Cold Molecular Gas in Merger Remnants. II. The Properties of Dense Molecular Gas

The sample used in this study is a subset of the CO imaging data of merger remnants (Ueda et al. 2014). Our sample is originally drawn from 51 optically selected merger remnants in the local (<200 Mpc) universe (Rothberg & Joseph 2004). The merger remnants were selected solely based on optical morphology that suggests an advanced merger stage, regardless of the strength of the starburst or AGN activities. Near-IR imaging shows single nuclei in all of the sample sources (Rothberg & Joseph 2004); however, radio continuum maps of NGC 3256 (Norris & Forbes 1995) reveal a double nucleus, which suggests an ongoing merger. In this study, we regard NGC 3256 as a merger remnant. The basic properties of our sample are summarized in Table 1. The exact fraction of these sources that result from a major merger as opposed to a minor merger is unknown because it is difficult to reverse the chronology and disentangle the exact mass and morphology of the progenitors. We estimated the far-IR (FIR) and IR luminosities of our sample using the Infrared Astronomical Satellite (IRAS) catalogs and the equation in Table 1 of Sanders & Mirabel (1996). The IR luminosities including the upper limits range from 1.4 × 10⁹ L_☉ to 3.3 × 10¹² L_☉. Two galaxies are classified as ULIRGs (10¹² L_☉ ≤ L_IR < 10¹³ L_☉), and 11 galaxies are classified as LIRGs (10¹¹ L_☉ ≤ L_IR <10¹¹ L_☉) (see Table 1).

Multiline observations toward 28 merger remnants were carried out using the LMT between 2014 October and 2015 May in its early science phase. In this early phase, the LMT operated with a 32 m active surface. The Redshift Search Receiver (RSR; Erickson et al. 2007) consists of two dual-polarization front-end receivers that are chopped between the ON and OFF source positions separated by 76'' in Azimuth, always integrating on-source. The back-end spectrometer covered the frequency range 73–111 GHz simultaneously. The spectral resolution is 31.25 MHz, which corresponds to 100 km s⁻¹ at 93 GHz. The primary beam size is 20'' at 110 GHz and 28'' at 75 GHz.

Data reduction was carried out using DREAMPY (Data REduction and Analysis Methods in PYthon), which is the pipeline software for the RSR data reduction written by G. Narayanan. After flagging scans affected by hardware or software problems, a linear baseline is removed from each spectrum. The rms noise level of the spectra at frequencies below 80 GHz is much higher than that for higher frequencies. There are no strong molecular lines in this frequency range. We thus excluded this frequency range and estimated the rms noise level of each spectrum using line-fee channels between ν_obs = 80 and 111 GHz. The rms noise levels in the frequency resolution of 31.25 GHz range between 0.14 and 0.40 mK (Avg. = 0.29 ± 0.01 mK) in the antenna temperature (${T}_{{\rm{A}}}^{* }$) unit.

We used the IDL GAUSSFIT function to identify molecular lines. We consider molecular lines whose peak intensity can be identified with a signal-to-noise ratio of >3 as "detected lines." Molecular lines detected with 2 < signal-to-noise ratio < 3 are considered to be "tentatively detected lines" if their velocities and line widths agree with those of other detected lines in the same sources. The Gaussian line fitting failed for C₂H (1–0) as this feature is a blend of two transitions, each with hyperfine structure. Therefore, for C₂H (1–0) we consider the line to be detected if at least two spectral channels at the correct frequency are above 3σ.

We used the CO (1–0) data of six sources (Arp 187, AM 0956-282, NGC 3597, AM 1300-233, AM 2055-425, and NGC 7252) obtained with the Atacama Large Millimeter/submillimeter Array (ALMA) 12 m array and the Atacama Compact Array (ACA: 7 m array + Total Power (TP) array) as part of 2011.0.00099.S, 2016.2.00006.S, and 2017.1.01003.S. In these projects, one spectral window was set to cover the redshifted CO (1–0) line. The bandwidth of the spectral window is 1.875 GHz and the frequency resolution is 488 kHz. In addition, we used the CO (1–0) data of NGC 3256 obtained with the ALMA 12 m (TM2) array and the ACA 7 m array as part of 2016.2.00042.S, 2016.2.00094.S, and 2018.1.00223.S. The data were obtained using single pointing. The full width at half maximum of the primary beam is ∼51'' at the observing frequency for a 12 m antenna. We adopt the typical systematic errors on the absolute flux calibration of 5% for the Band 3 data (e.g., Vilaro 2011; Andreani 2016).

