A Spatially Resolved Study of Hard X-Ray Emission in Kepler's Supernova Remnant: Indications of Different Regimes of Particle Acceleration (2024)

The NuSTAR observation of Kepler's SNR was performed from 2014 October 7 for an exposure time of 246 ks (Obs. ID: 40001020002, PI: F. Harrison), with pointing coordinates α_J2000 = 17^h30^m364 and δ_J2000 = −21°30'13''. We processed the data using nupipeline of the NuSTAR Data Analysis Software (NuSTARDAS version 2.0.0 with CALDB version 20210202) included in HEAsoft version 6.28.

The maps shown in this paper were obtained by summing the photon counts detected in each pixel by the two Cadmium–Zinc–Telluride (CZT) detectors Focal Plane Modules A and B (FPMA and FPMB) in a given energy band. We performed a spatially resolved spectral analysis for both FPMA and FPMB by extracting the spectra from different regions of the remnant using the nuproducts pipeline for an extended source. Spectra were rebinned to have at least 25 counts per bin. For each region, FPMA and FPMB spectra were fitted simultaneously. We used the nuproducts pipeline to produce the redistribution matrix file (RMF) and the ancillary response file (ARF), and to extract the background spectrum. For the background, we selected an extraction region for each spectrum, outside of the shell and in the same chip as the source extraction region.

We complemented NuSTAR data analysis with the analysis of an XMM-Newton European Photon Imaging Camera (EPIC) observation of Kepler's SNR, performed from 2020 March 19 for an exposure time of 140 ks (Obs. ID: 0842550101, PI: T. Sato). The observation has pointing coordinates α_J2000 = 17^h30^m369, δ_J2000 = −21°30'011, and was performed with the thick filter, in full-frame mode for the EPIC MOS cameras, and in large-window mode for the EPIC pn camera.

We processed the observation data files (ODF) using the emproc and the epproc tasks of the Science Analysis System (SAS) software, version 18.0.0, respectively, for the MOS and the pn cameras. The obtained event files were filtered for soft-proton contamination using the espfilt task, thus obtaining a screened exposure time of 108.2 ks for MOS 1, 110.1 for MOS 2 and 94.7 ks for the pn camera. Images were background subtracted by adopting the double-subtraction procedure described in Miceli et al. (2006), retaining only events with FLAG=0 and PATTERN ≤12. With this method we removed instrumental particles and diffuse X-ray background from the images by using the Filter Wheel Closed (FWC) ⁶ and the Blank Sky (BS) ⁷ files available at the XMM ESAC web pages. Count-rate images were obtained by mosaicking MOS 1 and MOS 2 maps and are vignetting corrected and adaptively smoothed (with the asmooth task) to a signal-to-noise ratio of 10.

We analyzed the EPIC pn spectra extracted from the same regions adopted for the NuSTAR spectral analysis. To take into account the vignetting effect in the spectra, we added a "weight" column to the pn event file with the evigweight SAS command. The spectra were extracted by using the evselect task, retaining only events with FLAG=0 and PATTERN ≤4. For each spectrum, we produced the RMF and ARF files, with the rmfgen and the arfgen tasks, respectively. The spectra were rebinned so as to have at least 25 counts per bin. For the background, we selected two extraction regions outside the shell: one, at south, for regions 1–5, and one, at north, for regions 6–11 and for the "Hard Knot" (see Section 3.3 and Figure 1 for the region selection). Spectral analysis of NuSTAR and XMM-Newton data was performed with the HEAsoft software XSPEC version 12.11.1 (Arnaud 1996). The spectra from different cameras were fitted simultaneously.

