HIGH SPATIAL RESOLUTION X-RAY SPECTROSCOPY OF THE IC 443 PULSAR WIND NEBULA AND ENVIRONS

J0617 was observed with the Chandra X-ray Observatory ACIS on 2012 February 6 (ObsID 13736) for ∼107.6 ks and again on 2012 February 8 (ObsID 14385) for 44.5 ks. Both observations used an identical instrument configuration which placed J0617 near the back-illuminated CCD (S3) aimpoint. The observations were taken in full-frame timed exposure mode using the standard 3.2 s frame time and the VFAINT telemetry format.

The data were reprocessed using the Chandra X-ray Center script acis_process_events (CIAO v. 4.5) to apply the latest time-dependent gain correction (CalDB 4.5.5) and to flag potential cosmic-ray background events. Only events imaged on the back-illuminated CCD S3 are used in this work. Point-like X-ray sources in the field were identified using the source-finding utility in the lextrct image-analysis program (Tennant 2006). The locations of sources identified in the two event lists were compared and were found to be in sufficient agreement for most purposes so that the two event lists were simply combined using the FTOOLS utility fmerge to produce a 152 ks duration final event list. In addition, a sub-pixel image was created by rebinning the events to one-half of the nominal (0492) ACIS pixel size in order to examine the finer details of the X-ray morphology in the immediate vicinity of J0617 (Section 3.1.2).

Spectral fitting reported here uses the XSPEC, v. 11.3.2g, spectral-fitting package (Arnaud 1996). Spectral redistribution matrices and ancillary response functions were generated using the CIAO tools mkacisrmf, mkarf, and mkwarf. Spectral analysis is confined to events within the 0.5–8.0 keV energy range. The energy range spans only 0.5–5.0 keV in those cases where a soft thermal-dominated spectrum produces a negligible number of high-energy source counts as is the case outside the PWN region.

The X-ray surface brightness and X-ray color or hardness ratio vary noticeably across the ∼8' × 8' S3 field of view. The "contour binning" method of Sanders (2006) was therefore applied to the merged data set in order to map the physical properties, deduced from spectral model fitting, in the regions containing J0617, its PWN, and portions of the surrounding diffuse thermal plasma. The contour binning method defines spatial bins (for spectral analysis) which cover contiguous regions of similar surface brightness and is motivated by the fact that surface brightness variations often follow changes in physical properties, such as those at shock fronts, in the X-ray-emitting medium.

For this purpose, the identified point sources were first removed from an image constructed from the merged event list and back-filled with a sampling of the adjacent background using the CIAO tools roi and dmfilth following the diffuse emission science thread.¹³ The resulting image was then accumulatively smoothed using a signal-to-noise ratio threshold of 30 and contour-binned using a signal-to-noise threshold of 100 using the accumulate_smooth and contbin utilities, respectively, from Sanders (2006).

An earlier observation of J0617 (ObsID 05531), taken 2005 January 12 using a similar instrument configuration, is used in analysis of the proper motion of J0617 (Section 3.1.1).

The analysis presented here also makes use of Hα and [O iii] images obtained 2012 November 23 using the Astronomical Research Cameras¹⁴ E2V 230-42 CCD (∼0493 pixel⁻¹) mounted on the 0.9 m Southeastern Association for Research in Astronomy telescope at Kitt Peak Observatory. Seeing conditions were ≲2''. Contemporaneous R and V images were used for continuum subtraction from Hα and [O iii], respectively. The continuum-subtracted images were registered to the X-ray data using 2MASS objects common to both wavelengths.

Archival observations of IC 443 at 330 MHz, 4.8, and 8.4 GHz, obtained with the Very Large Array (VLA),¹⁵ were also analyzed and compared to the X-ray data. All data were calibrated and reduced using the Astronomical Image Processing System (AIPS) data reduction package.¹⁶

Multiple 330 MHz observations were carried out from 2005 to 2007 using several VLA configurations (Castelletti et al. 2011) so that the final combined image is sensitive to a wide range of spatial structures from ∼6'' up to ∼70' and therefore samples both the PWN and the surrounding extended IC 443 SNR. See Castelletti et al. (2011) for further details of the 330 MHz observations and data reduction. The final combined image has an angular resolution of 17'' and a background noise level of 1.7 mJy beam⁻¹ after correcting for primary beam attenuations. The average SNR contribution in the region surrounding J0617 is 15 mJy beam⁻¹.

The 4.8 GHz observation was taken in the C configuration on 1997 August 26 and the 8.4 GHz observation in D configuration on 1997 December 31. The 4.8 GHz observation was taken with two 50 MHz tunings centered at 4.8851 and 4.8351 GHz and the 8.4 GHz observation was taken in two 50 MHz bands centered at 8.4351 and 8.4851 GHz. Both observations used 3C 138 as the flux calibrator and 0632+103 as a phase calibrator. These observations were first analyzed by Olbert et al. (2001). These data are only sensitive to structures on scales up to a little over $2\prime$ and thus are not able to sample the emission over the entire nebula as is possible at 330 MHz. Here, they were re-calibrated and reduced using standard data reduction techniques applied within AIPS. The data were self-calibrated in two rounds of phase-only calibration. The final, full resolution, 4.8 GHz image rms is 0.18 mJy beam⁻¹ with a beam size of ∼55 × 38 and the 8.4 GHz image rms is 0.076 mJy beam⁻¹ with a beam size of ∼81 × 71.

The deep Chandra image (Figure 1) reveals J0617 as the brightest point-like object in the field surrounded by a high-surface-brightness nearly circular ring. There are two "spokes" apparently connecting J0617 to the ring oriented roughly north–south which are possibly pulsar jets. Exterior to the ring is a comet-shaped nebula with its major axis oriented ∼50° east of north and with its apparent forward direction to the southwest. The cometary nebula has a hard X-ray spectrum as was noted by Olbert et al. (2001) and Gaensler et al. (2006). Predominantly soft X-ray emission surrounds the roughly 2' × 15 cometary nebula and extends throughout the S3 field of view (along with a few faint unrelated point-like sources). The surface brightness of this extended emission is spatially non-uniform varying by factors of 4–5 over spatial scales of order 1'. As shown by spectral analysis (Section 3.2), this extended diffuse emission is primarily thermal in nature whereas the cometary nebula, ring, and related features are dominated by hard non-thermal spectra.

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Analysis of these features is discussed in greater detail in the following subsections beginning with an estimate of the proper motion of J0617.

3.1.1. Constraints on the Proper Motion of CXOU J061705.3+222127

3.1.2. J0617, the Jet, and the Ring: Subpixel Imaging

Figure 1 displays the 2.0–4.0 keV subpixel-sampled region around J0617 including the ring-like and jet-like structures. This energy range best distinguishes the ring from other features and mutes the contribution from J0617 which is brightest at lower energies (Section 3.2.2). Figure 2 shows the broad-band surface brightness radial profile centered on the position of J0617, extending to 123, and including only azimuthal angles between PA 200° and 340° ($\pm 70^\circ$ of west) in order to avoid contributions from the jet-like features. This profile was obtained from the 1/2 pixel sampled image. Also shown is a model point-spread function for a monochromatic source at 2.5 keV generated using the Chandra Ray Tracer and MARX simulation tools. The ring appears as the peak at 48 with a (Gaussian) width of 12. These parameters were estimated by fitting the surface brightness profile with a combined power law plus Gaussian function. Another peak in the radial profile appears between J0617 and the ring. This feature is about 1'' from J0617 but adding an additional Gaussian component shows this feature is not statistically significant.

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The jet-like feature spans from the position of the pulsar northward and southward until it appears to intersect the ring. The ring brightens at these intersections. These intersections were described as compact emission components by Gaensler et al. (2006). The southern jet feature has a surface brightness about 75% higher than the northern jet in the 0.5–8.0 keV energy range.

The center of the ring is not coincident with the location of J0617. A spatial model representing an annulus was fit to the sub-pixel X-ray image in the 2–4 keV energy range after ignoring data within a 25 radius of the center of the ring (due to the brightness of the pulsar) and smoothing the data slightly (Figure 3). The model consists of two elliptical Gaussians plus a constant where one Gaussian has a positive amplitude and the other a negative amplitude in order to approximate an elliptical annulus. The location of the centroid of the ring model is 06^h17^m05166 + 22°21'2880. This location is offset by 27 (0.06 ${d}_{1.5}$ ly) from J0617 at PA ∼ 340°, i.e., the pulsar is roughly SSE of the ring center. The ring is close to circular. The best-fitting parameters result in an aspect ratio of 0.86 ± 0.05 and an angular eccentricity, ${\mathrm{cos}}^{-1}(b/a)=30\buildrel{\circ}\over{.} 7\pm 5\buildrel{\circ}\over{.} 6$ where a and b are the major and minor Gaussian widths. The PA is 84° ± 3°; the ellipse major axis is nearly in the east–west direction.