We first restored the calibrated measurement set using the observatory-provided reduction script and the appropriate versions of the Common Astronomy Software Applications (CASA) package. Flux rescaling was applied to the ACA 7 m array data of Arp 187, NGC 3597, and AM 1300-233 because the more appropriate catalog values of the amplitude calibrators are available in the ALMA Calibrator Source Catalogue. After the continuum subtraction, we combined the 12 m array data and the 7 m array data and created the 12 m+7 m images by adopting Briggs weighting of the visibilities (robust = 0.5). For 6/7 sources, we also made the TP images and combined them with the 12 m+7 m images using the CASA feather task. The data of NGC 3256 were not corrected with the zero-spacing information because the TP array data are not available. The maximum recoverable angular scale calculated from the minimum baseline of the 7 m array (∼9 m) is ∼358 at the observing frequency. We compared the flux density measured in the 12 m+7 m image of NGC 3256 with the literature single-dish measurement (Casoli et al. 1992a). The recovered flux is 90% in the central 44'' region. The image rms per channel and the synthesized beam size are summarized in Table 2.

We calculate the intensity ratios of the dense gas tracers (HCN (1–0), HCO⁺(1–0), and HNC (1–0)) to ¹³CO (1–0) of 20 merger remnants detected in ¹³CO (1–0). The intensity ratios are shown as a function of the IR luminosity in Figure 2. Eleven out of 20 sources are U/LIRGs (L_IR ≥ 10¹¹ L_☉), and the remaining nine sources are non-LIRGs (L_IR < 10¹¹ L_☉). While the HCN/¹³CO and HCO⁺/¹³CO intensity ratios are higher than the unity for most of the U/LIRGs, they are lower than the unity for the non-LIRGs. On average, the HCN/¹³CO and HCO⁺/¹³CO intensity ratios of the U/LIRGs are 4.2 and 2.8 times higher than the non-LIRGs, respectively, suggesting different interstellar medium (ISM) environments. The HCN/¹³CO and HCO⁺/¹³CO intensity ratios of one ULIRG (UGC 8058) are higher than 10, which is 1 order of magnitude higher than those of the other U/LIRGs. Even when we exclude UGC 8058, the average HCN/¹³CO and HCO⁺/¹³CO ratios of the remaining ten U/LIRGs are 2.1 and 1.7 times higher than those of the non-LIRGs, respectively. Since all the HNC/¹³CO intensity ratios of the non-LIRGs are upper limits, it is difficult to investigate its dependency on the IR luminosity.

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One possibility for the elevated HCN/¹³CO and HCO⁺/¹³CO intensity ratios is a high dense gas fraction. Since the critical densities of HCN (1–0) and HCO⁺(1–0) are 2–3 orders of magnitude higher than that of ¹³CO (1–0) (Tielens 2005), the HCN (1–0) and HCO⁺ emission can trace the dense molecular gas. These elevated line ratios imply high dense gas fractions in the U/LIRGs, which are also suggested by high HCN (1–0)/¹²CO (1–0) ratios that we derive in Section 6.1. Another possibility is IR radiative pumping. HCN can be vibrationally excited to v₂ = 1 by absorbing mid-IR (14 μm) photons (Carroll & Goldsmith 1981). Then, HCN can decay back to the vibrational-ground level (v = 0). The subsequent cascade from the J = 2 state can enhance the intensity of the HCN (1–0) emission compared to the case when the excitation is caused only by collisions (Sakamoto et al. 2010; Rangwala et al. 2011). However, several studies have concluded that the IR pumping is not the main mechanism to explain high HCN luminosities (e.g., Gao & Solomon 2004b; Imanishi et al. 2016). HCO⁺ has a similar vibrational bending state at 12 μm, but the excitation of HCO⁺ through IR radiative pumping is less than that of HCN (Imanishi et al. 2016). In this study, both HCO⁺/¹³CO and HCN/¹³CO ratios are enhanced in the U/LIRGs. The elevated line ratios can be partially but not fully explained by only IR pumping. A deficiency of ¹³CO is another possibility for the elevated line ratios in the U/LIRGs. It is known that the ¹³CO emission is unusually weak relative to ¹²CO in U/LIRGs. The ¹²CO/¹³CO line ratios exceed 20 and reach 50 for some sources (Aalto et al. 1991; Sliwa et al. 2017), which are much higher than the ¹²CO/¹³CO line ratio of disk galaxies (∼10; Paglione et al. 2001). Several scenarios can explain high ¹²CO/¹³CO ratios, including optical depth effects and abundance variations (e.g., Casoli et al. 1992b; Henkel & Mauersberger 1993).

