Unbiased Spectroscopic Study of the Cygnus Loop with LAMOST. I. Optical Properties of Emission Lines and the Global Spectrum

We have examined the Cygnus Loop using spectra from LAMOST DR 5 released on 2017 December. LAMOST (also known as Guo Shou Jing Telescope) features both a wide field of view (∼20 deg²) as well as a large aperture (∼4 m in diameter), and 16 spectrographs equipped with 32 4K × 4K CCDs allow us to obtain 4000 spectra simultaneously (Cui et al. 2012). Blue (3700–5900 Å) and red (5700–9000 Å) spectra are recorded separately with two CCDs. The spectral coverage is 3700–9000 Å, and a spectral resolution of R ≈ 1800 (corresponding a velocity resolution of ∼167 km s⁻¹) is achieved by placing slit masks of two-thirds width of the fibers (i.e., 22 in diameter; Zhao et al. 2012; Luo et al. 2015). LAMOST raw data are reduced with the LAMOST 2D pipeline (Luo et al. 2015), which are similar to those of the Sloan Digital Sky Survey (Stoughton et al. 2002). The LAMOST 2D pipeline include basic pre-processing such as dark and bias subtraction, flat-fielding, and sky subtraction. The final output of the LAMOST data (combining blue and red channels) are one-dimensional relative flux-calibrated spectra. The data presented in this work are reduced using version 2.9.7 of the pipeline and can be directly downloaded from the LAMOST DR5 archive.⁷ For spectra with a high signal-to-noise ratio (S/N; i.e., S/N ≥ 30 at 4350 Å), a precision of about 10% between 4100 and 9000 Å is generally expected according to a comparison of the spectra of common objects obtained on different nights (Xiang et al. 2015). In this paper, we adopt 10% calibration error, and the final uncertainties are the quadratic sum of the calibration errors and the flux uncertainties mainly arising from the baseline fluctuation in Gaussian fitting (see Section 2.2).

The field of the Cygnus Loop is included in one of the LAMOST regular surveys, the LAMOST Experiment for Galactic Understanding and Exploration (LEGUE; Deng et al. 2012). We found 2747 LAMOST DR5 spectra in the direction of the Cygnus Loop centered at (α_J2000, δ_J2000) = (20^h51^m, +30°40'), which are evenly distributed over the entire SNR as shown in Figure 1. The spectra were obtained on two separate dates, the details of which are summarized in Table 1.

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Table 1.  Observation Summary

Obs. Datea	Plan ID	Seeingb	Exposure Time	Number of Spectra
(yyyy mm dd)		(arcsec)	(s)	(count)
2016 Sep 30	HD205307N293856B01	32	4500	1543
2016 Nov 2	HD205307N293856V01	26	1800	1204

Notes.

^aThe observation median UTC. ^bFWHM of point-spread function measured during exposure representing the weather condition at a given date.

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Because all observations are a part of the LEGUE survey primarily targeting stars, they do not particularly aim to observe the SNR itself. For this reason, many of the spectra can possibly contain stellar emission (see below). To discriminate between spectra of the Cygnus Loop and those of other objects, we first screen all spectra automatically based on the presence of emission lines (i.e., [O iii] λ5007, Hα, and [S ii] λλ6717, 6731), considering that most stellar spectra do not exhibit emission lines except for peculiar stellar types such as Be, Herbig Ae/Be, and Wolf–Rayet stars. By comparing the mean intensity at wavelength ranges of the emission lines and its adjacent continuum level, 778 spectra show that the mean intensity is greater than the continuum level for one emission line or more. Then, we perform visual inspection to classify them into four groups; (I) SNR-dominated spectra, (II) SNR+stellar spectra, (III) stellar spectra with tentative SNR emission or ambiguous association with the SNR, and (IV) spectra not associated with the SNR. For Group II, we divide them into two subgroups, IIa and IIb: IIa spectra exhibit as rich emission lines as Group I shows, whereas only a few lines (Hα, [N ii], and [S ii] lines in most cases) are clearly detected in IIb spectra. Therefore, Group I and IIa spectra are mainly used for further analysis, yet Group IIb spectra are included when only [S ii] doublets are analyzed such as deriving electron densities (n_e, see Section 3.2). Finally, the numbers of spectra in Groups I, IIa, IIb, III, and IV are 75, 79, 214, 176, and 234, respectively, which are marked with different colors in Figure 1. Details of the spectrum classification are summarized in Table 2.

Group I contains 75 spectra dominated by SNR emission; Strong emission lines such as Hα, [S ii], [N ii], and [O iii] appear clearly, and stellar features such as absorption or a continuum, if present, are negligible when SNR emission lines are extracted. Their associations with the Cygnus Loop are also confirmed by their spatial correspondences to the optical emission from the SNR seen in Figure 1. Two exemplary spectra in Group I (obs. ID 470512087 and 470512137) are presented in Figure 2. The spectrum of obs. ID 470512087 is dominated by the strong [O iii] λλ4959, 5007 lines whereas that of obs. ID 470512137 features the Balmer-series lines (i.e., Hα, Hβ, Hγ, etc.). All Group I spectra at the entire wavelengths (3500–8900 Å) are shown in Figure A1.

