EXTENDED [C ii] EMISSION IN LOCAL LUMINOUS INFRARED GALAXIES

The Great Observatories All-sky LIRG Survey (GOALS; Armus et al. 2009) encompasses the complete luminosity-limited sample of the 202 LIRGs and ultraluminous infrared galaxies (ULIRGs) contained in the IRAS Revised Bright Galaxy Sample (Sanders et al. 2003) which, in turn, is a complete flux-limited sample of 629 galaxies having IRAS S_60 μm > 5.24 Jy and Galactic latitudes |b| > 5 °. There are 180 LIRG and 22 ULIRG systems in GOALS and their median redshift is z = 0.0215 (or ∼95.2 Mpc).

We have obtained Herschel/PACS FIR spectroscopic observations of the [C ii]157.7 μm emission line for 200 LIRG systems (241 individual galaxies) in the GOALS sample. Details regarding the processing and analysis of the data are described in DS13. Since the goal of this Letter is to analyze the [C ii] deficit in the extra-nuclear regions of LIRGs, in addition to the nuclear [C ii] and FIR fluxes calculated in DS13, we have also obtained their spatially integrated fluxes as extracted from a 3 × 3 spaxel box ((94)²/spaxel) centered around the nuclear spaxel. The extended emission is thus defined as the integrated flux minus the nuclear measurement, after performing a point-source aperture correction on the nuclear flux to the central 3 × 3 spaxel aperture. The same approach was taken to calculate the extended emission of the 63 μm dust continuum, which is also used to scale the IRAS FIR flux and L_IR down to the apertures used to extract the PACS spectra (see DS13 for more details). Errors in the line and continuum fluxes have been propagated into the analysis of, e.g., [C ii]/FIR. To calculate the IR luminosity surface density (Σ_IR) of the extended emission we use the projected physical area covered by the 3 × 3 PACS spaxel box centered around the galaxy minus that of the nuclear spaxel. For the starburst nuclei, however, we use the beam-corrected MIR sizes estimated from the Spitzer/IRS spectra and MIPS imaging, ${\Sigma _{\rm IR}}\,={L_{\rm IR}}\,/\pi r_{\rm MIR}^2$ (see DS13).

A galaxy is considered to be spatially resolved when more than 30% of the [C ii] and FIR continuum flux is extended, as defined above. This threshold is robust against observations of unresolved sources in which mis-pointings of up to ∼3'' would introduce a systematic underestimation of the nuclear flux that would mimic extended emission.²⁴ Because of possible contamination from a nearby companion galaxy, we exclude from this study LIRG systems in which individual galaxies are closer than 235 from each other (one-half of the PACS field of view). A total of 60 galaxies (25% of the sample) show extended [C ii] and FIR emission meeting these constraints. Their average extended [C ii] emission is 52%, with a maximum of 75%. The projected radial distance at which the extended emission is detected ranges from 1 to ∼12.5 kpc for the closest and farthest resolved galaxy, respectively, with a median of 4.3 kpc. While more luminous GOALS systems tend to be located farther away, a K-S test comparing the distance and luminosity distributions of the GOALS galaxies with L_IR ⩽ 10¹² L_☉ and those of galaxies classified as extended in this work, confirms that both sub-samples are indistinguishable in both quantities (D-values of 0.20 and 0.15 and p-values of 0.04 and 0.22, respectively).

Figure 1 shows the [C ii]/FIR ratio as a function of the S_ν 63 μm/S_ν 158 μm continuum flux density ratio (63/158 μm hereafter)²⁵ for the extra-nuclear emission observed in spatially resolved LIRGs in the GOALS sample. As expected, the extended emission regions follow the trend found for the LIRG nuclei (DS13) suggesting that the [C ii] deficit is related to the average temperature of the dust (T_dust). However, the extended regions show smaller [C ii] deficits (stronger [C ii] to FIR emission) and lower 63/158 μm ratios than the majority of the nuclei. The extended emission has a mean and median [C ii]/FIR ratio of (6.9 ± 2.6) × 10⁻³ and 6.6 × 10⁻³, respectively, which is a factor 2 larger than the LIRG nuclei. Figure 1 also reveals that the fractional extent of the [C ii] emission does not correlate with the FIR color of the extra-nuclear regions suggesting that galaxies with larger extended emission fractions do not have systematically colder or warmer T_dust. In the majority of LIRGs the extended emission has 63/158 μm ≲ 1 and [C ii]/FIR ⩾ 4 × 10⁻³, similar to those found in the extended disks of normal star-forming galaxies (Madden et al. 1993; Nikola et al. 2001; Mookerjea et al. 2011; Croxall et al. 2012), as well as in the diffuse component of the ISM in the Galactic plane (Shibai et al. 1991; Bennett et al. 1994; Nakagawa et al. 1998; Yasuda et al. 2008). This is consistent with our previous findings based on Spitzer/IRS spectroscopy showing that the physical properties of the extra-nuclear, kpc-scale star formation in LIRGs are very similar to those of normal star-forming galaxies with lower IR luminosities (${L_{\rm IR}}\,\sim \,10^{10\hbox{--}11}\,{L_\odot }$), and that the diversity of their integrated MIR spectra is driven by the nuclear, few central kpc starburst (Díaz-Santos et al. 2011).

