X-Ray Studies of the Pulsar PSR J1420–6048 and Its TeV Pulsar Wind Nebula in the Kookaburra Region

We analyzed archival Chandra and XMM-Newton data acquired on 2010 December 8 for 90 ks (Obs. ID 12545) and on 2018 February 19 for 91 ks (Obs. ID 0804250501), respectively, and a new NuSTAR observation acquired on 2021 May 11 for 130 ks (Obs. ID 40660002002; Mori et al. 2022). We reprocessed the Chandra data using chandra_repro of CIAO 4.14 along with CALDB 4.9.6 for the most recent calibration data. The XMM-Newton data were processed with the emproc and epproc tasks of SAS 20211130_0941. Because the XMM-Newton observation data were severely affected by particle flares, we used tight flare cuts (e.g., RATE<=0.1) that reduce the exposures substantially to <40 ks. Still, the data suffer from some contamination by residual flares, which could be a concern for spectral analysis of the faint and extended PWN. The flare background is less concerning for timing analysis of the pulsar, so we perform timing analysis with the PN data after applying a more typical flare cut of RATE<=0.4. ⁶ The NuSTAR data were reduced with nupipeline in HEASOFT v6.29 using the SAA_MODE=strict flag as recommended by the NuSTAR science operation center. We verified that using SAA_MODE=optimized did not change the results significantly (but see Section 2.2). Net exposures after this reduction are 90 ks, 65 ks, and 57 ks for Chandra, XMM-Newton/PN, and NuSTAR, respectively. Note that all errors reported in this paper are 1σ.

We searched the X-ray data for 68-ms pulsations of J1420 to confirm an earlier X-ray detection that was only suggestive (Roberts et al. 2001a). For the XMM-Newton data, we extracted 1–10 keV events within an R = 16'' circle centered at the pulsar position of (R.A., decl.) = (215034142, −60804124) (D'Amico et al. 2001) and applied a barycentric correction to the event arrival times. We then folded the arrival times using a range of test frequencies (f = 14.656955–14.657095 Hz) around one obtained by extrapolating the timing solution (Kerr et al. 2015) obtained by the Fermi Large Area Telescope (LAT; Atwood et al. 2009), and computed an H statistic (de Jager et al. 1989) for each test frequency. In this search, we held the frequency derivative $\dot{f}$ fixed at the LAT-measured value of $\dot{f}=-1.772\times {10}^{-11}\,\mathrm{Hz}\,{{\rm{s}}}^{-1}$. This search resulted in a significant detection at f = 14.657082 Hz (MJD 58168) with H ≈ 40, corresponding to a post-trial chance probability of p ≈ 5 × 10⁻⁷. The detection significance changes substantially between H ≈ 30 and H ≈ 60 depending on the region selection, presumably because of strong PWN emission.

In order to mitigate contamination by the PWN, we adopted a weighted H test (Kerr 2011), for which the probability of each event being a source photon is computed by fitting an image of a region around J1420 with the point-spread function (PSF) plus a constant. This yielded more stable (reliable) detection of the pulsations with H ≈ 50–60, corresponding to a post-trial p ≈ 10⁻⁹, regardless of the region selection as long as the region size was reasonable (e.g., R ≥ 10''). The probability-weighted 1–10 keV pulse profile is displayed in Figure 1 (top).

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We expected that X-ray pulsations might be more easily detected in the NuSTAR data because the pulsar's spectrum was inferred to be hard (Γ ≈ 0.5; Kuiper & Hermsen 2015). In NuSTAR images (Section 2.3.2), excess emission at the pulsar position was noticeable up to ∼30 keV, whereas the extended PWN was not significantly detected at energies above 20 keV, meaning that the pulsar emission is spectrally harder than the PWN emission. We therefore used the 3–30 keV and 3–20 keV bands for the pulsar and the PWN emission (e.g., Section 2.4.2), respectively. We extracted 3–30 keV source events within an R = 30'' circle centered at the brightest spot in the 10–30 keV smoothed images, and performed an H test in a range of f (14.655187–14.655320 Hz) holding $\dot{f}$ fixed at the LAT-measured value. Source pulsations with f = 14.655289 Hz on MJD 59345 were more significantly detected in the NuSTAR data (H ≈ 100 corresponding to a post-trial p = 6 × 10⁻¹⁷) than in the XMM-Newton data. The XMM-Newton and NuSTAR measurements of f yielded an average frequency derivative of −1.763 × 10⁻¹¹ Hz s⁻¹ which is similar to that measured by Fermi-LAT. The 3–30 keV pulse profile is displayed in Figure 1. We also checked to see if the pulsations persist at >20 keV. While the 20–30 keV pulse profile seemed to show a hint of the pulsations, the detection significance was low (H ≤ 10), likely due to the paucity of counts. We therefore relaxed the SAA_MODE cut (from strict to optimized ⁷ ) and were able to detect the 20–30 keV pulsations significantly with H ≈ 20 (p ≈ 3 × 10⁻⁴).

We arbitrarily adjusted the reference phases of the XMM-Newton and NuSTAR profiles to align their peaks; the results are displayed in Figure 1. The profiles show a sharp peak at phase ϕ ≈ 0.05 and a broad bump (Figure 1). The bump is visible in both the XMM-Newton and NuSTAR data, but a constant function can fit the profiles in the phase interval for the bump (ϕ = 0.25–0.9) with p = 0.01 and 0.9 for the NuSTAR and XMM-Newton profile, respectively; the existence of the broad bump is not definitive. A further investigation of the profile with the high timing resolution NuSTAR data revealed that the sharp peak is indeed narrow (Δϕ ≲ 0.1; Figure 1 bottom).

Previous Suzaku studies of K3 (Van Etten & Romani 2010; Kishishita et al. 2012) found that the source is elongated to the north where an apparent radio shell lies (Van Etten & Romani 2010). On a smaller scale, Ng et al. (2005) found an X-ray arc in 10 ks Chandra data (Obs. ID 2792) and suggested that it could be the termination shock. Moreover, the spectral softening detected in K3 (Van Etten & Romani 2010; Kishishita et al. 2012) may be manifested by a size shrinkage with increasing energy (e.g., An et al. 2014a; Nynka et al. 2014). In this section, we inspect the Chandra data to identify the small- and large-scale structures, and analyze the NuSTAR data to measure the size shrinkage of K3.

