Dense Molecular Gas in the Starburst Nucleus of NGC 1808

The target molecular lines were detected toward the central 1 kpc starburst disk. In this section, we present their spectra and integrated intensity images, defined as $I\equiv \int { \mathcal S }{dv}$, where the intensity ${ \mathcal S }$ (Jy beam⁻¹) is integrated over velocity v (km s⁻¹). Figure 2 shows a spectrum extracted from a circular region of diameter 3'' (∼156 pc) toward the galactic center, where the signal-to-noise ratio is highest for all lines. The central r < 100 region is referred to as the CND. The spectrum in the figure shows a number of lines from various molecular species. The most strongly detected lines in band 3 are HCN (1−0), HCO⁺ (1−0), CS (2−1), and the doublet of C₂H (1−0), followed by the rare isotopologues H¹³CN (1−0) and H¹³CO⁺ (1−0), as well as SiO (2−1) and HOC⁺ (1−0). In addition, the spectrum shows emission lines of HNCO (4−3), HN¹³C (1−0), and SO, although their detection is only marginal. The HCO⁺ (4−3) line was firmly detected in band 7; the line intensity ratio of HCO⁺ (4−3) to HCO⁺ (1−0) will be used as a diagnostic tool to probe the physical conditions of dense gas in Section 4. All lines presented here are first detections in NGC 1808, except HCN (1−0) and HCO⁺ (1−0), which were recently measured by Green et al. (2016) at lower resolution, and HCO⁺ (4−3), which was recently imaged at high resolution toward the nucleus, although to a lower spatial extent (Audibert et al. 2017). Single-dish observations of HCN (1−0) toward the galactic center were also reported in Aalto et al. (1994). The basic properties of the spectral lines toward the central 3'' aperture are listed in Table 1.

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Panels (b) and (c) of Figure 2 show azimuthally averaged integrated intensities of the five most prominent lines derived from naturally weighted data (angular resolution ∼2''). The C₂H (1−0) profile was derived from a single integrated image of fine-structure transitions (J = 3/2–1/2 and J = 1/2–1/2, each split into three hyperfine levels with F = J ± 1/2) listed in Table 1. All lines exhibit strong emission in the galactic center and a decrease to 0.1–0.2 of their maximum values at a radius of r ≳ 5''. The integrated intensity images (angular resolution ∼1''; derived using a robustness parameter of 0.5) of the lines including CO (3−2) are presented in Figure 3. At this resolution, the images show prominent emission in the CND as well as extended structure; the lines are firmly detected in the regions that surround the CND (marked by arrows in Figure 3). Following the notation in Salak et al. (2017), these regions are referred to as the central molecular clouds (CMCs). Beyond the CMCs lies the 500 pc ring—the outermost visible structure in the CO (3−2) integrated intensity image in the bottom-right panel of Figure 3; most lines were detected toward the southeastern part of the ring.

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Figure 4 shows the integrated intensity distributions of dense gas tracers in the CND. Note that the intensities of the HCN (1−0), CS (2−1), HCO⁺ (4−3), HCO⁺ (1−0), and CO (3−2) lines clearly exhibit a double-peak structure. The double peak is most symmetrical in the CS (2−1) line intensity, with similar peaks offset from the galactic center (core), marked by a black plus sign. This feature has been interpreted as a molecular gas torus with a radius of ∼30 pc surrounding an unresolved core offset from the midpoint between the peaks (Salak et al. 2017). All tracers (except C₂H) show that the core is located closer to the brighter southeast peak of the molecular gas tracers.

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The C₂H (1−0) line (integrated over the fine-structure components in Table 1) is detected in the CND with a notably different structure compared to other tracers; there is no clear indication of a double peak in the integrated intensity image of C₂H (1−0) shown in Figure 4. The line has been recognized as a tracer of photodissociation regions (PDRs), dominated by strong UV radiation. PDRs contain a relatively high fraction of C⁺, as well as hydrogen, resulting in efficient formation of simple molecules such as C₂H (Pety et al. 2005, 2017; Martín et al. 2014; Meier et al. 2015; Nagy et al. 2015; Nishimura et al. 2016a). Therefore, the molecule is expected to be prominent in the gas-rich starburst nucleus of NGC 1808. The integrated intensity ratios of C₂H (1−0) to HCN (1−0) and HCO⁺ (1−0) (Table 1) are similar to the values obtained by Martín et al. (2014) for a number of starburst and Seyfert galaxies.