We extracted the spectrum of the whole Kepler's SNR from NuSTAR FPMA and FPMB using a circle with radius of 3' and center coordinates α_J2000 = 17^h30^m4144 and δ_J2000 = −21°29'277, as shown in Figure 1. We modeled the FPMA and FPMB global spectra in the 4.1–30 keV band. We excluded the 3–4.1 keV band to avoid the strong contamination of thermal emission present in this energy band. We model the hard X-rays as nonthermal emission, by adopting a similar approach as Lopez et al. (2015). However, here we describe the continuum as synchrotron emission from an electron energy distribution limited by radiative losses (hereafter loss-limited model; Zirakashvili & Aharonian 2007), which has been shown to provide an accurate description of nonthermal X-ray emission in young SNRs (e.g., Zirakashvili & Aharonian 2010; Morlino & Caprioli 2012; Miceli et al. 2013; Tsuji et al. 2021). The spectrum of the loss-limited model is given by:

where ε is the photon energy, and ε₀ is the cutoff energy parameter. We include interstellar absorption (Tbabs model in XSPEC), with a hydrogen column density fixed to N_H = 6.4 × 10²¹ cm⁻² (as in Katsuda et al. 2015). We also include three ad hoc Doppler-broadened Gaussian components to model the Fe K line (at ∼6.4 keV; see Yang et al. 2013), the Cr and Mn emission lines and the Ni emission lines. Figure 2 shows the total spectra (FPMA and FPMB) of Kepler's SNR with the corresponding best-fit model and residuals. The best-fit values, with error bars at 68% confidence level, are reported in Table 1.

Table 1.Best-ft Values for Kepler's SNR NuSTAR Spectra

Parameter	Value
Fe K center (keV)
σ (keV)
Norm (10−4 photons cm−2 s−1)
ε0 (keV)
Norm (10−3)	29.0
χ2/d. o. f.	1115.82/918

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The fit provides χ²/d. o. f. = 1115.82/918 and an average cutoff energy parameter keV. This value of ε₀ corresponds to a roll-off frequency Hz, which is in good agreement with the estimate obtained by Nagayoshi et al. (2021; 1 × 10¹⁷ Hz) on the basis of the modeling of the broadband SED.

We fitted simultaneously the NuSTAR FPMA and FPMB spectra (in the 4.1–30 keV band), and the Suzaku HXD-PIN spectrum (in the 15–30 keV band), with the loss-limited model. We allowed the normalization of the Suzaku spectra to differ from that of the NuSTAR spectra within a 10% to account for the characteristic cross-calibration factor between the two telescopes (Madsen et al. 2017). We found that the hard X-ray flux of Kepler's SNR in the 15–30 keV band is erg cm⁻² s⁻¹ (F_X erg cm⁻² s⁻¹ for Suzaku HXD, taking into account the cross-calibration factor). Though this value is lower than that reported by Nagayoshi et al. (2021; erg cm⁻² s⁻¹), it is still consistent with it, considering the cross-calibration factor and the 90% statistical and systematic errors.

We performed a spatially resolved spectral analysis by analyzing the spectra extracted from the 11 regions shown in Figure 1. We focus on the outer rim of the shell, by defining regions with similar photon counts in the 8–30 keV band (N₈₋₃₀ ≈ 800) in order to investigate the relation between the shock velocity and the maximum energy of electrons accelerated at the shock front.

To ascertain the origin of the hard X-ray emission, we first focus on the NuSTAR spectra in the 8–30 keV band. The emission in this band is characterized by a featureless continuum, which can be modeled with a power law with spectral index Γ ∼ 3 in all 11 regions considered. For example, in the southern part of the shell, we obtain in region 2 and in region 5; similarly, in the northern limb, in region 7 and in region 10. By modeling this relatively flat emission as thermal Bremsstrahlung, we derive quite high plasma temperatures (namely, keV in region 2, keV in region 5, keV in region 7, and keV in region 10). We then consider the bulk of the hard X-ray emission to be nonthermal. However, we point out that, by including a thermal contribution to the hard X-ray spectra, our conclusions stay unaffected, as shown below.