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3.1.3. Morphology of the PWN

Figure 4 displays the 0.5–8.0 keV brightness profile along the major axis (PA 50°) of the comet-shaped PWN. The profile has been averaged over a ±30'' region perpendicular to this axis. The peak of the profile coincides with the pulsar and offsets upstream of the pulsar (toward the southwest) are taken as positive in this figure. The ring is clearly visible as secondary peaks on either side of the pulsar. The profile >5'' upstream of the pulsar decreases smoothly out to at least 2' from J0617 without any discernable structural features. As with the upstream profile, the downstream profile first declines steeply from the exterior of the ring but then it reaches a broad peak extending from 15'' to 25'' away from the pulsar. The profile then declines more slowly out to approximately 2' downstream without any additional features.

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The X-ray image does show that the surface brightness distribution upstream of the pulsar is bow-shaped. Parabolas were fit, by visual inspection, to the surface brightness contours in the upstream region of a smoothed image (with the ordinate axis of the parabolas constrained to be parallel to PA 50°) as shown in Figure 5. The parabolas are of the form ${(y{/d}_{s})=0.54(x{/d}_{s})}^{2}+1$ where d_s is the distance from the location of J0617 (at the focus) to the vertex of the parabola.

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There is no evidence for a bow shock in either the Hα or [O iii] images of this region and there is little or no correlation between the X-ray emission in the upstream direction with the optical line emission. However, as a close-up image of the region shows (Figure 6), there is Hα emission coincident with the jet-like X-ray feature. This is likely an accidental coincidence as there are many similar Hα features throughout the IC 443 SNR. Similarly, there is also a well-defined Hα wisp downstream of J0617 that runs roughly along the major axis of the PWN and thins in the downstream direction (Figure 7). This feature is also visible in the [O iii] image. There is no X-ray feature correlated with this wisp. Although its location is suggestive, it is unclear if this Hα wisp is related to the PWN as there are numerous wisps with similar morphology throughout the region that are obviously not related to the PWN proper.

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3.2.1. Regions Exterior to the PWN: Background SNR

Customarily, a background region is selected from those regions remote from the primary source, in this case the PWN, in order to isolate the source spectrum for analysis. However, J0617 is located along the line of sight through the extended X-ray emission associated with the SNR IC 443 and this emission is highly non-uniform as noted above. Several regions were visually selected and analyzed to quantify the spectral properties of this "background" throughout the field of view of the S3 chip. These regions are numbered 1 through 9 in Figure 8 and their spectra are shown in Figure 9. Assuming this emission is from hot plasma within the SNR, the observed variations may be due to a combination of different plasma temperatures, emission measures, elemental abundances, and intervening absorption. The simplest model that can account for all these variables in XSPEC is an absorbed optically thin thermal plasma model. The spectral analysis reported in this section is limited to the range 0.5–5.0 keV because of the paucity of source photons above 5 keV.

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It was found that the spectra of these "outlier" regions cannot be fit satisfactorily with a single-component absorbed (XSPEC model phabs) variable-abundance thermal emission (vmekal) model. A significant improvement could be made by adding either a second thermal component or a power-law (powlaw) component.

Resulting best-fit model parameters are listed in Table 1 for these outlier fields. These include the absorption column density, ${n}_{{\rm{H}}}$, the power-law index, Γ, the thermal component temperature, kT, the model component normalizations, K¹⁷ , the 0.5–5.0 keV flux, f, in erg cm⁻² s⁻¹ (uncorrected for absorption) and the ${\chi }^{2}$ fit statistic and number of degrees of freedom, dof. Here and elsewhere errors are 90% confidence extremes for a single interesting parameter unless otherwise noted.

Table 1.  Outlier Regions Spectral Fit Parameters

Regiona	1	2	3	4	5	6	7	8	9
Area (arcmin2)	4.75	1.96	1.53	3.80	2.95	4.23	5.07	2.02	3.03
Absorbed (Power Law + Variable MeKaL)b
${n}_{{\rm{H}}}/{10}^{22}$ (cm2)	${0.49}_{-0.05}^{+0.03}$	${0.37}_{-0.04}^{+0.03}$	${0.64}_{-0.12}^{+0.05}$	${0.51}_{-0.03}^{+0.04}$	${0.48}_{-0.07}^{+0.04}$	${0.48}_{-0.04}^{+0.03}$	${0.58}_{-0.06}^{+0.06}$	${0.48}_{-0.05}^{+0.09}$	${0.45}_{-0.03}^{+0.03}$
Γ	${2.99}_{-0.62}^{+0.33}$	${4.14}_{-0.77}^{+1.03}$	${3.52}_{-0.60}^{+0.60}$	${3.91}_{-0.30}^{+0.51}$	${3.52}_{-1.18}^{+0.68}$	${3.50}_{-0.36}^{+0.30}$	${2.17}_{-0.11}^{+0.10}$	${1.95}_{-0.09}^{+0.10}$	${2.26}_{-0.17}^{+0.12}$
kT (keV)	${0.69}_{-0.02}^{+0.02}$	${0.70}_{-0.01}^{+0.03}$	${0.79}_{-0.16}^{+0.05}$	${0.69}_{-0.02}^{+0.02}$	${0.68}_{-0.02}^{+0.03}$	${0.66}_{-0.02}^{+0.02}$	${0.68}_{-0.02}^{+0.03}$	${0.78}_{-0.06}^{+0.06}$	${0.68}_{-0.02}^{+0.02}$
${K}_{\mathrm{POW}}/{10}^{-4}$	${1.41}_{-0.92}^{+0.99}$	${0.04}_{-0.04}^{+0.04}$	${1.30}_{-0.96}^{+0.73}$	${2.66}_{-0.96}^{+1.51}$	${0.85}_{-0.80}^{+0.63}$	${1.71}_{-0.95}^{+0.63}$	${3.34}_{-0.45}^{+0.48}$	${2.06}_{-0.26}^{+0.27}$	${2.45}_{-0.51}^{+0.42}$
${K}_{\mathrm{THM}}/{10}^{-4}$	${12.10}_{-2.48}^{+5.11}$	${8.20}_{-2.19}^{+3.26}$	${3.26}_{-2.28}^{+3.52}$	${8.34}_{-3.71}^{+3.38}$	${3.01}_{-1.16}^{+1.64}$	${3.57}_{-0.23}^{+3.01}$	${2.88}_{-0.35}^{+1.09}$	${0.87}_{-0.15}^{+2.47}$	${4.16}_{-0.51}^{+8.03}$
${f}_{\mathrm{POW}}/{10}^{-13}$ (erg cm−2 s−1)	1.60	0.30	0.88	1.75	0.70	1.42	7.58	6.23	5.43
${f}_{\mathrm{THM}}/{10}^{-13}$ (erg cm−2 s−1)	8.59	6.74	1.57	6.43	2.68	4.31	3.18	1.04	5.32
${\chi }^{2}$/dof	356.6/238	251.0/180	176.6/161	346.4/222	314.2/188	359.7/220	507.0/278	307.9/259	381.9/262
Absorbed (Variable MeKaL + Variable MeKaL)c
${n}_{{\rm{H}}}/{10}^{22}$ (cm2)	${0.47}_{-0.05}^{+0.04}$	${0.33}_{-0.03}^{+0.03}$	${0.53}_{-0.10}^{+0.15}$	${0.47}_{-0.05}^{+0.07}$	${0.45}_{-0.09}^{+0.08}$	${0.48}_{-0.06}^{+0.06}$	${0.56}_{-0.06}^{+0.05}$	${0.49}_{-0.08}^{+0.09}$	${0.46}_{-0.04}^{+0.04}$
kT1 (keV)	${0.60}_{-0.04}^{+0.04}$	${0.65}_{-0.03}^{+0.03}$	${0.50}_{-0.07}^{+0.07}$	${0.60}_{-0.04}^{+0.04}$	${0.56}_{-0.08}^{+0.08}$	${0.55}_{-0.04}^{+0.05}$	${0.64}_{-0.02}^{+0.02}$	${0.64}_{-0.05}^{+0.05}$	${0.67}_{-0.02}^{+0.02}$
kT2 (keV)	${0.78}_{-0.02}^{+0.02}$	${0.74}_{-0.02}^{+0.15}$	${1.02}_{-0.09}^{+0.26}$	${0.80}_{-0.05}^{+0.11}$	${0.77}_{-0.05}^{+0.11}$	${0.82}_{-0.05}^{+0.09}$	${3.55}_{-0.30}^{+0.36}$	${4.72}_{-0.50}^{+0.78}$	${3.75}_{-0.51}^{+1.00}$
${K}_{1}/{10}^{-4}$	${3.19}_{-0.29}^{+3.18}$	${2.68}_{-0.57}^{+6.32}$	${4.27}_{-2.56}^{+2.65}$	${7.44}_{-4.07}^{+6.40}$	${1.72}_{-1.08}^{+1.57}$	${3.60}_{-1.38}^{+3.07}$	${6.81}_{-1.77}^{+1.95}$	${2.98}_{-0.89}^{+1.07}$	${7.39}_{-1.85}^{+4.43}$
${K}_{2}/{10}^{-4}$	${16.86}_{-9.10}^{+6.05}$	${9.13}_{-7.19}^{+2.60}$	${6.69}_{-2.44}^{+1.56}$	${12.19}_{-7.16}^{+4.94}$	${6.18}_{-3.37}^{+3.37}$	${6.60}_{-3.09}^{+1.94}$	${7.10}_{-1.33}^{+1.06}$	${5.68}_{-1.01}^{+0.50}$	${4.01}_{-0.87}^{+1.09}$
${f}_{1}/{10}^{-13}$ (erg cm−2 s−1)	2.52	2.39	0.70	3.37	0.88	2.32	3.43	1.22	5.97
${f}_{2}/{10}^{-13}$ (erg cm−2 s−1)	7.41	4.37	1.70	4.73	2.43	3.28	7.09	5.87	4.79
${\chi }^{2}$/dof	323.1/238	239.7/180	150.1/161	327.3/222	305.3/188	317.5/220	414.5/278	280.1/259	374.4/262

Notes.

