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A&A
Volume 628, August 2019
Article Number A71
Number of page(s) 30
Section Extragalactic astronomy
DOI https://doi.org/10.1051/0004-6361/201834088
Published online 08 August 2019

© ESO 2019

1. Introduction

Luminous and ultraluminous infrared galaxies (LIRGs: LIR(8−1000 μm) > 1011 L⊙; ULIRGs; LIR >  1012 L⊙) are known to host powerful starbursts, making them ideal for studying the properties of extreme star-forming environments. Since the discovery of (U)LIRGs as an important galaxy population by the Infrared Astronomical Satellite (IRAS), which found that 30%–50% of the total bolometric luminosity of galaxies in the local universe is emitted at infrared (IR) and sub-millimeter wavelengths (Soifer et al. 1986), CO observations of (U)LIRGs have been carried out to characterize the molecular gas responsible for the ongoing star formation, as well as to trace galaxy kinematics (e.g., Tinney et al. 1990; Sanders et al. 1991; Aalto et al. 1995; Solomon et al. 1997; Downes & Solomon 1998; Bryant & Scoville 1999; Yao et al. 2003; Narayanan et al. 2005; Papadopoulos et al. 2012a; Yamashita et al. 2017). Much of the interpretation of the data is reliant on the CO luminosity-to-molecular gas mass conversion factor, ; the commonly used “Milky Way” conversion factor, αMW  ≃  4 M⊙ (K km s−1 pc2)−1, has been called into question for its use with (U)LIRGs, for which alternative values have been proposed (e.g., Downes & Solomon 1998; Bolatto et al. 2013). The choice directly impacts upon estimates of the total gas mass, the star formation efficiency, and the gas depletion timescale, which can differ by almost an order of magnitude. In addition to CO, observations of high density and optically thin gas tracers have provided the opportunity to better assess the physical conditions of the interstellar medium (ISM), in part by determining the physical state of the gas more directly involved in the formation of future stars.

The advent of broadband receivers on millimeter-wave telescopes has enabled the detection of multiple lines at once, probing a range of optical depths, critical densities, and temperatures. In our present study, we make use of the 30 m Telescope of the Institut de Radioastronomie Millimétrique (IRAM-30 m) to detect multiple millimeter-wave lines from a sample of 55 nearby (U)LIRGs selected from the Great Observatories All-Sky LIRG Survey (GOALS, Armus et al. 2009). We focus here primarily on the 12CO(1→0) and 13CO(1→0) data, which is combined with new Herschel Space Observatory observations in order to estimate the conversion factor α from an assumed gas-to-dust mass ratio, the star formation efficiency, and gas depletion timescales, and to examine the relation between the 12CO(1→0)-to-13CO(1→0) ratio and the dust temperature. A complementary study of dense gas tracers HCN(1→0) and HCO+(1→0), observed as part of this IRAM campaign, was presented in Privon et al. (2015).

This paper is organized as follows: we describe our sample in Sect. 2. Observations and data reduction are summarized in Sect. 3. The main results are presented in Sect. 4. In Sect. 5 we determine the CO-to-H2 conversion factor Sect. 5.1, derive the star formation properties of the sample Sect. 5.3, and reexamine the 12CO/13CO relationship with dust temperature Sect. 5.4. Finally, we summarize our results in Sect. 6. Throughout this study, we adopt a Wilkinson Microwave Anisotropy Probe (WMAP) cosmology of H0 = 69.3 km s−1 Mpc−1, ΩΛ = 0.714 and Ωm = 0.286 (Hinshaw et al. 2013).

2. Sample

Our sources are selected from the GOALS sample, which consists of all 180 luminous and 22 ultraluminous nearby IR galaxy systems in the IRAS Revised Bright Galaxy Sample (f60 μm >  5.24 Jy: Sanders et al. 2003). The GOALS sample has been observed with the Hubble Space Telescope (HST; Haan et al. 2011; Kim et al. 2013), the Spitzer Space Telescope (Díaz-Santos et al. 2010, 2011; Petric et al. 2011; Stierwalt et al. 2013, 2014), the Herschel Space Observatory (Chu et al. 2017), the Galaxy Evolution Explorer (GALEX; Howell et al. 2010), and the Chandra X-ray Observatory (Iwasawa et al. 2011), making it the most complete multiwavelength sample of nearby, IR-bright galaxies. In addition, ground-based H I, radio, and near-IR spectroscopic data complement the space-telescope-based dataset. GOALS contains a sufficient number of LIRGs to cover the full range of galaxy-galaxy interactions and merger stages, including isolated sources. The sample of 55 (U)LIRGs observed for our present CO survey consists of GOALS sources accessible from Pico Veleta that had not been previously observed by the IRAM-30 m Telescope. Unfortunately, due to the lack of a public archive for the IRAM-30 m Telescope, previously observed data for GOALS galaxies cannot be obtained in its raw format, so a systematic data reduction could not be guaranteed. For this reason, we restricted the current study to the aforementioned sample of 55 (U)LIRGs.

In the observed sample, 48 of the galaxies are LIRGs or components of LIRGs, and seven are ULIRGs or component of ULIRGs. In the cases where each component of a system was observed independently, these were treated as individual sources throughout the analysis. The list of galaxies is presented in Table 1, along with LIR from Armus et al. (2009). As shown in the histogram of Fig. 1, our observed sources are representative of the complete GOALS sample in terms of luminosity.

Table 1.

Source list.

thumbnail Fig. 1.

Normalized histogram comparing LIR from the complete set of 202 GOALS galaxies and our observed sample. All LIR were obtained from Armus et al. (2009).

To compare our (U)LIRG sample with local spiral galaxies, we have used published observations from the HERA CO-Line Extragalactic Survey (HERACLES; Leroy et al. 2009) and the Five College Radio Astronomy Observatory (FCRAO; Young et al. 1995), for which CO and Herschel data are available. These include a total of 22 sources.

For comparison, our (U)LIRG sample has a median redshift (see Sect. 4 for details) of 0.0248 ± 0.0163 and a median log(LIR/L⊙) of (11.45 ± 0.33) according to Armus et al. (2009), where the errors indicate the standard deviation of the sample. On the other hand, the local comparison sample (both HERACLES and FCRAO) has a median redshift of 0.0023 ± 0.0018 and a median log(LIR/L⊙) of 10.28 ± 0.51.

3. Observations and data reduction

The observations1 presented in this study were carried out with the Eight Mixer Receiver (EMIR) multiband millimeter-wave receiver (Carter et al. 2012) at the IRAM-30 m Telescope on Pico Veleta, Spain, in five observing periods: June 2010, September 2011, December 2011, October 2012 (PI: K. Iwasawa), and March 2014 (PI: R. Herrero-Illana). The final March 2014 run was obtained during the director’s discretionary time in order to verify the 13CO line strength of three sources (IRAS F05189−2524, IRAS 22491−1808, and IRAS 07251−0248). We tuned the receiver to two frequency windows: one centered at the redshifted frequencies of HCN(1 → 0) and HCO+(1 → 0) (rest frequencies of 88.632 and 89.189 GHz, respectively; presented in Privon et al. 2015), and the other at the frequencies of 12CO(1 → 0) and 13CO(1 → 0) (rest frequencies of 115.271 and 110.201 GHz, respectively). The EMIR receiver has a total bandwidth of 8 GHz. All the observations were performed in wobbler switching mode. For the majority of the galaxies, the peak of their Spitzer IRAC channel 4 (i.e., 8 μm) emission was used as the pointing center. A complete journal of observations is presented in Table 2, along with the measured line intensities.