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Those showing both SNR emission and stellar features are classified into Group II. This can occur when diffuse emission from the Cygnus Loop and a background or foreground star are included within a single fiber. More than one-third of the first-screened spectra (IIa + IIb: 293) belong to this category, which is a natural consequence considering the fact that the LAMOST survey primarily intends to target stellar objects in this field. Group II spectra show clear emission lines from the Cygnus Loop as well as nonnegligible stellar features such as a series of hydrogen absorption features, Na i and Ca ii absorption, and a blue (or red) stellar continuum. In Figure 2, two IIa spectra are shown: obs. ID 470514090 and 475216086. The former spectrum shows the emission lines from the SNR on top of an F-type stellar spectrum featured by strong H and K of Ca ii whereas the latter shows the SNR emission as well as an M-type stellar spectrum characterized by a set of TiO bands. For this group, careful line identification is required, especially for those lines affected by strong absorption (see Section 2.2). The locations of Group II spectra (IIa and IIb marked by cyan and blue circles, respectively, in Figure 1) are spatially in a good agreement with the SNR emission shown in the DSS2 image.

Group III spectra exhibit emission lines of which the origin is unclear. When several emission lines not usually seen in stellar spectra are marginally detected, these spectra are classified into this group. In some cases, Group III spectra show a few strong emission lines such as Hα, [S ii] λλ6717,6731, or [O iii] λ5007. However, they do not have high [S ii]/Hα ratios, which is often used as a diagnostic of SNR origin (e.g., see McKee & Hollenbach 1980; Fesen et al. 1985; Long 1985), or this ratio cannot be measured properly because the Hα or [S ii] lines (or both) are contaminated or do not appear. Moreover, their spatial correspondences to the SNR emission shown in the DSS2 image are not often discernible. Ambiguity of their association is partially due to lack of narrowband images (e.g., Hα image). The presence of Balmer-dominated filaments from nonradiative shocks in the Cygnus Loop is well known (e.g., Raymond et al. 1983; Fesen et al. 1985; Long et al. 1992; Hester et al. 1994; Sankrit et al. 2000; Ghavamian et al. 2001; Blair et al. 2005; Medina et al. 2014; Katsuda et al. 2016), but these filaments are usually fainter than emission from radiative shocks. Since faint Balmer-dominated filaments may not be distinct in the DSS2 red image, it is currently inconclusive whether those showing Balmer lines only in Group III originate from the Cygnus Loop. For example, a spectrum of obs. ID 470509056 presents a weak Hα line only (see Figure 2). This spectrum might be related to one of Balmer-dominated filaments, but its location (α_J2000, δ_J2000) = (20:57:39.9, +30:40:05.7), relatively far away from the bright filaments, requires further verification. Likewise, no prominent lines except for [O iii] λλ4959,5007 (and weak [O ii] λ3727) are found in several Group III spectra, which are most likely associated with the SNR, too. For example, the spectrum of obs. ID 470516196 shows (see the zoomed-in spectrum near Hα in Figure 2) the presence of weak absorption at the wavelengths of [S ii] (and [N ii]), which implies that several emission lines from the SNR are oversubtracted during the removal of night sky lines. There are 176 spectra in this category, and most of them are located in the vicinity of the bright filaments or diffuse interior (see the spatial distribution of black circles in Figure 1). This suggests that Group III spectra are likely to be associated with the SNR, and further investigation will clarify their origin.

Group IV is for stellar-emission-only spectra. Two-hundred thirty-four spectra are classified based on no evidence for any association to the SNR. Figure 1 shows that Group IV spectra (yellow circles) are uniformly distributed over the entire remnant in general, which supports their nonassociation with the SNR.

For Group I and II, line identification is carried out to measure line intensities and to derive relative ratios. Those with high S/Ns clearly exhibit various emission lines as previously reported (e.g., Fesen et al. 1982; Fesen & Hurford 1996): [O ii] λ3727, [Ne iii] λ3869, [S ii] λλ4069, 4076, [O iii] λ4363, [Fe iii] λ4658, He ii λ4686, [O iii] λλ4959, 5007, [N i] λ5200, [N ii] λ5755, He i λ5876, [O i] λλ6300, 6364, [N ii] λλ6548, 6583, [S ii] λλ6717, 6731, [Ca ii] λλ7291, 7324, [O ii] λλ7320, 7330, and the Balmer lines (e.g., Hα, Hβ, Hγ, etc.).⁸ Various weak lines are also detected including [Fe ii] λ4359, [Fe iii] λ4986, [Fe ii] λ5158, [S iii] λ6312, He i λ7065, [Ar iii] λ7136, [Fe ii] λ7155, He i λ7281, and [Ni ii] λ7378. To handle bulk data consistently and efficiently, we do not aim to fit every detected line, only fitting those needed for further analysis. Consequently, intensities of 15 emission lines (i.e., [O ii] λ3727, [Ne iii], [O iii] λ4363, Hβ, [O iii] λ4959+, [N i], [N ii] λ5755, [O i] λ6300+, [N ii] λ6548+, Hα, and [S ii] λ6717+) are obtained for Groups I and IIa, and only [S ii] λ6717+ are obtained for Group IIb.