2.3.1. Chandra Images

We produced a Chandra image in the 2–7 keV band after removing point sources and correcting for exposure. This was done by following a procedure in the CIAO science thread. ⁸ We then adjusted the image scales and bins to identify structures in the PWN on various spatial scales (Figure 2).

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On a 40'' × 40'' scale, we identified two knots at 3'' and 7'' from the pulsar (Knot 1 and Knot 2; Figure 2(a)); compared to nearby backgrounds, the knots were detected at ∼3σ significance. Note that Knot 1 is listed in the Chandra source catalog, ⁹ but we do not find an IR or optical counterpart in the 2MASS and USNO catalogs. Furthermore, the knots appear to be more extended than nearby point sources with similar counts. Note also that there seems to be a slightly elongated structure (short and parallel to—but just east of—the jet indicated in Figure 2(b)), but this structure was detected only at the 2.5σ level. An image of a $2^{\prime} \times 2^{\prime}$ region near the pulsar is displayed in Figure 2(b). In this image, the torus structure in the east–west direction identified by Ng et al. (2005) is clearly visible. In addition, we found a narrow jet-like (∼20'') feature extending in the northeast direction. The jet-like structure is fainter but detected at a ≥3σ level, having 172 events in the 1–10 keV band within a 7'' × 17'' ellipse (excluding the pulsar and torus emission; Figure 2(b)) which contains estimated 119 background counts.

A larger-scale image is displayed along with VHE emission regions (H.E.S.S. Collaboration et al. 2018; Abdollahi et al. 2020) in Figure 2(c). The image reveals a prominent ∼7' tail (denoted as "Tail") and two short tails in the northwest direction. These tails seem to constitute the broad northern tail observed in the low-resolution Suzaku image (Van Etten & Romani 2010; Kishishita et al. 2012). In the south, a bright emission region is seen out to $\sim 2\buildrel{\,\prime}\over{.} 5$. The bright southern region and the northern "Tail" were also identified in our inspection of XMM-Newton MOS images. The "Tail" appears to partially overlap with a radio structure (Figure 2(d); see also Van Etten & Romani 2010). ¹⁰ The VHE emission regions are centered at 2'–3' north of the pulsar (white and cyan circles in Figure 2(c)) and also overlap well with the X-ray PWN. Note also that there is weak excess emission in the southwest (near the chip boundary). This region is 15%–20% brighter than other background regions, possibly indicating inhomogeneous sky emission on a larger scale as was seen in an ASCA image (e.g., Roberts et al. 2001b).

We also searched the Chandra images for a shell-like structure (e.g., supernova remnant) in several energy bands, but we did not find any. Additionally, we compared spectra of various regions within the FoV with blank-sky data ¹¹ to see if there is an excess of line emission, but we found none.

2.3.2. NuSTAR Image

We next produced 3–7 keV and 7–20 keV NuSTAR images of the source. To take into account the spatially nonuniform background, we carried out nuskybgd simulations. ¹² Although the simulated background images reproduced the aperture patterns well, the normalization of the simulated image differed from the observed one by <10% in each chip. Hence, we manually adjusted the background normalization to match the observed background counts in each chip. We combined FPMA and FPMB images after aligning them using the brightest spot in the 10–30 keV smoothed images (Section 2.2). Background-subtracted NuSTAR images of the K3 PWN show primarily the bright southern region (Figure 3), and the low- and high-energy morphologies do not appear significantly different.

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We produced 3–7 keV and 7–20 keV radial profiles to further investigate possible size shrinkage of K3 with energy. Although contamination from the pulsar can be minimized by pulse gating, the statistics would then be insufficient for a meaningful comparison, because the off-pulse intervals are narrow (Δϕ < 0.5; Figure 1 top). Therefore, we used all the pulse phases. Radial profiles in the low- and high-energy bands along with simulated background profiles are displayed in the top panel of Figure 3(c); the background profiles account for the observations at large radii as expected. To assess the relative contributions of the pulsar and extended emission, we fit the radial profile with a model composed of the PSF (pulsar), background, and a Gaussian function $A\exp (-{r}^{2}/2{w}^{2})$ (PWN); the best-fit functions are displayed in Figure 3(c). The inferred normalization factors for the background profiles were consistent with 1 at ≲1σ level, and the pulsar flux was estimated to be ≈10% of the PWN flux (see also Table 1) and dominates only in the innermost regions r < 20'' (Figure 3(c)).

Table 1. Spectral Analysis Results

Data	Instrument a	Energy Range	NH	Γ	F3−10 keV	χ2/dof
		(keV)	(1022 cm−2)		(10−13 erg s−1 cm−2)
PSR b	C	0.5–10	4.6 c	0.7 ± 0.2	${1.3}_{-0.1}^{+0.2}$	30/46
PSR d	N	3–30	4.6 c	0.7 ± 0.4	${1.5}_{-0.4}^{+0.6}$	21/22
PWN e	C	0.5–10	4.2 ± 0.5 ± 0.4	1.82 ± 0.23 ± 0.11	15.3 ± 0.9 ± 0.4	156/146
PWN e	N	3–20	4.2 f	$1.97\pm {0.06}_{-0.07}^{+0.08}$	16.5 ± 0.6 ± 0.6	168/170
PWN e	C + N	0.5–20	4.6 ± 0.3 ± 0.4	$1.98\pm {0.07}_{-0.06}^{+0.08}$	15.0 ± 0.7 ± 0.3	324/317
Torus	C	0.5–10	4.6 c	1.8 ± 0.3	0.7 ± 0.1	6/10
Jet	C	0.5–10	4.6 c	2.1 ± 0.7	0.2 ± 0.1	4/5
Tail	C	0.5–10	4.6 c	2.06 ± 0.26	${3.5}_{-0.4}^{+0.5}$	134/120

Notes.

^a C: Chandra, N: NuSTAR. ^b On+off-pulse emission. ^c Fixed at the value obtained from a joint fit of the Chandra+NuSTAR PWN spectra. ^d On−off-pulse emission. ^e The second error is a systematic uncertainty. See text for more details. ^f Fixed at the Chandra-measured value.

