ALMA OBSERVATIONS OF WARM DENSE GAS IN NGC 1614—BREAKING OF THE STAR FORMATION LAW IN THE CENTRAL KILOPARSEC^*

In Figure 1, we present images of the integrated CO (6–5) line emission, the continuum at 435 μm, the first moment map, and the second moment map. All images are overlaid by the same contours of the integrated CO (6–5) line emission at levels of [1, 2, 4, 8] × 2.7 Jy beam⁻¹ km s⁻¹. The line and the continuum emissions correlate closely with each other, both showing a ring configuration without a detectable nucleus. The ring has a diameter of ∼2'' (∼650 pc). In both the line and the continuum maps, the ring looks clumpy and can be decomposed into several knots. The first moment map shows a clear velocity gradient along the south–north direction, consistent with an inclined rotating ring. According to Olsson et al. (2010), the inner disk of NGC 1614 has an inclination angle of 51°. In the second moment map, the velocity dispersion in most regions in the ring is rather constant at the level of δv ∼ 40 km s⁻¹, though in some inter-knot regions it can be as low as δv ∼ 20 km s⁻¹. From the first moment map, the velocity gradient due to the rotation can be estimated to be $dV/dr \sim 0.3 \,\rm km\, s^{-1}\, \rm pc^{-1}$, corresponding to a line widening of ∼20 km s⁻¹ within individual beams (linear size: ∼80 pc). This is consistent with the lowest velocity dispersion seen in the second moment map.

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The channel maps (δv = 20.4 km s⁻¹) are shown in Figure 2, overlaid on the image of the integrated line emission. They provide more details about the rotating ring. First of all, given the relatively narrow local velocity dispersions (see the second moment map in Figure 1), the channel maps dissect the ring spatially. It appears that the spatial width of ring segments in individual channel maps are generally broader than that in the integrated emission map. This is because, by co-adding all channel maps, the integrated emission map is affected more severely by the (negative) sidelobes of different segments of the ring. This is a significant effect because some ring segments are separated by ∼3'', the angular scale limit of our interferometer observations. Indeed the total flux of the CO (6–5) line emission, f_CO(6–5) = 898 (± 153) Jy km s⁻¹ (the error being dominated by the calibration uncertainty) that is derived from the sum of the aperture photometry of individual channels (centered on the emission features for each given channel), is 31% higher than that measured on the integrated CO (6–5) line emission map. Comparison with the Herschel measurement of the integrated CO (6–5) line emission of NGC 1614 ($\rm 1423\pm 126\, \rm Jy\, km\, s^{-1}$ within a beam of ∼30''; van der Werf et al. 2010; Lu et al. 2014) yields an interferometer-to-single-dish flux ratio of 0.63 ± 0.12. This suggests that most warm dense gas in NGC 1614 is concentrated in the circumnuclear ring.

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Figure 3 shows plots of the velocity distributions of the central region ($\rm radius= 1{\buildrel{\prime\prime}\over{.}} 5 \simeq 500\, \rm pc$) and of the peak position ($\rm R.A.=04{^h}34{^m}00{\buildrel{\mathrm{s}}\over{.}}006$, decl. = −08°34'4447) of the integrated CO (6–5) line emission map. In order to reduce the noise, we used relatively broad bins of δv = 34 km s⁻¹. The velocity distribution has a FWHM of 272 km s⁻¹. Its shape is rather irregular and spiky, reflecting the clumpiness of the rotating ring and the narrow velocity dispersions of individual clumps (Figure 1). No evidence for any outflow/inflow of |δv| < 1200 km s⁻¹, nor any detection of the H¹³CN (8–7) line (rest-frame frequency = 690.552 GHz), can be found in the spectrum. In the velocity distribution of the peak position, which is in the northwestern quadrant of the ring (Figure 1), we also found no evidence of outflow/inflow or of the H¹³CN (8–7) line emission.

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The flux density of the 435 μm continuum measured by ALMA is $f_{435\,\mu \rm m}=269\pm 46\, \rm mJy$. The continuum correlates spatially with the CO (6–5) emission in the central kiloparsec of NGC 1614 (Figure 1). This suggests that dust heating and gas heating in the warm dense gas cores are strongly coupled, a conclusion also reached by Lu et al. (2014) in a Herschel FTS study of the CO SLED of LIRGs. NGC 1614 was observed by Herschel-SPIRE (Griffin et al. 2010) both in the photometry mode (J. Chu et al., in preparation) and in the FTS mode (van der Werf et al. 2010; Lu et al. 2014), with beams of ∼30''. Because the error of the continuum measured in the FTS mode is large (∼1 Jy), we estimated the total flux of the 435 μm continuum of NGC 1614 using SPIRE photometer fluxes $f_{350\mu \rm m, SPIRE}=1916\pm 134\, \rm mJy$ and $f_{500\,\mu \rm m, \rm SPIRE}=487\pm 34\, \rm mJy$. Assuming a power-law spectrum for the dust continuum (i.e., log f_ν depending on log ν linearly), we carried out linear interpolation in the logarithmic domain of the flux and of the frequency between 350 and 500 μm, and found $f_{435\,\mu \rm m, \rm SPIRE}=831\pm 58\, \rm mJy$. The ratio between f_435 μm and $f_{435\,\mu \rm m, \rm SPIRE}$ then yields an interferometer-to-single-dish flux ratio of 0.32 ± 0.06. This is a factor of ∼2 lower than the interferometer-to-single-dish flux ratio of the line emission, indicating that the distribution of dust is substantially more extended than that of the warm dense gas.

