SHOCK-ENHANCED C⁺ EMISSION AND THE DETECTION OF H₂O FROM THE STEPHAN'S QUINTET GROUP-WIDE SHOCK USING HERSCHEL^*

The PACS data cubes associated with the three partially overlapping pointings revealed extended [C ii] emission over most of the region defined by the H₂ filament (e.g., the blue emission in Figure 1(a)). Figures 2(a)–(e) show the extracted spectra from Regions A–E (see Figure 1(b)) for the [C ii] 158 μm (solid black) and [O i] 63 μm (solid red) displayed on the same radial velocity scale. To allow a better comparison, the [O i] 63 μm spectra were smoothed to the same velocity resolution as the [C ii] spectra (235 km s⁻¹).

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The extracted spectra show several unusual features. The [C ii] emission is strong, broad, and asymmetric, with typical total line widths exceeding 1000 km s⁻¹. This is consistent with broad warm H₂ emission (Cluver et al. 2010) observed with Spitzer with considerably poorer spectral resolution. Fainter emission from [O i] 63 μm is also detected in Regions A, B and C, covering the same velocity range as the [C ii]. In D and E, the [O i] seems to be only associated with the lower-velocity component of the [C ii] line. We note that the double-peaked profile evident in both the [C ii], CO, and [O i] profiles for Region A is very similar to that seen by Williams et al. (2002) with the VLA in H i emission. H i was not detected in the rest of the main north–south H₂ filament of Figure 1, i.e., sampled by Regions B, C, and D, nor in Region E.

The spectra also resemble the single-dish observations of the CO (1–0) transition of the cold molecular gas obtained with the IRAM 30 m telescope by Guillard et al. (2012). Except for Region B, where the IRAM beam is offset from the PACS extraction center by about 14 arcsec (more than half the FWHM of the IRAM beam at 112.8 GHz—the observing frequency of the CO line), the other pointings differ by no more than 4 arcsec. These spectra are shown superimposed on the PACS spectra in Figure 2, and have been smoothed to an effective spectral resolution of 235 km s⁻¹ to match the [C ii] resolution. Although the [C ii] data do not perfectly match the size and shape of the circular IRAM beam (FWHM 22''), the extracted square PACS spaxels in Regions A, B, and C show similar spectral components to the CO. In Regions B and C, a bright low-velocity component and a fainter high-velocity component are evident, whereas for A, the situation is reversed. The [C ii] emission seems to fill-in the velocity space between the two main components of the CO emission. The nearest IRAM spectrum to Region E is only offset by 2.6 arcsec in declination from the PACS spectrum and yet shows some differences from the PACS extraction. Recent CO observations made with PdB interferometer (P. Guillard et al., in preparation), show significant velocity gradients across that region in the molecular gas, and so the offset in the IRAM pointing may be responsible for the different line shape between the [C ii] and the CO. However, it is clear that both the CO and the [C ii] lines are broad there.²³ The overall similarity between the [C ii] line profiles, and the CO line profiles in the main part of the filament suggests a kinematic connection between the [C ii] emission (and in some cases the [O i] 63 μm emission) and the molecular gas.

In addition to being broad, the [C ii] emission is stronger than the [O i] emission (see Table 1 where the extracted line fluxes are presented). We will argue later that this is consistent with a warm diffuse gas heated by a network of low-velocity magnetic shocks (C-shocks) and/or turbulence. The weakness of the [O i] 63 μm emission is not consistent with strongly dissipative J-shocks (Draine et al. 1983; Hollenbach & McKee 1989; Flower & Pineau des Forêts 2012).

Single and multiple Gaussian line fitting of the extracted [C ii] (and [O i] where appropriate) was performed using the ISAP package developed for Infrared Space Observatory (ISO; Sturm et al. 1998). Line fluxes for the decomposed Gaussian fits are given in Table 2. Regions B, C, and D required three different velocity components spanning the range from 6000–7000 km s⁻¹ to provide a good fit to these data—in most cases very large line widths were required. Region C and E have the broadest fitted single components with FWHM of 630 and 750 km s⁻¹, respectively, although the composite spectra span over 1000 km s⁻¹ in total dispersion.

