DUST EMISSION AND STAR FORMATION IN STEPHAN'S QUINTET

The MIPS 70 μm and 160 μm data are from Spitzer pipeline version S11.0.2. In the pipeline default mosaic images, there are a few residual instrumental artifacts that are particularly noticeable at 70 μm. Because of this, these pipeline images were not used in this work. In their place, new images were used in which the instrumental artifacts were reduced by performing additional data reduction steps on the "basic calibrated data" (BCD) frames.

Specifically, for the 70 μm data, we observed an overall signal drift in time. To remove this, we masked out those pixels of each of the 468 non-stim BCD frames that are within a radius of 125'' of the SQ center (R.A. = 3390181, decl. = 33969183; J2000). For each BCD frame, a median was calculated from all unmasked pixels. These medians were plotted as a function of the BCD frame index (1–468). The resulting plot shows a clear discontinuity at frame index 313. We fit the sections prior to and post this discontinuity separately with a cubic spline function of order 1 or 2. The two fitted curves were connected to form one curve covering all the BCD frames. After being normalized by its mean, this curve was divided into the index-ordered BCD frames to remove the signal drift in time. The next step was to create a sky flat image by median filtering only unmasked data for a given detector pixel. The resulting sky flat image was normalized by its mean, and subsequently divided into each unmasked BCD frames. Finally, we used Spitzer MOPEX tool to mosaic these improved BCD frames into our final image used in this paper. With a much flatter sky background, our own mosaic image is significantly better than the pipeline counterpart.

For the MIPS 160 μm data, a similar procedure was used with all 522 non-stim BCD frames. In this case, the detector signal drifts in time differ significantly among individual readout modules. As a result, our signal drift removal was attempted on per readout module basis.

Background subtraction has been performed by fitting a tilted plane to the maps, after masking a large area covering the main group and, in the case of the 160 μm map, the galaxy NGC 7320c (that lies outside the field of view shown in Figure 1). The total area used to estimate the background is about 50% of the entire maps at both wavelengths. These areas are well outside the group emission, allowing good background measurements.

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In this paper, we have also made use of a large set of multiwavelength data to derive physical quantities or for morphological comparison with the emission seen on the infrared maps. Specifically, we utilized the Sloan Digital Sky Survey (SDSS) maps of SQ, obtained from the SDSS Data Archive (data release 7), the GALEX FUV map, which have been presented in Xu et al. (2005), the XMM-Newton soft X-ray map from Trinchieri et al. (2005), the Very Large Array (VLA) 21 cm line map from Williams et al. (2002), the Hα maps from Xu et al. (1999), the IRAC 3.6 μm map, obtained from the SSC archive, and the CO radio observations presented in Lisenfeld et al. (2002).

The fitting technique models a preselected set of the most prominent discrete sources as a sum of elliptical Gaussian convolved with the point-spread function (PSF). Seven parameters are calculated for each source: amplitude, the peak coordinates, the two Gaussian widths, the axis rotation angle, and the local background (included to avoid removal of any diffuse emission components). The fit is performed simultaneously for the 10 brightest sources seen on the 70 μm maps (see Figure 2): five compact sources (SQ A, H ii-SE, H ii-SW, SQ B, H ii-N), two sources to fit the emission from the AGN galaxy NGC 7319 (one for the central emission and one for a peripherical star formation region visible after the removal of the first component), two for the fit of the foreground galaxy NGC 7320 (one for the fit of the diffuse emission and one for a compact source), and one to fit the emission peaked in the middle of the shock region. The fit to the 70 μm map is performed first, keeping all the fitting parameters as free variables. This is followed by a constrained fit to the 160 μm map in which the relative position of the sources are fixed to the values obtained at 70 μm. In addition, a further constraint was that we kept the same shape and axis orientation for the five compact sources, as inferred by the 70 μm fit, allowing only a size change (to take into account the potentially more extended distribution of cold dust emission). This strategy was adopted because the higher resolution 70 μm map places the strongest constraints to the position and morphology of sources in the FIR. We did not use the highest resolution 8 μm map for this purpose since, whereas the emission detected at 70 and 160 μm is produced by the same kind of solid dust grains, the emission at 8 μm is dominated by line emission from polycyclic aromatic hydrocarbon (PAH) molecules. Model images from the fitting technique are shown in Figures 2 and 3. The best-fit parameters and the inferred total flux densities are shown in Table 1. At both 70 μm and 160 μm, the best-fit model images are remarkably similar to the original maps. On the "deconvolved" maps in each figure, it is possible to see the contribution from each Gaussian to the final map. Interestingly enough, the source at the position of the shock is much more predominant at 160 μm than at 70 μm, confirming the original impression that the emission in the shock region is brighter at 160 μm. It is also noteworthy that the position angle of the model source at 160 μm is aligned with the north–south orientation of the X-ray-emitting ridge whereas at 70 μm no such alignment is apparent. At both 70 and 160 μm, the east–west width of the fitted elliptical Gaussians at the shock position (FWHM ≈ 60'') is larger than that of the X-ray shock ridge (FWHM ≈ 20''). This indicates that the integrated emission is not necessarily entirely composed of emission from the shock ridge. A full description of the source fitting technique is given in Appendix A.

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To understand how the emission peaked in the shock region and the extended emission are distributed on the maps, we created FIR residual maps where the emission from all the sources fitted by the FIR map fitting technique, with the exception of the source associated with the shock, have been subtracted. The contours of these FIR residual maps are shown in Figure 4 overlaid on H i, X-ray, and FUV maps. As one can see, the emission on the FIR residual maps is uncorrelated and perhaps even anticorrelated with the H i distribution but well correlated with the soft X-ray flux. The FIR emission, as already seen on the original maps, peaks in the middle of the shock region and its overall extent is similar to the X-ray halo emission (similar to what was seen in the low excitation pure rotational lines of H₂ by Cluver et al. 2010). At first sight, this finding supports the idea that collisional heating is producing the observed FIR emission. However, a large part of the residual FIR emission covers areas emitting significant luminosity at UV wavelengths. The presence of these radiation sources complicates the interpretation of the dust emission in the shock region as well as for the extended emission (see Section 7).

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The FIR map-fitting technique, described previously, allows a precise measure of the flux coming from the compact star formation regions, the AGN galaxy NGC 7319 and the foreground galaxy NGC 7320, all modeled well by convolved elliptical Gaussians (although some sources are not detected at 160 μm). This technique allowed us not only to obtain the total source fluxes but also to derive accurately the source extent. In Figure 5, as an example, we show the contours of the "deconvolved" 70 μm and 160 μm emission at the position of SQ A overlaid on the 8 μm and 24 μm maps. The FIR emission has an MIR counterpart that peaks in the areas where FIR is higher. This is generally true for all the fitted FIR sources and it validates the use of apertures for the photometry of the compact sources at MIR 8 and 24 μm whose sizes are derived by the FIR fitting technique. Specifically, at 8 and 24 μm we used elliptical apertures having the same axial ratio and orientation as the 70 μm best-fit elliptical Gaussian axis and semi-axis lengths equal to 2.17σ_70 μm (this area includes 90% of an elliptical Gaussian total flux). We took sizes based on the 70 μm map fit because all the compact sources are clearly seen on that map. These apertures are depicted in red in Figures 6 and 7. The local background for the aperture photometry has been estimated on regions located nearby the central source, where other peaks of emission are not clearly seen (see green circles on Figures 6 and 7). In this way, we are confident that the background level has not been overestimated due to contamination by surrounding sources. We did not apply aperture correction for the photometry at 8 μm because this is close to unity for the chosen apertures (typical aperture size about 10 pixels), as reported by the IRAC Data Handbook. At 24 μm, the chosen apertures typically delimit the first outer ring of the PSF. In this case, we applied an aperture correction equal to 1.16 (MIPS Data Handbook). For the MIR photometry of the galaxies NGC 7319 and NGC 7320, we used large apertures covering most of the emission from these objects and we did not apply aperture corrections because of the large integration area.

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The uncertainties on the MIR photometry are given by the quadratic sum of the following contributions: (1) error on the aperture correction, (2) flux calibration uncertainty, and (3) background fluctuations. Since we used elliptical apertures, instead of typical circular apertures, we rather conservatively assumed that the relative error on the aperture correction is 10% (note that this error is applied only to aperture photometry at 24 μm). The flux calibration relative uncertainty is equal to 4% (IRAC and MIPS Handbook) while the error introduced by background fluctuations is derived from the variance of the background mean values in the several areas we selected nearby the sources. The measured fluxes and uncertainties for both MIR and FIR wavelengths are given in Table 2.

Since we are using different methods to derive the source fluxes on the MIR maps and the FIR maps, it is important to check that these two photometric techniques give consistent results. To verify this, we performed the source fitting technique on convolved MIR maps and derived the source fluxes exactly as we did for the FIR maps. Details of this test are shown in Appendix A. In Figure 8, we plot the ratio of the 24 μm fluxes inferred by the fitting technique and by aperture photometry for each source. For all the sources, except for H ii-SW, the difference between the fluxes obtained using different methods is less than 20%. The discrepancy between the fluxes for H ii-SW arises because of the presence of a compact 24 μm source at the nearby nucleus of NGC 7318a. ¹⁵ This source is included in footprint of the Gaussian returned by the fitting procedure but is outside the integration area used for the aperture photometry.

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Figure 9 shows the east–west profiles, along a line passing through the center of the shock ridge, extracted from the FIR residual maps, the X-ray, and the VLA 21 cm radio continuum maps convolved to the resolution of the 160 μm map (FWHM ≈ 40''). From these profiles, one can see that the FIR width is significantly larger than the shock ridge width as seen both in the X-ray and radio. Using the current data, it is impossible to say if this discrepancy is due to confusion with fainter unrelated infrared sources or to a systematic change in the width of the emitting region of the shock between the X-ray and the FIR. Nevertheless we estimated the flux coming from the shock ridge by fitting the FIR residual maps with a simple two-component model: a PSF convolved uniform ridge, used to fit the dust emission in the shock region and whose size (20'' × 80'') was derived from X-ray data, plus a uniform component. In this procedure, the level of the fitted uniform component is influenced by the fact that the actual FIR source is more extended than the X-ray source. Taking into account the ambiguity in identifying all the flux from the more extended FIR emission with the shock, we have assigned extremely conservative flux uncertainties. Specifically, the upper and lower limits defined by the quoted error bars in Table 2 are the fluxes contributed by the uniform emission component underlying the solid angle of the shock ridge (convolved with the PSF) in the cases the uniform emission component has a brightness equal to twice or zero times the value given by the fit.

