A FAR-INFRARED SPECTROSCOPIC SURVEY OF INTERMEDIATE REDSHIFT (ULTRA) LUMINOUS INFRARED GALAXIES

We used Herschel-SPIRE observations of the fields ELAIS-N1, ELAIS-S1, Lockman Hole, XMM, Bootes, CDFS, and FLS, obtained as part of HerMES (Oliver et al. 2012). For our sources, we employed the photometric catalogs at 250, 350, and 500 μm that were produced for each field by using a prior source extraction, guided by the position of known 24 μm sources. An extensive description of the cross-identification prior source extraction (XID) method is given in Roseboom et al. (2010, 2012). The main advantage of this method is that reliable fluxes can be extracted close to the formal ≈4−5 mJy SPIRE confusion noise (Nguyen et al. 2010) by estimating the flux contributions from nearby sources within one beam. The 24 μm prior positional information reduces the impact of confusion noise and so the approximate 3σ limit for the SPIRE catalog at 250 μm becomes ≈9−15 mJy. The drawback of this technique is that the resulting catalogs could be missing sources without a 24 μm counterpart, that is, 24 μm dropouts (see Magdis et al. 2011). All sources were originally selected to have S₂₅₀ > 150 mJy, although a subsequent deblending analysis of FLS01 yielded a flux density of S₂₅₀ = 80.6 mJy.

Our targets also benefit from ancillary Spitzer MIPS (24, 70, and 160 μm) and IRAC (3.6, 4.5, 5.8, and 8.0 μm) observations. Finally, six of our sources have been followed up with Infrared Spectrograph (IRS) spectroscopy. The IRS reduced spectra were downloaded from CASSIS.v6²⁵ (Lebouteiller et al. 2011) and PAH luminosities and EWs were measured using PAHFIT (Smith et al. 2007). The MIPS and SPIRE photometry for our sample is summarized in Table 2.

The (U)LIRGs in our sample were observed with the SPIRE FTS on board Herschel between 2012 March and 2013 January. The FTS observed 100 repetitions (13,320 seconds total integration time) on each target with sparse spatial sampling, in high spectral resolution (0.048 cm⁻¹) mode. The SPIRE FTS measures the Fourier transform of the spectrum of a source using two bolometer detector arrays, simultaneously covering wavelength bands of 194–313 μm (SSW) and 303–671 μm (SLW).

The data were reduced with the user pipeline (T. Fulton et al. 2014, in preparation) in HIPE version 11, or version 12.1 if the slightly wider frequency bands proved advantageous for fitting lines near the frequency band edges. All ULIRGs in our sample are extremely faint targets for the FTS, with continua ≪1 Jy, and therefore require processing beyond a standard reduction.

For those observations taken within the first eight hours of an FTS pair of observing days, a correction was made to the telescope model subtracted within the pipeline. This adjustment is necessary due to low detector temperatures during the SPIRE cooler recycle, which is not fully accounted for by the nonlinearity correction for certain detectors, and therefore the spectra fail to be properly calibrated. The empirical correction applied is based on the linear correlation of detector temperature and SLW flux density of point-source-calibrated spectra of dark sky observations (see Swinyard et al. 2014 for details). For correctly calibrated data, this relationship is flat.

A bespoke relative spectral response function (RSRF), constructed from selected long dark sky observations, was applied if found to improve the noise in the point source calibrated product. However, for most observations, the standard RSRF was used, which was constructed using the scans of all dark sky observations. Once reduced to the point-source-calibrated stage, the main issue affecting FTS observations of faint compact sources is imperfect subtraction of the telescope RSRF and, for the low-frequency end of SLW, the instrument RSRF. To correct the distortions introduced by the point source calibration of this extended telescope residual, a background subtraction was performed. For FTS observations of point sources, the target is positioned in the center of the SSW detector, which overlaps with the central SLW detector. Both detector arrays are set out in a closely packed hexagonal pattern, which essentially provides concentric rings of off-axis detectors around the respective center detector (see Swinyard et al. 2014 for the precise layout). The first ring of SLW detectors and the first and second rings for SSW were smoothed to remove small-scale noise and inspected to reject any outliers due to clipping before averaging the selected spectra. This average gives a measure of the residual background, which was subtracted from the respective on-axis detectors.