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The widths (w) of the best-fit Gaussian functions for the low- and high-energy profiles were determined to be 82'' ± 3'' and 75'' ± 2'', respectively. The measured widths differ only at the 1.6σ level and thus do not clearly require a size shrinkage with energy. Because the synchrotron burn-off effects should also produce spectral softening with increasing radius, we computed hardness ratios (ratio of the hard- and soft-band brightness) and show them in the bottom panel of Figure 3(c). The hardness ratio decreases nearly monotonically out to ∼200'', beyond which the background dominates. A linear fit to the hardness ratios (20'' ≤ r ≤ 190'') found a negative slope (i.e., spectral softening) at the ≈3σ level with χ²/dof = 10/17 (red line in the bottom panel of Figure 3(c)). Note, however, that the negative slope might be caused primarily by the two data points at R = 130''–140'', rather than by a gradual decrease. Ignoring the two points reduced the significance to a ≈2σ level, which still hints at a gradual decrease although a firm conclusion on the softening cannot be made with the current data.

In this section, we analyze X-ray spectra of the K3 PWN and its substructures that were identified in the Chandra images (Figure 2). The spectral softening measured for K3 (Van Etten & Romani 2010; Kishishita et al. 2012) implies a spectral curvature in its spatially integrated spectrum which may be detected in the broadband X-ray data taken with NuSTAR (e.g., Madsen et al. 2015a). Furthermore, the NuSTAR data may allow the detection of a spectral cutoff at >10 keV (e.g., An 2019). Because other point sources within the PWN may contaminate the NuSTAR spectra of the PWN, we estimate the contributions from the point sources using the high-resolution Chandra data.

2.4.1. Point Sources within the PWN

In the image analysis (Section 2.3.1), we detected 10 point sources and the pulsar J1420 within a $R\,=\,2\buildrel{\,\prime}\over{.} 5$ circle centered at the pulsar, using the wavdetect tool of CIAO. The point sources seen in the Chandra image are very faint, having 10–20 events within R = 2'' regions compared to 260 events for J1420. With so few counts, accurate spectral characterization of each source was unfeasible. However, these faint sources are unlikely to affect NuSTAR measurements of the PWN spectra (Sections 2.4.2 and 2.4.4). For a better assessment, we stacked the Chandra spectra of the 10 point sources using R = 2'' extraction regions. A summed background spectrum was constructed using R = 3'' circles near the source regions. We grouped the stacked spectrum to have at least five counts per bin and fit the spectrum with an absorbed power-law model employing the l statistic (Loredo 1992). For the Galactic absorption, we adopted the tbabs model along with the vern cross section (Verner et al. 1996) and angr abundances (Anders & Grevesse 1989) in XSPEC v12.12.0 (throughout this paper). Although the hydrogen column density N_H was not well-constrained, the model fit favored a very low value (consistent with 0), perhaps because of low-energy emission from a few soft, foreground sources—these soft X-ray sources do not have a significant contribution to >3 keV NuSTAR spectra. Therefore, we set N_H to 0 and found that a power-law model with a photon index of 1.2 ± 0.2 and absorption-corrected 3–10 keV flux ${F}_{3-10\,\mathrm{keV}}={2.3}_{-0.5}^{+0.6}\,\times {10}^{-14}\ \mathrm{erg}\ {\mathrm{cm}}^{-2}\ {{\rm{s}}}^{-1}$ fits the data; the latter is ≤2% of the PWN flux (see below). Note that using a larger N_H makes Γ softer (i.e., fewer counts in the NuSTAR band), and thus our estimation above is conservative.

To measure the pulsar spectrum with the Chandra data, we extracted events within an R = 2'' circle centered at the pulsar position. A background spectrum was extracted within two R = 2'' circles in the torus region. We grouped the source spectrum to have a minimum of five counts per spectral bin and employed the l statistic in the fit. The spectrum was well-fit with an absorbed power-law model for a frozen N_H = 4.6 × 10²² cm⁻², which was obtained from a joint fit of the Chandra+NuSTAR PWN spectra of a large region (see Section 2.4.2). The fit resulted in Γ = 0.7 ± 0.2 and F_{3−10 keV} = 1.3 × 10⁻¹³ erg cm⁻² s⁻¹ (Figure 4). Note that Kuiper & Hermsen (2015), using a likelihood method applied to the same Chandra data, obtained Γ = 0.46 ± 0.07 for ${N}_{{\rm{H}}}={3.35}_{-0.51}^{+0.74}\times {10}^{22}\ {\mathrm{cm}}^{-2}$. The difference in the measured photon indices seems to arise from its covariance with N_H; by fixing N_H to 3.35 × 10²² cm⁻², the photon index was fit to Γ = 0.4 ± 0.2, consistent with the results in Kuiper & Hermsen (2015).

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We also measured the pulsed spectrum of J1420 using the NuSTAR data. We extracted source events within a R = 30'' circle around the pulsar position and selected on- (ϕ = 0–0.1 and 0.38–0.7; Figure 1) and off-pulse (ϕ = 0.15–0.35 and 0.75–1.00) data for the source and background spectrum, respectively. The pulsed (on−off) spectrum was fit with an absorbed power-law model in the 3–30 keV band, and we found the best-fit parameters to be Γ = 0.7 ± 0.4 and ${F}_{3-10\,\mathrm{keV}}={1.5}_{-0.4}^{+0.6}\times {10}^{-13}\ \mathrm{erg}\ {\mathrm{cm}}^{-2}\ {{\rm{s}}}^{-1}$. The latter becomes ${F}_{3-10\,\mathrm{keV}}={6}_{-2}^{+3}\times {10}^{-14}\ \mathrm{erg}\ {\mathrm{cm}}^{-2}\ {{\rm{s}}}^{-1}$ when averaged over a spin cycle (Figure 4).

2.4.2. Spatially Integrated PWN Spectrum

To construct a broadband X-ray SED to be used in our SED modeling (Section 3), we measured the spatially integrated spectra of the PWN with the Chandra and NuSTAR data. For the Chandra analysis, we extracted the source spectrum within an $R\,=\,2\buildrel{\,\prime}\over{.} 5$ circle centered at the pulsar, excising the pulsar and other point sources (Section 2.4.1) using R = 2'' circles. This PWN region contains most of the bright nebula, but the outer part of the long "Tail" is not included (see Section 2.4.3 for the tail spectrum). Because background selection for the faint and extended nebula was a concern, we used the blank-sky data to choose optimal background regions by comparing the blank-sky background and the observed image. We note that the source region lies across four detector chips, and hence we adjusted the background region sizes taken in the four chips so that the sizes are approximately proportional to the source-region areas within the corresponding chips. We verified that the blank-sky data explained well the instrumental line emissions (e.g., Bartalucci et al. 2014) in the source and background regions and that the source and background spectra (including instrumental lines) agreed very well in the low- (≲ 1.5 keV) and high-energy (≳ 7 keV) bands, meaning that the background represents well the detector and sky background in the source region.