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To measure the MIR 8 and 24 μm emission from the shock region, we simply integrated the emission in the same rectangular area used before to define the shock ridge component in the fit of the FIR residual maps. The adopted apertures are shown in Figures 6 and 7. Before the integration, we masked all the areas inside the apertures we used for the photometry of other sources, because the MIR emission in that areas is mainly connected with the corresponding sources that we fitted and subtracted from the FIR maps before the measure of the shock region flux. For the fraction of the masked regions that falls inside the shock region integration area, we assumed that the surface brightness is equal to the average brightness on the other regions inside the aperture. The background level has been measured on areas around the rectangular aperture where no peaks of emission are clearly seen. The quoted error on the integrated fluxes is the sum of the contributions due to background fluctuation and flux calibration error.

We have measured the amount of extended flux on the FIR residual maps within a radius of 90'' from the shock center, an area approximately equal to that covered by the X-ray HALO region as defined in Trinchieri et al. (2005). We performed this flux measurement in the following way. First, we constructed radial curves of growth of the integrated emission on the FIR residual maps starting from the shock center. These curves of growth are shown in Figure 10. As one can see, the integrated emission continues to grow somewhat beyond the 90'' radius. However, we considered only the flux within this limit because it can be directly related to the X-ray halo extent. We took the curve of growth values for the integrated fluxes at 90'' and we subtracted the contribution from the shock region, estimated in Section 4.2. Similarly as before, the uncertainties on the fluxes are mainly due to the mutual contamination between shock ridge and extended emission. Therefore, we assumed the same conservative errors that we assigned to the shock region FIR fluxes. For the estimate of the extended MIR emission, we have used an analogous method. We constructed radial curves of growth, starting from the shock region center, after having masked all the compact sources and galaxies whose photometry has been described in Section 4.1 (note that the shock region is not masked). For the calculation of the MIR curves of growth, we took into account the missing areas, those that we masked, assuming that their brightness is equal to the average brightness inside the circular annuli passing through them. The derived curves are shown in Figure 10. Exactly as for the FIR measurements, we took the value of the curve of growth at 90'' and subtracted the emission from the shock region in order to obtain the integrated emission from the extended area corresponding to the X-ray halo. The flux uncertainties, in this case, are derived summing quadratically background fluctuation, calibration errors, and the error on the shock ridge flux.

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In this section, we describe the SED fits for the star formation regions SQ A, H ii-SE, H ii-SW, and SQ B. We fitted all the observed SEDs as the superposition of two components. The first component is the PDR/H ii region dust emission template that helps to fit the emission from warm dust located very close to young stars. The second component is the diffuse-photon-heated dust emission template that fits the emission from diffuse dust near star formation regions. This diffuse dust is heated by a combination of UV photons escaping from the PDR/H ii region and any ambient large scale UV/optical radiation field pervading the region. We performed the fit varying four free parameters: the amplitude of the H ii region/PDR SED template (determined by the parameter $F_{\rm 24}^{\rm H\,\mathsc{ii}}$, the fraction of 24 μm flux contributed by this component); the diffuse dust mass M_dust; and the strength and the color of the diffuse radiation field, determined by two parameters, χ_isrf and χ_color (see Appendix B for details). As one can notice, there are no degrees of freedom in these fits. Therefore, it is not possible to estimate the goodness of the fit (in the sense of the fidelity of the model) from a χ² test. Nonetheless we estimated the error on the best-fit dust masses and total dust luminosities from a multidimensional analysis of χ² near to its minimum. The uncertainty on the dust mass is the minimum dust mass variation that gives Δχ² = χ² − χ² _min values always greater than one, independently from the values of all the other parameters. The total luminosity error bar is determined by the lowest and highest values of the total luminosity in the subspace of fitting parameters determined by Δχ² ⩽ 1.

The SED fits are shown in Figure 14 (note that for H ii-SE and SQ B we used the 160 μm fluxes within the 70 μm source size to limit contamination from neighbors). Table 3 shows the best-fit parameters, together with the estimate of the uncertainty on the dust mass, the total infrared dust luminosity and the contribution to this total infrared luminosity from optical heating of diffuse dust by the diffuse radiation field, UV heating of diffuse dust by the diffuse radiation field and localized UV heating of dust in PDR/H ii regions. The predicted radiation fields needed to account for diffuse emission component are at least as strong as the local ISRF in the Milky Way with a strong variation in color. From the plots, one can see that the 24 μm emission is dominated by H ii region/PDR emission, as expected, while 8 μm and FIR points are generally dominated by diffuse emission, in accordance with fully self-consistent radiative transfer models of galaxies (Popescu et al. 2010). This is consistent with a picture where MIR emission is produced by regions very close to young stars whilst FIR emission and PAHs emission come from dust illuminated by dilute radiation fields, as observed in galaxy disks (e.g., Bendo et al. 2008)

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The observed SED of the Seyfert 2 galaxy NGC 7319 differs markedly from the SEDs we obtained for the other sources in SQ, for which the power emitted at 24 μm is typically a factor 10 or more smaller than that observed at 70 and 160 μm. For NGC 7319, the amount of energy emitted at MIR wavelengths is comparable to the FIR luminosity. We first tried to fit the SED of this galaxy using the same H ii region/PDR plus diffuse emission components as we have done previously for the star formation regions (we did not include a component of synchrotron emission, originating from the AGN, because an extrapolation of its infrared luminosity from the radio measurements of Aoki et al. (1999) gives values which are 6 orders of magnitudes lower than the observed infrared luminosities). The best fit is shown in the left panel of Figure 15. The fit tries to reproduce the high 24 μm flux with the H ii region template but, doing so, completely overestimates the 70 μm flux. A second attempt has been performed substituting the H ii region/PDR template with an AGN torus template (Fritz et al. 2006; see Appendix B). As one can see from the right panel of Figure 15, the observed data are reproduced much better in this case. Of course the limited number of data points does not allow any inference of the physical properties of the dusty torus or provide precise information on the radiation field. However, the fit does provide an indication that the majority of the 24 μm emission in this galaxy is powered directly by the AGN power-law radiation. The fitted parameters and the total dust luminosity derived from the AGN torus plus diffuse emission fit are shown in Table 3.

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The dust emission SED of the shock region contains MIR and FIR emission components which indicate an inhomogeneous structure of the emitting region. As one can see from the middle panels of Figure 4, the emission on the FIR residual maps shows a rough correlation with X-ray emission, especially near the center of the shock ridge, suggesting, as mentioned before in Section 3.2, that collisional heating of dust embedded in the hot (T ≈ 3 × 10⁶ K) shocked plasma powers at least some of the observed emission. However, the presence of significant 8 μm emission rules out the possibility that the observed dust emission is purely collisionally heated because PAH molecules are not expected to survive in a medium shocked by a wave traveling at more than 125 km s⁻¹ (Micelotta et al. 2010). The PAH emission must therefore either be physically unrelated to the shock, coming from another region along the line of sight, or, if associated with the shock, belonging to colder gas phases embedded in the X-ray plasma. The latter scenario would be consistent with the detection of H₂ molecular line ¹⁶ (Appleton et al. 2006; Cluver et al. 2010) and Hα (Xu et al. 1999) emission from the shock region. Peculiar ratios between the PAH line features have been detected toward the shock, which suggests an enhanced fraction of neutral and large PAHs compared to typical galaxy environments (Guillard et al. 2010).

The multiphase nature of the gas in the shock region implies that there are at least four potential sources of dust emission in this region: (1) diffuse dust collisionally heated in hot plasma, (2) dust in a colder medium and heated by a diffuse radiation field, (3) H ii/PDR dust emission from optically thick clouds with embedded star formation regions, and (4) cold dust emission from optically thick clouds without embedded star formation.

In practice, it is not possible to distinguish model prediction for (2) and (4) over the wavelength range of the currently available data, since the only difference would correspond to a very cold emission component from the interior, self-shielded regions of the optically thick clouds, which will only become apparent at longer submillimeter wavelengths. Therefore, we only consider explicitly here components (1)–(3), ignoring component (4). Furthermore, the four available data points are insufficient to simultaneously fit these three potential sources of dust emission, especially the diffuse-photon-heated and collisionally heated components, which are both predicted to peak at FIR wavelengths. Therefore, we decided to perform the SED fit in two different ways corresponding to the two opposite cases, where collisional heating is either responsible for the entire FIR emission or is completely negligible. We followed this approach in order to understand which mechanism is predominant in powering the diffuse dust emission. First, we fitted the shock region SED as a superposition of two components: the H ii region/PDR template, to fit MIR emission possibly associated with star formation regions and a collisionally heated dust SED template (see Appendix B.4). This model is appropriate for the case where photon-heated diffuse FIR emission is negligible compared to the collisionally heated dust emission. Given the plasma physical properties (fixed by the X-ray emission, as described in Appendix C), the free parameters in this fit are the amplitude of the H ii region template and the collisionally heated dust mass. We performed these fits for the highest and the lowest densities admitted by the X-ray data, however, the final results are quite similar. In the upper panels of Figure 16, we show the best fit obtained for the highest considered particle density n = 0.016 cm^-3 and temperature T = 3 × 10⁶ K. As one can see, the collisionally heated component (dashed curve) is sufficient to reproduce the observed data except the 8 μm point which, as already remarked, is too high to be due to PDR/H ii regions, requiring a diffuse-photon-heated contribution. The model curve shown (fitted in this case just to the three longer wavelength data points) was calculated assuming a power-law grain size distribution with exponent k = 2.5, the expected value in the case of equilibrium between dust injection (with a standard k = 3.5 interstellar distribution; Mathis et al. 1977) and sputtering of grains in hot plasmas (Dwek et al. 1990). The dust mass required to produce the observed FIR flux densities for the case where collisional heating, rather than diffuse photon heating, is considered is 2 × 10⁷  M_☉.

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The second fit was performed using the H ii region/PDR template and the photon-heated diffuse dust component. This combination of SED templates represents the case where the entire emission is powered by photons and collisional heating is negligible. Using this combination of SEDs, one can fit all the data points, including the 8 μm flux. The best-fit curve is shown in the lower panels of Figure 16. In this fit, the diffuse dust component dominates the emission in all the Spitzer bands, even at 24 μm, where the contribution of PDR/H ii regions is normally predominant. The fitted parameters are given in Table 3. We note that the diffuse radiation fields needed for the fit are colder than those needed to fit the star formation regions in Section 5.1.