Table 2.

Measured parameters.

The data were reduced using the Continuum and Line Analysis Single-dish Software (CLASS)2 package. For each scan, gain elevation calibration, platforming correction (when the Fast Fourier Transform Spectrometer (FTS) backend was used), and order one baseline subtraction were performed. Then, the scans for each galaxy were averaged together and the average spectrum was smoothed to ∼25 km s−1 resolution. A final linear baseline was subtracted over the channels that did not contain line emission. We obtained line fluxes by integrating all channels within the line profile. To account for systematic uncertainties, we added a standard 10% of error in quadrature to the rms of the fluxes, which is the uncertainty for IRAM-30 m data as estimated by the observatory3. Figure 2 contains an example of a resultant spectrum, and the spectra of the remaining galaxies are shown in Appendix A.

thumbnail Fig. 2.

Spectral line profiles for NGC 6286. Left panel: Herschel PACS 70 μm map (see Chu et al. 2017) with a logarithmic stretch to highlight the full extent of the infrared emission relative to the IRAM-30 m Telescope. Overlaid circles represent the pointing position and beam sizes (FWHM) corresponding to the 12CO and 13CO (inner), and HCN and HCO+ (outer) IRAM observations. The middle panel shows the continuum-subtracted CO spectra, fitted with Gaussian components. Velocity frame is defined according to the redshifts quoted in Table 3. Gray vertical lines correspond to the velocity integration limits of the FWZI. Right panel: continuum-subtracted spectra of 13CO (blue, solid line), HCN (red, dotted line), and HCO+ (green, dashed line) in the same velocity range as the CO spectrum. The spectra have been normalized to the peak of the CO line, and the normalization factor is shown for each line. The complete data set with all the observations, as well as a table with the fitted Gaussian components of the 12CO spectra is shown in Appendix A.

4. Results

In Tables 2 and 3 we present the measured and derived properties from the IRAM observations, respectively. From the 55 observed sources we detect 12CO in 53 (∼96%) and 13CO in 29 (∼52%), above a 3σ level. The only two sources with no 12CO detection (2MASX J11210825−0259399 and 2MASX J23181352+0633267) are subcomponents of LIRGs and, given the non-detections, were excluded from the analysis. Line intensities and luminosities for 13CO were obtained by integrating over the velocity range corresponding to the 12CO detections. We find that ∼54% of the sources show a multiple peak profile (see Figs. 2 and A.1). For that reason, the full width at half maximum (FWHM) cannot be clearly determined, so we calculate the full width at zero intensity (FWZI), which was obtained as the width where the sum of the fitted Gaussians of each source (see Fig. 2) is above 0.5 mK. The FWZI of our sample has a median value of 661 km s−1.

Table 3.

Derived parameters.

We derived the integrated CO luminosities, measured in K km s−1 pc2, via

(1)

(Solomon et al. 1992), where SCOΔv is the velocity integrated flux (Jy km s−1), νobs is the observed frequency (GHz), DL is the luminosity distance (Mpc), and z is the redshift of each source, which was obtained from a visual determination of the center of the spectral profile. We use a point source sensitivity of Jy K−1. Considering that νrest = νobs(1 + z) and substituting νrest(12CO) = 115.271 GHz and νrest(13CO) = 110.201 GHz, we can rewrite Eq. (1) in the useful form

(2)

where A12CO = 2.45 and A13CO = 2.68.

Three sources in our sample have available archive CO observations (Sanders et al. 1991) with the National Radio Astronomy Observatory (NRAO) 12 m telescope. Their CO flux for IRAS 22491−1808 ((55.0 ± 11.0)×108 K km s−1 pc2) is compatible with our results. On the other hand, their IRAS F05189−2524 and IRAS F14348−1447 measurements ((47.9 ± 9.6)×108 and (123.0 ± 24.6)×108 K km s−1 pc2, respectively), although significantly higher, most likely due to extended emission and the larger FWHM of the NRAO 12 m telescope (55 arcsec), are also compatible with our result within 2σ. To take the extended emission into account, we have performed aperture photometry as detailed in Sect. 5.1.

We obtained the molecular gas mass (MH2) from the integrated CO intensities assuming a constant CO-to-H2 conversion factor, α = 1.8 M⊙ (K km s−1 pc2)−1. The derivation of this factor is also explained in detail in Sect. 5.1.

5. Discussion

The relationship between the molecular gas content and the star formation properties (rate, efficiency, or depletion time) has been thoroughly studied (e.g., Leroy et al. 2008; Daddi et al. 2010; Genzel et al. 2010). Our study allows us to constrain several of these correlations with a large and uniformly observed sample. However, to that end we first need to investigate whether the conversion between CO and H2, α, is identical for local spiral galaxies and (U)LIRGs, as is often assumed, and determine its value.

5.1. Gas-to-dust ratio and determination of α

There are extensive discussions in the literature over the proper value of α to use when deriving molecular gas masses of (U)LIRGs (e.g., Solomon et al. 1997; Downes & Solomon 1998; Yao et al. 2003; Papadopoulos et al. 2012b; Bolatto et al. 2013). Prior to 1997, the standard was to make use of the value of α derived for the Milky Way, αMW ≃ 4 M⊙ (K km s−1 pc2)−1, with the reasoning that the molecular gas was bound in physically distinct, virialized clouds, in which increases (decreases) in the temperature of the gas, T, were offset by decreases (increases) in the gas density, ρ; that is,

(3)

(e.g., Scoville & Sanders 1987). However, arguments based on estimates of dynamical masses in (U)LIRGs led to the hypothesis that αMW was too high for this type of object. That is, the dynamical masses of (U)LIRGs as traced by CO kinematics were lower than the gas masses derived using αMW – and therefore the value of α in these extreme starburst galaxies should be at least proportionally lower (e.g., Downes & Solomon 1998). It was speculated that a primary difference between normal spiral galaxies and (U)LIRGs is that the “inter-cloud” medium regions of the latter population likely contain significant amounts of molecular gas (Solomon et al. 1997); this means that the molecular gas distribution is more uniform within the starburst region, invalidating the Milky Way assumption of discrete molecular clouds.

To address this issue, in this paper we assume that (i) the relative mass fraction of atomic and molecular hydrogen is similar among our galaxies (MHI/MH2 = γ), and (ii) any observed offset is driven by the physics setting the value of α for each population. Therefore, we assume that

(4)

where n and L subscripts are used for normal and LIRGs, respectively (see Bolatto et al. 2013, for an extensive discussion of dust-based conversion factor determinations). To proceed, we used for comparison the Key Insights on Nearby Galaxies: a Far-Infrared Survey with Herschel (KINGFISH)4 sample of local spiral galaxies observed with Herschel by Dale et al. (2012) that have pre-existing CO measurements in two surveys: the FCRAO extragalactic CO survey (Young et al. 1995), with 12CO(1-0) measurements, and the HERACLES survey from Leroy et al. (2009), with 12CO(2–1) observations, for which we have used a conversion factor of R21 = 0.8 for the conversion between 12CO(2–1) and 12CO(1–0) as suggested by the authors (Leroy et al. 2009). Both sets of data encompass most of the galaxies’ emission. In particular, the FCRAO sample was observed with a 14 m dish (i.e., FWHM as large as ≃45 arcsec), while the HERACLES galaxies were spatially mapped with the Heterodyne Receiver Array (HERA) multi-pixel receiver on the IRAM-30 m telescope.