The total dust mass in NGC 1614 can be estimated using the mid- and far-IR fluxes in the Spitzer/MIPS 24 μm band and in the Herschel 70, 100, 160, 250, 350, and 500 μm bands. The Herschel data are taken from J. Chu et al. (in preparation). A least-squares fit to the IR SED by a two-graybody model, with the emissivity spectral index β = 2 for both components, yields a total dust mass of M_{dust, total} = 10^{7.60 ± 0.07} M_☉ with a cold dust temperature of T_C = 35 ± 2 K (Figure 4). Fits by two-graybody models with β as a free parameter or by the model of Draine & Li (2007) yield very similar results. If dust in the central region has the same T_C, then $M_{\rm dust, cent} = f_{435\,\mu \rm m, \rm ALMA}/ f_{435\,\mu \rm m, \rm wSPIRE} \times M_{\rm dust, total}$. Taking into account the uncertainties due to the assumption on the cold dust temperature (∼50%), the dust mass in the central region observed by ALMA is M_{dust, cent} = 10^{7.11 ± 0.20} M_☉. NGC 1614 has a metallicity of 12 + log(O/H) = 8.65 ± 0.10 (Armus et al. 1989; Vacca & Conti 1992; Engelbracht et al. 2008; Modjaz et al. 2011). According to Rémy-Ruyer et al. (2014), for galaxies with 12 + log(O/H) > 8.5, the gas-to-dust ratio is 100 with a 1-σ uncertainty of ∼0.2 dex. Therefore, assuming M_gas/M_dust = 10^{2.0 ± 0.2}, the gas mass in the central region of NGC 1614 is M_{gas, cent} = 10^{9.11 ± 0.30} M_☉. This is consistent with the molecular gas mass (which should dominate the total gas mass) found in the same region (M_{gas, cent} = 10^9.30 M_☉, with a conversion factor of $X_{\rm CO} = 3\times 10^{20}\, \rm cm^{-2}\,(\rm K\, km\, s^{-1})^{-1}$; König et al. 2013). It should be pointed out that both the ALMA continuum observations and the SMA observations of CO (2–1) by König et al. (2013) detected mostly dust and gas emission in dense gas structures and missed significantly the diffuse emission; therefore, the dust and gas mass derived from these observations are lower limits.

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There has been a debate on whether there is an AGN in NGC 1614. Risaliti et al. (2000) argued, based on the detection of a hard X-ray source and its spectrum, that in the center of NGC 1614 there is a hidden AGN obscured by Compton-thick gas (N_H > 1.5 × 10²⁴ cm⁻²; Comastri 2004). However, such high column density gas in the nucleus, which will not be affected by the missing flux issue, is not detected in either the CO (6–5) map or the dust continuum map. Using the scaling factor between the gas mass and the continuum flux derived above, the non-detection of the continuum in the nucleus (σ = 0.6 mJy beam⁻¹) sets a 3σ upper limit for the gas surface density of N_H = 10^{23.1 ± 0.3} cm⁻². Since an AGN cannot hide itself in the emission of dust that absorbs its UV/optical/NIR radiation, our results can rule out this possibility with relatively high confidence. Indeed a Compton-thick torus with a radius of r = 20 pc (García-Burillo et al. 2014), which fills 23% of the ALMA beam, should be detectable in the continuum with a signal-to-noise ratio of s/σ ⩾ 7. The s/σ could be even higher since the T_d in a torus is likely much warmer than the assumed dust temperature of T_d = 35 K. The high-resolution MIR L-band observations of Väisänen et al. (2012) also argue against a Compton-thick AGN in NGC 1614. As pointed out by Olsson et al. (2010) and Herrero-Illana et al. (2014), the X-ray source detected by Risaliti et al. (2000) could be explained by low-mass X-ray binaries.

There is rich literature on molecular line observations in the sub-mm and mm bands for NGC 1614 (Young et al. 1986; Solomon & Sage 1988; Scoville et al. 1989; Sanders et al. 1991; Casoli et al. 1991; Gao & Solomon 2004a; Albrecht et al. 2007; Wilson et al. 2008; Olsson et al. 2010; Costagliola et al. 2011; König et al. 2013; Imanishi & Nakanishi 2013). The single dish CO (1–0) observations of Sanders et al. (1991) found a total molecular gas mass of 10^10.12 M_☉, assuming a standard conversion factor of $X_{\rm CO} = 3\times 10^{20}\, \rm cm^{-2}(\rm K\, km\, s^{-1})^{-1}$ and distance of D = 67.8 Mpc. This is consistent with the result of Casoli et al. (1991), but significantly larger than those obtained in earlier and less sensitive observations (Young et al. 1986; Solomon & Sage 1988). The OVRO observations of Scoville et al. (1989), with a beam of 4'' × 6'', allocated 30% of the total CO (1–0) emission within a nuclear region of radius = 1 kpc. The more recent and higher-resolution (275 × 240) observations of Olsson et al. (2010) resolved the central CO (1–0) line emission into an arc-like feature ∼3 kpc in length and ∼1.3 kpc in width, but did not resolve the ring. The SMA map of CO (3–2) (beam = 26 × 21; Wilson et al. 2008) and the ALMA maps of HCN/HCO⁺/HNC (4–3) (beam = 15 × 13; Imanishi & Nakanishi 2013) also did not resolve the ring.