^aNumbers correspond to the numbered regions shown in Figure 8. ^bAbundances tied to solar ratios for the groups CNO, Ne and Mg, Si and S, and Fe and Ni. ^cSame as (b) and abundances of second MeKaL model tied to those of first model.

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The first thermal component temperature is typically kT ∼ 0.5–0.8 keV. It was found that the second component usually had a steep power-law slope (photon index ${\rm{\Gamma }}\gtrsim 2.5$) or only a slightly higher temperature (kT ∼ 0.8–1.0 keV) suggesting that this component may represent the range of thermal emission temperatures expected along a given line of sight through the SNR rather than a true non-thermal component typically indicated by a power-law shape. This is true of most of these outlier regions except regions 7–9 where ${\rm{\Gamma }}\lt 2.3$ (or ${{kT}}_{2}\gt 3.5$ keV). In these cases, it is likely that there is truly a hard non-thermal component even if the two-kT model is formally a better fit as such high temperatures are atypical of SNR spectra. The PWN likely contributes this non-thermal emission component in regions 8 and 9 because they are immediately adjacent to the high-surface-brightness PWN.

The elemental abundances were not well constrained in any of these models but strong emission lines of H-like O and Ne, and He-like blends of Ne, Mg, Si, S are present throughout as shown in Figure 9 whereas Fe emission is weak. This is indicative of a Type II core collapse SN origin.

Overall, since the spatial scale of the observed brightness variations are of order 1', and the spectra of the different regions sampled also vary, none of these regions (nor any other region on S3) can be safely defined as a background to be used in fitting spectra of the PWN. Thus, the "blank sky" background¹⁸ appropriate to this observation is the only background used in subsequent spectral analysis with the exception of the pulsar, J0617, and the jet-like and ring features. For these objects, the space between the pulsar and ring is relatively faint and local backgrounds were chosen from this region.

3.2.2. Spectra and Timing of CXOU J061705.3+222127

The spectrum of J0617 was extracted from a 2 pixel (0984) radius circle centered at the location of the pulsar (see also Figure 2). A nearby background was obtained by combining data from five 2 pixel radius circles located interior to the ring and excluding the jet-like features. This results in an estimated 925 ± 35 net source counts in the 0.5–8.0 keV energy range. Absorbed blackbody and neutron star atmosphere (Pavlov et al. 1995; Zavlin 2009) models (plus a power-law component) were fit to the spectrum over the 0.5–8.0 keV energy range after grouping to ensure a minimum of 20 background-subtracted events per spectral energy bin. The spectrum, models, and fit residuals are shown in Figure 10. The neutron star atmosphere model assumed a distance to the star of 1.5 kpc, a radius ${R}_{\mathrm{NS}}=10$ km, a mass ${M}_{\mathrm{NS}}=1.4$ ${M}_{\odot }$ (corresponding to a gravitational redshift parameter ${g}_{r}\equiv {[1-2{{GM}}_{\mathrm{NS}}/({R}_{\mathrm{NS}}{c}^{2})]}^{1/2}=0.766$) and a magnetic field strength of 10¹³ G. The best-fitting model parameters, derived properties, and fit statistics are listed in Table 2, where ${T}^{\infty }$ and ${R}^{\infty }$ are the effective temperature and radius as measured by a distant observer, and ${L}_{{\rm{\Gamma }}}$ is the 0.5–8.0 keV luminosity of the non-thermal (power-law) component. Errors in Table 2 are at the 1σ (68%) confidence level. Both models provided acceptable fits to the data. These spectral properties are typical for a cooling neutron star although the blackbody model radius, ${R}^{\infty }=1.63$ km, implies emission from a small hotspot rather than the entire neutron star surface. They indicate a bolometric luminosity of (1–3) × 10³² erg s⁻¹.

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Table 2.  Spectral Fit Parameters and Derived Quantities for CXOU J061705.3+222127

Model	${n}_{{\rm{H}}}$	${T}^{\infty }$	${R}^{\infty }$	${L}_{\mathrm{bol}}^{\infty }$	Γ	${L}_{{\rm{\Gamma }}}$	${\chi }^{2}/\mathrm{dof}$
	(1022 cm−2)	(eV)	(km)	(1032 erg s−1)		(1031 erg s−1)
NSA	${0.63}_{-0.03}^{+0.02}$	${58.4}_{-0.4}^{+0.6}$	13.05	2.6 ± 0.1	${1.34}_{-0.35}^{+0.31}$	${1.0}_{-0.5}^{+1.4}$	42.2/42
BB	${0.61}_{-0.09}^{+0.13}$	${132.0}_{-7.0}^{+8.8}$	${1.63}_{-0.07}^{+0.09}$	${1.0}_{-0.1}^{+0.2}$	${2.00}_{-0.20}^{+0.30}$	${1.4}_{-0.5}^{+0.6}$	41.7/41

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A search for a possible periodicity in the X-ray flux from J0617 was restricted to periods $P\gt 6.5$ s due to the 3.24 s time resolution of the ACIS instrumental setup. The Rayleigh test yielded a maximum power at a period of 31.18 s. Applying the appropriate probability distribution (Groth 1975) sets an upper limit to the power at 99% confidence that translates to an upper limit on the pulsed fraction of 36% assuming a sine-wave signal and accounting for the background.

3.2.3. Spectra of the Jet and Ring

3.2.4. Spectra Upstream of the PWN

Spectra were extracted from a series of regions located upstream of the pulsar to search for a spectral transition between the non-thermal shocked PWN emission and thermal emission from shocked ambient medium further upstream. Figure 8 shows the locations of these regions. They are 40 × 100 pixel² (0.269 arcmin²) rectangles oriented with the long side perpendicular to the line of apparent motion of the pulsar. Table 3 presents the spectral fitting results for these regions (ordered left to right by increasing distance from J0617). As with the outlier regions discussed in Section 3.2.1, absorbed two-component models were applied. Both models provide similarly acceptable fits although the thermal plus power law is formally the superior model. With the exception of the region nearest to J0617, the temperature of the soft thermal component in all cases, ${kT}\sim 0.6-0.7$ keV, is consistent with the soft component deduced for the outlier regions of Section 3.2.1. Most regions have an obvious hard component (${\rm{\Gamma }}\lesssim 2.3$ or ${{kT}}_{2}\gt 3.5$ keV) that is poorly modeled by a second thermal component. For the non-thermal power-law (plus soft thermal) models, the trend is for the power-law index to steepen and both the power-law flux and its fraction of the total flux to decrease with distance from J0617. This is certainly true of the innermost three regions although the trend is less evident in the outer three regions where the power-law component is much weaker though still required in the modeling. While there is no abrupt spectral transition from non-thermal- to thermal-dominated emission, a non-thermal component is clearly present at least out to 2' upstream from J0617, which is consistent with the smoothly varying surface brightness distribution of this upstream region (cf. Figure 4 and Section 3.1.3).