We generated response files for the extended source region using the specextract tool of CIAO, grouped the spectrum to have a minimum of 100 counts per spectral bin, and fit the 0.5–10 keV spectrum with an absorbed power-law model (Figure 4). This model adequately describes the observed spectrum (χ²/dof = 156/146), and the fit-inferred parameter values are N_H = (4.2 ± 0.5) × 10²² cm⁻², Γ = 1.82 ± 0.23, and F_{3−10 keV} = (1.53 ± 0.09) × 10⁻¹² erg cm⁻² s⁻¹. These N_H and Γ values are similar to the previous measurements of Van Etten & Romani (2010) and Kishishita et al. (2012). Note, however, that they did not report the Galactic abundance and scattering cross section used for their absorption models, and thus we assumed that they used the vern cross section and angr abundances (the default in XSPEC). The PWN spectrum is better constrained by combining it with the NuSTAR data below.

As noted above, the Chandra-only fit results may significantly vary depending on the background selection, especially because of the covariance between N_H and Γ. Therefore, we analyzed the data with 10 different background selections to estimate systematic uncertainties (i.e., 1σ variation) and found that the best-fit parameters change by ΔN_H = ± 4 × 10²¹ cm⁻², ΔΓ = ± 0.11, and ΔF_{3–10 keV} = ± 4 × 10⁻¹⁴ erg cm⁻² s⁻¹. We report these systematic uncertainties as additional errors in Table 1.

To measure the NuSTAR spectrum of the PWN, we used $R\,=\,2\buildrel{\,\prime}\over{.} 5$ circles for extraction of the source spectra (Figure 4). As noted above, the NuSTAR background is nonuniform, and thus it was difficult to extract local background spectra on the same detector chip, especially for FPMA. We therefore used the nuskybgd simulations (Wik et al. 2014) to generate a background spectrum corresponding to the source region for each of FPMA and FPMB. We verified that the background model adequately explained the observed background spectra as well as the high-energy background (>30 keV) in the source spectra.

Because the pulsar emission was included in our phase-integrated NuSTAR spectra, we modeled those spectra with two power laws, one for the PWN and the other for the pulsar emission. We held the second power-law parameters fixed at Chandra-measured pulsar parameters and fit the 3–20 keV source spectra holding N_H fixed at 4.2 × 10²² cm⁻². An acceptable fit (χ²/dof = 168/170) was achieved with the best-fit parameters of Γ = 1.97 ± 0.06 and F_{3−10 keV} = (1.65 ±0.06) × 10⁻¹² erg cm⁻² s⁻¹. The NuSTAR-measured flux and photon index are consistent with the Chandra-measured ones at the ∼1σ level. To check this further, we inspected the NuSTAR spectra in the 3–10 keV band and found that the fit-inferred PWN Γ = 1.92 ± 0.10 is still consistent with the Chandra measurement. We also attempted to fit the 3–20 keV PWN spectra with a broken power-law model and found that a spectral break is not statistically required with an f-test probability of ≈0.5.

We assessed systematic uncertainties on the NuSTAR-inferred parameters. The NuSTAR fit results are not very sensitive to a modest change of N_H; varying it within the Chandra-estimated uncertainty of ±7 × 10²¹ cm⁻² (Table 1) changes Γ by ±0.04 and F_{3−10 keV} by ±5 × 10⁻¹⁴ erg cm⁻² s⁻¹ (min/max). The assumed pulsar spectral model may also introduce some uncertainties in the inferred spectral parameters. We therefore varied the pulsar model within the measurement uncertainties considering the covariance between Γ and F_{3−10 keV} of the pulsar. We found that the effects of the pulsar model are not significant; Γ varies by +0.05 and −0.03, and the change of F_{3−10 keV} is ΔF_{3−10 keV} =± 10⁻¹⁴ erg cm⁻² s⁻¹ (min/max). We also varied background regions for the nuskybgd simulations (see Wik et al. 2014, for more detail), generated 20 background spectra, and used them in our spectral fits. The best-fit parameters vary depending on the background used: ΔΓ = ± 0.04 and ΔF_{3−10 keV} =± 3 × 10⁻¹⁴ erg cm⁻² s⁻¹ (standard deviations; 1σ). We combine these systematic uncertainties in quadrature and report them in Table 1 (second errors).

To measure the PWN spectrum accurately, we jointly fit the 0.5–10 keV Chandra and 3–20 keV NuSTAR spectra of the PWN (Figure 4 and Figure 5(a)). Note that we modeled the Chandra spectrum with a single power law, whereas we modeled the NuSTAR spectra with two power laws—with the second power law representing the pulsar emission (fixed to the Chandra pulsar model; Table 1). The best-fit parameters for the PWN were inferred to be N_H = (4.6 ± 0.3) × 10²² cm⁻², Γ = 1.98 ± 0.07 and F_{3−10 keV} = (1.50 ± 0.07) × 10⁻¹³ erg cm⁻² s⁻¹. The cross-normalization factors for the NuSTAR FPMA and FPMB spectra with respect to the Chandra spectrum were slightly higher than, but consistent with, 1 at the ≲2σ level. We also achieved an acceptable fit to the PWN spectra with a broken power law (χ²/dof = 324/315). A comparison of the broken power-law and power-law fits found an f-test probability of 0.8, suggesting no significant evidence for spectral curvature or cutoff.

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It should be noted that we have again used the angr abundances for the quoted N_H value, to compare to previously published studies and be consistent throughout. Using the newer Wilms abundances (Wilms et al. 2000) gives, as expected, a higher column density of (6.94 ± 0.55) × 10²² cm⁻² but does not change the other spectral parameters.