In addition, HOC⁺ (1−0) was detected toward the CND. There is evidence that this molecule, an isomer of HCO⁺, is enhanced in PDRs where it can be efficiently produced, e.g., via the reactions ${{\rm{C}}}^{+}+{{\rm{H}}}_{2}{\rm{O}}\to {\mathrm{HOC}}^{+}+{\rm{H}}$ and ${\mathrm{CO}}^{+}+{{\rm{H}}}_{2}\to {\mathrm{HOC}}^{+}+{\rm{H}}$ (e.g., Savage & Ziurys 2004). The abundance ratio $[{\mathrm{HCO}}^{+}]/[{\mathrm{HOC}}^{+}]$ in Galactic objects is usually several hundreds (e.g., ∼270 in the Orion Bar and ∼360 in Sgr B2 (OH); Ziurys & Apponi 1995; Apponi et al. 1999). In extragalactic sources, the line has been detected in the Seyfert galaxy NGC 1068 (Usero et al. 2004) and star-forming galaxies NGC 253, M82, and M83 (Aladro et al. 2015) as a tracer of gas in the vicinity of star clusters with OB stars. The resolved image of HOC⁺ (1−0) in M82 suggests HOC⁺ enhancements toward regions of dense gas and PDRs (Fuente et al. 2008). In M82, the intensity ratio of the brightness temperatures ${T}_{{\rm{b}},{{\rm{H}}}^{13}{\mathrm{CO}}^{+}(1-0)}/{T}_{{\rm{b}},{\mathrm{HOC}}^{+}(1-0)}\sim 1\mbox{--}2$ was reported, which is comparable to the value of ∼1 measured for the CND of NGC 1808 (Table 1). On the other hand, the detection of both HOC⁺ (1−0) and SiO (2−1) (see below) in the CND, where a hard X-ray source (possibly an active galactic nucleus, AGN) resides, is similar to the results obtained for NGC 1068 (Usero et al. 2004). The presence of these tracers allows an alternative scenario, according to which the chemistry of HOC⁺ is affected by interaction with X-rays. In both M82 and NGC 1068, the abundance of HOC⁺ seems to be enhanced compared to that of the Galactic objects. The line intensity (brightness temperature) ratio of HCO⁺ (1−0) to HOC⁺ (1−0) in the CND of NGC 1808 is measured to be 19.0 ± 3.8. Although HCO⁺ (1−0) is optically thick, as shown in the Appendix, the ratio is still notably low, indicating an enhanced abundance of HOC⁺.

The SiO (2−1) emission was detected toward the CND. Although relatively weak, the SiO (2−1) line is valuable because it is a well-established tracer of shocked gas (e.g., Martín-Pintado et al. 1992; Schilke et al. 1997; García-Burillo et al. 2000; Kelly et al. 2017). The shocks in the CND may be associated with supernova explosions and other feedback from the nuclear starburst activity exerted on the dense gas. We discuss the distribution of the SiO (2−1) integrated intensity in the context of shock chemistry in Section 3.4. The tentative detection of HNCO (4−3) toward the CND is another indicator of the presence of shocked gas (e.g., Meier et al. 2015).

In the panels of the second and fourth rows, Figure 4 also shows the position–velocity diagrams (PVDs) derived along the major galactic axis (the position angle of 316° was determined in Salak et al. 2016) centered at the 93 GHz continuum peak (core). The PVDs show that the kinematics of the dense gas tracers in the CND is consistent with the overall rigid body rotation of the CND and the molecular torus discussed in Salak et al. (2017). In addition, the dense gas is also present in the high-velocity component denoted by the "core" in the lower-right panel in Figure 4. Note that the high-velocity core is remarkably bright in the HCO⁺ (4−3) line relative to HCO⁺ (1−0) and other tracers. Since the line is a tracer of high gas density, $n\gtrsim {10}^{5}\,{\mathrm{cm}}^{-3}$, the data show that the core exhibits enhanced gas excitation compared to the rest of the CND. This condition will be explored in more detail in Sections 3.3 and 4.

The ALMA observations in cycles 1 and 2 have produced the data cubes of two CO lines, J =  1−0 and J = 3−2, and two HCO⁺ lines, J = 1−0 and J = 4−3, at comparable angular resolution and sensitivity (corrected for missing flux by ACA observations). The critical densities of these lines range from $\sim {10}^{2}\,{\mathrm{cm}}^{-3}$ for CO (1−0) to >10⁴ cm⁻³ for HCO⁺ (4−3) (Shirley 2015) over a wide range of temperatures found in molecular clouds, allowing us to probe the physical conditions (temperature and density) in diffuse and dense clouds across the central 1 kpc (Section 4). The line intensity ratio of CO (3−2) to CO (1−0), defined as ${R}_{\mathrm{CO}}\equiv {W}_{\mathrm{CO}(3-2)}$/${W}_{\mathrm{CO}(1-0)}\approx {T}_{{\rm{b}},\mathrm{CO}(3-2)}$/${T}_{{\rm{b}},\mathrm{CO}(1-0)}$, where $W=\int {T}_{{\rm{b}}}{dv}$ is the integrated intensity in brightness units (${T}_{{\rm{b}}}$ [K]), was presented in Salak et al. (2017).

The line intensity ratio of HCO⁺ (4−3) to HCO⁺ (1−0), defined as ${R}_{{\mathrm{HCO}}^{+}}\equiv {W}_{{\mathrm{HCO}}^{+}(4-3)}/{W}_{{\mathrm{HCO}}^{+}(1-0)}\approx {T}_{{\rm{b}},{\mathrm{HCO}}^{+}(4-3)}/{T}_{{\rm{b}},{\mathrm{HCO}}^{+}(1-0)}$, is shown in Figure 5. The ratio is highest in the CND: in the central r < 1'', the average value is ${R}_{{\mathrm{HCO}}^{+}}=0.420\pm 0.022$ and the maximum value within the central 50 pc is ${R}_{{\mathrm{HCO}}^{+}}^{\max }(r\lt 0\buildrel{\prime\prime}\over{.} 5)=0.622\pm 0.027$ derived at original resolution (panel (a)), where the statistical uncertainty is 1σ. Since the two lines were measured in different ALMA bands, there is also a calibration uncertainty of the order of 5%; a similar error also applies to the ratio R_CO. The ratio is typically 0.3–0.4 in the compact sources detected around the CND. Note that the maximum value is spatially coincident with the 93 GHz continuum peak (plotted as contours) but not with the molecular torus (double peak). This result indicates that the high excitation of dense gas traced by HCO⁺ in the core may be generated by the activity of the starburst nucleus within the central r < 30 pc (Krabbe et al. 1994; Busch et al. 2017; Salak et al. 2017) possibly coexisting with an embedded Seyfert 2 type low-luminosity AGN (Véron-Cetty and Véron 1985; Kotilainen et al. 1996). The high ${R}_{{\mathrm{HCO}}^{+}}$ in the core can be explained by the presence of dense gas heated by shocks.