Table 3.  Upstream Spectral Fit Parameters

Regiona	1	2	3	4	5	6
Absorbed (Power Law + Variable MeKaL)b
${n}_{{\rm{H}}}/{10}^{22}$ (cm2)	${0.61}_{-0.08}^{+0.09}$	${0.40}_{-0.04}^{+0.06}$	${0.40}_{-0.05}^{+0.06}$	${0.40}_{-0.05}^{+0.05}$	${0.40}_{-0.06}^{+0.08}$	${0.37}_{-0.05}^{+0.06}$
Γ	${2.08}_{-0.15}^{+0.15}$	${2.13}_{-0.24}^{+0.23}$	${2.19}_{-0.28}^{+0.27}$	${2.59}_{-0.38}^{+0.39}$	${2.41}_{-0.47}^{+0.44}$	${2.43}_{-0.42}^{+0.41}$
kT (keV)	${0.39}_{-0.05}^{+0.10}$	${0.70}_{-0.09}^{+0.06}$	${0.67}_{-0.10}^{+0.07}$	${0.72}_{-0.04}^{+0.12}$	${0.68}_{-0.08}^{+0.07}$	${0.71}_{-0.09}^{+0.10}$
${K}_{\mathrm{POW}}/{10}^{-5}$	${6.50}_{-0.98}^{+1.15}$	${3.01}_{-0.71}^{+0.87}$	${2.45}_{-0.66}^{+0.82}$	${2.39}_{-0.78}^{+1.01}$	${1.59}_{-0.66}^{+0.89}$	${1.62}_{-0.61}^{+0.79}$
${K}_{\mathrm{THM}}/{10}^{-5}$	${7.12}_{-2.53}^{+3.76}$	${3.79}_{-0.79}^{+0.93}$	${2.91}_{-0.70}^{+0.79}$	${2.75}_{-0.64}^{+0.71}$	${3.32}_{-0.71}^{+0.81}$	${2.65}_{-0.59}^{+0.68}$
${f}_{\mathrm{POW}}/{10}^{-13}$ (erg cm−2 s−1)	1.60	0.78	0.60	0.41	0.32	0.32
${f}_{\mathrm{THM}}/{10}^{-13}$ (erg cm−2 s−1)	0.26	0.31	0.23	0.22	0.26	0.23
${\chi }^{2}$/dof	135.5/146	120.1/116	111.7/ 99	97.8/ 90	58.6/ 84	66.5/ 80
Absorbed (Variable MeKaL + Variable MeKaL)c
${n}_{{\rm{H}}}/{10}^{22}$ (cm2)	${0.63}_{-0.09}^{+0.10}$	${0.71}_{-0.13}^{+0.10}$	${0.79}_{-0.11}^{+0.14}$	${0.37}_{-0.04}^{+0.06}$	${0.40}_{-0.06}^{+0.06}$	${0.36}_{-0.05}^{+0.07}$
kT1 (keV)	${0.38}_{-0.05}^{+0.06}$	${0.32}_{-0.03}^{+0.07}$	${0.29}_{-0.05}^{+0.04}$	${0.71}_{-0.03}^{+0.05}$	${0.67}_{-0.07}^{+0.06}$	${0.70}_{-0.09}^{+0.07}$
kT2 (keV)	${4.16}_{-0.70}^{+1.04}$	${2.55}_{-0.39}^{+0.51}$	${2.40}_{-0.38}^{+0.56}$	${3.37}_{-1.09}^{+1.43}$	${4.37}_{-1.67}^{+8.06}$	${3.63}_{-1.23}^{+3.23}$
${K}_{1}/{10}^{-4}$	${0.90}_{-0.31}^{+0.54}$	${1.31}_{-0.59}^{+0.81}$	${1.65}_{-0.71}^{+2.24}$	${0.33}_{-0.04}^{+0.07}$	${0.39}_{-0.07}^{+0.08}$	${0.30}_{-0.07}^{+0.07}$
${K}_{2}/{10}^{-4}$	${1.36}_{-0.10}^{+0.11}$	${0.87}_{-0.10}^{+0.08}$	${0.69}_{-0.07}^{+0.08}$	${0.31}_{-0.05}^{+0.08}$	${0.23}_{-0.06}^{+0.07}$	${0.24}_{-0.06}^{+0.07}$
${f}_{1}/{10}^{-13}$ (erg cm−2 s−1)	0.31	0.30	0.24	0.28	0.31	0.26
${f}_{2}/{10}^{-13}$ (erg cm−2 s−1)	1.54	0.74	0.55	0.36	0.29	0.29
${\chi }^{2}$/dof	144.1/146	134.0/116	115.2/ 99	107.9/ 90	65.5/ 84	72.3/ 80

Notes.

^aRegions upstream (southwest) of J0617 (see Figure 8), numbered by increasing distance from J0617. ^bAbundances fixed to those of Outlier region 6 (see Table 1). ^cSame as (b) and abundances of second MeKaL model tied to those of first model.

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3.2.5. Spectra of the PWN: Contour Binning

The contour binning method of Sanders (2006) was applied to a region containing the pulsar, PWN, and immediate surroundings as described in Section 2. By definition, this binning method traces the decrease in surface brightness with distance from J0617. Using this prescription, the PWN is subdivided into roughly concentric "annuli" with the innermost region containing J0617, the ring and the jet. The outermost of these regions is indicated in Figure 8 by the thick irregular contour surrounding J0617. By design, each region contains roughly 10⁴ X-ray events. Because the extended thermal emission from the IC 443 SNR is so spatially non-uniform, the contour binning method did not satisfactorily bin the regions beyond the PWN.

The results of model fits to the spectra of these regions are given in Table 4 (a 3 pixel (148) radius circle centered on J0617 was excluded from the innermost region, denoted Region 1 for spectral analysis; regions 2 through 7 lie sequentially ourward). In addition to model parameters and derived properties listed previously (Tables 1 and 3), Table 4 includes fluxes, ${f}^{\mathrm{cor}}$, corrected for absorption along the line of sight. The spectra were fit on the extended 0.5–8.0 keV energy range and fluxes listed in Table 4 are over this same interval.

Table 4.  Pulsar Wind Nebula Spectral Fit Parameters

Regiona	1	2	3	4	5	6	7
Area (arcmin2)	0.048	0.091	0.157	0.266	0.365	0.531	0.722
Absorbed Power Law
${n}_{{\rm{H}}}/{10}^{22}$ (cm2)	${0.56}_{-0.04}^{+0.04}$	${0.53}_{-0.03}^{+0.03}$	${0.56}_{-0.03}^{+0.04}$	${0.52}_{-0.03}^{+0.03}$	${0.51}_{-0.03}^{+0.03}$	${0.47}_{-0.03}^{+0.03}$	${0.41}_{-0.02}^{+0.02}$
Γ	${1.50}_{-0.03}^{+0.06}$	${1.54}_{-0.05}^{+0.06}$	${1.69}_{-0.03}^{+0.06}$	${1.78}_{-0.06}^{+0.06}$	${1.91}_{-0.06}^{+0.06}$	${2.06}_{-0.06}^{+0.06}$	${2.28}_{-0.07}^{+0.07}$
${K}_{\mathrm{POW}}/{10}^{-4}$	${1.35}_{-0.09}^{+0.10}$	${1.54}_{-0.10}^{+0.11}$	${1.79}_{-0.11}^{+0.13}$	${1.84}_{-0.12}^{+0.12}$	${1.98}_{-0.13}^{+0.14}$	${2.02}_{-0.13}^{+0.14}$	${2.08}_{-0.13}^{+0.14}$
${f}_{\mathrm{POW}}/{10}^{-13}$ (erg cm−2 s−1)	6.84	7.56	7.20	6.72	6.20	5.42	4.61
${f}_{\mathrm{POW}}^{\mathrm{cor}}/{10}^{-13}$ (erg cm−2 s−1)	9.14	10.11	10.21	9.71	9.40	8.61	7.78
${\chi }^{2}$/dof	289.2/293	336.7/302	278.9/295	326.5/285	294.4/282	353.2/274	375.6/254
Absorbed (Power Law + Variable MeKaL)b
${n}_{{\rm{H}}}/{10}^{22}$ (cm2)	${0.64}_{-0.07}^{+0.35}$	${0.67}_{-0.16}^{+0.25}$	${0.75}_{-0.11}^{+0.28}$	${0.77}_{-0.15}^{+0.18}$	${0.67}_{-0.10}^{+0.18}$	${0.60}_{-0.09}^{+0.15}$	${0.47}_{-0.07}^{+0.09}$
Γ	${1.55}_{-0.04}^{+0.09}$	${1.53}_{-0.03}^{+0.03}$	${1.77}_{-0.13}^{+0.14}$	${1.89}_{-0.11}^{+0.05}$	${1.95}_{-0.09}^{+0.12}$	${2.03}_{-0.09}^{+0.12}$	${1.97}_{-0.09}^{+0.10}$
kT (keV)	${0.11}_{-0.03}^{+0.15}$	${0.36}_{-0.28}^{+0.06}$	${0.36}_{-0.10}^{+5.12}$	${0.32}_{-0.04}^{+0.09}$	${0.29}_{-0.05}^{+0.04}$	${0.37}_{-0.06}^{+0.03}$	${0.67}_{-0.06}^{+0.11}$
${K}_{\mathrm{POW}}/{10}^{-4}$	${1.46}_{-0.13}^{+0.31}$	${1.49}_{-0.47}^{+0.47}$	${2.05}_{-0.37}^{+0.45}$	${2.20}_{-0.33}^{+0.36}$	${2.14}_{-0.71}^{+0.36}$	${1.98}_{-0.23}^{+0.33}$	${1.41}_{-0.16}^{+0.47}$
${K}_{\mathrm{THM}}/{10}^{-4}$	${69.94}_{-69.89}^{+3837.17}$	${1.02}_{-1.02}^{+6.70}$	${0.35}_{-0.27}^{+4.52}$	${0.79}_{-0.48}^{+7.59}$	${1.89}_{-1.37}^{+8.93}$	${0.69}_{-0.24}^{+3.03}$	${0.61}_{-0.12}^{+1.14}$
${f}_{\mathrm{POW}}/{10}^{-13}$ (erg cm−2 s−1)	6.81	7.56	6.99	6.44	5.98	5.20	4.10
${f}_{\mathrm{THM}}/{10}^{-13}$ (erg cm−2 s−1)	0.00	0.00	0.16	0.24	0.21	0.28	0.70
${f}_{\mathrm{POW}}^{\mathrm{cor}}/{10}^{-13}$ (erg cm−2 s−1)	9.40	10.10	10.85	10.60	9.81	8.62	6.39
${f}_{\mathrm{THM}}^{\mathrm{cor}}/{10}^{-13}$ (erg cm−2 s−1)	0.80	0.08	2.03	3.57	2.46	1.62	1.98
${\chi }^{2}$/dof	284.8/287	336.7/301c	267.2/289	298.0/279	258.8/276	276.3/268	215.5/248
Absorbed (Variable MeKaL + Variable MeKaL)d
${n}_{{\rm{H}}}/{10}^{22}$ (cm2)	${0.54}_{-0.05}^{+0.07}$	${0.53}_{-0.06}^{+0.07}$	${0.65}_{-0.14}^{+0.18}$	${0.51}_{-0.05}^{+0.15}$	${0.69}_{-0.15}^{+0.08}$	${0.44}_{-0.04}^{+0.10}$	${0.41}_{-0.06}^{+0.07}$
kT1 (keV)	${0.08}_{-0.00}^{+79.82}$	${1.03}_{-0.79}^{+78.87}$	${0.63}_{-0.24}^{+0.19}$	${0.46}_{-0.13}^{+0.16}$	${0.71}_{-0.05}^{+0.07}$	${0.41}_{-0.04}^{+0.35}$	${0.65}_{-0.06}^{+0.06}$
kT2 (keV)	${14.70}_{-3.12}^{+4.27}$	${23.60}_{-19.58}^{+56.30}$	${9.11}_{-1.61}^{+2.85}$	${7.86}_{-1.37}^{+1.65}$	${7.98}_{-1.80}^{+2.20}$	${4.98}_{-0.58}^{+1.18}$	${5.37}_{-0.81}^{+1.23}$
${K}_{1}/{10}^{-4}$	${305.73}_{-305.73}^{+342.30}$	${1.67}_{-1.67}^{+2.49}$	${1.59}_{-1.27}^{+2.67}$	${1.83}_{-1.32}^{+5.53}$	${3.35}_{-1.66}^{+1.72}$	${2.22}_{-1.16}^{+3.76}$	${2.69}_{-1.01}^{+1.85}$
${K}_{2}/{10}^{-4}$	${5.73}_{-0.95}^{+0.40}$	${5.95}_{-5.95}^{+0.34}$	${5.67}_{-1.61}^{+0.72}$	${5.89}_{-0.36}^{+0.44}$	${4.44}_{-0.87}^{+0.92}$	${5.25}_{-0.52}^{+0.37}$	${3.81}_{-0.40}^{+0.35}$
${f}_{1}/{10}^{-13}$ (erg cm−2 s−1)	0.38	0.91	1.70	0.75	4.25	1.02	2.18
${f}_{2}/{10}^{-13}$ (erg cm−2 s−1)	6.35	6.62	5.41	5.84	1.97	4.30	2.54
${f}_{1}^{\mathrm{cor}}/{10}^{-13}$ (erg cm−2 s−1)	0.38	0.91	1.70	0.75	4.25	1.02	2.18
${f}_{2}^{\mathrm{cor}}/{10}^{-13}$ (erg cm−2 s−1)	8.74	9.11	9.44	8.63	7.65	6.96	5.32
${\chi }^{2}$/dof	280.0/287	337.3/296	266.0/289	301.4/279	254.2/276	277.5/268	212.4/248

