EXPLAINING THE [C ii]157.7 μm DEFICIT IN LUMINOUS INFRARED GALAXIES—FIRST RESULTS FROM A HERSCHEL/PACS STUDY OF THE GOALS SAMPLE

Systematic spectroscopic observations of far-infrared (FIR) cooling lines in large samples of local star-forming galaxies and active galactic nuclei (AGNs) were first carried out with the Infrared Space Observatory (ISO; e.g., Malhotra et al. 1997, 2001; Luhman et al. 1998; Brauher et al. 2008). These studies showed that [C ii]157.7 μm is the most intense FIR emission line observed in normal, star-forming galaxies (Malhotra et al. 1997) and starbursts (e.g., Nikola et al. 1998; Colbert et al. 1999), dominating the gas cooling of their neutral interstellar medium (ISM). This fine-structure line arises from the ²P_3/2 → ²P_1/2 transition (E_ul/k = 92 K) of singly ionized Carbon atoms (ionization potential = 11.26 eV and critical density, $n^{\rm cr}_{\rm H} \simeq 2.7\times 10^3\,{cm^{-3}}$; $n^{\rm cr}_{\rm e^-} \simeq 46\,{cm^{-3}}$) which are predominantly excited by collisions with neutral hydrogen atoms; or with free electrons and protons in regions where $n_{\rm e^-}/n_{\rm H} \gtrsim 10^{-3}$ (Hayes & Nussbaumer 1984). Ultraviolet (UV) photons with energies >6 eV emitted by newly formed stars are able to release the most weakly bound electrons from small dust grains via photo-electric heating (Watson 1972; Draine 1978). In particular, polycyclic aromatic hydrocarbons (PAHs) are thought to be an important source of photo-electrons (Helou et al. 2001) that contribute, through kinetic energy transfer, to the heating of the neutral gas which subsequently cools down via collision with C⁺ atoms and other elements in photo-dissociation regions (PDRs; Tielens & Hollenbach 1985; Wolfire et al. 1995).

The [C ii]157.7 μm emission accounts, in the most extreme cases, for as much as ∼1% of the total IR luminosity of galaxies (Stacey et al. 1991; Helou et al. 2001). However, the [C ii]/FIR ratio is observed to decrease by more than an order of magnitude in sources with high L_IR and warm dust temperatures (T_dust). The underlying causes for these trends are still debated. The physical arguments most often proposed to explain the decrease in [C ii]/FIR are: (1) self-absorption of the C⁺ emission, (2) saturation of the [C ii] line flux due to high density of the neutral gas, (3) progressive ionization of dust grains in high far-UV field to gas density environments, and (4) high dust-to-gas opacity caused by an increase of the average ionization parameter.

Although self-absorption has been used to explain the faint [C ii] emission arising from warm, AGN-dominated systems such as Mrk 231 (Fischer et al. 2010), this interpretation has been questioned in normal star-forming galaxies due to the requirement of extraordinarily large column densities of gas in the PDRs (Luhman et al. 1998, Malhotra et al. 2001). Furthermore, contrary to the [O i] or [C i] lines, the [C ii] emission is observed to arise from the external edges of those molecular clouds exposed to the UV radiation originated from starbursts, as for example in Arp 220 (Contini 2013). Therefore, self-absorption is not the likely explanation of the low [C ii]/FIR ratios seen in most starburst galaxies, except perhaps in a few extreme cases, like NGC 4418 (Malhotra et al. 1997).

The [C ii] emission becomes saturated when the hydrogen density in the neutral medium, n_H, increases to values ≳ 10³ cm⁻³, provided that the far-UV (6–13.6 eV) radiation field is not extreme (G₀ ≲ 10⁴; where G₀ is normalized to the average local interstellar radiation field; Habing 1968). For example, for a constant G₀ = 10², an increase of the gas density from 10⁴ to 10⁶ cm⁻³ would produce a suppression of the [C ii] emission of almost two orders of magnitude due to the rapid recombination of C⁺ into neutral carbon and then into CO (Kaufman et al. 1999). However, PDR densities as high as 10⁴ cm⁻³ are not very common. [O i]63.18 μm and [C ii]157.7 μm ISO observations of normal star-forming galaxies and some IR-bright sources confine the physical parameters of their PDRs to a range of G₀ ⩽ 10^4.5 and 10² ≲ n_H ≲ 10⁴ cm⁻³ (Malhotra et al. 2001). On the other hand, the [C ii] emission can be also saturated when G₀ > 10^1.5 provided that n_H ≲ 10³ cm⁻³. In this regime, the line is not sensitive to an increase of G₀ because the temperature of the gas is well above the excitation potential of the [C ii] transition.

It has also been suggested that in sources where G₀/n_H is high (≳ 10² cm³) the [C ii] line is a less efficient coolant of the ISM because of the following reason. As physical conditions become more extreme (higher G₀/n_H), dust particles progressively increase their positive charge (Tielens & Hollenbach 1985; Malhotra et al. 1997; Negishi et al. 2001). This reduces both the amount of photo-electrons released from dust grains that indirectly collisionally excite the gas, as well as the energy that they carry along after they are freed, since they are more strongly bounded. The net effect is the decreasing of the efficiency in the transformation of incident UV radiation into gas heating without an accompanied reduction of the dust emission (Wolfire et al. 1990; Kaufman et al. 1999; Stacey et al. 2010).

In a recent work, Graciá-Carpio et al. (2011) have shown that the deficits observed in several FIR emission lines ([C ii]157.7 μm, [O i]63.18 μm, [O i]145 μm, and [N ii]122 μm) could be explained by an increase of the average ionization parameter of the ISM, 〈U〉.²⁴ In "dust bounded" star-forming regions the gas opacity is reduced within the H ii region due to the higher 〈U〉. As a consequence, a significant fraction of the UV radiation is eventually absorbed by large dust grains before being able to reach the neutral gas in the PDRs and ionize the PAH molecules (Voit 1992; González-Alfonso et al. 2004; Abel et al. 2009), causing a deficit of photo-electrons and hence the subsequent suppression of the [C ii] line with respect to the total FIR dust emission.

Local luminous IR galaxies (LIRGs; L_IR = 10^{11 − 12} L_☉) are a mixture of single galaxies, disk galaxy pairs, interacting systems and advanced mergers, exhibiting enhanced star formation rates (SFRs), and a lower fraction of AGNs compared to higher luminous galaxies. A detailed study of the physical properties of low-redshift LIRGs is critical for our understanding of the cosmic evolution of galaxies and black holes since (1) IR-luminous galaxies comprise the bulk of the cosmic IR background and dominate star formation activity between 0.5 < z < 2 (Caputi et al. 2007; Magnelli et al. 2011; Murphy et al. 2011; Berta et al. 2011) and (2) AGN activity may preferentially occur during episodes of enhanced nuclear star formation. Moreover, LIRGs are now assumed to be the local analogs of the IR-bright galaxy population at z > 1. However, a comprehensive analysis of the most important FIR cooling lines of the ISM in a complete sample of nearby LIRGs has not been possible until the advent of the Herschel Space Observatory (Herschel hereafter; Pilbratt et al. 2010) and, in particular, its Photodetector Array Camera and Spectrometer (PACS; Poglitsch et al. 2010).