We then fitted the spectra in the 4.1–30 keV band (4.1–8 keV for EPIC pn and 4.1–30 keV for NuSTAR FPMA and FPMB) using the loss-limited model with an additional Gaussian component to take into account the Fe K line. We also added a further Gaussian component in regions 8–11 to model the Cr/Mn K line detected therein. The spectra from all regions, with the corresponding best-fit model and residual, are shown in Appendix B, Figure 6. The best-fit values for all regions (with the corresponding χ²/d. o. f. ) are shown in Table 2 (error bars are at 68% confidence level).

Table 2.Best-fit Values for Spectra from Regions Labeled from 1 to 11

Region #	Fe K center	σ	Norm	ε0	Norm	χ2/d. o. f.
	(keV)	(keV)	(10−6 photons cm−2 s−1)	(keV)	(10−3)
1		<0.08				107.08/97
2						117.76/90
3						97.02/93
4						117.52/118
5						175.24/128
6						168.34/121
7						189.15/154
8						123.26/111
9						158.83/131
10						108.60/109
11						121.37/98
Hard Knot						466.54/340

Note. All errors are at the 68% confidence level.

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As a crosscheck, we verified that our assumption on the nonthermal origin of the hard X-ray emission is consistent with the broadband X-ray spectrum. To this end, we fit the spectra of all the regions in the 0.3–30 keV (0.3–8 keV for EPIC pn and 3–30 keV for NuSTAR FPMA and FPMB) by adding thermal components to the loss-limited model derived above.

The soft X-ray spectra (0.3–4.1 keV) for the northern regions show prominent thermal emission features, as the Fe-L line complex in the 0.7–1.2 keV band, and the Si, S, Ar, Ca K lines, respectively at ∼1.86, keV ∼2.48 keV, ∼3.11 keV, and ∼3.86 keV. All the spectra are shown in Appendix B, Figure 7, with the corresponding best-fit model and residuals.

The spectra extracted from southern regions (regions 1–5, characterized by a fainter thermal emission) are well described by two components of isothermal optically thin plasma in nonequilibrium of ionization (NEI) with nonsolar abundances and Doppler broadening (bvrnei model in XSPEC), in addition to the absorbed loss-limited model (the parameters of the loss-limited model are fixed to the best-fit values shown in Table 2). We also included two Gaussian lines to take into account missing Fe-L lines in the bvrnei model (as in Katsuda et al. 2015). The spectra extracted from northern regions (regions 6–11, characterized by a brighter thermal emission) were fitted by adding three thermal components to the loss-limited model (with parameters fixed to the values in Table 2). We found a degeneracy between the Fe abundance, the normalization and the temperature (kT_h ) of the hottest component of the plasma. Nagayoshi et al. (2021) found keV so we decided to set an upper limit of 4 keV for kT_h . The values of the best-fit parameters are listed in Tables 3 and 4. This model provides a good description of the spectra of all regions (1 < χ²/d. o. f. < 1.4). We conclude that the modeling of the synchrotron emission adopted in the analysis of the "hard" spectra is consistent with the broadband X-ray spectra and provides a robust description of the nonthermal emission in Kepler's SNR.

Lastly, we analyzed the spectrum of the knot with the brightest hard X-ray emission, which we spotted in the 15–30 keV band map of Kepler's SNR. In particular, we extracted the EPIC pn, FPMA, and FPMB spectra from the circular region indicated by the cyan circle in the lower left panel of Figure 1.

We modeled the spectra in the the 4.1–30 keV band (4.1–8 keV for EPIC pn and 4.1–30 keV for NuSTAR FPMA and FPMB) by adopting the loss-limited model (with the additional Gaussian component) described in detail in Section 3.3. Spectra from the hard knot, with the corresponding best-fit model and residual, are shown in Figure 3, while the best-fit values (with errors at the 68% confidence level) are shown in Table 2.

