High Dense Gas Fraction in Intensely Star-forming Dusty Galaxies

Figure 1 shows the lensed stellar emission observed with HST (the foreground lensing source has been subtracted using GALFIT) compared to the resolved dust (observed by SMA and PdBI), molecular gas (observed by PdBI), and radio continuum (observed by VLA) emission. Dust absorbs the rest-frame UV stellar light emitted by massive OB stars at rest-frame UV, which is, in turn, re-emitted at FIR wavelengths. Therefore, there are two main components contributing to the total SFR in star-forming galaxies, one unobscured component traced by rest-frame UV emission and one obscured component traced by FIR emission. This simplified picture is exactly what we are witnessing in Figure 1. The dust emission detected by the SMA and PdBI represents the obscured star formation, and it is preferentially located in regions where stellar light is faint, because it has been absorbed. On the other hand, stellar emission is detected in dust-poor regions, where no dust or molecular gas emission is detected.

In order to analyze the excitation conditions of the molecular gas in SDP.9, we have modeled its CO SLED by using all available CO line data, taken from this and previous work (see Table 1). It should be noted that, due to lack of low-J (${J}_{\mathrm{up}}\leqslant 3$) ¹²CO observations for SDP.11, which trace the bulk of its molecular gas, we only study in this work the CO SLED of SDP.9 (Figure 2). The inclusion of the ¹²CO(1–0) and ¹²CO(3–2) transitions in SDP.9 improves the sampling of the CO SLED in this source with respect to the analysis presented in Lupu et al. (2012). The ¹²CO(3–2) emission had been already presented in Omont et al. (2013) at low spatial resolution, and with a line flux similar to the one reported here from our high spatial resolution data. For a reference, we also include in Figure 2 the CO SLED of different sources: the classical submillimeter galaxy (SMG) population (Bothwell et al. 2013), high-redshift lensed ULIRGs (Frayer et al. 2011; Harris et al. 2012; Lupu et al. 2012; ALMA Partnership et al. 2015), HFLS3 at $z\sim 6.34$ (Riechers et al. 2013), and local (U)LIRGs (Papadopoulos et al. 2014; Rosenberg et al. 2015). The shape of the observed CO SLED reveals a highly excited molecular ISM in SDP.9, much more excited than the average SMG (median redshift of $z\sim 2.3$), SDP.81 at $z\sim 3$, slightly more excited than some local merger/starbursts such as NGC 6240 (Papadopoulos et al. 2014), and less excited than some local AGNs such as Mrk 231. The similarity between the CO SLED of SDP.9 and HFLS3 is very remarkable.

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In order to model the CO line ladder in SDP.9, we use the non-LTE radiative transfer code Myradex,²² with an escape probability of $\beta =(1-{e}^{-\tau })/\tau$ in an expanding spherical geometry. MyRadex solves the same problem as RADEX (van der Tak et al. 2007), but with a different approach to solve the statistical equilibrium problem. We adopt a CO abundance relative to H₂ of 10⁻⁴. The CMB temperature is set to ${T}_{\mathrm{CMB}}=7.004\,{\rm{K}}$. We made a grid of CO line ladders with the following parameter ranges: number density of molecular hydrogen ${n}_{{{\rm{H}}}_{2}}={10}^{2}$–10⁸ cm⁻³, kinetic temperature ${T}_{\mathrm{kin}}={10}^{0.5}\mbox{--}{10}^{3}\,{\rm{K}}$, and velocity gradient ${dv}/{dr}=1\mbox{--}{10}^{3}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{pc}}^{-1}$. We then convert the velocity gradient to column density, where the latter is used as an input for Myradex, following Zhang et al. (2014b). From the model grid, we calculate the likelihood distributions for all parameter combinations following Ward et al. (2003). We assume that the CO column length is less than 2 times the CO-emitting size. We marginalize the parameters by integrating the likelihood distribution over all other parameters. The best fit gives the following results: $n({{\rm{H}}}_{2})=3.2\,\times \,{10}^{5}$ ${\mathrm{cm}}^{-3},{dv}/{dr}=18.2\,\mathrm{km}\ \,\ {{\rm{s}}}^{-1}$ ${\mathrm{pc}}^{-1},{T}_{\mathrm{kin}}\,=\,{10}^{1.7}\,{\rm{K}}$, ${N}_{{{\rm{H}}}_{2}}\,=\,2.5\,\times \,{10}^{22},{M}_{{{\rm{H}}}_{2}}\,=\,1.3\,\times {10}^{11}\,{M}_{\odot }$, and ${X}_{\mathrm{CO}}=1.0\,{\rm{K}}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$. Therefore, the modeling of its CO SLED suggests that the molecular gas in SDP.9 is likely dominated by a warm and dense component, which is much more excited than the average submillimeter population at higher redshift (Bothwell et al. 2013).