The optimal reduction spectra were examined for spectral features at the positions of expected lines. Due to the faint nature of the targets, many of the lines are <5σ, and since low-frequency noise in an FTS spectrum can easily mimic a faint line of similar significance, two checks were performed for reliability and to gain statistically robust line measurements, both utilizing the un-averaged point-source-calibrated data. These two methods are described in R. Hopwood et al. (2014, in preparation). First, a Jackknife technique was used to minimize the chance of spurious detections. Each un-averaged set of 200 scans was divided into groups of sequential subsets. An average was taken for each subset, and this repeated for subsets of decreasing number, i.e., 2 sets of 100 scans, then 4 sets of 50 scans, down to spectra averaged from 10 scan subsets. In order to assess the realness of a potential detection, the results were plotted for a visual comparison of each averaged spectra in a subset and across subset size. Spectra of 10 scans should present as random noise unless there is high systematic noise, which can manifest as a detection in the fully averaged spectrum. The comparison of spectra averaged from 20 scans or more should start to show a consistent peak at the line position for all subsets, while the nearby data should still present as more random, with peaks of less significance.

Second, a bootstrap method was used to measure the line flux for any line assessed as potentially real and to provide a background level, which adds a second reliability check. For any given observation, the un-averaged scan set was randomly sampled until the number in the parent population (of 200) was reached. These random scans were then averaged and line measurements taken using the same basic fitting technique as for a standard average spectrum. The instrumental line shape of the FTS is well approximated by a sinc function (see Swinyard et al. 2014, R. Hopwood et al. 2014, in preparation for more details). Therefore, for unresolved lines, sinc functions were fitted simultaneously with a polynomial of the order of three for the continuum. Several of the detected [C ii] lines were found to be partially resolved and so a sinc convolved with a Gaussian was fitted in these cases, using the sincGauss function within HIPE. When bootstrapping the line measurements, a more aggressive baseline subtraction was performed to each scan prior to resampling. A set of random frequency positions was also generated and the same line fitting process applied. The resampling and fitting was repeated 10,000 times for each observation and a Gaussian fitted to the resulting line flux distribution to obtain the mean line flux. The Gaussian width was taken as the associated 1σ uncertainties. The distributions obtained from the set of random frequency positions establishes a background level, above which a real spectral feature is strongly suggested. This level was generally ∼2σ, so for any line found to be at <2σ, the bootstrapped flux density is taken as an upper limit, but only if the detection is supported by the Jackknife and other visual checks.

The full extracted spectra are presented in Figure 1 while in Figure 2 we show the detected lines along with the best-fit model. The derived flux densities, line widths, luminosities, and 3σ upper limits for the undetected lines are summarized in Table 3. In total, we detect [C ii] 157.7 emission from 12 out of the 14 sources in our spectroscopic sample. The [O i] 145 line is also detected in one of our sources (SWIRE5), while [N ii] 205, remains undetected for the entire sample. For the three sources with photometric redshifts, we do not detect any lines at the expected frequencies or by letting the redshift vary as a free parameter in the fitting process. In Table 3, we provide the upper limits of the lines measured at the expected frequencies based on their photometric redshifts. However, since the actual redshift of these sources remains largely unconstrained, we choose to omit them from the subsequent analysis.

Zoom In Zoom Out Reset image size

Zoom In Zoom Out Reset image size

We carried out follow-up, CO single-dish observations for nine galaxies in our sample. We used the Eight MIxer Receiver (EMIR; Carter et al. 2012) on the IRAM 30 m telescope at Pico Veleta, Spain, in 2012 June for six northern sources and the Swedish Heterodyne Facility Instrument (Vassilev et al. 2008) on the Atacama Pathfinder EXperiment ²⁶ (APEX; Güsten et al. 2006) 12 m telescope from 2012 August to October (run ID 090.B-0708A) and from 2013 April to July (run ID 091.B-0312A) for three southern sources (CDFS1, CDFS2, and ELAISS).

IRAM observations were carried out at 1.2, 2.0, and 3.0 mm (E0, E1, and E2 bands of EMIR), primarily targeting the CO[1−0] emission (ν₀ = 115.271 GHz) line from our galaxies. If CO[1−0] was not accessible, we searched for CO[2−1] (ν₀ = 230.538 GHz) or CO[3−2] (ν₀ = 345.796 GHz). When possible, we carried out simultaneous observations of two lines using E0/E1 (CO[1−0], CO[2−1]) or E1/E2 (CO[2−1], CO[3−2]) EMIR band combinations. The broadband EMIR receivers were tuned in single sideband mode, with a total bandwidth of 4 GHz per polarization which covers a velocity range of around 12,000 km s⁻¹1 at 3 mm, 8000 km s⁻¹ at 2 mm, and ∼5000 km s⁻¹ at 1.2 mm. The observations were carried out in wobbler-switching mode, with reference positions offset by 2' in azimuth.

We spent two to five hours on each galaxy, resulting in a noise level of 0.5−1.5 mK per 30 km s⁻¹ channel for all sources. The system temperatures were relatively stable with an average of ∼100 K at 3 mm, ∼280 K at 2 mm, and ∼300 K at 1.2 m, in $T^{*}_{\rm A}$. The pointing was regularly checked on continuum sources and yielded an accuracy of 3'' rms. The temperature scale used is in main beam temperature, T_mb. At 3 mm, 2 mm, and 1.2 mm, the telescope half-power beam width is 27'', 17'', and 10'', respectively, and the main beam efficiencies (η_mb = $T^{*}_{\rm A}/T_{\rm mb}$) are 0.85, 0.70, and 0.64, respectively, with S/T_mb = 4.8 Jy K⁻¹ for all bands.