At each detector position, we simultaneously fit a polynomial continuum and all the targeted lines with individual SINC profiles in frequency. For each SINC profile, we initially fixed the FWHM at the value for an unresolved line (1.44 GHz). The targeted lines are the CO rotational transitions, known water lines, [N ii] 205 μm, [C i] 370, and 609 μm. The only clearly detected line is the water line p-H₂O (1₁₁0₀₀) at ν_rest 1113.3 GHz (= 269.28 μm), which is detected S/N > 5 in four SSW detectors: SSWD4, SSWE3, SSWE4, and SSWC4. The SSW spectrum for detector D4 is shown in Figure 3, where the zoomed-in region shows the p-H₂O (1₁₁0₀₀) line, detected at a S/N of ∼10 (see Table 1). We refitted this line allowing the FWHM to vary, but the line was still found to be unresolved at 324 km s⁻¹ (1.44 GHz) resolution. This is in strong contrast to the [C ii] and [O i] emission which appears much broader. The SPIRE fitted heliocentric velocities and FWHM for the detected positions are provided in Table 2. The heliocentric radial velocity of the H₂O line for SSW D4 is 6457 ± 120 km s⁻¹, which places it close to the line-center of the broad, but asymmetric [C ii] emission from the same position (PACS Region C of Figure 2(c)). Table 2 also provides the central velocity and FWHM for the other detections in SSW E3, E4, and C4. Note that there appears to be a significant radial velocity difference between the center of the SQ shock near SSW D4 and the SSW C4 (shock-south) and SSW E3 (shock-north) detector positions. This follows the general trend of lower heliocentric velocities in the southern part of the shocked filament (Guillard et al. 2012).

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Interestingly, no other H₂O lines are detected (Table 3 provides upper limits). On the para-H₂O ladder, the next highest ground-state transition is the p-H₂O (2₀₂ 1₁₁) line at 987 GHz, and on the otho-ladder, the o-H₂O (1₁₀ 1₀₁) at 557 GHz. Neither of these or other higher-order lines are detected at 3σ levels of <0.48–0.2 × 10⁻¹⁷ W m⁻², 3–5 times lower than the detection of the pH₂O (1₁₁ 0₀₀) line.

Table 3. Upper Limits to Important Undetected Lines

SPIRE	Line	Rest ν	R.A.	Decl.	Line Fluxb	Beam FWHM	Comment
Detectora		(GHz)	(J2000)	(J2000)		(arcsec)
SLWC3	CO 4–3	461.040	22 36 00	33 58 04	<1.1	46	3σ upper limit
SLWC3	CO 5–4	576.267	22 36 00	33 58 04	<0.46	37	3σ upper limit
SLWC3	CO 6–5	691.473	22 35 00	33 58 04	<0.27	31	3σ upper limit
SLWC3	CO 7–6	806.651	22 35 00	33 58 04	<0.21	26	3σ upper limit
SLWC3	CO 8–7	921.800	22 35 00	33 58 04	<0.34	23	3σ upper limit
SLWC3	pH2O 202111	987.927	22 35 00	33 58 04	<0.48	21	3σ upper limit
SLWC3	pH2O 211202	752.033	22 35 00	33 58 04	<0.26	28	3σ upper limit
SLWC3	oH2O110101	556.936	22 35 00	33 58 04	<0.47	38	3σ upper limit
SSWD4	[N ii] 205 μm	1461.132	22 35 00.4	33 58 04.2	<0.27	14	3σ upper limit
SSWD4	OH$_c^+$	1033.004c	22 35 00.4	33 58 04.2	<0.45	21	3σ upper limit
SLWC3	OH$_a^+$	909.045c	22 35 00.4	33 58 04.2	<0.30	23	3σ upper limit
SLWC3	OH$_b^+$	971.803c	22 35 00.4	33 58 04.2	<0.28	22	3σ upper limit

Notes. ^aRegions defined in Figure 1. ^bFluxes in units of 10⁻¹⁷ W m⁻². ^cOH⁺ rest frequencies from Bekooy et al. (1985).

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The [N ii] λ205 μm line (ν_rest = 1461.13 GHz), a line often associated with H ii regions, is not detected, nor are any of the higher-J CO lines, commonly found in SPIRE spectra of higher-excitation galaxies detected convincingly. Upper limits for these and other commonly encountered ISM lines are also given in Table 3.

Spitzer IRS observations obtained as part of a large spectral mapping program (Cluver et al. 2010) contain important spatial information about molecular hydrogen cooling and PAH emission across the SQ filament. For comparison with the PACS regions, we performed matching extractions of the IRS data cubes covering the same areas as the PACS Regions A–E. The spectra, shown in Figure 4, are strongly dominated by molecular hydrogen lines.

