THE SPATIAL EXTENT OF (U)LIRGs IN THE MID-INFRARED. I. THE CONTINUUM EMISSION

The sample on which we base our analysis is the Great Observatories All-Sky LIRG Survey (GOALS; Armus et al. 2009). GOALS comprises a complete, flux-limited sample of galaxies in the local universe drawn from the Revised Bright Galaxy Sample (RBGS; Sanders et al. 2003) selected to be systems in the (U)LIRG luminosity class. Armus et al. (2009) describe in detail the characteristics of the GOALS sample and Petric et al. (2010) present a comprehensive statistical analysis of the MIR spectral features as probed with Spitzer/IRS. Using a number of MIR diagnostics, Petric et al. (2010) estimate the AGN contribution to the MIR luminosity of the systems and, based on their apparent morphology, classify each galaxy into a stage of interaction (from isolated systems to advanced mergers). Hubble Space Telescope (HST) high spatial resolution optical and near-IR imaging for a fraction of the GOALS sample are presented by Haan et al. (2010). We refer the reader to these papers for further details. Out of the 291 galaxies (202 systems) included in the GOALS sample (see Armus et al. 2009), a total of 221 are used for this study. This is the number of individual galaxies for which IRS staring observations are available. Figure 1(a) presents the distribution of the galaxies as a function of their IR luminosity while Figure 1(b) shows it as a function of the distance. For reference, on the right panel we also indicate the projected linear scales that can be resolved at a given distance at 13.2 μm using the IRS 5–15 μm spectra.

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The total IR luminosities of our systems were calculated using their IRAS flux densities and luminosity distances (see Armus et al. 2009, for details on the cosmology adopted), and following the prescription described in Sanders & Mirabel (1996). Since the spatial resolution of Spitzer is much higher than that of IRAS, there are MIPS 24 μm Spitzer fluxes for 99 individual galaxies within multiple systems. For these, we distributed the L_IR of the system among the galaxies proportionally to their 24 μm flux. For those systems without 24 μm measurements of individual galaxies, the L_IR was evenly distributed among the members of the system. Due to this redistribution of the L_IR, there are now 35 galaxies with IR luminosities lower than 10¹¹ L_☉  in our sample (see Figure 1(a)). In Table 1, we present the final L_IR and distance of the galaxies.

Table 1. Properties of the Sample

Galaxy	R.A.	Decl.	Distance	log LIR	FEE13.2 μm	Core Size	IRAS
Name	(J2000)	(J2000)	(Mpc)	(L☉)		(kpc)	log(f60 μm/f100 μm)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
NGC 0023	00h09m534	+25°55m27s	65.2	11.12	0.67 ± 0.03	2.62 ± 0.02	−0.239 ± 0.004
MCG-02-01-051	00h18m509	−10°22m36s	117.5	11.18	0.28 ± 0.06	2.28 ± 0.02	−0.111 ± 0.007
ESO350-IG038	00h36m525	−33°33m17s	89.0	11.28	0.07 ± 0.08	1.57 ± 0.01*	0.135 ± 0.003
NGC 0232	00h42m458	−23°33m41s	95.2	11.28	0.37 ± 0.06	2.09 ± 0.01	⋅⋅⋅
NGC 0232	00h42m528	−23°32m27s	95.2	10.93	0.15 ± 0.07	1.79 ± 0.01*	⋅⋅⋅
MCG+12-02-001	00h54m039	+73°05m05s	69.8	11.50	0.42 ± 0.06	1.65 ± 0.01	−0.123 ± 0.006
⋅⋅⋅	...	...	...	...	...	...	...

Notes. Columns: (1) Galaxy name. Multiple systems are indicated with the same name but providing the right ascension and declination of the individual galaxies. (2) Right ascension (J2000). (3) Declination (J2000). (4) Luminosity distance (see Armus et al. 2009 for details). The L_IR is accurate to within 0.01 dex (U et al. 2011, in preparation). (5) IR luminosity of the galaxy (see Section 2.1 for details on its calculation). (6) FEE at 13.2 μm (FEE_13.2 μm). (7) Size (FWHM) of the galaxy core at 13.2 μm (see the Appendix). The asterisks denote galaxies with unresolved cores (FWHM within 10% of that of the unresolved stellar PSF). The colons indicate galaxies whose IRS spectra have been contaminated by a close companion galaxy. In these cases, the FEE_13.2 μm and the core size are not reliable. (8) IRAS log(f_60 μm/f_100 μm) color. Values are given only for sources with a unique IRAS color, i.e., not associated with two individual galaxies.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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All galaxies in GOALS have been observed in staring and/or mapping mode with the Spitzer/IRS instrument using all instrument modules (SL, LL, SH, and LH). They also have IRAC (Fazio et al. 2004) and MIPS (Rieke et al. 2004) imaging observations at all bandpasses (J. M. Mazzarella et al. 2011, in preparation). The analysis presented in this paper is based on IRS SL staring observations covering the 5 to ∼15 μm wavelength range with a spectral resolution of R ∼  60–130. As mentioned earlier, the aim of the study is to separate and quantify the EE of (U)LIRGs from the contribution of the unresolved nuclear component. Thus, we limit our study to the shortest wavelengths where the spatial resolution of IRS (∼36 at 13.2 μm) is sufficient to separate regions of physical scales that range from 0.22 kpc, at the distance of the closest LIRG (∼12 Mpc), to 7 kpc at ∼400 Mpc where the farthest ULIRG of the sample is located (see Figure 1). The median distance of our Galaxy sample is 99 Mpc, at which the spatial resolution is 1.7 kpc (also at 13.2 μm). In order to test the validity of some of the results obtained from the IRS SL spectroscopy, we also used the 8 μm IRAC imaging (see the Appendix and J. M. Mazzarella et al. 2011, in preparation for details).