In this work we present the first results obtained from Herschel/PACS spectroscopic observations of a complete sample of FIR selected local LIRGs that comprise the Great Observatories All-sky LIRG Survey (GOALS; Armus et al. 2009). Using this complete, flux-limited sample of local LIRGs, we are able for the first time to perform a systematic, statistically significant study of the FIR cooling lines of star-forming galaxies covering a wide range of physical conditions: from isolated disks where star formation is spread across kiloparsec scales to the most extreme environments present in late stage major mergers where most of the energy output of the system comes from its central kiloparsec region. In particular, in this paper we focus on the [C ii]157.7 μm line and its relation with the dust emission in LIRGs. We make use of a broad set of mid-IR diagnostics based on Spitzer/IRS spectroscopy, such as high ionization emission lines, silicate dust opacities, PAH equivalent widths (EW), dust luminosity concentrations, and mid-IR colors, to provide the context in which the observed [C ii] emission and [C ii]/FIR ratios are best explained. The paper is organized as follows: In Section 2 we present the LIRG sample and the observations. In Section 3 we describe the processing and analysis of the data. The results are presented in Section 4. In Section 5 we put in context our findings with recent results from intermediate- and high-redshift surveys started to be carried out by ALMA and in the future by Cornell–Caltech Atacama Telescope (CCAT). The summary of the results is given in Section 6.

2.1. The GOALS Sample

2.2. Herschel/PACS Observations

2.3. Spitzer/IRS Spectroscopy

3.1. Data Processing

3.2. Data Analysis

To obtain the [C ii] flux of a particular source we use an iterative procedure to find the line and measure its basic parameters. First, we fit a linear function to the continuum emission, which is evaluated at the edges of the spectrum, masking the central 60% of spectral elements (where the line is expected to be detected) and without using the first and final 10%, where the noise is large due to the poor sampling of the scanning. Then, we fit a Gaussian function to the continuum-subtracted spectrum and calculate its parameters. We define a line as not detected when the peak of the Gaussian is below 2.5 times the standard deviation of the continuum, as measured in the previous step. On the other hand, if the line is found, we return to the original, total spectrum and fit again the continuum using this time a wavelength range determined by the two portions of the spectrum adjacent to the line located beyond ±3σ from its center (where σ is the width of the fitted Gaussian) and the following ±15% of spectral elements. We then subtract this continuum from the total spectrum and fit the line again. The new parameters of the Gaussian are compared with the previous ones. This process is repeated until the location, sigma, and intensity of the line converge with an accuracy of 1%, or when reaching 10 iterations. Due to the merger-driven nature of many LIRGs, their gas kinematics are extremely complicated and, as a consequence, the emission lines of several sources present asymmetries and double peaks in their profiles. However, despite the fact that the width determined by the fit is not an accurate representation of the real shape of the line, it can be used as a first order approximation for its broadness. Therefore, instead of using the parameters of the Gaussian to derive the flux of the line, we decided to integrate directly over the final continuum-subtracted spectrum within the ±3σ region around the central position of the line. The associated uncertainty is calculated as the standard deviation of the latest fitted continuum, integrated over the same wavelength range as the line. Absolute photometric uncertainties due to changes in the PACS calibration products are not taken into account (the version used in this work was PACS_CAL_32_0).²⁷

We obtained the line fluxes for our LIRGs from the spectra extracted from the spaxel at which the [C ii] line + continuum emission of each galaxy peaks within the PACS FoV. The Spitzer/IRS and Herschel pointings usually coincide within ≲ 2''. There are a few targets for which the IRS pointing is located more than half a spaxel away from that of PACS. In these cases, we decided to obtain the nuclear line flux of the galaxy by averaging the spaxels closest to the coordinates of the IRS pointing. These values are used only when PACS and IRS measurements are compared directly in the same plot. There is one additional LIRG system, IRAS 03582+6012, for which the PACS pointing exactly felt in the middle of two galaxies separated by only 5''. This LIRG is not used in the comparisons of the [C ii] emission to the IRS data since the two individual sources cannot be disentangled.

As mentioned in Section 2.3, the angular size of a PACS spaxel is roughly similar (within a factor of two) to that of the aperture used to extract the Spizer/IRS spectra of our galaxies. Because the PACS beam is under-sampled at 160 μm (FWHM ∼ 12'' compared with the 96 size of the PACS spaxels), and most of the sources in the sample are unresolved at 24 μm in our MIPS images (which have a similar angular resolution as PACS at ∼80 μm), an aperture correction has to be performed to the spectra extracted from the emission-peak spaxel of each galaxy to obtain their total nuclear fluxes. This was the same procedure employed to obtain the mid-IR IRS spectra of our LIRGs. The nominal, wavelength-dependent aperture correction function provided by HIPE ver. 8.0 works optimally when the source is exactly positioned at the center of a given spaxel. However, in some occasions the pointing of Herschel is not accurate enough to achieve this and the target can be slightly misplaced ≲ 3'' (up to 1/3 of a spaxel) from the center. In these cases, the flux of the line might be underestimated. We explored whether this effect could be corrected by measuring the position of the source within the spaxel. However, some LIRGs in our sample show low surface-brightness extended emission, either because of their proximity and/or merger nature, or simply because the gas and dust emission are spatially decoupled. This, combined with the spatial sub-sampling of the PACS/IFS detector and the poor S/N of some sources prevented us from obtaining an accurate measurement of the spatial position and angular width of the [C ii] emission and therefore from obtaining a more refined aperture correction. Thus, we performed only the nominal aperture correction provided by HIPE.

The IRAS FIR fluxes used throughout this paper were calculated as FIR = 1.26 × 10⁻¹⁴ (2.58 S_60 μm + S_100 μm) (W m⁻²), with S_ν in (Jy). The FIR luminosities, L_FIR, were defined as $4\pi \,D_{\rm L}^2\,{\rm FIR}$ (L_☉). The luminosity distances, D_L, were taken from Armus et al. (2009). This definition of the FIR accounts for the flux emitted within the 42.5–122.5 μm wavelength range as originally defined in Helou et al. (1988). The FIR fluxes and luminosities of galaxies were then matched to the aperture with which the nuclear [C ii] flux was extracted (see above) by scaling the integrated IRAS FIR flux of the LIRG system with the ratio of the continuum flux density of each individual galaxy evaluated at 63 μm in the PACS spectrum (extracted at the same position and with the same aperture as the [C ii] line) to the total IRAS 60 μm flux density of the system.

In Table 1 we present the [C ii]157.7 μm flux, the [C ii]/FIR ratio, and the continuum flux densities at 63 and 158 μm for all the galaxies in our sample. Future updates of the data in this table processed with newer versions of HIPE and PACS calibration files will be available at the GOALS Web site: http://goals.ipac.caltech.edu.