We check the relationship between the spatial extent of molecular gas obtained from previous high-resolution CO imaging and the intensity ratios calculated in Section 4.1. Ueda et al. (2014) found that about half of the merger remnants have extended disks of molecular gas traced by the CO and suggest that those extended gas disks can rebuild stellar disks and form disk-dominated late-type galaxies (LTGs). On the other hand, the merger remnants with compact gas disks are candidates that could become early-type galaxies (ETGs).

In Figure 3, we plot the intensity ratios of 17 sources as a function of the size of the molecular gas disk relative to the stellar component (R_ratio = R₈₀/R_eff in Table 1). R₈₀ is the radius from the galactic center, which contains 80% of the CO flux, and R_eff is the radius of the isophote containing half of the total K-band luminosity. Seven out of the 17 merger remnants with CO maps have molecular gas disks with R_ratio > 1, and 10 sources have molecular gas disks with R_ratio < 1. In general, the HCN/¹³CO, HCO⁺/¹³CO, and HNC/¹³CO ratios do not depend on R_ratio. One galaxy (UGC 8058) stands out as having both exceptionally large R_ratio and molecular line ratios and is the most IR luminous galaxy in our sample. When we exclude UGC 8058, the average HCN/¹³CO ratio of sources with R_ratio > 1 (0.92 ± 0.29) is comparable to that of sources with R_ratio < 1 (0.92 ± 0.15). Thus, the HCN/¹³CO intensity ratios are not likely to be affected by the different evolutionary pathways predicted by the CO spatial extent. This is suggested from the comparison of the HCN/¹³CO between ETGs and LTGs. The HCN/¹³CO intensity ratios of ETGs range from 0.18 to 0.58 (Krips et al. 2010; Crocker et al. 2012). They are consistent with the HCN/¹³CO intensity ratios of spiral galaxies and dwarf galaxies with normal SFRs (e.g., Krips et al. 2010; Matsushita et al. 2010; Watanabe et al. 2014). No significant difference between the different morphological types of galaxies (i.e., ETG and LTG) has been found.

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It is proposed that a high HCN/HCO⁺ line ratio can be a tracer of AGN-dominated systems (Kohno et al. 2001; Imanishi et al. 2007), although the line ratio changes depending on the observed angular scale. For instance, the HCN (1–0)/HCO⁺(1–0) luminosity ratio of NGC 1068 is estimated to be 1.64 ± 0.03 from single-dish measurements (Ω_PB ∼ 24''; Aladro et al. 2015). Meanwhile, it is ∼2.0 at the AGN position and its surrounding regions using interferometric measurements (θ_beam ∼ 6''; Viti et al. 2014). Since the large beam of a single-dish covers various regions such as the nucleus, circumnuclear disk, and starburst ring of NGC 1068, the line ratio is affected by contaminations from those regions with different chemical compositions.

The HCN (1–0)/HCO⁺(1–0) luminosity ratios of the merger remnants are presented in Figure 4 (left). The mean ${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{{\mathrm{HCO}}^{+}}^{{\prime} }$ of the merger remnants is 0.88 ± 0.08. The line ratios of two merger remnants that host X-ray-detected AGNs are presented by the black open circles in Figure 4 (left). Although they are higher than the mean ratio, they are similar to other merger remnants within the errors. This result is consistent with the previous study by Privon et al. (2015). While they found that the HCN (1–0) emission is enhanced in AGN-dominated systems, some composite and SB-dominated systems have HCN/HCO⁺ line ratios, which are comparable to those of AGN-dominated systems. Therefore, the global low-J HCN/HCO⁺ line ratio should be treated with caution when it is used as an indicator of an AGN.

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For comparison, we plot the HCN/HCO⁺ luminosity ratios of 44 local U/LIRGs in the subsample of the GOALS (Privon et al. 2015) in Figure 4 (left). The mean ${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{{\mathrm{HCO}}^{+}}^{{\prime} }$ of the late-stage mergers and early/mid-stage mergers are 1.02 ± 0.15 and 0.92 ± 0.12, respectively (Table 5). The mean ratio of the late-stage mergers decreases to 0.77 ± 0.08 when the AGN-dominated systems are excluded. These mean ratios are consistent with that of the merger remnants. There is no significant difference among the different merger stages at kpc scales.

