance is 12 σ , implying thecorrelation is statistically significant. No correlation wasfound between N H and Γ or any other combination ofparameters.We further tried to fit the Chandra data with a sin-gle N H value of 0 . × cm − for the entire nebula,and found that the fits became worse, having average χ per average dof of 555/547 compared to the value of538/546 for the fit with variable N H . The single N H fitturned the large N H regions into spectrally hard regionswhich are not visible in the NuSTAR map. However, we note that quantitative comparison with the
NuSTAR map is difficult unless we know the details of the broad-band spectrum in each region. DISCUSSION
We have presented the first hard X-ray images ofMSH 15 − above ∼ E break = 6 keV in the spectrum of entire PWN.From the spatially resolved spectral analysis, we foundthat the spectral index varies sinusoidally in the azimuth2direction from ∼ ′′ (1.5 pc) from the pulsar and monotonicallyincreases with distance from 1.6 to 2.5 (Fig. 7). Thesetrends were observed with both NuSTAR and
Chandra .We found that spectral hardness turns over at R = 35 ′′ and decreases more slowly beyond R ∼ ′′ along the jet(Fig. 7), and showed that there is a previously unrecog-nized shell-like structure of radius ∼ ′ in the N H map(Fig. 9). Image
The
NuSTAR images in the hard band ( > ∼ m can both be measured:∆( − m ) = (cid:18) ǫ (cid:19) (1 + 2 ǫ + (3 + 2 α r ) m ρ / α r ) m b ) , where m x is the index of an assumed power-law functionfor a quantity x ∝ R m x ( x = ρ or b for mass densityand magnetic-field strength, respectively), α r is the en-ergy index of the radio spectrum, and ǫ is a confinementparameter (e.g., ǫ = 1 for conical jets, Reynolds 2009).For the values we derive for MSH 15 − of α r = 0 . . , and m = − . . m ρ + 1 . m b = 2 . ǫ. This condition requires either that the mass in the flowis not constant (for instance, due to mass evaporatedfrom thermal gas filaments joining the outflow; Lyutikov2003), or that magnetic flux is not conserved (for in-stance, due to turbulent amplification or reconnection):either m b or m ρ , or both, must be positive. Various com-binations of gradients can reproduce our results. For in-stance, a conical flow ǫ = 1 requires 1 . m ρ +1 . m b = 1 . ǫ = 0 .
44 (roughly parabolic) would have m ρ ∼ = − m b ,which could be satisfied with both constant density andconstant magnetic field, or with one dropping as fast asthe other increases. Spectra of the Entire PWN
We find that the integrated spectrum of the entire neb-ula measured with
NuSTAR is a simple power law with photon index 2.06 (Table 2). This is similar to values pre-viously reported based on
BeppoSAX and
INTEGRAL data (Γ = 2 . ± .
01, 2 . ± .
05; Mineo et al. 2001;Forot et al. 2006). The
Chandra -measured parametersfor a single power-law model above 2 keV imply a harderspectrum than that measured with
NuSTAR (see Ta-ble 2), which is also seen in the spectra extracted forother inner regions (e.g., Figs. 6 and 7). We note thatour
Chandra spectral fit results are consistent with thatmeasured previously with
BeppoSAX (Γ = 1 . ± . ′ aperture, Mineo et al.2001).Since the large aperture include many subregions withdifferent spectral parameters, we expect to see a harderspectrum at high energies if the spectra of the subre-gions are simple power laws in the 0.5–20 keV. However,the 3–20 keV NuSTAR spectra are much softer than the
Chandra spectra, which is the opposite to what is ex-pected from a sum of simple power-law spectra. We findthat contamination of the pulsar and the backgroundscan explain only ∼ .