In conclusion, the FIR part of the SED from the shock can be fitted by a cold continuum component either from collisional heating, which is cold due to the limited ambient density of plasma particles and the underabundance of small stochastically heated grains, or from photon heating, which is cold due to the low ambient density of photons coupled with a low UV to optical ratio. The only real discriminant favoring photon heating would be the 8 μm emission which, as a PAH tracer, cannot be explained by collisional heating. However, it is not entirely clear, on the basis of the current data, that the 8 μm emission really does all originate from the shock region.

In a completely analogous way as for the shock region emission, we tried to model the observed extended emission SED by including a collisionally heated dust emission component. This is motivated by the fact that the FIR residual maps show the presence of extended emission in the area of the brightest component of the X-ray halo emission (the so-called HALO in Trinchieri et al. 2005). In the upper panels of Figure 17, we show the SED fit performed adding two components: H ii regions plus collisionally heated dust emission. In this fit, the adopted plasma physical parameters, derived in Appendix C, are n = 0.001 cm^-3 and T = 6 × 10⁶ K and we again assumed k = 2.5. Using this combination of SEDs, one can roughly reproduce the SED longward of 24 μm, but the collisionally heated component dominates only the 160 μm flux. The dust mass inferred from this fit (constrained, as in the case for the model fit to the shock SED incorporating collisional heating, only by the three longer wavelength points) is 1.0 × 10⁸  M_☉.

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In the lower panel of Figure 17, we show the fit performed adding H ii region and diffuse-photon-heated emission. As before for the shock region, using these two components one can fit the entire spectra including the 8 μm point. In this fit, H ii region emission dominates at 24 and 70 μm while the diffuse emission is responsible for the 8 and 160 μm fluxes. The fitted parameters are shown in Table 3. As for the shock emission, we note that the extended emission component requires a very cold FIR component from the fit even though, observationally speaking, this is a somewhat less robust conclusion, since it really needs to be confirmed with longer wavelength photometry.

For the SED fit of the foreground galaxy NGC 7320, we used again the usual combination of H ii region plus diffuse-photon-heated dust emission components. The best fit is shown in the left panel of Figure 18. The relative contribution of H ii regions to the 24 μm flux is reduced compared to the star formation regions, whose SED fits have been shown before. This might be physically understandable since, in this case, we are fitting the emission of a galaxy as a whole, including all the diffuse interstellar medium (ISM) containing small dust particles whose stochastically heated emission can account for a major part of the total MIR emission (e.g., Popescu et al. 2000).

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We attempted to fit the observed emission for this source with a combination of H ii region plus diffuse-photon-heated dust emission. However, this source shows a very peculiar MIR to FIR ratio and, as a consequence, we have not managed to fit the entire spectra. As shown in the right panel of Figure 18, the FIR points are highly underestimated by the best-fit curve. If no systematic errors are present in our measurements, it might be that H ii-N is a distant background source and the intrinsic colors are heavily redshifted. This possibility is strongly supported by the presence of a red spiral galaxy at the position of H ii-N, clearly visible on recently released high-resolution HST color maps of SQ (Hubble Servicing Mission 4 Early Release Observations, observers: K. Noll et al., available at http://hubblesite.org/newscenter/archive/releases/2009/25/image/x/).

The measurements of UV, recombination line, and dust emission from sources in SQ can in principle be used to derive SFR, provided proper account is taken of the absorption of the UV/optical photons by dust and subsequent re-emission in the MIR/FIR spectral regimes. Several authors have provided empirically based relations achieving this for spiral galaxies on scales of kpc. Calzetti et al. (2007) presented an Hα luminosity based SFR relation: SFR(M_☉ yr⁻¹) = 5.3 × 10⁻⁴²[L(H_α)_obs + (0.031 ±  0.006)L(24 μm)]. In this relation, the 24 μm luminosity is used to estimate the Hα luminosity obscured by dust. Bigiel et al. (2008) combined GALEX FUV and Spitzer 24 μm fluxes to obtain SFR per unit area maps of a sample of spiral galaxies. Like Calzetti et al. (2007), they used a UV-SFR calibration and they used the 24 μm flux to measure the obscured UV flux.

Simple application of the Calzetti relation to SQ is hampered by the lack of pure measurement of Hα emission driven by star formation. As one can see from Figures 4 and 5 from Sulentic et al. (2001), the shock region Hα emission shows a diffuse component that reflects the north–south ridge seen in the soft X-ray regime. This diffuse Hα emission cannot be considered for SFR measurements because, as demonstrated by Xu et al. (2003) from spectral line analysis, the Hα emission in the shock region is dominated by shock excitation rather than star formation. In addition, it is not clear that the semiempirical relations derived for spiral galaxies should apply to the sources in SQ.

Therefore, we adopted a new approach, using only observational indicators of star formation activity available for all sources in SQ, and utilizing the results of the fits to the dust emission SEDs given in Section 5. Our method to estimate SFRs is based on a UV-SFR calibration. ¹⁷ Specifically, we adopted the calibration by Salim et al. (2007):

$$\begin{equation} \mbox{SFR}_{\rm UV}=1.08\times 10^{-28} F_{\rm{UV}} {\,M_{\odot }\;{\rm yr^{-1}}}, \end{equation} \tag{ 2 }$$

where F_UV is the FUV luminosity density in units of erg s⁻¹ Hz⁻¹ which would be observed in the GALEX FUV band in the absence of dust. F_UV can be written as

$$\begin{equation} F_{\rm UV}=F_{\rm UV}^{\rm direct}+F_{\rm UV}^{\rm abs,local}+F_{\rm UV}^{\rm abs,diffuse}, \end{equation} \tag{ 3 }$$

where F^direct _UV is the directly observed unabsorbed component of FUV luminosity density, F^abs,local _UV is the FUV luminosity density locally absorbed by dust in star formation regions, and F^abs,diffuse _UV is the FUV luminosity density absorbed by dust in the diffuse medium surrounding the star formation regions.

We measured F^direct _UV for each source by performing aperture photometry on the GALEX FUV map in a completely analogous way to the photometry we performed on the Spitzer MIR maps, including the construction of the curve of growth after masking the galaxies NGC 7319 and NGC 7320 and the star formation regions (see Figure 10). The final flux densities, shown in Column 4 of Table 4, include the correction for Galactic foreground extinction (E(B − V) = 0.079, Schlegel et al. 1998; A(FUV) = 8.24*E(B − V), Wyder et al. 2007). Values for the obscured emission components F^abs,local _UV and F^abs,diffuse _UV were extracted from the fits to the dust emission SEDs by noting that the total infrared luminosity emitted by dust and powered by UV photons can be written as

$$\begin{equation} L_{\rm dust,UV}=L_{\rm UV}^{\rm abs,local}+L_{\rm UV}^{\rm abs,diffuse}, \end{equation} \tag{ 4 }$$

where L^abs,local _UV is the luminosity of dust emission in star formation regions, dominated by UV photon heating, and L^abs,diffuse _UV is the part of the diffuse dust luminosity powered by UV photons, respectively, tabulated in Columns 6 and 8 of Table 3. Since the intrinsic SEDs of the young stellar population are rather flat at UV wavelengths (Kennicutt 1998), it then follows that

$$\begin{equation} F_{\rm UV}^{\rm abs,local}=\frac{L_{\rm UV}^{\rm abs,local}}{\Delta \nu (\mbox{UV})} \end{equation} \tag{ 5 }$$

and

$$\begin{equation} F_{\rm UV}^{\rm abs,diffuse}=\frac{L_{\rm UV}^{\rm abs,diffuse}}{\Delta \nu (\mbox{UV})}, \end{equation} \tag{ 6 }$$

where Δν ≈ 1.8 × 10¹⁵ Hz is the UV frequency width. The total obscured UV luminosity density F^abs _UV = F^abs,local _UV + F^abs,diffuse _UV and SFRs are shown in Columns 6 and 7 of Table 4.

Table 4. Measured Optical–UV Luminosities, Star Formation Rates, and Gas Amount for the Detected SQ Dust Emitting Sources

Source	L(Hα) a	SFRHα	Fdirect UV	Ldust,UV	Fabs UV	SFRUV	SFRUV/A	$\Sigma ({\rm H\,\mathsc{i}})$	Σ(H2)	Σ(H+)	Zd b
	(1040 erg s-1)	(M☉ yr-1)	(1027 erg s-1 Hz−1)	(1042 erg s-1)	(1027 erg s-1 Hz−1)	(M☉ yr-1)	(10−3  M☉ yr-1 kpc−2)	(M☉ pc-2)	(M☉ pc-2)	(M☉ pc-2)
SQ A	9. ± 2	0.7 ± 0.2	2.75	8.09	4.49	0.78	6.4	7.9	6.0	...	0.002
H ii-SE	6.6 ± 1.5	0.5 ± 0.1	2.32	5.44	3.02	0.58	5.8	<0.40 c	...	...	...
H ii-SW	3.9 ± 0.5	0.2 ± 0.04	2.11	1.99	1.10	0.35	5.5	3.2	<1.7 c	...	...
SQ B	1.3 ± 0.3	0.2 ± 0.05	0.31	4.18	2.32	0.28	2.7	5.2	4.0	...	0.002
NGC 7319	...	...	2.01	...	...	≳0.22	...	...	...	...	...
Shock	...	...	6.98	5.09	2.83	1.05	3.1	...	9.1	3.0	0.007
Extended	...	...	22.7	30.21	16.78	4.26	1.0	...	...	2.4	0.01

Notes. Column 1: source name; Column 2: Hα luminosity; Column 3: star formation rate (SFR) derived from the Hα and 24 μm luminosity using the relation given by Calzetti et al. (2007); Column 4: observed GALEX FUV luminosity density corrected for Galactic extinction; Column 5: UV powered infrared dust luminosity; Column 6: absorbed UV luminosity density derived by dividing the UV powered dust luminosity L_dust,UV by Δν(UV) = 1.8 × 10¹⁵ Hz; Column 7: SFR based on the inferred total (obscured and unobscured) UV luminosity density, using the relation by Salim et al. (2007); Column 8: SFRs in Column 7 divided by the projected emission area; Column 9: average neutral hydrogen mass column density; Column 10: average molecular hydrogen mass column density; Column 11: average X-ray-emitting plasma mass column density; Column 12: dust-to-gas ratio Z_d (note that for each source only the corresponding available gas masses are considered for the estimate of Z_d). ^aWe measured the H_α fluxes from the interference filter maps published in Xu et al. (1999). The quoted flux uncertainties are the quadratic sum of background fluctuations and flux calibration uncertainty (≈10%). ^bThe dust-to-gas ratio is equal to Z_d = M_d/(1.4 × M_gas) where M_d is the dust mass inferred by the SED fit, M_gas is equal to N(H) × πR² with R = FWHM(rad) × distance the source size as derived from the 70 μm source fit (the factor 1.4 is applied to take into account the contribution from noble gasses). ^cThe value of $\Sigma ({\rm H\,\mathsc{i}})$ for H ii-SE is an upper limit because H i is not detected at that position on the maps by Williams et al. (2002). No value is given for Σ(H₂) because the area was not observed by Lisenfeld et al. (2002). The value of Σ(H₂) for H ii-SW is an upper limit because CO has not been detected at that position.