APEX observations were carried out in average weather conditions with precipitable water vapor 0.4 < PWV < 1.5 and in wobbler-switching mode, with a symmetrical azimuthal throw of 20'' and a frequency of 0.5 Hz. Pointing was checked every hour and found to be better than 3'' (with a beam size of 20''). The focus was checked on the available planets, especially after sunrise when the telescope deformations are largest. The on-source integration time was ∼2 hr for CDFS2 and ELAISS and ∼8 hr for CDFS1, targeting the CO[3−2] emission line in all sources using APEX1 and APEX2 (214—275 GHz and 267—378 GHz, respectively). The achieved rms was around 0.4 mK for CDFS1 and 0.9 mK for the other two sources.

Both sets of spectra (APEX and IRAM) were reduced using CLASS (within the GILDAS-IRAM package). In short, each spectrum was averaged and reduced using linear baselines, and then binned to 50−60 km s⁻¹. To determine the properties of the emission lines (observed flux, velocity centroid, and FWHM), we fitted Gaussian functions to the observed spectra. We obtained fits for all galaxies with a single Gaussian and with two Gaussian functions (in this case fixing the FWHM in each component to the same value). For all sources, a single Gaussian provided the best fit to the data, although in some cases there is evidence of a double-horned profile. Considering a line detected when the integrated signal is larger than >3σ, we have solid detections for at least one line per source. The median line width of our sample is 416 km s⁻¹ and ranges from 238 to 538 km s⁻¹. Given the angular distance of the sources (average value 1000 Mpc), our beam subtends between 50 and 100 kpc, and all galaxies can be considered unresolved, at least as far as their molecular component is concerned. All spectra along with the best-fit models are presented in Figure 3, while the properties of the fitted lines are summarized in Table 4.

Zoom In Zoom Out Reset image size

Table 4. CO IRAM and APEX Observations

Source	zCOa	Line	SCOΔv	ΔVFWHM	log $L^{\prime }_{\rm CO}$	log LIR	log $L^{\prime }_{\rm CO[1\hbox{--}0]}$b
			(J km s−1)	(km s−1)	(K km s−1 pc2)	(L☉)	(K km s−1 pc2)
BOOTES1	0.352	CO[1−0]	1.63 ± 0.28	184 ± 43	10.21 ± 0.08	12.69	10.21 ± 0.08
	0.352	CO[2−1]	7.58 ± 1.10	416 ± 71	10.09 ± 0.06	12.69	10.21 ± 0.08
BOOTES2	0.249	CO[1−0]	2.01 ± 0.38	378 ± 74	9.81 ± 0.08	11.80	9.81 ± 0.08
BOOTES3	0.216	CO[1−0]	6.19 ± 0.81	627 ± 82	10.17 ± 0.05	11.87	10.17 ± 0.05
SWIRE4	0.248	CO[1−0]	3.40 ± 0.57	556 ± 105	10.04 ± 0.07	11.79	10.04 ± 0.07
SWIRE5	0.366	CO[1−0]	2.78 ± 0.52	476 ± 145	10.29 ± 0.08	12.06	10.29 ± 0.08
	0.367	CO[2−1]	8.20 ± 1.15	531 ± 104	10.16 ± 0.06	$_{^{\prime \prime }}$	$_{^{\prime \prime }}$
FLS02	0.436	CO[2−1]	3.36 ± 0.81	347 ± 124	9.93 ± 0.04	12.41	10.05 ± 0.05
	0.436	CO[3−2]	5.76 ± 1.10	380 ± 77	9.81 ± 0.08	$_{^{\prime \prime }}$	10.11 ± 0.16
CDFS1	0.289	CO[3−2]	11.15 ± 2.29	290 ± 64	9.72 ± 0.08	11.79	10.03 ± 0.16
CDFS2	0.248	CO[3−2]	17.05 ± 5.57	423 ± 198	9.77 ± 0.14	11.82	10.07 ± 0.28
ELAISS	0.265	CO[3−2]	12.13 ± 3.60	273 ± 150	9.68 ± 0.12	11.59	9.98 ± 0.24

Notes. ^aTypical uncertainty, Δz = 0.001. ^bFor sources where CO[1–0] observations are not available, we adopt r₂₁ = 0.75 and r₃₂ = 0.5.