Before our ALMA observations, the best angular resolution for any CO rotation lines was obtained by König et al. (2013) in their SMA observations of the CO (2–1) line, with a beam of 050 × 044. In Figure 5, we compare their CO (2–1) map with our CO (6–5) map. In the ring the two maps have good correspondence, though the CO (6–5) emission looks clumpier, most likely due to the better angular resolution. König et al. (2013) noticed a strong asymmetry in the CO (2–1) distribution between the eastern and western sides of the ring, and interpret it as a consequence of the feeding of the ring by the dust lane on the northwest of the ring. In the CO (6–5) map, we still see this asymmetry albeit being less prominent than in CO (2–1). When smoothed to a common beam, the ratio between the two emissions is rather constant in most regions of the ring, with a median brightness temperature ratio of 0.72 (Figure 5). The east quadrant of the ring has the highest brightness temperature ratio (∼1). This could be due, at least partially, to a slight mismatch between the two maps, given the steep gradient in both maps in this region. On the other hand, this seems to be consistent with the stronger east–west asymmetry seen in the CO (2–1) map than in the CO (6–5) map. König et al. (2013) argued that the reason of the asymmetry could be the feeding of the ring by a dust lane on the northwest of the ring. In this scenario, the east quadrant has higher CO (6–5)/CO (2–1) ratio than the west quadrant because it has less diffuse gas (freshly fed by the dust lane) compared to the west quadrant. The nucleus is not detected in either map. The CO (6–5) 3-σ upper limit of 742 M_☉ pc⁻² (N_H = 10^22.86 cm⁻²) for the surface density of the warm dense gas, derived by assuming the same relation between Σ_Gas and CO (6–5) surface brightness in the ring region (Equation (3)), is consistent with the upper limit set by the 435 μm continuum. If the conversion factor advocated by Downes & Solomon (1998) for (U)LIRGs is used, which is a factor of ∼6 lower than the standard value adopted in Equation (3), the result is a significantly lower value for the upper limit of Σ_Gas in the nucleus. In the region north of the ring, where significant CO (2–1) emission is found, little CO (6–5) emission is detected and the brightness temperature ratio is <0.1.

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Most star formation in NGC 1614 is occurring in the circumnuclear starburst ring. Soifer et al. (2001) found that 72% of the 12 μm flux of NGC 1614 measured by IRAS is contained within the 2'' beam of their Keck observations. The comparison between the high-resolution 8.4 GHz map of the central kiloparsec region (Herrero-Illana et al. 2014) and that of a lower-resolution map at the same frequency by Schmitt et al. (2006) indicates that ∼67% of the total SFR is contributed by the starburst ring and the nucleus. The star formation in the ring has been studied by Alonso-Herrero et al. (2001) using a Hubble Space Telescope (HST) Pa α map, Díaz-Santos et al. (2008) using a Gemini 8 μm map, Väisänen et al. (2012) using a 3.3 μm polycyclic aromatic hydrocarbon (PAH) map obtained with UIST (an imager-spectrometer for integral field spectroscopy) at UKIRT, Olsson et al. (2010) and Herrero-Illana et al. (2014) using VLA and Merlin radio continuum maps. While the NIR and MIR observations may still be affected by the dust obscuration associated with the dense gas (Imanishi & Nakanishi 2013), the radio continuum is an SFR indicator insensitive to dust obscuration.

In the left panel of Figure 6, we compare the CO (6–5) contours with the radio continuum at 8.4 GHz (beam = 041 × 026, Herrero-Illana et al. 2014). The CO (6–5) knots in the ring (Table 2) are marked in the image. While there is a radio nucleus, the CO map has a hole at the ring's center. Herrero-Illana et al. (2014) argued that the radio nucleus is not an AGN, which is consistent with our conclusion that there is no (Compton-thick) AGN in NGC 1614 (Section 3.2). In the other two panels of Figure 6, the CO (6–5) emission is compared to the thermal and nonthermal radio emission components, respectively. Following Herrero-Illana et al. (2014), the thermal radio emission is estimated using a high-resolution, extinction-corrected Pa-α map obtained from a set of HST NIR narrow- and broadband images. The method involves the comparison of a Pa-α equivalent width map as well as an NIR color (F160W/F222M) image to stellar population synthesis models (Starburst99; Leitherer et al. 1999) to derive a spatially resolved dust obscuration map with which to correct the original Pa-α image (see also Díaz-Santos et al. 2008). The details of this procedure can be found in the Appendix. As a final step, the nonthermal component is derived by subtracting from the total radio emission the thermal component. The thermal fraction of the radio continuum at 8.4 GHz is found to be 51% in the ring region (100 < r < 350 pc).