For Group I spectra (i.e., SNR-dominated spectra), line intensities are measured by a Gaussian fit with a linear baseline to each line profile. When two or more emission lines are adjacent, such as Hα and [N ii] λ6548+ or [S ii] λ6717+, a single baseline from a wider wavelength range is used for all of these lines. Integrated intensities normalized to Hβ are listed in Table 3. Although LAMOST sky subtraction using principal component analysis reduces the averages of residuals down to ∼3% (Bai et al. 2017), several emission lines, especially weak lines, could still be contaminated by the residuals. For instance, relatively weak [O iii] λ4363 might be affected by Hg line at 4358 Å arising from mercury streetlights, and [O i] λ6300+ can be contaminated by imperfect subtraction of the strong [O i] night sky emission. When the determination of the baseline is problematic or the emission feature is damaged, only upper limits are quoted.

For Group IIa spectra (i.e., SNR+stellar spectra), most of line intensities are measured in the same way as those for Group I. When hydrogen absorption is significant or other stellar features contaminate the neighborhood of an emission line, however, additional treatment is applied (see examples in Figure 3). For Hα or Hβ lying on top of a stellar absorption feature, the absorption feature is first fitted with a negative Gaussian (or a Lorentz profile for some cases with a wider wing). For instance, Obs. ID 470514090 shows a series of H absorption features, which is fitted by a negative Gaussian (green line in Figure 3). Then, the fitted absorption profile is used as a baseline to fit the emission line from the SNR. Also, when the star along the line of sight is an M type, TiO bands can dominate its spectrum. In such cases, [O iii] λ4959 is adjacent to one of TiO bands (e.g., see obs. ID 475216086 in Figure 3), so we only use its redward range (marked with blue "x" in Figure 3) for baseline fitting. Measured line intensities relative to Hβ for Group IIa spectra are listed in Table 4.

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In spite of the 10% precision expected for high-S/N spectra (Xiang et al. 2015, see also Section 2.1), note that there are indications of larger errors in some spectra. The Balmer decrements, Hα/Hβ, should be close to 2.9 in the recombining plasma of SNR shocks (Hummer & Storey 1987), and the typical reddening to the Cygnus Loop E(B–V) (Fesen et al. 2018) would increase that ratio to 3.1–3.2. Spectra in Tables 3–4 below span the range from 2.02 to 6.25. Relatively slow shocks in partly neutral gas can produce higher Balmer decrements (Raymond 1979), but the high [O III]/Hβ ratios of those spectra show that they are not such slow shocks. A higher reddening could account for some of the spectra with large Balmer decrements, and the western limb of the Cygnus Loop shows the interaction of the shock with a dense cloud having E(B–V) up to about 0.5 (Fesen et al. 2018), but even that would not account for Balmer decrements above 4. We conclude that some of the measured Balmer line ratios are erroneous by factors of 1.5 or more. This might be an offset between the red and blue sections of the spectra, but there is no obvious correlation between Balmer decrements and ratios between other lines at the red and blue ends of the spectrum. We therefore caution that the uncertainties are larger than might have been expected, and those with Hα/Hβ < 2.9 or >4.0 are denoted with open symbols in Figures 4–8.

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For the 154 Group I and IIa spectra in total, we measure line intensities relative to Hβ. To the best of our knowledge, this is the largest sample of optical spectra with line measurement observed in the Cygnus Loop, which does not just focus on bright filaments but covers all regions of the SNR. As listed in Tables 3 and 4 and presented in the sample spectra in Figure 2, the relative strengths of line emission vary significantly at different positions within the Cygnus Loop, and correlations among line ratios of different elements or different transitions are observed. As previously noticed (e.g., Fesen et al. 1982, hereafter, F82), the intensity of [O iii] λ4959+ relative to Hβ varies over two orders of magnitude (from 0.15 to ≳25 in Group I), and other lines such as [O ii] λ3727, [N ii] λ6548+, and [S ii] λ6717+ also vary in intensity over an order of magnitude, suggesting the presence of diverse physical conditions inside the single remnant. Note that dereddening is not applied here since the LAMOST spectra are only relatively flux calibrated (Section 2.1). However, as extinction to the remnant is relatively low (e.g., E(B–V) = 0.08 mag, Parker 1967), we postulate this does not affect our results significantly, in particular, when we compare emission lines nearby. To demonstrate the effect of extinction, line ratios using measured intensities and those of dereddened intensities in F82 are overplotted as a reference (see Figures 4–8).

3.1.1. Line Ratios of Different Elements

Systematic correlations appear between line ratios of different elements, especially with the same ionization state. For example, those with a high-ionization state such as [Ne iii] and [O iii] λ4959+ show a tight correlation (correlation coefficient⁹ of R = 0.90) with each other (Figure 4(a)). This is a natural consequence of the fact that lines from high-ionization species tend to be strong where lines from other elements with high ionization are strong. Similarly, close correlations of [N i] with [O i] λ6300+ and [N ii] λ6548+ with [S ii] λ6717+ are also present (Figures 4(b) and (c)). Where low-ionization or neutral species emit strongly, lines from other low-ionization species appear to be strong, while lines from high-ionization species become weaker.