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Figure 4 also shows the model result of running PAHFIT (Smith et al. 2007b) on the spectra. The red lines show the fits to atomic and molecular lines (mainly H₂), and the green line under each spectrum shows the fitted PAH features. The results of the fit, converted into line fluxes, are presented in Table 1. It is clear from the spectra that the H₂ lines, 0–0 S(0) to S(5), dominate the spectrum of the SQ filament, with faint emission from [Ne ii] 12.8 μm. Stronger emission from the [Si ii] 34.8 μm line is likely shock-excited (Cluver et al. 2010).

The IRS spectra in Figure 4 show that in the filament, the 6.3 and 7.7 μm PAH bands, usually associated with star formation are very weak, especially in PACS Regions B, C, and E. Faint 11.3 μm PAH is detected at most positions, although the total power in all of the PAH lines is small. In Table 1, we tabulate the power in the 7–8 μm PAH features (defined as the sum of the 7.4, 7.6, 7.8, 8.3, and 8.6 μm bands if present), as well as the integral over the main PAH bands (PAH_tot defined here as the sum of all the common PAH features from 6.3–17 μm). We find ratios of 0.35 < H_2tot/PAH_7–8 < 5.2, and 0.19 < H_2tot/PAH_tot < 1.2, values that are incompatible with photodissociation region (PDR) photoelectric heating efficiencies and observations of normal galaxies (see Section 5.3). This property, and the absence of a strong enough soft X-ray flux led to the conclusion that the warm H₂ detected by Spitzer must be shock excited (see also Guillard et al. 2009). The values with the lowest H₂/PAH ratios are Regions A and D, both of which are known to contain some star formation. Here, some PDR heating of the gas may be present, but not dominant.

Unusually large H₂/PAH ratios are also found in the turbulent bridge region between the Taffy galaxies (Peterson et al. 2012), and in a subset of radio galaxies where shock-excitation is believed to heat the H₂ to several hundred K (Ogle et al. 2010; Guillard et al. 2012), as well as in a subset of active galactic nucleus (AGN) dominated galaxies in the SINGS survey (Roussel et al. 2007).

Later in the paper, we will compare the far-IR spectra with the mid-IR spectral properties from these IRS extractions.

Observations of the IR continuum observations in SQ have been hampered by poor spatial resolution at the longer wavelengths with ISO and Spitzer (Xu et al. 2003; Cluver et al. 2010; Natale et al. 2010; Guillard et al. 2010). New PACS and SPIRE observations have recently been made (P. Guillard et al. 2013, in preparation), and we borrow some of the results from that paper to compare with the spectral line properties. Photometry was extracted from archival Spitzer 24 μm (Cluver et al. 2010), and the new observations in the PACS 100 and 160 μm and SPIRE 250, 350, and 500 μm bands. A full description of the photometric Herschel observations is given in the companion paper of P. Guillard et al. 2013, in preparation).

In order to gain the best possible measurement of the mid- to far-IR luminosity from the PACS spectroscopic extraction regions, we followed a two-step process. First we convolved the 24, 100, 160, 250, and 350 μm maps to a spatial resolution appropriate for the 500 μm SPIRE image (∼29 arcsec FHWM). We then extracted a spectral energy distribution (SED) at these five wavelengths from each of the Regions A–E shown in Figure 1(b). This allowed us to fit the 24–500 μm SED with a modified black-body and a mid-infrared power-law (see Casey et al. 2012 for a description of the method). We computed the gas masses from the dust masses, assuming a dust-to-gas mass ratio of 0.006 (Xu et al. 2003). We call this the "smoothed" SED model.

Secondly, in order to estimate the far-IR (FIR) fluxes (Helou et al. 1985; Dale & Helou 2002) in each region, on an angular scale comparable with the [C ii] data, we re-extracted the 160 μm fluxes at the full resolution of the 160 μm map. We then normalized the smoothed SED model to the value at 160 μm from the full-resolution map to derive FIR flux per aperture over the range 42–122 μm. Figure 5 shows the SED obtained from the smoothed data, as well as the SED after tying it to the full resolution 160 μm data, for two examples, Regions A and E. The effect of scaling the SED results in only a minor change when the dust emission is extended (as in the case of Region E). The low flux value for the 24 μm point in Region E, when scaled to the resolution of the 160 μm observation (red point), is evidence for a dearth of small grains (see later). The FIR properties measured in each of the five PACS apertures calculated by this method are given in Table 4.