Table 1. Herschel/PACS Measurements for the GOALS Sample

Galaxy	R.A.	Decl.	Dist.	[C ii]157.7 μm	[C ii]/FIR	Sν63 μm cont.	Sν158 μm cont.
Name	(hh:mm:ss)	(dd:mm:ss)	(Mpc)	(× 10−15 W m−2)	(× 10−3)	(Jy)	(Jy)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)
NGC 0023	00h09m534	+25°55m26s	65.2	1.385 ± 0.022	4.13 ± 0.09	6.17 ± 0.08	6.85 ± 0.08
NGC 0034	00h11m065	−12°06m26s	84.1	0.624 ± 0.018	0.85 ± 0.03	16.39 ± 0.13	9.02 ± 0.06
Arp256	00h18m509	−10°22m36s	117.5	0.967 ± 0.020	2.96 ± 0.07	6.70 ± 0.08	4.42 ± 0.09
⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅

Notes. Columns: (1) galaxy name; (2) and (3) right ascension and declination (J2000) of the position from which the Herschel/PACS spectrum was extracted (Section 3.2); (4) distance to the galaxies taken from Armus et al. (2009); (5) [C ii]157.7 μm flux as measured from the spaxel at which the [C ii] line + continuum emission of the galaxy peaks within the PACS FoV, that is, within an effective aperture of ∼94 × 94 (Section 3.2); (6) [C ii] to FIR flux ratio, where the FIR fluxes have been scaled to match the aperture of the [C ii] measurements; (7) continuum flux density at 63 μm under the [O i] line extracted at the same position and with the same aperture size as (5); (8) same as (7) but for the continuum at 158 μm under the [C ii] line. There are 11 galaxies for which the Spitzer/IRS pointing is located >47 from the position of the [C ii]+continuum peak. For these, we include an extra entry in the table with the [C ii] flux and continuum measurements obtained at the position of the IRS slit. They are marked with asterisks next to the names. Future, updated versions of these data can be found at the GOALS Web site: http://goals.ipac.caltech.edu.

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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4.1. The [C ii]/FIR Ratio: Dust Heating and Cooling

The FIR fine-structure line emission in normal star-forming galaxies as well as in the extreme environments hosted by ULIRGs has been extensively studied for the past two decades. A number of works based on ISO data already suggested that the relative contribution of the [C ii]157.7 μm line to the cooling of the ISM in PDRs compared to that of large dust grains, as gauged by the FIR emission, diminishes as galaxies are more IR luminous (Malhotra et al. 1997; Luhman et al. 1998; Brauher et al. 2008). Figure 1 display the classical plot of the [C ii]/FIR ratio as a function of the FIR luminosity for our LIRG sample. In addition, we also show for reference those galaxies observed with ISO compiled by Brauher et al. (2008) that are classified as unresolved and located at redshifts z > 0.003, similar to the distance range covered by GOALS. As we can see, our Herschel data confirm the trend seen with ISO by which galaxies with L_FIR ≳ 10¹¹ L_☉ show a significant decrease of the [C ii]/FIR ratio. GOALS densely populates this critical part of phase-space providing a large sample of galaxies with which to explore the physical conditions behind the drop in [C ii] emission among LIRGs. For the 32 galaxies with measurements obtained with both telescopes, the higher angular resolution Herschel observations of the nuclei of LIRGs are able to recover an average of ∼87% of the total [C ii] flux measured by ISO.

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4.1.1. The Average Dust Temperature of LIRGs

Figure 2 (upper panel) shows the [C ii]157.7 μm/FIR ratio for the GOALS sample as a function of the FIR PACS S_ν 63 μm/S_ν 158 μm continuum flux density ratio. We chose to use this PACS-based FIR color in the x-axis instead of the more common IRAS 60/100 μm color mainly because of two main reasons: (1) this way we are able plot data from individual galaxies instead of being constrained by the spatial resolution of IRAS, which would force us to show only blended sources; (2) by using the 63/158 μm ratio we are probing a larger range of dust temperatures within the starburst (T ∼ 50 → 20 K); with the colder component probably arising from regions located far from the ionized gas-phase, and closer to the PDRs where the [C ii] emission originates. For reference, we show the relation between the PACS 63/158 μm and IRAS 60/100 μm colors in the Appendix. The ULIRGs in the GOALS sample (red diamonds) have a median [C ii]/FIR = 6.3 × 10⁻⁴, a mean of 6.6 (± 0.8) × 10⁻⁴, and a standard deviation of the distribution of 3.7 × 10⁻⁴. LIRGs span two orders of magnitude in [C ii]/FIR, from ∼10⁻² to ∼10⁻⁴, with a mean of 3.4 × 10⁻³ and a median of 2.6 × 10⁻³. The L_[C ii] ranges from ∼10⁷ to 2 × 10⁹ L_☉.

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Our results are consistent with ISO observations of a sample of normal and moderate IR-luminous galaxies presented in Malhotra et al. (1997) and further analyzed in Helou et al. (2001). The GOALS sample, though, populates a warmer FIR color regime. Despite the increase in dispersion at 63/158 μm ≳ 1.25 or [C ii]157.7 μm/FIR ≲ 10⁻³ (basically in the ULIRG domain), the fact that we find the same tight trend independently of the range of IR luminosities covered by the two samples suggests that the main observable linked to the variation of the [C ii]/FIR ratio is the average temperature of the dust (T_dust) in galaxies.

This interpretation agrees with the last physical scenario described in the Introduction, in which an increase of the ionization parameter, 〈U〉, would cause the far-UV radiation from the youngest stars to be less efficient in heating the gas in those galaxies. At the same time, dust grains would be on average at higher temperatures due to the larger number of ionizing photons per dust particle available in the outer layers of the H ii regions, close to the PDRs. Indeed, the presence of dust within H ii regions has been recently observed in several star-forming regions in our Galaxy (Paladini et al. 2012). Both effects combined can explain the wide range of [C ii]157.7 μm/FIR ratios and FIR colors we observe in the most warm LIRGs. Variations in n_H, though, could be responsible for the dispersion in [C ii]/FIR seen at a given 63/158 μm ratio.

To further support these findings, the bottom panel of Figure 2 shows that the ratio of [C ii]157.7 μm flux to the monochromatic continuum at ∼158 μm under the line (the [C ii] EW) of the warmest galaxies is only a factor of ∼4 lower than the average [C ii] EW displayed by colder sources at 63/158 μm ≲ 1. This implies that the decrease of the [C ii]/FIR ratio seen in our LIRGs is primarily caused by a significant increase in warm dust emission (peaking at λ ≲ 60–100 μm), most likely associated with the youngest stars, that is not followed by a proportional enhancement of the [C ii] emission line.

The best fit to the data in Figure 2 (upper panel) yields the following parameters:

$$\begin{eqnarray} &&\log \left(\frac{{[C\,{\scriptsize {II}}]}}{\rm FIR}\right) = -2.68(\pm 0.02) - 1.61(\pm 0.09)\log \left(\frac{S_{63\,\mu {\rm m}}}{S_{158\,\mu {\rm m}}}\right) \nonumber\\ \end{eqnarray} \tag{ 1 }$$

with a dispersion of 0.28 dex. We note that the [C ii]/FIR ratios predicted by the fitted relation for sources with FIR colors 63/158 μm ≲ 0.4 are probably overestimated, as it is already know that galaxies showing such cool T_dust have typical [C ii]/FIR ∼ 10⁻² (e.g., Malhotra et al. 2001).

