Molecular gas in VV 114

# ALMA Multi-line Observations of the IR-bright Merger VV 114

Toshiki Saito11affiliationmark: 2 2affiliationmark: , Daisuke Iono22affiliationmark: 3 3affiliationmark: , Min S. Yun44affiliationmark: , Junko Ueda22affiliationmark: , Kouichiro Nakanishi22affiliationmark: 3 3affiliationmark: 5 5affiliationmark: , Hajime Sugai66affiliationmark: , Daniel Espada22affiliationmark: 5 5affiliationmark: , Masatoshi Imanishi22affiliationmark: 3 3affiliationmark: 7 7affiliationmark: , Kentaro Motohara88affiliationmark: , Yosiaki Hagiwara22affiliationmark: , Ken Tateuchi88affiliationmark: , Minju Lee11affiliationmark: 22affiliationmark: and Ryohei Kawabe11affiliationmark: 2 2affiliationmark: 3 3affiliationmark: Department of Astronomy, Graduate school of Science, The University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 133-0033, Japan National Astronomical Observatory of Japan, 2-21-1 Osawa, Mitaka, Tokyo, 181-8588, Japan The Graduate University for Advanced Studies (SOKENDAI), 2-21-1 Osawa, Mitaka, Tokyo 181-0015, Japan Department of Astronomy, University of Massachusetts, Amherst, MA 01003, USA Joint ALMA Observatory, Alonso de Córdova 3107, Vitacura, Casilla 19001, Santiago 19, Chile Kavli Institute for the Physics and Mathematics of the Universe (WPI), The University of Tokyo, 5-1-5 Kashiwanoha, Kashiwa, Chiba 277-8583, Japan Subaru Telescope, 650 North A’ohoku Place, Hilo, HI 96720, USA Institute of Astronomy, The University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-0015, Japan
###### Abstract

We present ALMA cycle 0 observations of the molecular gas and dust in the IR-bright mid-stage merger VV 114 obtained at 160 – 800 pc resolution. The main aim of this study is to investigate the distribution and kinematics of the cold/warm gas and to quantify the spatial variation of the excitation conditions across the two merging disks. The data contain 10 molecular lines, including the first detection of extranuclear CHOH emission in interacting galaxies, as well as continuum emission. We map the CO (3–2)/CO (1–0) and the CO (1–0)/CO (1–0) line ratio at 800 pc resolution (in the units of K km s), and find that these ratios vary from 0.2 – 0.8 and 5 – 50, respectively. Conversely, the 200 pc resolution HCN (4–3)/HCO (4–3) line ratio shows low values ( 0.5) at a filament across the disks except for the unresolved eastern nucleus which is three times higher (1.34 0.09). We conclude from our observations and a radiative transfer analysis that the molecular gas in the VV 114 system consists of five components with different physical and chemical conditions; i.e., 1) dust-enshrouded nuclear starbursts and/or AGN, 2) wide-spread star forming dense gas, 3) merger-induced shocked gas, 4) quiescent tenuous gas arms without star formation, 5) H gas mass of (3.8 0.7) 10 M (assuming a conversion factor of = ) at the tip of the southern tidal arm, as a potential site of tidal dwarf galaxy formation.

galaxies: individual (VV 114, IC 1623, Arp 236) — galaxies: interactions — galaxies: starburst — galaxies: nuclei — ISM: molecules

## 1. Introduction

Galaxy interactions and mergers play important roles in triggering star formation and/or fueling the nuclear activity in the merging host galaxies (Hopkins et al., 2006). Recent high resolution simulations of major mergers show that large scale tidal forces as well as small scale turbulence and stellar feedback can significantly influence the distribution of gas, forming massive clumps of dense gas with = 10 – 10 M (e.g., Teyssier et al., 2010; Hopkins et al., 2013). These simulations also predict that the star formation not only increases as the galaxies first collide, but it also persists at a higher rate throughout the merger process, peaking at the final coalescence.

(Ultra-)Luminous Infrared Galaxies (U/LIRGs; Soifer et al., 1987) at low redshifts are almost exclusively strongly interacting and merging systems (Kartaltepe et al., 2010), often found at the mid to final stages of the merger. The elevated level of infrared luminosity originates from the reprocessed emission from the dust particles surrounding the starburst or the Active Galactic Nuclei (AGNs), both of which are likely triggered by the tidal interaction. The highest gas surface densities ( = 5.4 10 – 1.4 10 M pc) and consequently the highest star formation activities ( = 1000 M yr kpc) are usually found near the compact nuclear region (e.g., Arp220, NGC 6240; Downes & Solomon, 1998; Engel et al., 2010; Wilson et al., 2014). Dense molecular gas ( 10 – 10 cm) in U/LIRGs directly shows nuclear gas distribution and kinematics (e.g., Iono et al., 2004; Sakamoto et al., 2014). They are often surrounded by diffuse gas ( 10 – 10 cm) that may or may not be directly associated with star formation activities.

It has been demonstrated that the HCN (4–3) and HCO (4–3) emission lines, whose critical densities are 8.5 10 and 1.8 10 cm, respectively, can be used as tracers of the dense gas (e.g., Iono et al., 2013; Garcia-Burillo et al., 2014; Imanishi & Nakanishi, 2014). On the other hand, CO (1–0) and CO (1–0) line emission, whose critical densities are 4.1 10 and 1.5 10 cm, respectively, have been used extensively for tracing the global gas distribution and kinematics in merging U/LIRGs (e.g., Yun et al., 1994; Iono et al., 2004; Ueda et al., 2014). In addition, the ratio of these lines (e.g. CO/CO and HCN/HCO) have been used to investigate the properties of the ISM (Casoli et al., 1992; Aalto et al., 1997) or to search for buried AGNs (e.g., Imanishi et al., 2007; Imanishi & Nakanishi, 2014). Limitations in sensitivity and angular resolution have been the major obstacles in understanding the detailed distribution and kinematics of both dense and diffuse gas, and investigating the spatial variation of the line ratios and the physical condition of gas.

In this paper, we present Atacama Large Millimeter/submillimeter Array (ALMA) cycle 0 observations of the IR-bright merging galaxy VV 114. VV 114 is one of the best samples for studying the gas response during the critical stage when the two gas disks merge (Iono et al., 2005; Wilson et al., 2008). The target molecular lines include CO (1–0), CO (1–0), CO (3–2), HCN (4–3) and HCO (4–3), and we also present the maps of CHOH (2–1), CS (2–1), CN (1–0), CN (1–0), and CS (7–6) lines which were observed simultaneously within the same band. The main aim of this study is to investigate the distribution and kinematics of the diffuse and dense molecular gas and to quantify the spatial variation of the excitation conditions across the two merging disks.