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Based on the FIR fluxes and [C ii] line strength (summed over all the velocity components detected within each PACS aperture), we calculate the [C ii]/FIR ratio, and this is given Table 1. It can be seen that these ratios are unusually large, ranging from ∼0.04 (Regions A and D) to 0.06–0.08 (Regions B, C, and E). In general, [C ii]/FIR ratios of less than 1% are common in normal galaxies (see Figure 8). Interestingly, the regions that have the highest [C ii]/FIR ratios are also the same regions that show the most extreme [C ii]/PAH ratios. Those regions with known star formation (Regions A and D) have lower ratios, indicating that the star formation influences the results by lowering both ratios.

We also approximately measure the intensity ratio of the [C ii] to CO (J = 1–0) transition based on the spectra of Figure 2, given that the extraction regions for the [C ii] are square and not always precisely aligned with the IRAM 30 m beam. The CO spectra were converted to Jansky units from antenna temperature assuming a value of 6.2 Jy K⁻¹, a value appropriate for compact emission smaller than the 22 arcsec beam. We also scaled the [C ii] extracted fluxes by a factor of 1.54 to account for the difference in the areas of the [C ii] and CO extractions. If the emission is clumpy on the arcsec scale, this scaling may not be appropriate, and the [C ii]/CO ratio would be lower. The results range from 1000 < I([C ii])/I(CO J = 1–0) < 1700 in Regions B–E, and 2400 in Region A (which includes emission from the SQ-A star forming region). These values are on the low-end of the distribution of values found in the Milky Way and other nearby galaxies (e.g., Stacey et al. 1991, 2010). One might be tempted to conclude that the low values of the I([C ii])/I(CO) ratio point toward a low-excitation PDR model, but this is not the case because the same regions also have very elevated [C ii]/FIR ratios placing them outside of any standard PDR model (see Stacey et al. 2010; Figure 3). Low metallicity is also unlikely to be the explanation. The average metallicity of the gas (summed over all the velocity components) is either mildly sub-solar or approximately solar (see Section 5.3 for a more complete discussion). Furthermore, our observations of the I([C ii])/I(CO) ratio deviate significantly (to lower values) from those measured in the LMC/SMC. We will show later that shock models are capable of reproducing the observed ratios.

Could the [C ii] emission we observe be the result of collisional excitation of the ground-state C+ ions by hot electrons in the plasma associated with a faint population of H ii-region population scattered throughout the filament? Although there is evidence for a sparsely scattered population of H ii regions in the shock based on optical and mid-IR measurements (Appleton et al. 2006; Cluver et al. 2010; Guillard et al. 2010), we can directly rule this out from our own observations. Firstly, our SPIRE observations, which cover similar regions to those observed by PACS, show no detection of the [N ii] 205 μm nebula line down to a 3σ uncertainty of 2.7 × 10⁻¹⁸ W m⁻² for detector SSW D4 (centered close to Region C) and 2.0 × 10⁻¹⁸ W m⁻² for the average flux over the four inner detectors which were seen to show H₂O emission. The [N ii] 205 line, because its ionization potential is 14.53 eV (Oberst et al. 2006), almost always arises in H ii regions. The lower limit to the ratio of [C ii] to [N ii], after making a minor renormalization for the area of the SPIRE beams to that of PACS extraction area, is I(C⁺)/I([N ii] 205) > 36 for Region C. These values are significantly higher than those expected for diffuse ionized emission over a realistic range of densities by a factor of >7.

This is not a surprise, since it has been known for some time that the SQ filament contains only a scattering of compact H ii regions along its length (see Xu et al. 2003; Oberst et al. 2006; Trancho et al. 2012). These H ii regions occupy a small volume of the filament. Furthermore, the mass of gas required to explain the strength of the [C ii] line is far too large to be associated with the observed compact H ii regions. Guillard et al. (2009) estimated the mass of ionized gas to be 1.2 × 10⁶ M_☉ over an aperture of 5.2 × 2.1 kpc², based on the emission measure of the Hα line obtained across the filament by Xu et al. (2003), and assuming reasonable conditions in the diffuse medium for the post-shocked gas. This is at least an order of magnitude below the total warm molecular mass in the same aperture.