Notes.

^aRegions ordered outward from J0617 numbering 1 through 7, respectively. ^bAbundances tied to solar ratios for the groups CNO, Ne and Mg, Si and S, and Fe and Ni. ^cAbundances frozen to best-fit values before errors on free parameters estimated. ^dSame as (b) and abundances of second MeKaL model tied to those of first model.

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An absorbed power-law model provided a statistically superior fit to the spectra of the three innermost regions. An absorbed two-component (powerlaw and vmekal or two vmekal) model was needed for the outer zones but one component is always hard (${\rm{\Gamma }}\lt 2$ or ${kT}\gt 5$ keV) and dominates the 0.5–8.0 keV flux; again, indicating a true non-thermal component is present as argued in Section 3.2.1. For this reason, the two vmekal component model is not considered further. The soft thermal component in the two-component non-thermal model is generally cooler, ${kT}\lesssim 0.4$ keV, throughout these PWN regions than in the "outlier" fields (Section 3.2.1) but note that the soft component contributes at most 5% of the flux in all but the outermost PWN region. The outermost region is similar to the outlier regions 7–9 (Table 1) in that its soft thermal component temperature is 0.67 keV and its power-law index is ∼2. Unlike these outlier regions, nearly all the flux in even this outermost PWN region is provided by the non-thermal model component.

To test the significance of the low temperature in the inner zones, the fits were repeated with the vmekal model temperature parameter fixed to its value in the outermost zone, kT = 0.67 keV. This results in some additional flux in the 1–2 keV band which forces the power-law index to flatten slightly to compensate. However, this is only a modest change in slope and within the errors obtained if the thermal model temperature were left as a free parameter. For example, in the fourth zone, Γ decreases from 1.9 ± 0.1 to 1.8 ± 0.1.

Maps of several of the resulting best-fitting model parameters are displayed in Figure 11 for the single-component absorbed powerlaw model. These maps show that the power-law slope smoothly increases with distance from J0617, that the intensity decreases, and that the best-fitting column density is roughly constant but decreases in the outermost zone. This latter trend is perhaps influenced by the simplicity of this single-component model.

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3.2.6. Spectra of the PWN: Comparisons to Radio Data

The X-ray emission in the J0617 PWN is clearly dominated by a non-thermal component suggesting a synchrotron emission source. Radio images of the region (Olbert et al. 2001; Castelletti et al. 2011) also show a cometary morphology which may imply a similar origin. However, the radio and X-ray data have much different spatial resolution and sensitivity so that a direct comparison is non-trivial. Specifically, the signal to noise of the higher frequency radio data is too low to allow for measurements in small regions for comparison with the X-ray fluxes. Instead, by cutting the upper and lower uv range of the 4.8 and 8.4 GHz measurements to a common ∼17 × 077 region (see Figure 8) with equal coverage at both frequencies (and at 330 MHz), radio spectral index measurements of roughly the whole J0617 PWN can be obtained. Comparison of the coverage after cutting showed no apparent gaps in the coverage and thus both frequencies should be sensitive to emission over a similar range of spatial scales. The data were therefore re-imaged and convolved with a circular beam of size $8\buildrel{\prime\prime}\over{.} 5$ and the images were blanked for emission falling below a three sigma cutoff before measurements were taken of the total flux of this region. This yields nearly equal fluxes at all three frequencies, 84.3 ± 7.6, 87.6 ± 3.0, and 87.0 ± 0.6 mJy at 330 MHz, 4.8 and 8.4 GHz, respectively, and therefore a flat spectral index of ${\alpha }_{{\rm{R}}}=0.01$ in the radio band consistent with Olbert et al. (2001) and Castelletti et al. (2011).

The combined 330 MHz image does not suffer from these sensitivity issues but does not have the high spatial resolution of the X-ray data. Therefore, instead of the contour binning regions of Section 3.2.5, a set of successively larger elliptical annuli approximating the innermost five contour binning regions was analyzed at both 330 MHz and X-rays. As before, the X-ray spectrum is predominantly non-thermal and a single absorbed powerlaw model provided an acceptable fit. Here, J0617 was not excluded since it cannot be cleanly masked out of the low-resolution radio image. The 330 MHz radio fluxes were calculated by integrating over each region after subtracting an estimated contribution due to emission from the surrounding SNR as noted in Section 2.3. Table 5 summarizes the geometry and the radio and X-ray properties for these regions.

Table 5.  Pulsar Wind Nebula X-Ray and Radio Spectral Fit Parameters

Regiona	1	2	3	4	5
Area (arcmin2)	0.05	0.10	0.14	0.22	0.34
${n}_{{\rm{H}}}/{10}^{22}$ (cm2)	${0.40}_{-0.03}^{+0.03}$	${0.53}_{-0.03}^{+0.04}$	${0.57}_{-0.03}^{+0.03}$	${0.52}_{-0.03}^{+0.03}$	${0.51}_{-0.03}^{+0.03}$
Γ	${1.47}_{-0.05}^{+0.05}$	${1.61}_{-0.06}^{+0.06}$	${1.73}_{-0.06}^{+0.06}$	${1.81}_{-0.06}^{+0.06}$	${1.93}_{-0.06}^{+0.06}$
${K}_{\mathrm{POW}}/{10}^{-4}$	${1.38}_{-0.08}^{+0.08}$	${1.58}_{-0.11}^{+0.12}$	${1.77}_{-0.12}^{+0.13}$	${1.64}_{-0.11}^{+0.12}$	${1.88}_{-0.12}^{+0.13}$
${f}_{\mathrm{POW}}/{10}^{-13}$ (erg cm−2 s−1)	7.67	7.02	6.74	5.76	5.73
${f}_{\mathrm{POW}}^{{cor}}/{10}^{-13}$ (erg cm−2 s−1)	9.65	9.61	9.73	8.42	8.76
${\chi }^{2}$/dof	299.6/305	271.8/289	274.1/285	285.5/269	370.3/268
${f}_{330\mathrm{MHz}}$ (mJy)	5.0 ± 0.9	11.0 ± 3.1	11.5 ± 5.6	10.5 ± 8.4	18.0 ± 13.0
$\tilde{\nu }$ (GHz)	${0.02}_{-0.02}^{+0.16}$	${1.12}_{-1.0}^{+5.1}$	${27}_{-20}^{+66}$	${128}_{-88}^{+218}$	${826}_{-479}^{+945}$

Note.