As explained in Petric et al. (2010), all data were reduced using the S15, S16, and S17 IRS pipelines at the Spitzer Science Center.¹² The pipelines were changed to modify certain header keywords, produce new flat-fields, lower SL and LL fringes by 1%–20%, and provide better treatment of ramp slopes. The changes made between the pipelines should not systematically alter the measurements presented here. The reduction includes ramp fitting, dark sky subtraction, droop correction, linearity correction, and wavelength and flux calibration.

The backgrounds in the high-resolution data were subtracted for all objects with dedicated sky observations (∼60% of the sources). For the low-resolution data without dedicated background observations, off-source nods were used for sky subtraction. Large objects in PID 30323 had dedicated background pointings. Bad pixel mask files were combined such that the final masks flagged all the individual bad pixels, if they were marked as bad in one individual exposure. Basic calibrated data sets (BCDs) for each nod were combined by determining the median if more than five BCDs were available, otherwise the average was used with 3σ clipping. Finally, two dimensional coadds for each nod position and SL module were created.

In this subsection, we briefly summarize how, using 5–15 μm Spitzer/IRS SL staring observations, we can estimate the FEE of the galaxies as a function of wavelength, FEE_λ. More technical details of our analysis, as well as information on the specific treatment of the IRS data, are provided in the Appendix.

We commence the analysis with the two-dimensional co-added files of the GOALS sample reduced as described above (see Petric et al. 2010). We use the exact algorithms of the SSC pipeline, as well as the grid mapping of the slits on the IRS detector identified by the pseudo-rectangles of the "wavesamp" file to extract the spatial profiles of each source along the slit as a function of wavelength for each order and nod position. We follow the same approach to obtain the spatial profiles of a standard star (HR7341; PID: 1432) that we use as the reference point-spread function (PSF) of an unresolved source.

For each wavelength resolution element, we fit the spatial profiles of the stellar PSF and the galaxy with Gaussian functions in order to calculate their peaks of emission and full width at half-maximums (FWHMs). The FWHM of the Gaussian used to fit the galaxy profile is what we call the galaxy "core" size (see below). We then scale the peak of the spatial profile of the stellar PSF to the maximum of the spatial profile of the galaxy and subtract it. What remains is the spatial profile of the EE of the galaxy at a given wavelength. This EE (EE_λ) divided by the integrated emission of the galaxy all along the slit is what we define as the FEE as a function of wavelength, FEE_λ. We refer the reader to the Appendix for a more detailed explanation on its rather challenging calculation and the corrections that have to be applied to obtain reliable values. So formally

$$\begin{equation} {\rm FEE}_\lambda =\frac{\mbox{EE}_\lambda }{E_\lambda (\rm total)}, \end{equation} \tag{ 1 }$$

where FEE_λ, EE_λ, and E_λ(total) are the FEE (ranging from zero to unity), the EE, and the total emission of the galaxy at a given wavelength, respectively. Note that since we are scaling the stellar PSF to the maximum of the spatial profile of the galaxy, we implicitly assume that its nuclear emission is entirely produced by the central unresolved component. Therefore, the values of EE_λ and the FEE_λ calculated in this manner are lower limits to the true EE. We report as the final FEE_λ at a given wavelength the average of the values obtained for each one of the two nod positions of the IRS slits. Comparing the difference between the two nods, we calculate the statistical uncertainty of the FEE_λ. The final uncertainty includes additional sources of error and depends on the details of the target (see the Appendix for more information). For reference, the typical uncertainty on the FEE is between 0.05 and 0.15 (see Table 1).

Since the projection of the IRS slit over the galaxies does not entirely cover the size of the emitting region, we visually inspected their corresponding IRAC 8 μm images in order to examine whether the slit was placed systematically along a privilege direction over the disk of the galaxies. We found that, most likely due to the large size of our sample, the position angle of the slit was randomly distributed along different directions on the galaxies and was not oriented systematically along bars, spiral arms, or regions of enhanced SF. As a consequence, variations in the intrinsic inclinations of the disks in more extended systems do not bias our findings.

If one ignores projection effects or details on the intrinsic geometry of a source, the spatial profile of a galaxy as a function of wavelength, and consequently the estimated FEE_λ, depends primarily on the origin of the emission within the galaxy. The MIR continuum emission, PAH features, emission lines, as well as absorption features do not always originate from the same physical regions. Therefore, it is reasonable to expect that the FEE_λ function varies among the galaxies. We find three different FEE_λ types, whose shapes are similar among the galaxies examined here. We exclude from this study eight sources (4% of the sample) that appear practically unresolved in the 5–15 μm range and for which their FEE_λ ≃  0. We also exclude 11 galaxies (5% of the sample) whose FEE_λ could not be classified in any of the three types.