The ratio of [S ii] λ6717+/Hα is a well-known shock diagnostic (e.g., Mathewson & Clarke 1973): a high [S ii] λ6717+/Hα ratio (i.e., ≳0.4) indicates SNRs whereas a low ratio (often ∼0.1) indicates H ii regions. In Figure 4(d), the intensity of [S ii] λ6717+ is compared with the Hα intensity. Except for a few points, the [S ii] λ6717+/Hα ratios measured from the Group I and IIa spectra well exceed 0.4, corroborating the SNR origin. The observed ratios mostly range between 0.4 and 2.0 (between dotted lines in Figure 4(d)), and the median is ∼1.1 (dashed line). Besides those with [S ii] λ6717+/Hα ≥ 0.4, there are 10 spectra (4 Group I and 6 Group IIa) showing significantly weak [S ii] λ6717+ emission relative to Hα (i.e., 0.13 ≲ [S ii] λ6717+/Hα ≲ 0.34). Half of them are along the interior filaments (like position H of F82), four are located at the outskirts of the bright NE region NGC 6992, and one is near the bright SW region NGC 6960. These spectra show either strong [O i] λ6300+ and/or [O ii] λ3727 line emission or high [O iii] λ4959+/Hβ ratio, or both. Because of their locations as well as their spectral features, their emission is probably associated with the Cygnus Loop.

We compare [N ii] λ6548+/Hα and [O i] λ6300+/Hα ratios with respect to [S ii] λ6717+/Hα in Figure 5, which are previously known to correlate, especially for extragalactic SNRs (e.g., Smith et al. 1993; Gordon et al. 1998; Lee et al. 2015; Long et al. 2018). The [N ii] λ6548+/Hα ratios of the Cygnus Loop show a fairly good correlation with the [S ii] λ6717+/Hα ratios (R ≃ 0.75), verifying it as the secondary shock indicator. A linear fit to the correlation is performed, which gives [N ii] λ6548+/Hα = (0.10 ± 0.04) + (0.98 ± 0.03) × [S ii] λ6717+/Hα (dashed line in Figure 5 (left panel)). On the other hand, [O i] λ6300+/Hα shows no evidence for correlation with [S ii] λ6717+/Hα (R = 0.17, see Figure 5 (right panel)). This is somewhat surprising because [O i] λ6300+ lines are considered to be a useful discriminant for shock-heated gas, and this ratio shows a good correlation with [S ii] λ6717+/Hα as [N ii] λ6548+/Hα for extragalactic SNRs (e.g., Gordon et al. 1998, see also Lee et al. 2015). We attribute the lack of correlation partly to observational difficulties because the [O i] emission from the night sky can contaminate the LAMOST spectra, especially those with low S/Ns (see Tables 3–4). However, the correlation is not apparent in the samples of F82, either. Also, the correlation appears weak for SNRs in some other galaxies (see Figure 11 of Lee et al. 2015). Thus, the correlation between [O i] λ6300+/Hα and [S ii] λ6717+/Hα may be limited to radiative SNRs with bright optical emission lines and needs a more careful investigation.

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3.1.2. Line Ratios of Different Transitions

In Figure 6, we examine line ratios of the same element such as oxygen or nitrogen with different transitions. The largest variation among all possible combination of line ratios is seen in the intensities of [O ii] λ3727 and [O iii] λ4959+ emission relative to Hβ, which range from ∼0.15 to ∼40. Such a large span clearly depicts the diversity of physical conditions within the Cygnus Loop (e.g., Fesen et al. 1982; Levenson et al. 1998). As previously reported in F82, we also note that the ratio of [O ii] λ3727/Hβ is no less than ∼4 in any case (see Figures 6(a) and (b)), whereas both [O i] λ6300+/Hβ and [O iii] λ4959+/Hβ can be as low as ∼0.15. This distinction of the [O ii] λ3727/Hβ ratios (i.e., [O ii] λ3727/Hβ ≳ 4) has been seen in other Galactic SNRs as well as extragalactic SNRs (e.g., see Figures 3 and 4 of Fesen et al. 1985), which can be used to separate SNRs from H ii regions.

The intensities of [O ii] λ3727 and [O iii] λ4959+ relative to Hβ appear to correlate moderately (R = 0.54, Figure 6(a)) whereas [O ii] λ3727 and [O i] λ6300+ do not show an apparent correlation (Figure 6(b)). However, as guided by the data from F82 (diamonds in Figure 6(b)), the general trend would exist in a way that the [O ii] λ3727/Hβ ratios tend to decrease as the [O i] λ6300+/Hβ ratios increase.