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The line ratios ${R}_{{\mathrm{HCO}}^{+}}$ and ${R}_{\mathrm{CO}}$ in Table 2 were derived as average values within selected regions of diameter 2'' (circles in Figure 5). Regions R1 and R2 correspond to the CMCs, whereas regions R3, R4, and R5 are part of the 500 pc ring. These regions have been investigated in detail because both lines of CO and HCO⁺ as well as the continuum at 93 and 350 GHz were detected, allowing us to probe the physical conditions of the gas using a line ratio analysis. Since the region size, comparable to the size of the synthesized beam, is equivalent to a physical scale of ∼100 pc, the derived values are beam-averaged and reflect mean values at 100 pc scale. The derived velocity widths ΔV are FWHM values obtained from Gaussian fitting of the spectra within the regions.

Table 2.  Molecular Gas Parameters in the Selected Regions (Diameter 2'')

Region	Coordinatesa	${R}_{{\mathrm{HCO}}^{+}}$	${R}_{\mathrm{CO}}$	${I}_{\mathrm{CO}(1-0)}$	${N}_{\mathrm{CO}}$	${\rm{\Delta }}{V}_{\mathrm{CO}(1-0)}$	${\rm{\Delta }}{V}_{{\mathrm{HCO}}^{+}(1-0)}$
	$({\rm{s}},^{\prime\prime} )$			$(\mathrm{Jy}\,\mathrm{km}\,{{\rm{s}}}^{-1})$	$(\times {10}^{18}\,{\mathrm{cm}}^{-2})$	$(\mathrm{km}\,{{\rm{s}}}^{-1})$	$(\mathrm{km}\,{{\rm{s}}}^{-1})$
C	42.331, −45.877	0.420 ± 0.022	0.935 ± 0.025	37.1	6.9	151.1 ± 2.0	135.9 ± 3.8
R1	42.402, −42.909	0.303 ± 0.032	0.686 ± 0.063	16.5	3.0	89.0 ± 3.9	65.6 ± 2.4
R2	42.590, −45.159	0.282 ± 0.055	0.664 ± 0.034	23.0	4.2	111.2 ± 1.8	96.4 ± 4.1
R3	42.788, −46.658	0.072 ± 0.020	0.641 ± 0.009	28.6	5.3	97.4 ± 1.7	79.9 ± 4.6
R4	42.815, −51.127	0.337 ± 0.042	0.725 ± 0.027	30.0	5.5	68.4 ± 1.2	71.1 ± 3.3
R5	42.543, −51.068	0.356 ± 0.048	0.763 ± 0.042	18.4	3.4	70.2 ± 1.6	53.0 ± 2.1

Note. The ${R}_{{\mathrm{HCO}}^{+}}$ and ${R}_{\mathrm{CO}}$ ratios were derived at a common angular resolution of the CO (1–0) line (2670 × 1480) from Salak et al. (2017). The uncertainty is 1σ of the mean value; it does not include the calibration (absolute intensity) uncertainty of ∼5%.

^aThe expressed coordinates have common values of $(\alpha ,\delta )=({05}^{{\rm{h}}}{07}^{{\rm{m}}},-37^\circ 30^{\prime} )$.

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In Table 3, we list the intensity ratios of the band 3 lines HCN (1–0), HCO⁺ (1–0), C₂H (1–0), CS (2–1), and CO (1–0) detected throughout regions C and R1–R5 defined in Figure 3. In general, HCN (1–0) and CS (2–1) are regarded as dense gas tracers, HCO⁺ (1–0) and C₂H (1–0) are expected to be bright in PDRs, whereas CO (1–0) is a tracer of bulk molecular gas. High-sensitivity data cubes (natural weighting) were used in deriving the line intensity ratios. Below, we summarize some clear trends, observed in the line ratios, reflecting the complex physical and chemical structures of the starburst region. The trends are illustrated in panel (c) of Figure 5.

• 1.  
  All dense gas tracers, such as HCN (1–0), HCO⁺ (1–0), and C₂H (1–0), are generally enhanced with respect to CO (1–0) in the CND (region C).
• 2.  
  HCN (1–0) is enhanced with respect to HCO⁺ (1–0) and CS (2–1) in the CND. The ratios of HCN (1–0) with respect to these two lines are remarkably uniform among regions R1–R5. In the CND, the ratios of HCN (1–0) with respect to HCO⁺ (1–0) and CS (2–1) are ∼1.5 and ∼1.4 larger compared to the average of the ratios in the other regions, respectively.
• 3.  
  The ratio of HCN (1–0) to HCO⁺ (1–0) is close to unity in all regions except in the CND.
• 4.  
  C₂H (1–0) is slightly enhanced with respect to HCO⁺ (1–0) and CS (2–1) in the CND, showing line intensity ratios similar to those of HCN (1–0).
• 5.  
  The intensity of C₂H (1–0) is generally low compared that of to HCN (1–0), HCO⁺ (1–0), and CS (2–1) in the 500 pc ring (regions R3–R5).
• 6.  
  The ratio of HCO⁺ (1–0) to CS (2–1) exhibits no significant variation among all investigated regions.