4.1.2. The Link between Mid-IR Dust Obscuration and FIR Re-emission

The strength of the 9.7 μm silicate feature is defined as ${S_{\rm 9.7\,\mu m}}\equiv \ln (f_{\lambda _P}^{{\rm obs}}/f_{\lambda _P}^{{\rm cont}})$; with $f_{\lambda _P}^{{\rm cont}}$ and $f_{\lambda _P}^{{\rm obs}}$ being the un-obscured and observed continuum flux density measured in the mid-IR IRS spectra of our LIRGs and evaluated at the peak of the feature, λ_P, normally at 9.7 μm (see Stierwalt et al. 2013 for details on how it was calculated in our sample). Negative values indicate absorption, while positive ones indicate emission. By definition, S_9.7 μm measures the apparent optical depth toward the warm, mid-IR emitting dust. Figure 3 shows that there is a clear trend (r = 0.65, p_r = 0; κ = 0.47) for LIRGs with stronger (more negative) S_9.7 μm to display smaller [C ii]/FIR ratios, implying that the dust responsible for the mid-IR absorption is also accountable for the FIR emission. The formal fit (solid line) can be expressed as:

$$\begin{equation} \log \left(\frac{{[C\,{\scriptsize {II}}]}}{\rm FIR}\right)=-2.32(\pm 0.02) + 0.83(\pm 0.05)\,{S_{\rm 9.7\,\mu m}} \end{equation} \tag{ 2 }$$

with a dispersion in the y-axis of 0.30 dex.

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Within the context described in the previous section, the contrast between the inner layer of dust that is being heated by the ionizing radiation to T ≳ 50 K and that of the cold dust at T ≲ 20 K emitting at λ ≳ 150 μm would create both (1) the silicate absorption seen at 9.7 μm due to the larger temperature gradient between the two dust components and (2) the increasingly higher 63/158 μm ratios seen in Figure 2 due to the progressively larger amount of dust mass that is being heated to higher temperatures. This scenario is consistent with the physical properties of the ISM found in the extreme environments of ULIRGs, in which the fraction of total dust luminosity contributed by the diffuse ISM decreases significantly, and the emission from dust at T ∼ 50–60 K arising from optically thick "birth clouds" (with ages ≲ 10^{7 − 8} Myr) accounts for ≳80% of their IR energy output (da Cunha et al. 2010). Furthermore, our findings are also in agreement with recent results showing that the increase of the silicate optical depth in LIRGs is related with the flattening of their radio spectral index (1.4 to 8.44 GHz) due to an increase of free–free absorption, suggesting that the dust obscuration must largely be originated in the vicinity and/or within the starburst region (Murphy et al. 2013).

There are a few galaxies that do not follow the correlation fitted in Figure 3, showing very large silicate strengths (S_9.7 μm < −2) and small [C ii]/FIR ratios (<10⁻³) typical of ULIRGs or, in general, warm galaxies (see color coding or Figure 2). We would like to note that the trend found for the majority of our sample only reaches S_9.7 μm values up to around −1.5 which, interestingly, is only slightly larger than the apparent optical depth limit that a obscuring clumpy medium can explain (Nenkova et al. 2008). Larger (more negative) values of the silicate strength can only be achieved by a geometrically thick (smooth) distribution of cold dust, suggesting that the extra dust absorption seen in these few galaxies may not be related with the star-forming region from where the [C ii] and FIR emissions arise.

But then, what is the origin of this excess of obscuration? One possibility is that it is caused by foreground cold dust not associated with the starburst. This has been seen in some heavily obscured Compton-thick AGNs, where most of the deep silicate absorption measured in these objects seems to originate from dust located in the host galaxy (Goulding et al. 2012; González-Martín et al. 2012). Alternatively, the presence of an extremely warm source (different from the star-forming region(s) that are producing the FIR and [C ii] emission) could contribute with additional emission of hot dust (T ≳ 150 K) to the mid-IR. If at the same time this source is deeply buried (optically thick) and embedded in layers of progressively colder dust (geometrically thick), it could produce a cumulative absorption that we would measure via the strength of the silicate feature while still contributing to the emission outside of it (see Levenson et al. 2007; Sirocky et al. 2008).

While both explanations are plausible, the second is favored by the fact that these extremely obscured galaxies show MIPS 24/70 μm ratios very similar, or even slightly higher than those found for the rest of the LIRGs in the sample. If foreground cold dust was the responsible for the excess of obscuration, we would expect these galaxies to show abnormally low 24 μm luminosities with respect to the FIR. We find that this is not the case, in agreement with recent results based on radio observations of a sub-sample of LIRGs in GOALS (Murphy et al. 2013). Furthermore, the existence of an additional hot and obscured dust component in these LIRGs is also consistent with the results presented in Stierwalt et al. (2013), where it is shown that there is a trend for LIRGs with moderate silicate strengths (${S_{\rm 9.7\,\mu m}}\gtrsim -1.5$) to show higher S_ν 30 μm/S_ν 15 μm ratios as the S_9.7 μm becomes stronger (more negative). That is, more obscured LIRGs have increasingly larger fluxes at 30 μm, in agreement with our findings in the previous section. However, galaxies showing the most extreme silicate strengths (${S_{\rm 9.7\,\mu m}}<-1.5$) do not have proportionally higher 30/15 μm ratios. On the contrary, they show ratios similar to those of warm LIRGs with mild silicate strengths (or even lower than expected given their extreme S_9.7 μm), supporting the idea that in these particular galaxies the dust producing this additional absorption and excess of mid-IR emission (λ ≲ 20 μm) represents a component of the overall nuclear starburst activity different than the star-forming regions that drive the FIR cooling.

4.1.3. The Compactness of the Mid-IR Emitting Region

The compactness of the starburst region of a galaxy has been proven to be related to many of its other physical properties (Wang & Helou 1992). For example, all ULIRGs in the GOALS sample have very small mid-IR emitting regions, with sizes (measured FWHMs) <1.5 kpc (Díaz-Santos et al. 2010). LIRGs, on the other hand, span a large range in sizes as well as in how much of their mid-IR emission is extended. The later property is parameterized in Díaz-Santos et al. (2010) by the fraction of extended emission, FEE_λ, which measures the fraction of light emitted by a galaxy that is contained outside of its unresolved component at a given wavelength λ. The complementary quantity 1 −FEE_λ measures how compact the source is, which in turn is proportional to its luminosity surface density, Σ. We note that in this paper we use the word compactness as an equivalent to light concentration, i.e., as a measurement of the amount of energy per unit area produced by a source, and not as an absolute measurement of its size.

It has been shown that the compactness of the mid-IR continuum emission of LIRGs (evaluated at λ_rest = 13.2 μm) is related to their merger stage, mid-IR AGN-fraction and most importantly, to their FIR color (Díaz-Santos et al. 2010). LIRGs with higher IRAS S_ν 60 μm/S_ν 100 μm ratios are increasingly compact. In other words, for a given L_IR, the dust in sources with FIR colors peaking at shorter wavelengths is not only hotter but also confined toward a smaller volume in the center of galaxies. In Section 4.1.1 we found that the [C ii]/FIR ratio is related to the average T_dust of our galaxies. Thus, we should expect to see a correlation between the [C ii] deficit and the luminosity surface density and compactness of LIRGs in the mid-IR. This is shown in Figure 4, where a clear trend is found for galaxies with higher luminosity surface densities at 15 μm, Σ_15 μm (top panel), or small FEE_13.2 μm (bottom panel), i.e., more compact, to show lower [C ii]/FIR ratios, irrespective of the origin of the nuclear power source.