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In Figure 7, the radial profiles of the emissions are compared. The peak of the radial distribution of the thermal radio is shifted (by ∼70 pc) toward the smaller radius compared to that of the CO (6–5) radial distribution. The peak of the distribution of the total radio emission also has a small offset compared to that of the CO (6–5), while the radial profile of nonthermal radio emission is similar to that of the CO (6–5) in the ring region. The radio profile of CO (2–1) (König et al. 2013) is also shown in the same plot. If we compare the CO (2–1) profile with the profile of CO (6–5), which has been smoothed to the same resolution of CO (2–1), we see that the former is significantly more extended than the latter. Beyond r ∼ 400 pc, the cold and diffuse molecular gas probed by CO (2–1) emission is devoid of any significant star formation (as revealed by the profiles of the radio emissions).

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In Figure 8, we plot the SFR surface density (Σ_SFR) versus the gas surface density (Σ_Gas; i.e., the Kennicutt–Schmidt law) for the nuclear starburst and individual cells (3 pixels, pixel = 0089) in the ring, using the thermal and nonthermal maps to derive Σ_SFR and the CO (6–5) map (smoothed and regridded to match the radio maps) to obtain Σ_Gas. The SFR can be estimated from the nonthermal and thermal radio luminosities using two formulae given in Murphy et al. (2012), respectively:

$$\begin{eqnarray} &&\left({{\rm SFR}^{\rm nth}_\nu \over M_\odot \, \rm yr^{-1}} \right)\rm = 6.64\times 10^{-29}\left({\nu \over GHz}\right)^{\alpha ^{nth}}\left({L^{nth}_\nu \over erg\, s^{-1}Hz^{-1}}\right).\nonumber\\ \end{eqnarray} \tag{ 1 }$$

and

$$\begin{eqnarray} \left({{\rm SFR}^{\rm th}_\nu \over M_\odot \,\rm yr^{-1}} \right)\rm & = & \rm 4.6\times 10^{-28}\left({T_e\over 10^4 \, K}\right)^{-0.45} \nonumber \\ & & \times \rm \left({\nu \over GHz}\right)^{0.1} \left({L^{th}_\nu \over erg\, s^{-1}\, Hz^{-1}}\right), \end{eqnarray} \tag{ 2 }$$

where T_e = 10⁴ K, ν = 8.4 GHz, and α^nth = 1.2 (Herrero-Illana et al. 2014). For individual cells in the ring, we also plotted in Figure 8 the Σ_SFR versus Σ_Gas relation with the Σ_SFR estimated from the total radio emission, assuming a constant nonthermal fraction (f_nth = 0.5) and the SFR versus L^nth relation in Equation (1).

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The gas surface density was estimated using the CO (6–5) surface brightness as follows. According to König et al. (2013), the total H₂ mass in the ring is $M_{\rm H_2} = 10^{8.97}\, M_\odot$ (for D = 67.8 Mpc), estimated using the CO (1–0) map of Olsson et al. (2010) and assuming a conversion factor of $\rm 3\times 10^{20}\, \rm cm^{-2}\, (\rm K\, km\, s^{-1})^{-1}$. Dividing this by the integrated CO (2–1) flux of the ring, S_CO(2–1) = 65.4 ± 6.9 Jy km s⁻¹ (König et al. 2013) and assuming a brightness temperature ratio of 0.72 between CO (6–5) and CO (2–1) (Figure 5), we have

$$\begin{equation} \left({\Sigma _{\rm Gas}\over M_\odot \, {\rm pc}^{-2}} \right) = 20.3\times \left({f_{\rm CO(6-5)}\over \rm Jy\, arcsec^{-2} \, km\, s^{-1}} \right). \end{equation} \tag{ 3 }$$

In the ring region, only cells that are detected in both radio and CO (6–5) maps above a 3-σ threshold are plotted (therefore the random errors are <0.12 dex for these data points). In the nuclear region (r < 100 pc), the 3σ upper limit for Σ_Gas was derived using the CO (6–5) map assuming the same relation for the ring region (Equation (3)). For individual cells in the ring, the Σ_SFR versus Σ_Gas relation is systematically above that for local starbursts (Kennicutt 1998), indicating a higher star formation efficiency (SFE). This is because, by relating the SFR to the warm dense gas probed by the high-resolution ALMA observations of CO (6–5), much of the cold diffuse gas probed by low J CO (more extended than the warm dense gas) is excluded from the Σ_Gas in our results. It is worth noting that we used a standard CO conversion factor ($X_{\rm CO} = 3\times 10^{20}\, \rm cm^{-2}(\rm K\, km\, s^{-1})^{-1}$) for NGC 1614 data. In the literature, arguments for high SFE in (U)LIRGs are very often based on results obtained using a CO conversion factor ∼5 times lower than the standard value (e.g., Daddi et al. 2010; Genzel et al. 2010).