Because the results may still be influenced by Chandra's background, we checked them with the 10 Chandra background selections and found 1σ variations of the parameters to be ΔN_H = ± 0.4 × 10²² cm⁻², ΔΓ = ± 0.03, and ΔF_{3−10 keV} = ± 2 × 10⁻¹⁴ erg cm⁻² s⁻¹. The joint-fit results also vary depending on the NuSTAR background simulation and the pulsar model. Uncertainties due to the former and the latter were estimated to be ΔN_H = ± 10²¹ cm⁻², ΔΓ = ± 0.04, and ΔF_{3−10 keV} = ± 10⁻¹⁴ erg cm⁻² s⁻¹ (1σ), and ΔN_H = ± 10²¹ cm⁻², ${\rm{\Delta }}{\rm{\Gamma }}{=}_{-0.03}^{+0.06}$, and ΔF_{3−10 keV} = ± 10⁻¹⁴ erg cm⁻² s⁻¹ (min/max), respectively. These systematic uncertainties are combined in quadrature and reported in Table 1.

2.4.3. Chandra Spectra of the Substructures in the PWN

2.4.4. Spatially Resolved Spectra of the PWN

To investigate the properties of particle flow in the K3 PWN using a multizone emission model, we collected radio and TeV SED measurements from the literature (Roberts et al. 1999; Aharonian et al. 2006; Van Etten & Romani 2010) and took Fermi-LAT data from the 4FGL DR-3 catalog (Fermi-LAT collaboration et al. 2022). We then added them to our X-ray measurements to construct a broadband SED of the source (Figure 5). Note that Van Etten & Romani (2010) regarded the radio measurements as upper limits for the radio emission of the PWN because an association between the X-ray PWN and the apparent radio shell was not established. We also take the K3 excess and the shell emission as the lower and upper limits, respectively, for our SED analysis.

The K3 PWN was detected as an extended source (4FGL J1420.3−6046e) in the Fermi-LAT 4FGL DR-2 and DR-3 catalogs (e.g., gll_psc_v28.fit; Abdollahi et al. 2020; Fermi-LAT collaboration et al. 2022), and the bright gamma-ray pulsar J1420 is within the PWN. The nebular emission was modeled by a power law with photon index Γ = 2.00 ± 0.13 and Γ = 2.05 ± 0.09 (green in Figure 6) in the DR-2 and DR-3 catalog, respectively. In our inspection of the LAT SEDs reported in the catalogs, we found that low-energy (≲ 20 GeV) flux points of the PWN exhibit a rapidly falling trend with increasing energy (two blue points at ≲ 20 GeV in Figure 6). This trend is reminiscent of the exponentially cut-off pulsar spectrum (red in Figure 6). We suspect that some of the high-energy SED tail of the gamma-ray pulsar 4FGL J1420.0−6048 (LAT counterpart of J1420) was ascribed to the PWN model in the catalogs. This speculation is supported by the fact that the PWN is flagged as a "variable" source probably because it was confused with J1420, as noted by Abdollahi et al. (2020). Therefore, we use only the >20 GeV SED points.

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The broadband SED in the radio to VHE band is presented in Figure 5(a). Note that we adopted X-ray SED data from within $R\,=\,2\buildrel{\,\prime}\over{.} 5$ (Section 2.4.2) and thus integrate our computed X-ray SEDs only out to that distance (see below).

We applied our phenomenological multizone emission model (Kim & An 2020b) to the broadband SED and the measured X-ray profiles of photon index and brightness of K3. In the model, the pulsar supplies electrons and magnetic field B to the PWN. The spin-down power ${\dot{E}}_{\mathrm{SD}}$ of the pulsar goes into energies of the particles (${\dot{E}}_{e}\equiv {\eta }_{e}{\dot{E}}_{\mathrm{SD}}$) and B (${\dot{E}}_{B}\equiv {\eta }_{B}{\dot{E}}_{\mathrm{SD}}$) in the PWN, and the pulsar's gamma-ray radiation (${L}_{\gamma }\equiv {\eta }_{\gamma }{\dot{E}}_{\mathrm{SD}}$). As was done in Gelfand et al. (2009), we assume ${\dot{E}}_{\mathrm{SD}}$ evolves over time following ${\dot{E}}_{\mathrm{SD}}(t)={L}_{0}{\left(1+\tfrac{t}{{\tau }_{0}}\right)}^{-\tfrac{n\,+\,1}{n-1}},$ where τ₀ = 2τ_c /(n − 1) − t_age and n is the braking index (assumed to be 3 in this work). We further assume a constant η_e , so ${\dot{E}}_{e}$ also evolves with the same time dependence as ${\dot{E}}_{\mathrm{SD}}$. Electrons with a power-law energy distribution, ${{dN}}_{e}/d{\gamma }_{e}{dt}={N}_{0}{\gamma }_{e}^{-{p}_{1}}$, are injected at the termination shock and flow in the PWN via advection and diffusion.

The emission model assumes a spherical flow whose properties, magnetic field strength B, flow speed V_flow, and diffusion coefficient D, are assumed to be power laws: $B{(r)={B}_{0}(r/{R}_{\mathrm{TS}})}^{{\alpha }_{{\rm{B}}}}$, ${V}_{\mathrm{flow}}{(r)={V}_{0}(r/{R}_{\mathrm{TS}})}^{{\alpha }_{{\rm{V}}}}$, and $D\,={D}_{0}{({\gamma }_{e}/{10}^{9})(B/100\mu {\rm{G}})}^{-1}$, where R_TS is the distance from the pulsar to the termination shock. These properties are time-independent in our model, but in reality are likely to change with time because of the time-dependent energy injection ${\dot{E}}_{\mathrm{SD}}$ (see Section 4.3). We estimate η_B by comparing the time-integrated ${\dot{E}}_{\mathrm{SD}}$ to the space-integrated magnetic energy density: ${\eta }_{B}{\int }_{0}^{{t}_{\mathrm{age}}}{\dot{E}}_{\mathrm{SD}}{dt}=4\pi {\int }_{{R}_{\mathrm{TS}}}^{{R}_{\mathrm{PWN}}}({B}^{2}/8\pi ){r}^{2}{dr}$. η_γ is computed by comparing the measured L_γ to the present-day ${\dot{E}}_{\mathrm{SD}}({t}_{\mathrm{age}})$. We then require η_e + η_B + η_γ ≲ 1.