Table 5. Mean Luminosity Ratios of the Dense Gas Tracers

Samples	${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{{\mathrm{HCO}}^{+}}^{{\prime} }$	${L}_{\mathrm{HNC}}^{{\prime} }/{L}_{\mathrm{HCN}}^{{\prime} }$	References
Merger remnants	0.88 ± 0.08	0.43 ± 0.05	1
Late-stage mergers	1.02 ± 0.15	0.52 ± 0.03	2
Early/Mid-stage mergers	0.92 ± 0.12	0.60 ± 0.09	2
Nonmerging LIRGs	1.38 ± 0.11	0.56 ± 0.07	2

References. (1) This work; (2) Privon et al. (2015).

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The HNC (1–0)/HCN (1–0) luminosity ratios of the merger remnants are presented in Figure 4 (right). The HNC/HCN luminosity ratios of seven merger remnants detected in both molecular lines range from 0.29 to 0.69, and the mean line ratio is 0.43 ± 0.05. The upper limits of ${L}_{\mathrm{HNC}}^{{\prime} }/{L}_{\mathrm{HCN}}^{{\prime} }$ of nine merger remnants are below 0.74. These results are consistent with the previous measurements of local IR-bright galaxies (Cicone et al. 2020) and spiral galaxies (Jiménez-Donaire et al. 2019), and suggest PDR-dominated sources (Baan et al. 2008). We plot the HNC/HCN luminosity ratios of 44 local U/LIRGs (Privon et al. 2015) in Figure 4 (right). The HNC/HCN luminosity ratios of all the U/LIRGs except for one galaxy are lower than unity. The mean ${L}_{\mathrm{HNC}}^{{\prime} }/{L}_{\mathrm{HCN}}^{{\prime} }$ of the late-stage mergers and early/mid-stage mergers are 0.52 ± 0.03 and 0.60 ± 0.09, respectively (Table 5). These are consistent with the mean ${L}_{\mathrm{HNC}}^{{\prime} }/{L}_{\mathrm{HCN}}^{{\prime} }$ of the merger remnants within the errors. Both HNC/HCN and HCN/HCO⁺ line ratios do not show differences among the different merger stages in kpc scales.

The HNC/HCN line ratio has been proposed as a tool for probing the gas kinematic temperature (T_kin), based on observations toward the Galactic sources. The HNC/HCN abundance ratios are close to unity in dark cloud cores at lower temperatures (Hirota et al. 1998), whereas they are as low as ∼0.013 in the vicinity of the Orion KL hot cores (Schilke et al. 1992). The HNC/HCN abundance ratio seems to decrease with increasing temperature. This is supported by the chemical models that predict that HNC tends to be selectively destroyed by neutral–neutral reactions at higher temperatures (Graninger et al. 2014). According to the empirical calibration derived by Hacar et al. (2020), the HNC/HCN luminosity ratios of 0.31–0.70 correspond to T_kin = 14–32 K, which are lower than the typical T_kin of star-forming galaxies estimated from ammonia observations (Mangum et al. 2013). Moreover, the HNC/HCN luminosity ratio of one nonmerging LIRG exceeds unity, which corresponds to T_kin < 10 K. Such low kinetic temperatures are unusual for IR-bright galaxies (T_kin ≥ 40 K; Aalto et al. 2007). High HNC/HCN line ratios (>1) have been found in local U/LIRGs and could be explained by IR radiative pumping or by XDRs (Aalto et al. 2007). From these observational results, we conclude that it is unlikely that the HNC/HCN line ratio averaged across an extragalactic source can be used as a tracer of the gas kinetic temperature.