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Excluding those LIRGs for which only upper limits on their mid-IR size or L_[C ii] are available, we perform a linear fit to the data and obtain the following parameters for the correlation between [C ii]/FIR and Σ_15 μm:

$$\begin{equation} \log \left(\frac{{[C\,{\scriptsize {II}}]}}{\rm FIR}\right) = 1.19(\pm 0.30)-0.38(\pm 0.03)\times \log (\Sigma _{\rm 15\,\mu \rm m}) \end{equation} \tag{ 3 }$$

with a dispersion in the y-axis of 0.21 dex.

4.2. The Role of Active Galactic Nuclei

It is known that the contribution of an AGN to the IR emission in LIRGs increases with L_IR (Veilleux et al. 1995; Desai et al. 2007; Petric et al. 2011; Alonso-Herrero et al. 2012). This is most noticeable at mid-IR wavelengths (Laurent et al. 2000; Armus et al. 2007; Mullaney et al. 2011) but a non-negligible fraction of the FIR emission of ULIRGs can also be powered by an AGN. The EW of mid-IR PAH features is a simple diagnostic that has been widely used for the detection of AGN activity in galaxies at low and high redshifts (Genzel et al. 1998; Armus et al. 2007; Desai et al. 2007; Spoon et al. 2007; Pope et al. 2008; Murphy et al. 2009; Menéndez-Delmestre et al. 2009; Veilleux et al. 2009; Petric et al. 2011; Stierwalt et al. 2013). Broadly speaking, the PAH EW decreases as a component of hot dust at T ≳ 300 K, normally ascribed to an AGN, starts to increasingly dominate the mid-IR continuum emission of the galaxy. In addition, the hard radiation field of an AGN could be able to destroy a significant fraction of the smallest PAH molecules (Voit 1992; Siebenmorgen et al. 2004). In particular, a galaxy is regarded as mid-IR AGN-dominated when its 6.2 μm PAH EW ≲ 0.3, and it is classified as a pure starburst when 6.2 μm PAH EW ≳ 0.5 (although these limits are not strict). Sources with intermediate values are considered composite galaxies, in which both starburst and AGN may contribute significantly to the mid-IR emission.

4.2.1. [C ii]157.7 μm Deficit in Pure Star-Forming LIRGs

Figure 5 shows the [C ii]/FIR ratio as a function of the IR luminosity surface density, Σ_IR, of the LIRGs in GOALS, color-coded as a function of their 6.2 μm PAH EW. As we can see, when only pure star-forming galaxies are considered (6.2 μm PAH EWs ⩾ 0.5 μm), the [C ii]/FIR ratio drops by an order of magnitude, from 10⁻² to ∼10⁻³. This indicates that the decrease in [C ii]/FIR among the majority of LIRGs is not caused by a rise of AGN activity but instead is a fundamental property of the starburst itself. It is only in the most extreme cases, when [C ii]/FIR < 10⁻³, that the AGN could play a significant role. In fact, powerful AGNs do not always reduce the [C ii]/FIR ratio, as shown also in Sargsyan et al. (2012). Stacey et al. (2010) also find that the AGN-powered sources in their high-redshift galaxy sample display small [C ii]/FIR ratios. However, they speculate that except for two blazars, the deficit seen in these sources could be caused compact, nuclear starbursts (with sizes less than 1–3 kpc) perhaps triggered by the AGN. We will return to this discussion in Section 4.2.2.

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The result obtained above also implies that the [C ii]157.7 μm line alone is not a good tracer of the SFR in most local LIRGs since it does not account for the increase of warm dust emission (Figure 2) seen in the most compact galaxies that is usually associated with the most recent starburst. In Figure 5 we fit the data to provide a relation between the [C ii]/FIR ratio and the Σ_IR for pure star-forming LIRGs. The analytic expression of the fit is:

$$\begin{equation} \log \left(\frac{{[C\,{\scriptsize {II}}]}}{\rm FIR}\right) = 1.21(\pm 0.24)-0.35(\pm 0.03)\times \log (\Sigma _{\rm IR}) \end{equation} \tag{ 4 }$$

with a dispersion in the y-axis of 0.15 dex. The slope and intercept of this trend are indistinguishable (within the uncertainties) from those obtained in Equation (3), which was derived by fitting all data-points including low 6.2 μm PAH EW sources with measured mid-IR sizes. This further supports the idea that the influence of AGN activity is negligible among IR-selected galaxies with 10⁻³ < [C ii]/FIR < 10⁻² and that the increase in IR luminosity of these sources is due to a boost of their warm dust emission.

4.2.2. The Influence of AGNs in the [C ii] Deficit

Figure 6 shows the [C ii]157.7 μm/FIR ratio as a function of the 6.2 μm PAH EW for the LIRGs in GOALS. Starburst sources with large PAH EWs have a mean [C ii]/FIR ratio of 4.0 × 10⁻³ with a standard deviation of 2.6 × 10⁻³. As the 6.2 μm PAH EW becomes smaller the dispersion increases and we find galaxies with both very small ratios as well as sources with normal values (or slightly lower than those) typical of purely star-forming sources (see also Sargsyan et al. 2012).

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If AGNs contribute significantly to the FIR emission of LIRGs and/or suppress PAH emission via photo-evaporation of its carriers, we would expect AGN-dominated sources to show significantly low [C ii]/FIR ratios and small PAH EWs. We have used the Spitzer/IRS spectra of our galaxies to identify which of them are hosting an AGN based on several mid-IR diagnostics: (1) [Ne v]14.32 μm/[Ne ii]12.81 μm > 0.5; (2) [O iv]25.89 μm/[Ne ii]12.81 μm > 1; (3) S_ν 30 μm/S_ν 15 μm < 6 (i.e., α > −2.6 for S_ν ∝ ν^α); as well as (4) the 6.2 μm PAH EW itself (see constraints above). All these thresholds are rather restrictive and ensure that the contribution of an AGN to the mid-IR luminosity of a galaxy is at least 25%–50%. In Figure 6 we mark those sources that have at least two positive indicators of AGN activity as red stars. We note that this excludes sources with low 6.2 μm PAH EWs and no other AGN signatures, and is a more conservative cut than applied in Petric et al. (2011) to identify potential AGNs. Strikingly, these sources are not preferentially found at the bottom left of the parameter space but instead as many as 2/3 show [C ii]/FIR > 10⁻³, typical of star-forming sources with large 6.2 μm PAH EWs. This suggests that the impact of the AGN on the FIR luminosity of these mid-IR dominated AGN LIRGs is very limited, unless the it contributes to both the [C ii] and FIR in the same relative amount as the starburst does.