VV 114 is a gas-rich ( = 5.1 10 M; Yun et al., 1994) nearby (D = 82 Mpc; 10 = 400 pc) interacting system (Figure 1) with high-infrared luminosity ( = 4.7 10 ; Armus et al., 2009). The projected nuclear separation between the two optical galaxies (VV 114E and VV 114W) is about 6 kpc. Frayer et al. (1999) found a large amount of dust ( = 1.2 10 M) distributed across the system with a dust temperature of 20 – 25 K. About half of the warmer dust traced in the mid-IR (MIR) is associated with the eastern galaxy, where both compact (nuclear region) and extended emission is found (Le Floc’h et al., 2002). Rich et al. (2011) found a bimodal distribution of velocity dispersions of several atomic forbidden lines and emission line ratios indicative of composite activity explained by a combination of wide-spread shocks and star formation. The wide-spread star formation is also revealed by Pa observation using ANIR camera mounted on miniTAO (Tateuchi et al., 2012, see also Appendix A.1). Iono et al. (2013) (hereafter paper I) identified a highly obscured AGN and compact starburst clumps using sub-arcsecond resolution ALMA cycle 0 observations of HCN (4–3) and HCO (4–3) emission.

This paper is organized as follows. We describe our observations and data reduction in §2, and results in §3. In §4 and §5, we provide molecular line ratios and physical parameters, such as the gas/dust mass, the gas temperature, and the gas density. In §6, we present the properties of “dense” gas (§6.1), the comparison between molecular gas and star formation (§6.2), the discussions of the CO isotope enhancement (§6.3), the gas-to-dust mass ratio (§6.4), the fractional abundances of CS, CHOH, and CN relative to H6.5), and a potential tidal dwarf galaxy formations at the tip of the tidal arms of VV 114 (§6.6). We summarize and conclude this paper in §7. Throughout this paper, we adopt H = 73 km s Mpc, = 0.27, and = 0.73.

## 2. Observations and Data Reduction

Observations toward VV 114 were carried out as an ALMA cycle 0 program (ID = 2011.0.00467.S; PI = D. Iono) using fourteen – twenty 12 m antennas. The band 3 and band 7 receivers were tuned to the CO (1–0),  CO (1–0), CO (3–2), HCN (4–3), and HCO (4–3) line emissions in the upper side band (see Table 1). The CO (1–0) data were obtained on November 6, 2011 and May 4, 2012 in the compact and extended configurations, respectively. The CO (1–0) data were obtained on May 27 and July 2, 2012 in the compact configuration. The CO (3–2) emission was observed on November 5, 2011 in the compact configuration (7-point mosaic). The HCN (4–3) and HCO (4–3) data were obtained on July 1, 2, and 3, 2012 in the extended configuration (3-point mosaic), simultaneously. Each spectral window had a bandwidth of 1.875 GHz with 3840 channels, and two spectral windows were set to each sideband to achieve a total frequency coverage of 7.5 GHz in these observations. The spectral resolution was 0.488 MHz per channel. J1924-292, J0132-169, Uranus (Neptune for band 3 observations) were used for bandpass, phase, and flux calibrations. Detailed observational parameters are shown in Table 1.

We used the delivered calibrated data and mapping was accomplished using the clean task in CASA (McMullin et al., 2007). We made the data cubes with a velocity width of 5 km s for the CO line and 30 km s for the other lines. All maps in this paper, except for CO (3–2), are reconstructed with a Briggs weighting (robust = 0.5; Briggs & Cornwell, 1992) and analyzed with MIRIAD and AIPS. The CO (3–2) images are created with uniform weighting (see §3.2). The synthesized beam size of the CO (1–0), CO (1–0), CO (3–2), and HCN (4–3) were 197 135 (P.A. = 82.3 deg.), 177 120 (P.A. = 85.8 deg.), 164 117 (P.A. = 112.6 deg.), and 046 038 (P.A. = 51.5 deg.), respectively. We also detected CN (1–0), CN (1–0), CS (2–1), CHOH (2-1), and CS (7–6) line emission for the first time in VV 114. The properties of these molecular lines are summarized in Table 2. All images which we constructed are corrected for primary beam attenuation. The on-source times of band 3 and band 7 were about 40 minutes and 80 minutes, and the rms noise levels of the channel maps with 30 km s resolution are 1.0 mJy beam and 0.8 mJy beam, respectively. Furthermore, we made continuum maps at each observing frequency by adding the line-free channels. The rms level of the continuum images were 0.05 mJy beam, 0.11 mJy beam, and 0.07 mJy beam for band 3, band 7 in the compact configuration, and band 7 in the extended configuration, respectively. The continuum emission was subtracted in the -plane before making the line images. Throughout this paper, the pixel scales of the band 3 and the band 7 images are set to 03/pixel and 008/pixel, respectively, and only the statistical error is considered unless mentioned otherwise. The systematic error on the absolute flux is estimated to be 5% and 10% for both sidebands in band 3 and band 7, respectively.

In the following sections, we estimate the missing flux of each molecular line for which the single dish data are available in literature. Although the effect of missing flux becomes critical when we evaluate the global gas properties and the corresponding line ratios, the effect is negligible when we discuss structures that are smaller than the “maximum recoverable scale” (MRS) of each configuration of ALMA. This is estimated from the minimum baseline lengths of the assigned antenna configurations and the observed frequencies. The MRS of our observations are 8″ and 7″ in band 3 and band 7, respectively (Table 1). Therefore the missing flux effect in this paper is negligible, since we derive physical parameters (e.g., molecular gas mass) only for structures smaller than 2″.

## 3. Results

Molecular line and continuum images are shown in Figures 2, 3, 4, 5, and 6. The channel maps and the spectra of all line emissions are shown in Appendix A.2 and A.3.