For nitrogen, the [N ii] λ6548+/Hβ ratio seems to correlate with the [N i]/Hβ (R = 0.69, Figure 6(c)) while the [N ii] λ5755/Hβ has no correlation with [N i]/Hβ (R = −0.03, Figure 6(d)). Note that [N ii] λ6548+/λ5755 is sensitive to electron temperature (see Section 3.2). Then, the different trends seen in Figures 6(c) and (d) imply the variation of temperature inside the remnant. However, we should be cautious to interpret the trends because those with large [N i]/Hβ ratios (i.e., [N i]/Hβ ≳ 0.7) also have relatively large uncertainties, and those with the large [N i]/Hβ ratios (except one data point from F82) do not appear in Figure 6(d) due to nondetection of the [N ii] λ5755 line. The presence of the correlation should be further examined with high signal-to-noise data.

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Electron temperatures of ionized plasma are commonly derived from a set of forbidden line emission emitted by metastable levels of positive ions, such as [O iii], [N ii], and [S ii]. A main representative is the ratio of [O iii] λ4959+/λ4363 (e.g., Osterbrock & Ferland 2006, OF06, hereafter). The [O iii] ratios in comparison with the [O iii] λ4959+ intensities relative to Hβ are shown in Figure 7 (left panel). Adopting the exponential approximation of OF06 expressed as

$$\begin{eqnarray}&&\displaystyle \frac{{j}_{\lambda 4959}+{j}_{\lambda 5007}}{{j}_{\lambda 4363}}=\displaystyle \frac{7.90\exp (3.29\times {10}^{4}/T)}{1+4.5\times {10}^{-4}{n}_{{\rm{e}}}/{T}^{1/2}},\end{eqnarray} \tag{ 1 }$$

[O iii] line temperatures for Group I and IIa are estimated in Figure 7 (right panel). In addition, we calculate theoretical ratios at a density of 100 cm⁻³ using version 8 of the CHIANTI database (Dere et al. 1997; Del Zanna et al. 2015), which are overlaid with a dotted line. CHIANTI consists of critically evaluated set of up-to-date atomic data, together with user-friendly programs written in Interactive Data Language and Python to calculate the spectra from optically thin, collision-dominated astrophysical plasma.¹⁰ Up to ∼50,000 K, the ratios from CHIANTI are consistent with those from the exponential approximation, but they start to deviate at higher temperatures.

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Overall, [O iii] temperatures from Group I and IIa spectra range between ∼30,000 K and 80,000 K, which are in good agreement with previous estimates (e.g., Miller 1974; Fesen et al. 1982). However, a few cases with the [O iii] ratios less than ∼10 indicate that the temperature exceeds ∼10⁵ K, which is above the equilibrium formation temperature. Such a high temperature has been reported previously (e.g., T_e ≳ 80,000 K, Sankrit et al. 2014), which would occur in the narrow ionization zone just behind an X-ray producing (nonradiative) shock (e.g., Blair et al. 2005). The emission from these regions, however, could be too faint to be detected by LAMOST. Hence, there is a possibility that the overestimation of the [O iii] λ4363 intensity leads the [O iii] ratios to be less than ∼10. Fitting its underlying baseline is sometimes uncertain due to the presence of absorption features nearby. In fact, Group IIa spectra, which are more affected by stellar features, tend to have lower [O iii] ratios than Group I spectra, implying that the overestimation of [O iii] λ4363 is conceivable.

Another temperature diagnostic is the ratio of [N ii] λ6548+/λ5755. In Figure 8, we compare the [N ii] and the [O iii] ratios and derive the [N ii] temperature in the same manner as Figure 7. Again, adopting the exponential approximation of OF06, the theoretical [N ii] ratio as a function of temperature (T) is given by

$$\begin{eqnarray}&&\displaystyle \frac{{j}_{\lambda 6548}+{j}_{\lambda 6583}}{{j}_{\lambda 5755}}=\displaystyle \frac{8.23\exp (2.50\times {10}^{4}/T)}{1+4.4\times {10}^{-3}{n}_{{\rm{e}}}/{T}^{1/2}},\end{eqnarray} \tag{ 2 }$$

shown with a solid line in Figure 8 (right panel). Also, theoretical ratios from the CHIANTI database are overlaid with a dotted line. Note that the [N ii] λ5755 line is poorly detected in most Group IIa spectra due to its faintness; hence, only Group I spectra are used to estimate [N ii] temperature. The resultant [N ii] temperatures are mostly between 10,000 and 15,000 K, which is substantially lower than those from the [O iii] ratios (see Figure 7). Also, there is no clear correlation between [N ii] temperatures and [O iii] temperatures. The higher temperature inferred from [O iii] with a higher ionization state and no correlation between [N ii] and [O iii] is a natural feature of a region behind a radiating shock, where cooling and recombination to the lower-ionization state occur in succession. This trend has been reported in the literature (e.g., Miller 1974; Fesen et al. 1982) and is also found in other SNRs. For example, Pauletti & Copetti (2016) show the spatial variations in temperature maps of the SNR N49 in the Large Magellanic Cloud, which clearly demonstrate higher temperatures for [O iii] line ratios compared to the [S ii], [O ii], and [N ii] temperatures and different spatial distribution of the temperatures through the SNR.