Table 3.  Line Intensity Ratios in Selected Regions (Diameter 2'')

Region	$\tfrac{\mathrm{HCN}(1-0)}{{\mathrm{HCO}}^{+}(1-0)}$	$\tfrac{\mathrm{HCN}(1-0)}{{{\rm{C}}}_{2}{\rm{H}}(1-0)}$	$\tfrac{\mathrm{HCN}(1-0)}{\mathrm{CS}(2-1)}$	$\tfrac{{\mathrm{HCO}}^{+}(1-0)}{{{\rm{C}}}_{2}{\rm{H}}(1-0)}$	$\tfrac{{\mathrm{HCO}}^{+}(1-0)}{\mathrm{CS}(2-1)}$	$\tfrac{{{\rm{C}}}_{2}{\rm{H}}(1-0)}{\mathrm{CS}(2-1)}$	$\tfrac{\mathrm{CO}(1-0)}{\mathrm{HCN}(1-0)}$	$\tfrac{\mathrm{CO}(1-0)}{{\mathrm{HCO}}^{+}(1-0)}$	$\tfrac{\mathrm{CO}(1-0)}{{{\rm{C}}}_{2}{\rm{H}}(1-0)}$
C	1.46 ± 0.04	3.01 ± 0.12	3.30 ± 0.11	2.06 ± 0.09	2.26 ± 0.08	1.10 ± 0.04	6.09 ± 0.20	8.88 ± 0.38	18.3 ± 1.2
R1	0.98 ± 0.05	2.65 ± 0.26	2.12 ± 0.12	2.69 ± 0.25	2.15 ± 0.12	0.80 ± 0.07	11.6 ± 1.1	11.5 ± 0.9	30.8 ± 5.0
R2	1.04 ± 0.05	2.59 ± 0.31	2.50 ± 0.18	2.49 ± 0.29	2.41 ± 0.17	0.97 ± 0.10	16.6 ± 1.2	17.2 ± 1.1	42.8 ± 8.1
R3	1.00 ± 0.06	3.68 ± 0.34	2.90 ± 0.26	3.66 ± 0.36	2.89 ± 0.28	0.80 ± 0.08	18.1 ± 1.2	18.2 ± 1.5	66.5 ± 9.7
R4	0.96 ± 0.05	2.87 ± 0.23	2.35 ± 0.19	2.98 ± 0.24	2.44 ± 0.20	0.82 ± 0.07	16.0 ± 1.1	15.4 ± 1.1	46.1 ± 5.5
R5	0.99 ± 0.04	3.34 ± 0.44	2.04 ± 0.13	3.38 ± 0.45	2.06 ± 0.13	0.61 ± 0.07	11.7 ± 0.7	11.5 ± 0.8	39.0 ± 8.5

Note. The ratios of intensities (in units of Kelvin) are derived from Gaussian fitting of spectral lines. The C₂H (1–0) line refers to the triplet $J=3/2\to 1/2$. The uncertainties include statistical errors, but not calibration (absolute intensity) uncertainties (∼5% for high signal-to-noise ratio).

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The presence of strong emission from dense gas tracers HCN (1–0), HCO⁺ (1–0), CS (2–1), and C₂H (1–0) suggests that the CND is a large PDR, abundant in dense gas and dominated by star formation feedback. The detection of tracers such as SiO (2–1) toward the nucleus support the picture of shocked dense gas. Below, we present the ratio of HCN (1–0) to HCO⁺ (1–0) in more detail and discuss its possible origin.

The most firmly detected dense gas tracers in band 3 are HCN (1–0) and HCO⁺ (1–0). Since the discovery of an enhancement of the intensity ratio of the two lines, defined as ${R}_{{\rm{H}}}\,\equiv {W}_{\mathrm{HCN}(1-0)}/{W}_{{\mathrm{HCO}}^{+}(1-0)}\approx {T}_{{\rm{b}},\mathrm{HCN}(1-0)}/{T}_{{\rm{b}},{\mathrm{HCO}}^{+}(1-0)}$, where $W\,\equiv \int {T}_{{\rm{b}}}{dv}$ is the integrated intensity, in a number of AGNs, the ratio has been used as an indicator of Seyfert activity in galaxies (Kohno et al. 2001, 2003; Imanishi et al. 2006). The origin of high R_H, also observed for higher J transitions (Hsieh et al. 2012; Izumi et al. 2013, 2016; Imanishi & Nakanishi 2014), is not fully understood, but some authors have suggested the following explanations: difference in gas density (the critical density of HCN (1–0) is larger than that of HCO⁺ (1–0)), high-temperature chemistry (radiative or mechanical heating), X-ray-dominated chemistry (in X-ray dominated regions, XDRs), infrared pumping, and electron excitation (e.g., Meijerink et al. 2006; Krips et al. 2008; Harada et al. 2010, 2013; Tafalla et al. 2010; Aalto et al. 2012, 2015; Izumi et al. 2013; Matsushita et al. 2015; Goldsmith & Kauffmann 2017). A difference in opacities may also be a cause of variation in optically thick nuclear regions (Meier & Turner 2012; Meier et al. 2014). If the two lines are moderately optically thick, and we have estimated that τ > 1 in the core of NGC 1808 (Appendix), then the diagnostic method needs to be supported by independently measured column densities of the two species to clarify whether the ratio reflects the actual abundance ratio. We performed this calculation (under local thermodynamic equilibrium, LTE, approximation) in the Appendix for the center position and found that ${N}_{\mathrm{HCN}}\gt {N}_{{\mathrm{HCO}}^{+}}$ in the CND region. This result is also supported by the line intensity ratio of the ¹³C isotopic species of the two molecules, which is found to be ${{ \mathcal S }}_{{{\rm{H}}}^{13}\mathrm{CN}(1-0)}/{{ \mathcal S }}_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}(1-0)}\,=1.93\pm 0.53$. If the two lines are optically thin, the ratio is proportional to the ratio of column densities as ${{ \mathcal S }}_{{{\rm{H}}}^{13}\mathrm{CN}(1-0)}$/${{ \mathcal S }}_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}(1-0)}\approx {T}_{{\rm{b}},{{\rm{H}}}^{13}\mathrm{CN}(1-0)}$/${T}_{{\rm{b}},{{\rm{H}}}^{13}{\mathrm{CO}}^{+}(1-0)}\,=\,({\mu }_{{{\rm{H}}}^{13}\mathrm{CN}}$/${\mu }_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}}{)}^{2}{N}_{{{\rm{H}}}^{13}\mathrm{CN}}$/${N}_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}}$, where the ratio of the permanent dipole moments of the two molecules is ${({\mu }_{{{\rm{H}}}^{13}\mathrm{CN}}/{\mu }_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}})}^{2}=0.59$ (e.g., Mangum & Shirley 2015). From these considerations, the column density ratio of the two isotopic species becomes ${N}_{{{\rm{H}}}^{13}\mathrm{CN}}/{N}_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}}\,=3.3\pm 0.9$.