### 3.1. Line Emissions in Band 3

#### 3.1.1 12Co (1–0)

The integrated intensity, velocity field, and velocity dispersion maps of VV 114 are shown in Figures 2a, 2b, and 2c, respectively. The total CO (1–0) integrated intensity of VV 114 is 594.6 1.6 Jy km s, which is 1.3 times larger than that detected using the NRAO 12 m telescope (461 Jy km s; Sanders et al., 1991). This is because the pointing center for the NRAO 12 m observation was 250 southwest of the CO centroid identified from the ALMA map (NRAO 12 m: 01h07m45.7s, -17d30m36.5s; CO centroid: 01h07m47.2s, -17d30m25.8s). At the adopted distance of VV 114 (86 Mpc), the 197 135 beam of the CO (1–0) observation gives us a resolution of 790 pc 540 pc. The two crosses shown in all images represent the peaks obtained from the miniTAO/ANIR s-band observation, and we regard them as the progenitor’s nuclei.

The integrated CO (1–0) intensity map of VV 114 (Figure 2a) shows that the diffuse/cold gas forms two arm-like structures and a filamentary structure located at the center of the image. The global gas distribution is consistent with the previous CO (1–0) observations (Yun et al., 1994). The southeastern (SE) arm clearly follows the tidal arm seen in the HST/ACS image (Figure 1; Evans, 2008), while the northwestern (NW) arm has no counterpart in any other wavelengths. The region from the center of VV 114 to the eastern nucleus shows a strong concentration of molecular gas ( 55 west of the eastern nucleus), and we refer to this region as the “overlap” region with a molecular “filament” (see Figure 2).

The CO (1–0) velocity field map of VV 114 (Figure 2b) shows a significantly broad velocity range across the galaxy disks ( 600 km s). The SE arm has a blue-shifted velocity from 5650 km s to 5920 km s, while the NW arm has a red-shifted velocity from 5950 km s to 6160 km s. One possibility for the larger velocity width in the SE arm may be a highly inclined tidal arm. Two other arm-like features are also detected in the CO (1–0) observations. One arm is located 40 northeast of the eastern nucleus and shows an arc around the eastern nucleus in the velocity range of 5810 km s to 6180 km s. The other arm is located 100 west of the SE arm and has a strong peak ( 262.5 1.0 Jy km s) in the velocity range of 5610 km s to 5900 km s.

The overlap region has the highest velocity dispersion ( 110 km s) (Figure 2c). The NW arm has an average velocity dispersion of 30 km s, while the SE arm has 40 km s. These values are significantly higher than the dispersions seen in Giant Molecular Clouds (GMCs) in the LMC (2 – 14 km s; Minamidani et al., 2008; Fujii et al., 2014) and slightly higher than that in Giant Molecular Associations (GMAs) in the Antennae galaxy (6 – 36 km s; Ueda et al., 2012). We suggest that the main contribution to the CO (1–0) velocity dispersion is inter cloud turbulent medium along the tidal arm, and/or shocked region induced by the tidal interaction, rather than the velocity dispersion of the GMCs/GMAs.

#### 3.1.2 13Co (1–0)

The integrated intensity, velocity field, and velocity dispersion maps of CO (1–0) are shown in Figures 2d, 2e, and 2f, respectively. The integrated CO (1–0) intensity map of VV 114 (Figure 2d) shows a filamentary structure across the galaxy disks, which is consistent with the region where the CO (1–0) filament is detected. The total CO (1–0) integrated intensity is 5.9  Jy km s. The strongest peak is located 42 southwest of the eastern nucleus. The CO (1–0) velocity field map of VV 114 (Figure 2e) shows a narrower velocity range (5670 – 6000 km s) than that of the CO (1–0) emission (5600 – 6200 km s). This suggests that the CO (1–0) emission mainly comes from two components, the eastern galaxy and the blue-shifted component of the overlap region. The CO (1–0) velocity dispersion map of VV 114 (Figure 2f) shows a high velocity dispersion component ( 100 km s) between the eastern nucleus and the overlap region. This significant velocity dispersion may be caused by a superposition of clouds (see the double-peak spectrum at R39 shown in Appendix A.3).

#### 3.1.3 CS (2–1) and CH3Oh (2k–1k)

The CS (2–1) and CHOH (2–1) lines are only detected at the overlap region (Figures 2g, 2h, 2i, 3a, 3b, and 3c). This is the first detection of the CHOH (2–1) emission in a merger-induced overlap region. We observed the blended set of 2 – 1 ( = 96.756 GHz, = 28.0 K), 2 – 1 E ( = 96.745 GHz, = 20.1 K), 2 – 1 A ( = 96.741 GHz, = 7.0 K), and 2 – 1 E ( = 96.739 GHz, = 12.5 K), thermal transitions of CHOH (hereafter designated the 2 – 1 transition). The distribution of these molecular lines is clearly different from the other dense gas tracers detected in the current program. The peaks of CS (2–1) and CHOH (2–1) are coincident with one of the peaks of CO (1–0) to within 05. The total CS (2–1) and CHOH (2–1) integrated intensities are 0.4 0.1 Jy km s and 0.5 0.1 Jy km s, respectively. The signal to noise is too low to resolve the velocity structure.

#### 3.1.4 Cn (13/2–01/2) and CN (11/2–01/2)

Two radical CN rotational transitions N = 1 – 0 (J = 3/2 – 1/2 and 1/2 – 1/2) are detected at the eastern nucleus. The = 3/2 – 1/2 transition is extended toward the overlap region (Figures 3d, 3e, 3f, 3g, 3h, and 3i). We can not resolve their multiplet because of the coarse frequency resolution (11.5 MHz 30 km s). Because the critical density of CN is high ( 10 cm), the CN emission mainly comes from denser gas regions than regions traced by CO (1–0). The J = 3/2 – 1/2 transition shows a similar distribution to the CO (1–0) emission, but it is less extended over the overlap region. The total CN (1–0) and CN (1–0) integrated intensities are 2.0 0.1 Jy km s and 5.4 0.3 Jy km s, respectively. The highest velocity dispersion in the CN (1–0) image is also detected between the eastern nucleus and the overlap region, and this is likely caused by a superposition of clouds similar to the case of the CO (1–0) image (see Appendix  A.3).

### 3.2. Line Emission in Band 7

#### 3.2.1 12Co (3–2)

The CO (3–2) emission maps are presented in Figure 4. The estimated missing flux in our ALMA observation is 21 1 % (James Clerk Maxwell Telescope (JCMT): 2956 133  and ALMA: 2343.7 4.7 ; Wilson et al., 2008; Saito et al., 2013). Although our CO (3–2) observation recovers more flux than the Submillimeter Array (SMA) observation (1530 16 ; the missing flux = 48 15 %; Wilson et al., 2008), there are significant negative sidelobes at the north and south of the image which is likely the cause of missing flux. We made the CLEANed image with a uniform uv weighting to minimized the sidelobe level (Thompson et al., 2001).