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The line ratios of [S ii] λ6717/λ6731 (e.g., Osterbrock & Ferland 2006) and [O ii] λ3729/λ3726 (e.g., Pradhan et al. 2006) are among common diagnostic tools for deriving the electron density (n_e). As the latter pair is closely located in wavelength, it is not resolved in the LAMOST spectra (R ∼ 1800). In Figure 9 (left panel), we compare the [S ii] λ6717/λ6731 ratios with the relative intensity of [S ii] λ6717+. Because the [S ii] doublet is clearly detected even in the Group IIb spectra in most cases, Group I, IIa, and IIb are used for the n_e estimate. The [S ii] ratios mostly range between 1.0 and 1.5 while some outliers having extremely low or high values are present (see below).

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Using the CHIANTI calculations, we estimate the electron density from the [S ii] λ6717/λ6731 line ratios (Figure 9, right). [S ii] electron densities mostly range between ≲20 and ≈500 cm⁻³, which are consistent with previous estimates (e.g., Miller 1974; Fesen et al. 1982). Two significant outliers are the lowest (∼0.31) and highest (∼1.76) [S ii] ratios, which come from obs. ID 475211106 (Group I) and 475216066 (Group IIa) spectra as shown in the insets. The two spectra clearly show different trends: [S ii] λ6731 is much stronger than [S ii] λ6717 in obs. ID 475211106, and vice versa for obs. ID 475216066. The ratios outside the range given by the high- (≳1.4) and low- (≲0.5) density limits indicate measurement errors, which possibly result from the sky spectrum contaminated by the diffuse SNR emission or unapparent confusion with other emission sources (see more in Section 4.2).

We investigate shock parameters to explain the measured line ratios of the global spectrum by using the shock code developed by Raymond (1979) and Cox & Raymond (1985) with updated atomic parameters. Among the parameters necessary for the calculation of the forbidden lines of O and S, we updated the electron collision strengths to the recently calculated ones for O i (Zatsarinny & Tayal 2003), O ii (Kisielius et al. 2009), O iii (Storey et al. 2014), and S ii (Tayal & Zatsarinny 2010). The code assumes an 1D steady flow, using the Rankine–Hugoniot jump conditions to find the post-shock gas parameters. Then it uses the fluid equations to compute the density, temperature, and velocity as the gas cools. The perpendicular component of the magnetic field is assumed to be frozen in, and it is compressed with the gas as it cools. Time-dependent ionization calculations including photoionization are used to compute the cooling rate and the emissivities of spectral lines.

Shock emission analysis of individual filaments in the Cygnus Loop has been carried out in several previous studies (Miller 1974; Raymond 1979; Fesen et al. 1982; Hester et al. 1983; Raymond et al. 1988; Blair et al. 1991; Danforth et al. 2001, and references therein). According to these studies, the optical spectra of bright filaments can be modeled by either complete or incomplete shocks with shock speeds in the range of 60–140 km s⁻¹ and ambient densities 4–20 cm⁻³. We have run shock models for shock speed v_s = 60–200 km s⁻¹ and pre-shock density n₀ = 10 cm⁻³. For the magnetic field strength B₀, we adopt 5 μG, which is close to the median total magnetic field strength (6 μG) of the diffuse (n ≤ 300 cm⁻³) interstellar cloud (Heiles & Troland 2005; Crutcher et al. 2010). For the abundances of chemical elements, we use the solar abundances suggested by Asplund et al. (2009), Scott et al. (2015b), and Scott et al. (2015a). The abundances of the elements that show strong lines in the global spectrum are [N/H] = 7.83, [O/H] = 8.69, [Ne/H] = 7.93, and [S/H] = 7.12 where [X/H] is the log of number of X atoms per 10¹² H atoms. One complication in shock modeling is the pre-shock ionization levels of H and He that affect the post-shock structure and, therefore, the emission-line fluxes (Raymond 1979; Shull & McKee 1979; Cox & Raymond 1985; Sutherland & Dopita 2017). We present a grid of models (Model F) where H is fully ionized and He is in ionization equilibrium with shock radiation. The presence of neutral H would have an effect similar to that of lowering the shock velocity at full ionization (Cox & Raymond 1985). For comparison, we also present a grid of models (Model P) where H is partially ionized. In this model, the ionization fractions of H and He are determined by balancing the upstream ionizing flux with the incoming ion flux, which is a good approximation for slow shocks (Shull & McKee 1979; Sutherland & Dopita 2017). At v_s ≥ 110 km s⁻¹, H is fully ionized in model P, and the difference between the two models becomes negligible. Hence, we present Model F with v_s = 60–200 km s⁻¹, whereas Model P with v_s = 90–130 km s⁻¹ are used for comparison. Pre-shock ionization levels of the these cases are summarized in Table 6. Finally, the models do not include emission from the photoionization precursor, which can be important for shocks faster than about 150 km s⁻¹ (Dopita & Sutherland 1996). However, the precursor emission is faint and diffuse, so its contribution in a 22 fiber would be small.