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As a check of the consistency between our method to derive SFRs and the Hα–24 μm SFR relation of Calzetti et al. (2007), we used the latter to derive SFR for the compact star formation regions in SQ which are the objects closest resembling galaxies. The Hα fluxes have been measured on the interference filter maps published in Xu et al. (1999) while the 24 μm fluxes are those derived by aperture photometry (Section 4.1). The results are shown in Columns 2 and 3 of Table 4. As one can see comparing Columns 3 and 7 of that table, the SFR inferred with our method are consistent with the results found using the Calzetti relation (except for H ii-SW but in that case the SED fitting was performed without varying χ_color because of the non-detection of the source at 160 μm).

In the absence of a homogeneous set of observations of gas tracers for the gas phases of interest, namely, H i, H₂, and X-ray-emitting plasma, we proceeded differently for the several sources in determining gas masses. For the star formation regions SQ A, H ii-SE, H ii-SW, and SQ B, we measured gas mass column densities from the H i map published by Williams et al. (2002) and the CO maps of Lisenfeld et al. (2002). Specifically, we measured the average atomic and molecular hydrogen column density in the observed areas close to the position of the starburst regions. The inferred gas mass column densities are shown in Columns 9 and 10 of Table 4 (note that for some values only upper limits are available and no CO observation is available for H ii-SE).

Gas in the shock region is mainly in the form of X-ray-emitting plasma and molecular gas (Guillard et al. 2009). From the X-ray luminosities, measured by Trinchieri et al. (2005), we determine the X-ray gas mass M_X ≈ 10⁹  M_☉ (see Appendix C for details). Dividing the total gas mass by the physical area covered by the shock (330 kpc²), we obtained the hot gas mass surface density shown in Column 11 of Table 4. To determine the molecular gas mass surface density, we measured the average of several observed positions within the shock area on the CO maps by Lisenfeld et al. (2002) to obtain Σ(H₂) = 9 M_☉ pc⁻². As one can see from Figure 1 of that paper, most of the observations were performed in the upper part of the shock region. Guillard et al. (2010) and Appleton et al. (2006) found a cold and warm molecular gas surface mass densities in the central parts of the shock region, respectively, equal to 5 M_☉ pc⁻² and 3.2 M_☉ pc⁻². Interestingly enough, the sum of these two values is very close to the cold molecular gas surface density we measured in the upper parts of the shock region.

For the extended emission, the measurement of the corresponding neutral and molecular gas masses cannot be realistically performed because the extended emission cover irregular parts of the large H i distribution in SQ and there are no CO observations covering the whole group with enough sensitivity to detect a plausible extended molecular hydrogen distribution. The measurement of the corresponding X-ray-emitting gas mass is instead rather straightforward since it can be derived by the X-ray halo luminosity, as for the shock region (see Appendix C). Dividing the total X-ray gas mass by the projected X-ray halo emission area (a circle of radius ≈40 kpc), we determined the hot gas mass surface density shown in Column 11 of Table 4.

The results of the SED fitting to the constituent components of SQ indicate that star formation activity and photons from old stars are the major agents powering the observed global dust emission from the group, supplemented by photons produced by the accretion flows in the AGN and possibly, in the case of the X-ray-emitting regions, by collisional heating. In our quantitative discussion of star formation activity in SQ, we will adopt an initial working hypothesis that the collisional heating mechanism is minor compared with photon heating in the X-ray sources. We will scrutinized this hypothesis in detail in Section 7.2, where we discuss physical constraints of the fraction of the infrared emission that can be collisionally powered.

Under this working hypothesis, we can gather together the information from Table 4 to obtain a total global SFR of 7.5 M_☉ yr^-1 for SQ in its entirety. This global SFR does not seem particularly discrepant from that typically found for most of the galaxies of similar mass in the local universe that are clearly not so strongly interacting as SQ galaxies. Using the empirical relation between galaxy stellar mass and SFR for field galaxies shown in Figure 17 of Brinchmann et al. (2004), we can estimate the typical SFR of galaxies having the same stellar mass of SQ galaxies, of order of ≈10¹¹  M_☉ (see Table 5). For this value of the stellar mass, the mode of the distribution is at SFR ≈ 1 M_☉ yr^-1. Therefore, since we estimated the SFR in a field containing four galaxies, the expected SFR would be ≈4 M_☉ yr^-1, comparable to the measured value. Thus, it seems that the star formation efficiency of SQ in relation to field galaxies is largely independent of whether the gas is inside or outside the main stellar disk. In fact, of the total global SFR of 7.5 M_☉ yr^-1 for SQ, 2.2 and 5.3 M_☉ yr^-1 can, respectively, be ascribed to the SED components for star formation regions and X-ray sources in Figure 19. This is a very remarkable result indicating, as it does, that the bulk of star formation activity in SQ is apparently associated with X-ray-emitting structures, occurring far away from the galaxy centers, either at the peripheries of the galaxies or in the IGM. Furthermore, the total extragalactic SFR is well in excess of the SFRs of the previously studied individual examples of extragalactic compact star formation regions, SQ A and SQ B.

To quantify the efficiency of star formation in the various components of SQ in relation to that of the disks of individual galaxies, we plotted in Figure 20 the SFR per unit area for dust emission sources in SQ as a function of the gas mass surface density. On the same diagram, as reference, we plotted the relations found by (Kennicutt et al. 2007, hereafter K07) and (Bigiel et al. 2008, hereafter B08) for star formation regions inside nearby spiral galaxies. This figure shows a wide range of star formation efficiencies, which we discuss below for each of the structural components, with special emphasis on the extended component of star formation which dominates the global SF activity in SQ.

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7.1.1. Discrete Star Formation Regions

7.1.2. Star Formation Associated with the Shock

The average SFR in the shock region (3.1 × 10⁻³ M_☉yr^-1 kpc⁻²) seems to be well in agreement with the empirical SFR–gas surface density relation in Figure 20. Thus, at first sight, the shock does not seem to have had much effect on the star formation activity in the stripped interstellar gas, neither triggering enhanced star formation through shock compression of dense clouds of gas, nor suppressing star formation through heating and dispersion of the clouds. The observational situation is however complex in that the star formation observed toward this region could be happening inside the extended features connected with the incoming galaxy NGC 7318b, seen through, but not obviously physically coexistent with the shock region. This is supported by the local morphology of the UV and MIR emission that seems to follow the optical shape of the intruder, instead of showing a linear north–south ridge resembling the shocked gas emission morphology. These two scenarios could in principle be combined since the ISM of the intruder galaxy has presumably been shocked as well and this could have triggered the observed star formation out of the gas associated with the intruder galaxy. In addition, it is conceivable that some fraction of the UV luminosity, albeit probably a minority, could be due to gas cooling rather than from massive stars.

It is also of interest to compare our constraints on the SFR in the shock region with the luminosity of the radio synchrotron emission from the shocked gas. Traditionally radio synchrotron measurements are compared to infrared emission measurements in the context of the radio–FIR correlation for individual galaxies, for which we use here the relation given by Pierini et al. (2003):

$$\begin{equation} \log L_{1.4\;{\rm GHz}}=1.10\times \log L_{\rm FIR} -18.53, \end{equation} \tag{ 7 }$$

where L_1.4 GHz is the luminosity at ν = 1.4 GHz in units of W Hz^-1 and L_FIR is the total FIR luminosity in units of W. We used the relation from Pierini et al. (2003) since it was derived from data covering cold dust emission longward of >100 μm, where, as in the case for the SQ shock region, most of the power is radiated. Using the value we measured for the shock region FIR luminosity, L_FIR = 1.5 × 10³⁶ W, we obtain for the predicted radio luminosity L_1.4 GHz = 1.8 × 10²¹ W Hz. This value is 20 times smaller than the radio luminosity derived from the radio measurement in Xu et al. 03: L_1.4 GHz = 3.7 × 10²² W Hz. The high radio/infrared luminosity ratio (which would be higher still with respect to the photon-powered component if collisional heating was important) points to the existence of an additional source of relativistic particles in the SQ shock, accelerated at the shock itself (see, e.g., Blandford & Eichler 1987), which dominates the population of particles accelerated in sources more directly linked to star formation regions such as supernova remnants. This confirms and strengthens the preliminary results of Xu et al. (2003), and, bearing in mind that the total radio emission from SQ is dominated by the emission from the shock region, suggests that caution is needed in using radio synchrotron measurements to infer SFRs in groups involving strong dynamical interactions of galaxies with the IGM.

7.1.3. Star Formation Associated with the Extended Emission

Our measurements have shown that both the obscured and visible components of the star formation in SQ are distributed in a widespread pattern, loosely coincident both with the overall dimensions of the group as well as with the extended "halo" of X-ray emission. This current morphology of SQ star formation can readily be accounted for in terms of the several galaxy–galaxy or galaxy–IGM interactions which have occurred in the group. In this standard scenario, the gas that is currently converted into stars is interstellar in origin (as we will discuss later in this section). However, the data are also consistent with a rather different scenario, in which the reservoir of gas out of which stars are being formed is the hot gas phase of the intragroup medium.