The CO (3–2) integrated intensity map of VV 114 (Figure 4a) shows two arm-like structures and a filamentary structure similar to the CO (1–0) image, and the strongest peak is at 55 west of the eastern nucleus. The global gas distribution is consistent with the previous CO (3–2) observations (Iono et al., 2004; Wilson et al., 2008). The CO (3–2) velocity field map of VV 114 (Figure 4b) also shows significant broad velocity range across the galaxy disks ( 600 km s), similar to the CO (1–0) velocity field map. The SE arm has a blue-shifted velocity from 5650 km s to 5920 km s, while the NW arm has a red-shifted velocity from 5950 km s to 6160 km s. Other two arm-like features are also detected. One located 40 northeast of the eastern nucleus shows an arc around the eastern nucleus and has red-shifted velocities from 5810 km s to 6180 km s. This arm coincides with the NE arm detected in the CO (1–0). The other one located at 100 west of the SE arm has a strong peak ( 262.5 0.9  Jy km s) and blue-shifted velocities from 5610 km s to 5900 km s. This arm also coincide with the SW arm detected in the CO (1–0). From the CO (3–2) velocity dispersion map of VV 114 (Figure 4c), we find that the overlap region has the highest velocity dispersion ( 110 km s). The velocity dispersion of the NW arm is 30 km s, while the SE arm is 60 km s.

#### 3.2.2 HCN (4–3) and HCO+ (4–3)

The HCN (4–3) and HCO (4–3) images are shown in Figures 4d, 4e, 4f, 4g, 4h, and 4i. While the HCN (4–3) emission is only seen near the eastern nucleus of VV 114 and is resolved into four peaks, the HCO (4–3) emission is more extended and has at least 10 peaks in the integrated intensity map. The total integrated intensities of HCO (4–3) and HCN (4–3) are 15.3 0.4 Jy km  s and 4.4 0.2 Jy km s, respectively. The higher HCO (4–3) flux observed with the SMA (17 2 mJy, Wilson et al., 2008) using a 28 20 beam is likely attributed to missing flux by the ALMA observation. A compact component in the eastern nucleus is unresolved with the current resolution, and the upper limit to the size is 200 pc. The HCN (4–3) emission is not detected in the overlap region, where both the high CO (1–0) velocity dispersion and the significant CHOH (2–1) and HCO (4–3) detection suggest the presence of shocked gas (Krips et al., 2008). We concluded in paper I from their source size, line widths, and the relative strengths of HCN (4–3) and HCO (4–3) that the unresolved eastern nucleus harbors an obscured AGN, and the dense clumps in the western galaxy are related to extended starbursts.

#### 3.2.3 Cs (7–6)

The CS (7–6) emission has the highest critical density ( 10 cm) of all of the lines detected in our observations. The CS (7–6) emission is marginally (S/N 4) detected at the eastern nucleus (Figure 5), and the total flux is 0.5 0.1 Jy km s.

### 3.3. Continuum Emission

The continuum image at 110 GHz shows a filamentary structure similar to the molecular line image (Figure 6a). We construct low resolution (133 112) and high resolution (045 038) images of the 340 GHz continuum (Figures 6b, and 6c) using the combined data (compact + extended) and the extended configuration data, respectively. We find that the filamentary structure and the unresolved eastern nucleus are both present in dust continuum. The total flux of the 110 GHz and the low resolution 340 GHz continuum emission are 10.3 0.2 mJy and 38.6 0.3 mJy, respectively. The estimated missing flux relative to the JCMT 340 GHz observation (Wilson et al., 2008) is 75 4 % (SMA: 79 7 %). The difference in the recovered flux between CO (3–2) and 340 GHz continuum emission may be caused by the difference in the distribution. The 110 GHz and 340 GHz continuum emission is detected at the eastern nucleus (S/N 50 and 70) and the filamentary structure (S/N 8 and 24) identified in the CO (1–0) image, both with high significance.

## 4. Spatially resolved line ratios

We assign 39 “R” boxes (20 20; R1 – R39; see Figure 7) for the band 3 and CO (3–2) data and 15 smaller “S” boxes (12 12; S0 – S14; see Figure 8) for the rest of the data to estimate the physical parameters, such as the molecular gas mass (), dense gas mass (), dust mass (), star formation rate (SFR), kinetic temperature (), gas density (), gas column density (), and molecular abundance relative to H ([]/[H]). The positions of the boxes are chosen to cover the CO (3–2) emission (R1 – R39) and the HCO (4–3) emission (S0 – S14). The sizes of the boxes are chosen such that they are comparable to the beam size. Before deriving the parameters and line ratios at each box, we first matched the range between our data set and reconstructed the integrated intensity image of each line. The shortest baseline lengths are set to 13.5 k and 40.0 k for the molecular lines in the band 3 and the band 7, respectively, and the images are convolved into the same resolution (20 15 with a P.A. of 83 deg, 12 10 with a P.A. of 119 deg). For each ratio, the two integrated intensity images were expressed in the units of K km s before calculating the ratio at locations where both lines are detected above 3 . The derived box-summed spectra are listed in Appendix A.3. We carried out a multi Gaussian fit (one - three components) to reproduce the box-summed spectra, and labeled the components as “a”, “b”, and “c” from the bluest peak (e.g., the bluest peak at R21 is labeled as R21a).

### 4.1. 12Co (3–2)/12Co (1–0), R3−2/1−0

The CO (3–2)/CO (1–0) ratio, , can be used as an indicator of the dense/warm gas content relative to the total molecular gas. The of VV 114 varies from 0.2 to 0.8, as shown in Figure 7 (left) and Table 6. This range is larger than the same ratios derived for normal spirals, which is typically 0.15 – 0.5 when observed with a similar linear resolution (Warren et al., 2010). At the edge and the center of the filament, is higher (0.53 – 0.69) than the highest peaks of each arm ( 0.4). This suggests that the CO emitting gas at the filament have higher excitation conditions than normal spirals, while the conditions of each arm of VV 114 are consistent with arms and nuclei of normal spirals. The at the eastern nucleus is 0.76 0.01. It is suggested that the is much higher (3.12 0.03 in NGC 1068; Tsai et al., 2012) for gas surrounding an AGN, and the low in VV 114 may be due to the difference in filling factor (160 140 pc beam averaging for NGC 1068, while 800 pc box averaging for VV 114). It is possible, however, that the nuclear excitation conditions are different from source to source.