Figures 3 and 4 show the HCN(3–2), HCO⁺(3–2), and HNC(3–2) spectra of SDP.9 and SDP.11, respectively, along with previously detected lines in these sources. Thanks to the depth provided by the ALMA and VLA observations, all dense $J=3\mbox{--}2$ transitions and HCN(1–0) and HCO⁺(1–0) lines have been detected in SDP.9. In SDP.11, the HCN(3–2) and HCO⁺(3–2) transitions have been detected. The velocity-integrated line fluxes (and $3\sigma$ upper limits) of all observed transitions are shown in Table 1. All velocity-integrated line fluxes have been calculated from the zero-moment maps. To calculate the upper limit for the nondetected transitions, we have assumed that their width is the same as the mid-J CO lines and that there is no velocity offset with respect to the detected dense gas tracers.

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In SDP.9, the widths of the HCN(3–2), HCO⁺(3–2), and HNC(3–2) transitions are similar to the CO and water lines and are also centered at the same velocity. However, it seems (although the relatively low S/N prevents robust results) that the line profiles are slightly different. In contrast, despite that the molecular gas lines in SDP.11 have similar profiles, they are shifted with respect to each other by $\sim 100\,\mathrm{km}\,{{\rm{s}}}^{-1}$, with the shift being more evident in the HCN(3–2). The different line profiles and velocity offsets (taken with caution, as the S/N of the line profiles is not superb) might suggest that the different transitions are arising from different places across the galaxies. These results add to the similarities and differences found between dense and CO lines in previous analysis of high-redshift sources. For example, Riechers et al. (2011b) found that the HCO⁺(4–3) transition in the Cloverleaf quasar at z = 2.56 is narrower than the CO lines, suggesting that the densest gas is more spatially concentrated. Furthermore, Danielson et al. (2011) found that the velocity centroid of the HCN(3–2) emission in SMM J2135-0102, a lensed SMG at $z\sim 2.3$, is redshifted by approximately $\sim 230\pm 100\,\mathrm{km}\,{{\rm{s}}}^{-1}$ with respect to the redshift derived from ¹²CO lines.

Figure 5 shows the 3–2 to 1–0 luminosity ratio for the HCN and HCO⁺ transitions in SDP.9 and SDP.11 (note that only upper limits are available for SDP.11 because the $J=1\mbox{--}0$ transitions have not been detected for this source). We see that the HCN(3–2)/HCN(1–0) line ratio in both sources is in agreement with the highest values found in local galaxies. The HCN(3–2)/HCN(1–0) line ratios could actually be compatible with a trend suggesting higher excitation in more IR-luminous galaxies. On the other hand, the HCO⁺(3–2)/HCO⁺(1–0) line ratios of SDP.9 and SDP.11 are similar to the average value found in local starbursts (Graciá-Carpio et al. 2008; Juneau et al. 2009), which does not seem to correlate with the total IR luminosity, although no HCO⁺ transitions have been detected at the low-luminosity end. The line HCN SLED of SDP.9 is also compatible with that found for Arp 193, a classical starburst in the local universe, but suggests a less excited dense molecular gas reservoir than in NGC 6240 (Papadopoulos et al. 2014). All these results suggest that the excitation conditions of the dense molecular gas in some high-redshift sources are not significantly different from what can be found in the local universe, despite that SDP.9 and SDP.11 are more luminous than most low-redshift sources studied so far in HCN and HCO⁺.