Particle evolution (in space and energy) is computed in 1000 spatial zones and 10⁴ γ_e bins and for 10⁵ time steps, considering radiative and adiabatic losses (e.g., Tang & Chevalier 2012). We compute the synchrotron and ICS spectra of the particles in each of the emission zones. For the ICS seed photons, we use the CMB (T_CMB = 2.7 K with energy density u_CMB = 0.26 eV cm⁻³) and IR (T_IR with energy density u_IR) radiation; the parameters for the latter are adjusted to match the VHE SED. We project the computed emission onto the tangent plane of the observer, construct spatially integrated and resolved SEDs, and compare them with measurements (e.g., Figure 5). For the comparison, we integrate the model emission over the projected areas appropriate for the SED measurements (i.e., 25 for X-ray and 012 for VHE). Note that the Fermi-LAT measured the size of the K3 PWN to be 0123 using a disk model, whereas H.E.S.S. measured it to be 008 using a Gaussian model (1σ width). In this work, we adopt the LAT-measured size, but a different size could be accommodated by our model with a change of u_IR.

Because there are many covariant parameters, it is infeasible to determine all of them with the given measurements of the broadband SED and radial profiles. Therefore, we make some assumptions about the PWN flow. For B, we assume transverse configuration (e.g., Bucciantini et al. 2022) and magnetic flux conservation: i.e., α_V + α_B = −1 (Reynolds 2009). We further assume an age of t_age = 9 kyr based on the gamma-ray-to-X-ray flux ratio (see Kargaltsev et al. 2013), and R_TS = 0.14 pc and R_PWN = 10.75 pc according to the torus size (∼5'') and the VHE size of the PWN (012), respectively, for an assumed distance of d = 5.6 kpc. As the X-ray emission seems to be confined within a certain radius from the pulsar, the PWN properties (B and V_flow) may change abruptly at the boundary. We verified that the model-computed emissions did not alter much whether or not we used such abrupt changes in our modeling, because the predicted brightness is very low in the outer regions (e.g., Figure 5(d)).

Some of the model parameters can be roughly estimated based on the observations. As Klein–Nishina suppression for electron scattering from IR and CMB seed photons is expected at ≳100 TeV, the ICS emission of K3 occurs mostly in the Thomson regime. Then, for the observed ICS to synchrotron SED peak ratio of ∼4 and an assumed u_IR in the galaxy of ≈1 eV cm⁻³, $\tfrac{{B}^{2}}{8\pi }\approx \tfrac{{u}_{\mathrm{IR}}+{u}_{\mathrm{CMB}}}{4}$ gives B ≈ 4μG. For this B, ≈20 keV photons observed from K3 imply a maximum γ_e of ≈5 × 10⁸. The uncooled spectrum of the electrons can be directly inferred from the IR-to-optical (synchrotron) and the LAT (ICS) SEDs. With the lack of IR/optical measurements, a LAT photon index of ≈1.7 measured by differencing the two >20 GeV LAT points (Figure 6) implies a p₁ = 2Γ − 1 of ≈2.4.

Using the aforementioned estimates as a guide, we optimized the model to match the broadband SED and radial profiles of the X-ray brightness and photon index. An optimized model is displayed in Figure 5 with parameters given in Table 2. We found that particle transport is dominated by advection that carries the particles to ∼12 pc over the age of 9 kyr as compared to the diffusion length $2\sqrt{{{Dt}}_{\mathrm{age}}}$ of ≈2 pc and ≈5 pc for VHE (e.g., γ_e ≈ 10⁷) and X-ray emitting (e.g., γ_e ≈ 10⁸) electrons, respectively. The diffusion length scale for the highest-energy electrons (γ_e ≈ 10⁹) is comparable to the advection length scale.

Table 2. Parameters for the Multizone SED Model

Parameter	Symbol	Value
Spin-down power	${\dot{E}}_{\mathrm{SD}}$	1037 erg s−1
Characteristic age of the pulsar	τc	13,000 yr
Age of the PWN	tage	9000 yr
Size of the PWN	Rpwn	10.75 pc
Radius of termination shock	RTS	0.14 pc
Distance to the PWN	d	5.6 kpc
Index for the particle distribution	p1	2.33
Minimum Lorentz factor	${\gamma }_{e,\min }$	104.45
Maximum Lorentz factor	${\gamma }_{e,\max }$	109.24
Magnetic field	B0	5.1 μG
Magnetic index	αB	−0.06
Flow speed	V0	0.14c
Speed index	αV	−0.94
Diffusion coefficient	D0	1.2 × 1026 cm2 s−1
Energy fraction injected into particles	ηe	0.9
Energy fraction injected into B field	ηB	0.007
Temperature of IR seeds	TIR	10 K
Energy density of IR seeds	uIR	1.7 eV cm−3
CMB temperature	TCMB	2.7 K
CMB energy density	uCMB	0.26 eV cm−3

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In our model, the most energetic particles in K3 have energies of ≈10¹⁵ eV and cool substantially via synchrotron emission over the pulsar's age (Figure 5(b)). Therefore, the synchrotron spectra in outer regions are softer than those in inner regions (i.e., spectral softening by synchrotron burn-off effects). The computed radial profiles of Γ and brightness depend sensitively on the flow properties (e.g., B, α_B , D₀, etc.) and thus provide crucial information on the model parameters. For example, a model with a large B or α_B has difficulty accommodating the large X-ray/VHE extension of the source (≈10 pc) because particles would have cooled efficiently via synchrotron radiation in the inner zones, giving fainter emission at large distances. In contrast, a model with a smaller B would make the Γ and brightness profiles flatter. Moreover, such a low-B model requires more particles (i.e., larger η_e ) to match the observed SED. Then the observed ${\dot{E}}_{\mathrm{SD}}={10}^{37}\ \mathrm{erg}\ {{\rm{s}}}^{-1}$ of J1420 may be insufficient to provide the required amount of particles; i.e., η_e + η_B + η_γ > 1 for a measured η_γ of ≈7% for J1420.

The VHE emission primarily arises from the ICS from the IR seeds (Figure 5(a)) by electrons with energies of ≈10 TeV. The H.E.S.S. flux (> TeV) is lower than (but within uncertainties of) the LAT flux (<1 TeV), possibly indicating a cross-calibration issue. We adjusted our model to match the H.E.S.S. measurements because they have smaller uncertainties. Our model slightly overpredicts the >10 TeV SED points, especially the highest-energy one. It may be due to statistical fluctuations, but if real, the highest-energy measurement is hard to explain with our simple model. Given that the ICS emission at the highest energies is mainly produced in inner regions (see Section 4.3), reducing the IR seeds in those regions may help to reconcile the small discrepancy. It should be noted that the u_IR value we used is higher than the Galactic average dust emission (e.g., Vernetto & Lipari 2016) but is similar to values inferred for other PWNe (e.g., Torres et al. 2014), as PWNe are in crowded regions.