### 4.2. 12Co (1–0)/13Co (1–0), R12/13

In general, the CO lines has higher optical depths than the CO (1–0) line. Therefore, the measured CO (1–0)/CO (1–0) line intensity ratio, , gives a lower limit to the CO/CO abundance ratio (hereafter [CO]/[CO]). We present the image of VV 114 in Figure 7 (center). The increases from the arms ( 17) to the filament (15 – 32). Observationally, increases towards the central region of galaxies (Aalto et al., 1995), where the gas is generally warmer and denser. Aalto et al. (1995) suggest that the moderate optical depth of CO (1–0) emission and/or the high [CO]/[CO] environment can increase the in nuclei of U/LIRGs. In order to understand which of the two (optical depths or abundances) is dominant, we calculated and mapped the optical depth of the CO (1–0) and the CO (1–0) as shown in Table 14 and Figure 10. We provide an interpretation of these results in §5.2.

### 4.3. Hcn (4–3)/hco+ (4–3), RHCN/HCO+

In paper I, the HCN (4–3) and HCO (4–3) maps of VV 114 allowed us to investigate the central region at 200 pc resolution for the first time, and we find that both the HCN (4–3) and HCO (4–3) in the eastern nucleus are compact ( 200 pc), and broad [290 km s for HCN (4–3)]. We present the HCN (4–3)/HCO (4–3), , image of VV 114 in Figure 8. From the higher along with the past X-ray and NIR observations, we suggest the presence of an obscured AGN in the eastern nucleus. We also detect a 3 – 4 kpc long filament of dense gas, which is likely to be tracing the active star formation triggered by the ongoing merger, and this is consistent with the results from the numerical model by Teyssier et al. (2010) who predict that the fragmentation and turbulent motion of dense gas across the merging disk is responsible for forming dense gas clumps with masses of 10 – 10 M.

We present the image in Figure 8. The overlap region does not show significant HCN (4–3) emission, and we provide the 3  upper limit in Table 7. Three out of the four boxes (i.e., S1 – S3) in the eastern nucleus have low ( 0.5) whereas S0 has a high (1.34 0.09). It is suggested that such a high value is only produced around AGN environments (e.g., Kohno et al., 2001; Harada et al., 2013; Iono et al., 2013; Izumi et al., 2013; Imanishi & Nakanishi, 2014).

## 5. Derivation of physical parameters

In this section, we derive the molecular gas mass (§5.1), and the physical parameters using the radiative transfer code RADEX (§5.2) for each box defined in §4. The column density is derived using the optically thin CO line under the LTE assumption. We estimate the beam filling factor and the relative molecular abundance of molecule (hereafter expressed as []/[H]) (§5.3). Finally, we calculate the dust mass using the 340 GHz continuum emission (§5.4).

### 5.1. Molecular Gas Mass Derivation

The molecular gas mass M is derived by;

 MX=αXL′X[M⊙], (1)

where is the molecular line luminosity-to-H mass conversion factor and is the velocity integrated flux (Solomon & Vanden Bout, 2005). We use the conversion factor known to be appropriate for U/LIRGs ( = 0.8 M; Downes & Solomon, 1998). This is consistent with the value derived by Sliwa et al. (2013) in VV 114 ( =  M). The molecular gas mass derived at the boxes defined in §4 ranges between 0.2 10  and 4.8 10  M (Table 10). We also calculate the dense gas mass using = 10 M (Gao & Solomon, 2004) and the HCN (4–3) luminosity which is converted to the HCN (1–0) luminosity using HCN (4–3)/HCN (1–0) = 0.63 (paper I; Imanishi et al., 2007). The dense gas mass ranges between 1.8 10  and 3.8 10  M (Table 11).

We note that the CO luminosity-to-H mass conversion factor, , is very uncertain, and varies significantly from source to source (0.4 – 0.8 for LIRGs; Downes & Solomon, 1998; Yao et al., 2003; Papadopoulos et al., 2012; Bolatto et al., 2013). It may be possible that varies from region to region within a galaxy. While one would ideally adopt a spatially varying for a better quantification of the H mass, such a study is beyond the scope of this present paper. For simplicity, here we adopt a constant across all regions in VV 114, bearing in mind that the uncertainties could be as large as a factor of two. The same applies to (Gao & Solomon, 2004).

We used the non-LTE radiative transfer code RADEX (van der Tak et al., 2007) and varied the parameters until the residuals between the observed line fluxes and the modeled line fluxes are minimized in a sense. We assumed a uniform spherical geometry ( = 1.0 ), and derived the physical conditions of molecular gas (, , and ). RADEX uses an escape probability approximation to solve the non-LTE excitation assuming that all lines are from the same region. Since the molecular lines in the band 7 have significantly higher critical densities than that in the band 3, we used two sets of molecular lines; (case 1) 20 box-summed CO (1–0), CO (1–0), and CO (3–2), and (case 2) 12 box-summed HCN (4–3), HCO (4–3), CO (3–2), and CO (1–0), to solve for the degeneracy of the physical parameters. In case 2, we made the uv and beam-matched HCN (4–3), HCO (4–3), and CO (3–2) images (12 10 resolution with the P.A. = 119 deg.), and we defined three HCO (4–3) peaks as E0, E1, and E2 (Figure 9). We also use the and beam-matched CO (1–0) data to constrain the , allowing us to vary the [HCN]/[HCO] in case 2. All line parameters, such as the upper state energies and the Einstein coefficients, were taken from the Leiden Atomic and Molecular Database (LAMDA; Schöier et al., 2005). In order to find the set of physical parameters that can reproduce the observed line intensities, we run RADEX by varying , , and for case 1, and , , and [HCN]/[HCO] for case 2. The adopted are 10, 10, and 10 cm, at E0, E1, and E2, respectively.