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We have also fitted the CO and HCN SLEDs of SDP.9 simultaneously with the single excitation component large velocity gradient (LVG) modeling. To do this, we have assumed that both CO and HCN transitions come from the same region with the same excitation conditions. We keep the HCN abundance (relative to ${{\rm{H}}}_{2}$) to be $2\times {10}^{-8}$, which is an average value in local galaxies (Omont 2007; Krips et al. 2008). We derive the likelihood distributions for both grids of HCN and CO and marginalize the matrix in the same way as in Section 4.2. The best fit gives the following results: $n({{\rm{H}}}_{2})={10}^{4.5}\,{\mathrm{cm}}^{-3}$, ${T}_{\mathrm{kin}}={10}^{1.8}\,{\rm{K}},{dv}/{dr}={10}^{1.48}$ $\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{pc}}^{-1},N({{\rm{H}}}_{2})={10}^{22.5}$, $M({{\rm{H}}}_{2})={10}^{11.2}\,{M}_{\odot }$, and ${X}_{\mathrm{CO}}\;=1.4\,{\rm{K}}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{cm}}^{-2}$. We see that the ${T}_{\mathrm{kin}}$ and column density are consistent with the CO-based results. However, the ${{\rm{H}}}_{2}$ volume density is $\rho ={10}^{4.5}\,{\mathrm{cm}}^{-3}$, lower than the CO-based value. It is likely because the CO excitation is close to an LTE condition that it is not sensitive to density.

Figure 6 compares the total IR and dense molecular gas luminosities of SDP.9 and SDP.11 with a sample of local and high-redshift starbursts and QSOs taken from the literature (Greve et al. 2006; Riechers et al. 2006; Gao et al. 2007; Bussmann et al. 2008; Graciá-Carpio et al. 2008; Juneau et al. 2009; Danielson et al. 2011; García-Burillo et al. 2012). It should be pointed out that the line fluxes reported in Bussmann et al. (2008) and Juneau et al. (2009) do not seem to take into account the fact that their galaxies are larger than the beam size of their single-dish observations, thus missing a fraction of the dense gas line fluxes. We see that the correlation between IR and line luminosity for both low-redshift galaxies and SDP.9 and SDP.11 can be described by a single relation. Therefore, we find no clear evidence of enhanced SFR at a given line luminosity in SDP.9 and SDP.11 when compared to local LIRGs/ULIRGs. This is mainly because the correlation between ${L}_{\mathrm{IR}}$ and ${L}_{\mathrm{dense}}$ for local galaxies is not especially tight, but instead has a significant dispersion of $\pm 0.5\,\mathrm{dex}$ (see Figure 6).

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The detected HCN(3–2) emission in SMM J2135-0102 reported by Danielson et al. (2011) has line and IR luminosities that are also in agreement with the spread of the local correlation, also supporting the fact that a single relation can be applied at low and high redshift (Greve et al. 2006). Gao et al. (2007) presented HCN(1–0) observations of two SMGs and two QSOs and compiled previous HCN(1–0) detections and upper limits from the literature to conclude that high-redshift sources systematically lie above FIR/HCN correlation for nearby galaxies by about a factor of 2. This does not seem to be in agreement with our results for SDP.9 and SDP.11. However, it should be pointed out that the sample used in Gao et al. (2007) has a significant contribution of high-redshift QSOs (even at redshift $z\sim 6$) whose dense molecular gas properties do not necessarily have to be similar to the classical population of high-redshift SMGs (median redshift of $z\sim 2.3$; Chapman et al. 2005) or $z\sim 1$ ULIRGs as studied here. Furthermore, the total IR luminosities in the former sources might be affected by the AGNs, so not all of the total IR luminosity is due to star formation. If that was actually the case, and only the total IR luminosity due to star formation was considered, the points would be closer to the local relation. Riechers et al. (2006) reported detections of HCN(1–0) and HCO⁺(1–0) in the Cloverleaf quasar at z = 2.56, and their points are also compatible with the local relation (see Figure 7).