There is a correlation between the gas-to-dust ratio and both the stellar mass (Cortese et al. 2016) and metallicity (e.g., Rémy-Ruyer et al. 2014). These two correlations are likely linked through the mass-metallicity relation (Tremonti et al. 2004). To check whether we expect a variation of gas-to-dust ratios among our samples, we compared with the Two Micron All-Sky Survey (2MASS) H-band luminosity, which is a first order tracer of the stellar mass of galaxies. As shown in Fig. 3, we do not find any trend, either in our sample or in the comparison FCRAO or HERACLES sources, so no stellar mass correction was applied to our derived gas-to-dust ratios. The reason why a clear dependency is not seen in the figure is likely to be in the mass-metallicity relation itself: while we expect a difference in metallicity of ∼0.1 dex for a stellar mass variation of two orders of magnitude (the range of GOALS galaxies is 9.5 <  log(M⋆) < 11.5) (Torrey et al. 2018), there is a large scatter between the two magnitudes, of approximately ∼0.2 − 0.3 dex. This scatter is the cause of why we do not see variations with the gas-to-dust ratio over the traced range of stellar masses. From Fig. 3 it is also noticeable that two sources from the FCRAO comparison sample (NGC 3077 and NGC 4569) have significantly lower H-band luminosities than any other source in this study. These were excluded from the analysis below, as they are not representative of the global characteristics of both populations.

thumbnail Fig. 3.

Ratio between the CO luminosity and the dust mass as a function of the rest-frame H-band luminosity, tracer of stellar mass. There is no obvious trend in our sample (in black) or in the local comparison samples (in red). Given the low H-band luminosity of NGC 3077 and NGC 4569, these were excluded from the comparison. Details are given in the main text.

To obtain the dust properties of the galaxies, both for our sources and for the local comparison samples, we constructed far infrared (FIR) spectral energy distributions (SEDs) using the new Herschel photometric catalog by (Chu et al. 2017) between 70 and 350 μm in order to perform a model fitting. Although the angular resolution of the IRAM-30 m telescope (∼22″) is generally sufficient to encompass most of the FIR extension of each galaxy, this is not always the case, as shown in the left panels of the molecular gas observations of Figs. 2 and A.1, where we have plotted the IRAM beam sizes over the Herschel 70 μm images. In order to compare gas (derived from CO) and dust (derived from FIR) properties, it is essential to consider the same apertures for both datasets. To ensure this, we convolved our Herschel images to the angular resolution of our IRAM-30 m data using Gaussian smoothing, and performed aperture photometry centered in the IRAM-30 m pointing position. We did not smooth our Herschel Spectral and Photometric Imaging Receiver (SPIRE) 350 μm images, which already have a resolution (∼25″) comparable with the 12CO measurements. We excluded our 500 μm images due to their coarser resolution than the IRAM-30 m beam.

We then fit each SED to an optically thin modified blackbody to derive the dust temperatures, Tdust, and masses, Mdust for each galaxy (see Appendix B). To calculate the dust masses, Scoville et al. (2016) argue for the use of a common mass-weighted dust temperature for all sources (Tdust = 25 K), instead of that obtained from their individual SED fits, which is more representative from localized warm, luminous regions. In this paper we follow this strategy, so we note that any comparison between samples must take this difference into account. For our sample, the use of a fixed Tdust = 25 K yields an average Mdust 1.53 times higher than when a SED fitted temperature is used.

By integrating below the fitted blackbody we directly obtain the luminosity between 42.5 and 122.5 μm, LFIR. Additionally, we also calculate the total infrared (TIR) luminosity (between 3 and 1100 μm, LTIR), making use of the prescription provided by Dale & Helou (2002):

(5)

using the Spitzer Multiband Imaging Photometer (MIPS) 24 μm data from Mazzarella et al. (in prep.) for our galaxies (after applying the same Gaussian smoothing described above), and the local sample data from Dale et al. (2007, 2009) and Engelbracht et al. (2008). We note that the TIR luminosities are obtained from galaxy-integrated photometry, and thus are not matched to the IRAM beam. All fitted parameters (plus LTIR) are presented in Table 4. For completeness, we provide as well the galaxy-integrated parameters obtained by using the total flux for each filter (including SPIRE 500 μm in this case). Unless specifically mentioned otherwise, throughout this paper we always refer to or use the parameters obtained from the SED fitting to the aperture-matched photometry. For details on the modified blackbody SED fitting, we refer the reader to Appendix B.

Table 4.

Derived dust parameters and luminosities for our (U)LIRG sample.

In Fig. 4 we show the gas-to-dust mass ratio (MH2/Mdust) for both our (U)LIRGs and the local control sample (FCRAO + HERACLES) as a function of the star formation rate (SFR) surface density (ΣSFR; obtained from Leroy et al. 2013 and Díaz-Santos et al. 2017), showing that the two populations have distinctly different ΣSFR and thus physical conditions (e.g., Díaz-Santos et al. 2017). The top panels of the figure show the gas-to-dust mass ratios obtained by deriving the dust masses based on the fitted 250 μm continuum, using a mass absorption coefficient of κ(250 μm) = 0.48 m2 kg−1 (see Appendix B for details) and by leaving Tdust and β as free parameters. The middle panels are the same as the top, but for a fixed emissivity index of β = 1.8 (Planck Collaboration XXI 2011). Finally, the bottom panels show the gas-to-dust mass ratios obtained by fixing β and assuming a fixed 25 K dust temperature for every source, as proposed by Scoville et al. (2016). For the remainder of the discussion we have adopted the results from the latter method, while we occasionally refer to the results obtained when letting Tdust free.

thumbnail Fig. 4.

Gas-to-dust mass ratio for both the reference sample, consisting of HERACLES (red diamonds) and FCRAO (red squares) sources, and our (U)LIRG sample (black circles) as a function of ΣSFR. Horizontal lines show the median value for each sample, and shaded areas indicate their median absolute deviations. Top panels: Mdust has been obtained leaving β as a free parameter in the SED fit and using the fitted Tdust to derive dust mass. Middle panels: emissivity index has been fixed to β = 1.8, but Mdust is still obtained from the fitted dust temperatures. Finally, in the bottom panels, emissivity is fixed to 1.8, and dust masses are obtained assuming a fixed 25 K dust temperature (see main text for further details). Left panels: results of using a Milky Way CO-to-H2 conversion factor (α = 4). To make the gas-to-dust mass ratio of (U)LIRGs consistent with the reference sample, α has been modified to the value quoted in the right panels. For the remainder of this work, a fixed dust emissivity of β = 1.8 is assumed, and we adopt a CO-to-H2 factor of α = 1.8 for (U)LIRGs, as required to make the median gas-to-dust mass ratio of (U)LIRGs match that of the reference sample of (non-LIRG) spiral galaxies.

If a Milky Way α is adopted for the reference sample of normal star-forming galaxies, we find that in order to match the offset between the median gas-to-dust ratio of (U)LIRGs relative to the reference sample, within their median absolute deviations, it is necessary to adopt a value (K km s−1 pc2)−1, assuming a fixed Tdust. If we instead use the dust temperatures from SED fitting to derive the dust masses, we require in order to match the gas-to-dust ratios. Our derived value of α is compatible with the values derived by Downes & Solomon (1998, α = 0.8), Papadopoulos et al. (2012b, α = 0.6 ± 0.2), and Scoville et al. (2015) for the (U)LIRG Arp 220 (α ∼ 2).