Given that the SQ filament is known to emit soft X-rays, it is reasonable to ask whether X-rays could heat the gas in the filament. We have shown in previous papers, based on older X-ray data, that the X-ray emission is insufficient to heat the observed warm H₂ emission over the area of the whole filament (Appleton et al. 2006; Cluver et al. 2010). However, since then, new, much deeper Chandra data have become available, which included 97 ks observations (O'Sullivan et al. 2009) which have sufficient depth and spatial resolution to allow a direct comparison with our [C ii] and H₂ data extracted over our 18.8 × 18.8 arcsec² PACS apertures. The results of the X-ray temperature and abundance fits to the X-ray spectra allow us to obtain reliable X-ray luminosities over these areas (see Table 6). From these results, we can show that the [C ii] to X-ray luminosity ratio, L([C ii])/L_Xsoft, varies from 3 to 11 depending on the region. Thus, the X-ray emission is far too faint to explain both the warm H₂ and the [C ii] emission, since the efficiency for heating gas by X-rays is a few percent at most. Only if the X-ray flux was underestimated significantly, could X-rays be the main heat source. This is unlikely since fits to the X-ray data do not suggest a large intervening column, nor does the observed H₂ emission seen in the IRAM observation have enough column density to provide significant X-ray obscuration. Thus, we can be confident that the X-rays are not the primary heating source for the main cooling lines.

Table 6. X-Ray Properties of PACS Regions

PACS	kTb	Zb	LXsoftb,c	LXsoft/LFIR)	[C ii]/LXsoft	H2tot/LXsoft
Regiona	(keV)	(solar)	(1033 W)	(1033 W)
A	0.39 ($^{+0.13}_{-0.06}$)	1.33 ($^{+1.33}_{-1.20}$)	0.90 ($^{+0.02}_{-0.02}$)	0.005	11.1 (1.7)	13.4 (0.4)
B	0.62 ($^{+0.06}_{-0.05}$)	0.12 ($^{+0.06}_{-0.04}$)	3.31 ($^{+0.25}_{-0.25}$)	0.029	2.9 (0.5)	4.6 (0.4)
C	0.71 ($^{+0.05}_{-0.09}$)	0.18 ($^{+0.09}_{-0.06}$)	3.35 ($^{+0.25}_{-0.25}$)	0.023	3.4 (0.6)	5.5 (0.4)
D	0.70 ($^{+0.07}_{-0.09}$)	0.45 ($^{+2.04}_{-0.26}$)	1.66 ($^{+0.18}_{-0.18}$)	0.012	3.6 (0.6)	6.7 (0.8)
E	0.60 ($^{+0.07}_{-0.08}$)	0.15 ($^{+0.12}_{-0.06}$)	2.19 ($^{+0.21}_{-0.21}$)	0.018	3.5 (0.6)	5.9 (0.6)

Notes. ^aPACS regions as defined in Figure 1(b) and Table 1 covering 18.8 × 18.8 arcsec². ^bSoft X-rays (0.5–2 keV) derived from extractions from the Chandra observations by O'Sullivan et al. (2009). ^cAssuming D = 94 Mpc.

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It has been known for many years that C⁺ ions can be excited in PDRs in the diffuse ISM (Tielens & Hollenbach 1985; Watson 1972; Glassgold & Langer 1974; Draine 1978; Hollenbach 1989; Bakes & Tielens 1994). The dominant mechanism is believed to be the heating of gas by photoelectric ejection of electrons from PAH molecules and small grains. The warm gas (mainly the abundant H i and H₂) would then excite [C ii] emission collisionally. Various authors have provided evidence that PAHs dominate over both small and large grains in terms of photoelectric heating efficiency (Watson 1972; Hollenbach & Tielens 1999; Habart et al. 2004). The heating of the diffuse gas may be further enhanced if the metallicity of the gas is low, because UV photons can excite a larger volume at smaller net G, thereby increasing the heating efficiency (see discussion of extended PDRs by Madden et al. 1997; Israel & Maloney 2011).

One direct measure of the efficiency of photoelectric heating is the flux ratio of the [C ii] to total emission from PAH features in the mid-IR spectrum [C ii]/PAH_tot. Here we define PAH_tot as the sum of the PAH feature fluxes from 6 to 17 μm. For diffuse regions in the Galaxy (e.g., Habart et al. 2003), this is typically few percent, and has been directly measured recently in a variety of extragalactic environments (Beirão et al. 2012; Croxall et al. 2012) ranging from 2% to 5%. Figure 8 (see also Table 1, Column 7) shows the [C ii]/PAH ratio for the five PACS regions plotted against far-IR color temperature. Also shown are spatially resolved points from Croxall et al. (2012) for NGC 1097 and NGC 4559—two nearby galaxies observed in the Herschel KINGFISH program (Kennicutt et al. 2011). The plot emphasizes the unusually large ratios of [C ii]/PAH_tot in the SQ shock compared with normal diffuse emission in the outer parts of galaxies.

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Our measured values of [C ii]/PAH_tot ratio range from values of 17%–18% (Regions A and D) to 40%–70% in Regions B, C, and E. The large [C ii]/PAH ratios we observe, especially in Region E, strongly argue against heating of the [C ii] emission by photoelectron from PAH molecules in a diffuse UV field as the primary mechanism for the [C ii] emission, since the efficiency of the photoelectric effect would have to be unusually large to explain the observed result.