• 1.  
  Constant/featureless. 111 (50%) (U)LIRGs display a constant FEE_λ across the whole IRS 5 − 15 μm wavelength range (see Figure 2, left panel). No MIR feature appears more extended than another or even than the continuum emission. This implies that there is no differentiation in the spatial distribution of the type of emitting region along the IRS slit. These constant FEE_λ functions range between ∼0.1 up to ∼0.85 among the galaxies of this type. A representative member of this type is NGC 3110 that, in particular, has a constant FEE_λ of ∼0.65.
• 2.  
  PAH and line extended. 37 galaxies (17%) of the sample show MIR features which are clearly more extended than the continuum emission (see Figure 2, central panel). More than ∼20% of the flux detected in several PAH features and emission lines is extended, and in some sources it can be as high as 70%. In these types of galaxies, the bulk of the continuum emission originates from a region more compact than that giving rise to the MIR spectral features. The fact that these two components of emission are spatially decoupled suggests that, contrary to the previous type of FEE_λ, different physical processes are responsible for the energy production in the nucleus and in the disk. This could be due to the presence of either an AGN or an intense starburst in the nucleus producing a strong MIR continuum, compared to a more quiescent SF on the disk where older stellar populations may heat the gas and PAH molecules. A representative member of this type is NGC 1365.
• 3.  
  Silicate extended. Another 54 (24%) galaxies of the sample show a rather interesting FEE_λ shape in which the maximum peaks around 10 μm (see Figure 2, right panel). Inspecting the FEE_λ closely, it appears that there is an increase between ∼8 and 12 μm, around the wavelength range where the 9.7 μm silicate absorption feature is present. We attribute this maximum to an extinction effect in these systems. Galaxies containing very obscured nuclei will show little or not at all "unresolved emission," at wavelengths dominated by the silicate absorption feature. As mentioned earlier, we always normalize the spatial profile of an unresolved point source to the source profile at every wavelength and subtract it in order to determine the value of FEE_λ. Consequently, if the nucleus of a galaxy is very extinguished, any residual emission within the 9.7 μm band, when compared to the emission at any other wavelength that is not affected by the absorption feature, would be interpreted as an excess in the FEE originating from the outer disk of these galaxies, where the extinction is less extreme. This is reflected in the form of FEE_λ we compute and implies that the silicate strength (i.e., the apparent optical depth) calculated from the integrated spectrum of these galaxies may not be representative of their nuclei (see Spoon et al. 2004). A representative member of this type is MCG+08-11-002.

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The presence of these types of FEE_λ suggests that the mechanism by which local (U)LIRGs produce the MIR emission in their disks and nuclear regions varies from one source to the next. There is a great diversity not only in the integrated spectrum of an LIRG/ULIRG, but also in the spatial distribution of the regions responsible for the formation of the various MIR features, such as PAHs, emission lines, and dust continuum. The different FEE_λ types indicate that in some galaxies the emission from PAHs, atomic, or molecular lines is more extended than the dust continuum emission, while in others their extent is similar. These variations are clearly related to the location and intensity of the physical process producing the emission detected, such as young star clusters or an AGN. Our results suggest that not all local (U)LIRGs are to be a priori considered as compact, uniform MIR emitters. There has been an interesting such case reported already, VV114, a system with L_IR =  4 × 10¹¹ L_☉ harboring an AGN, for which high-resolution ground-based MIR imaging (Soifer et al. 2001), as well as 5–15 μm ISO/CAM spectral maps reveal that nearly 60% of the MIR emission is extended (Le Floc'h et al. 2002). In these types of systems, the MIR is not necessarily dominated by an AGN or a single burst of SF. Moreover, in the cases of purely starburst-driven (U)LIRGs, the PAH and continuum emission may not be associated with the same SF event but instead are probably excited, as a whole, by different stellar populations. For example, the 11.3 μm PAH emission is more representative of recent SF events with ages greater than 8–10 Myr, while current SF, less than 8–10 Myr in age, is better traced by the [Ne ii]12.81 μm or MIR continuum emission (Díaz-Santos et al. 2010). In these galaxies, older SF traced by PAH emission is more extended and is more typical of galactic disks, while recent SF, associated with MIR continuum emission, is more compact and concentrated toward the nucleus.

The histogram in Figure 3 presents the distribution of the median FEE_λ, calculated over the whole 5–15 μm range, for all the galaxies in our sample (black histogram). 32% of the galaxies have a median FEE_λ larger than 0.5, that is, at least 50% of their MIR is extended. In addition, more than 90% of the galaxies have a median FEE_λ larger than 0.1.

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High-resolution MIR images of a handful of local (U)LIRGs have revealed rather compact emission originating from a few hundred parsecs around their nuclei (Soifer et al. 2000, 2001; Díaz-Santos et al. 2008). This trend is also present in our data, even though the physical scales we probe with Spitzer are larger. In Figure 3, we also show three histograms of the median FEE_λ for galaxies grouped in three ranges of IR luminosity. We note that galaxies with L_IR <  10^11.25 L_☉ (red histogram) and 10^11.25 L_☉ ⩽  L_IR <  10¹² L_☉ (orange) display similar median values of their FEE_λ distributions. The median of each histogram is 0.46 and 0.39, respectively, which is in agreement with previous studies based on smaller samples of LIRGs (Pereira-Santaella et al. 2010). The median values of the low IR luminosity bins are very similar to that found for the median FEE_λ of the whole sample of galaxies, 0.40. However, we find that the median of the corresponding distribution for ULIRGs (blue histogram) is only 0.14. A Kolmogorov-Smirnov (K-S) test comparing the two LIRG sub-samples with that of the ULIRG indicates significance levels lower than 1 × 10⁻⁵, implying that it is very unlikely that ULIRGs are drawn from the same parent distribution as LIRGs. Our data therefore suggest that, as a whole, the median FEE_λ of ULIRGs is 2–3 times lower than that of LIRGs.