The HCN (1–0)/CO (1–0) line ratio has been used as a proxy for the dense gas fraction (Gao & Solomon 2004b; Juneau et al. 2009). We calculate the HCN (1–0)/CO (1–0) luminosity ratios (${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{\mathrm{CO}}^{{\prime} }$) of 20 merger remnants when at least either HCN or CO luminosity was determined. We used literature values of ${L}_{\mathrm{CO}}^{{\prime} }$ measured with the IRAM 30 m telescope for 11/20 sources (Solomon et al. 1997; Zhu et al. 1999; Garland et al. 2005; Bertram et al. 2006; Jütte et al. 2010; Costagliola et al. 2011; García-Burillo et al. 2012; Aladro et al. 2015; Herrero-Illana et al. 2019). The beam of the IRAM 30 m telescope at ∼115 GHz (Ω_PB ∼ 22'') is ∼2'' smaller than the LMT beam at ∼88 GHz (Ω_PB ∼ 24''). To account for the unmatched beam sizes, we added an additional 20% uncertainty to the CO luminosity when calculating the HCN/CO luminosity ratio. We made the same correction to the CO luminosity for the control samples. We used literature ${L}_{\mathrm{CO}}^{{\prime} }$ of UGC 2238 measured with the National Radio Astronomy Observatory (NRAO) 12 m telescope (Sanders et al. 1991). The beam of the NRAO 12 m telescope (Ω_PB ∼ 55'') is much larger than the LMT beam, and the past CO imaging study reveals that the CO emission is distributed inside and outside the LMT beam (R_CO = 205; Ueda et al. 2014). Hence, we consider ${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{\mathrm{CO}}^{{\prime} }$ of UGC 2238 as a lower limit. We calculated ${L}_{\mathrm{CO}}^{{\prime} }$ of seven sources using the ALMA CO (1–0) maps. We measured the CO integrated intensity within 24'', which is the same as the LMT beam at ∼88 GHz. We added an additional 10% uncertainty to ${L}_{\mathrm{CO}}^{{\prime} }$ of NGC 3256 to account for the missing flux. Since the data of the remaining six sources were corrected with the zero-spacing information, we have not made any additional correction. Similarly, we measured ${L}_{\mathrm{CO}}^{{\prime} }$ of NGC 2782 using the PdBI CO (1–0) map (Hunt et al. 2008). Ueda et al. (2014) have found that the data suffer from missing flux. The recovered flux is 54%. We thus use ${L}_{\mathrm{CO}}^{{\prime} }$ of NGC 2782 as the lower limit. The literature and derived CO luminosities are summarized in Table 4.

The HCN/CO luminosity ratios of the 20 merger remnants are shown as a function of the IR luminosity in Figure 5. There is a positive correlation between ${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{\mathrm{CO}}^{{\prime} }$ and L_IR. In our sample, the average ${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{\mathrm{CO}}^{{\prime} }$ of the U/LIRGs is 3 times higher than that of the non-LIRGs. This suggests that the U/LIRGs have a higher dense gas fraction when compared to the non-LIRGs. The median ${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{\mathrm{CO}}^{{\prime} }$ of the merger remnants is 0.045 (Table 6). Adapting the standard luminosity-to-mass conversion factors (α_CO = 4.35 M_☉ (K km s⁻¹ pc²)⁻¹ and ${\alpha }_{\mathrm{HCN}}=10\,{M}_{\odot }$ (K km s⁻¹ pc²)⁻¹; Gao & Solomon 2004b; Bolatto et al. 2013), the HCN/CO luminosity ratio of 0.045 corresponds to a dense gas fraction (M_dense/${M}_{{{\rm{H}}}_{2}}$) of ∼10%, where M_dense is the dense molecular gas mass and ${M}_{{{\rm{H}}}_{2}}$ is the molecular gas mass. The largest HCN/CO luminosity ratios correspond to a dense gas fraction of order unity. It is known that the CO luminosity-to-mass conversion factor in U/LIRGs is lower than the standard value (e.g., α_CO = 0.6–0.8; Downes & Solomon 1998; Papadopoulos et al. 2012). When a small α_CO is adopted, the dense gas fraction increases.

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Table 6. Dense Gas Fraction, SFR_dense, and SFE

Samples	${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{\mathrm{CO}}^{{\prime} }$		${L}_{\mathrm{IR}}/{L}_{\mathrm{HCN}}^{{\prime} }$		${L}_{\mathrm{IR}}/{L}_{\mathrm{CO}}^{{\prime} }$		References
	mean	median	mean	median	mean	median
Merger remnants	0.070 ± 0.020	0.045	(2.9 ± 0.5) × 103	2.4 × 103	150±30	123	1
Late-stage mergers	0.093 ± 0.021	0.063	(2.0 ± 0.3) × 103	2.1 × 103	170±40	117	2,3
Early/Mid-stage mergers	0.093 ± 0.027	0.050	(1.6 ± 0.5) × 103	1.3 × 103	87±17	65	2,3
Nonmerging LIRGs	0.098 ± 0.012	0.078	(8.5 ± 0.6) × 102	8.5 × 102	89±12	72	2,3
Late-type galaxies	0.061 ± 0.008	0.049	(7.5±1.0) × 102	5.1 × 102	39±6	28	4

References. (1) This work; (2) Privon et al. (2015); (3) Herrero-Illana et al. (2019); (4) Gao & Solomon (2004).