Specifically, we consider a scenario in which the hot IGM is cooling and condensing into clouds which are the sites of the star formation providing the UV powered component of the extended infrared emission. If this is occurring in a steady state, in which the rate at which the removal of hot gas by cooling is balanced by accretion of further primordial gas (that is, we assume that variation in the accretion rate have longer timescales than the cooling timescale), we can write

$$\begin{equation} \mbox{SFR}_{\rm hot}\le \frac{M_{\rm hot}}{\tau _{\rm hot}}, \end{equation} \tag{ 8 }$$

where M_hot and τ_hot, respectively, denote the mass and cooling timescale of the X-ray-emitting medium, and the inequality denotes the fraction of the cooling gas that ultimately condenses into stars. If the observed X-ray emission is the main component of luminosity of the hot medium, and taking observational values for the X-ray-emitting plasma from Trinchieri et al. (2005) of M_hot = 1.0 × 10¹⁰  M_☉ and τ_hot ≈ 0.3 × 10¹⁰ yr (see Section 7.2.2), we obtain SFR_hot ⩽ 3 M_☉ yr⁻¹, comparable to the observed value of 5.3 M_☉ yr⁻¹ for star formation seen toward the X-ray-emitting halo. In reality, however, one would expect a large fraction of the cold gas resulting from the cooling of the gas to be recycled into the hot medium due to the feedback of mechanical energy from the newly formed stars, in which case SFR_hot would be substantially less the upper limit from Equation (8). Thus, if X-ray emission driven by gas–gas collisions is the dominant cooling path for the X-ray halo, one would conclude that the bulk of the star formation would not be directly fueled out of the IGM. On the other hand, as shown in Section 7.2.2, our Spitzer FIR data, coupled with astrophysical constraints on the injection rate of grains into the hot medium do not at present rule out the possibility that the dominant cooling mechanism of the halo is FIR emission driven by gas–grain collisions. At present, therefore, we cannot rule out star formation out of a primordial IGM purely on considerations of gas fueling.

A more powerful constraint would be to consider the efficiency at which such a mode would have to operate at. Unfortunately, the total mass of molecular cold gas, M_cold on a global scale in the halo is unknown, preventing a direct empirical measurement of star formation efficiency of the halo on the Kennicutt–Schmidt (KS) diagram. One can, however, estimate M_cold under our simple steady state scenario by writing

$$\begin{equation} \frac{M_{\rm hot}}{\tau _{\rm hot}}\approx \frac{M_{\rm cold}}{\tau _{\rm cold}}, \end{equation} \tag{ 9 }$$

where τ_cold is the typical timescale spent by the gas in the cold molecular phase before being converted into stars, which is the timescale for the collapse of a molecular clouds to form stars, multiplied by the mean number of times the cold gas is recycled into the hot medium through mechanical feedback before condensing into a star. Even allowing for several cooling cycles of the hot gas before condensing into stars, the very short collapse timescale of a few million years for molecular clouds—some 3 orders of magnitude shorter than τ_hot—makes it likely that τ_hot ≫ τ_cold, which in turn implies M_hot ≫ M_cold. If this is the case, the cold gas amount, related to the extended emission, that we should add to Σ_gas would be negligible, and the position of the point for the SQ halo on the KS diagram would be well to the left of the relation for star-forming galaxies, as shown in Figure 20. This would require a more efficient star formation process in the IGM than is typically observed to occur in the disks of star-forming field galaxies, which would seem to be counterintuitive to the naive expectation that denser, colder reservoirs of gas closer to the minimum of the gravitational potential wells associated with individual galaxies should form stars more easily. On the other hand, a definition of efficiency in terms of gas surface density over scales much larger than the star formation regions may have limited predictive power in this context. Furthermore, any star formation in a cooling hot IGM would not be expected to occurring in rotationally supported systems similar to the galaxies used to define the KS relation, so may have a different relation to the local gas density.

The second, more conventional scenario to explain the widespread star formation in the extended halo component of SQ, is to invoke interstellar gas as the source of cold gas fueling most of the star formation. In this scenario, tidal interactions between galaxies or hydrodynamical interactions of the ISM with the IGM remove cold galaxy material that, for SQ, produces a similar SFR as would have been the case for a similar amount of gas inside field galaxies. For groups in general the statistical relation of neutral gas observed within and outside the member galaxies to the X-ray emission characteristics of the IGM indeed indicates that at least some of the cold gas in the IGM medium originates in the galaxies, and that at least some of the X-ray-emitting gas also has an interstellar origin (e.g., Verdes-Montenegro et al. 2001; Rasmussen et al. 2008). More direct evidence of the removal of interstellar gas and dust through galaxy interactions in high density environments is provided by observations of interacting galaxies in clusters, for example, through Herschel imaging of extraplanar dust emission associated with stripped atomic and molecular gas around the Virgo cluster galaxy NGC 4438 (Cortese et al. 2010).

In SQ, there is direct morphological evidence for bursting sources associated with tidally removed interstellar gas in the form of SQ A and SQ B, and a hint that other less prominent components of the FIR emission in the IGM may also be associated with tidal features, such as the enhancement of H_α and MIR/FIR emission seen toward the bridge linking the intruder galaxy with the AGN host galaxy. In this picture, the extended emission is a conglomeration of discrete sources similar in nature to SQ A and SQ B but much more numerous and of lower power. The fact that SQ A and SQ B are likely to have a fundamentally interstellar origin despite their present location outside the galaxies is further supported by the rather high value of the dust-to-gas ratio we have found for these sources, Z_d = 0.002, which is a signature of a high gas metallicity. The one puzzling aspect of the extension of this scenario to the global star formation in the IGM of SQ is the lack of prominent star formation associated with the bulk of the H i in the IGM located to the south and east of the group. However, as shown by Figure 5 of Williams et al. (2002), the gas column density in these clouds (generally less than ≈3 × 10²⁰ atoms cm^-3) is rather low compared to the values found for the brightest star formation sites in SQ. Therefore, it is plausible that star formation is inhibited in these clouds because of the low gas density.

Finally, we remark that if stripped neutral and molecular interstellar gas was the only source of cold gas powering star formation, one would expect a rapid quenching of star formation activity in SQ in the future, whereas if the star formation were fueled by a cooling primordial IGM, the star formation activity would simply follow the accretion rate onto the group of the primordial IGM. Thus, measurement of the UV and MIR/FIR luminosity functions of well-defined statistical samples of galaxy groups, now being defined through deep optical spectroscopical surveys such as the Galaxy And Mass Assembly survey (GAMA; Driver et al. 2009), may offer a way of quantifying the relative importance of these modes of star formation on the dynamical halo mass of groups in the local universe.

Previous searches for infrared emission counterparts of the hot X-ray-emitting components of the IGM of nearby objects have almost exclusively targeted the ICM of rich galaxy clusters, either using a stacking analysis for X-ray or optical selected clusters from the IRAS all sky survey (Giard et al. 2008; Roncarelli et al. 2010) or in detailed imaging observations of the Coma Cluster and other clusters with ISO or Spitzer (Stickel et al. 1998, 2002; Quillen et al. 1999; Bai et al. 2007; Kitayama et al. 2009). All these studies have either yielded upper limits or marginal apparent detections of the ICM at far-IR brightness levels far fainter than those we have measured toward the X-ray-emitting IGM of SQ with Spitzer. Furthermore, even the apparent detections of the ICM were susceptible to confusion with foreground cirrus or the background galaxy population due to the accidental similarity (Popescu et al. 2000) in far-IR color of the collisionally and photon-heated emissions, so realistically must be treated as upper limits to any collisionally heated emission from the ICM (Bai et al. 2007). Although intracluster dust has been unambiguously detected at optical wavelengths, through statistical studies of the reddening of background sources through large numbers of clusters (Chelouche et al. 2007) this has been at a low abundance of about 10⁻⁴ in the dust-to-gas mass ratio, consistent both with the non-detections of the ICM in infrared emission and with specific predictions by Popescu et al. (2000) of the dust content of typical ICMs.

In the present work, we have been able to sidestep the confusion problems afflicting the previous attempts to detect infrared emission from the ICM in clusters only by virtue of the much higher far-IR brightness levels measured toward the X-ray-emitting structures in SQ. These high brightness levels, together with the correspondence of the infrared emission morphologies with those seen in the UV, and the evidence from our fits to the infrared emission SEDs described in Section 5.3 however suggest that a major part of the dust emission is photon heated. This, in turn, raises an apparent paradox that the closest spatial correlation between dust emission and gas column density is not, as might be expected for photon heating, with the cool H i and molecular gas component, but rather with the hot X-ray-emitting component. In our discussion on star formation in SQ, we identified a possible way out of this paradox by postulating that the extragalactic star formation in SQ is fueled by gas from a hot IGM, whose cooling is enhanced by grains injected into the hot IGM. Here, we use the relative levels of detected emission at infrared, X-ray, and UV/optical wavelengths to constrain the possible sources of grains and the resulting collisionally driven cooling of the hot plasmas, considering separately the two main X-ray-emitting structures corresponding to the shock and the halo regions.

7.2.1. The Shock Region

The main constraint on the collisional heating of dust in the X-ray-emitting plasma downstream of the shock is given by the high dust-to-gas mass ratio that would be required to reproduce the FIR measurements in the case that grain heating by a diffuse radiation field can be neglected. For pure collisionally heated emission from grains in a homogeneous medium, a dust mass M_d = 2 × 10⁷  M_☉ (see Section 5.3) would be required, which, taken together with the measured X-ray-emitting gas mass, M_X ≈ 10⁹  M_☉ (see Appendix C), would imply a dust-to-gas ratio for the hot plasma of Z_d = 0.02. This value is high in comparison with expectations based on a balance between injection of grains and their removal through sputtering. Assuming that the shock is propagating into a stripped ISM or through the ISM of the intruder galaxy, characterized by a dust-to-gas ratio comparable to the Milky Way value, we can derive the amount of dust mass per unit time $\dot{M_{\rm D}}$ that is injected downstream of the shock:

$$\begin{equation} \dot{M_{\rm D}}=V_{\rm sh}A\rho _{\rm up}Z_{\rm d,up}, \end{equation} \tag{ 10 }$$

where V_sh = 600 km s^-1 is the shock velocity (Guillard et al. 2009), A = 330 kpc² is the projected area of the shock front (corresponding to 20 × 80 arcs² on the sky), ρ_up ≈ 1.1n_H m_H = 4.5 × 10⁻²⁷ g cm^-3 is the upstream gas density (n_H = 0.01/4 cm^-3) and Z_d,up = 0.01 is the assumed dust-to-gas ratio for the gas upstream of the shock front. The resulting dust injection rate is $\dot{M_{\rm D}}=0.14 {\,M_{\odot }\;{\rm yr^{-1}}}$. To estimate grain destruction through sputtering in collisions with heavy particles, we use the formula of Draine & Salpeter (1979) for the dust sputtering timescale:

$$\begin{equation} \tau _{\rm sp}=2\times 10^{6}\frac{a}{n_{\rm H}} \;{\rm yr}, \end{equation} \tag{ 11 }$$

where a is the dust size in μm and n_H is the proton number density in cm^-3. Assuming n_H ≈ 0.01 cm^-3 and a = 0.1 μm, we get τ_sp = 2 × 10⁷ yr. Explicit calculation of the cooling of the shock gas due to gas–gas and gas–grain collisions, taking into account the evolution of the grain size distribution (under the assumption that there are no further sources of grains), shows that the gas cooling timescale is t_cool ≈ 7 × 10⁷ yr, more than three times larger than τ_sp (Natale 2010). Under these circumstances, a conservative estimate for the dust-to-gas ratio downstream of the shock can be derived by dividing the total mass of dust predicted to be at any time downstream of the shock to the measured hot gas mass, that is,

$$\begin{equation} Z_{\rm d,down}=\frac{\dot{M_{\rm D}}\tau _{\rm sp}}{M_{\rm X}}. \end{equation} \tag{ 12 }$$