We now explore whether the spatial extent of the MIR continuum of (U)LIRGs is a smooth function of their IR luminosity or whether there is a certain L_IR above which their properties change drastically making their emission substantially more concentrated. The blue circles in Figure 4(a) show the FEE of the 13.2 μm continuum emission (FEE_13.2 μm) as a function of the L_IR for the galaxies in our sample. The size of the circles scales with their distance. As we can see, LIRGs display a wide range of FEE_13.2 μm. They vary from compact systems (FEE_13.2 μm ≃  0) to others which are very extended (FEE_13.2 μm ≃  0.85). No clear trend with L_IR is evident over the decade in IR luminosity covered by the LIRGs. However, if we examine the median value of the FEE_13.2 μm calculated in different luminosity bins (black line), this appears to decrease as the L_IR of the galaxies increases, going from ≃ 0.5 at L_IR ≃  10^10.3 L_☉  to ≃ 0.1 at L_IR ≃  10^12.3 L_☉ . Moreover, for IR luminosities above ∼10^11.8 L_☉ , just below the nominal transition between LIRGs and ULIRGs, the maximum of the FEE_13.2 μm (upper dashed line) drops abruptly, and only a few galaxies have FEE_13.2 μm values larger than 0.2. Indeed, all ULIRGs are unresolved¹⁴ (see Figure 4(b)) and have FEEs_13.2 μm ≲  0.2.

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One may consider that the decrease of the median FEE_13.2 μm with L_IR is due to the loss of spatial resolution (see Figures 4(b) and 1(b)). The more luminous systems tend to be at larger distances and hence their unresolved nuclear component progressively accounts for a larger fraction of their total flux. This bias would affect our ability to measure large values of FEE_13.2 μm for distant sources as they become progressively unresolved. We define as unresolved those galaxies whose "core" angular sizes are within 10% of the stellar PSF. We indicate this limit as a dotted line in Figure 4(b). At this point, it is important to differentiate between the core size of a galaxy, used to establish whether it is resolved or not, and its measured FEE. While the former is merely a Gaussian fit to the spatial profile of the nuclear emission of a galaxy from which an FWHM is obtained, the latter also accounts for possible low surface brightness emission which is probably more extended than the core of the galaxy. As a consequence, sources classified as unresolved in Figure 4(b) may still display non-zero FEE_13.2 μm values in Figure 4(a).

If our ability to measure the FEE and the size of the MIR emitting region of the galaxies were totally dominated by the instrumental resolution, the fraction of unresolved sources would be a monotonically increasing linear function of distance. To examine this, we divided our sample in three distance bins at [25–75], [75–125], and [150–250] Mpc, each doubling the distance of the previous one, and calculated the fraction of unresolved sources in each one. We find that the corresponding fraction of unresolved sources is 16% (9/55), 33% (29/88), and 45% (18/40). That is, as the distance doubles, the fraction of unresolved sources nearly doubles. However, there are sources up to ≃ 240 Mpc, for which we can measure a FEEs_13.2 μm ≃  0.7 independently of their L_IR, implying that we are still able to resolve the EE at those distances if present.

Hence, the steep drop of the maximum value of FEE_13.2 μm above L_IR ∼ 10^11.8 L_☉  cannot be explained by a progressive increasing of the distance to the galaxies. We note that all 10 ULIRGs found at distances up to 200 Mpc, where we are still able to measure large values of FEE_13.2 μm, are unresolved and display FEEs_13.2 μm <  0.2 (see Figure 4(b)). However, 68% (54/80) of LIRGs at similar distances, between 100 and 200 Mpc are resolved and have large FEEs_13.2 μm reaching values up to 0.7. If ULIRGs were drawn from the same parent population as LIRGs, one would expect to resolve around six out of these 10 ULIRGs, which is not the case. Therefore, it appears that there is a real threshold in the distribution of the compactness of IR bright galaxies happening at L_IR ∼ 10^11.8 L_☉, with higher luminosity systems being more compact.

When we examine only the LIRGs of our sample, we find that, independently of the distance, there are systems with more than 50% of their MIR continuum emission originating outside the unresolved central region. This implies that the EE in these systems is larger than the contribution of the unresolved nuclear region to their total MIR luminosity. In fact, we are able to resolve sizes (FWHMs) of LIRG cores up to ∼10 kpc, much larger than the spatial resolution at any given distance. However, to ascertain a representative physical size for the sources in a given luminosity range is quite challenging since our sample is flux limited rather than distance limited. Both the FEE and the size of a source depend on whether we can resolve their emission. The resolution though is a function of the distance, and at the same time more luminous galaxies are seen at larger distances. Hence, upper limits on the sizes of sources also depend on their luminosities. If we simply compute the mean core size of LIRGs using only those systems that are resolved, which are those found above the dotted line in Figure 4(b), the result is 3.1 kpc, while the median is 2.7 kpc. A more thorough analysis can be performed using the survival analysis package ASURV,¹⁵ which properly takes into account the lower and/or upper limits in a given distribution. If we use this approach, we find that the mean core size of LIRGs at 13.2 μm is 2.6 ± 0.1 kpc.

Regarding the ULIRG sub-sample, establishing a typical size for the region from which their EE originates is even more challenging since all of them are unresolved. If we consider the ULIRGs located up to a distance of ∼100 Mpc as the reference, we can estimate an upper limit for their core sizes of ∼1.5 kpc, which is agreement with previous findings (e.g., Soifer et al. 2001).