The measured line ratios are compared with the model calculations in Table 7. Considering that bright filaments in the Cygnus Loop are often assumed to have typical shock velocities around 100 km s⁻¹ in the literature, most models in Table 7 (i.e., v_s ≳ 80 km s⁻¹) can reasonably reproduce the measurements within a factor of two or three. Models F120 and P110 show good agreement in the temperature-sensitive ratios (especially for [N ii] λ6548+/5755 ratios), consequently tracing shock velocity but predicting slightly large [O iii] λ4959+/Hβ and small [O ii] λ3727+/[O iii] λ4959+ ratios. In fact, all models except F60 and P90 produce lower [O ii]/[O iii] ratios than the observed one, and all but F60, P90, and F200 give higher [O iii]/Hβ than the observed. This may indicate a mixture of low- (≲100 km s⁻¹) and high-speed shocks with the presence of partially ionized H. In addition, the observed [O ii] λ3727+/[O iii] λ4959+ ratio higher, which is than those shown in most of the shock models, could result from depletion of carbon and silicon since [O ii] λ3727+/[O iii] λ4959+ is sensitive to these elemental abundances (Raymond 1979; Fesen et al. 1982).

Note that the F120 or P110 models are not necessarily the best shock models to explain the global spectrum. Because we do not compare all measurable line ratios between the data and the models, it could be unfair to choose the best shock model to describe the global properties of the Cygnus Loop just based on Table 7. However, the current results verify that the global spectrum can be characterized by fast (v_s ≳ 100 km s⁻¹), radiative shocks and suggest the necessity of modifying the model parameters such as the elemental abundances. We will make detailed comparisons among different shock models and also discuss the spatial variation of shock parameters in our forthcoming paper.

One of the main results that the LAMOST data show is that the line intensities inside the remnant vary more significantly than was previously thought, perhaps because earlier studies selected bright filaments. The uncertainties in the LAMOST data that cannot be explicitly estimated would account for some of the variation (see below). However, the large variation in the line ratios can still have an important impact on understanding the evolutionary stages of SNRs as well as characteristics of extragalactic SNRs, particularly because a small variation in line strength within a single SNR is often a fundamental assumption for these studies (e.g., Daltabuit et al. 1976; Fesen et al. 1985). The most commonly used ratios for that purpose are Hα/[N ii] λ6548+, Hα/[S ii] λ6717+, and [S ii] λ6717/λ6731 (e.g., Blair & Kirshner 1985; Fesen et al. 1985; Lee et al. 2015; Winkler et al. 2017). The former two ratios probe the N/H and (to some degree) S/H abundances, consequently representing local metallicity, and the [S ii] doublet ratio is a well-known diagnostic of electron density. As the total number of spectroscopic pointings inside the Cygnus Loop increases more than an order of magnitude compared to previous studies, it would be meaningful to provide new ranges of these line ratios and to revisit their trends.

Figure 11 shows histogram distributions of Hα/[N ii] λ6548+, Hα/[S ii] λ6717+, and [S ii] λ6717/λ6731. Group I and IIa spectra are included for all cases, and Group IIb are also used for the [S ii] doublet the same as Figure 9 shows. The distributions of Group I spectra (red bars in Figure 11) show that the ranges of the Hα/[N ii] λ6548+, Hα/[S ii] λ6717+, and [S ii] λ6717/λ6731 ratios are 0.42–2.84, 0.55–5.07, and 0.31–1.54, respectively. When Group IIa are included, these ranges increase by a factor of 2–3 whereas the case of the [S ii] doublet does not show much change even if Group IIb are included. This suggests that the presence of Group IIa outliers that significantly increase the ratio range are likely due to some errors resulting from imperfect subtraction of the Hα absorption feature. In addition, we also note that the ratio range of those with 2.9 ≤ Hα/Hβ ≤ 4.0 in Group I (i.e., excluding those with large uncertainties in the Balmer line ratio, Section 2.2) is as wide as that of all Group I. In fact, it is a natural consequence that uncertainties related to Hα/Hβ such as a mismatch between blue and red spectra or any calibration errors depending on wavelength cannot affect these ratios significantly as the Hα, [N ii] λ6548+, and [S ii] λ6717+ lines are located very closely to each other.

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Fesen et al. (1985) collected previous observational results about these ratios in several Galactic SNRs (see their Table 5). The minimum and maximum values of each ratio combining all previous studies of the Cygnus Loop in their table are 0.66–1.25, 0.61–1.76, and 1.00–1.51 for Hα/[N ii] λ6548+, Hα/[S ii] λ6717+, and [S ii] doublet, respectively (marked with dotted lines in Figure 11). Note that the largest number of observations included in Fesen et al. (1985) is 18 (Parker 1964) while the number of Group I and IIa spectra are 75 and 79, respectively. We examine the Group I spectra that give significantly large Hα/[N ii] λ6548+ (≳1.5) and Hα/[S ii] λ6717+ (≳2.0) ratios. There are six and five Group I spectra with such large Hα/[N ii] λ6548+ and Hα/[S ii] λ6717+, respectively, and four of them are in common. All of these outliers except one (obs. ID 470503149) show strong [O iii] λ4959+ emission relative to Hβ, and more than half have [O iii] λ4959+/Hβ ≳ 6 implying their association with incomplete shocks. It is clear that the line ratios resulting from the LAMOST data are more diverse than those in the literature although a part of this diversity is due to the errors in the LAMOST ratios. For [S ii] λ6717/λ6731, most of Group I (and IIa) spectra well agree with the previous range except the one (obs. ID 475211106) as noted in Figure 9. This is reasonable because its variation is tightly constrained by electron density. As mentioned in Section 3.2, however, the spectrum of obs. ID 475211106 is problematic since its [S ii] doublet ratio is smaller than the high-density limit (i.e., lower than 0.5). It is difficult to explain such a low ratio by any common errors including calibration, data reduction, and background confusion, because the emission lines including [S ii] doublet in that spectrum are clearly detected with high S/Ns and their line profiles are also well-shaped (i.e., no possible residuals from sky subtraction). Further observations with high spatial precision and high spectral resolution are needed to clarify the origin of this abnormal ratio.