Applying this formula, the expected value for the X-ray plasma dust-to-gas ratio is Z_d,down ≈ 3 × 10⁻³, a factor of ≈7 smaller than the value inferred from the data, for the case where the entire FIR dust emission is powered by collisional heating. This is only a crude estimate for the dust abundance, which might take higher values if the line-of-sight depth of the shock was assumed to be larger than the projected width seen on the sky, but which on the other hand is an overestimate compared to predictions taking into account the true evolution of grain size downstream of the shock. In any case, it is evident that the measured dust-to-gas ratio is much larger than the predicted Z_d,down, and a further source of dust grains would be required if collisional heating were to be a significant driver of the FIR emission.

The most obvious such source would be the reservoir of grains in the cold component of the gas in the shock region, which could be potentially released into the hot gas by ablation if the clouds were in relative motion to the hot gas. As already mentioned, the presence of cold gas is implied by the detection of 8 μm emission and has been directly demonstrated by the detection of molecular hydrogen in the MIR rotational lines (Cluver et al. 2010). Guillard et al. (2009) modeled the H₂ emitting clouds as cooling pre-existing clouds in the upstream medium, a scenario which would predict the clouds to be in relative motion to the hot gas downstream of the shock. Another possibility which might potentially account for an FIR counterpart to the shock is to invoke heating of grains upstream of the shock by the UV radiation from the cooling clouds downstream of the shock. A quantitative treatment of all these effects would however require a self-consistent model for the passage of the shock through a two-phase medium which tracked the exchange of photons, gas, and dust between the phases, which is beyond the scope of this paper.

It is appropriate to emphasize here that even in the case that the collisional heating is relatively unimportant in bolometric terms, the effect on the gas cooling timescale is not negligible. Detailed calculations for a steady state one-dimensional homogeneous model, considering dust sputtering and dust cooling, show that the cooling timescale is shorter by a factor of ≈2–3 (Natale 2010) for shock velocities and gas densities similar to those characteristic of the shock in SQ. From this perspective, it would be important to have more direct empirical constraints on the gas cooling mechanism using the improved sensitivity, angular resolution, and wavelength coverage of the Herschel Space Observatory. Using the simple approach described above, we estimate the surface brightness of the radiation emitted by collisionally heated dust to be equal to 1.4 MJy sr^-1 at 150 μm, the wavelength where the flux density is predicted to peak according to the collisional-heated dust model we used for the shock region SED fit (see Figure 16).

7.2.2. The Extended Emission

As for the shock, the detection of substantial 8 μm emission toward the extended X-ray-emitting halo indicates the presence of a component of dust in cold gas phases, shielded from collisions with electrons and ions in the hot plasma, which can only be heated by photons. Rather interestingly, the curves of growth we constructed after removing or masking the galaxies and the compact star formation regions from the infrared and FUV maps (Figure 10) show a very similar profile at all wavelengths. This is a strong indication that FUV sources are associated with the FIR extended emission and, therefore, star formation is the main mechanism powering the extended emission.

The total luminosity of the extended dust emission is 4 × 10⁴³ erg s^-1, a factor ≈130 higher than the X-ray halo luminosity (Trinchieri et al. 2005; see also Appendix C). This large difference between the dust emission and X-ray luminosities implies that collisional heating of dust grains could still be important for the cooling of the hot halo gas even if it only powers a small fraction of the dust luminosity. We define the fraction F_coll of dust emission that is collisionally powered, by the relation

$$\begin{equation} L_{\rm IR}^{\rm coll}=F_{\rm coll}L_{\rm IR}, \end{equation} \tag{ 13 }$$

where L^coll _IR is the dust luminosity that is powered by collisional heating.

A first physical constraint on F_coll that we can apply is the requirement that the gas cooling timescale τ_cool is not larger than the dynamical hot gas timescale, given by the sound crossing time τ_cross. Including dust cooling, τ_cool is equal to

$$\begin{equation} \tau _{\rm cool}=\frac{3}{2}\frac{kT}{\mu m_{\rm H}}\left(\frac{M_{\rm X}}{L_{\rm X}+F_{\rm coll}L_{\rm IR}}\right), \end{equation} \tag{ 14 }$$

where T = 6 × 10⁶ K is the gas temperature, M_X = 10¹⁰  M_☉ is the X-ray-emitting gas mass, and L_X and L_IR are the X-ray and infrared luminosities. Requiring that τ_cool>τ_cross = 2R_halo/c_s , where R = 35 kpc is the halo radius and c_s ≈ 300 km s^-1 is the sound speed, one obtains F_coll < 0.05.

Another constraint can be derived from an estimation of the dust injection rate into the hot gas. For equilibrium between dust injection and sputtering, one would have

$$\begin{equation} \dot{M_{\rm d}}=F_{\rm coll}\frac{M_{\rm d}}{\tau _{\rm sp}}=2.4F_{\rm coll} {\rm \frac{M_\odot }{yr}}, \end{equation} \tag{ 15 }$$

where $\dot{M_{\rm d}}$ is the dust injection rate, τ_sp = 2 × 10⁸ yr is the sputtering timescale (calculated using formula (11) with n_H = 0.001 cm^-3 and a = 0.1 μm), and M_d = 4.7 × 10⁸  M_☉ is the inferred dust mass producing the extended emission.

The first dust injection sources we consider are the halo stars. As described in Appendix E, we have derived an upper limit to the dust injection rate from halo stars based on the observed R-band halo surface brightness (Moles et al. 1998) and the theoretical predictions for stardust injection by Zhukovska et al. (2008): $\dot{M_{\rm d}}=0.075 {\,M_{\odot }\;{\rm yr^{-1}}}$. Substituting this value in Equation (15), we get F_coll < 0.03. A similar procedure could be followed considering the dust injection from type II supernovae given the inferred SFR associated with the extended emission. Empirical studies of Galactic supernova remnants have shown the yield of condensate per supernova event to be of the order of 0.01–0.1 M_☉ (Green et al. 2004; Fischera et al. 2002). Relating the frequency of core collapse supernova events to the SFR in the extended component of SQ, we estimated $\dot{M_{\rm d}}=7\times 10^{-4} {\,M_{\odot }\;{\rm yr^{-1}}}$ assuming 0.01 M_☉ of dust produced in each supernova. Therefore, supernovae dust injection cannot be considered important in replenishing dust in the hot medium. Finally, we considered the mechanism proposed by Popescu et al. (2000) where dust in IGM external to a cluster can be introduced into the hot ICM in the supersonic accretion flow of barions onto the cluster. In the case of SQ, the baryonic accretion rate can be estimated to be of the order of the current IGM seen in X-ray divided by a Hubble time which is ≈2 M_☉ yr^-1. Even if we consider that there is maybe a cooler component of the accreting IGM not visible in the X-ray (Mulchaey 2000), it does not seem plausible to achieve dust accretion rate for the particular case of SQ much greater than 0.01 M_☉ yr^-1 for reasonable values of the dust-to-gas ratio in the accreting material.

Given these estimates, we can conclude that if there is a contribution of collisional-heated dust to the total observed dust emission, this should only be of the order of a few percent and maintained by direct injection from the in situ stellar population. This however is sufficient to maintain a collisionally powered FIR luminosity of up to ≈10⁴² erg s^-1, which is several times the X-ray luminosity.

Such a level of FIR cooling could help to provide a natural explanation for the rather low ratio of ∼0.02 for the ratio of the mass of baryons in the hot X-ray-emitting halo of ∼M_X = 2 × 10¹⁰  M_☉ to the dynamical mass of ∼10¹²  M_☉. ¹⁸ For the concordance cold dark matter cosmology, this ratio should be ∼0.09 in the absence of significant dissipative effects (see, e.g., Figure 9; Frenk et al. 1999). Recalling that the total baryonic mass currently locked in stars in SQ of ∼10¹¹  M_☉ is comparable to the expected total mass of baryons, it is apparent that this scenario is also quantitatively consistent with the efficient condensation of the IGM accreting onto the group into stars, as postulated in Section 7.1. Some empirical indication of efficient star formation in groups has been found by Tran et al. (2009), who showed that the group environment is more conducive to star formation than either the cluster or field environment. In general, enhanced cooling due to an FIR collisionally powered luminosity of a few times L_X would, since it promotes the condensation of hot X-ray-emitting gas into stars, also provide an alternative explanation for the steeper L_X–T_X relation observed for groups with lower virial velocities, an effect that is otherwise attributed to thermal or kinetic feedback from AGNs (e.g., Cavaliere & Lapi 2008).

In summary, the detection and recognition of the putative collisionally heated component of FIR emission from SQ will be a crucial measurement with wide ranging implications for the nature of star formation in the group, the division of baryons between hot gas, cold gas and stars, and the thermodynamic properties of the IGM in SQ. Although such a detection will be very challenging, requiring a combination of excellent surface brightness sensitivity, spectral grasp, and angular resolution at submillimeter wavelengths, it could be achieved by the planned Space Infra-Red Telescope for Cosmology and Astrophysics (SPICA, Nakagawa 2010; Swinyard et al. 2009), as illustrated by the following estimates: assuming the upper limit F_coll = 0.03, we predict the SED of the collisionally powered component of the extended emission to peak at a level of 0.15 MJy sr^-1 at 190 μm.