While ∼18% of our sample appears to have significant AGN contribution to the mid-IR emission (Petric et al. 2011), the fraction in which the AGN dominates the bolometric luminosity of the galaxy is much smaller. To investigate this, we use two of the indicators described above, the [O iv]25.89 μm line and the 6.2 μm PAH EW, and the formulation given in Veilleux et al. (2009) to calculate the bolometric AGN fraction of those galaxies with at least two mid-IR AGN detections. We find that only four (20%) of these galaxies have contributions >50% in both indicators (black crosses in Figure 6). Two galaxies have [C ii]/FIR < 10⁻³ (33%) and two (14%) a larger ratio.

To quantitatively assess the relationship between AGN activity and the [C ii]/FIR ratio among galaxies hosting an AGN, it is important to estimate first the AGN contribution to the FIR flux. If we assume that the ratio of [C ii]157.7 μm to 6.2 μm PAH emission of the star-forming LIRGs in GOALS is constant, as is the case for most normal, lower luminosity galaxies (Helou et al. 2001; Croxall et al. 2012; Beirão et al. 2012), we can calculate the expected evolution of the [C ii]/FIR ratio as a function of the 6.2 μm PAH EW if we also assume that pure starbursts have a typical 6.2 μm PAH EW_SB = 0.65 μm and [C ii]/FIR = 4.0 × 10⁻³ (as shown above), and that the average L_FIR/νL_ν 6 μm ratios for pure star-forming galaxies and AGNs are ∼15 and ∼1, respectively. The value for star-forming galaxies varies from ∼12–25 in our sample while the value for AGNs has been estimated from the intrinsic AGN spectral energy distribution of Mullaney et al. (2011). The predicted trend is shown in Figure 6 as a solid black line, which agrees very well with the location of the AGNs identified with at least two mid-IR indicators (red stars). Under these assumptions, the 6.2 μm PAH EW has to be reduced by a factor of ∼15 with respect to the 6.2 μm PAH EW_SB, i.e., down to ≃ 0.05 μm, before the AGN can contribute 50% to the L_FIR. In fact, 2/3 of galaxies with EWs lower than this threshold have been identified as harboring an AGN by two or more mid-IR diagnostics. Therefore, only when the AGN contribution to the FIR flux is significant do we see a noticeable decrease of the [C ii]/FIR ratio (always <10⁻³). We note however that the contrary might not be necessarily true since there are galaxies with low [C ii]/FIR ratios but with 6.2 μm PAH EWs ≳ 0.5 μm.

We emphasize that this prediction does not account for possible destruction of PAH molecules due to the AGN. However, if the reduction of the PAH EW was entirely due to this effect, we would expect a linear correlation between the [C ii]/FIR ratio and the 6.2 μm PAH EW, which is described by the dashed line in Figure 6. As we can see, the mid-IR AGN-dominated galaxies do not follow the predicted trend, suggesting that PAH destruction is not important in LIRGs with [C ii]/FIR ≳ 10⁻³ at least at the scales probed by Herschel and Spitzer, in agreement with the results obtained in Díaz-Santos et al. (2011).

Nearly half of galaxies with [C ii]/FIR < 10⁻³ and 6.2 μm PAH EW < 0.05 μm have no other direct mid-IR diagnostic that reveals the presence of an AGN. Interestingly, all of them are among the outliers found in Figure 3, showing an excess in the S_9.7 μm with respect to their observed [C ii]/FIR. We argued in Section 4.1.2 that these galaxies are probably hosting an extremely warm and compact source, optically and geometrically thick, not associated with the star-forming regions producing the bulk of the [C ii] and FIR. The energy source of this component is unknown, though, since both an AGN or an ultra-compact H ii region could generate such mid-IR signatures. However, the monochromatic νL_ν 63/15 μm ratios displayed by these objects are ≳ 5 (see color-coding in Figure 6), significantly higher than the typically flat spectrum seen in QSOs and pure AGN sources (Elvis et al. 1994; Mullaney et al. 2011) in which the hot dust emission dominates the mid-IR wavelengths up to ∼30–50 μm, with νL_ν = constant, and fading beyond. This adds evidence to the result obtained above that this type of deeply embedded objects only dominate the luminosity of the galaxy in the mid-IR.

Furthermore, we would like to emphasize that the fact that the source of this warm, compact emission does not produce the detected PAH or [C ii] emissions rules out models where PAH obscuration is invoked to explain the low PAH EWs found in these sources, since their observed [C ii] flux compared to that of the FIR is also very low, implying that it is not extinction but rather the fact that the PDR emission of the warmest dust component in these LIRGs is actually extremely limited.

At intermediate redshifts, z ∼ 1–3, it has been found that IR-luminous galaxies span a wide range in [C ii]/FIR ratios: ∼10⁻²–10^−3.5 (Stacey et al. 2010). A surprising discovery came from the most luminous systems, and the fact that many of them show values of this ratio similar to those found in local, lower luminosity galaxies (e.g., Maiolino et al. 2009; Hailey-Dunsheath et al. 2010; Sturm et al. 2010; Stacey et al. 2010). These results, added to a number of recent findings obtained from the analysis of mid-IR dust features of star-forming galaxies using Spitzer/IRS spectroscopy (e.g., Pope et al. 2008; Murphy et al. 2009; Desai et al. 2009; Menéndez-Delmestre et al. 2009; Díaz-Santos et al. 2010, 2011; Rujopakarn et al. 2011; Stierwalt et al. 2013) are pointing toward an emerging picture in which the local counterparts of the dominant population of IR-bright galaxies at intermediate and high redshifts (z > 1) are not extremely dusty systems with similar IR luminosities (i.e., local ULIRGs) but rather galaxies with more modest SFRs, or L_IR ≃ 10^{10 − 12} L_☉ (starbursts and LIRGs). Therefore, since GOALS is a complete, flux-limited sample of 60 μm rest-frame selected LIRGs systems in the local universe covering an IR luminosity range from ∼10¹⁰ to ∼10¹² L_☉, the empirical relations we find can be used to estimate what might be seen in similar surveys of intermediate- and high-redshift IR-luminous galaxies.

Recently, Elbaz et al. (2011) has found that the majority of star-forming galaxies, from the nearby universe and up to z ∼ 2, follow a "main sequence" (MS) that is depicted by a specific SFR (SSFR_MS) that increases with redshift. Galaxies in the MS are characterized by producing stars in a quiescent mode, with very low efficiencies (L_IR/M_gas ≲ 10 L_☉/M_☉) and extended over spatial scales of several kiloparsecs (Daddi et al. 2010; Magdis et al. 2012). On the other hand, galaxies with high SSFRs are currently experiencing a strong and very efficient, but short-lived (less than few hundred megayears) starburst event, some of them probably consequence of a major merge interaction. The SSFR of local galaxies is anti-correlated with their compactness as measured in the mid-IR, as well as from radio wavelengths (see also Murphy et al. 2013). Therefore, the trends of [C ii]/FIR with FEE_13.2 μm, Σ_15 μm, and Σ_IR found in Sections 4.1.3 and 4.2.1 tell us not only about the compactness of the starburst region but also about the main mode of star formation itself. Sources with high [C ii]/FIR ratios should belong to the MS while galaxies with low ratios will likely be compact, starbursting sources.