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The differences between the nuclear and extended emission are more clearly seen in Figure 2, which shows that the ratio between the FIR color of the extra-nuclear and nuclear regions is clearly correlated with the excess of [C ii] deficit seen in the nuclei with respect to that observed in the disks, regardless of the distance at which the extended emission is measured or on the distance to the galaxy (see color-coding). That is, for a given T_dust of the extended emission, LIRGs with warmer nuclei show larger differences between their nuclear and extra-nuclear [C ii] deficits.

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As shown in DS13, there is a clear trend for pure star-forming LIRGs having more compact IR emission to display lower [C ii]/FIR ratios. Figure 3(a) shows that the extended emission regions in spatially resolved galaxies follow an anti-correlation between [C ii]/FIR and Σ_IR similar to that seen for the LIRG nuclei, with slopes of −0.39 ± 0.07 and −0.35 ± 0.03 respectively, suggesting that these correlations are likely driven by the same physical process. However, the extra-nuclear regions (green filled circles) are offset by more than an order of magnitude toward lower Σ_IR and show higher [C ii]/FIR ratios on average than their nuclei (red open circles).

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To understand this offset we can decompose it as a simultaneous shift in [C ii]/FIR and Σ_IR along the slope of the observed trend, plus a horizontal shift in Σ_IR. The shift along the correlation is determined by the ratio between the median [C ii]/FIR measured in the extra-nuclear regions and that of the starburst nuclei. The additional horizontal shift in Σ_IR represents the beam filling-factor of the star-forming regions in the LIRG disks with respect to that of the nuclei. We estimate this relative filling-factor to be 0.06$^{+0.13}_{-0.04}$ by minimizing the difference between the median Σ_IR of the extended and nuclear emissions (see Figure 3(b)). The uncertainties in the filling factor account for the dispersion of the [C ii]/FIR versus Σ_IR correlation in the x-axis as well as for variations in the properties of the ISM that would modify the [C ii]/FIR ratio, such as changes in the fractional contribution of [C ii] emission associated with the diffuse ionized medium.

This methodology has been recently used in combination with the PDR models developed by Wolfire et al. (1990) to argue for the presence of large-scale star formation in high-redshift galaxies (Hailey-Dunsheath et al. 2010; Stacey et al. 2010; Ferkinhoff et al. 2014). These models relate the radius (R) and L_IR of the starburst region to the strength of the UV interstellar radiation field (ISRF), G₀, in units of the local Galactic value (1.6 × 10⁻³ erg s⁻¹ cm⁻²; Habing 1968). We can compare the relative beam filling factor of the extra-nuclear star-forming regions derived from Figure 3 to that predicted by the models. Wolfire et al. (1990) consider two geometric configurations for the starburst region. One in which the molecular clouds are immerse in a smooth ISRF and another in which a central, ionizing source is surrounded by a geometrically thick, molecular medium. Each one follows a relation such that ${G_{\rm 0}}\,\propto \,\lambda \,{L_{\rm IR}}\,/\,R^3$ and ${G_{\rm 0}}\,\propto \,{L_{\rm IR}}\,/\,R^2$, respectively, with λ being the mean free path of a UV photon within the starburst region. If we assume a hydrogen density, n_H, in the range of ∼10^2–5 cm⁻³, we can use Figure 4 of Stacey et al. (2010), which is based on the PDR models from Kaufman et al. (1999), to estimate the [C ii]/FIR ratio as a function of G₀. Although neither model fits our observed trend of [C ii]/FIR with Σ_IR, the model with a compact, nearby ionizing source, i.e., ${G_{\rm 0}}\,\propto \,R^{-2}$ (dashed line in Figure 3), is closest to our data. If we use M82 as our reference starburst (with the following properties: ${G_{\rm 0}}\,=\,1000$ and ${L_{\rm IR}}\,\sim \,3\,\times \,10^{10}\,{L_\odot }$, Lord et al. 1996; D ∼ 420 pc, Joy et al. 1987), the beam filling factor predicted by this configuration for the extra-nuclear star-forming regions would be ∼1% that of M82. This value is significantly lower than our inferred 6%, when we compare them to the LIRG nuclei using the observed correlation in Figure 3. We explore the reasons for this difference below.