In order to put our results for the GOALS sample in the context of the less luminous but more numerous galaxies of our local universe, we have analyzed the low luminosity sources from the starburst sample of Brandl et al. (2006). We selected galaxies with L_IR ⩽  10¹¹ L_☉  where the IRS slit was well centered on their nuclei (see their Figure 1): IC 342, Mrk 52, NGC 520, NGC 660, NGC 1097, NGC 1222, NGC 3628, NGC 4088, NGC 4676, NGC 4945, NGC 7252, and NGC 7714. Our measurements are plotted as red squares in Figures 4(a) and (b). We find that the FEE_13.2 μm of these systems ranges between ∼0.4 and 0.8 and is within the values shown by GOALS galaxies with similar IR luminosities. This suggests that the extent of the MIR continuum emission in starburst galaxies and in the low luminosity tail of the GOALS LIRGs is comparable.

Finally, we should mention that our study provides no evidence that LIRGs with small FEE_13.2 μm have the highest IR luminosities since the most point-like sources do not appear to be systematically the most luminous in the 5–15 μm range (see also Figure 3). Instead, as mentioned above, all LIRGs show the same scatter in the FEE_13.2 μm at any given distance. It is only above the threshold of L_IR ∼ 10^11.8 L_☉ when we observe a significant reduction of the FEE_13.2 μm to values ≲0.2.

We have shown that there is a strong evolution of the compactness of the MIR continuum emission at L_IR ∼ 10^11.8 L_☉. What is the physical process responsible for this? It is known that most ULIRGs are merging systems with clear signs of interactions (e.g., Clements et al. 1996; Murphy et al. 2001). Could it be that the merging processes in (U)LIRGs which drive the material of the galaxies to their nuclei causing massive SF is the same reason that makes them appear more compact in the MIR?

The galaxies in our sample were classified in five stages: (1) no obvious sign of disturbance in their IRAC or HST morphologies, or published evidence that the gas is in dynamical equilibrium (i.e., undisturbed circular orbits); (2) early stage, where the galaxies are within 1' of each other, but little or no morphological disturbance can be observed; (3) the galaxies exhibit bridges, strong disturbance but they do not have a common envelope and each optical disk is relatively intact; (4) the optical disks are completely destroyed but two nuclei can be distinguished; (5) the two interacting nuclei are merged but structure in the disk indicates the source has gone through a merger. The classification was proposed by Petric et al. (2010) and it is based on HST imaging, 3.6 μm Spitzer IRAC images as well as optical Sloan Digital Sky Survey (SDSS) images of the sources (see also Surace 1998). In Figure 5, we plot total (black) histograms of the FEE_13.2 μm for each interaction stage and also divided in three IR luminosity bins (red, orange, and blue, as in Figure 3). We study 214 (out of the 221) galaxies for which the stage of merger is available. We observe that the most advanced mergers (stage 4) tend to have low FEE_13.2 μm values, i.e., they are more compact. K-S tests performed between the total, stage 4 FEE_13.2 μm distribution and those of the rest of merging stages yield significance values always lower than 0.01. K-S tests performed among the 0–3 merging stage data sets provide significance values between 0.4 and 0.75. This implies that in fact galaxies classified as to be at merging stage 4 are systematically more compact than those in earlier interaction stages.

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Regarding the IR luminosity bin distributions, we see that merging stage 4 systems are not necessarily the most IR luminous only (see also Rigopoulou et al. 1999) but 15% (8/54) have IR luminosities lower than 10^11.25 L_☉. On the other hand, we find that the vast majority, 89% (16/18), of ULIRGs are systems classified as mergers in their final stage of interaction and all have FEE_13.2 μm ⩽  0.2, in agreement with previous findings. Similarly, galaxies at the stage 4 of interaction with 10^11.25 L_☉ ⩽  L_IR <  10¹² L_☉ also tend to show lower FEE_13.2 μm values (like ULIRGs) than less luminous systems. LIRGs and less IR luminous systems are spread uniformly in the FEE_13.2 μm versus L_IR parameter space up to the merging stage 2 (the histograms are flat within the uncertainties).

Another reason why LIRGs and ULIRGs may appear compact in the MIR is the presence of a dominant AGN. We know that the AGN activity is more prevalent in high IR luminosity systems (e.g., Veilleux et al. 1995, 2009), so we would expect that as the AGN emission starts to dominate the IR energy output of a galaxy, it should appear progressively less extended.

For all galaxies in our sample, the contribution of an AGN to their MIR emission has been estimated by Petric et al. (2010) using a number of line and continuum features. We use their estimates of the AGN contribution fraction to the MIR emission calculated by means of the so-called "Laurent diagram" (Laurent et al. 2000), which is based on the 15 μm/5.5 μm continuum and 6.2 μm PAH/5.5 μm ratios (see Figure 3 of Petric et al. 2010). By comparing the data in this parameter space with representative ratios of pure AGN, PDR, and H ii regions, it is possible to infer the contribution of these components to the total galaxy emission. In Figure 6, we present the FEE_13.2 μm as a function of this AGN fraction for the 210 galaxies for which it could be derived. The galaxies are again displayed as circles, the size of which scales with their IR luminosity. It is clear that as the AGN contribution to the MIR approaches unity, the maximum FEE_13.2 μm at the different AGN-fraction bins (upper dashed line) decreases and the galaxies become progressively more compact. In addition, the median FEE_13.2 μm (solid line) also decreases as the AGN fraction increases, although more smoothly. In fact, only 5 out of the 30 AGN-dominated galaxies¹⁶ have FEE_13.2 μm > 0.2. Independently of the L_IR, it is interesting to see that 60% (15/25) of the AGN-dominated galaxies with FEE_13.2 μm ⩽  0.2 are in the final stage of interaction, while only 12% (3/25) are in the third, 0 in the second, 20% (5/25) in the first, and 8% (2/25) in the zeroth (see Figure 5).