Download table as:  ASCIITypeset image

Line luminosities, L_CO (measured in L_☉), and $L^{\prime }_{\rm CO}$ (measured in K km s⁻¹ pc²) were derived using Equations (1) and (3) of Solomon & Vanden Bout (2005)

$$\begin{equation} {L_{\rm CO} = 1.04 \times 10^{-3} S_{\rm CO} \Delta u \nu _{\rm rest}(1+z)^{-1}D^{2}_{\rm L}}, \end{equation} \tag{ 1 }$$

where L_CO is measured in L_☉, the luminosity distance D_L is in megaparsecs, the velocity integrated flux, S_COΔu, in Jy km s⁻¹, the rest-frame frequency of the observed line, ν_rest, in GHz, and

$$\begin{equation} {L^{\prime }_{\rm CO} = 3.25 \times 10^{7} S_{\rm CO}\Delta u \nu ^{-2}_{\rm obs}D^{2}_{\rm L}(1+z)^{-3}}. \end{equation} \tag{ 2 }$$

As discussed, for four sources we targeted and detected the CO[1−0] emission line so the derived $L^{\prime }_{\rm CO}$ corresponds to $L^{\prime }_{\rm CO[1\hbox{--}0]}$. For the remaining five sources (FLS2, BOOTES2, CDFS1, CDFS2, and ELAISS), we converted the observed $L^{\prime }_{\rm CO}$ = $L^{\prime }_{\rm CO[2\hbox{--}1]}$ or $L^{\prime }_{\rm CO}$ = $L^{\prime }_{\rm CO[3\hbox{--}2]}$ to $L^{\prime }_{\rm CO[1\hbox{--}0]}$, adopting r₂₁ = 0.75 and r₃₂ = 0.5 (e.g., Dannerbauer et al. 2009; Ivison et al. 2010a; Rigopoulou et al. 2013; Aravena et al. 2014). For XMM01 and HLSW-01 (SWIRE6), we adopt the CO[1–0] measurements reported by Fu et al. (2013) and Scott et al. (2011), respectively.

Various Galactic and extragalactic studies of the [C ii] emission (e.g., Tielens & Hollenbach 1985; Stacey et al. 1991; Meijerink et al. 2007; Rigopoulou et al. 2013) have established that it predominantly originates from photodissociation regions (PDRs) in the outer layers of molecular clouds exposed to intense FUV radiation and have put it forward as a potentially powerful tracer of the star formation activity. Indeed, using L_FIR (L_FIR = L_{42.5–122.5 μm}) as an SFR indicator (e.g., Kennicutt et al. 1998), the majority of normal galaxies in the local universe seem to obey a universal linear L_C ii−L_FIR relation with a constant L_C ii/L_FIR ratio, albeit with a significant scatter (e.g., Malhotra et al. 2001). However, extending the study of [C ii] in local (U)LIRGs has revealed that they appear to deviate from this relation exhibiting lower L_C ii/L_FIR ratios, i.e., they are [C ii] deficient with respect to their infrared luminosity (e.g., Malhotra et al. 1997; Luhman et al. 1998, 2003; Diaz-Santos et al. 2013; Farrah et al. 2013).

Extrapolating observations of the local universe to high-z galaxies, a natural expectation would be that high-z (U)LIRGs would also appear [C ii] deficient with respect to local normal galaxies. However, the detections of [C ii] emission from distant (z > 1), star-forming galaxies have come to challenge this picture, revealing that ULIRGs can exhibit L_C ii/L_FIR ratios similar to that of local normal galaxies and a factor of ∼10 larger compared to local (U)LIRGs (e.g., Hailey-Dunsheath et al. 2010; Stacey et al. 2010; Valtchanov et al. 2011; Riechers et al. 2013). While these studies seem to suggest a strong evolution in the [C ii] emission between local (z < 0.2) and z > 1 (U)LIRGs, it is unclear what drove this evolution.

Rigopoulou et al. (2014) found that the majority of Herschel−selected (U)LIRGs have L_C ii/L_FIR ratios similar to that of high-z star-formation-dominated ULIRGs and local normal galaxies, suggesting that the transition of the properties in the ISM of the (U)LIRG phenomenon was already in place by z ∼ 0.3. Here, by using the same sample, we bridge the gap between the local and high-z galaxies and provide a continuous sampling of the L_C ii−L_FIR relation over the last 10 billion years for a wide range of extragalactic sources.