5.2. Impact of varying ISM assumptions

We stress that our derived value of α strongly depends on two assumptions: a constant gas-to-dust ratio and a constant relative fraction of atomic to molecular hydrogen gas, γ. Some studies have claimed evidence of the gas-to-dust ratio of (U)LIRGs being compatible with that of normal galaxies (see, e.g., Wilson et al. 2008). However, these ratios are calibrated based on a lower value of α for (U)LIRGs, falling in a circular argument.

In any case, even if either of the two ratios is proven to be different in LIRGs, the following relation derived from Eq. (4) and the offset between samples seen in Fig. 4 should still hold:

(6)

We note that if the assumption is made that the gas-to-dust mass ratio and α are constant, but instead we vary the relative fraction of atomic to molecular gas between the two samples, the end result would be a decrease in γ for the (U)LIRGs. In particular, we would get (1 + γn)/(1 + γL)=2.2. This equation yields unphysical negative γL values for any γn value below 1.2. The observed difference in Fig. 4 between the two is unlikely thus to be ascribed solely to a different γ.

5.3. Star formation efficiencies and gas depletion timescales

Figure 5 shows the FIR (derived from the modified blackbody SED fits) and the TIR (obtained from Eq. (5)) luminosities as a function of the for our sample of GOALS galaxies and for the local comparison samples. In optically thick environments, and in the absence of significant dust heating by an active galactic nucleus (AGN), the plot of LTIR, FIR versus is essentially a comparison between the energy generated by the embedded starburst(s) versus the total reservoir of gas available to form new stars.

thumbnail Fig. 5.

Total and far IR luminosities versus the CO luminosity. Solid lines show linear fits to our (U)LIRG sample, yielding and . Dashed lines are fits including the comparison samples, which also show linear slopes when using LTIR (0.97 ± 0.06) or LFIR (1.05 ± 0.06). To avoid AGN contamination, only those (U)LIRGs with an AGN bolometric fraction <0.20 (obtained from Díaz-Santos et al. 2017) were plotted and fitted.

For the purpose of fitting the data, we excluded (U)LIRGs where an AGN contributes > 20% to the energy output, where we used the AGN bolometric fractions obtained from the combination of several mid-IR diagnostics (Díaz-Santos et al. 2017). The reason behind this exclusion is to avoid contamination in the estimation of the star formation rates, efficiencies, and gas depletion times, as strong AGN can contribute significantly to the FIR luminosity. These sources were not excluded from the analysis in Sect. 5.1 because there is not a known dependence of gas-to-dust mass ratio with AGN fraction, and our size sample does not allow us to study possible effects on it. No sources were removed from the local comparison sample, which is not dominated by AGN by design.

Three sources were discarded based on the above AGN criterion: NGC 0958, UGC 05101, and IRAS F05189−2524. Furthermore, to avoid the instability of ordinary least-squares fits when both dependent and independent variables have an associated error, we followed the same approach as Greve et al. (2014) and used a Bayesian method to fit the data. Specifically, we used Josh Mayer’s Python port5 of the LINMIX_ERR IDL package (Kelly 2007).

The combined fit (our (U)LIRG sample and the local, normal, star-forming sources) to the data in Fig. 5 has the functional form

(7)

with median Pearson correlation coefficients of ρ = 0.923 and ρ = 0.915, respectively, and a robust statistical significance (p-values of 4.1 × 10−28 and 5.0 × 10−26, respectivey). We note that LTIR is derived from integrated-galaxy photometry (see Eq. (5)), while LFIR is obtained from integrating the fit to the aperture-matched SEDs. More luminous galaxies, with warmer dust, will have a larger contribution to the emission from shorter wavelengths (our fit uses 70 <  λ/μm <  350), and thus LFIR could be underestimated for those sources. We find, however, that there is no significant difference in the use of LTIR or LFIR for our sample. By comparison, Greve et al. (2014) derived a linear value for the slope of (1.00 ± 0.05) and (0.99 ± 0.04) for L(8 − 1000 μm) and L(50 − 300 μm), respectively. Their luminosity dynamic range was 10.29 ≤ log(L(8 − 1000μm))≤12.56. We also note that their sample included high-z galaxies which, if they had not been included, would have caused the slope to be sub-linear. We only find a very slight steepening in the slope of the fit to the (U)LIRGs with respect to the local comparison sample, but not as pronounced as found by Gao & Solomon (2004), where a clear super-linear slope is derived.

A way of interpreting the relation between infrared and CO luminosities is through the star formation efficiency, which is the ratio of the total energy from young massive stars per unit of star-forming molecular gas, and which is usually represented by . However, the use of can be misleading, as it cannot be directly converted into a MH2 estimate without the use of an α conversion factor, which we showed to vary between the samples in Sect. 5.1.

We can rework the above in terms of the gas depletion timescales, tdep = M(H2)/SFR, where the molecular gas mass is derived using α = 1.8 M⊙ (K km s−1 pc2)−1 for (U)LIRGs (see Sect. 5.1), and the Milky Way value for the local sample. The star formation rate (SFR) is obtained from the infrared and UV luminosity (see Murphy et al. 2011)

(8)

where we have used our aperture-matched, SED-derived FIR luminosity, while the UV luminosities (integrated luminosity within the GALEX far ultraviolet (FUV) filter; λeff = 1528 Å) were obtained from Howell et al. (2010) for the (U)LIRGs, and from the GALEX Ultraviolet Atlas of Nearby Galaxies (Gil de Paz et al. 2007) for the local comparison sample. Most of the UV emission is expected to be inside the IRAM-30 m beam, thus any correction would be within the errors.

Figure 6 presents the variation of tdep as a function of LTIR, FIR. Fits to the trends considering all three samples combined yield the correlations

(9)

thumbnail Fig. 6.

Depletion time as a function of TIR and FIR luminosities. Solid lines are fits to the (U)LIRG sample, where log(tdep)  =  (−0.25 ± 0.10)log(LTIR)+(11.54 ± 1.05) and log(tdep)  =  (−0.26 ± 0.09)log(LFIR)+(11.61 ± 0.96). Dashed lines are a fit to the combined sample and yield log(tdep)  =  (−0.19 ± 0.07)log(LTIR)+(10.89 ± 0.77) and log(tdep)  =  (−0.20 ± 0.06)log(LFIR)+(10.95 ± 0.67). This trend implies that gas is consumed faster in (U)LIRGs and thus star formation is more efficient in these systems, compared to lower luminosity spiral galaxies.

with median Pearson correlation coefficients of ρ = −0.396 and ρ = −0.454, respectively, and p-values of 0.006 and 0.001, showing a moderately strong statistical significance.

We obtain a median tdep of 1.3 Gyr for the local sample, compared to the 2.1 Gyr from Kennicutt (1998) or 2.35 Gyr from Bigiel et al. (2011). This timescale is obtained assuming there is not gas replenishing and that there is a constant star formation rate. We note that tdep increases by a factor of two to three if interstellar gas recycling is considered (Ostriker & Thuan 1975; Kennicutt et al. 1994). Nevertheless, the above correlation shows that LTIR = 1011 L⊙ LIRGs would deplete their available gas in ∼630 Myr, whereas LTIR = 1012 L⊙ ULIRGs would deplete their gas in ∼400 Myr, a period more than three times shorter than for local normal spiral galaxies. The compression of the molecular gas clouds due to large-scale shocks, which would enhance star formation, has been proposed to account for this difference (Jog & Solomon 1992; Barnes 2004; Genzel et al. 2010). However, the quoted depletion times are obtained from the total molecular gas (as traced by 12CO), and not specifically from the dense gas phase of the molecular medium, which is expected to be more closely associated to regions where star formation is imminent.