The Seyfert 2 galaxy NGC 7319 is the most powerful source of IR emission in SQ and is the only galaxy where we found enhanced infrared emission in the central regions. The total IR luminosity is 9.6 × 10⁴³ erg s^-1. Of this, we deduced from the SED fitting using a combination of the AGN torus template and the diffuse dust emission component (see Section 5.2) that 4.1 × 10⁴³ erg s^-1 are emitted by dust in the torus and 5.5 × 10⁴³ erg s^-1 by diffuse dust. As one can see from the SED best fit, shown in Figure 15, the 24 μm MIR emission is dominated by the torus emission which also contributes ≈25% of the 8 μm emission. This is consistent with the observed morphology at 8 and 24 μm emission, which is a combination of a central source plus a disk component in the case of the 8 μm map and a dominant central source in the case of the 24 μm map (see Figure 1). According to the SED fit, the FIR 70 and 160 μm emission is due to diffuse dust emission. This is also consistent with the brightness distributions on the Spitzer FIR maps which show the emission to be partially resolved, with extents inferred from the FIR map fitting technique of 5 and 12 kpc at 70 and 160 μm, respectively. This extended FIR emission is centered at the position of the AGN, potentially indicating the presence of star formation regions distributed on kpc scales in the surrounding areas. However, as one can see from Figure 1 of Gao & Xu (2000), the CO emission is predominantly from the northern regions of this galaxy. Therefore, the locations of the bulk of cold gas, where the star formation sites should be, and the cold dust emission are not coincident suggesting that star formation may not be the main phenomena powering the FIR dust emission.

Overall, the diffuse dust emission in the inner disk, together with the absence of H i (Williams et al. 2002) and the displacement of the molecular hydrogen emission suggest that galaxy–galaxy interactions have removed gas from the central regions on kpc scales, as has plainly also happened in the other late-type SQ galaxies. In the case of NGC 7319, the interactions have apparently also induced gas flows that have triggered AGN activity. This raises the question whether the AGN itself might be the source of photons powering the surrounding diffuse dust emission in this galaxy. According to the standard AGN unification theory, the AGN torus of a Seyfert 2 galaxy is viewed edge-on, which, in the case of NGC 7319, would imply that the plane of the torus is almost perpendicular to the galaxy disk, since NGC 7319 is seen basically face-on (see SDSS g-band map in Figure 1). In this configuration, it would indeed be plausible that accretion powered radiation, escaping into the polar direction from the AGN torus structure could propagate into the galaxy disk and contribute to the diffuse radiation field in the central parts of the galaxy. An especially efficient coupling between the dust and radiation would be expected if the polar axis of the AGN torus were to be parallel to the diffuse dusty disk of the host galaxy.

One indirect indication that the radiation from an AGN with this orientation may be responsible for at least part of the diffuse FIR emission in NGC 7319 comes from the rather low observed UV/FIR luminosity ratio, which is qualitatively consistent with the expected strong attenuation of the direct UV light from an AGN to which the line of sight passes through the torus. From the measured FUV luminosity, L_FUV = 4 × 10⁴² erg s^-1, and from the 60 and 100 μm luminosities extrapolated from the SED best fit, L_60 μm = 2 × 10⁴³ erg s^-1 and L_100 μm = 3.7 × 10⁴³ erg s^-1, we have found L_FUV/L_60 μm = 0.2 and L_FUV/L_100 μm = 0.1. These values are several factors lower than the average values found by Popescu & Tuffs (2002) for galaxies of similar morphological type (L_UV/L_60 μm = 1 and L_UV/L_100 μm = 0.6) and by Xu et al. (2006) for galaxies of similar L_FUV + L_60 μm total luminosity (L_UV/L_60 μm = 0.5).

A scenario in which the diffuse dust emission in NGC 7319 is powered by the AGN also seems to be broadly consistent with simple constraints on the UV luminosity of the AGN derived from the observed hard X-ray luminosity. Specifically, for L_2–10 keV = 2.8 × 10⁴² erg s^-1 (Trinchieri et al. 2005) and adopting the bolometric corrections for AGN galaxies with similar L_2–10 keV by Vasudevan et al. (2010), κ_2–10 keV ≈ 10–30, one predicts a total UV luminosity from the AGN of L_AGN = κ_2–10 keV L_2–10 keV = (2.8–8.4) × 10⁴³ erg s^-1. The upper end of this range is comparable to the total MIR/FIR luminosity of the AGN and AGN host galaxy. If the AGN were indeed powering the diffuse dust emission in the inner disk one would expect that future FIR observations of angular resolution sufficient to image the diffuse dust emission could be used to determine some basic geometrical properties of the AGN. Specifically, one would expect a cone structure for the component of diffuse dust heated by the AGN, with a strong radial color gradient, and with a symmetry axis aligned with the polar axis of the torus.

Finally, we draw attention to a further FIR-emitting feature potentially connected to the AGN, whose origin has still to be clarified. This is the bridge which apparently connects the AGN to the center of the shock region, appearing in the X-ray (Trinchieri et al. 2005), Hα (Xu et al. 1999), and warm H₂ line emission (Cluver et al. 2010). The presence of a cold dust emission from this feature is hinted by a slight asymmetry of the FIR emission on the 160 μm residual map (see Figure 4). High-resolution FIR observations would also be useful to elucidate the correspondence between dust emission and the gas distribution in this bridge feature.

The technique we developed for the fitting of the Spitzer FIR maps is similar to the CLEAN algorithms used in radio astronomy but with some additional characteristics: (1) all the sources are fitted at the same time and (2) an intrinsic finite source width is allowed. Our basic assumption is that all the sources we model are sufficiently well described by elliptical Gaussians or a combination of them. This is not necessarily true because some sources can, in principle, differ significantly from this simple shape. However, this simple approach has been sufficient for a good fitting of the FIR maps. The function F(x,y), describing an elliptical Gaussian on a map, is defined by the following formulae:

$$\begin{eqnarray} &&F(x,y)=B_{\rm loc}+A\times e^{-U/2} \end{eqnarray} \tag{ A1 }$$

$$\begin{eqnarray} &&U=(x^{\prime }/\sigma _x)^2+(y^{\prime }/\sigma _y)^2 \end{eqnarray} \tag{ A2 }$$

$$\begin{eqnarray} &&x^{\prime }=(x-x_s)\cos \theta -(y-y_s)\sin \theta \end{eqnarray} \tag{ A3 }$$

$$\begin{eqnarray} &&y^{\prime }=(x-x_s)\sin \theta +(y-y_s)\cos \theta. \end{eqnarray} \tag{ A4 }$$

The first two equations define the shape of the elliptical Gaussian while the last two are the coordinate transformations between the map and the frame defined by the elliptical Gaussian axis. For each source, the fitting procedure has to provide seven parameters: A (the Gaussian amplitude), (x_s , y_s ) (the position of the source center), (σ_x , σ_y ) (the Gaussian widths in two orthogonal directions), Θ (the rotation angle of the Gaussian axis from the array axis), and an offset value B_loc (the local background for each source).

A real image is not just the sampling of the original signal, of course, but it is the sampling of the convolution of the signal with the PSF of the telescope optics–detector instrument. Using the program STINYTIM, ¹⁹ we obtained theoretical PSFs of the MIPS instrument for both 70 and 160 μm bands. Figures 21 and 22 show the theoretical PSFs for the 70 μm and 160 μm bands and their profiles. In panel (b) of these figures, it is shown also the radial profile of an empirical PSFs (kindly provided by G. Bendo). Although there are some intrinsic differences between empirical and theoretical profiles, we decided to use theoretical PSFs because they can be sampled at any desired rate and do not contain noise that would be added to the fit (however, we made some tests to determine the level of uncertainty introduced by using theoretical PSFs instead of real ones in our fitting procedure. We have found that the difference on the final results is negligible compared to other sources of error, e.g., only ≈5% on the inferred source fluxes).

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The first step of our fitting procedure is to assume a distribution of elliptical Gaussian sources, with initial trial values of the parameters, in an array of the same size of the data. First from a direct inspection of the FIR maps and then after some iterations, we identified 10 main sources to be fitted using elliptical Gaussians (see Figure 2): two for NGC 7320 (one for the disk emission plus one for a compact H ii region), one each for SQ A and SQ B, two for NGC 7319 (one for the circumnuclear emission plus one for a H ii region), one for a source located north of NGC 7319 (H ii-N), two for NGC 7318b (the two compact H ii regions located on the southern spiral arms H ii-SE and H ii-SW), and one for a source peaked in the middle of the shock region. Convolving this array with a theoretical PSF, an artificial image is obtained that can be compared with the real data. Varying the parameters of the elliptical Gaussians, it is possible to improve the agreement between artificial and real images until a certain degree of accuracy is reached. To minimize χ² and find the best-fit model parameters, we used the Levemberg–Marquardt (LM) algorithm (see Bevington & Robinson 1992), implemented by the IDL routine MPFIT2DFUN. ²⁰ Although this algorithm is less dependent on the initial trial values of the parameters, compared with other χ² minimization methods, the results are inevitably dependent on these. Therefore, it is a good rule to assign the initial values as close as possible to the real ones (or better to which we believe are the real ones). The criteria we used to choose the initial values for the free parameters are the following.

• 1.  
  Amplitude. Any number of the order of the peak amplitude of the source (this fitted parameter has been found almost independent from the initial value).
• 2.  
  Position. Initial positions near the peaks of the sources.
• 3.  
  Gaussian widths. Derived approximately from the apparent width of the source.
• 4.  
  Rotation angle. Any number.
• 5.  
  Local background. initial value equal to zero.

As one can notice, the choice of the initial values does not require to know in advance any parameter but the approximate positions of the source centers and roughly the sizes of the Gaussians. All this information can be easily derived from the data. The fitting procedure improves the quality of the results (in the sense that we obtain a smoother fit residual map and a lower reduced χ²) if we consider only the regions close to the sources for the fit. We created a mask to exclude all the pixels that are too distant from the calculation, that is more than 2–3 times the apparent sizes, from the source centers.