Because >80%–90% of the UV and optical light of star-forming LIRGs and ULIRGs is reprocessed by dust into the IR wavelengths (Howell et al. 2010), the L_IR/M_⋆ ratio is equivalent to their SSFR since the SFR is directly proportional to the IR luminosity, with SFR_IR/L_IR = 1.72 × 10⁻¹⁰ M_☉ yr⁻¹ L_☉⁻¹ (as derived in Kennicutt 1998). Using Equation (13) from Elbaz et al. (2011) we calculate that the SSFR of MS galaxies in the local universe is SSFR_MS ≃ 0.09 Gyr⁻¹. However, this equation does not take into account the dependence of the SSFR_MS on the stellar mass of galaxies. Thus, we combine it with the SFR versus M_⋆ correlation obtained from the Sloan Digital Sky Survey sample by Elbaz et al. (2007), using a power-law index of 0.8 for the dependence of the SFR on M_⋆ (their Equation (5)) and after normalizing it by the SSFR_MS at z = 0. This joint equation assumes that the exponential dependence of the SFR_MS as a function of M_⋆ does not vary with z, which is roughly the case at least up to z ∼ 2–3 (see, e.g., Karim et al. 2011). We have used this normalization factor to derive the excess of SSFR in our galaxies (also called "starburstiness:" SSFR/SSFR_MS). If we define starbursting galaxies as those having a SSFR > 3 × SSFR_MS, then ∼68% of the galaxies in GOALS would be classified as such.

Figure 7 shows the [C ii]/FIR ratio as a function of the integrated SSFR normalized to the representative SSFR_MS of galaxies at z ∼ 0 for our LIRG sample. The stellar mass values are taken from Howell et al. (2010) and were derived directly either from the Two Micron All Sky Survey K-band or the 3.6 μm IRAC luminosities using the M_⋆/L conversions from Lacey et al. (2008). The solid line represents a fit to pure star-forming galaxies with 6.2 μm PAH EWs ⩾ 0.5 μm. The Pearson's test yields r = −0.65 (p_r = 0), while the Kendall's test provides κ = −0.47. The correlation coefficient derived from the robust fit is −0.76. We note that the SFR and M_⋆ plotted here represent integrated measurements of our galaxies while the [C ii] and FIR values were obtained from a single PACS spaxel, probing an area of ∼94 × 94, which at the median distance of our LIRGs is equal to a projected physical size of ∼4 kpc on a side (similar to a 05 beam at z ∼ 2); an aperture big enough to contain most of the galaxies' emission. In fact, if a 3 × 3 spaxel aperture is used instead, the fit yield virtually the same parameters as those reported below (within the uncertainties).

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The trend between [C ii]/FIR and normalized SSFR is not surprising since the IR luminosity appears in both quantities. Nevertheless, the correlation is indeed practical in terms of its predictive power. For example, we can see that there are no star-forming MS galaxies with [C ii]/FIR < 10⁻³. Their median ratio is 4.2 × 10⁻³. On the other hand, starbursting sources show a larger range of ratios, from 10⁻² to 10⁻⁴, with a median of 1.9 × 10⁻³. The correlation between the [C ii]/FIR and the SSFR/SSFR_MS is given by the following equation:

$$\begin{eqnarray} \log \left(\frac{{[C\,{\scriptsize {II}}]}}{\rm FIR}\right) &=& {-}1.86(\pm 0.03)-1.09(\pm 0.07) \nonumber\\ &&\times \log \left(\frac{{\rm SSFR}}{{\rm SSFR}_{{\rm MS}}}\right) \end{eqnarray} \tag{ 5 }$$

with a dispersion in the y-axis of 0.26 dex. If the separation between MS and starbursting galaxies (high/low [C ii]/FIR) at any given redshift is related to an increase of the star formation efficiency (higher L_IR/$M_{\rm H_2}$; see, e.g., Graciá-Carpio et al. 2011; Sargent et al. 2013) then this equation can be applied to predict the [C ii] luminosity of star-forming galaxies at any z for which a measurement of the (far-)IR luminosity and stellar mass are available as long as their SSFR is normalized to the SSFR_MS at that z to account for the increase in gas mass fraction (M_gas/M_⋆) and therefore SSFR of MS galaxies at higher redshifts (Daddi et al. 2010; Magdis et al. 2012). Conversely, in future large IR surveys like those projected with the CCAT, this relation could be used for estimating the SSFR or stellar mass of detected galaxies when their [C ii] and FIR luminosities are known.

As an example, in Figure 7 we show two intermediate-redshift z ∼ 1.2 galaxies from (Stacey et al. 2010; SMMJ123633 and 3C368) and three high-redshift z ∼ 4.5 sub-millimeter galaxies (SMGs; LESS 61.1 and LESS 65.1: Swinbank et al. 2012; LESS 033229.3: De Breuck et al. 2011; Wardlow et al. 2011) marked as open black squares and diamonds, respectively. To calculate the SFR of the SMGs we assumed that their L_IR ≃ 2 × L_FIR. Since Equation (13) from Elbaz et al. (2011) is calibrated only up to z ∼ 3 and the dependence of the SSFR_MS on M_⋆ is also uncertain beyond this redshift, we normalized the SSFR of the SMGs by the SSFR_MS at z = 3. As we can see, three galaxies follow the correlation suggesting that they are starbursting sources with [C ii]/FIR ratios consistent with their normalized SSFRs. On the other hand, the two remaining high-z SMGs show significantly lower [C ii]/FIR ratios than the average of LIRGs for the same normalized SSFR. In particular, one of them display a [C ii]/FIR more than an order of magnitude lower than the value predicted by the fit to our local galaxy sample. Interestingly, both SMGs lie in the parameter space where most of the mid-IR identified AGN are located (red stars). This may suggest that these two galaxies could harbor AGN or unusually week [C ii] emission for their normalized SSFR.

Equations (3) and (4) can also be used to predict the mid- and total IR luminosity surface density of star-forming galaxies at high redshifts for which the [C ii] and FIR fluxes are known, such as those that may be found in future spectroscopic surveys with the X-Spec instrument on CCAT. With instantaneous coverage over all the atmospheric windows between 190 and 440 GHz, X-Spec will access the [C ii] line at redshifts from ∼3.5 to ∼9. Moreover, if a measurement of the rest-frame mid-IR luminosity of galaxies is also available, this correlation can be further used to estimate the physical size of the star-forming region in the mid-IR. This is particularly useful for z ≳ 3 sources detected with Herschel in deep fields. In these cases, the predicted mid-IR size of galaxies could be compared with direct measurements of the size of their FIR emitting region as observed with ALMA on physical scales similar to those we are probing in our GOALS LIRGs with PACS.