We note the strong dependence of depletion time (Eq. (9)) with αCO. Indeed, if dust masses were derived using the fitted Tdust instead of the fixed 25 K, the relation would be log(tdep)= − 0.36log(LTIR)+12.46, implying an even larger difference (one order of magnitude) in the depletion time between (U)LIRGs and the comparison local sample.

Finally, if fitted Tdust are used to estimate the dust masses, our data also show a clear correlation between the depletion time and the dust temperature as shown in Fig. 7. The fit of the combined data yields

(10)

thumbnail Fig. 7.

Depletion time versus dust temperature, using Tdust fitted values to obtain Mdust. Dust tmeperature is obtained from the SED model fit. The solid line represents the linear fit for the (U)LIRGs, yielding log(tdep)=(−5.5 ± 1.0)×10−2 Tdust + (10.1 ± 0.3). The dash lines represent the best fit considering also our local comparison sample; the fit yields log(tdep)=(−6.9 ± 0.8)×10−2 Tdust + (10.6 ± 0.2),

with ρ  =   − 0.812, and a robust statistical significance (p-value of 1.1 × 10−7). This trend shows a very sensitive variation, with depleting times being one order of magnitude lower with an increase of ∼15 K. In other words, the star formation efficiency (∝1/tdep) increases by a factor of ten by such variation in the dust temperature.

5.4. The 12CO / 13CO line intensity ratio

In this sub-section, we examine the relationship between the 12CO/13CO line intensity ratio and the dust temperature. In Fig. 8 we present a plot of 12CO/13CO for the (U)LIRGs in our sample versus the 60 μm–100 μm IRAS flux density ratio f60/f100, which is used as a proxy for the dust temperature. We do not use here our SED-fit-derived Tdust so as to be able to systematically compare with previous studies on LIRGs (for which Herschel photometry is not available). We have confirmed nonetheless the very good correlation between f60/f100 and the derived Tdust for our sample, finding Tdust  =  (14.1 ± 1.2)(f60/f100)  +  (20.6  ±  0.8). The data from the present study are compared with published results from Aalto et al. (1995) and Costagliola et al. (2011). The former is formed of 31 local spiral galaxies, starbursts, interacting systems, and luminous mergers, while the latter includes a representation of 12 Seyferts, starbursts, and LIRGs. Our results are in agreement with those studies, finding lower values of 12CO/13CO for f60/f100 <  0.8, and a relatively steep enhancement for f60/f100 >  0.8. This cutoff point corresponds to ∼32 K. This general trend is also in agreement with Milky Way measurements of molecular clouds (Barnes et al. 2015). Only two of the sources in our sample present a lower-limit value that seems at odds with this behavior, showing too large 12CO/13CO ratios (> 21.4 and > 27.6) for their FIR color (0.48 and 0.59). These are NGC 6907 and UGC 05101, and they are marked in Fig. 8 with their names.

thumbnail Fig. 8.

12CO over 13CO intensity ratio plotted vs. the IRAS flux ratio f60/f100, used as a proxy for the dust temperature. For the line ratios, the uncertainties were derived using a Monte Carlo simulation using 10 000 samples and following a similar prescription to Crocker et al. (2012). The sources are from different samples: this work (black circles), Aalto et al. (1995, blue squares), and Costagliola et al. (2011, green diamonds). Errors are plotted at 1σ level, although x-axis errors are not appreciable for many sources. The two labeled sources are at odds with the rest of the sample for their observed f60/f100 ratio.

The above relation can be explained as a result of the decreasing optical depth of the 12CO line with increasing ISM temperature (e.g., Young & Sanders 1986; Aalto et al. 1995). Increased linewidths in diffuse or turbulent gas may also result in decreased line optical depths and elevated line ratios (see, e.g., Polk et al. 1988; Aalto et al. 1995, 2010; König et al. 2016).

In addition to optical depth effects, the relative 12CO and 13CO abundances ratio will impact the intensity ratio. The less abundant isotopomer of 13CO will become selectively photodissociated in diffuse gas since it cannot self-shield like 12CO. Furthermore, stellar nucleosynthesis will alter the 12C/13C abundance ratio and low-metallicity gas is expected to have high 12C/13C ratios (see, e.g., Casoli et al. 1992; Henkel et al. 2014; Tang et al. 2019). The ejecta of massive stars are also expected to have higher 12C/13C abundance ratios, which means that in the early stages of a starburst 12CO/13CO abundance ratios may be higher. Indeed, there seems to be an enrichment of the ISM due to a young starburst and/or a top-heavy initial mass function (Sliwa et al. 2017).

6. Summary

We observed 55 (U)LIRGs with the IRAM-30 m Telescope. In this work, we have focused on the 12CO(1 − 0) transition as a tracer of molecular gas. We summarize our results as follows:

  1. We observed 12CO and 13CO simultaneously, in the same band, obtaining detection rates of 96% and 56% for 12CO and 13CO, respectively, as expected from 13CO being much less abundant than 12CO.

  2. We have used Herschel data to construct the far infrared SED of the emitting region inside the IRAM-30 m beam for each galaxy in our sample, and fitted the SED to a modified blackbody model, obtaining the dust masses and temperatures, as well as LFIR. We also have systematically fitted local galaxies from HERACLES and FCRAO, for which both CO and Herschel data are available, to be used as a local comparison sample. Complementarily, we have used MIPS data to derive the total IR luminosities, LTIR, for both samples.

  3. We have determined an average CO-to-H2 conversion factor for (U)LIRGs of (K km s−1 pc2)−1, ∼2.2 times smaller than the accepted conversion factor for local spiral galaxies, for an assumed constant gas-to-dust mass ratio between the local comparison sample and the (U)LIRGs sample. This value is obtained by assuming a fixed dust temperature of 25 K for every source. If the SED fitted temperatures are used instead, the average value of α for (U)LIRGs would be .

  4. We confirm the close linear correlation between the CO luminosity and LTIR, FIR. We have also found an enhancement in the star formation efficiency for more IR-luminous systems. Consequently, the depletion time for these systems is shorter, following a log − log correlation with LIR, TIR. However, this effect with tdep is not observed in the higher density phase of molecular gas. When Mdust are derived from fitted Tdust, the tdep also shows a clear decreasing trend with dust temperature, implying an increase of one order of magnitude in the star formation efficiency per increase of ∼15 K.

  5. We have re-examined the variation between the ratio of 12CO and its isotopologue 13CO with the dust temperature, as traced by the proxy f60/f100. Our data confirm previous results, with cooler galaxies having lower 12CO/13CO ratios, with a steep increase above f60/f100 ∼ 0.8.

1

Based on observations carried out with the IRAM-30 m Telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany) and IGN (Spain).