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For comparison, we plot the HCN/CO luminosity ratios of the late-stage mergers, early/mid-stage mergers, and nonmerging galaxies (Privon et al. 2015; Herrero-Illana et al. 2019) and the LTGs (Gao & Solomon 2004b) in Figure 5. There appears to be little correlation between ${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{\mathrm{CO}}^{{\prime} }$ and L_IR for L_IR < 10¹¹ L_☉, but ${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{\mathrm{CO}}^{{\prime} }$ is strongly correlated with L_IR at higher L_IR. The histogram of ${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{\mathrm{CO}}^{{\prime} }$ in each sample is shown in Figure 6 (left). We compute the Kolmogorov–Smirnov (K-S) statistic on the merger remnant sample and the control sample. The P-values from the K-S test are summarized in Table 7. The P-values for our sample and the samples in the different stages of mergers are large (≥0.38), suggesting that the populations are not significantly different. Numerical simulations predict that the dense gas fraction largely increases during the merging process, modifying the global gas density distribution of merging galaxies (e.g., Juneau et al. 2009; Bournaud 2011; Moreno et al. 2019). However, we do not find such a trend in this study, assuming that the same luminosity-to-mass conversion factors can be adopted for all the mergers regardless of the merger stages. The mean ${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{\mathrm{CO}}^{{\prime} }$ is consistent between the early/mid-stage and the late-stage (Table 6), and decreases in the postmerger stage. The HCN/CO luminosity ratios of the nonmerging LIRGs are relatively high (Figure 6), and the P-value for the merger remnants and the nonmerging LIRGs is small (≪0.05). This implies that a high dense gas fraction may play a crucial role in enhancing star formation in nonmerging galaxies, compared to merger remnants.

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Table 7. Kolmogorov–Smirnov Test P-value

Samples	${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{\mathrm{CO}}^{{\prime} }$	${L}_{\mathrm{IR}}/{L}_{\mathrm{HCN}}^{{\prime} }$	${L}_{\mathrm{IR}}/{L}_{\mathrm{CO}}^{{\prime} }$
Merger remnants—Late-stage mergers	0.38	0.53	0.95
Merger remnants—Early/Mid-stage mergers	0.81	0.03	0.04
Merger remnants—Nonmerging LIRGs	≪0.05	≪0.05	0.03
Merger remnants—Late-type galaxies	0.44	≪0.05	≪0.05

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We calculate the IR-to-HCN (1–0) luminosity ratio, which is a proxy for the SFE_dense (=SFR/M_dense). The IR/HCN luminosity ratios of the 21 merger remnants are shown as a function of the IR luminosity in Figure 7. While the luminosity ratios vary from source to source ((1.1–6.5) × 10³ L_☉/(K km s⁻¹ pc²)), there is no dependency of ${L}_{\mathrm{IR}}/{L}_{\mathrm{HCN}}^{{\prime} }$ on L_IR. The best-fit line for the merger remnants (the solid black line) is almost flat in Figure 7. This can be expected based on the well-known correlation between ${L}_{\mathrm{HCN}}^{{\prime} }$ and L_IR (Gao & Solomon 2004a). However, the mean ${L}_{\mathrm{IR}}/{L}_{\mathrm{HCN}}^{{\prime} }$ of the merger remnants is about 4 times higher than the mean ${L}_{\mathrm{IR}}/{L}_{\mathrm{HCN}}^{{\prime} }$ (∼776 L_☉/(K km s⁻¹ pc²)) derived using more than 800 data points of various sources, including resolved cores and giant molecular clouds (GMCs) in the Galaxy, resolved galaxy disks, and entire galaxies (Jiménez-Donaire et al. 2019).