In Figure 6, we plot the [C ii] line luminosity as a function of far-infrared luminosity for local normal galaxies (Malhotra et al. 2001), local (U)LIRGs from the GOALS and HERUS samples (Diaz-Santos et al. 2013; Farrah et al. 2013), high-z (z > 1) star-forming galaxies (Stacey et al. 2010; Hailey-Dunsheath et al. 2010; Valtchanov et al. 2011; Cox et al. 2011; Ivison et al 2010a; Swinbank et al. 2012; Rawle et al. 2013; George et al. 2013; Riechers et al. 2013; Ferkinhoff et al. 2014), high-z AGNs and QSOs (Iono et al. 2006; Wagg et al. 2010; Gallerani et al. 2012), and for our sample of z ∼ 0.3 (ULIRGs). Fitting the local normal galaxies yields

$$\begin{equation} {\rm {log}({{L}}_{\rm C\, {\scriptsize{II}}}) = (-2.51 \pm 0.31) + \rm {log}({{L}}_{\rm FIR})}, \end{equation} \tag{ 3 }$$

revealing a constant L_C ii/L_FIR ratio albeit with a considerable scatter. As shown in Figure 6, the majority of star-forming galaxies (with [C ii] measurements) at all redshifts and infrared luminosities follow this relation (within the scatter), suggesting that L_C ii can trace L_FIRand therefore the SFR within a factor of 2.5 at all epochs. However, as discussed above and as evident from the skewed tail of the L_C ii/L_FIR distribution (see the inset panel of Figure 6), outliers from this relation do exist and are predominantly the local (U)LIRGs (L_FIR > 5 × 10¹¹ L_☉), high-z, AGN-dominated sources, and a small fraction of high-z star-forming galaxies. These sources appear [C ii] deficient with respect to their L_FIR exhibiting, on average, a lower L_C ii/L_FIR ratio compared to that of local normal galaxies and the majority of high-z star-formation-dominated ULIRGs. This trend implies an evolution in the star-forming regions of (U)LIRGs. Indeed, focusing on our sample of intermediate redshift (U)LIRGs, we find that only 2 out of the 14 targets appear to be [C ii] deficient, while the rest exhibit L_C ii/L_FIR ratios similar to that of local normal galaxies and high-z star-forming galaxies. Interestingly, these two sources are also classified as AGNs. In what follows, we will investigate the impact of an AGN on the observed L_C ii/L_FIR ratio of our sample.

Zoom In Zoom Out Reset image size

A possible explanation for deviations from the general L_C ii−L_FIR trend could be the strong contribution of an AGN to the bolometric infrared output of the source. If L_C ii is predominantly associated with star formation, while L_FIR arises from a mixture of AGNs and star formation activity, it would result in a decreased L_C ii/L_FIR ratio with respect to purely star-forming galaxies. This scenario holds under the assumption that even if [C ii] can be excited by AGN activity (both in PDRs and XDRs), its contribution to the total [C ii] emission is typically found to be small (e.g., Crawford et al. 1985; Unger et al. 2000; Stacey et al. 2010).

To investigate this scenario, we perform an AGN/host galaxy decomposition for five sources in our sample that benefit from mid-IR IRS spectra, using the SED decomposition method of Mullaney et al. (2011). This method employs a host-galaxy and an intrinsic AGN template SED to measure the contribution to the infrared output of these two components. The technique identifies the best-fitting model SED for the observed infrared data (spectra and photometry) through χ² minimization and by varying the values of a set of free parameters (for details, see Magdis et al. 2013). The best-fit model SEDs are shown in Figure 7. Out of the five sources with available IRS spectra, two are classified as AGNs (Bootes1 and FLS2) and three as star-forming or composites based on optical or mid-IR spectroscopy.

Zoom In Zoom Out Reset image size

From the various output parameters, we focused on the contribution of an AGN in the far-infrared emission (f_AGN). For star-forming and composite sources (classified based on the EW of the 6.2 μm PAH feature), we find a negligible (if any) contribution of an AGN to L_FIR. For the two AGNs, which also happen to have L_C ii/L_FIR similar to that of local ULIRGs, we derive f_AGN = 0.31 (BOOTES1) and f_AGN = 0.51 (FLS2). We note that given the poor fit to the rest-frame mid-IR data for these two sources, these values should be treated with caution and the exact contribution of an AGN to the L_FIR remains largely unconstrained. However, even if we correct the L_FIR by a factor of two the L_C ii/L_FIR of these two sources remain approximately ∼3 times lower compared to the rest of the sample. Therefore, while the existence of an AGN can partially affect the L_C ii/L_FIR values for these systems, the AGN contribution to L_FIR cannot fully explain the observed [C ii] deficit. Furthermore, the rest of the sources in our sample that are classified as AGNs fall within the scatter of the L_Cii−L_FIR relation defined in Equation (3), suggesting that there is no direct correlation between the existence of an AGN and the observed L_C ii/L_FIR ratio. Similar results have been reached by Diaz-Santos et al. (2013) and Farrah et al. (2013) based on a sample of local ULIRGs and using a number of far-IR lines. However, we should stress that in our sample, as well as in the majority of local ULIRGs, the far-IR output is dominated by star formation (e.g., Genzel et al. 1998; Rigopoulou et al. 1999; Armus et al. 2007; Desai et al. 2007; Petric et al. 2011). On the other hand, sources where AGN activity dominates the far-IR output of the sources, both in the local universe as well as at high-z, the origin of the [C ii] deficit can be explained through the contamination of L_FIR by AGN activity (e.g., Stacey et al. 2010; Wagg et al. 2010; Sargsyan et al. 2012).