The distributions of the line intensity ratios, R_H, across the central 1 kpc starburst region of NGC 1808, are shown in Figure 6. The figure reveals the following important characteristics of the measured ratios: (1) R_H is enhanced in the CND (central region of 200 pc diameter) where the pixel-averaged ratio is ${R}_{{\rm{H}}}(r\lt 2^{\prime\prime} )=1.45\pm 0.08$; (2) R_H is also enhanced to ∼1.5 in a narrow, elongated feature indicated with an arrow in Figure 6(a). The "S" feature coincides with a molecular spiral pattern distributed around the CND (Salak et al. 2017). Figure 6(b) shows a spatially smoothed distribution of R_H: the ratio is at its maximum in the galactic center and decreases to near unity throughout the starburst disk (see Table 3). This result is also apparent in panel (e), where the azimuthally averaged R_H is plotted as a function of galactocentric distance. Note also in panel (f) that there is no indication of significant enhancement of R_H in the core (high-velocity component at offset 0'' and 1050 km s⁻¹ ≲ V_LSR ≲ 1100 km s⁻¹) compared to the rest of the CND. This behavior is different from the excitation of HCO⁺, expressed as a ratio of brightness temperatures ${R}_{{\mathrm{HCO}}^{+}}\,\equiv {T}_{{\rm{b}},{\mathrm{HCO}}^{+}(4-3)}/{T}_{{\rm{b}},{\mathrm{HCO}}^{+}(1-0)}$, which is clearly elevated in the core (shown below in Figure 9(b)), and implies that caution is needed when R_H is interpreted as a result of gas excitation.

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Applying the nuclear activity diagnostic method of Kohno et al. (2001) and Imanishi et al. (2006), the nucleus of NGC 1808, with its ratios of ${T}_{{\rm{b}},\mathrm{HCN}(1-0)}/{T}_{{\rm{b}},{\mathrm{HCO}}^{+}(1-0)}=1.46\pm 0.04$ and ${T}_{{\rm{b}},\mathrm{HCN}(1-0)}/{T}_{{\rm{b}},\mathrm{CO}(1-0)}=0.164\pm 0.005$, lies in the boundary region between pure AGN and starburst activity, and thus can be regarded as a composite of coexisting AGN and starburst. This result is in agreement with the observed activity of the nucleus, where starburst activity and a tentative AGN have been found.

The origin of the distribution of R_H in the CND and spiral pattern is not clear. Similar results have been reported, e.g., from ALMA observations of the CNDs of the nearby Seyfert galaxies NGC 1068, NGC 1097, and NGC 613 by García-Burillo et al. (2014), Martín et al. (2015), and Miyamoto et al. (2017), respectively. Although NGC 1808 is not a "pure" AGN, its nuclear value of R_H is still enhanced with respect to the surrounding starburst regions, an observation that requires explanation. One recently proposed scenario is that R_H can be enhanced in the CNDs of Seyfert galaxies in the environment of high-temperature gas chemistry (Harada et al. 2010, 2013). Indeed, high gas temperatures have been measured in the nuclei of Seyfert (Izumi et al. 2013; Miyamoto et al. 2015) and starburst galaxies (Ando et al. 2017; Gorski et al. 2017). Then the question is: what is the heating source in starburst-dominated galactic nuclei? With ${L}_{{\rm{X}}}\sim 1\times {10}^{39}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$, the X-ray luminosity of the AGN in NGC 1808 is relatively weak (Terashima et al. 2002; Jiménez-Bailón et al. 2005), and there is no evidence of a plasma jet from the core. Furthermore, the spiral arm that exhibits high R_H is ∼200 pc away from the galactic core, making the radiation from the AGN an unlikely driving force. In this context, we consider the possibility of star formation feedback. In a vigorous starburst, multiple supernova explosions are the main sources of interstellar shocks and a flux of cosmic rays. A similar explanation that involves shocks has been proposed for the observed line intensities in the outflow of Mrk 231 (Aalto et al. 2012). This scenario seems plausible for the CND and nuclear spirals in NGC 1808, because shocks produced by cloud collisions, supernova explosions, and other feedback in H ii regions can heat the gas. Since numerous "hot spots" are found throughout the central 1 kpc disk, elevated R_H in principle should not be confined to the galactic center.