Cluver et al. (2010) showed that the 24 μm Spitzer emission from the molecular shock is very weak, perhaps even absent at the shock-center (near Region C) suggesting a dearth of small grains. This can now be quantified more precisely with the new combined Herschel- and Spitzer-derived SED (P. Guillard et al. 2013, in preparation). The 24 μm point for Region E (scaled to the 160 μm resolution—red point in lower panel of Figure 5) shows that it is extremely low, in sharp contrast to the same point in Region A known to contain some star formation (upper panel of Figure 5). Since small grains radiate most efficiently in the 20–30 μm range, it is unlikely that the [C ii] emission could arise from photoelectric heating from small grains, since they seem depleted over much of the filament. Most of the emission from Region E comes from long-wavelength emission, presumably from larger grains where the photoelectric heating of [C ii] is the most inefficient (Bakes & Tielens (1994).

PACS Regions B, C, and E also show unusually high [C ii]/FIR ratios (Table 1). These values ([C ii] between 6% and 7% of the FIR) are much larger than that seen in the diffuse ISM which is typically <1%, and exceeds by at least a factor of two the maximum theoretical efficiency for photoelectric heating of [C ii] by small grains (∼3%) discussed by Bakes & Tielens (1994). To put these values in a more cosmic perspective, we show in Figure 9, the [C ii]/FIR ratio versus the FIR IR luminosity for the five extracted regions overlaid on a plot shown by Stacey et al. (2010) for galaxies in both the nearby and distant universe. Interestingly, the Regions A and D, where the gas filament is contaminated by star formation, show lower [C ii]/FIR ratios, whereas the other regions in SQ that lie in more "pure shock" environments away from known H ii regions, have higher ratios. This suggests that the signature of shocked or turbulently heated gas can be masked by star formation—perhaps explaining why such large ratios are not commonly seen in galaxies with powerful star formation.

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In Figure 10, we show one regime where the observations of the SQ shock seems to fall closer to the norm seen in other galaxies. Here we plot the [O i] 63 μm/[C ii] ratio as a function of the FIR dust color F (60 μm)/F (100 μm) from Malhotra et al. (2001) based on their work with ISO for a set or normal galaxies. Although the points lie to the extreme in color temperature (we determine these colors from the SED fits of P. Guillard et al. 2013, in preparation), the points seem to form an extension of those found for normal galaxies. Recent spatially resolved observations of M82 with PACS (Contursi et al. 2013) show a tail of points which also extend into this region. They mainly arise in the cooler outer parts of M82, with some points possibly being associated with the starburst wind. Malhotra et al. interpreted their plot as an indication that [O i] is excited more, with respect to C⁺, as the dust temperature rises. Our results for SQ appear to confirm that this trend remains true for the gas and dust in the SQ filament, even though we have argued that the process that excites the [C ii] (and presumably [O i]) is not UV radiation in a PDR. In some ways this is unfortunate, because if one is confronted with far-IR diagnostics alone, it is hard to separate shock or turbulently induced gas from a low-density PDR, since both can exist as a diffuse, warm component in the ISM.

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It is interesting to ask what contribution to the [C ii] emission might be expected from a standard PDR (solar abundance), given the low values of far-UV field strength G_o of 1.4 Habing units in SQ measured by Guillard et al. (2010). Such UV radiation must be present to ionize the carbon. Based on the models of Kaufman et al. (1999) and adopting a reasonable density of ∼10³ cm ⁻³, this low G-field would be expected to contribute a surface brightness in [C ii] emission of 1–2 × 10⁻⁶ erg s⁻¹ cm⁻² sr ⁻¹, or between 0.8 and 1.6 × 10⁻¹⁷ W m⁻², for the extraction apertures used in our PACS regions. Thus, the UV radiation field necessary to ionize carbon would contribute between 10% and 15% of the emission detected in the SQ filament regions.