The cutoff energy parameter ε₀ is a crucial factor in order to characterize the acceleration mechanism in SNRs, because it is determined by the balance between acceleration and cooling in the synchrotron emission process. Zirakashvili & Aharonian (2007) derived a relation between ε₀, the Bohm factor, and the shock velocity,

By adopting the same approach as Tsuji et al. (2021), we show in the left panel of Figure 4 the values of ε₀ obtained from the spectral fittings of the regions with a proper-motion measurement available either in Katsuda et al. (2008) or in Coffin et al. (2022), as a function of the corresponding v_sh. We mark with different colors data points derived for southern regions (black) and northern regions (red). In northern regions we obtain, on average, lower shock velocities and higher ε₀ values than in southern regions (, , for regions 2–5 and regions 6–9/11, respectively). Moreover, the figure shows that southern and northern regions identify two distinct clusters. This suggests the presence of two different regimes of electron acceleration in the same SNR. If we describe each of the two clusters with Equation (3), we can derive the corresponding best-fit values of the Bohm diffusing factor, obtaining η = 6.6 ± 1.6 in the north and reaching the Bohm limit in the south. These values are similar to those derived by Tsuji et al. (2021), who find η ∼ 0.3–4. However, Tsuji et al. (2021) adopted a distance of 4 kpc (instead of 5 kpc) to derive the shock velocity from the proper-motion measurements, thus obtaining lower velocities than those reported in the left panel of Figure 4, which is in line with their lower values of η.

Taking into account these results, we can estimate the acceleration time of electrons (Malkov & Drury 2001; Vink 2020) as

where δ accounts for the energy dependence of the diffusion coefficient, and typically ranges between 0.3 and 0.7 (see Strong et al. 2007). Considering δ = 0.5 and taking the values we found in the northern shell (v_sh = 1800 km s⁻¹, η = 1 and ε₀ = 0.64 keV), we derive yr. Such a high value of the acceleration time may suggest that the electrons started to accelerate before the interaction of the shock with the CSM, which produced a deceleration of the northern shock front. Aharonian & Atoyan (1999) suggested that the shock velocity should be larger than 2000 km s⁻¹ to emit synchrotron X-rays (see also Vink 2008). Thus the existence of synchrotron X-rays implies that the deceleration should happen recently. Similar situation happens in a superbubble with synchrotron X-rays, 30 Dor C (Bamba et al. 2004), where the supernova shock just hit the shell of the superbubble and emit synchrotron X-rays (Yamaguchi et al. 2009) although Lopez et al. (2020) suggests the superbubble itself accelerate electrons.

In this framework, the current shock velocity may not be representative of the shock conditions over the whole acceleration process. We then explore an alternative scenario, by studying the relationship between the synchrotron cutoff energy and the average shock velocity, in all the regions selected for our spatially resolved spectral analysis. We derived for each region as , where r_sh is the radius of the shock. We estimated r_sh for regions 1–11 by measuring the distance between the shock front and the center of the remnant (whose position was carefully derived by Sato & Hughes 2017). The measuring procedure was performed detecting the edge at the azimuthal center of each region on the Chandra flux image in the 4.1–6 keV band, to exploit the high spatial resolution of the Chandra mirrors (we associated to the angular distance an error of 15).

Figure 4 (right panel) shows the values of ε₀ obtained from the spectral fittings of the 11 regions analyzed as a function of the corresponding . Again, in northern regions we obtain, on average, lower shock velocities and higher ε₀ values than in southern regions (, , for regions 1–5 and regions 6–11, respectively). Moreover, also in this plot, southern and northern regions clearly identify two distinct clusters. Therefore, by adopting the average shock velocities, we recover the presence of two different regimes of electron acceleration in the Kepler's SNR. Each of the two clusters can be well described by Equation (3) with a specific value of η. We then derive the corresponding best-fit values of the Bohm diffusing factor, obtaining η = 9.3 ± 0.4 in the north and η = 6.2 ± 0.2 in the south, with a null hypothesis probability of ∼90%. These values of η are higher than those derived with the current shock velocities. This is because the deceleration of the shock front makes the current velocities systematically lower than the average velocities (see Equation (3) for the dependence of η on v_sh). Therefore, the values of the Bohm factors should be taken with some caution.