^aElliptical annuli numbered from inner to outer 1–5.

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If the SNR-background-subtracted 330 MHz radio flux and the non-thermal (power-law component) X-ray emission arise from the same physical mechanism, then their spectral shapes should be simply related. The slopes of these spectra are obviously different: the radio spectrum, ${\alpha }_{{\rm{R}}}$, is flat, at least on average over the entire region, while ${\alpha }_{{\rm{X}}}\equiv {\rm{\Gamma }}-1\simeq 0.5-1$ depending on the (elliptical) region. For a power-law X-ray spectrum with a photon index Γ and normalization ${K}_{\mathrm{POW}}={10}^{-4}{K}_{-4}$ photons (cm² s keV)⁻¹ at E = 1 keV, the energy flux spectrum is ${F}_{\nu ,{\rm{X}}}\propto {K}_{-4}{\nu }^{-{\rm{\Gamma }}+1}$. Extrapolation of this X-ray spectrum toward lower frequencies intersects the extrapolation of the radio spectrum, ${F}_{\nu ,{\rm{R}}}={F}_{1\;\mathrm{GHz}}{(\nu /1\;\mathrm{GHz})}^{-{\alpha }_{{\rm{R}}}}$, at frequency $\tilde{\nu }$ when

$$\begin{eqnarray*}&&({\alpha }_{{\rm{X}}}-{\alpha }_{{\rm{R}}})\mathrm{log}\tilde{\nu }=\mathrm{log}({K}_{-4}/{F}_{1\mathrm{GHz}})+8.3838{\alpha }_{{\rm{X}}}-4.1798,\end{eqnarray*}$$

where $\tilde{\nu }$ is in units of GHz and ${F}_{1\;\mathrm{GHz}}$ is in mJy. Inserting the appropriate values from Table 5, and assuming ${\alpha }_{{\rm{R}}}=0$ everywhere (and no uncertainty in the radio flux densities), the estimated frequencies $\tilde{\nu }$ are as listed in the last row of Table 5. In the X-ray hard (flat) inner elliptical regions 1 and 2, the extrapolation crosses the radio spectrum at frequencies lower than 4.8 or 8.4 GHz which means that there should be at least two breaks in a power-law spectrum or the radio spectrum is not flat in those regions.

Deep Chandra/ACIS observations show the point-like object, CXOU J061705.3+222127, has an X-ray spectrum dominated by a thermal component with parameters typical of a cooling neutron star. The fit with a hydrogen atmosphere (NSA) model shows an effective temperature ${T}_{\mathrm{eff}}^{\infty }\approx 6.8\times {10}^{5}$ K and a bolometric luminosity ${L}_{\mathrm{bol}}^{\infty }\approx 2.6\times {10}^{32}$ erg s⁻¹ (see Table 2). Such temperature and luminosity are very close to those obtained from the NSA fit of the thermal component of the Vela pulsar (Pavlov et al. 2001), whose age τ is about 20–30 kyr, larger than the characteristic spin-down age ${\tau }_{\mathrm{sd}}\equiv P/2\dot{P}=11$ kyr (Lyne et al. 1996). Similar temperature and luminosity for τ ∼ 30 kyr were obtained in some neutron star cooling models (e.g., Page et al. 2009). Therefore, we can expect that age of the neutron star in J0617 is a few times 10⁴ years. It is consistent with the IC 443 age ∼30 kyr estimated by Chevalier (1999), although some authors inferred much younger ages for this SNR (e.g., Petre et al. 1988 suggested $\tau \sim 3$ kyr).

Compared to the NSA model, the blackbody fit of the thermal component gives a higher temperature, ${T}_{\mathrm{BB}}\approx 1.5\times {10}^{6}$ K, and a smaller radius, ${R}_{\mathrm{BB}}\approx 1.6{d}_{1.5}$ km, similar to the Vela pulsar. Such emission could emerge from a hot spot on the neutron star surface heated by precipitation of relativistic particles from the pulsar magnetosphere, or it could reflect strong nonuniformity of the surface temperature due to anisotropy of heat conductivity of the neutron star crust caused by very strong magnetic fields (see, e.g., Geppert & Viganò 2014). The non-detection of pulsations with $P\gt 6.5$ s does not contradict the small size of the emitting region because such young pulsars have much shorter periods.¹⁹

Since the NSA and blackbody models yield fits of about the same quality, we cannot prefer one model to the other based solely on the observations. However, the NSA fit looks somewhat more preferable because it gives reasonable cooling neutron star properties at the expected SNR age and distance.

The detection of the nonthermal power-law component in the neutron star spectrum and the presence of the non-thermal X-ray nebula around the neutron star show that CXOU J061705.3+222127 is a rotation-powered pulsar. The nonthermal component, presumably emitted from the pulsar's magnetosphere, dominates the pulsar spectrum at $E\gtrsim 1.7$ keV. The spectral slope and the "isotropic luminosity" of the nonthermal component (${L}_{{\rm{\Gamma }}}\equiv 4\pi {d}^{2}{f}_{\mathrm{pl}}^{\mathrm{cor}}$) are also close to those of the Vela pulsar,²⁰ for both thermal component models used in fit.

Since pulsations have not been detected, we do not know the pulsar's spin-down properties, $\dot{E}$ and ${\tau }_{\mathrm{sd}}$. We, however, can constrain them from a comparison of the PWN 0.5–8 keV luminosity ${L}_{\mathrm{pwn}}\approx 1.4\times {10}^{33}{d}_{1.5}^{2}$ erg s⁻¹ (given by the sum of the non-thermal components of the seven contour-binning regions of Section 3.2.5) with the X-ray luminosities of PWNe produced by pulsars with known $\dot{E}$ and ${\tau }_{\mathrm{sd}}$. Assuming ${d}_{1.5}=1$ and using Figure 5 from Kargaltsev & Pavlov (2008), Figure 2 from Li et al. (2008), and Figure 3 from Kargaltsev et al. (2012), we obtain a range of possible spin-down luminosities $\dot{E}\approx (1$–$30)\times {10}^{36}$ erg s⁻¹, with the most likely value around $3\times {10}^{36}$ erg s⁻¹. Similarly, using Figure 5 from Li et al. (2008), we obtain a range of possible spin-down ages, ${\tau }_{\mathrm{sd}}\sim 10$–100 kyr, with the most likely value around 20 kyr, consistent with the age estimates from the properties of the thermal component. From these estimates we obtain constraints on the period, P ∼ 0.1–0.6 s, and the surface magnetic field, B ∼ (0.4–$4)\times {10}^{13}$ G, with most likely values around 0.25 s and $2\times {10}^{13}$ G, respectively.

Note that the true pulsar's X-ray luminosity is apparently much higher than the above-estimated ${L}_{{\rm{\Gamma }}}$ because the (distance-independent) ratio ${L}_{\mathrm{pwn}}/{L}_{{\rm{\Gamma }}}\sim 100$–200 is much larger than for any known pulsar-PWN pair (see Figure 5 in Kargaltsev & Pavlov 2008). This suggests that the pulsar beam misses the Earth, which could also be the explanation for non-detection of the pulsar in the radio and γ-rays.

J0617 is separated from the apparent center of the IC 443 SNR by 15' in a direction nearly due south. This corresponds to a projected length ${s}_{\perp }=2\times {10}^{19}{d}_{1.5}$ cm and a projected velocity ${v}_{\perp }=640\;{d}_{1.5}{\tau }_{4}^{-1}$ km s⁻¹. This is below the observed upper limit (Section 3.1.1) of $310\;{d}_{1.5}$ km s⁻¹ if ${\tau }_{4}\equiv \tau /{10}^{4}\;\mathrm{years}\gtrsim 2$, which is consistent with the possible IC 443 age and the spin-down age estimated above from the empirical ${L}_{\mathrm{pwn}}$–${\tau }_{\mathrm{sd}}$ correlation. The true speed is ${v}_{\mathrm{psr}}={v}_{\perp }{(\mathrm{sin}i)}^{-1}$, where i is the angle between the direction of motion and the line of sight. Observed pulsar speeds range up to ∼1000 km s⁻¹(e.g., Arzoumanian et al. 2002) which constrains the angle: $\mathrm{sin}i\gtrsim 0.64{\tau }_{4}^{-1}{d}_{1.5}$, assuming J0617 was born in the center of IC 443 (e.g., $i\gtrsim 19^\circ$ for ${\tau }_{4}\sim 2$, ${d}_{1.5}=1$). The angle i is larger for more typical pulsar velocities—for instance, $32^\circ \lesssim i\lesssim 53^\circ$ for v = 400 km s⁻¹ and a reasonable age range $2\lesssim {\tau }_{4}\lesssim 3$, at ${d}_{1.5}=1$.