Acknowledgments

We thank the anonymous referee for the useful comments. We also thank Nick Scoville for his discussion and comments on the paper. We are grateful to Manuel González for his help in the preparation of the scripts and during the observations. This work is based on observations carried out under project numbers 099-10, 092-11, 227-11, 076-12, 222-13, and D01-13 with the 30m telescope. IRAM is supported by INSU/CNRS (France), MPG (Germany), and IGN (Spain). We thank the director of IRAM 30m for the approval of the discretionary time requested. RHI, MAPT, and AA acknowledge support from the Spanish MINECO through grants AYA2012-38491-C02-02 and AYA2015-63939-C2-1-P. G.C.P. was supported by a FONDECYT Postdoctoral Fellowship (No. 3150361). G.C.P. also acknowledges support from the University of Florida. G.C.P. and A.S.E. were supported by the NSF grant AST 1109475. A.S.E. was also supported by the Taiwan, R.O.C. Ministry of Science and technology grant MoST 102-2119-M-001-MY3. T.D.-S. acknowledges support from ALMA-CONICYT project 31130005 and FONDECYT regular project 1151239. This work was supported in part by National Science Foundation grant No. PHYS-1066293 and the hospitality of the Aspen Center for Physics. 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.

References

  1. Aalto, S., Booth, R. S., Black, J. H., & Johansson, L. E. B. 1995, A&A, 300, 369 [NASA ADS] [Google Scholar]
  2. Aalto, S., Beswick, R., & Jütte, E. 2010, A&A, 522, A59 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  3. Armus, L., Mazzarella, J. M., Evans, A. S., et al. 2009, PASP, 121, 559 [NASA ADS] [CrossRef] [Google Scholar]
  4. Barnes, J. E. 2004, MNRAS, 350, 798 [NASA ADS] [CrossRef] [Google Scholar]
  5. Barnes, P. J., Muller, E., Indermuehle, B., et al. 2015, ApJ, 812, 6 [NASA ADS] [CrossRef] [Google Scholar]
  6. Bianchi, S. 2013, A&A, 552, A89 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  7. Bigiel, F., Leroy, A. K., Walter, F., et al. 2011, ApJ, 730, L13 [NASA ADS] [CrossRef] [Google Scholar]
  8. Blain, A. W., Barnard, V. E., & Chapman, S. C. 2003, MNRAS, 338,733 [NASA ADS] [CrossRef] [Google Scholar]
  9. Bolatto, A. D., Wolfire, M., & Leroy, A. K. 2013, ARA&A, 51, 207 [Google Scholar]
  10. Bryant, P. M., & Scoville, N. Z. 1999, AJ, 117, 2632 [NASA ADS] [CrossRef] [Google Scholar]
  11. Carter, M., Lazareff, B., Maier, D., et al. 2012, A&A, 538, A89 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  12. Casoli, F., Dupraz, C., & Combes, F. 1992, A&A, 264, 55 [NASA ADS] [Google Scholar]
  13. Chu, J. K., Sanders, D. B., Larson, K. L., et al. 2017, ApJS, 229, 25 [NASA ADS] [CrossRef] [Google Scholar]
  14. Cortese, L., Bekki, K., Boselli, A., et al. 2016, MNRAS, 459, 3574 [NASA ADS] [CrossRef] [Google Scholar]
  15. Costagliola, F., Aalto, S., Rodriguez, M. I., et al. 2011, A&A, 528, A30 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  16. Crocker, A., Krips, M., Bureau, M., et al. 2012, MNRAS, 421, 1298 [NASA ADS] [CrossRef] [Google Scholar]
  17. Daddi, E., Elbaz, D., Walter, F., et al. 2010, ApJ, 714, L118 [Google Scholar]
  18. Dale, D. A., & Helou, G. 2002, ApJ, 576, 159 [NASA ADS] [CrossRef] [Google Scholar]
  19. Dale, D. A., Gil de Paz, A., Gordon, K. D., et al. 2007, ApJ, 655, 863 [NASA ADS] [CrossRef] [Google Scholar]
  20. Dale, D. A., Cohen, S. A., Johnson, L. C., et al. 2009, ApJ, 703, 517 [NASA ADS] [CrossRef] [Google Scholar]
  21. Dale, D. A., Aniano, G., Engelbracht, C. W., et al. 2012, ApJ, 745, 95 [NASA ADS] [CrossRef] [Google Scholar]
  22. Davies, J. I., Bianchi, S., Cortese, L., et al. 2012, MNRAS, 419, 3505 [NASA ADS] [CrossRef] [Google Scholar]
  23. Díaz-Santos, T., Alonso-Herrero, A., Colina, L., et al. 2010, ApJ, 711, 328 [NASA ADS] [CrossRef] [Google Scholar]
  24. Díaz-Santos, T., Charmandaris, V., Armus, L., et al. 2011, ApJ, 741, 32 [NASA ADS] [CrossRef] [Google Scholar]
  25. Díaz-Santos, T., Armus, L., Charmandaris, V., et al. 2017, ApJ, 846, 32 [NASA ADS] [CrossRef] [Google Scholar]
  26. Downes, D., & Solomon, P. M. 1998, ApJ, 507, 615 [NASA ADS] [CrossRef] [Google Scholar]
  27. Draine, B. T., & Lee, H. M. 1984, ApJ, 285, 89 [Google Scholar]
  28. Engelbracht, C. W., Rieke, G. H., Gordon, K. D., et al. 2008, ApJ, 678, 804 [NASA ADS] [CrossRef] [Google Scholar]
  29. Gao, Y., & Solomon, P. M. 2004, ApJ, 606, 271 [NASA ADS] [CrossRef] [Google Scholar]
  30. Genzel, R., Tacconi, L. J., Gracia-Carpio, J., et al. 2010, MNRAS, 407, 2091 [NASA ADS] [CrossRef] [Google Scholar]
  31. Gil de Paz, A., Boissier, S., Madore, B. F., et al. 2007, ApJS, 173, 185 [NASA ADS] [CrossRef] [Google Scholar]
  32. Greve, T. R., Leonidaki, I., Xilouris, E. M., et al. 2014, ApJ, 794, 142 [NASA ADS] [CrossRef] [Google Scholar]
  33. Haan, S., Surace, J. A., Armus, L., et al. 2011, AJ, 141, 100 [NASA ADS] [CrossRef] [Google Scholar]
  34. Henkel, C., Asiri, H., Ao, Y., et al. 2014, A&A, 565, A3 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  35. Hinshaw, G., Larson, D., Komatsu, E., et al. 2013, ApJS, 208, 19 [NASA ADS] [CrossRef] [Google Scholar]
  36. Howell, J. H., Armus, L., Mazzarella, J. M., et al. 2010, ApJ, 715, 572 [NASA ADS] [CrossRef] [Google Scholar]
  37. Iwasawa, K., Sanders, D. B., Teng, S. H., et al. 2011, A&A, 529, A106 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  38. Jog, C. J., & Solomon, P. M. 1992, ApJ, 387, 152 [NASA ADS] [CrossRef] [Google Scholar]
  39. Kelly, B. C. 2007, ApJ, 665, 1489 [NASA ADS] [CrossRef] [Google Scholar]
  40. Kennicutt, Jr., R. C. 1998, ARA&A, 36, 189 [Google Scholar]
  41. Kennicutt, Jr., R. C., Tamblyn, P., & Congdon, C. E. 1994, ApJ, 435, 22 [Google Scholar]
  42. Kim, D.-C., Evans, A. S., Vavilkin, T., et al. 2013, ApJ, 768, 102 [Google Scholar]
  43. König, S., Aalto, S., Muller, S., et al. 2016, A&A, 594, A70 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  44. Leroy, A. K., Walter, F., Brinks, E., et al. 2008, AJ, 136, 2782 [NASA ADS] [CrossRef] [Google Scholar]
  45. Leroy, A. K., Walter, F., Bigiel, F., et al. 2009, AJ, 137, 4670 [NASA ADS] [CrossRef] [Google Scholar]
  46. Leroy, A. K., Walter, F., Sandstrom, K., et al. 2013, AJ, 146, 19 [NASA ADS] [CrossRef] [Google Scholar]
  47. Murphy, E. J., Condon, J. J., Schinnerer, E., et al. 2011, ApJ, 737, 67 [NASA ADS] [CrossRef] [Google Scholar]
  48. Narayanan, D., Groppi, C. E., Kulesa, C. A., & Walker, C. K. 2005, ApJ, 630, 269 [NASA ADS] [CrossRef] [Google Scholar]
  49. Ostriker, J. P., & Thuan, T. X. 1975, ApJ, 202, 353 [NASA ADS] [CrossRef] [Google Scholar]
  50. Papadopoulos, P. P., van der Werf, P. P., Xilouris, E. M., et al. 2012a, MNRAS, 426, 2601 [NASA ADS] [CrossRef] [Google Scholar]
  51. Papadopoulos, P. P., van der Werf, P., Xilouris, E., Isaak, K. G., & Gao, Y. 2012b, ApJ, 751, 10 [NASA ADS] [CrossRef] [Google Scholar]
  52. Petric, A. O., Armus, L., Howell, J., et al. 2011, ApJ, 730, 28 [NASA ADS] [CrossRef] [Google Scholar]
  53. Planck Collaboration XXI. 2011, A&A, 536, A21 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  54. Polk, K. S., Knapp, G. R., Stark, A. A., & Wilson, R. W. 1988, ApJ, 332, 432 [NASA ADS] [CrossRef] [Google Scholar]
  55. Privon, G. C., Herrero-Illana, R., Evans, A. S., et al. 2015, ApJ, 814, 39 [NASA ADS] [CrossRef] [Google Scholar]
  56. Rémy-Ruyer, A., Madden, S. C., Galliano, F., et al. 2014, A&A, 563, A31 [NASA ADS] [CrossRef] [EDP Sciences] [Google Scholar]
  57. Sanders, D. B., Scoville, N. Z., & Soifer, B. T. 1991, ApJ, 370, 158 [NASA ADS] [CrossRef] [Google Scholar]
  58. Sanders, D. B., Mazzarella, J. M., Kim, D.-C., Surace, J. A., & Soifer, B. T. 2003, AJ, 126, 1607 [Google Scholar]
  59. Scoville, N. Z., & Sanders, D. B. 1987, in Interstellar Processes, eds. D. J. Hollenbach, & H. A. Thronson, Jr., Astrophys. Space Sci. Libr., 134, 21 [NASA ADS] [CrossRef] [Google Scholar]
  60. Scoville, N., Sheth, K., Walter, F., et al. 2015, ApJ, 800, 70 [NASA ADS] [CrossRef] [Google Scholar]
  61. Scoville, N., Sheth, K., Aussel, H., et al. 2016, ApJ, 820, 83 [NASA ADS] [CrossRef] [Google Scholar]
  62. Sliwa, K., Wilson, C. D., Aalto, S., & Privon, G. C. 2017, ApJ, 840, L11 [NASA ADS] [CrossRef] [Google Scholar]
  63. Soifer, B. T., Sanders, D. B., Neugebauer, G., et al. 1986, ApJ, 303, L41 [NASA ADS] [CrossRef] [Google Scholar]
  64. Solomon, P. M., Downes, D., & Radford, S. J. E. 1992, ApJ, 398, L29 [NASA ADS] [CrossRef] [Google Scholar]
  65. Solomon, P. M., Downes, D., Radford, S. J. E., & Barrett, J. W. 1997, ApJ, 478, 144 [NASA ADS] [CrossRef] [Google Scholar]
  66. Stierwalt, S., Armus, L., Surace, J. A., et al. 2013, ApJS, 206, 1 [NASA ADS] [CrossRef] [Google Scholar]
  67. Stierwalt, S., Armus, L., Charmandaris, V., et al. 2014, ApJ, 790, 124 [NASA ADS] [CrossRef] [Google Scholar]
  68. Tang, X. D., Henkel, C., Menten, K. M., et al. 2019, A&A, in press, https://doi.org/10.1051/0004-6361/201935603 [Google Scholar]
  69. Tinney, C. G., Scoville, N. Z., Sanders, D. B., & Soifer, B. T. 1990, ApJ, 362, 473 [NASA ADS] [CrossRef] [Google Scholar]
  70. Torrey, P., Vogelsberger, M., Hernquist, L., et al. 2018, MNRAS, 477, L16 [NASA ADS] [CrossRef] [Google Scholar]
  71. Tremonti, C. A., Heckman, T. M., Kauffmann, G., et al. 2004, ApJ, 613, 898 [NASA ADS] [CrossRef] [Google Scholar]
  72. Wilson, C. D., Petitpas, G. R., Iono, D., et al. 2008, ApJS, 178, 189 [NASA ADS] [CrossRef] [Google Scholar]
  73. Yamashita, T., Komugi, S., Matsuhara, H., et al. 2017, ApJ, 544, 96 [NASA ADS] [CrossRef] [Google Scholar]
  74. Yao, L., Seaquist, E. R., Kuno, N., & Dunne, L. 2003, ApJ, 588, 771 [NASA ADS] [CrossRef] [Google Scholar]
  75. Young, J. S., & Sanders, D. B. 1986, ApJ, 302, 680 [NASA ADS] [CrossRef] [Google Scholar]
  76. Young, J. S., Xie, S., Tacconi, L., et al. 1995, ApJS, 98, 219 [NASA ADS] [CrossRef] [Google Scholar]