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We have found that galaxies classified as mergers in their final stage of interaction tend to have low FEE_13.2 μm values and, in particular for ULIRGs, FEE_13.2 μm <  0.2. We also show now that the fraction of ULIRGs in merging stage 4 that are AGN dominated is 60% (9/15). The fraction of galaxies with 10^11.25 L_☉ ⩽  L_IR <  10¹² L_☉ and FEE_13.2 μm ⩽  0.2 (first FEE_13.2 μm bin in Figure 5, stage 4) that are AGN dominated is 33% (5/15)¹⁷ while for lower luminosity systems is 33% (1/3). Moreover, the fraction of AGN-dominated galaxies classified as mergers at stage 4 with FEE_13.2 μm > 0.2 is 0%, independently of the IR luminosity. That is, all AGN-dominated galaxies in the stage 4 of interaction are compact.

Independently of the process that dominates the IR emission in galaxies (either an AGN or a starburst), we should expect to observe harder radiation fields and higher dust temperatures within more compact environments. In this section, we explore whether the EE we detect in the 5–15 μm wavelength range, that traces warm small dust grains and molecules, depends on the amount of cold dust of our sources. We first calculate the IRAS log(f_25 μm/f_60 μm) color of the galaxies, which is a well-known IR broadband AGN diagnostic (de Grijp et al. 1985), but we find that it does not correlate with the extent of the MIR continuum emission. We also explore whether there is a dependence on the Spitzer log(f_24 μm/f_70 μm) and log(f_70 μm/f_160 μm) colors but do not find any clear trend. However, when we plot in Figure 7 the FEE_13.2 μm as a function of the FIR IRAS log(f_60 μm/f_100 μm) color, a correlation is visible. Despite the large scatter, galaxies with cold FIR colors appear to be more extended in their MIR continuum. The Spearman rank correlation coefficient is −0.67 with a significance level of effectively 0, while the Kendall test provides a value of −0.49, implying that the correlation is real. We fitted our data with an outlier-resistant linear fit algorithm provided by the IDL function robust_linefit,¹⁸ and the best-fit parameters are given in the following equation:

$$\begin{equation} {\rm FEE}_{13.2\,\mu {\rm m}}=0.04\pm 0.02-(1.83\pm 0.11)\times \log \left(\frac{f_{60\,\mu {\rm m}}}{f_{100\,\mu {\rm m}}}\right), \end{equation} \tag{ 2 }$$

where FEE_13.2 μm is the FEE of a given galaxy at 13.2 μm, and f_60 μm and f_100 μm are the IRAS flux densities (f_ν) at 60 and 100 μm, respectively. The data have a scatter of 0.2 in the y-axis and 0.1 in the x-axis. The uncertainties in the parameters of the fit have been calculated using bootstrapping resampling analysis. In order to avoid interacting systems for which only one IRAS color has been measured due to its limited spatial resolution, we have used only 142 sources for which there is a unique association between one galaxy (one FEE_13.2 μm measurement) and one IRAS color. In addition to the correlation, Figure 7 also shows that nearly all galaxies whose MIR emission is dominated by an AGN (i.e., have a high AGN fraction according to the estimates of Petric et al. 2010) are located at the lower right corner of the plot, which means that they are more compact, and have warmer FIR colors. Even if we exclude AGN-dominated systems and consider only starburst galaxies with an AGN fraction close to zero, the correlation is still present.

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This result has an interesting implication for the forthcoming studies of the cold dust emission of LIRGs/ULIRGs with the Herschel Space Telescope. Figure 7 suggests that "cold" FIR-selected (U)LIRGs will likely present large FEE_13.2 μm values. As a result, one would expect that a large fraction of their MIR continuum emission originates in their extended component (see the previous section). Furthermore, based on the study by Bothun & Rogers (1992), the IRAS log(f_60 μm/f_100 μm) colors of our Galaxies suggest that they have very strong dust temperature gradients (their Section 4.1 and Table 3). Consequently the cold, FIR emission from these systems will be more extended than the warmer MIR emission. Taking this into account, the FEE we derive for the MIR continuum emission based on our Spitzer/IRS observations places a lower limit to the extent of the FIR continuum emission. Therefore, despite the limitations of our long-slit MIR spectra, one may obtain a rough estimate on how much of the FIR emission is extended in any LIRG/ULIRG.