All regions imaged by Chandra surrounding J0617 and its PWN have a strong thermal emission component, likely emitted from the IC 443 SNR. This likely means that J0617 lies within this warm plasma, but a simple line-of-sight projection cannot be ruled out (and, thus, the distance to J0617 remains unknown). The typical temperature of this warm plasma is ${kT}\sim 0.7$ keV (Section 3.2.1) corresponding to a sound speed, ${c}_{s}={(\gamma {kT}/\mu {m}_{{\rm{H}}})}^{1/2}\approx 430\;{({kT}/0.7\;\mathrm{keV})}^{1/2}{(0.6/\mu )}^{1/2}$ km s⁻¹ for a γ = 5/3 gas and molecular weight $\mu \simeq 0.6$, appropriate for fully ionized medium with roughly cosmic abundances. Thus, if J0617 is within this plasma and not just lying along the same line of sight, then the pulsar motion cannot be highly supersonic; the Mach number ${\mathcal{M}}={v}_{0}{/c}_{s}\lesssim 2.3$ for ${v}_{0}\lt {10}^{3}$ km s⁻¹. Here, ${v}_{0}$ is the speed with respect to the ambient medium; ${v}_{0}\sim {v}_{\mathrm{psr}}$ in the absence of any bulk motions in the plasma. Whether the speed is supersonic, transonic, or subsonic has a strong bearing on the shape of the nebula (which is also influenced by its orientation relative to the line of sight) and the properties of the particle and electromagnetic field flow within the nebula. This is addressed in more detail in Section 4.3.

Assuming, for the present, that J0617 and its PWN are embedded in the IC 443 SNR, the ambient thermal pressure, ${p}_{\mathrm{thm}}=\rho ({kT}/\mu {m}_{{\rm{H}}})$, where ρ is the ambient mass density, can be estimated with the aid of the vmekal model fit parameters. The vmekal model norm is ${K}_{\mathrm{THM}}={10}^{-14}{(4\pi {d}^{2})}^{-1}\int {n}_{e}{n}_{{\rm{H}}}{dV}$ $\simeq {10}^{-14}{(4\pi {d}^{2})}^{-1}{n}_{{\rm{H}}}^{2}V$, where n_H is the hydrogen number density, and V is the volume of the emitting region. The volume can be expressed in terms of the area A of the region image (in arcmin²) and the average depth ${l}_{19}$ (in units of 10¹⁹ cm) of the region along the line of sight: $V=1.8\times {10}^{55}{{Al}}_{19}{d}_{1.5}^{2}$ cm³. Using this expression for V and assuming that fully ionized hydrogen gives the main contribution, the hydrogen number density and the ambient thermal pressure can thus be estimated as follows:

$$\begin{eqnarray*}{n}_{{\rm{H}}} & = & 0.39\;{K}_{-4}^{1/2}{({{Al}}_{19})}^{-1/2}\;{\mathrm{cm}}^{-3},\\ {p}_{\mathrm{thm}} & \simeq & 2{n}_{{\rm{H}}}{kT}=0.92\times {10}^{-9}{K}_{-4}^{1/2}{({{Al}}_{19})}^{-1/2}\;{kT}\;\mathrm{dyn}\;{\mathrm{cm}}^{-2},\end{eqnarray*}$$

where ${K}_{\mathrm{THM}}={10}^{-4}{K}_{-4}$ and kT is in units of keV.

The n_H and ${p}_{\mathrm{thm}}$ estimates are proportional to ${l}_{19}^{-1/2}$, which depend on the SNR geometry and the J0617 position within the SNR. J0617 lies, in projection, about 15' ($2\times {10}^{19}{d}_{1.5}$ cm) from the center of the ∼20' radius IC 443 remnant (assuming a spherical remnant). Thus, a chord through the remnant along the line of sight to J0617 should have a length of about $2\times {10}^{19}$ cm or less, so typical expected values are ${l}_{19}\sim 1$ (corresponding to $\sim 7\buildrel{\,\prime}\over{.} 5$ in the sky plane).

Using the values from spectral fits to the nine outlier regions, Table 1, the mean hydrogen densities (and standard deviations) for the low- and high-temperature vmekal components are ${n}_{{\rm{H}}}/{l}_{19}^{-1/2}=0.5\pm 0.1$ and 0.6 ± 0.2 cm⁻³. The corresponding pressures are ${p}_{-9}/{l}_{19}^{-1/2}=0.7\pm 0.2$ for the low-temperature component (where ${p}_{\mathrm{thm}}={10}^{-9}{p}_{-9}$ dyn cm⁻²). For the high-temperature component in regions 1 through 6 the pressures are 1.4 ± 0.4, but they average 5 ± 2 for regions 7 through 9 because of the much higher temperatures determined for those regions, averaging 4 keV compared to only 0.8 keV for the high-temperature component in regions 1–6 (and 0.6 keV for the low-temperature component in all regions).

The cometary shape observed from many PWNe is generally attributed to motion of the system relative to the ambient medium. In the case of powerful, young, subsonically moving pulsars such as the Crab, a distinct jet-torus structure may be present near the pulsar related to axial symmetry in the wind caused by rotation of the pulsar. In other systems, particularly older pulsars moving supersonically through a cold interstellar medium, the PWN structure consists of a forward bowshock and an extended tail.

J0617 appears to have some attributes of both these extremes. It has a distinct, nearly circular, ∼5''-radius circumstellar ring encircling jet-like features and a $\sim 2\prime \;\times \;1\buildrel{\,\prime}\over{.} 5$ comet-shaped nebula. In analogy to the Crab, the ring may define a TS where the ultrarelativistic free-flowing equatorial wind slows to sub-relativistic speeds, referred to as the inner ring in the Crab (Weisskopf et al. 2000), or the ring may be a torus of shocked pulsar wind similar to the one that lies some distance beyond the inner ring of the Crab. Since in both cases the symmetry axis of the J0617 ring should be the spin axis of the pulsar, the ellipticity of the ring implies the angle ζ between the line of sight and the spin axis is about 30° (see Section 3.1.2). If we assume that the spin axis coincides with the direction of motion, similar to many other pulsars (Johnston et al. 2005), and J0617 originated at the center of IC 443, then the pulsar velocity can be estimated as ${v}_{\mathrm{psr}}\sim 400$–600 km s⁻¹, for ${d}_{1.5}=1$ and ${\tau }_{4}\sim 2$–3 (see Section 4.1), comparable to the speed of sound in the ambient medium estimated in Section 4.2. The relatively small ζ value corresponds to a distance from the SNR center to the pulsar of $s\sim 4\times {10}^{19}{d}_{1.5}$ cm. This requires the SNR must be elongated along the line of sight if J0617 is still within the SNR. For instance, if the SNR is a prolate spheroid whose polar axis is parallel to the line of sight, then this axis must be a factor of 2 longer than the equatorial radius and the length of the chord through the SNR along the line of sight to J0617 becomes ${l}_{19}\sim 7{d}_{1.5}$ (cf. Section 4.2).

In this geometry the north–south jet-like features could be true pulsar jets (e.g., similar to the inner jets of the Vela pulsar; Pavlov et al. 2003) of $\sim {10}^{17}{d}_{1.5}$ cm (deprojected) length. The fact that the southern jet is brighter than the northern jet can be explained by the Doppler boosting, i.e., the outflow in the southern jet is approaching the observer, which implies that the pulsar is also approaching and located in the front part of the SNR. The offset of the apparent ring center from the pulsar (see Figure 3) could be explained similar to that of the Crab inner ring (Weisskopf et al. 2012), e.g., as caused by an intrinsic azimuthal asymmetry due to nonuniformity of the ambient medium or even a simple geometric displacement caused by a non-equatorial ring.

In this interpretation the observed X-ray PWN beyond the ring is comprised of a shocked pulsar wind outflow. Its cometary shape is formed by the ram pressure caused by the motion of J0617 relative to the ambient medium. The misalignment of ∼50° between the symmetry axis of the comet-shaped PWN and the direction toward the SNR center could be explained by bulk motion of the SNR matter in the vicinity of J0617 with a velocity of a few hundred km s⁻¹ (e.g., due east or east–southeast).

We should note that the ellipticity of the J0617 ring derived from the image analysis (Section 3.1.2) is subject to large systematic uncertainties due to the ring faintness and the (apparent) ring-jet intersections. Therefore, we cannot exclude the possibility that the true ellipticity is much smaller than 30°, i.e., the ring is nearly circular. In this case, if we assume that the pulsar's spin axis is aligned with direction of motion, we would have to conclude that J0617 could not originate at the center of the IC 443 SNR. However, if we allow a strong misalignment between the spin axis and the direction of motion (e.g., similar to IGR J11014–6103; Pavan et al. 2014), then the circular shape of the ring would not impose restrictions on the direction of motion and birthplace of the pulsar. Nevertheless, if the jet-like features are indeed the jets, they would lie nearly along the line of sight and would be exceptionally long. Thus, some ellipticity of the ring is required if it is associated with the equatorial pulsar wind.

The cometary shape of the larger PWN may offer some additional guidance in interpreting the observed properties of J0617. In general, the pulsar wind flows non-radiatively until it encounters the TS, while the shocked pulsar wind, confined between the TS and a contact discontinuity (CD) that separates the shocked pulsar wind from shock-heated ambient material, emits synchrotron radiation. The shapes of the TS, CD and the outer (forward) shock, which separates the shocked ambient gas from unshocked ambient gas, depend on the Mach number.