In order to explore the scenario of a chemistry supported by shocks, we investigated the intensity distribution of SiO (2–1) and the 93 GHz continuum shown in panels (c) and (d) of Figure 6. While SiO (2–1) is a well-known tracer of dense shocked gas, the 93 GHz continuum is dominated by free–free thermal emission produced in H ii regions and a minor contribution of synchrotron nonthermal emission from supernova remnants (Salak et al. 2017). This is where molecular clouds are in direct contact with hot gas (PDRs) ionized by massive stars and shocks in supernova explosions. Since SiO (2–1) is detected only toward the nucleus (Figure 6(c)), it does not reveal any clear spatial correlation with the enhanced R_H beyond the CND. In the CND, however, the intensity peak of SiO (2–1) is coincident with R_H at the resolution of 2''. Furthermore, there is a marginal spatial correlation between the 93 GHz continuum and high R_H even beyond the CND; the continuum exhibits a patchy ring at a radius of ∼300 pc (Figure 6(d)) and coincides with the distributions of star formation tracers such as Paα, [Fe ii], and hot molecular hydrogen gas (Busch et al. 2017). Note that this ring is smaller than the 500 pc ring marked in Figure 3. Figure 6(e) shows an increase in the azimuthally averaged R_H at r ∼ 6''; this radius corresponds to the star-forming ring. Although modest values of R_H are found at the continuum peaks along the ring, many of the high-R_H regions lie near the peaks inside the ring. This may imply that the ratio R_H in the nuclear spiral pattern, which is a part of the ring, is in some ways affected by star formation activity.

The detections of SiO, HNCO (Figure 2), and radio continuum indicate the presence of shocked gas in the CND and CMCs. Although shocked gas is a favorable environment for the enhancement of R_H in the high-temperature chemistry scenario, further observations of SiO or CH₃OH, which is another well-established shock tracer, at higher sensitivity and resolution would clarify whether the observed R_H is closely related to shock heating. Also, the possibility of electron excitation (Goldsmith & Kauffmann 2017) as a key factor in regulating R_H in regions such as the SF ring cannot be ruled out, especially if the ratio is predominantly large in cloud envelopes where gas densities are relatively low (Kauffmann et al. 2017). The observed correlation of R_H with the 93 GHz continuum implies that electron excitation may be responsible for the observed ratios to some extent. Higher angular resolution observations of the SF ring and CND could shed light on the issue. It should be noted that the line intensity ratios involving C₂H (1–0), which is a PDR tracer, behave in a similar way to those of HCN (1–0) with respect to tracers such as HCO⁺ (1–0), CS (2–1), and CO (1–0) (Figure 5(c)); the C₂H (1–0) line, which is moderately optically thin (see the Appendix), is prominent in the CND, indicating high column densities. These trends can be tested in chemical models based on star formation feedback (PDR environment). To analyze the observed line intensity ratios in greater detail, it is important to estimate the physical conditions in the CND and the rest of the starburst disk, which is the subject of the next section.

The non-LTE calculations were carried out using the radiative transfer program RADEX (van der Tak et al. 2007) applied on the line intensity ratios of CO (3–2)/CO (1–0), HCO⁺ (4–3)/HCO⁺ (1–0), HCN (1–0)/H¹³CN (1–0), HCO⁺ (1–0)/H¹³CO⁺ (1–0), HCN (1–0)/HCO⁺ (1–0), and H¹³CN (1–0)/H¹³CO⁺ (1–0). The ratios that involve the ¹³C-bearing molecules are available only for the CND where H¹³CN (1–0) and H¹³CO⁺ (1–0) were firmly detected. Nevertheless, the analysis of the CND yields important information regarding the physical conditions of the dense gas, because all four J = 1−0 lines of hydrogen cyanide and formylium have comparable critical densities and, unlike CO (1–0), can be regarded as probes of gas with densities of the order ${n}_{{{\rm{H}}}_{2}}\gtrsim {10}^{3}\,{\mathrm{cm}}^{-3}$. Another advantage of using the ¹³C-bearing molecules is that their transitions are likely optically thin; the ratios of the column densities, necessary in RADEX calculations, can be constrained. For a given molecular column density and a one-dimensional velocity width, ΔV, the program can derive the line intensity ratio as a function of kinetic temperature (T_k) and density of molecular (hydrogen) gas (${n}_{{{\rm{H}}}_{2}}$). We assume a background temperature of ${T}_{\mathrm{bg}}=2.73\,{\rm{K}}$ due to the cosmic microwave background radiation. The geometry related to the photon escape probability is set to be an expanding sphere, equivalent to the large velocity gradient approximation (Sobolev 1957; Goldreich & Kwan 1974; Scoville & Solomon 1974; Goldsmith et al. 1983). The ratio of the column density of a molecular species X to the velocity width, N_X/ΔV, is related to a velocity gradient ΔV/Δr via ${N}_{{\rm{X}}}={f}_{{\rm{X}}}{n}_{{{\rm{H}}}_{2}}{\rm{\Delta }}V/({\rm{\Delta }}V/{\rm{\Delta }}r)$, where ${f}_{{\rm{X}}}\equiv [{\rm{X}}]/[{{\rm{H}}}_{2}]$ is the relative abundance and ${n}_{{{\rm{H}}}_{2}}$ is the number density of H₂ molecules.