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The IR/HCN luminosity ratios of the control samples are also plotted in Figure 7. There appears to be a difference in ${L}_{\mathrm{IR}}/{L}_{\mathrm{HCN}}^{{\prime} }$ among the samples. The mean ${L}_{\mathrm{IR}}/{L}_{\mathrm{HCN}}^{{\prime} }$ are (2.9 ± 0.5) × 10³ for the 16 merger remnants with HCN detections, (2.0 ± 0.3) × 10³ for the late-stage mergers, (1.6 ± 0.5) × 10³ for the early/mid-stage mergers, (8.5 ± 0.6) × 10² for the nonmerging LIRGs, and (7.5 ± 1.0) × 10² for the LTGs in the unit of L_☉/(K km s⁻¹ pc²). We find that the mean ratio increases from the early-stage mergers to the late-stage mergers and the merger remnants (Table 6). The mean ${L}_{\mathrm{IR}}/{L}_{\mathrm{HCN}}^{{\prime} }$ of the merger remnants is more than 3 times higher than those of the nonmerging LIRGs and the LTEs. The histogram of ${L}_{\mathrm{IR}}/{L}_{\mathrm{HCN}}^{{\prime} }$ in each sample is shown in Figure 6 (middle). The K-S test gave P-value = 0.53 for our sample and the sample of late-stage mergers (Table 7). In contrast, it gave P-values smaller than 0.05 for our sample and the other three control samples, suggesting that the populations are different. According to García-Burillo et al. (2012), the SFE_dense averaged across the entire galaxy varies for different galaxy types. They assembled a sample of ∼100 normal galaxies and U/LIRGs and found that ${L}_{\mathrm{IR}}/{L}_{\mathrm{HCN}}^{{\prime} }$ is on average a few times higher in the U/LIRGs (∼1400 ± 100) compared to the normal galaxies (∼600 ± 70). However, in the merger remnant sample, not only U/LIRGs but also non-LIRGs show high ${L}_{\mathrm{IR}}/{L}_{\mathrm{HCN}}^{{\prime} }$. Along with our new finding that the IR/HCN luminosity ratio increases along the merger sequence, these results suggest that the SFE_dense is enhanced during dynamical interactions and mergers.

We calculate the IR-to-CO (1–0) luminosity ratio, which is also a proxy for the SFE. The IR/CO luminosity ratios of the merger remnants and the control samples are plotted in Figure 8. The luminosity ratios are distributed over 2 orders of magnitudes and increase with the IR luminosity, suggesting that the SFE is enhanced in active star-forming galaxies. The mean ${L}_{\mathrm{IR}}/{L}_{\mathrm{CO}}^{{\prime} }$ of the 18 merger remnants with CO detections is (1.5 ± 0.3) × 10² L_☉/(K km s⁻¹ pc²). This is comparable to the late-stage mergers ((1.7 ± 0.4) × 10² L_☉/(K km s⁻¹ pc²)) and about 2 times higher than those of the early/mid-stage mergers and the nonmerging LIRGs. These similarities and differences are also shown by the histograms of ${L}_{\mathrm{IR}}^{{\prime} }/{L}_{\mathrm{CO}}$ (Figure 6 (right)) and the results of the K-S test (Table 7). Overall, these results agree with the previous studies utilizing large samples of optically selected galaxies. As Violino et al. (2018) found using the depletion time (=1/SFE), the depletion time of the early-stage mergers, which are observed as galaxy pairs, are consistent with those of nonmerging LIRGs. Pan et al. (2018) found that the SFE is enhanced in closer pairs of equal-mass galaxies. We also find a similar trend that the SFE is enhanced in the merger remnants and the late-stage mergers, although the exact fraction of these samples that result from a major merger is unknown since it is difficult to reverse the chronology and disentangle the exact mass and morphology of the progenitors.

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We find that, on average, the IR/HCN and IR/CO luminosity ratios of the merger remnants are comparable to those of the late-stage mergers and higher compared to the early/mid-stage mergers, the nonmerging LIRGs, and the LTGs. This result suggests that not only the SFE but also the SFE_dense are increased by dynamical interactions and mergers. In addition, the SFEs do not change significantly between pre- and post-coalescence. A high efficiency of converting gas into stars has been commonly proposed as a possibility for intense star formation in galaxy mergers. Recently observational studies have been conducted to check this enhancement (e.g., Michiyama et al. 2016; Pan et al. 2018; Violino et al. 2018). As seen in the previous sections, we investigate the SFE_dense and SFE of galaxies at different stages of mergers, finding enhanced SFE_dense in the merger remnants. The SFE enhancement in galaxy pairs and mergers has been predicted by simulations (e.g., Di Matteo et al. 2007; Moreno et al. 2020). The parsec-resolution simulation shows that the compressive turbulence generates an excess of dense gas along the merging process, leading to an enhanced SFE (Renaud et al. 2014). By using zoom-in simulations of major mergers identified in the cosmological simulation, Sparre & Springel (2016) find that the SFR enhancement is driven by the increase in the molecular gas reservoir during the galaxy-pair period, leading to an increased SFE close to the final coalescence. When the gas is compressed by dynamical interactions and reaches high densities, the star formation timescale is shorter than the cloud evaporation timescale, implying that a large fraction of the gas is converted into stars before the cold clouds are evaporated by thermal conduction. Therefore, stars form much more efficiently than normal star-forming gas. This zoom-in simulation also shows that the gas is turned into stars with high efficiency even after the final coalescence (Sparre & Springel 2016). Our result is consistent with this theoretical prediction, indicating that the merging process affects the star formation properties of the gas in the postmerger phase.