In the supersonic case, ${\mathcal{M}}\gg 1$, the shapes of these surfaces ahead of the moving pulsar resemble paraboloids whose sky projections look bow-like if the angle between the pulsar velocity and the line of sight is large enough. The shocked pulsar wind at the bow apex is confined in a thin layer, and thus the TS and CD surfaces upstream from the central source are close to each other, ${R}_{\mathrm{TS}}(\theta )\sim {R}_{\mathrm{CD}}(\theta )$ at $\theta \ll 1$, where θ is the polar angle with respect to the symmetry axis of the flow. The TS standoff distance can be estimated from the balance between the bulk wind pressure inside the TS and the ram pressure of the ambient matter:

$$\begin{eqnarray}&&\dot{E}/[4\pi {{cR}}_{\mathrm{TS}}^{2}(\theta =0)]\sim \rho {v}_{0}^{2}\end{eqnarray} \tag{ 1 }$$

(assuming the pulsar wind is isotropic inside the TS). At arbitrary θ the pressure balance defines a surface ${R}_{\mathrm{TS}}(\theta )$. An analytical solution for ${R}_{\mathrm{TS}}(\theta )$ was derived by Wilkin (1996) in the thin-layer approximation, it agrees well with numerical simulations (e.g., Bucciantini et al. 2005) for small θ and high ${\mathcal{M}}$. For $\theta \ll 1$, the Wilkin formula can be approximated by the parabola ${(y/{R}_{0})=C(x/{R}_{0})}^{2}+1$ with $C=0.3$, where ${R}_{0}={R}_{\mathrm{TS}}(0)$, $-y$ is along the direction of motion, $(x/y)=\mathrm{tan}\theta$, and the pulsar is at the focus x = y = 0. Although the head of the observed cometary PWN resembles a parabola, the fit to the X-ray contours in Section 3.1.3 gives a substantially larger coefficient of the quadratic term, C = 0.54 instead of 0.3. The sharper (narrower) head of the observed PWN²¹ and the smooth surface brightness profile ahead of the pulsar (i.e., the lack of any structure that could be identified with a TS; see Figure 5) provides additional evidence that the pulsar motion is not supersonic.

In the transonic case, ${\mathcal{M}}\sim 1$, the ambient thermal pressure contributes, in addition to the ram pressure, to the right hand side of Equation (1). Since ${c}_{s}^{2}=\gamma {p}_{\mathrm{thm}}/\rho$, the total pressure can be written as ${p}_{\mathrm{thm}}+\rho {v}_{0}^{2}=\rho {v}_{0}^{2}$ $(1+{\gamma }^{-1}{{\mathcal{M}}}^{-2})$, and the stand-off distance for the CD can be estimated as ${R}_{\mathrm{CD}}(0)\sim$ ${R}_{\mathrm{TS}}(0)\sim {\dot{E}}^{1/2}{(4\pi c\rho {v}_{0}^{2})}^{-1/2}{(1+{\gamma }^{-1}{{\mathcal{M}}}^{-2})}^{-1/2}$ $\sim {10}^{17}(\dot{E}/\sim 3\times {10}^{36}$ $\mathrm{erg}{{\rm{s}}}^{-1}{)}^{1/2}$ ${p}_{-9}^{-1/2}{(1+\gamma {{\mathcal{M}}}^{2})}^{-1/2}$ cm. Inserting plausible parameter values for the pulsar and the ambient medium (estimated in Sections 4.1 and 4.2), ${R}_{\mathrm{CD}}(0)\sim {10}^{17}$ cm which corresponds to $4\buildrel{\prime\prime}\over{.} 5{d}_{1.5}^{-1}$ or roughly the observed ring radius. In this transonic case, there is no longer a general analytic solution, but the parabolic approximation for the CD head at $\gamma {{\mathcal{M}}}^{2}\gtrsim 0.7$ gives $C\approx 0.3+0.2{(\gamma {{\mathcal{M}}}^{2})}^{-1}$. It becomes close to the measured C = 0.54 at $\gamma {{\mathcal{M}}}^{2}\approx 0.8$, or ${\mathcal{M}}\approx 0.7$ for γ = 5/3.

In the subsonic limit, ${\mathcal{M}}\ll 1$, the canonical bow-shock model must be abandoned because the thin layer assumption, ${R}_{\mathrm{TS}}\sim {R}_{\mathrm{CD}}$, does not apply even in the forward direction. Instead, the flow can be treated as incompressible so that Laplace's equation for the velocity field, with appropriate boundary conditions, correctly describes the hydrodynamics. Near the pulsar, the flow is again idealized as purely radial, whereas at large distances the velocity must be uniform and directed opposite the direction of motion of the pulsar. The solution is then the sum of a uniform flow and a radial flow from the pulsar with speed falling as the square of the radius. Since the post-shock radial velocity component must be about $c/3$ at the TS outer boundary (Kennel & Coroniti 1984) but $\sim {v}_{0}\ll c/3$ at the CD (where the two velocity components cancel), ${R}_{\mathrm{TS}}(0)\ll {R}_{\mathrm{CD}}(0)$, and the CD standoff distance is ${R}_{\mathrm{CD}}{(0)={(c/3{v}_{0})}^{1/2}{R}_{\mathrm{TS}}(0)\simeq 18({v}_{0}/300\;\mathrm{km}\;{{\rm{s}}}^{-1})}^{-1/2}{R}_{\mathrm{TS}}(0)$. We do not clearly see the CD in our images, perhaps because it is blurred by instabilities. However, if we assume ${R}_{\mathrm{CD}}(0)\sim 15\prime\prime$–30'' (see Figures 5 and 6), then the above estimate gives ${R}_{\mathrm{TS}}(0)\sim 1\prime\prime$–2'' (for ${v}_{0}=300$ km s⁻¹), much smaller than the ring radius, ∼5''. This means the ring may be analogous to the Crab's torus while the TS may be hidden in the wings of the pulsar's PSF (see Figure 2). Note that the relative motion cannot be highly subsonic for reasonable estimates of v₀ since ${c}_{s}\sim 400$ km s⁻¹.

The overall shape of the PWN also depends on the Mach number. In the supersonic and transonic regimes, numerical solutions (Bucciantini et al. 2005) show the ${R}_{\mathrm{TS}}(\theta )$ surface develops a bullet shape with the TS elongated in the downstream direction (θ = π) and terminating in a Mach disk oriented perpendicular to the direction of motion. Simulations show the ratio ${R}_{\mathrm{TS}}{(\pi )/{R}_{\mathrm{TS}}(0)\sim (1+{{\mathcal{M}}}^{2})}^{1/2}$ for lower ${\mathcal{M}}$, reaching a limit of ∼5 for ${\mathcal{M}}\gg 1$. This amount of elongation is incompatible with observations of J0617, again suggesting the flow is not supersonic. Note that a circular ring is only conceivable if the pulsar wind was purely radial producing a limb-brightened spherical emission region outside the TS. However, pulsar winds are known to be highly aspherical resulting in emission morphologies like the Crab torus. As we mentioned above, if the ring is a torus, then the spin axis is predominantly along the line of sight.

Finally, in the supersonic and transonic regimes, the expected shocked pulsar wind speeds in the tail (roughly along the CD) are 0.3–0.5c (Bucciantini et al. 2005), whereas they are only of order ${v}_{0}\sim 300$ km s⁻¹ in the subsonic case. Particles in this flow will only radiate at X-ray energies, E ∼ 1 keV, for a time $\tau \sim 200{(E/1\;\mathrm{keV})}^{-1/2}{(B/50\;\mu {\rm{G}})}^{-3/2}$ years due to their synchrotron losses. Here, B is the equipartition magnetic field defined (Pacholczyk 1970) as $B={(6\pi {c}_{12}(1+k)L/({fV}))}^{2/7}$ where f is the filling factor in a volume V producing a synchrotron luminosity L over some spectral range, ${c}_{12}$ a constant dependent on this spectral range and the spectral slope (index), and the ion to electron energy ratio k = 0 for a pure pair plasma. From the flux density in the radio band, ∼86 mJy (Section 3.2.6), a volume of that region of 10⁵⁴ cm³ assuming a filled prolate ellipsoid, and a flat radio spectrum extending to 100 GHz (${c}_{12}=7\times {10}^{6}$), the field strength is $B\sim 65{(\mathrm{sin}i)}^{2/7}$ μG. The length of the J0617 nebular tail extends roughly 15 or $2\times {10}^{18}{d}_{1.5}{(\mathrm{sin}i)}^{-1}$ cm implying a velocity of ∼500 ${(\mathrm{sin}i)}^{-5/7}$ km s⁻¹ for this synchrotron age. This is somewhat larger than the subsonic velocity estimate and only approaches the transonic velocity estimate as $i\to 0$°.

In summary, the shape of the forward region of the J0617 PWN and the size of its surrounding ring implies a transonic (or mildly subsonic) net flow because of the additional flow collimation that occurs at low ${\mathcal{M}}$. The size of the circular ring is compatible with the standoff distance of a TS unless the flow is subsonic in which case the ring is larger than the TS by a factor of 20 or so. In any case, the near circularity of the ring implies either emission from a limb-brightened spherical emission region or emission from a toroidal region with symmetry axis nearly along the line of sight. Neither of these two conclusions is satisfactory, however, as the former belies the known predominantly azimuthal emission geometry associated with rotating magnetized neutron stars and the latter implies a pulsar orientation unlikely to produce the observed shape of the larger cometary PWN.