The mean values μ (standard deviation) of the ratios are 1.04 (0.45), 1.13 (0.64), and 1.27 (0.16) for Hα/[N ii] λ6548+, Hα/[S ii] λ6717+, and [S ii] doublet, respectively, when Group I spectra are only considered. These values are changed when Group IIa (and IIb) spectra are included, but the change is not significant. Corresponding mean values listed in Fesen et al. (1985) range from 0.88–0.99, 1.00–1.08, and 1.19–1.40, respectively, which well agree with the newly measured μ despite the diversity of the ratio ranges that Group I (and IIa) show. In other words, although the standard deviations of the line ratios are larger than the previous measurements, their mean values are overall consistent. This result implies that as the number of observations (i.e., area that spectroscopy covers) increases, the range of the line ratios might widen, but their mean values can remain the same. This supports the validity of these line ratios as a probe of the evolutionary state or as a tracer of the elemental abundance of the ambient medium.

Another aspect that the LAMOST data, particularly those from the faint filaments, show is the possible contribution of background emission including the precursor emission, the Galactic Hα emission, and the Geocoronal Hα. By targeting bright filaments in the Cygnus Loop, previous studies (e.g., Fesen et al. 1982, 1985, and references therein) can consequently minimize (and subtract off) the background contribution in their sample spectra. The slightly lower Hα/[N ii] λ6548+ and Hα/[S ii] λ6717+ ratios reported in Fesen et al. (1985) than those derived from the LAMOST data could be explained by this. On the contrary, the spectra of poorly resolved (e.g., the Magellanic Clouds) or unresolved (other distant galaxies) SNRs can be affected by these background sources more significantly. In particular, the precursor emission is very diffuse, so its contribution to a global spectrum of an extragalactic SNR would not be negligible compared to bright filaments of the Cygnus Loop or any other bright filaments of Galactic SNRs studied earlier. We will examine the effect of the precursor using shock models in the forthcoming paper.

It is worthwhile to point out that the corresponding ratios of the global spectrum, referred to as "global ratios" hereafter (0.86, 0.92, and 1.16, see Table 7), are systematically lower than the μ values. In particular, since a single spectrum obtained from a spatially unresolved SNR in an external galaxy would be analogous to the global spectrum, it is critical to understand features of the global spectrum and how to interpret them correctly. The global spectrum can be considered to be the brightness-weighted summation while μ is a result of unweighted summation. When outliers have extremely large or small ratios, this can affect μ regardless of their brightness but less so for the global spectrum if the outliers are rather faint. On the other hand, the global spectrum is always dominated by spectra with high surface brightness. In the case of Group I (and IIa), there are particularly large Hα/[N ii] λ6548+ and Hα/[S ii] λ6717+ ratios so that the μ values become relatively larger than those of the global spectrum. Interestingly, the [S ii] doublet ratio of the global spectrum is smaller than μ of Group I, indicating that the bright Group I spectra tend to have small [S ii] ratios tracing high-density regions. This is consistent with the aforementioned description of the global spectrum, which represents the bright spectra usually emitted by dense material swept-up by radiative shocks.

To avoid the effect of the outliers, a median value of each ratio is also examined: 0.92. 0.94, and 1.31 for Hα/[N ii] λ6548+, Hα/[S ii] λ6717+, and [S ii] doublet, respectively, in the case of Group I spectra. The smaller values for Hα/[N ii] λ6548+ and Hα/[S ii] λ6717+ and larger one for the [S ii] doublet compared to μ are a natural consequence of the outliers. These median values can be interpreted as the most common ratios from the sample spectra. Comparing the median ratios with the global ratios, the Hα/[N ii] λ6548+ and Hα/[S ii] λ6717+ ratios show better consistency than μ, but the global [S ii] ratio is again smaller than the median. The better agreement seen in the former two line ratios could support their validity, meaning that these ratios from the global spectrum can probe the overall abundance of the SNR. This can be reasonable if emitting material inside an SNR is mostly ambient ISM with uniform abundance. However, in the case of young core-collapse SNRs where newly formed ejecta can significantly contribute, a global spectrum might give a misleading value for the abundances of the SNR. In the case of [S ii] doublet, it again shows that the ratio of the global spectrum is smaller than the median value. Hence, this further suggests that the electron density measured from the global spectrum is likely to be biased toward denser regions.