We recompare ${L}_{\mathrm{IR}}/{L}_{\mathrm{HCN}}^{{\prime} }$ between the merger remnants and the nonmerging LIRGs by matching the range of their L_IR. We select sources with 10¹¹(L_⊙) ≤ L_IR < 10¹²(L_⊙) (i.e., LIRGs) from the merger remnant sample and plot ${L}_{\mathrm{IR}}/{L}_{\mathrm{HCN}}^{{\prime} }$ as a function of ${L}_{\mathrm{HCN}}^{{\prime} }/{L}_{\mathrm{CO}}^{{\prime} }$ in Figure 9. We find that these two samples occupy two different regions in the plot. The merger remnants show higher SFE_dense and lower dense gas fraction, whereas the nonmerging LIRGs show lower SFE_dense and higher dense gas fraction. This suggests that the different modes of star formation may be taking place in these samples. Merger remnants have a high SFE_dense due to the ISM turbulence (Krumholz & McKee 2005), which could help compress the diffuse gas reservoirs, hence efficiently boosting star formation. On the other hand, star formation could be enhanced in nonmerging galaxies by increasing the dense gas. An enrichment of the molecular gas reservoir has also been proposed as a possibility for intense star formation.

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Another possibility for the different distributions presented in Figure 9 is that the conversion factor from the HCN luminosity into the dense gas mass (${\alpha }_{\mathrm{HCN}}$) is not the same between the merger remnants and the nonmerging LIRGs. If ${\alpha }_{\mathrm{HCN}}$ for the merger remnants is higher by a factor of ∼3 than ${\alpha }_{\mathrm{HCN}}$ for the nonmerging LIRGs, the data points of the merger remnants would shift toward the bottom right in Figure 9 and overlap with the distribution of the nonmerging LIRGs. The dense gas conversion factor derived by Gao & Solomon (2004b) has been widely used for all extragalactic environments. This conversion factor is derived under the assumption that the HCN (1–0) emission originates from a virialized cloud core with an average density of 3 × 10⁴ cm⁻³ and a brightness temperature of 35 K. However, the dense gas conversion factor depends on various factors, such as the density and the excitation condition. If the brightness temperature of the HCN emitting clumps is larger than 35 K, or if their averaged density is less than 3 × 10⁴ cm⁻³, the conversion factor can become smaller (Shimajiri et al. 2017). Several observational studies and simulations have investigated variations in ${\alpha }_{\mathrm{HCN}}$ (e.g., Krumholz & Tan 2007; Wu et al. 2010; Mills & Battersby 2017; Vollmer et al. 2017). Shimajiri et al. (2017) compare the HCN (1–0) luminosity in the Galactic GMCs with the dense molecular gas mass estimated from Herschel column density maps and suggest that variations in ${\alpha }_{\mathrm{HCN}}$ could be related to the far-ultraviolet field, that is, to gas excitation and/or chemistry variations. Onus et al. (2018) found that the dense gas conversion factor is ${\alpha }_{\mathrm{HCN}}\simeq 14$ M_☉ (K km s⁻¹ pc²)⁻¹ using hydrodynamical simulations, but the uncertainty is a factor of ∼2 mainly due to variations in the HCN abundance. The dense gas conversion factor can vary from source to source, and the variation at a factor of ∼3 level could be plausible.

Another possibility is that the dense gas is rapidly depleted in the merger remnants, resulting in an apparent high SFE_dense and a lower dense gas fraction. Di Matteo et al. (2007) found that an increase in the SFR is correlated with an increase in the SFE in modeled galaxy pairs and mergers, but the SFE peak is slightly delayed in time compared to the SFR peak for the most intense starbursts. The gas is more rapidly depleted by the merger-induced intense star formation, and then the amount of gas content decreases in merged galaxies. This condition can make an apparent high SFE as the SFE_dense is computed by SFR/M_dense.