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The fact that, as suggested by our results, the same relation between total IR and dense gas luminosities can be applied to galaxies at both low and high redshift might indicate that some high-redshift sources are more IR luminous (have higher SFR) just because they have more dense molecular gas.

It has been obtained in various previous works that the relation between ${L}_{\mathrm{IR}}$ and ${L}_{\mathrm{HCN}}^{{\prime} }$ from $J\geqslant 1$ has a slope equal to 1, meaning that all those dense gas tracers are correlated with the SFR, and indicating that the SFR in the dense gas is not likely affected by the free-fall time (Zhang et al. 2014a). Actually, because the free-fall time is related to the density by ${\tau }_{\mathrm{ff}}\propto {n}^{-0.5}$, it would be lower for higher-J transitions, but still a similar ${L}_{\mathrm{IR}}\mbox{--}{L}_{\mathrm{dense}}$ relation is seen for ¹²CO(1–0), ¹²CO(4–3), HCN(1–0), HCN(4–3), and other dense gas tracers (Wu et al. 2010; Reiter et al. 2011; Greve et al. 2014; Zhang et al. 2014a). We have represented a fit with slope equal to unity with the black dashed lines in Figure 6. It can be seen that, for the HCN(1–0) transition, and within the uncertainties, SDP.9 is still compatible with a linear relation, and actually most previous fits to the ${L}_{\mathrm{IR}}\mbox{--}{L}_{\mathrm{HCN}(1-0)}$ are compatible with a linear relation (García-Burillo et al. 2012; Privon et al. 2015). The same seems to be true for the HCN(3–2) transition for both SDP.9 and SDP.11, although the spread of the points for local galaxies prevents a robust determination of the slope.

The dense molecular line luminosities can be combined with the total IR luminosity of SDP.9 to determine its star formation efficiency and dense gas depletion time. We note that we do this calculation only for SDP.9 because we have not detected the dense $J=1\mbox{--}0$ transitions in SDP.11. The dense-to-total IR luminosity ratio (a proxy of the star formation efficiency of the dense gas phase) in SDP.9 is ${L}_{\mathrm{HCN}(1-0)}^{{\prime} }/{L}_{\mathrm{IR}}\sim 0.7\,\times \,{10}^{-3}\,L^{\prime} /{L}_{\odot }$ (implying a dense gas depletion time of ${\tau }_{\mathrm{dep}}\sim 40\,\mathrm{Myr}$, assuming ${M}_{\mathrm{dense}}[{M}_{\odot }]=10\,{L}_{\mathrm{HCN}(1-0)}^{{\prime} }\,[{\rm{K}}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{pc}}^{2}]$; see García-Burillo et al. 2012) is compatible (within the scatter) with the average value reported for LIRGs in the local universe (García-Burillo et al. 2012; Privon et al. 2015), where no significant correlation has been found between the dense gas depletion time and the total IR luminosity (Gao & Solomon 2004a). Actually, a large scatter of ${L}_{\mathrm{HCN}(1-0)}^{{\prime} }/{L}_{\mathrm{IR}}$ values has been found in the literature, interpreted by Privon et al. (2015) as a lack of a simple link between ${L}_{\mathrm{HCN}(1-0)}^{{\prime} }$ and the mass of the dense gas directly associated with star formation.