01 of the photon index discrep-ancy of the
NuSTAR and
Chandra measurements, whilethe measured difference is 0.15. The correction for thepulsar, the RCW 89 contamination and the backgroundvariation in the data seem not to explain the discrepancybetween the
NuSTAR and the
Chandra results.We find that the discrepancy between the
NuSTAR and the
Chandra measurements is likely to be caused, atleast in part, by imperfect cross calibration of the instru-ments. However, if the break is real, it implies a breakin the energy distribution of the shock accelerated elec-trons at ∼
200 TeV (having the peak synchrotron powerat 6 keV) for a magnetic field strength of 10 µ G, assum-ing synchrotron emission (e.g., Equation 5 in TC12).We note that a spectral break in the X-ray band has re-cently been reported for G21.5 − Spectral Variation
Using the broadband X-ray data obtained with
NuS-TAR and
Chandra , we find an azimuthal variation ofthe spectral index. For the PWN 3C 58, Slane et al.(2004) suggested a possible azimuthal variation of thespectral hardness based on a scenario where current flowsout from the pulsar’s pole and returns in the equator(Blandford 2002). However, Slane et al. (2004) did notfind an obvious azimuthal variation in the PWN 3C 58within R ∼ − at R =1.5–4.5 pc. Furthermore, we find theazimuthal spectral variation in MSH 15 − is likely si-nusoidal and different from that of the flux. This az-imuthal spectral variation of the emission may hint at alarge scale current flow, however, it could also be due toazimuthal diffusion of jet particles in MSH 15 − .A radial change of the spectral index of MSH 15 − was reported by Sch¨ock et al. (2010). While they inte-grated the spectrum over the full azimuthal angle, wemeasured the profiles for the northern and the jet di-rections separately because the two regions are different.3We found that significant softening with radius is seenin both directions, more significantly in the northern re-gion. Interestingly, the radial profile of the photon index(rate of spectral steepening) flattens with radius as isalso seen in 3C 58 (Slane et al. 2004).An outflow model considering both diffusion andadvection was developed by Tang & Chevalier (2012)(TC12 hereafter), where they calculated the change ofthe spectral index with distance from the central pulsarwith an assumed electron injection spectrum and diffu-sion coefficient, and were able to reproduce the radialvariation of the spectral index for three compact PWNe,the Crab nebula, G21.5 − R in theBohm limit), are longer than their ages (Equation 2 inTC12): t esc ≈ , (cid:18) R PWN (cid:19) (cid:18) E e
100 TeV (cid:19) − (cid:18) B µ G (cid:19) yr , where R PWN is the radius of the PWN, E e is the energyof synchrotron emitting particles, and B is the magnetic-field strength in the PWN. Using the size R ∼
10 pc, E e = 100–600 TeV (Forot et al. 2006; Nakamori et al.2008), and an estimation of the magnetic-field strengthof 8–17 µ G (Gaensler et al. 2002; Aharonian et al. 2005),we find that t esc is 5000–7000 yr, greater than the spin-down estimated age of τ c = 1700 yr. Since the pho-ton spectrum we are using in this work corresponds toa smaller E e , t esc can be larger than the above estima-tion. However, we note that there have been suggestionsthat the true age of the PWN is > ∼ > ∼ yr) PWNe.For young PWNe, TC12 uses a reflecting boundary con-dition at the outer edge of the PWN. We note that theTC12 model is for spherically symmetric PWNe and maynot be optimal for MSH 15 − . However, the azimuthalvariation in the northern nebula is not large (see Fig. 6),and thus the model may provide a reasonable descriptionof the source in that region.In this model, the angular size of the ‘flat’ region wherethe radial profile of the spectral index is flat can beused to estimate the diffusion coefficient (Equation 14 ofTC12). This is calculated using the following equations: θ flat ≈ θ (cid:18) / h ν R ν i / − (cid:19) and ν R = 1 × (cid:18) D cm s − (cid:19) (cid:18) R PWN (cid:19) (cid:18) µ G B (cid:19) Hz , where θ flat is the angular size of the region that has a flatphoton index profile, θ is the angular size of the PWN, ν is the photon frequency, and D is the diffusion coefficient.We find that photon index profile steepens more slowlybeyond R = 71 ′′ and R = 110 ′′ in the northern andthe jet regions, respectively. Note that the radial pro-file of the spectral index in the northern nebula shows a flat region between R = 70 ′′ –200 ′′ although the profileseems not to show any flat region in the southern neb-ula. We use the value for the northern nebula for thesize of the flat region of TC12. Assuming the size of thesource is R PWN ∼ ′′ and using the above formulaewith ν = 2 . × Hz (1 keV), we estimated the diffu-sion coefficient to be 4–13 × cm s − for B =8–17 µ G,which is slightly larger than that estimated for 3C 58 bynumerical modeling (2 . × cm s − , TC12).Using the diffusion coefficient we estimated above, wecalculate the critical particle energy E R for which thediffusion distance is equal to the size of the PWN (seeTable 3 of TC12) and where the electron distribution hasa break (Gratton 1972), using formulae given by TC12: R = (4 D/QE R ) and Q = 1 . × − B erg s − . ForMSH 15 − , we find E R to be 130–190 TeV for B =8–17 µ G. It is interesting to note that this is similar tothe maximum electron energies inferred from broadbandSED modeling (130 or 250 TeV; Nakamori et al. 2008),and that inferred from the possible spectral break at6 keV we measured in Section 3.3.1.We note that the spectrum in the jet direction is signifi-cantly softer in the innermost J1 region compared to thatin the farther J2 region. Such behavior is not expectedin simple advection and/or diffusion models, since thesynchrotron emitting particle spectrum only softens withdistance. This simple picture may not be appropriate inthe regions where the particle flow may be more compli-cated due to magnetic hoop stress as suggested for thissource by Yatsu et al. (2009). The authors found a ring-like structure with R ∼ ′′ using Chandra data and in-terpreted the structure as the termination shock for thisPWN. Based on the morphology, the authors further sug-gested that the shock accelerated particles are divertedand squeezed towards the poloidal direction right belowthe ring due to magnetic hoop stress (e.g., Lyubarsky2002). We also find that the jet structure becomes nar-rower to R ∼ ′′ and then broader. Furthermore, thespectral hardness turn-over, non-monotonic variation ofthe spectral index (see Fig. 7), happens near the loca-tion where the jet is narrowest, which might be occur-ring because of the compression of the magnetic fieldsand particles. The 2-D Spectral Maps