The two scenarios considered above, namely, synchrotron emission originating from (i) electrons accelerated in the current shock conditions (i.e., freshly accelerated electrons in a high magnetic field), and (ii) electrons accelerated well before the interaction with the dense CSM at north (i.e., longer acceleration times, possibly associated with a lower magnetic field, as in Nagayoshi et al. 2021), may be considered as two limiting cases, bracketing the actual evolution of the system.

Nevertheless, regardless of the shock velocity adopted (current velocity versus average velocity), our conclusions do not change, as both the plots shown in Figure 4 point toward a more efficient (i.e., closer to the Bohm limit) electron acceleration in the north than in the south.

On the other hand, a scenario in which ε₀ does not depend on the shock velocity is also possible. We tested this possibility by fitting the data points of Figure 4 with a constant ε₀ and obtained a null hypothesis probability of ∼15%, which is well below the value obtained in the loss-limited case but still statistically acceptable. However, a framework where ε₀ does not depend on v_sh would indicate that the maximum electron energy is not limited by radiative losses, and, as explained in Section 1, this would imply a magnetic field lower than 30 μG (assuming ε₀ = 0.5 keV), which is at odds with the observations (Völk et al. 2005; Parizot et al. 2006; Rettig & Pohl 2012; Reynolds et al. 2021).

The cutoff energies discussed above were obtained by assuming that the X-ray continuum above 4 keV is ascribed to synchrotron radiation. We then checked how a possible contamination of thermal emission in the hard X-ray spectra of northern regions (where thermal emission is the highest) affects our results. We found that if we model the hard continuum of regions 6–11 with a combination of synchrotron radiation and thermal Bremsstrahlung, the value of ε₀ systematically increases with the contribution of thermal emission. The values of ε₀ for regions 6–11 shown in Table 2 and Figure 4 should then be considered as lower limits. This means that the acceleration efficiency in the north may be even higher (and the Bohm diffusing factor lower) than that derived by neglecting the contribution of thermal emission to the hard X-ray continuum. We conclude that the evidence of more efficient acceleration in the northern part of Kepler's SNR is solid. Southern regions, where the thermal emission has a lower surface brightness, are less affected by thermal contamination and the synchrotron component is better constrained. We note that Tsuji et al. (2021) finds small-scale variations in ε₀, with local peaks reaching values of the order of 1.5 keV (higher than those reported in our Table 2). This may be due to the absence of NuSTAR data for Kepler's SNR in Tsuji et al. (2021) and to the different size of the extraction regions (our regions being significantly larger than theirs).

We note that in the southern part of Kepler's SNR, where the ambient density is similar to that observed in Tycho's SNR (Blair et al. 2007), we recover similar results as those obtained for Tycho's SNR by Lopez et al. (2015), who found that the cutoff energy increases with the shock velocity (i.e., where the ambient density is low). At odds with Tycho's SNR, however, Kepler's SNR is interacting with a much denser environment in the north (4–7 times denser; Blair et al. 2007; Katsuda et al. 2008), where we register a different regime of particle acceleration.

The presence of two different acceleration regimes and of a higher acceleration efficiency in regions 6–11 might be explained by considering the turbulent magnetic field generated in the interaction between the shock front and the dense CSM in the north. Inoue et al. (2012) modeling RX J1713.7–3946 SNR with a 3D magnetohydrodynamic (MHD) simulation show that a shock wave that sweeps a cloudy medium generates an amplified magnetic field, as a result of the dynamo action induced by the turbulent shock-cloud interaction (See also Orlando et al. 2008). An amplified magnetic field may lead toward a more efficient acceleration process and to a lower η Bohm factor. This interpretation is in line with the findings obtained for RX J1713.7-3946 by Sano et al. (2015), who observed that the synchrotron photon index is anticorrelated with the X-ray intensity. Indeed, we found the highest value of ε₀ in the "Hard Knot" region, which we identified in the northern part of the shell as a bright feature in the 15–30 keV map (see Figure 1 and Table 2). In general, our findings show that in Kepler's SNR the ε₀ parameter is high in the region where the shock interacts with high-density CSM, thus indicating a similar scenario as that proposed for RX J1713.7–3946.