It appears that on the linear scale of 100 pc, the tight correlation previously found between Σ_SFR versus Σ_Gas (Kennicutt 1998; Genzel et al. 2010; Leroy et al. 2013; Yao et al. 2003; Iono et al. 2004; Wilson et al. 2008) breaks down in the central kiloparsec of NGC 1614. In particular, the non-detections of the nucleus in both CO (6–5) and CO (2–1) maps set a lower-limit of the Σ_SFR-to-Σ_Gas ratio about an order of magnitude above the nominal value, corresponding to a very short gas exhaustion timescale of M_gas/SFR < 10 Myr. The low extinction (Alonso-Herrero et al. 2001; Kotilainen et al. 2001; Díaz-Santos et al. 2008) and low PAH emission (Väisänen et al. 2012) also indicate an ISM depression in the nuclear region. The star formation timescale associated with the thermal radio is ∼10 Myr and that with the nonthermal radio is ∼100 Myr. Alonso-Herrero et al. (2001) argued that, based on detections of deep CO stellar absorption, NGC 1614 harbors a nuclear starburst older than 10 Myr, which could have blown away the ambient ISM (Väisänen et al. 2012). If the timescale for the feedback effects, including both the gas consumption by star formation and mass loss by superwinds, is significantly shorter than 10 Myr (the dynamic timescale of the nuclear region is only τ ∼ 1 Myr), then the deviation of the nucleus from the Σ_SFR versus Σ_Gas relation may indeed be due to the feedback of the old nuclear starburst. This is consistent with the results of García-Burillo et al. (2012) who found that NGC 1614 has the highest value of the SFE (estimated from the FIR/HCN ratio) among a sample of normal star-forming galaxies and mergers, and argued that this could be due to the exhaustion of the dense molecular gas by starburst activity.

In the starburst ring, the correlation between Σ_{SFR, th} and Σ_Gas is rather weak (Spearman's rank correlation coefficient ρ = 0.37 with the significance of its deviation from zero p = 0.20). Also, the correlation between Σ_{SFR, total} (estimated using total radio emission) and Σ_Gas has a large scatter, and is only marginally significant (ρ = 0.64 and p = 0.0023). This is consistent with the systematic offset between the radial profiles of the total radio and CO (6–5) in Figure 7. While the weak correlation between Σ_{SFR, th} and Σ_Gas could be mainly due to the uncertainties associated with the obscuration correction of the Pa α (the thermal radio is estimated using the obscuration-corrected Pa α), this cannot explain the lack of correlation between Σ_{SFR, total} and Σ_Gas. We have already seen a breakdown of the Σ_SFR-to-Σ_Gas correlation in the nucleus, and interpreted it as a consequence of starburst feedback. The same scenario can be applied to the individual cells in the ring. Given the high resolutions of the radio and CO (6–5) maps, these cells correspond to star formation regions of linear scales of ∼100 pc. On such fine scales, the Σ_SFR-to-Σ_Gas relation could be sensitive to the local star-formation history. Indeed, Alonso-Herrero et al. (2001) suggested that in NGC 1614 the starburst propagates like a "wild fire" from the nucleus outward. Väisänen et al. (2012) proposed that even the ring is stratified in terms of the star formation age. In a CO (1–0) survey of M33, Onodera et al. (2010) found a breakdown of the Kennicutt–Schmidt law on the linear scale of ∼80 pc, and attributed it to the various evolutionary stages of giant molecular clouds (GMCs) and to the drift of young clusters from their parent GMCs. These interpretations are applicable to our results, although our ALMA observations probe an even tighter correlation between CO (6–5) and SFR in a LIRG associated with a starburst merger.