Appendix A: Observed spectra and fitted Gaussian line components

Figure A.1 presents the same results as Fig. 2 for our complete sample. We have also tabulated in Table A.1 the Gaussian components that were fitted to the 12CO spectra.

thumbnail Fig. A.1.

Herschel images and IRAM-30 m spectra. Figure 2 provides details.

thumbnail Fig. A.1.

continued.

thumbnail Fig. A.1.

continued.

thumbnail Fig. A.1.

continued.

thumbnail Fig. A.1.

continued.

thumbnail Fig. A.1.

continued.

thumbnail Fig. A.1.

continued.

thumbnail Fig. A.1.

continued.

thumbnail Fig. A.1.

continued.

thumbnail Fig. A.1.

continued.

thumbnail Fig. A.1.

continued.

thumbnail Fig. A.1.

continued.

thumbnail Fig. A.1.

continued.

thumbnail Fig. A.1.

continued.

Table A.1.

Fitted Gaussian line components to the 12CO spectra.

Appendix B: Modified blackbody model SED fitting

Assuming that all dust grains have the same size and and composition, their emission can be modeled by an optically thin modified blackbody,

(B.1)

where S(ν) is the flux density, Q(ν) is the emissivity, B(ν, T) is the blackbody intensity, N and σ are the number of identical dust particles and their cross section, respectively, and D is the distance to the dust cloud.

We have used Herschel data from both PACS (70, 100, and 170 μm) and SPIRE (250 and 350 μm, excluding 500 μm for having a too coarse resolution) to construct the SED of each source. To do so, we smoothed the images to the FWHM of the IRAM-30 m observations, except for the 350 μm images, which already have an angular resolution comparable with the IRAM-30 m beam. We then used a χ2 minimization method to obtain the best model. The emissivity index β (where κ(ν)∝νβ) was fixed to a value of β = 1.8, to avoid degeneracies between β and Tdust in χ2 minimization fits (Blain et al. 2003).