Finally, because GOALS is a complete flux-limited sample of local LIRGs, we are able to predict the contamination of sources hosting AGNs in future large-scale surveys with both [C ii] and FIR measurements. In Table 2 we provide the percentages of galaxies with mid-IR detected AGNs classified in different [C ii]/FIR and S_ν 63 μm/S_ν 158 μm bins. The values provided in the table were computed using two conditions for the detection of the AGN that serve as upper and lower limits for the estimated fractions (Columns 2 and 3). The first was based on the 6.2 μm PAH EW only and the second required of an additional mid-IR diagnostic to classify the galaxy as harboring an AGN (see above). For example, we predict an AGN contamination (based on the 6.2 μm PAH EW only) of up to ∼70% for [C ii]/FIR < 5 × 10⁻⁴, which implies that at least ∼1/3 of IR-selected sources with extremely low [C ii]/FIR ratios will be powered by starbursts. Moreover, at the levels of [C ii]/FIR ⩾ 5 × 10⁻⁴ or 63/158 μm < 2, the AGN detection fraction is expected to be ≲ 20%–25%.

We obtained new Herschel/PACS [C ii]157.7 μm spectroscopy for 200 LIRG systems in GOALS, a 60 μm flux-limited sample of all LIRGs detected in the nearby universe. A total of 241 individual galaxies where observed in the [C ii]157.7 μm line. We combined this information together with Spitzer/IRS spectroscopic data to provide the context in which the observed [C ii] luminosities and [C ii]/FIR ratios are best explained. We have found the following results.

• 1.  
  The LIRGs in GOALS span two orders of magnitude in [C ii]/FIR, from ∼10⁻² to 10⁻⁴, with a median of 2.8 × 10⁻³. ULIRGs have a median of 6.3 × 10⁻⁴. The L_[C ii] range from ∼10⁷ to 2 × 10⁹ L_☉ for the whole sample. The [C ii]/FIR ratio is correlated with the FIR S_ν 63 μm/S_ν 158 μm continuum color. We find that all galaxies follow the same trend independently of their L_IR, suggesting that the main observable linked to the variation of the [C ii]/FIR ratio is the average dust temperature of galaxies, which is driven by an increase of the ionization parameter, 〈U〉.
• 2.  
  There is a clear trend for LIRGs with deeper 9.7 μm silicate strengths (S_9.7 μm), higher mid-IR luminosity surface densities (Σ_MIR), smaller fractions of extended emission (FEE_13.2 μm) and higher SSFRs to display lower [C ii]/FIR ratios. These correlations imply the dust responsible for the mid-IR absorption must be directly linked to the process driving the observed [C ii] deficit. LIRGs with lower [C ii]/FIR ratios are more warm and compact (higher mid- and IR luminosity surface densities, Σ_(M)IR), regardless of what is the origin of the nuclear power source. However, this trend is clearly seen also among pure star-forming LIRGs only, implying that it is the compactness of the starburst, and not AGN activity as identified in the mid-IR, that is the main driver for the declining of the [C ii] to FIR dust emission. This implies that the [C ii] luminosity is not a good indicator of the SFR in LIRGs with high T_dust or large Σ_IR since it does not scale linearly with the warm dust emission most likely associated to the youngest stars. There are a small number of LIRGs that have a larger [C ii]/FIR ratio than suggested by their deep S_9.7 μm and warm dust emission. The origin of the energy source of these LIRGs is unknown, although they likely contain a deeply buried, compact source with little or no PDR emission.
• 3.  
  Pure star-forming LIRGs (6.2 μm PAH EW ⩾ 0.5) have a mean [C ii]/FIR = 4.0 × 10⁻³ with a standard deviation of 2.6 × 10⁻³, while galaxies with low 6.2 μm PAH EWs span the entire range in [C ii]/FIR. A significant fraction (70%) of the LIRGs in which an AGN is detected in the mid-IR have [C ii]/FIR ratios ⩾10⁻³, similar to those of starburst galaxies suggesting that most AGNs do not contribute substantially to the FIR emission. Thus, only in the most extreme cases when [C ii]/FIR < 10⁻³ might the AGN contribution be significant.
• 4.  
  The completeness of the GOALS LIRG sample has allowed us to provide meaningful predictions about the [C ii], Σ_MIR, and AGN contamination of large samples of IR-luminous high-redshift galaxies soon to be observed by ALMA or CCAT. In a FIR selected survey of high-z LIRGs we expect to find up to ∼70% of AGN contamination for [C ii]/FIR < 5 × 10⁻⁴, which implies that at least 1/3 of IR-selected sources with extremely low [C ii]/FIR will be powered by starbursts. Moreover, above this ratio the AGN fraction is expected to be ≲ 20%–25%. For deep fields with [C ii] and FIR emission measurements we can predict the IR luminosity surface density of galaxies, which could be compared with direct measurements of the size of their FIR emitting region as observed with ALMA on physical scales similar to those we are probing in our GOALS LIRGs with PACS.

We thank the referee for useful comments and suggestions which significantly improved the quality of this paper. We also thank David Elbaz, Alexander Karim, J. D. Smith, Moshe Elitzur, and J. Graciá-Carpio for very fruitful discussions. L.A. acknowledges the hospitality of the Aspen Center for Physics, which is supported by the National Science Foundation Grant No. PHY-1066293. V.C. acknowledges partial support from the EU FP7 Grant PIRSES-GA-2012-31578. This work is based on observations made with the Herschel Space Observatory, an European Space Agency Cornerstone Mission with science instruments provided by European-led Principal Investigator consortia and significant participation from NASA. The Spitzer Space Telescope is operated by the Jet Propulsion Laboratory, California Institute of Technology, under NASA contract 1407. This research has made use of the NASA/IPAC Extragalactic Database (NED), which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration, and of NASA's Astrophysics Data System (ADS) abstract service.

In Section 4.1.1, Figure 2, we show the [C ii]157.7 μm/FIR ratio as a function of the PACS-based S_ν 63 μm/S_ν 158 μm ratio for the galaxies in the GOALS sample observed with Herschel, and explain the reasons for adopting and plotting this FIR color instead the more commonly used IRAS-based S_ν 60 μm/S_ν 100 μm color. Here we show a comparison between both, to provide the reader with a tool for interpreting our results in terms of IRAS colors, if necessary. Figure 8 shows that the FIR ratios correlate well (r = 0.89, p_r = 0), as expected, with a slope of 1.80 ± 0.08, an intercept of 0.30 ± 0.02, and a dispersion in the y-axis of 0.10 dex. We note that part of the scatter is caused by LIRG systems comprised by more than one galaxy, for which we have used their individual 63/158 μm ratios but the same 60/100 μm ratio, as they correspond to a single, unresolved IRAS source. Nevertheless, independently of which of these FIR colors we utilize, the same overall trend seen in Figure 2 emerges, namely warmer galaxies display smaller [C ii]/FIR ratios. As mentioned in Section 4.1.1, when we use the IRAS FIR colors of integrated systems, our LIRG sample follows the same trend found for normal and moderate IR-luminous galaxies observed by ISO. However, when using the 63/158 μm ratio, the anti-correlation is tighter than that obtained when the emission from entire systems is employed, likely due to the fact that we are able to disentangle the true FIR colors of individual galaxies. Moreover, the observed 63/158 μm continuum ratios span a much larger dynamical range (a factor of ∼10, in contrast with the factor of ∼3 covered by the integrated 60/100 μm ratios), which translates in a more accurate sampling of the average dust temperature of LIRGs.

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