The column density N_CO is estimated from the CO (1–0) integrated intensity (within 2'' regions) applying a CO-to-H₂ conversion factor of ${X}_{\mathrm{CO}}=0.8\times {10}^{20}\,{\mathrm{cm}}^{-2}{({\rm{K}}\mathrm{km}{{\rm{s}}}^{-1})}^{-1}$ (Salak et al. 2014) and an abundance ratio of $[\mathrm{CO}]/[{{\rm{H}}}_{2}]\,={10}^{-4}$. The equation applied is ${N}_{{{\rm{H}}}_{2}}={X}_{\mathrm{CO}}{W}_{\mathrm{CO}}$, where W_CO is the integrated intensity in K km s⁻¹. The resulting column densities of H₂ are of the order ${N}_{{{\rm{H}}}_{2}}\sim 3\mbox{--}7\times {10}^{22}\,{\mathrm{cm}}^{-2}$ (Table 2). A Galactic conversion factor of ${X}_{\mathrm{CO}}=2\,\times {10}^{20}\,{\mathrm{cm}}^{-2}{({\rm{K}}\mathrm{km}{{\rm{s}}}^{-1})}^{-1}$ would yield column densities of ${N}_{{{\rm{H}}}_{2}}\sim 1\mbox{--}2\times {10}^{23}\,{\mathrm{cm}}^{-2}$ averaged over 100 pc. In general, the conversion factor is applicable in the case of optically thick molecular clouds in virial equilibrium, and therefore results in an upper limit for the molecular gas mass (Solomon et al. 1987). Although CO (1–0) emission is usually optically thick in molecular clouds in galactic disks, the optical depth in a starburst nucleus can have moderate values due to high velocity dispersion (e.g., ${\tau }_{\mathrm{CO}(1-0)}\sim 2\mbox{--}5$ in NGC 253; Meier et al. 2015).

A lower limit of N_CO toward the galactic center position can be obtained by assuming optically thin CO (1–0) emission in LTE. For an abundance ratio $[\mathrm{CO}]/[{{\rm{H}}}_{2}]={10}^{-4}$ and excitation temperature T_ex = 31 K, we obtain ${N}_{{{\rm{H}}}_{2}}\sim 1\times {10}^{22}\,{\mathrm{cm}}^{-2}$, which is expectedly smaller than the value derived using X_CO. Note that a lower excitation temperature would result in a lower column density.

The column density of ${N}_{{\mathrm{HCO}}^{+}}$ is more difficult to estimate, because ${\tau }_{{\mathrm{HCO}}^{+}(1-0)}\gt 1$. In this analysis, we adopt an abundance ratio of $[{\mathrm{HCO}}^{+}]/[{{\rm{H}}}_{2}]={10}^{-8}$ reported in previous works (e.g., Hogerheijde et al. 1997). This is a crude estimate, because the abundance of HCO⁺, as a molecular ion, is highly sensitive to the ionization degree of molecular gas, which may vary between regions and decrease in dense gas due to recombination (e.g., Papadopoulos 2007). This assumption yields the column densities of the order ${N}_{{\mathrm{HCO}}^{+}}\sim {10}^{14}\,{\mathrm{cm}}^{-2}$, consistent with those observed in dark molecular clouds in the Galaxy (Sanhueza et al. 2012) and nearby star-forming galaxies (Aladro et al. 2015).

The FWHM velocity width (ΔV) can be calculated from Gaussian fitting of the spectra toward the selected regions. Averaged over 100 pc, the velocity widths range between 50 and 150 km s⁻¹ and are typically somewhat larger for CO (1–0) than for HCO⁺ (1–0) in most of the regions (Table 2). Some of the line broadening in the central 100 pc region is produced by galactic rotation. Extremely large line widths in regions R1–R5 may be an indicator of small-scale dynamics (e.g., cloud rotation and relative velocities of unresolved clouds) and stellar feedback (e.g., gas outflows). All calculations were conducted using ${\rm{\Delta }}V=50\,\mathrm{km}\,{{\rm{s}}}^{-1}$, which is a typical observed value within individual pixels of the image. Since the results of RADEX calculations depend on the ratio N/ΔV, we fix ΔV and vary N over three orders of magnitude (Section 4.3).

The results of calculations are shown in Figures 7 and 8, and summarized in Table 4. The plotted curves are the average values of the observed line intensity ratios in the selected 2'' regions (Table 2). The physical conditions (density and temperature) are estimated from the areas where the intensity ratios intersect in the parameter space. Below, we discuss some important characteristics of the diagrams for each investigated region. The analysis begins with the dense gas tracers in the CND and then expands to other circumnuclear regions.

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Table 4.  Physical Conditions Derived with RADEX

Region	${N}_{\mathrm{CO}}$ (cm−2)	${T}_{{\rm{k}}}\,({\rm{K}})$	$\mathrm{log}({n}_{{{\rm{H}}}_{2}}/{\mathrm{cm}}^{-3})$	$\mathrm{log}({n}_{{{\rm{H}}}_{2}}/{\mathrm{cm}}^{-3})$
			$({R}_{\mathrm{CO}})$	$({R}_{{\mathrm{HCO}}^{+}})$
CND	7 × 1018	40	3.7–4.0	5.3–5.4
CMC	4 × 1018	30	3.2–3.5	5.4–5.6
500 pc ring (upstream)	5 × 1018	30	3.0–3.2	4.5–4.8
500 pc ring (downstream)	4 × 1018	30	3.2–3.5	5.4–5.6
Stream (nuclear outflow)	1 × 1018	>30	1.3–3.0	...