A stronger correlation is found between Σ_{SFR, nth} and Σ_Gas in the starburst ring (ρ = 0.81 and p = 1.6 × 10⁻⁵). This is puzzling because, given the longer star formation timescale associated with the nonthermal radio, this relation should be more sensitive to the star formation history than the Σ_{SFR, th} and Σ_Gas relation. It is likely that the Σ_{SFR, nth} and Σ_Gas correlation is driven by other factors than the Kennicutt–Schmidt law. One possibility is that it is due to the correlation between the magnetic field strength and the gas density (Fiebig & Guesten 1989; Helou & Bicay 1993; Niklas & Beck 1997). Observationally, this correlation extends from the smallest (Fiebig & Guesten 1989) to the largest cosmic scales (Vallée 1990, 1995), and has the form of B∝n^k for n > 10² cm⁻³, where B is the magnetic field strength, n the gas density, and k = 0.5 ± 0.1 (Fiebig & Guesten 1989). Since the emissivity of the nonthermal (synchrotron) radiation is proportional to B², the B-versus-n correlation leads naturally to a localized (∼linear) correlation between nonthermal surface brightness and gas surface density. Another possibility is that the nonthermal radio and the CO (6–5) correlate with each other because they are both powered by cosmic rays (CRs). Indeed, CSO observations of $\rm ^{12}$CO(6–5) and $\rm ^{13}$CO(6–5) by Hailey-Dunsheath et al. (2008) of the nuclear starburst in the central 180 pc of NGC 253 suggested that warm molecular gas is most likely to be heated by an elevated density of CRs or by turbulence. In order to test whether CRs dominate the heating of warm molecular gas in NGC 1614, we carried out model-fitting using theoretical models (Meijerink & Spaans 2005; Kazandjian et al. 2012, 2014) of the cosmic ray dominated regions (CDRs) and photon dominated regions (PDRs) to fit the emission lines of ¹²CO, ¹³CO, HCN, HNC, and HCO⁺. These are mostly single dish data for the entire system of NGC 1614 (Sanders et al. 1991; Albrecht et al. 2007; Costagliola et al. 2011; N. Lu et al. 2014, in preparation), plus some high-resolution interferometry data for the central region taken from the literature (Wilson et al. 2008; Olsson et al. 2010; König et al. 2013; Imanishi & Nakanishi 2013) and from this work. The results show that PDR models with strong mechanical heating (by turbulence) provide the best fit while CDR models fit the data rather poorly. Details of these results will be presented elsewhere (R. Meijerink et al., in preparation). This is consistent with Rosenberg et al. (2014a) who modeled the Herschel observations of $\rm ^{12}$CO up to upper J = 13 and $\rm ^{13}$CO up to upper J = 6, together with data of other sub-mm lines taken from the literature, of NGC 253. They found that mechanical heating by turbulence is necessary to reproduce the observed molecular emission and CR heating is a negligible heating source. Rosenberg et al. (2014b) reached a similar conclusion for Arp 299A, a nuclear starburst in Arp 299 (a merger-induced LIRG). In principle, the turbulence can be related to the CRs through shocks generated by supernova remnants (SNRs) that can both power the turbulence (Draine 1980) and accelerate CRs (Drury et al. 1994). However, given the very different mechanisms for energizing low-velocity turbulence and for CR acceleration by SNR shocks, it is unlikely that this can explain the localized correlation between Σ_{SFR, nth} and Σ_Gas in the starburst ring down to the linear scale of 100 pc.

In this section, we compare NGC 1614 with NGC 34, another local LIRG observed by our team using ALMA band-9 receivers (Xu et al. 2014). Both galaxies are late-stage mergers (Neff et al. 1990; Schweizer & Seitzer 2007). As shown in Table 3, they have similar absolute K-band magnitude M_K (indicating similar stellar mass), similar total gas mass as obtained by H i and CO observations, and similar total SFR as derived from the IR+UV luminosities (U et al. 2012). On the other hand, as revealed by the ALMA observations and high angular resolution observations in other bands, the two galaxies are very different in the central kiloparsec.

Table 3. Comparison between NGC 1614 and NGC 34

	NGC 1614		NGC 34
R.A. (J2000)a	$\rm 04{^h}34{^m}00{\buildrel{\mathrm{s}}\over{.}}03$		$\rm 00{^h}11{^m}06{\buildrel{\mathrm{s}}\over{.}}54$
Decl. (J2000)a	−08°34'451		−12°06'275
Distance (Mpc)	67.8		84.1
LIR (L☉)b	1011.65		1011.49
MK (mag)c	−24.59		−24.46
$M_{\rm H\,\scriptsize{I}}$ (M☉)d	109.45		109.72
$\rm SFR_{\rm tot}\, ({M}_\odot \, \rm yr^{-1}$)e	51.3		34.7
$M_{\rm H_2, \rm tot}$ (M☉)f	1010.12		1010.15
Mdust, tot (M☉)g	107.60		107.48
AGN	No		Yes
Merger mass ratio	4:1–5:1		3:2–3:1
S8.4 GHz, tot (mJy)h	41.1
SCO(6 − 5), tot (Jy km s−1)i	1423 ± 126		937 ± 63
$S_{435\,\mu \rm m, \rm tot}$ (mJy)j	831 ± 58		517 ± 36
Central Starburst
Morphology	Circumnuclear ring		Nuclear disk
Radius (pc)	rin = 100, rout = 350		100
$S_{8.4\,\rm GHz, \rm cent}$ (mJy)k	26.5		15.2
$\rm SFR_{\rm cent}\, (M_\odot \, \rm yr^{-1}$)l	32.8		26.0
ΣSFR ($M_\odot \, \rm yr^{-1}\, \rm kpc^{-2}$)m	92.8		827.6
$M_{\rm H_2, \rm cent}$ (M☉)n	108.97		108.76
ΣGas (M☉ pc−2)o	103.54		104.40
SCO(6–5), cent (Jy km s−1)p	898 ± 153		1004 ± 151
$S_{435\,\mu \rm m, \rm cent}$ (mJy)q	269 ± 46		275 ± 41
Mdust, cent (M☉)r	107.11		106.97