It was firmly established by a Chandra image (Ng et al. 2005) and detection of radio and gamma-ray pulsations (D'Amico et al. 2001; Weltevrede et al. 2010) that J1420 is associated with the K3 PWN. The energetic pulsar (${\dot{E}}_{\mathrm{SD}}={10}^{37}\ \mathrm{erg}\ {{\rm{s}}}^{-1}$) has a power-law spectrum with a photon index Γ = 0.7 and a flux F_3−10keV = 1.3 × 10⁻¹³ erg cm⁻² s⁻¹, which corresponds to a 3–10 keV X-ray luminosity of ≈5 × 10³² erg s⁻¹ for the assumed distance of 5.6 kpc. For its f = 14.66 Hz and $\dot{f}=-1.77\times {10}^{-11}\ \mathrm{Hz}\ {{\rm{s}}}^{-2}$, the measured emission properties of J1420 appear to accord with correlations seen in rotation-powered pulsars (RPPs) between temporal and emission properties: e.g., correlations of Γ and X-ray luminosity L_X,PSR with ${\dot{E}}_{\mathrm{SD}}$, τ_c , P = 1/f, and $\dot{P}=-\dot{f}/{f}^{2}$ (e.g., Li et al. 2008). The measured properties of J1420 and K3 are also in accordance with correlations found between properties of other RPP/PWN systems; e.g., the Γ and X-ray luminosity L_X,pwn of PWNe are correlated with the P, $\dot{P}$, τ_c , ${\dot{E}}_{\mathrm{SD}}$, Γ, and L_{X, PSR} of the pulsars (Gotthelf 2003; Li et al. 2008). Therefore, we conclude that J1420/K3 is not significantly different from other RPP/PWN systems.

Using the XMM-Newton and NuSTAR data, we unambiguously detected the X-ray pulsations of J1420 up to 30 keV (Section 2.2), which supports the idea that J1420 is a soft γ-ray pulsar as suggested by Kuiper & Hermsen (2015). The X-ray pulse profile of J1420, with a sharp peak and a broad bump, is similar to that of another soft γ-ray pulsar PSR J1418−6058. Intriguingly, these two pulsars seem to exhibit similar gamma-ray pulse profiles having a smaller peak followed by a bridge and a brighter peak. ¹³ In the case of PSR J1418−6058, the sharp X-ray peak phase-aligns with the smaller gamma-ray peak (Kim & An 2020a), but the X-ray and gamma-ray phase alignment is unclear in the case of J1420 because the existing LAT timing solution does not cover the X-ray epochs. As the relative phasing can provide clues to the spin orientation of the pulsar, further LAT timing studies are warranted.

In the Chandra data, we identified several small-scale X-ray features: knots and a torus-jet structure. Although "Knot 1" may be a point source overlapping with the torus by chance, the nondetection of an IR or optical counterpart in the 2MASS and USNO catalogs within <5'' and the rather broad spatial distribution observed for Knot1 (compared to other point sources with similar counts) suggest that it may be a diffuse PWN. If so, we may speculate, based on its location (near the jet base), that Knot 1 may correspond to a dynamical feature near the jet base similar to those seen in the Crab Nebula (e.g., Hester et al. 2002). Knot 2 is also close to the jet but not well-aligned with it. Hence, the nature of Knot 2 remains uncertain.

The torus-jet structure we found (Figure 2(a)) can be interpreted as the termination shock (e.g., Ng et al. 2005) and a collimated jet. The torus radius of ∼5'' corresponds to 0.14 pc for the assumed distance of 5.6 kpc and is consistent with the size of a termination shock formed by pressure balance (e.g., Kargaltsev & Pavlov 2008). Therefore, the termination shock interpretation of the torus is plausible. Thus, the spin orientation of J1420 may be inferred by a torus model (Ng & Romani 2004); the directions of the torus and the jet suggest that the position angle of the spin axis is ≈40° east from the north (i.e., along the jet), and an aspect ratio of ∼0.6–0.7 of the torus morphology may suggest that the spin axis is ∼35°–45° into or out of the tangent plane if the torus is a ring as is observed in the Crab Nebula. Further, the fact that a southern jet is not detected may imply that the northern jet is pointing out of the plane. These crude estimates need to be updated by more precise torus modeling (e.g., Ng & Romani 2004), which can be further checked with pulse profile modeling (e.g., Harding & Muslimov 1998; Romani & Watters 2010).

The long northern tail detected by Suzaku was interpreted as a trail of the pulsar that had been born 3' northwest at the center of an apparent radio shell (Van Etten & Romani 2010, see also Figure 7). In this scenario, the three tails in the Chandra image (Figure 2(c)) may be related to the pulsar's polar and equatorial outflows (Figure 7 bottom) analogous to those observed in Geminga (Posselt et al. 2017). In this picture, the much more prominent (top) tail ("Tail" in Figure 2(c)) is the bent, originally approaching polar jet, the middle tail is the equatorial outflow, and the bottom tail is the bent counter jet (Figure 7 bottom). The putative radio shell discovered by Van Etten & Romani (2010) might be compressing the PWN in the southeast, and the narrow inner jets (Figure 2 middle) might have been blocked by the shell, turning into the broad tails over the course of the pulsar's motion (e.g., Figure 7, bottom). The compressed southern region would have stronger magnetic field and hence brighter synchrotron emission. Then particles in the south would cool rapidly via the synchrotron process, and their VHE emission would be extended in the other direction, perhaps accounting for the offset VHE emission. Alternatively, if the pulsar's motion is very small, one can speculate that the irregular morphology might be caused by inhomogeneities in the ambient medium (e.g., asymmetric reverse shock interaction; Van Etten & Romani 2010). These scenarios can be distinguished by a measurement of the pulsar's proper motion. In the bent outflow scenario, the pulsar is expected to move 0014(13kyr/t_age) yr⁻¹ in the southeast direction; a future high-resolution observatory (e.g., Lynx or AXIS; Gaskin et al. 2019; Mushotzky et al. 2019) might be able to detect this proper motion with a ≳ 20 yr baseline (e.g., in the 2030s).