The fitting technique as described until now has been applied successfully to the 70 μm FIR map. The fitting of the 160 μm map has been performed in a slightly different way because one cannot clearly see on this map all the compact sources that are detected on the 70 μm. This effect is most probably due to both lower resolution and intrinsic color differences. Since our goal was to produce consistent SEDs of the main sources in SQ, we introduced new constrains for the fit of the 160 μm map. We assumed that the center position of each source on the 160 μm map is the same as derived from the 70 μm map fitting. We only allowed a common shift of all the source positions in order to correct possible small differences in the astrometry of the two maps. Then we assumed that the orientation angles and the ratio of the elliptical Gaussian axial widths (σ_x , σ_y ) for the compact sources (SQ A, H ii-SE, H ii-SW, SQ B, H ii-N, and the H ii regions in NGC 7319 and NGC 7320) are the same as those inferred from the 70 μm map fit. Therefore, we assumed that the shape of the emitting compact sources is similar at 70 and 160 μm even if the size can be different. This is actually expected because colder emission can come from regions that are simply farther away from the central heating source in the case of star formation regions.

Figures 2 and 3 show the results of our fitting technique for the 70 μm and 160 μm maps in four panels: (1) the background subtracted Spitzer FIR map of SQ, (2) the best-fit image obtained with our method, (3) the fit residuals, and (4) the "deconvolved" map (that is actually the map showing the elliptical Gaussians whose PSF convolution gives the best-fit map). As one can see, this method produces best-fit maps with remarkable similarity to the original maps (χ² _70 μm/N_free = 0.8, χ² _160 μm/N_free = 0.7). The "deconvolved" map at 70 μm shows, apart from the emission of the foreground galaxy NGC 7320 and AGN galaxy NGC 7319, many discrete compact sources that are responsible for the several peaks seen on the real map. There is a rather extended source that peaks in the middle of the shock region, even though some excess of emission is still seen on the fit residual map at this position suggesting that the accuracy of the fit is not very good for this faint source. At 160 μm, the emission is dominated by the AGN galaxy, the foreground galaxy, and the source peaked on the shock region. It is quite interesting that the Gaussian used to fit the emission at the position of the shock is very well aligned along the main axis of the shock ridge. However, the east–west width of this Gaussian is too large to be related only to the X-ray ridge (see Section 4.2). Some compact star formation regions are undetected (or only marginally detected) at 160 μm, as we somehow expected because no peaks are clearly seen at their position.

The main fitted parameters and the derived flux densities for each of the fitted sources can be found in Table 1. The uncertainties on the integrated fluxes are derived from the covariance matrix provided by the LM χ² minimization algorithm. For the estimate of the error on each point of the map, necessary to evaluate χ² we considered the variance of background fluctuations on each map. On the final integrated fluxes for each source a 10% error is added due to flux calibration uncertainties (MIPS data handbook). As one can notice from Table 1, the inferred 160 μm sizes for the AGN galaxy NGC 7319 and the compact sources H ii-SE, SQ B, and H ii-N are much larger than the 70 μm size. In the case of the AGN galaxy, the size difference can be physically understood if one thinks that additional warm emission come from the central part of the galaxy and, therefore, the 70 μm flux is more peaked toward the center (see also discussion in Section 7.3). The larger 160 μm size for the compact sources arises because of the confusion with fainter sources close to the main central source. For these sources, we derived from the deconvolved 160 μm Gaussians the amount of flux within one 70 μm FWHM from the peak. These reduced 160 μm fluxes are quoted within brackets in Table 2.

Since in Section 5, we performed source SED fitting including MIR and FIR measurements, performed, respectively, using aperture photometry and the map fitting technique, it is important to understand how different the fluxes obtained by the fitting procedure are compared to those we would have obtained by aperture photometry on a high-resolution map. To quantify this difference, we made a test using the higher resolution 24 μm map where dust emission morphology looks remarkably similar to the 70 μm emission (at least if one considers the main sources of emission). We convolved the 24 μm MIR map to match the resolution of the 70 μm map, resampled the map to match the pixel size of the 70 μm map, and then performed the Gaussian fitting technique on the convolved map. The convolution has been done using the kernel function created by Carl Gordon (Gordon et al. 2008). For the fit we assumed the same distribution of Gaussians as in the fit of the FIR maps, but leaving all the parameters free. The convolved map and the fit results are shown in Figure 23. In Table 6 and Figure 8, we compared the results from aperture photometry (described in Section 4.1) and Gaussian fitting. For all but one source (H ii-SW), the fluxes derived using the two different methods are consistent within the uncertainties and also the inferred source sizes are close to those found at 70 μm (the problem with H ii-SW arises because of the vicinity of the nucleus of NGC 7318a that is much brighter in the MIR than in the FIR). Based on the results of this test, we are confident that the two photometric techniques give consistent results.

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Dust in H ii and PDR, close to young stars, is warm and emits predominantly in the MIR. To model this emission, we used an SED template derived by the fitting of Milky Way star formation region infrared emission with the theoretical model of Groves et al. (2008). The Galactic star formation regions considered are the radio-selected sample of Conti & Crowther (2004). The template is the average fitted spectra of the observed emission from these regions. Further details will be given in a forthcoming paper (Popescu et al. 2010, Section 2.9). The template is shown in the left panel of Figure 11.

To fit the diffuse dust emission, we created a grid of theoretical SEDs of emission from dust heated by a uniform radiation field. The code we used to calculate dust emission, developed by Joerg Fischera (details will be given in J. Fischera et al. 2010, in preparation), assumes a dust composition including graphite, silicates, iron, and PAH molecules. The abundances and size distributions are the same as in Table 2 of Fischera & Dopita (2008). Dust emission is calculated taking into account the stochastic temperature fluctuations of dust grains following the numerical method described by Guhathakurta & Draine (1989), combined with the step wise analytical solution of Voit (1991). We created the set of SEDs by varying the intensity and the color of the radiation field heating the dust and keeping the dust composition fixed. The standard shape of the radiation field spectra, adopted by the dust emission code, is that derived by Mathis et al. (1983) to model the Galactic local ISRF. In this spectrum, the stellar contribution consists of four components: a UV emission from early-type stars plus three blackbody curves at temperatures T₂ = 7500 K, T₃ = 4000 K, and T₄ = 3000 K used to reproduce, respectively, the emission from young/old disk stars and red giants. Each blackbody curve is multiplied by a dilution factor W_i that defines its intensity. The whole spectrum is multiplied by a parameter, χ_isrf, whose value is unity when the spectrum intensity is the same as in the local radiation field. In order to consider different colors of the radiation field, we defined a second parameter, χ_color, that multiplies only the blackbody curves used to model the old disk population and the red giant emission (blackbody temperatures T₃ and T₄). For a range of values of χ_isrf (0.1, 0.3, 0.5, 1, 2, 4) and χ_color (0.25, 0.5, 1, 2, 4), we calculated the corresponding dust emission and created the set of models for the SED fit. The result of increasing the χ_isrf value is that the overall intensity of the radiation field is higher and, therefore, the equilibrium dust temperature is higher, leading to a warmer emission in the FIR (see the left panel of Figure 12). A value of χ_color higher than unity increases the relative contribution of the cold stellar emission, which peaks in the optical range. These wavelengths are more efficiently absorbed by big grains than by PAH molecules (and small grains). As a consequence, by varying this parameter, one modifies the ratio between the peak intensity at the FIR, produced by big grains and the peak intensity at 8 μm, due to PAH molecules which are mainly heated by UV photons (see the right panel of Figure 12). A similar effect would have also been produced by varying the relative abundance of PAH molecules and solid grains.

We selected a theoretical dusty torus SED between those created by A. Feltre et al. (2010, in preparation), using the model presented by Fritz et al. (2006). In this model, the characteristic of the torus, supposed to be homogeneous, is defined by several parameters: opening angle, external to internal radius ratio, equatorial optical depth at 9.7 μm and two parameters, β and γ, that determine the radial and the angular density profile, respectively, according to the formula ρ(r, θ) = αr^−β e^{−γ|cos(θ)|}, where r is the radial coordinate and θ is the angle between a volume element and the equatorial plane (note that α is determined by the torus optical depth). We selected a model with a large opening angle (140°), with an angular gradient in the density profile (β = 0, γ = 6), external to internal radius ratio equal to 30 and equatorial optical depth τ(9.7 μm) = 6. The chosen parameters are well inside the range of values found by Fritz et al. (2006) from the fitting of a sample of Seyfert 2 galaxies. Then, we extracted the output SED in the equatorial view, according to the Seyfert 2 classification of NGC 7319, the AGN galaxy in SQ. The extracted SED is the template we used for fitting the AGN torus emission and it is shown in the right panel of Figure 11.

Finally, we needed to model the emission from collisionally heated dust. For this purpose, we used a code, created by J. Fischera, based on the works by Guhathakurta & Draine (1989) and Voit (1991) for calculating the stochastical heating of the dust grains and using the results of Draine & Salpeter (1979) and Dwek (1987) to determine the heating rates due to dust–plasma particle collisions. Dust composition is assumed to be a mix of graphite (47%) and silicates (53%). PAH molecules are not included but, since they have an extremely small destruction timescale when embedded in hot plasmas with T>10⁶ K, their abundance is expected to be negligible. In order to perform the calculations, one needs to specify the physical properties of the plasma, i.e., density, temperature, and metallicity. The exact value of metallicity is not important because dust is predominantly heated by collisions with electrons, provided mainly by ionized hydrogen and helium. Plasma temperature and density are derived from X-ray data (see Appendix C). An important phenomenon that should be taken into account while preparing the SED models is dust destruction due to sputtering (Draine & Salpeter 1979). Because the efficiency of sputtering depends on the grain size, we expect that the size distribution of grains in hot plasmas is different from that of dust in the cold ISM, typically assumed to be n(a) ∝ a^−k with k = 3.5 (Mathis et al. 1977). Therefore, we created a set of SEDs varying (1) the plasma physical parameters (see Table 7) and (2) the exponent k of the size distribution in the range [1, 3.5]. A k value lower than 3.5 means that the relative number of big grains is higher compared to the standard size distribution. Since the destruction timescale due to dust sputtering is directly proportional to the grain size (Draine & Salpeter 1979), a higher relative abundance of big grains is indeed expected in hot plasmas. Once the heating rates due to collisions are fixed, a change in k modifies the color of the emitted radiation (see Figure 13). This happens because big grains are generally colder than small grains, and do not provide warm dust emission due to stochastic heating. Therefore, changing their relative abundance, one can obtain colder or warmer SEDs.