4.7.1. The HCN/HNC Ratio

4.7.2. The HCN/HCO⁺ Ratio

The ratio between the HCN and CO low-J transitions is arguably the cleanest indicator of the the fraction of the total gas reservoir residing in the dense phase, and it has been proposed to be a unique tool to explore the star formation mode of star-forming galaxies: isolated disk versus merger-driven starbursts (Papadopoulos & Geach 2012). Figure 7 includes a comparison between the high-density (HCN and HCO⁺ emission) and low-density (CO emission) molecular gas tracers for SDP.9, the only one of the two sources studied in this work with detections in all those transitions at both $J=3\mbox{--}2$ and $J=1\mbox{--}0$. While the ratio for the $J=3\mbox{--}2$ transitions (both HCN/CO and HCO⁺/CO) and the $J=1\mbox{--}0$ HCO⁺/CO are in very good agreement with the values found for local galaxies (Baan et al. 2008), the $J=1\mbox{--}0$ HCN/CO ratio in SDP.9 is higher than most of the local sources. This indicates that SDP.9 contains a larger dense molecular gas reservoir with respect to the total molecular gas than those found in local galaxies. Since SDP.9 is more IR luminous than most galaxies studied so far in the local universe, their higher dense gas fraction might be associated with its higher SFR.

Assuming the relation between the dense molecular gas mass and the HCN(1–0) luminosity ${M}_{\mathrm{dense}}\sim 10\times {L}_{\mathrm{HCN}(1-0)}^{{\prime} }$ $[{\rm{K}}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{pc}}^{-2}]$ (Gao & Solomon 2004b; García-Burillo et al. 2012), we obtain ${M}_{\mathrm{dense}}\sim 8.4\times {10}^{10}\,{M}_{\odot }$, which is slightly smaller than the total molecular gas mass estimated from the LVG modeling of the CO SLED (${M}_{{{\rm{H}}}_{2}}\sim 1.3\times {10}^{11}\,{M}_{\odot }$; see Section 4.2). This suggests that a very large fraction of the molecular gas in SDP.9 is in the form of dense gas. The ${L}_{\mathrm{HCN}(1-0)}^{{\prime} }/{L}_{\mathrm{CO}(1-0)}^{{\prime} }\sim 0.37$ found for SDP.9 is similar to the values found for the most luminous sources in the local universe (Gao & Solomon 2004a; García-Burillo et al. 2012), and it is also compatible with a correlation indicating that more luminous galaxies have higher dense gas fractions (or equivalently higher ${L}_{\mathrm{HCN}(1-0)}^{{\prime} }/{L}_{\mathrm{CO}(1-0)}^{{\prime} }$ ratios).

We should point out that there are several uncertainties in the derivation of the dense molecular gas mass. As discussed in Papadopoulos et al. (2014), the ${\alpha }_{\mathrm{HCN}}$ factor might be lower than typically assumed in extreme starbursts if their dense gas is much warmer and/or in unbound states. Additionally, the HCN/CO line ratio traces the dense gas mass fractions only if both lines are collisionally excited. In strong starbursts, HCN can also be excited by mid-IR pumping (see also Section 4.7.2), thus producing enhanced HCN/CO line ratios without large amounts of dense molecular gas. Furthermore, the possible presence of an AGN in SDP.9 might also produce enhanced HCN luminosity (Privon et al. 2015).

As mentioned above, observations of local galaxies conclude that the $J=1\mbox{--}0$ HCN/CO line ratio is an excellent way to discriminate between different star formation modes. Compact, merger-driven, extreme starbursts are associated with high $J=1\mbox{--}0$ HCN/CO ratios, whereas lower values are found for isolated star-forming disks with more extended star formation (Solomon et al. 1992; Gao & Solomon 2004b). SDP.9 might belong to the former group as expected from its high IR luminosity (Engel et al. 2010), and, in fact, the ${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{\mathrm{CO}}^{{\prime} }$ luminosity ratio of SDP.9 is compatible with it being a merger-driven starburst.

According to the models presented in Meijerink et al. (2007), the HCN/CO ratio in SDP.9 suggests a density of $\sim (2\mbox{--}3)\times {10}^{5}\,{\mathrm{cm}}^{-3}$, which is compatible with the density derived from the LVG modeling of the CO SLED, ${n}_{{{\rm{H}}}_{2}}\sim 3.2\times {10}^{5}\,{\mathrm{cm}}^{-3}$ (see Section 4.2).