Although we will argue below that the metallicity of the gas is not likely to be a large factor in explaining the results, we next consider what the consequences of reduced metallicity might be in a diffuse PDR. Israel & Maloney (2011) have detected [C ii]/FIR ratios in some regions of the Large Magellanic Cloud (LMC) which range from 1% to 5% (Cloud 9 in LMC-N11 has the highest value), and several regions in the Small Magellanic Cloud (SMC) with elevated values of 0.5%–2%, still unusual compared with most galaxies. These authors argue that PDR models in low metallicity environments can just, but only just, reconcile the [C ii]/FIR ratios in the LMC. The models of Bakes & Tielens (1994) can asymptotically approach values of 5% for low values of G₀. Although one could argue that in the SQ filament, even lower values of G₀ are likely, the extreme value of [C ii]/FIR = 6%–7% seen in the pure-shock regions of B and E seem to push the model to the limit. When combined with the extremely large values of [C ii]/PAH discussed earlier, it seems reasonable to question whether PDR heating of the gas with these large ratios is the only possible way that [C ii] can be heated.

The oxygen metallicity of the gas in the SQ filament has recently been measured using optical emission lines with an IFU by Iglesias-Paramo et al. (2012). The results depend on the velocity regime being considered. Gas consistent with shock-excitation is seen in two main velocity features around 6000–6300 km s⁻¹, and around 6600 km s⁻¹. The low-velocity feature, which is broadly associated with the intruder galaxy's (NGC 7318b) velocity (and corresponding to the broad left-hand peak seen in both the [C ii] and CO spectra shown in Figure 2) has close to solar metallicity, but the higher velocity gas was found to have an oxygen metallicity of 12 + log O/H = 8.35, similar to the SMC. However, this result does not agree with the earlier measurements of Xu et al. (2003) who found 12 + log(O/H) = 8.76—slightly super-solar. The differences may be due, in part, to the different methods used, but may also be due to the difficulty of measuring metallicity when the lines are broad and faint. If we accept that the higher velocity component in the [C ii] and CO profiles could be of lower metallicity, how might this effect our interpretation of the global ratios, such as [C ii]/PAH and [C ii]/FIR? The answer is that the effect is minimal, since the average metallicity of the gas, integrated over the whole profile, is likely to be no less than 0.75 solar, especially as the lower-velocity component dominates the integral flux of the [C ii] in most of the cases shown in Figure 2. As mentioned earlier, no large differences in the I([C ii])/I(CO J = 1–0) ratio between the low- and high-velocity components are obvious, again suggesting that if the higher-velocity component in the [C ii] profiles has reduced metallicity, it must also be compensated for in the CO abundance.

We note that Sargsyan et al. (2012) have noticed large [C ii]/PAH ratios, particularly in galaxies with known AGN. In this case, extinction in the mid-IR was cited as a possible explanation, although no deep silicate features were observed. Furthermore, P. Guillard et al. (in preparation) have discovered similar cases in radio galaxies which already have been shown to contain shocked molecular hydrogen. Thus, although rare, galaxies with extreme [C ii]/PAH ratios are beginning to emerge from the Herschel data. Could shock-heating, or CRs accelerated in the shock be the answer?

We have shown that the bulk of the gas mass in the shock has to be warm (T > 50 K) to account for the observed high [C ii] cooling rate. Since we have ruled out UV and X-ray heating, we are left with two possible heating sources of the gas. The first is CRs, and the second is the dissipation of kinetic energy through turbulence and shocks.

The SQ intergalactic filament was discovered through its synchrotron radiation in the centimeter waveband (Allen & Hartsuiker 1972; van der Hulst & Rots 1981), and thus, CRs are present in the filament. Following the same calculation done in Nesvadba et al. (2010) and Ogle et al. (2010), we compute the CR ionization rate needed to heat the observed gas mass at T ∼ 100 K. For CRs, the heating energy per ionization is ∼13 eV for H₂ gas (Glassgold et al. 2012). To heat the gas we need an ionization rate per nucleon ζ of 1 to 2.5 × 10⁻¹⁴ s⁻¹.

Each ionization destroys one H₂ molecule. For the gas to be molecular, the creation rate of H₂ ($\gamma _{{\rm H_2}} \times n(H\,\scriptsize{I}) \times n({\rm H})$) should be higher than the destruction rate ζ × n(H₂), where γ_H2 is the H₂ formation rate coefficient. From Milky Way observations, γ_H2 ∼ 1–3 × 10⁻¹⁷ cm³ s⁻¹ (Jura 1975). If the molecular fraction of the gas is f_H2 = 2 × n(H₂)/n(H), then the gas can be molecular if γ_H2 > ζ × f_H2/(2n(H) × (1 − f_H2)). For the SQ shock, f_H2 > 0.95, (based on the lack of H i detected in the filament), and so γ_H2 > 9.5 × ζ/n(H). For such a high molecular fraction, we would need n(H) ≫ 1 × 10³ cm³ for molecules to survive if the heating comes from CRs, unless the formation rate of H₂ per collision is much larger than the Galactic value. For example, if we assume n(H) is 1000 cm⁻³, then γ_H2 would be 1.9 × 10⁻¹⁶ cm³ s⁻¹.²⁵ Therefore, we conclude that in order for CR heating to be viable, it would require much higher densities of the molecular gas than is observed.