Several SNRs are known to emit γ-rays up to TeV energy (e.g., Ackermann et al. 2013; HESS Collaboration et al. 2018; Aleksić et al. 2012). Xiang & Jiang (2021) reported a likely detection (with ∼4σ significance) of γ-ray emission in the 0.2–500 GeV band from the region of Kepler's SNR by analyzing Fermi Large Area Telescope (LAT) data. Using the same Fermi LAT data, Acero et al. (2022) confirmed this detection up to 6σ. Moreover, Prokhorov et al. (2022) reported the detection of VHE emission from Kepler's SNR based on a deep observation of HESS.

In this section, we model the SED of Kepler's SNR for the nonthermal emission, using radio (DeLaney et al. 2002), X-ray (NuSTAR FPMA and FPMB in the 8–30 keV band from this work and HXD-PIN from Nagayoshi et al. 2021), GeV (Xiang & Jiang 2021), and TeV (Prokhorov et al. 2022) data, and give some constraints on the particle energy distribution and on the ambient density and magnetic field.

We use the radiative code naima (version 0.9.1, Zabalza 2015) to model the SED. We considered a leptohadronic one-zone stationary model to describe the multiband emission spectrum. In this model, the synchrotron and inverse Compton (IC) emission are assumed to stem from the same electron distribution, which is described by a power law with an exponential cutoff. We considered the same seed photon field as Nagayoshi et al. (2021) for the IC emission: the cosmic microwave background radiation (CMBR), a far-infrared (FIR) component (T = 29.5 K and u_FIR = 1.08 eV cm⁻³), and a near-infrared (NIR) component (T = 1800 K and u_NIR = 2.25 eV cm⁻³). As for the hadrons, we assumed a power-law energy distribution with an exponential cutoff. The model that best reproduces the observed data is shown in Figure 5 (left panel).

Our model gives for the leptonic part a spectral index α = 2.44 and a cutoff energy E_cut = 16 TeV. The electrons emit synchrotron radiation in a magnetic field of 100 μG. For the hadronic part we assumed the same spectral index and an energy cutoff of 500 TeV. The total kinetic energy of protons (W_p ), interacting with a post-shock medium with density of 20 cm⁻³ (consistent with the density value of the shock–CSM interacting region; Kasuga et al. 2021), was set to be 15 times the electrons total kinetic energy (W_p = 4.2 × 10⁴⁸ erg). As a comparison we also modeled the SED using the value for the magnetic field proposed by Nagayoshi et al. (2021; B=40 μG, see Figure 5 right panel), with α = 2.44 and E_cut = 35 TeV for the leptonic part. For the hadronic part of the model we adopted the same assumption as before but with W_p = 5.4 × 10⁴⁸ erg (4 times the electrons total kinetic energy) and a post-shock medium density of 5 cm⁻³. This last case gives a poor fit compared with the case where the magnetic field is higher.

Table 3.Best-fit Values for Broadband Spectra of Southern Regions (1–5)

Component	Parameter	#1	#2	#3	#4	#5
TBabs	nH (1022 cm−2)	0.64 (fixed)
Gauss 1	Fe L + O K (keV)	0.708 (fixed)
	Norm (10−4 photons cm−2 s−1)					11.6
Gauss 2	Fe L+Ne K (keV)	1.227 (fixed)
	Norm (10−4 photons cm−2 s−1)					0.15
brvnei 1	kT1 (keV)				0.68	0.721
	O	1(fixed)		2.2	0.31	1 (fixed)
	Ne	1 (fixed)		1 (fixed)	<0.5	1 (fixed)
	Mg	1 (fixed)		4.80485	0.9	4.3
	Si	1 (fixed)			9.0	1 (fixed)
	Fe			51	50	107
	τ1 (109 cm−3 s)	<0.6		<0.62	0.83	1.20
	Velocity (104 km s−1)	0		0	0	0.64
	EM1 (1056cm−3)				4.6	4.16
brvnei 2	kT2 (keV)	>3.88	>3.89	>3.93	>3.91	>3.95
	O	1 (fixed)	<2.5	<1.7	5	1 (fixed)
	Ne				5.2
	Mg				2.3	14.0
	Si				37	170
	S				48
	Ar				36
	Ca	1 (fixed)
	Fe				26.8
	Ni	=Fe
	τ2 (109cm−3 s)				5.12	7.14
	Velocity (104 km s−1)				0.42	0.57
	EM2 (1056 cm−3)				0.113	0.095
	χ2/d. o. f.	458.98/456	403.14/355	423.15/443	608.79/573	824.00/626