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It is intriguing to note that no significant radio emission coinciding with the bright X-ray emission is seen in the southern region. In contrast to K3, other young or middle-aged PWNe exhibit morphological similarity in the radio and X-ray bands (Ng et al. 2005; Matheson & Safi-Harb 2010). It is unclear what causes the lack of radio emission in K3, but it implies that both B and particle energies are high in the south of K3, such that the electrons emit synchrotron radiation above the radio band. These may be related to a reverse shock interaction. If so, we may speculate that the reverse shock interaction started rather recently, and thus the electrons have not cooled sufficiently to produce significant radio emission; i.e., the synchrotron peak frequency ${\nu }_{\mathrm{SY}}\propto B{\gamma }_{e,\min }^{2}$ lies above the ∼GHz radio band.

Although the multizone model reproduced the observed data broadly, the parameter values are not well-constrained, due to model assumptions and parameter covariance. In particular, it is clear that the K3 PWN has some substructures (Figure 2) and is not spherically symmetric (Figure 7). Moreover, the particle flow in the PWN may be very complex due to pulsar motion and reverse shock compression (e.g., Van Etten & Romani 2010, Section 4.2). Our model, with the assumptions of spherical flow, homogeneous IR seed photons and smooth particle distribution, does not take into account the complex morphology and flows in the bent outflow and/or compressed regions, which may introduce some inaccuracy to the parameter estimations; e.g., the α_B + α_V = − 1 relation may not be valid. In addition, the PWN properties B and V_flow were assumed to be constant in time; these might be higher at early times, as ${\dot{E}}_{\mathrm{SD}}$ was larger. This effect has some influence on the old particles in outer regions and would make their spectra softer than was predicted by our model. However, the broadband SED might be little affected, because the X-ray emission from the outer zones is weak (e.g., Figure 5). It should also be noted that the complex parameter covariance of the SED model was not thoroughly investigated, and there are likely other sets of parameters that may explain the data equally well. Hence, the parameters reported in Table 2 may represent only the average properties, and they need to be taken with caution. Nonetheless, we discuss below a few intriguing parameters inferred from the modeling.

The spectral softening demands a reasonably strong B, but if it is too strong, the model-predicted brightness profile drops too rapidly with increasing distance to match the measured X-ray profiles. Our model-inferred B₀ ≈ 5 μG is comparable to those inferred from a one-zone (3–4 μG; Kishishita et al. 2012; Zhu et al. 2018) or a two-zone model (8 μG; Van Etten & Romani 2010). We further found that the magnetic index α_B is also small (−0.06), meaning that B in the PWN does not vary much spatially. The particle motion is mainly driven by the bulk motion V_flow, and for the assumed age of 9 kyr, V₀ = 0.14c and α_V = − 0.94 (V ∼ 1/r) are sufficient to carry the particles to the outer boundary of the PWN. These model parameters as well as the hard X-ray emission of K3 suggest that electrons are accelerated to very high energies (≈1 PeV) in the system.

The inferred parameters for the K3 PWN are generally similar to those for the middle-aged Rabbit PWN associated with PSR J1418−6058, which has a similar τ_c (10 kyr) to J1420's, but the diffusion coefficients D₀ differ by an order of magnitude because their observed radial profiles of Γ are very different (Park et al. submitted). X-ray spectral softening was insignificant in the Rabbit PWN, and thus a large value of D₀ was required by the model to homogenize the effects of synchrotron cooling. An alternative explanation for the lack of softening, negligible diffusion, required an unreasonably low value of B to avoid a sharp spectral cutoff before the edge of the nebula (see below). For the D₀ values inferred for the two PWNe, the primary particle transport mechanisms were also inferred to differ: advection-dominant for K3 and diffusion-dominant for Rabbit. However, it should be noted that, for the highest-energy particles (γ_e ≈ 10⁹), the effect of diffusion is comparable to that of advection even in K3. While the parameters inferred by our phenomenological model may not be accurate, the distinctions (i.e., Γ profiles) observed between the two PWNe convincingly suggest that their diffusion properties differ. This may be related to the evolution of the PWNe and their interaction with the putative supernova remnants and/or the ambient medium. These need to be investigated with more physically motivated evolution models.

Although the particle transport in K3 is dominated by advection, the mild and steady increase of Γ with distance is different from those expected in purely advective flows. In these cases, all the particles at a certain radius have the same age (cooling time). Thus, in inner regions, where the cooling break is above X-ray energies, the synchrotron spectral index in the X-ray band does not change radially. As the particles propagate outward in the later evolutionary stage, the cooling break moves to lower energies, eventually to X-rays. From that radius, the X-ray spectrum softens rapidly with increasing radius (age). This trend is almost universally observed in 1D pure-advection models (e.g., Reynolds 2003). Such a trend can turn into a steadily increasing one (observed in K3) if particles of different ages can mix. This can be achieved by non-radial backflows that bring older (outer) particles back into the inner regions and/or by diffusion. Although the former may play a role in K3 (e.g., in the southern region), the details of the backflows are not well-known—and thus they are difficult to incorporate into our spherically symmetric model. Hence, we relied on particle diffusion in this work. For the X-ray emitting electrons, the diffusion length scale in K3 was estimated to be ∼5 pc (or longer for the highest-energy electrons), which is sufficient to mix particles of various ages (say, 12 pc for advection). Note that Tang & Chevalier (2012) demonstrated that Γ profiles flatten at large distances in models with reflecting outer boundary conditions probably by producing backflows, whereas Γ steadily increases with distance in the absence of the backflow (i.e., transmitting outer boundary). The Suzaku measurement of the Γ profile of K3 seems to exhibit a flattening (Figure 5), but a better measurement with finer radial bins is needed to confirm it.

Our model predicts a cooling break at γ_e ≈ 10⁷. Because particles with that Lorentz factor emit ICS radiation at ≈1 TeV, spatial variations of emission below (i.e., LAT band) and above it (i.e., H.E.S.S. band) are expected to be substantially different, as is demonstrated in Figure 8, which displays model-predicted VHE SEDs and effective photon indices in the LAT and H.E.S.S. bands. It should be noted that this is only for demonstration, and the actual uncertainties on the spatially resolved SED points would vary depending on the instrument and exposure. The slope of the LAT SED does not vary spatially, because the <1 TeV emission is produced by uncooled electrons, whereas the cooling effect is clearly visible in the TeV band. Our model predicts a significant spectral softening in the H.E.S.S. band at a level similar to that seen in the X-ray band (Figure 5(c)). This can be tested with deeper VHE observations of the source (e.g., by CTA; Actis et al. 2011).

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