We can rewrite Eq. (B.1) in terms of the dust mass, Md, as

(B.2)

where κ(ν) is the so-called grain absorption cross section per unit mass or mass absorption coefficient. This parameter is highly uncertain (see, e.g., Draine & Lee 1984; Davies et al. 2012; Bianchi 2013). For our model we have adopted an intermediate value of κ(250 μm)=0.48 m2 kg−1. Complementary to the dust masses and temperatures, we have derived LFIR from direct integration below the fitted curve between 42.5 and 122.5 μm. Figure B.1 shows an example for the fit in the galaxy NGC 0958.

thumbnail Fig. B.1.

SED fitting for NGC 0958. Red lines show the Herschel photometry with its uncertainty. The best model is shown as a solid blue line and the shaded area represents the uncertainty in the fit.

All Tables

Table 1.

Source list.

In the text
Table 2.

Measured parameters.

In the text
Table 3.

Derived parameters.

In the text
Table 4.

Derived dust parameters and luminosities for our (U)LIRG sample.

In the text
Table A.1.

Fitted Gaussian line components to the 12CO spectra.

In the text

All Figures

thumbnail Fig. 1.

Normalized histogram comparing LIR from the complete set of 202 GOALS galaxies and our observed sample. All LIR were obtained from Armus et al. (2009).
In the text
thumbnail Fig. 2.

Spectral line profiles for NGC 6286. Left panel: Herschel PACS 70 μm map (see Chu et al. 2017) with a logarithmic stretch to highlight the full extent of the infrared emission relative to the IRAM-30 m Telescope. Overlaid circles represent the pointing position and beam sizes (FWHM) corresponding to the 12CO and 13CO (inner), and HCN and HCO+ (outer) IRAM observations. The middle panel shows the continuum-subtracted CO spectra, fitted with Gaussian components. Velocity frame is defined according to the redshifts quoted in Table 3. Gray vertical lines correspond to the velocity integration limits of the FWZI. Right panel: continuum-subtracted spectra of 13CO (blue, solid line), HCN (red, dotted line), and HCO+ (green, dashed line) in the same velocity range as the CO spectrum. The spectra have been normalized to the peak of the CO line, and the normalization factor is shown for each line. The complete data set with all the observations, as well as a table with the fitted Gaussian components of the 12CO spectra is shown in Appendix A.
In the text
thumbnail Fig. 3.

Ratio between the CO luminosity and the dust mass as a function of the rest-frame H-band luminosity, tracer of stellar mass. There is no obvious trend in our sample (in black) or in the local comparison samples (in red). Given the low H-band luminosity of NGC 3077 and NGC 4569, these were excluded from the comparison. Details are given in the main text.
In the text
thumbnail Fig. 4.

Gas-to-dust mass ratio for both the reference sample, consisting of HERACLES (red diamonds) and FCRAO (red squares) sources, and our (U)LIRG sample (black circles) as a function of ΣSFR. Horizontal lines show the median value for each sample, and shaded areas indicate their median absolute deviations. Top panels: Mdust has been obtained leaving β as a free parameter in the SED fit and using the fitted Tdust to derive dust mass. Middle panels: emissivity index has been fixed to β = 1.8, but Mdust is still obtained from the fitted dust temperatures. Finally, in the bottom panels, emissivity is fixed to 1.8, and dust masses are obtained assuming a fixed 25 K dust temperature (see main text for further details). Left panels: results of using a Milky Way CO-to-H2 conversion factor (α = 4). To make the gas-to-dust mass ratio of (U)LIRGs consistent with the reference sample, α has been modified to the value quoted in the right panels. For the remainder of this work, a fixed dust emissivity of β = 1.8 is assumed, and we adopt a CO-to-H2 factor of α = 1.8 for (U)LIRGs, as required to make the median gas-to-dust mass ratio of (U)LIRGs match that of the reference sample of (non-LIRG) spiral galaxies.
In the text
thumbnail Fig. 5.

Total and far IR luminosities versus the CO luminosity. Solid lines show linear fits to our (U)LIRG sample, yielding and . Dashed lines are fits including the comparison samples, which also show linear slopes when using LTIR (0.97 ± 0.06) or LFIR (1.05 ± 0.06). To avoid AGN contamination, only those (U)LIRGs with an AGN bolometric fraction <0.20 (obtained from Díaz-Santos et al. 2017) were plotted and fitted.
In the text
thumbnail Fig. 6.

Depletion time as a function of TIR and FIR luminosities. Solid lines are fits to the (U)LIRG sample, where log(tdep)  =  (−0.25 ± 0.10)log(LTIR)+(11.54 ± 1.05) and log(tdep)  =  (−0.26 ± 0.09)log(LFIR)+(11.61 ± 0.96). Dashed lines are a fit to the combined sample and yield log(tdep)  =  (−0.19 ± 0.07)log(LTIR)+(10.89 ± 0.77) and log(tdep)  =  (−0.20 ± 0.06)log(LFIR)+(10.95 ± 0.67). This trend implies that gas is consumed faster in (U)LIRGs and thus star formation is more efficient in these systems, compared to lower luminosity spiral galaxies.
In the text
thumbnail Fig. 7.

Depletion time versus dust temperature, using Tdust fitted values to obtain Mdust. Dust tmeperature is obtained from the SED model fit. The solid line represents the linear fit for the (U)LIRGs, yielding log(tdep)=(−5.5 ± 1.0)×10−2 Tdust + (10.1 ± 0.3). The dash lines represent the best fit considering also our local comparison sample; the fit yields log(tdep)=(−6.9 ± 0.8)×10−2 Tdust + (10.6 ± 0.2),
In the text
thumbnail Fig. 8.

12CO over 13CO intensity ratio plotted vs. the IRAS flux ratio f60/f100, used as a proxy for the dust temperature. For the line ratios, the uncertainties were derived using a Monte Carlo simulation using 10 000 samples and following a similar prescription to Crocker et al. (2012). The sources are from different samples: this work (black circles), Aalto et al. (1995, blue squares), and Costagliola et al. (2011, green diamonds). Errors are plotted at 1σ level, although x-axis errors are not appreciable for many sources. The two labeled sources are at odds with the rest of the sample for their observed f60/f100 ratio.
In the text
thumbnail Fig. A.1.

Herschel images and IRAM-30 m spectra. Figure 2 provides details.
In the text
thumbnail Fig. A.1.

continued.
In the text
thumbnail Fig. A.1.

continued.
In the text
thumbnail Fig. A.1.

continued.
In the text
thumbnail Fig. A.1.

continued.
In the text
thumbnail Fig. A.1.

continued.
In the text
thumbnail Fig. A.1.

continued.
In the text
thumbnail Fig. A.1.

continued.
In the text
thumbnail Fig. A.1.

continued.
In the text
thumbnail Fig. A.1.

continued.
In the text
thumbnail Fig. A.1.

continued.
In the text
thumbnail Fig. A.1.

continued.
In the text
thumbnail Fig. A.1.

continued.
In the text
thumbnail Fig. A.1.

continued.
In the text
thumbnail Fig. B.1.

SED fitting for NGC 0958. Red lines show the Herschel photometry with its uncertainty. The best model is shown as a solid blue line and the shaded area represents the uncertainty in the fit.
In the text

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