Notes. ^aCoordinates of the nucleus in the 8.4 GHz radio continuum. ^bIR luminosity between 8–1000 μm (Armus et al. 2009). ^cAbsolute K-band magnitude (Rothberg & Joseph 2004). ^dTotal mass of neutral atomic hydrogen gas, taken from compilation by Kandalyan (2003). ^eTotal star formation rate (U et al. 2012). ^fTotal mass of molecular hydrogen gas (assuming $X_{\rm CO} = 3\times 10^{20}\, \rm cm^{-2}(\rm K\, km\, s^{-1})^{-1}$); NGC 1614: Sanders et al. (1991); NGC 34: Kruegel et al. (1990). ^gTotal dust mass; NGC 1614: this work; NGC 34: Esquej et al. (2012). ^hTotal flux of the 8.4 GHz radio continuum (Schmitt et al. 2006). ⁱTotal flux of the CO (6–5) emission (N. Lu et al. 2014, in preparation). ^jTotal flux of the 435 μm continuum emission; NGC 1614: this work; NGC 34: Xu et al. (2014). ^kFlux of the 8.4 GHz radio continuum in the central region; NGC 1614: Herrero-Illana et al. (2014); NGC 34: Condon et al. (1991). ^lThe SFR of central starburst: SFR_cent = SFR_tot × f_cent, where $f_{\rm cent} = S_{8.4\,\rm GHz,\rm cent}/S_{8.4\,\rm GHz,\rm tot} = 0.64$ for NGC 1614, and f_cent = 0.75 for NGC 34. ^mMean SFR column density of the central starburst. ⁿMass of molecular hydrogen gas in the central region; NGC 1614 ($X_{\rm CO} = 3\times 10^{20}\, \rm cm^{-2}(\rm K\, km\, s^{-1})^{-1}$): König et al. (2013); NGC 34 ($X_{\rm CO} = 0.5\times 10^{20}\, \rm cm^{-2}(\rm K\, km\, s^{-1})^{-1}$): Fernandez et al. (2014). ^oMean gas column density of the central starburst ($M_{\rm Gas} = 1.36\times M_{\rm H_2}$). ^pFlux of the CO (6–5) emission in the central starburst region; NGC 1614: this work; NGC 34: Xu et al. (2014). ^qFlux of the 435 μm continuum emission in the central starburst region; NGC 1614: this work; NGC 34: Xu et al. (2014). ^rDust mass in the central starburst region; NGC 1614: this work; NGC 34: Xu et al. (2014).

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First of all, our ALMA data ruled out a Compton-thick AGN in NGC 1614. By comparison, there is a weak AGN in NGC 34 according to the X-ray data (Brightman & Nandra 2011; Esquej et al. 2012), and the ALMA results (Xu et al. 2014) are consistent with the AGN being Compton thick. Nevertheless, for both galaxies, the central kiloparsec is dominated by starburst activity and AGN contributions to both dust and gas heatings are insignificant (Xu et al. 2014; Stierwalt et al. 2013). In NGC 34, the starburst is concentrated in a compact nuclear disk of r ∼ 100 pc, with very high Σ_{SFR, th} and Σ_Gas. In NGC 1614, a starburst ring between r_in = 100 pc and r_out = 350 pc dominates the central region, with moderate mean Σ_{SFR, th} and mean Σ_Gas compared to other local starbursts (Figure 8). It is worth pointing out that different CO conversion factors have been adopted for the two cases: for the nuclear starburst in NGC 34, the ALMA observations showed that the molecular gas is concentrated in a well organized disk controlled mostly by the gravity of stars (Xu et al. 2014). Therefore, we choose to use the conversion factor for (U)LIRGs: $X_{\rm CO} = 0.5\times 10^{20}\, \rm cm^{-2}(\rm K\, km\, s^{-1})^{-1}$ (Scoville et al. 1997; Downes & Solomon 1998). On the other hand, for the starburst ring in NGC 1614, the ALMA observations presented here and the SMA observations of König et al. (2013) reveal that much of the CO emission is clumped in individual knots associated with giant molecular associations (GMAs), which might be self-gravitating. In this case, a standard Galactic CO conversion factor is more appropriate (Papadopoulos et al. 2012): $X_{\rm CO} = 3.0\times 10^{20}\, \rm cm^{-2}(\rm K\, km\, s^{-1})^{-1}$. Nevertheless, these conversion factors are very uncertain and are the major error sources for the molecular gas mass estimates.

In Figure 9, we compare the spectral line energy distributions (SLEDs) of the total CO emission (measured by single-dish observations) of these two galaxies, taken from observations of Herschel-SPIRE FTS observations (N. Lu et al. 2014, in preparation). The CO SLED of NGC 1614 peaks around upper J = 5–7, while that of NGC 34 reaches a plateau after a rapid increase, and the peak is around upper J = 9. In order to further investigate the physical conditions of these two galaxies, we modeled the observed CO SLEDs using simple two-component RADEX large velocity gradient (LVG) radiative transfer models (van der Tak et al. 2007), and adopting a similar procedure to that in Kamenetzky et al. (2012). Admittedly, results from such model fittings suffer significant degeneracy between parameters (Rosenberg et al. 2014a). Nevertheless, they are useful for translating the information in the CO SLED into quantitative estimates of physical parameters of the gas, albeit with large uncertainties. We find that both SLEDs can be well fit by the combination of a cool and a warm component. Both galaxies have similar gas densities of (10^2.5, 10^2.6) cm⁻³ and (10⁴, 10⁴) cm⁻³, for the cool and warm components in (NGC 34, NGC 1614), respectively. However, the kinetic temperature of the warm component in NGC 34 (890 K) is two times higher than that of NGC 1614 (445 K), consistent with the fact that the nuclear starburst in NGC 34 is five times more compact than the circumnuclear starburst ring in NGC 1614. It is worthwhile noting that the AGN contribution to the warm gas in NGC 34 is insignificant (Xu et al. 2014). Given the overall similarities between the two host galaxies (Table 3), it is likely that the staunch difference between the two central starbursts is caused by the difference in the merging processes that the two LIRGs have experienced.