We varied the gas kinetic temperature within a range of = 5 – 300 K using steps of d = 5 K, and a gas density of = using steps of d = . For case 1, we fixed [CO]/[H] = 1.4 10 (Davis et al., 2013) and [CO]/[] = 70, which are the Galactic values (Wilson & Rood, 1994). In case 2, we changed the parameters, = 5 – 400 K using steps of d = 5 K, = using steps of d = , and fixed [CO]/[H] = 1.0 10 and [HCO]/[H] = 1.0 10, which are the standard values observed in Galactic molecular clouds (Blake et al., 1987). We varied [HCN]/[HCO] from 1 – 10, in steps of one. The parameters we used are summarized in Table 9. We list the results that are within the 95 % confidence level with 3-degree of freedom () (Tables 12 and 13). Finally, we created velocity-averaged channel maps of and the optical depth of the transitions (Figure 10).

We note that the uncertainty of the for case 2 did not strongly affect the results, while that of the [CO]/[] for case 1 changed. The effect of varying the [CO]/[] will be discussed in §5.2.1. Future multi-transition HCN/HCO/CO/CO imaging will help us to derive these parameters directly.

#### 5.2.1 Case 1

The (box-averaged) kinetic temperature near the eastern nucleus (R21a) is constrained to within 25 – 90 K (the best fit is 50 K), as shown in Table 12. The (58.8 2.9 K) obtained from the LTE assumption at R21a (see §5.3) is higher than the best-fitted . In fact, we also find five regions (R10b, R11b, R14, R16, and R25a) that show similarly high excitation temperatures. Four out of five regions are in the central filament. In general, spontaneous emission dominates over collisional excitation in sub-thermally excited conditions, and hence should be lower than . One reason for this discrepancy could be attributed to the incorrect assumption of [CO]/[CO]. By varying this abundance ratio, we find that the temperature reversal (i.e. ) occurs only when [CO]/[CO] 150. This is consistent with the results obtained by Sliwa et al. (2013) who used RADEX along with their multi CO and CO line data to find evidence of a cold/dense molecular gas component with extremely high [CO]/[CO] of 229, which is 3 times higher than that of the Galactic value (Wilson & Rood, 1994).

The derived at the other regions are generally higher than 100 K. The derived in each region are typically 10 – 40 K, which may suggest sub-thermal conditions. The kinetic temperatures derived at the SE and NW arms are estimated to be 90 K, with higher temperature at the NW arm. The NW arm is also associated with relatively strong Pa emission and s-band emission, which is consistent with the higher relative temperature due to star-forming activities (Minamidani et al., 2008). However, this is inconsistent with the general understanding that strong tidal shear in tidal arms prevents active star formation to occur (Aalto et al., 2010).

The derived in most of the boxes are less than 10 cm, which is consistent with the critical densities of the low- CO lines observed here. The highest density of 10 – 10 cm is estimated at R21a, and this is consistent with the location of the eastern nucleus. Since we also observed the strongest HCN (4–3) and HCO (4–3) emission at R21a at the same line-of-sight velocity (Iono et al., 2013, see also Appendix A.3), it is possible that the main contribution to the CO emission at R21a arises from dense gas (10 – 10 cm) near the eastern nucleus, with a minor contribution from the diffuse gas clouds along the same line of sight observed within the same beam. In contrast to the eastern nucleus, the boxes that cover the western galaxy (R1 – R11 and R26 – R29) show moderately dense condition of 10 – 10 cm. This extended and moderately dense gas is associated with the disk-like structure seen in optical images (Evans, 2008), and the star formation traced in Pa emission and UV/X-ray emission (Grimes et al., 2006; Tateuchi et al., 2012). We note that the strongest off-nuclear Pa peak (R27 in Table 10; SFR = 3.15 0.05 M yr) coincides with relatively low gas density ( 10 cm). The density of the surrounding region labeled R25a is similar (10 – 10 cm) and this is comparable to the nucleus of the eastern galaxy. The secondary Pa peak (R29; SFR = 0.92 0.05 M yr) is not associated with any molecular line emission.

It is usually believed that the CO (1–0) emission is optically thick (), while the CO (1–0) emission is optically thin () even in luminous mergers (Davis et al., 2013). In most regions, we find that the optical depth of the CO (1–0) line is 1 (Figure 10). In contrast, the CO (1–0) opacity at the eastern nucleus and the filament is moderately optically thick ( 1). However, the elevated at the eastern nucleus (see §4) cannot be explained by the relatively low CO (1–0) opacity alone (the opacity has to be 0.1; see also Wilson et al. (2009)). Finally, we find that indeed the CO (1–0) emission is optically thin () averaged over the whole galaxy, except for the southern dust lane ( = 0.3 – 1.5).

From these results, we suggest that the peak of the molecular gas in the central 800 pc of the eastern galaxy is cold ( = 25 – 90 K), dense ( = 10 – 10 cm), and moderately optically thick ( 3), while peaks in the overlap region are warm ( 50 K, best-fitted is 95 and 175 K at R39a and R39b, respectively), moderately dense ( = 10 – 10 cm), and moderately optically thick ( 1). The derived density of the eastern galaxy is slightly higher than the range of values found in U/LIRGs using low- CO emission with kpc resolution ( = 10 – 10 cm; Downes & Solomon, 1998). In addition, the low opacities predicted from these analyses are consistent with earlier results that investigate the opacities in M82 ( = 0.5 – 4.5; Mao et al., 2000) and U/LIRGs ( = 3 – 10; Downes & Solomon, 1998), and the central region of NGC 6240 ( = 0.2 – 2; Iono et al., 2007). However, the derived temperature of the eastern galaxy is inconsistent with the high values found in nearby starburst galaxies M82, NGC 253, and NGC 6240 (Wild et al., 1992; Jackson et al., 1995; Seaquist & Frayer, 2000; Iono et al., 2007). The disagreement is possibly due to the uncertainties in the [CO]/[CO], or the difference in the observed molecular gas tracers.

#### 5.2.2 Case 2

The values for , , and the optical depth of HCN (4–3) and HCO (4–3) are shown in Table 8. The derived parameters for the unresolved component E0, are 100 K, = 10 – 10 cm, and [HCN]/[HCO] 5. The lower limit to the kinetic temperature is higher than those of E1 and E2, mainly due to the unusually high and . In contrast to E0, the derived parameters near E1 show high H densities ( = 10 – 10 cm). The overlap region (E2), where the star-formation rate (1.70 0.05 M yr) is lower than the eastern nucleus, has densities in the range of = 10 – 10 cm. Finally, the optical depths for the HCO (4–3) and HCN (4–3) lines are calculated for each gas clump, yielding 0.7 and 0.2 for E0, 0.2 and 0.6 for E1, and 0.4 and 0.4 for E2.