We presented 2-D maps of the spectral parameters.The maps visualize the properties of the source very well,and can be compared with 3-D PWN models.We showed that the 2-D map of N H has a shell-likestructure. The density is low near the central pulsar, in-creasing out to R ∼ ′ (see also Figs. 6 and 7). We notethat the fit value of N H could in principle be degener-ate with other spectral parameters. However, we do notfind clear evidence of correlation between N H and photonindex or flux from our analysis (see Section 3.3.4), andusing a constant N H degrades the fit significantly.A higher column density is observed in the south andthe east directions (see Fig. 9). If the material respon-sible for N H was produced by the supernova, one wouldexpect the pulsar to have a kick in the opposite directionof the material, towards the north-east direction, whichis consistent with the direction of the kick velocity forPSR B1509 −
58 estimated by Rots (2004) based on 28004days of timing. However, Livingstone & Kaspi (2011)found no evidence of proper motion using 28 years oftiming data. Nevertheless, we do not see any enhancedemission in the shell-like structure, which makes the su-pernova ejecta scenario less plausible.Alternatively, the structure may be an interstellar bub-ble produced by the stellar wind of the supernova pro-genitor (e.g., Castor, McCray & Weaver 1975). In thewind model, the size of the bubble is given by a simpleformula: R s ( t ) = 28 ˙ M V n ! / t / pc , where ˙ M is the mass loss rate of the progenitor in unitsof 10 − M ⊙ yr − , V is the speed of the wind in unitsof 2000 km s − , n is the number density (cm − ) ofthe interstellar medium, and t is the time in units of10 yr. The radius of the ring structure we observe is ∼ ∼ ′ was formed by the stellar wind, the structure would haveto avoid being swept up or destroyed by the SN ejecta.If the supernova ejecta did not fill a full spherical shell, apart of the wind-produced shell can be left over. In thiscase, density of the shell is expected to be higher in thedirection where the supernova ejecta were less dense. Wesee such a trend when comparing our N H map with theradio image of the SNR (Figs. 2 and 3 of Gaensler et al.1999); there are more ejecta in the northern region thanin the southern region.We have estimated the mass of hydrogen contained inthe observed shell-like structure. Using the measured ra-dial profile of N H shown in Figure 7d, the excess masscompared to the central region is ∼ M ⊙ , large com-pared to the ∼ M ⊙ one would estimate for a spherewith R = 5 pc for typical interstellar density of 1 cm − .Furthermore, the large amount of material in the struc-ture should produce H I emission, which we do not see inthe 20 cm map (Fig. 4 of Gaensler et al. 1999). This maybe because the radio continuum emission was not sub-tracted in the radio map and/or because the X-ray mea-surement is sensitive only to foreground material whilethe radio observations are sensitive to both foregroundand background structures.We note that we cannot unambiguously rule out thepossibility of a constant N H over the field; the observed N H being an artifact of a more complex underlying con-tinuum. Thus, it is very difficult to clearly interpret thestructure using X-ray observations only. Nevertheless,if the shell-like structure in the N H map is intrinsic tothe source, it may support the idea of the existence ofan underdense region around the supernova progenitor,which was suggested to explain the discrepancy betweenthe pulsar’s characteristic age of ∼ > SUMMARY
We have presented energy-resolved images of thePWN MSH 15 − in the hard X-ray band ( E > R < ∼ ′′ ), we show thatthe size shrinkage with energy can be explained with aparticle advection model. Using this model, we discussproperties of the wind outflow in the jet direction. Wefind that the combined NuSTAR / Chandra spectrum ofthe entire PWN requires a break at 6 keV, which may bedue to cross-calibration effects. However, if the spectralbreak is intrinsic to the source, it implies a break in theshock accelerated electron distribution. We measuredthe spectral index profiles on large scales ( R ∼ ′ ) inthe northern and jet directions. The spectrum softenswith radius in both directions, an effect we interpretwith a combined diffusion/advection model; furthernumerical simulations with the model are required formore accurate interpretation. We find an interestingsinusoidal variation of the spectral hardness in theazimuthal direction which may have implications for theparticle diffusion in the PWN. Such a variation has notbeen seen in other PWNe, though it has been predictedin pulsar current flow models (Blandford 2002). We finda spectral hardness turn-over in the jet direction at adistance of ∼ ′′ from the pulsar. Finally, we presented2-D maps of spectral parameters of the source, andfind that the N H map shows an interesting shell-likestructure which implies high particle density. However,this feature could result from a complex underlyingcontinuum, and so requires further confirmation.This work was supported under NASA Contract No.NNG08FD60C, and made use of data from the NuSTAR mission, a project led by the California Institute of Tech-nology, managed by the Jet Propulsion Laboratory, andfunded by the National Aeronautics and Space Admin-istration. We thank the
NuSTAR
Operations, Softwareand Calibration teams for support with the executionand analysis of these observations. This research hasmade use of the
NuSTAR