By virtue of the negative K-correction, SMGs are systems with IR luminosities in the ULIRG range, almost independently of their redshift. Recent studies of SMGs, based on various diagnostics including the MIR and FIR wavelength range, have suggested that they are systems dominated by SF (Pope et al. 2008; Murphy et al. 2009). In addition, interferometric observations of their CO content and radio continuum emission reveal that they host large amounts of dust and molecular gas ($\hbox{$M_{{\rm H}_2}$}\sim 10^{10\hbox{--}11}\,\hbox{$M_{\odot }$}$) which may fuel prodigious SF rates of several hundred solar masses per year (Neri et al. 2003; Chapman et al. 2004; Greve et al. 2005; Daddi et al. 2009; Tacconi et al. 2008). Analysis of the kinematics of their ionized gas emission using the Hα emission redshifted in the near-infrared indicates that SMGs as well as some high-redshift ULIRGs are extended up to several kpc scales (e.g., Alexander et al. 2010). Taking into account the limits on the spatial resolution of the present day data, some sources display motions which can be attributed to organized rotating disks, and others appear to belong to interacting systems (Tacconi et al. 2008; Bothwell et al. 2010; Ivison et al. 2010). Recent studies of the FIR continuum and [C ii] 158 μm emission of high-z IR luminous galaxies also suggest that the SF in these sources is extended over several kpc (Kovács et al. 2010; Hailey-Dunsheath et al. 2010).

It is well accepted that in the local universe the MIR emission traces the SF regions emitting in Hα and correlates with the presence of molecular gas. Based on our analysis, we find no evidence that the local ULIRGs of the GOALS sample are extended in the MIR to the sizes suggested by the Hα or CO measurements of high-z sources. It is true that the Spitzer spatial resolution is quite limited, but we have shown that even the closest ULIRGs in our sample have unresolved cores and FEE_13.2 μm ≲  0.2. Instead, the LIRG population displays resolved emission extended over several kpc scales, like SMGs.

On the other hand, it is still uncertain whether high-redshift IR luminous sources are simple scaled up analogues of local, less luminous systems in terms of all their physical properties. Integrated MIR spectra of SMGs (Pope et al. 2008; Menéndez-Delmestre et al. 2009) do display PAH equivalent widths more typical of local LIRGs rather than the weaker values found for local ULIRGs (Desai et al. 2007). However, some recent works suggest that the SF law in SMGs is similar to that of local ULIRGs and is much more efficient than in local, less IR luminous disk-like galaxies, or than in high-z BzK galaxies (Daddi et al. 2010a, 2010b; Genzel et al. 2010). We will address the issue of the spectral properties of SF in local LIRGs and ULIRGs in our next paper, where we analyze separately the nuclear and EE of the PAH features, emission lines, and the 9.7 μm silicate feature of the galaxies in the GOALS sample.

In order to calculate the fraction of extended emission (FEE_λ) as a function of wavelength, we used as input data the two-dimensional IRS coa2ds files obtained as explained in Petric et al. (2010). Due to the limited spatial resolution of Spitzer, we performed the analysis using only the SL module (see Section 2.2), which covers a wavelength range from ∼5.5 μm to ∼14.5 μm (SL2 order: ∼5.5 μm to ∼7.5 μm; SL1 order: ∼7.5 μm to ∼14.5 μm). Details regarding the steps taken for the reduction and creation of the coa2ds can be found in Petric et al. (2010). We used version 18.7 of the wavesamp file which contains the information on the projection of the spatial and spectral elements of the IRS slits onto the two-dimensional detector array via a set of pseudo-rectangles. Each pseudo-rectangle defines the spatial direction that crosses an IRS spectrum at a given wavelength. Therefore, to extract the spatial profiles of a galaxy as a function of wavelength, we interpolated the IRS spectrum along the direction traced by each pseudo-rectangle. The same approach was taken to produce the spatial profiles of the standard star used as our reference PSF representing an unresolved source. Each spatial profile was fitted with a Gaussian function leaving as free parameters its maximum intensity, position, and FWHM. Indeed, the latter gives us a measure of the size of the source's "core" at each wavelength (i.e., the Gaussian component of the extended emission; see Figure 4(b)). To calculate the unresolved emission of the galaxy, we scaled the maximum of the PSF spatial profile to the maximum of the galaxy spatial profile and subtracted it. The remaining flux is the EE of the galaxy. We also measured the total emission of the galaxy by integrating the flux over the entire spatial profile defined by the IRS slit. The EE divided by the total emission of the galaxy is the FEE. This calculation was repeated for each wavelength resolution element (pseudo-rectangle) and consequently the FEE is a function of λ (FEE_λ). The calculation of the FEE_λ has some advantages over other methods used to ascertain the compactness of a galaxy, such as the concentration index or the Gini coefficient. The concentration index relies on aperture photometry and therefore does not provide an estimate the shape of the spatial distribution of the PSF, mixing both unresolved and resolved emission. The Gini coefficient is also totally independent of the shape of the galaxy. As a consequence, the growth of the physical size of the unresolved component of the galaxy with distance is not taken into account and it is intrinsically included in the Gini statistics, which would make the interpretation of our results even more challenging.

Since the pixel size of the IRS SL detector is 18 × 18, the IRS spectra are undersampled below ∼10 μm. The undersampling affects the spatial distribution of the flux of unresolved sources over the pixels of the detector. As a result, the exact pixel intensity depends on where the source is located on it at a sub-pixel scale. Since an IRS spectrum does not run along the columns of the detector but displays a slight curvature, the spatial profile of the source at each spectral resolution element is not centered at the same sub-pixel position for all wavelengths. Therefore, the undersampling introduces an intrinsic variation on the shape of the spatial profiles as a function of the wavelength, which is reflected in a change of the FWHM as well as the maximum value of the fitted Gaussian to the spatial profiles. The effect of the undersampling can be seen in Figure 8 where the FWHM and maximum of the spatial profiles of the PSF are shown as a function of the wavelength (red lines: top and middle panels). We note that the FWHM and maximum may vary as much as 50% in the SL2 module. This factor is very important because, in order to calculate the amount of EE of a galaxy at a given wavelength, we need to scale the maximum of the PSF to the maximum of the profile of our source. If a galaxy is unresolved, its fitted maximum will present the same behavior as the maximum of the PSF and the wiggling pattern created by the undersampling will cancel out. If, on the contrary, a galaxy is resolved, its spatial profile will not be affected by the undersampling, but the profile of our PSF will be and will introduce this pattern in the calculation of the FEE_λ.