We believe that the most likely heating source for the gas in the filament is the dissipation of kinetic energy released through a turbulent cascade from a large scale (set by the size of the intruder galaxy and its high velocity) to a small scale, with most of the dissipation being at small scales. This heating source was proposed by Guillard et al. (2009) to account for the warm H₂ emission in SQ, and shown to be viable for the similar heating of warm H₂ in the bridge between the Taffy galaxies (Peterson et al. 2012).

There is no shortage of available energy to be dissipated in a high-velocity collision between, in this case, NGC 7318b and a pre-existing H i filament. The turbulent heating rate per unit H₂ molecule, Γ_turb = (3/2) × 2m_H(σ²)/τ_d, where τ_d = L/σ is the dissipation timescale. Here, σ is the characteristic velocity dispersion of the gas, L is the characteristic length for the system, and m_H is the mass of the hydrogen atom. Given the observed velocity widths of typically ΔV(FWHM) = 400–800 km s⁻¹, then σ = ΔV(FWHM)/2.36 for a Gaussian distribution, lies in the range 170–340 km s⁻¹. For a galaxy colliding with gas clumps with scales of order 4–8 kpc, the dissipation time is τ_d ∼ 25 Myr, and Γ_turb = 2–8 × 10⁻³¹ W molecule⁻¹, or approximately 4–5 times the cooling rate of the C⁺ ions (5–8 × 10⁻³² W H⁻¹—see Figure 6), and a similar magnitude for the warm H₂.

Thus, turbulence is quite capable of delivering energy at the right rate for a significant period of time. This energy is likely to be funneled to the smallest scales through a network of low-velocity shocks (Guillard et al. 2009; Lesaffre et al. 2013) or intermittent vortices (Godard et al. 2009) via supersonic turbulence. Using a similar model, B. Goddard et al. (in preparation) show that turbulent dissipation can explain unusually high [C ii] emission seen in high-latitude clouds in the Galaxy, predicting a doubling of the emission compared with PDR models.

In a remarkably predictive paper, Lesaffre et al. (2013) demonstrate that even quite low velocity shocks passing through a diffuse (10²–10³ cm⁻³) irradiated molecular medium can significantly boost the [C ii] signal so that it becomes almost as bright as the 0–0 H₂ S(1) line. These authors, who were working with previously published H₂ excitation diagrams for SQ and diffuse gas in the Chamaeleon cloud, showed that the H₂ excitation in SQ could be modeled by low-velocity C-shocks in a diffuse molecular medium. When considering mildly UV-irradiated gas (sufficient to ionize the carbon), they showed that in 7–10 km s⁻¹ C-shocks, the [C ii] emission can become almost as bright as the H₂ emission. In their model, 70% of the [C ii] emission comes from shocked gas with only 30% from the PDR associated with the ionization of the carbon. Furthermore, these models predict weak [O i] 63 μm emission, largely because of the much lower compression of C-shocks versus more powerful J-shocks. Although their model underpredicts the ratio of [C ii] to 0–0 S(0) H₂ line, a network of low-velocity C-shocks is a promising direction for explaining the observations presented here.

Excluding the SQ-A star formation region, the ratio of I([C ii])/I(CO J = 1–0) is observed to lie between 1000 and 1700 in the filament. We have shown that, taken together with the high values of [C ii]/FIR ratio, these values are not consistent with PDR models.

A proper model of the I([C ii])/I(CO) ratio for the shock case is non-trivial and is highly dependent on the specific conditions, including magnetic field, density, and the treatment of the turbulent line broadening which affects the optical depth, and is beyond the scope of the present paper. The Lesaffre et al. models somewhat underpredict the I([C ii]/I(CO J = 1–0) ratios observed here, but were optimized for a different set of observational constraints.

Preliminary shock modeling, which includes post-processing with a Large Velocity Gradient (LVG) code, is able to reproduce I([C ii])/I(CO J = 1–0) ratios of 700–3000 for pre-shock densities of 10³ cm⁻³. Future models of the SQ system, incorporating these kinds of models, will also have to take into account energy input to the gas from much higher velocity shocks, which Cluver et al. (2010) suggested may help to explain the relatively strong [Si ii] 34.8 μm line-cooling in the filament, as well as possible cooling in important far-UV lines.