Therefore, we cannot rule out that for sources where AGN activity dominates the far-IR output of the sources, both in the local universe as well as at high-z, the origin of the [C ii] deficit as reported in various studies is not due to contamination of L_IR by AGN activity (e.g., Stacey et al. 2010; Wagg et al. 2010; Sargsyan et al. 2012).

Various studies of [C ii] emission from normal galaxies and local (U)LIRGs have established an observational trend where sources with lower L_C ii/L_FIR values tend to have warmer dust temperatures (e.g., Malhotra et al. 1997). Since the L_C ii/L_FIR ratio depends on the efficiency of the heating of gas by photoelectrons from dust, it is indeed expected to be sensitive to the physical conditions of the ISM. A possible explanation for the observed trend was offered by Malhotra et al. (1997) based on the study of the colors and the [C ii] emission of local ULIRGs. They suggested that the [C ii] deficit of warmer sources could be explained by a high G₀/n_H ratio in the neutral galactic medium, where G₀ is the incident far-UV 6−13.6 eV radiation field and n_H the total hydrogen gas density. In this scenario, more extreme G₀/n_H ratios would lead to an increase in the positive charge of the dust particles, which would result in a reduction of the amount of photo-electrons (with sufficient kinetic energy) released from dust grains, and consequently, in a decrease of the efficiency in the transformation of the incident UV radiation into gas heating.

In a more general scenario, the observed deficits of various far-IR atomic lines could be the result of a higher average ionization parameter of the ISM, 〈U〉 (Luhman et al. 2003; Abel et al. 2009), defined as the dimensionless ratio of the incident ionizing photon density to the hydrogen density

$$\begin{equation} {U = \frac{Q_{\rm H}}{4 \pi R^{2}n_{\rm H}c}}, \end{equation} \tag{ 4 }$$

where Q_H is the number of hydrogen ionizing photons, R is the distance of the ionizing sources to the PDR, and c is the speed of light. Assuming an average stellar population and size of star-forming regions, the above relation yields

$$\begin{equation} {U \propto \frac{G_{\rm 0}}{n_{\rm H}}}. \end{equation} \tag{ 5 }$$

For fixed n_H, higher levels of ionization (i.e., higher 〈U〉 values) would result in a higher ratio of ionized to atomic hydrogen and therefore in a decreased gas opacity in the H ii regions, since less hydrogen atoms will be available to absorb UV photons. Subsequently, this will lead to a decreased gas-to-dust opacity, as dust will have to compete for UV photons with fewer neutral hydrogen atoms in the H ii regions. 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; Abel et al. 2009), causing a deficit of photo-electrons and hence, suppression of the [C ii] line with respect to the total FIR dust emission. Higher 〈U〉 values will also translate into larger numbers of photons per dust particle and therefore higher dust temperature or warmer far-IR colors for sources with lower L_C ii/L_FIR (or other atomic lines) ratios. We note that the assumption of fixed n_H appears to be valid based on the observation that (L_Oi + L_C ii)/L_FIR varies as a function of far-IR color (S₆₀/S₁₀₀).

In Figure 8, we plot the L_C ii/L_FIR ratio as a function of the L₆₀/L₁₀₀ color and dust temperature for the same sample of galaxies as in Figure 6. For the local galaxies we used the available IRAS photometry, while for our intermediate-z and high-z literature sources we convolved the best-fit SED with the IRAS filters. To convert the observed flux ratios of the sources drawn form the literature to dust temperatures, we assumed a MBB with a fixed dust emissivity index β = 1.5. In both panels, the local sample is color-coded based on the infrared luminosity of the sources. It appears that the strong anti-correlation between the L_C ii/L_FIR ratio and the dust temperature, as already observed in the local universe by various authors (e.g., Diaz-Santos et al. 2013), holds at all luminosities and all redshifts. The best fit to the data yields the relation

$$\begin{equation} \rm log\left(\frac{{{L}}_{\rm C\, \scriptsize{II}}}{{{L}}_{\rm FIR}}\right) = (-3.09 \pm 0.06) + (-2.53 \pm 0.21) log\left(\frac{{{L}}_{\rm 60}}{{{L}}_{\rm 100}}\right), \end{equation} \tag{ 6 }$$

with a scatter of 0.3 dex, suggesting a strong dependence between the L_C ii/L_FIR ratio and the dust temperature at all epochs, with warmer sources exhibiting lower L_C ii/L_FIR ratios.