Note. Solar abundances from Anders & Grevesse (1989). The τ lower limit is set to be 5 × 10⁸ cm⁻³ s. The abundance upper limit is set to be 1000 times the solar one. The velocity upper limit is set to be 1 × 10⁴ m s⁻¹. Abundances consistent with their solar values were fixed to 1.

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Table 4.Best-fit Values for Broadband Spectra of Northern Regions (6–11)

Component	Parameter	#6	#7	#8	#9	#10	#11
TBabs	nH (1022 cm−2)	0.64 (fixed)
Gauss 1	Fe L + O K (keV)	0.708 (fixed)
	Norm (10−4 photons cm−2 s−1)	18.5			25.2	22.1
Gauss 2	Fe L+Ne K (keV)	1.227 (fixed)
	Norm (10−4 photons cm−2 s−1)	0.83			1.18	0.584099
Gauss 3	Cr K+Mn K (keV)	5.6 (fixed)
	Norm (10−4 photons cm−2 s−1)	/	/		0.006	0.0024
brvnei 1	kT1 (keV)	0.409				0.341519
	C	2.0	7.8		7.0	31	<7
	N	0 (fixed)
	O					1.40	0.34
	Ne	4.1			6.1	12.8	2.9
	Mg					29	1(fixed)
	Fe					275	70
	Ni	=Fe
	τ1 (109cm−3 s)					0.993	1.08
	Velocity (104 km s−1)	>0.74		0 (fixed)	0.60		0.65
	EM1 (1056 cm−3)
brvnei 2	kT2 (keV)	0.97		1.43	1.23	1.15	1.50
	O	42	20	27	33	11.2175	30
	Ne	46	1 (fixed)		40	9.00606	22
	Mg	58	61	72	69	18.4	46
	Si	180	230	270		114	300
	S	290	380	470	480	183	450
	Ar	350	370	520	520	240	250
	Ca	>600	>800	>700	>800	360	>100
	Fe	28	69	90	70	24.8	1 (fixed)
	Ni	=Fe
	τ2 (109cm−3 s)	57				38.0	32
	Velocity (104 km s−1)						0.48
	EM2 (1056 cm−3)	0.121
brvnei 3	kT3 (keV)	>3.91	>3.98	>3.97	>3.95	>3.96	>3.88
	Ne		1 (fixed)
	Si	1 (fixed)		<50	1 (fixed)		28
	S		1 (fixed)
	Ar		lt500	1 (fixed)	lt500	1 (fixed)
	Ca	1 (fixed)					190
	Fe	>900	>800	>800	>900	>970	190
	Ni	=Fe
	τ3 (109cm−3 s)				6.50		6.49
	Velocity (104 km s−1)	0.59				1	>0.9
	EM3 (1056 cm−3)					0.0078
	χ2/d. o. f.	834.12/662	927.60/713	748.64/644	860.19/681	7748.25/628	545.85/494

Note. Solar abundances from Anders & Grevesse (1989). The τ lower limit is set to be 5 × 10⁸ cm⁻³ s. The abundance upper limit is set to be 1000 times the solar one. The velocity upper limit is set to be 1 × 10⁴ m s⁻¹. Abundances consistent with their solar values were fixed to 1.

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Table 5.Match between Regions with Proper-motion Measurements Available in the Literature and Regions from This Work

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