The higher linear resolution observations of HCN (4–3) and HCO (4–3) toward NGC 1097 (Izumi et al., 2013) revealed that the gas in the central region of NGC 1097 has = 70 – 550 K and = 10 – 10 cm. Moreover, by comparing to LVG models, Krips et al. (2008) found that HCN and HCO emission in AGN-dominated sources appears to emerge from regions with lower H densities, higher temperatures, and higher HCN abundance relative to starburst-dominated (SB-dominated) galaxies. Our results obtained toward VV 114 are consistent with these previous results.

### 5.3. Filling factor and Column Density under LTE

In order to determine the bulk properties of the CO emitting gas, we used an excitation temperature analysis (Davis et al., 2013). The excitation temperature at each box can be calculated from

 Tex=T0⎛⎝ln⎡⎣(Tb,CO(1−0)ΦAT0(1−e−τCO)+1eT0/Tbg−1)−1+1⎤⎦⎞⎠−1 (2)

where [= 5.53 K for CO (1–0) emission], is the frequency of the transition, is the Planck’s constant, is the Boltzmann’s constant, is the brightness temperature of CO (1–0) emission in Kelvin, is the optical depth of the CO (1–0) emission, and is the cosmic microwave background temperature (2.73 K). Using estimated from the RADEX calculation (§5.2), we estimate the beam filling factor ,

 ΦA=Tb,CO(1−0)Tkin (3)

The optical depth of the CO (1–0) emission is also estimated from the RADEX calculation in §5.2. Assuming that the CO and CO arise from the same molecular cloud, and that the CO (1–0) is optically thick, we estimate the optical depth of a given molecule using,

 τX≃ln⎡⎣(1−Tb,XTb,CO(1−0))−1⎤⎦ (4)

where is the optical depth of a given transition, and is the observed brightness temperature for transition X. Using and , we estimate the column density for a given molecule from,

 NX=3k8π3μ2B(J+1)exp(2hJ(J+1)kTex)(1−exp(−hνkTex))
 ×τX1−e−τX1J(Tex)−J(Tbg)∫T∗RdV (5)
 J(T)=hνk1exp(hν/kT)−1 (6)

where is the dipole moment, is the rotational constant, is the lower energy level, and is the integrated intensity (Wilson et al., 2009). The derived column densities are listed in Tables 14 and 15.

### 5.4. Dust Mass and ISM Mass Derivation from 340 GHz continuum

We calculated the dust mass from the 340 GHz (880 m) continuum emission (Table 3) using (Wilson et al., 2008),

 Mdust=74220S340D2Le17Td−1κ340M⊙ (7)

where is the 340 GHz flux in Jy and is the luminosity distance in Mpc. We assumed a dust emissivity, , and the dust temperature of 39.4 K (Wilson et al., 2008). The box-summed dust masses ranges between 2.0 10  and 2.8 10  M (Table 10). We note that we used the Draine & Lee (1984) dust model for , because the derived from observations has a large error (Henning et al., 1995).

### 6.3. CO Isotope Ratio Enhancement in the Molecular “Filament”

We suggest from our RADEX modelings that the eastern nucleus and the overlap region have extremely high [CO]/[CO] ( 200), which is at least two times higher than the Galactic value ( 70; Wilson & Rood, 1994). The Pa peaks roughly coincide with the regions where high [CO]/[CO] are expected, suggesting that the increased [CO]/[CO] is related to the star formation activity. Similarly high values are seen in the overlap region of NGC4038/9 (Wilson et al., 2003) and the Taffy (Zhu et al., 2007). Zhu et al. (2007) suggested that the extreme [CO]/[CO] value in the bridge is explained by three scenarios, 1) selective isotope photodissociation in the diffuse clouds and shocked region, 2) CO enrichment around starburst activities, and/or 3) the destruction and recombination of molecules after shock. We briefly explain each scenario below, but our current data is insufficient for us to identify the exact cause of the high [CO]/[CO] in VV 114.

The first possibility of [CO]/[CO] enhancement is the deficiency in CO. Sheffer et al. (1992) suggest that selective isotope photodissociation can reduce the CO abundance in diffuse clouds, because CO is self-shielded to a greater extent. Thus, the ISM surrounding young starbursts and/or shocked regions show elevated [CO]/[CO] (Zhu et al., 2007). The ISM in the nuclei and the overlap region of VV 114 show extremely high [CO]/[CO], presumably due to intense starburst activities and/or large-scale shocks.

The second possibility is that massive stars end their life as supernovae and expel a large amount of C in the interstellar medium. While the elemental abundances (e.g. C and S) are not directly related to the molecular abundances (e.g., CS; Casoli et al., 1992), once the synthesized elements are dispersed in the interstellar medium, molecules (e.g., CO, CS, and CN; Henkel et al., 2014) form as soon as the temperature and density conditions are favorable. This occurs with a timescale of a few 10 yr (Langer & Graedel, 1989).

For the overlap region, the destruction and recombination of molecules after shocks (see §6.5) are possible mechanisms to enhance the [CO]/[CO] (the third possibility). The recombination timescale of H and CO molecules after shock destruction are shorter than that of CO, since ionized photons from shocked regions lead to selective isotope photodissociation (Zhu et al., 2003). Shielded regions from the radiation field are needed to form rare CO (Abundant CO can form self-shielded regions). Moreover, the rare isotope molecules generally need a longer time to form, because collisions between molecules and dust grains are less frequent (Zhu et al., 2007).

### 6.4. Gas-to-Dust Ratio, MH2/Mdust

The gas-to-dust ratio, /, provides an important measure of the relative abundance between gas and metallicity. The average / over the entire galaxy is often derived in single-dish work, and typical / is 200 – 300 for local U/LIRGs (Contini & Contini, 2003; Yao et al., 2003; Seaquist et al., 2004), and 15 – 231 in high-z sources (Solomon & Vanden Bout, 2005). Wilson et al. (2008) found / = 357 95 from a sample of 13 U/LIRGs, including VV 114, observed at kpc resolution.