Zoom In Zoom Out Reset image size

This trend also provides hints about the physical origin of the observed difference of the L_C ii/L_FIR ratio between the local and distant ULIRGs. Several studies have shown that the majority of high-z star-forming galaxies with ULIRG-like luminosities are colder than galaxies in the local universe with similar L_IR (e.g., Hwang et al. 2010; Magdis et al. 2010, 2012b; Symeonidis et al. 2013). This is clearly depicted in Figure 8, where the bulk of high-z star-forming galaxies from the literature that have [C ii] measurements exhibit lower L₆₀/L₁₀₀ with respect to local ULIRGs. Note that all high-z star-forming galaxies in this sample have L_IR > 10¹² L_☉. Similarly, we find that our sample of Herschel-selected intermediate redshift (U)LIRGs are on average colder than local ULIRGs with 〈T_d〉 = 34 K compared to 42 K for local ULIRGs.

As discussed above, the observed trend is compatible with the physical scenario in which the variation of L_C ii/L_FIR is caused by an increase of 〈U〉 in [C ii] deficient sources. Diaz-Santos et al. (2013; Díaz-Santos et al. 2014), showed that for local (U)LIRGs the observed decrease of L_C ii/L_FIR ratio in warmer sources, i.e., sources with higher 〈U〉, is linked to the luminosity surface density of the mid-IR emitting region; warm, [C ii] deficient sources are associated with compact starbursts. Furthermore, based on resolved [C ii] observations, they found that [C ii] deficient regions of local luminous LIRGs are restricted to their nuclei with extra nuclear emission showing L_C ii/L_FIR ratios similar to that of normal galaxies. The implications of these findings for the high-z galaxies are discussed in Section 6.

Finally, we note that variation of the L_C ii/L_FIR ratio could also be driven by galactic scale metallicity effects. For example, higher dust temperatures could result from the increased hardness of the radiation field and the transparency of the ISM toward lower metallicities, which enhances the ionization of gas. In combination with the longer mean free path lengths of ionizing photons in metal-poor galaxies, the filling factors of ionized gas media are bound to grow drastically (e.g., De Looze et al. 2014). Furthermore, more UV photons might reach the neutral PDR gas in low metal abundance environments, where the hard radiation field reduces the PAH abundance and/or charges dust grains in PDRs, resulting in a reduced [C ii] line emission. Apart from the CII deficit, metallicity variations could also be responsible for the observed scatter in the L_C ii–L_FIR relation.

In a recent study, Graciá-Carpio et al. (2011) reported a strong anti-corellation between the relative strength of the far-IR lines and the infrared luminosity to molecular gas mass ratio, L_IR/$M_{\rm H_{\rm 2}}$. In particular, they argued that galaxies with high SFEs (L_IR/$M_{\rm H_{\rm 2}}$; Sanders & Mirabel 1985) tend to have weaker far-IR emission lines as a consequence of an increased ionization parameter. Indeed, in a simplified scenario, the radiation field should be proportional to the number of available ionizing photons (L_IR) per hydrogen molecule ($M_{\rm H_{\rm 2}}$). They concluded that for fixed hydrogen density, the observed [C ii] deficit that starts to appear at L_IR/$M_{\rm H_{\rm 2}}$ > 80 L_☉/M_☉ can be understood if the ionization parameter is an order of magnitude larger compared to sources with lower L_IR/$M_{\rm H_{\rm 2}}$ (〈U〉 ∼10⁻³ to 10^−2.5 for the latter). Interestingly, the value of L_IR/$M_{\rm H_{\rm 2}}$ ≈ 80 L_☉/M_☉ where the far-IR line deficits start to manifest is also similar to the limit that separates between the two modes of star formation (merger driven starbursts versus normal quiescent galaxies, e.g., Daddi et al. 2010a, 2010b; Genzel et al. 2010). Here, we test this scenario for our sample of intermediate redshift (U)LIRGs by using our CO and M_dust measurements.

A great source of uncertainty in this investigation is the derivation of $M_{\rm H_{\rm 2}}$ estimates that are dependent on the adopted CO-to-M_gas conversion factor (α_CO), which is known to vary by a factor of six between local normal galaxies and local ULIRGs (e.g., Downes & Solomon 1998; Bolatto et al. 2013). Here, instead of using a single α_CO value for all sources, we take advantage of the dust mass estimates for our galaxies and employ the dust to gas mass ratio technique (e.g., Magdis et al. 2011a, 2012b). Adopting a solar metallicity and the dust to gas mass ratio versus metallicity relation (δ_GDR − Z) of Leroy et al. (2011), we find an M_gas/M_dust ratio of ∼80. Then, using the M_dust estimates for our sample, we derive the gas mass and the corresponding error for our sources, taking into account the M_dust uncertainties, as well as assuming a 0.2 dex uncertainty in the adopted metallicity and therefore in the assumed M_gas/M_dust ratio. A full description of the limitations inherent in this approach are presented in Magdis et al. (2012b).