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Therefore, before the calculation of the FEE_λ of a galaxy, we need to correct the maximum of the PSF, in a manner which takes into account the undersampling in the spatial profile of the galaxy, which in turn depends on its compactness. In order to calculate how compact the galaxy is, we compare its fitted FWHM with that of the unresolved PSF at each wavelength and correct accordingly the maximum of the PSF. A zero correction means that the galaxy is totally unresolved, as is the PSF. A full correction is applied when the galaxy is much more extended than the PSF and implies that we have to correct the maximum of the PSF as if it was not affected by the undersampling at all. What is this correction factor?

The correction factor to the maximum of the PSF is the value of the FWHM of the PSF normalized to its real value at the same wavelength. This is because even if the FWHM and the maximum of the spatial profile of an unresolved source oscillate as a function of the wavelength due to the undersampling, the total flux does not. As a consequence, the patterns of the FWHM and the maximum of the PSF are "synchronized" (the maximum of one is the minimum of the other; see Figure 8, top and middle panels, red lines) and thus we can use the value of the FWHM to correct the maximum to its real value. In this we assume that the "real" (highest) spatial resolution that can be achieved at a given wavelength is the one defined by the minimum of the lower envelope showed by the pattern of the FWHM function of the PSF. Values larger than this are affected by the undersampling and cause the FWHM of the spatial profiles to be overestimated and, conversely, the maximum to be underestimated. Therefore, in order to correct for the undersampling, we multiply the maximum of the PSF by the ratio of its observed-to-minimum (real) FWHM. As we mentioned above, this correction depends on how resolved a galaxy is. In unresolved sources, the correction is not necessary, while in very extended galaxies it needs to be fully applied. In order to demonstrate the success and accuracy of the method, in Figure 8 we show the FWHM, maximum, and FEE_λ function of three galaxies resolved in a different degree. The final FEE_λ at a given wavelength is the average of the values obtained for each one of the two nod positions of the IRS slits, and the uncertainty is the difference between both.

We can see that the FEE_λ function (bottom panel, green line), once corrected for the undersampling effect, shows almost no residuals of the wiggling pattern that can be seen in the FWHM and maximum functions (top and middle panels) of the galaxies and the PSF. Furthermore, the correction works very well for almost unresolved sources (left panels), very extended sources (right panels), as well as for intermediate-resolved sources (center panels). As an example, we show in the bottom panels, together with the FEE_λ function (in green), the FEE_λ function that would have been obtained if we had not applied the correction factor at all (lower orange line) or if it had been fully applied (top orange line), that is if we had not taken into account the a priori knowledge on how extended our Galaxy is. The comparison of the FWHMs of the galaxy and the PSF is therefore essential in order to know to which extent the correction factor must be applied at a given wavelength. This is specially true for galaxies that are slightly resolved at certain wavelengths, as is the case of UGC 08739 (middle panel).

There were a few cases, however, where an accurate FEE_λ function could not be accurately recovered for the SL2 order (IC 4734, ESO 279-G011, MCG-02-33-098, CGCG 468-002, and MCG-05-12-006). These are galaxies that show FWHM functions that do not present a wiggling pattern despite the fact they are almost unresolved. Therefore, their FEE_λ functions from ∼5.5 μm to ∼7.5 μm are very uncertain.

In addition, we checked whether the FEE as a function of the wavelength obtained with the IRS spectra is consistent with the value that can be calculated from the IRAC images at 8 μm. To do so we performed a PSF-fitting analysis to the images in the same way as we did for the spatial profiles of the IRS spectra at each wavelength. First, we used a sub-sampled point response function (PRF) for the 8 μm IRAC bandpass provided by the SSC and interpolated it to the sub-pixel position in the image where the galaxy was located. Then, we rebinned the PRF to the pixel size of the IRAC mosaic, scaled it to the peak of the emission of the galaxy, and subtracted the unresolved emission represented by this scaled PRF. Finally, we measured the remaining flux in an area approximately equal to that used for measuring the integrated emission of the galaxy in the IRS slit (see Section 2.4). Using Equation (1) as for the spectroscopy, the FEE_8 μm obtained from the IRAC 8 μm imaging is the ratio of the remaining emission to the total integrated emission of the galaxy measured in the same aperture.

There are some cases where the FEE_8 μm is greater than the FEE calculated from the IRS spectra. This is due to the different surfaces used for measuring the emission of the galaxy in each case (for imaging and spectroscopy). Although both apertures have the same area, the former has the shape of a box while the one of the IRS slit is very elongated. Since, as it is said above, the slit was not oriented in a preferred direction over the galaxies, a boxy-shaped aperture used for measuring the emission will generally lead to a higher FEE because of its symmetry around the central region of the galaxy which in many cases is axisymmetric. Therefore, the fact that the FEE_8 μm is slightly above those calculated using the IRS data for some galaxies is totally consistent with the approach taken and shows that both calculations of the FEE, using imaging and spectroscopy, are in agreement.