We use the gas and dust masses derived in §5.4 to investigate the distribution of / (Figure 12). The smallest value of (128 16)  occurs in the eastern nucleus, which is similar to the Galactic value (100; Hildebrand, 1983), while higher values of (371 118)  and (339 60)  occur in the western nucleus and the overlap region, respectively. The clear differences between the two nuclei may suggest a local gradient in the metallicity. For the overlap region, cold dust associated with diffuse gas clouds cannot avoid the collision. This tends to increase the /, because shocks destruct dust particles preferentially (Zhu et al., 2007). On the other hand, the low / in the eastern nucleus may be due to intense starbursts producing dust-rich environments.

### 6.5. Fractional Abundances of CS, CH3OH, and CN

Table 15 shows the properties of the detected molecular lines which are not used in the RADEX calculations. Either the dense gas component of VV 114 has extreme variations in excitation among the molecular clumps in the filament (see §6.1), or there is widespread chemical differentiation across the filament. The fractional abundances [] of the different astrochemical species provide evidence of varying chemical influences due to star formation, physical conditions, and dynamics across the galaxy disks. We use the H column densities, derived from the RADEX calculations, which are 10, 10, and 10 cm at R18 (AGN), R21a (starburst), and R39a (overlap region), respectively. Column densities of each molecules are determined by equation (7) assuming an optically thin emission under LTE. The values determined from equation (3) are 38.7 1.9 K, 58.8 2.9 K, and 52.6 2.6 K at R18, R21a, and R39a, respectively. The derived [] are listed in Table 15.

In Figure 13, we show the fractional abundances for CS, CHOH, and CN in VV 114, and the same ratios for a sample of nearly galaxies, NGC 253, M82, and IC 342, taken from line surveys available in the literature (Henkel et al., 1988; Mauersberger et al., 1989; Huettemeister et al., 1997; Martín et al., 2006). M82 has a relatively old starburst at its core, with an average stellar population age of 10 Myr (Konstantopoulos et al., 2009). This creates strong UV fields, therefore the PDR dominates its chemistry (Aladro et al., 2011). Figure 13 shows that R39a has higher CHOH abundance than M82, and small CS and CN abundances. A pure PDR similar to M82 may explain the molecular abundances we observe in R18.

The molecular abundances for the overlap region and NGC 253 share similar characteristics. NGC 253 is thought to be in an early stage of starburst evolution, and has young stellar populations in its nucleus ( 6 Myr; Fernández-Ontiveros et al., 2009). The chemistry in the nucleus of NGC 253 is dominated by large-scale shocks (Aladro et al., 2011), and we suggest that the overlap region of VV 114 is also dominated by shocks. The low at the overlap region are further evidences for a shock dominated region (Krips et al., 2008).

### 6.6. Merger-driven Tidal Dwarf Galaxy Formation

Tidal dwarf galaxies (TDGs) are gas-rich irregular galaxies made out of stellar and gaseous material pulled out by tidal forces from the disks of the colliding parent galaxies into the intergalactic medium. They are found at the ends of long tails and host active star-forming regions (Braine et al., 2000). Hibbard et al. (2001) and Gao et al. (2001) found the HI gas mass of 4.1 10 M and the molecular gas mass of 4 10 M at the edge of the southern tail of NGC 4038/9.

We found an elevated (0.36 0.01), SFR (0.10 0.05 M yr), and ( 3.8 10  M) at the edge of the southern tidal arm (R38). The derived SFR and of R38 are comparable to those of TDG candidates in other galaxies (Braine et al., 2001). The gas depletion time of (0.40 0.22)  Gyr is shorter than the rest of the gas in the tidal arm ( 0.5  Gyr). According to the RADEX modeling, while the ranges of and are not confined well, the best fitting values (35 K, 10 cm) are slightly higher than those in the middle of the tidal arm, R36a and R37a (25 – 30 K, 10 – 10 cm). We suggest that R38 is a forming tidal dwarf galaxy at the edge of the tidal arm of VV 114. Future high sensitivity optical and high resolution HI observations will allow us to constrain the star formation and the atomic gas properties of R38.

## 7. Conclusion

We investigate the physical conditions of the molecular gas in the mid-stage merger VV 114. We present high-resolution observations of molecular gas and dust continuum emission in this galaxy using ALMA band 3 and band 7. This study includes the first detection of extranuclear CHOH (2–1) emission in interacting galaxies. The results can be summarized as follows:

1. We find that the CO (1–0) and CO (3–2) lines show significantly extended structures (i.e., the northern and southern tidal arms), the central filament across the galaxy disks, and double-peaks in the overlap region, while the CO (1–0) line is only detected at the central filament. The filament is also identified by the strong CN (1 – 0), HCO (4–3), 110 GHz, and 340 GHz continuum emission.

2. Higher (0.5 – 0.8) and (20 – 50) are detected at the central filament. These higher ratios indicate that the central filament has highly excited (but not thermalized) molecular ISM, and the eastern nucleus is nearly thermalized when it is observed with a 800 pc beam.

3. The unresolved eastern nucleus has the highest (1.34 0.09), while the dense gas clumps near the eastern nucleus have significantly lower values ( 0.5). The broad HCN (4–3) and HCO (4–3) ( 290 km s) emission lines seen in the unresolved eastern nucleus suggests an obscured AGN (see also paper I).

4. Radiative transfer analysis of the CO (1–0), CO (3–2), and CO (1–0) emission enables us to map physical parameters of the “diffuse” gas of an interacting LIRG with 800 pc scale for the first time. The analysis suggests that “diffuse” gas clouds in the filament have warmer/denser conditions than those in the galaxy disks. This is consistent with predictions from merger simulations. Our analysis also suggest that the [CO]/[CO] is enhanced in the central filament. The extremely high [CO]/[CO] values are more important than the moderately optically thick CO (1–0) emission to explain the high in VV 114.

5. Radiative transfer analysis of the HCN (4–3), HCO (4–3), and CO (3–2) allow us to compare the dense gas clouds around AGN, starburst activities, and the overlap region. These results show that dense gas clouds around AGN have = 10 – 10 cm and 100 K with [HCN]/[HCO] 5, while gas clumps around starburst activities show = 10 – 10 cm and = 40 –100 K with [HCN]/[HCO] 4. In addition, the analysis shows that the overlap region has = 10 – 10 cm and = 5 – 90 K with [HCN]/[HCO] = 1 – 9.

6. The spatially resolved Kennicutt-Schmidt law in VV 114 clearly connects the “starburst” sequence with the “normal disk” sequence. Most of the data points near the “starburst” sequence are found in the nuclei and the overlap region, whereas the data points near the “