In Figure 9  (left), we plot the L_C ii/L_FIR ratio as a function of L_IR/$M_{\rm H_{\rm 2}}$,²⁸ focusing on the sample for which we have [C ii] and [CO] measurements. This figure reveals a clear trend, with sources that deviate more than 1σ from the L_C ii–L_FIR relation of Equation (3) exhibiting the highest SFEs. A Kendal's tau ranking test yields a correlation coefficient of ρ = −0.9 and a p-value of 4×10⁻⁵, suggesting a statistically significant anti-correlation between the two parameters. For comparison, we also include a sample of local disks and local ULIRGs, adopting an α_CO ²⁹ conversation factor of 4.5 and 0.8, respectively (e.g., Downes & Solomon 1998; Rosolowsky et al. 2007; Bolatto et al. 2008, 2013; Sliwa et al. 2012). The majority of intermediate redshift (U)LIRGs in our sample fall in the locus of local disks, while the two [C ii] deficient sources have SFEs similar to that of local ULIRGs. Similar to Graciá-Carpio et al. (2011), we conclude that low L_C ii/L_FIR values are directly linked to high SFEs.

Zoom In Zoom Out Reset image size

Using the derived $M_{\rm H_{\rm 2}}$ values from the δ_GDR − Z method and the CO measurements, we can also estimate the α_CO values using the CO-to-$M_{\rm H_{\rm 2}}$ formula:

$$\begin{equation} \rm M_{\rm H_{\rm 2}} = \alpha _{\rm CO} \times L^{\prime }_{\rm CO}. \end{equation} \tag{ 7 }$$

The inferred α_CO values for the entire sample range from 6 to 1. [C ii] deficient sources have a mean 〈α_CO〉 = 1.5, comparable to that of local ULIRGs. On the other hand, sources that follow the L_C ii–L_FIR relation of Equation (3) have a mean 〈α_CO〉 = 5.3, similar to that of local normal galaxies.

Given the uncertainties coupled with the $M_{\rm H_{\rm 2}}$ estimates, to ensure that the result is not an artefact of the derived α_CO values, in Figure 9 (right), we plot the L_C ii/L_FIR ratio as a function of the direct observables L_IR/$L^{\prime }_{\rm CO}$. In this plot, we also add a sample of high-z ULIRGs, along with the samples presented in the L_C ii/L_FIR−L_IR/$M_{\rm H_{\rm 2}}$ plot. Again, we find that there is a strong anti-correlation between the two ratios, with increasing L_IR/$L^{\prime }_{\rm CO}$ for decreasing L_C ii/L_FIR, at all redshifts and luminosities.

It is worth to attempting to put constraints on its spatial origin, namely, whether it predominantly originates from PDRs or from ionized H ii regions. For this task, ionized nitrogen [N ii] 205 μm can provide crucial information. With an ionization potential of 14.53 eV, slightly above that of hydrogen, [N ii] emission traces H ii regions. On the other hand, the ionization potential of carbon is slightly below that of hydrogen, and consequently can arise both from H ii regions and from PDRs. As [N ii] and [C ii] have very similar critical densities for excitation in ionized gas regions, their line ratio is insensitive to the hardness of the radiation field. Thus, for a given metallicity, their flux ratio can be used as a diagnostic tool to estimate the fraction of carbon emission arising from the H ii regions (where both [C ii] and [N ii] are present) versus that arising from the neutral phase (where [N ii] is absent). In a H ii region with fixed metallicity, the expected ratio of the two lines is practically independent of the gas density and assuming gas phase abundances of n([N ii])/n_e = 7.9 × 10⁻⁵ and n([C ii])/n_e = 1.4 × 10⁻⁴ (Savage & Sembach 1996), we expect a ratio of line luminosities L_C ii/L_[N ii] ≈ 2−3 in the case where both lines originate from ionized gas regions (Oberst et al. 2006; Decarli et al. 2014).

Since we do not have [N ii] detection for any of our sources, we can only place lower limits in the L_C ii/L_[N ii] ratio of our sample by using the [C ii] measurements and the [N ii] upper limits. While based on the lower limits, we cannot decisively quantify the fraction of [C ii] emission arising from the PDRs for the majority of the sources the L_C ii/L_[N ii] lower limits are well above the theoretical expectations (L_C ii/L_[N ii] > 3.2) for the case where [C ii] emission originates purely from H ii regions. In particular, it appears that >50% of [C ii] emission in intermediate redshift ULIRGs arises from PDRs, similar to high-z ULIRGs (Decarli et al. 2014) and local starbursts (Rigopoulou et al. 2013).