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The morphology of NGC 1614—one prominent tail and one relatively small secondary tail—suggests an unequal mass encounter (mass ratio ≳ 4: 1) and/or a scenario in which one of the galaxies experienced a retrograde passage. Several authors have argued for a high mass ratio encounter; Rothberg & Joseph (2006) note the isophotal shape of NGC 1614 and its correspondence with simulations of high mass ratio mergers, while Väisänen et al. (2012) identify a possible remnant body of the lower-mass companion. Both Rothberg & Joseph (2006) and Väisänen et al. (2012) come to the same conclusion—that NGC 1614 is a 4:1 mass ratio merger—but the former assumes the nuclei have already merged and the latter relies on the identification of an interacting galaxy.

NGC 34 has no clear evidence for dual nuclei, suggesting the two galaxies have already coalesced. Owing to the asymmetry of integrated brightness of the two tidal tails Schweizer & Seitzer (2007) argue that this system is the result of a merger of two disk galaxies with a mass ratio between 3:2 and 3:1. The disky isophotal shape of the remnant (which shows no evidence for a disk in the K-band morphology) is consistent with a formation scenario of a major but unequal mass merger (Rothberg & Joseph 2006; Naab et al. 2006). Preliminary dynamical modeling of this system is consistent with the aforementioned mass ratio and both disks experiencing prograde interactions (G. C. Privon et al., in preparation). This dynamical model is consistent with the system being observed ∼250–300 Myr since the first passage of the two galaxies, somewhat lower than the suggested 400 Myr age of the stellar disk (Schweizer & Seitzer 2007).

Hence, NGC 34 has experienced a major merger of two galaxies of similar mass, which was catastrophic and destroyed both progenitor disks (Schweizer & Seitzer 2007). Simulations by Cox et al. (2008) exploring the effect of mass ratio on merger-induced starbursts found a decreasing burst strength with increasing primary/secondary mass ratio; given the previously mentioned estimates of the mass ratios for NGC 34 and NGC 1614, the star formation surface densities are consistent with this interpretation. It might be that the higher mass ratio merger experienced by NGC 1614 caused less efficient torquing of the gas, leading to much of the central gas settling into the nuclear ring (with the help of either the inner Lindblad resonance associated with a bar (Olsson et al. 2010) or the non-axisymmetric potential caused by a minor merger (Combes 1988; Knapen et al. 2004; Mazzuca et al. 2006)) rather than collecting in the center, as in NGC 34. This may also hint at the answer to the question why NGC 1614 has not yet developed an AGN (Väisänen et al. 2012) while NGC 34 has. According to Hopkins (2012), the built-up of a centrally peaked dense gas disk is a necessary condition for triggering of the AGN activity in late stage mergers.

An alternate explanation for NGC 1614's comparatively lower Σ_SFR, if the scenario proposed by Väisänen et al. (2012) is accurate, is that the merger has simply not yet run to completion and so has not yet caused the final funneling of gas toward the nucleus at the time of the merger (e.g., Mihos & Hernquist 1994; Hopkins 2012). Olsson et al. (2010) and König et al. (2013) both show that indeed most of the molecular gas in NGC 1614 sits in the dust lane (outside the ring) and even further out. It could be that the relatively minor perturbation of the first pass (which led to the northeast tail) created the outward propagating starburst (i.e., the "wild fire"), as revealed by the nuclear ring and the weak and old nuclear starburst, while a future merger will trigger a much stronger nuclear starburst as seen in NGC 34.

With current knowledge of the encounters in NGC 34 and NGC 1614, we cannot firmly assign the cause for the different starburst characteristics in the two systems. It is likely to be due to the effect of different mass ratios, but we cannot rule out other possible causes such as different current phases of the encounters and different encounter geometries. While NGC 34 represents a large population of LIRGs with starburst nuclei (e.g., Arp 220), NGC 1614 represents those with circumnuclear starburst rings, which are also common in LIRGs. Among the GOALS sample, at least five other LIRGs (NGC 1068, NGC 5135, NGC 7469, NGC 7552, and NGC 7771) have such rings. Future dynamical models (G. C. Privon et al., in preparation) matched to the kinematics and morphology of NGC 34 and NGC 1614 may provide a more concrete answer to the question of how the two galaxies, and the two LIRG populations they represent, developed such different central starbursts over the merging process.