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The dense gas in the CND is first analyzed by using the line intensities of HCN (1–0), H¹³CN (1–0), HCO⁺ (1–0), HCO⁺ (4–3), and H¹³CO⁺ (1–0), whose ratios are defined as ${R}_{{\mathrm{HCO}}^{+}}\equiv {T}_{{\rm{b}},{\mathrm{HCO}}^{+}(4-3)}$/${T}_{{\rm{b}},{\mathrm{HCO}}^{+}(1-0)}=0.420\pm 0.022$, ${R}_{{\rm{H}}}\,\equiv {T}_{{\rm{b}},\mathrm{HCN}(1-0)}$/${T}_{{\rm{b}},{\mathrm{HCO}}^{+}(1-0)}=1.46\pm 0.04$, ${r}_{\mathrm{HCN}}\equiv {T}_{{\rm{b}},\mathrm{HCN}(1-0)}$/${T}_{{\rm{b}},{{\rm{H}}}^{13}\mathrm{CN}(1-0)}=12.8\pm 1.8$, ${r}_{{\mathrm{HCO}}^{+}}\equiv {T}_{{\rm{b}},{\mathrm{HCO}}^{+}(1-0)}$/${T}_{{\rm{b}},{{\rm{H}}}^{13}{\mathrm{CO}}^{+}(1-0)}\,=17.0\pm 7.1$, and ${r}_{{\rm{H}}}\equiv {T}_{{\rm{b}},{{\rm{H}}}^{13}\mathrm{CN}(1-0)}$/${T}_{{\rm{b}},{{\rm{H}}}^{13}{\mathrm{CO}}^{+}(1-0)}=1.93\pm 0.53$. The RADEX calculations were carried out in a temperature range of 5 K ≤ T_k ≤ 500 K and a density range of ${10}^{2}\,{\mathrm{cm}}^{-3}\leqslant {n}_{{{\rm{H}}}_{2}}\lt {10}^{7}\leqslant {\mathrm{cm}}^{-3}$, where the applied molecular parameters were acquired from the Leiden Atomic and Molecular Database⁵ (Schöier et al. 2005). We assumed that $[{\mathrm{HCO}}^{+}]/[{{\rm{H}}}_{2}]={10}^{-8}$ and ${[}^{12}{\rm{C}}]/{[}^{13}{\rm{C}}]\sim 20\mbox{--}50$ (Salak et al. 2014), and the velocity width was fixed to ΔV = 50 km s⁻¹. The calculations were carried out for four setups, as described below.

In setup 1, the applied column densities were ${N}_{\mathrm{HCN}}\,=2.3\,\times {10}^{15}\,{\mathrm{cm}}^{-2}$, ${N}_{{{\rm{H}}}^{13}\mathrm{CN}}=6.6\times {10}^{13}\,{\mathrm{cm}}^{-2}$, ${N}_{{\mathrm{HCO}}^{+}}=7.0\,\times {10}^{14}\,{\mathrm{cm}}^{-2}$, and ${N}_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}}=2.0\times {10}^{13}\,{\mathrm{cm}}^{-2}$. The values were selected to satisfy ${[}^{12}{\rm{C}}]/{[}^{13}{\rm{C}}]=35$ and ${N}_{{{\rm{H}}}^{13}\mathrm{CN}}/{N}_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}}=3.3$, derived assuming optically thin emission of these isotopic species (Section 3.4) and the same HCN to HCO⁺ abundance ratio; note that this ratio assumes that the abundance of HCN is not significantly enhanced with respect to HCO⁺, and that the emission is close to LTE.

Setup 2 adopted the same column density as HCO⁺, but a higher ratio ${[}^{12}{\rm{C}}]/{[}^{13}{\rm{C}}]=50$, resulting in ${N}_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}}\,=1.4\times {10}^{13}\,{\mathrm{cm}}^{-2}$. Again, ${N}_{{{\rm{H}}}^{13}\mathrm{CN}}/{N}_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}}=3.3$, yielding ${N}_{{{\rm{H}}}^{13}\mathrm{CN}}=4.6\times {10}^{13}\,{\mathrm{cm}}^{-2}$, and, assuming a non-enhanced abundance of HCN, ${N}_{\mathrm{HCN}}=2.3\times {10}^{15}\,{\mathrm{cm}}^{-2}$. Setup 3 adopted ${[}^{12}{\rm{C}}]/{[}^{13}{\rm{C}}]=20$, so that the column densities are ${N}_{{{\rm{H}}}^{13}\mathrm{CN}}=1.2\times {10}^{14}\,{\mathrm{cm}}^{-2}$ and ${N}_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}}=3.5\times {10}^{13}\,{\mathrm{cm}}^{-2}$; the other parameters are unchanged.

By contrast, setup 4 adopted an enhanced abundance of HCN relative to HCO⁺. We kept the same values of ${N}_{{\mathrm{HCO}}^{+}}\,=7.0\times {10}^{14}\,{\mathrm{cm}}^{-2}$ and ${N}_{{{\rm{H}}}^{13}\mathrm{CN}}/{N}_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}}=3.3$, but assumed that ${N}_{\mathrm{HCN}}/{N}_{{\mathrm{HCO}}^{+}}=6.6$, i.e., that there is an enhancement by a factor of ∼2 (${N}_{\mathrm{HCN}}=4.6\times {10}^{15}\,{\mathrm{cm}}^{-2}$). (Increasing ${N}_{{{\rm{H}}}^{13}\mathrm{CN}}/{N}_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}}$ too by the same factor resulted in a much less constrained solutions.) High abundance ratios have been proposed to explain the elevated R_H in a number of active galactic nuclei (e.g., Izumi et al. 2013; Miyamoto et al. 2017). Judging from the trends in the results of setups 1–3, we set the ratio ${[}^{12}{\rm{C}}]/{[}^{13}{\rm{C}}]=25$, which yielded ${N}_{{{\rm{H}}}^{13}{\mathrm{CO}}^{+}}=2.8\times {10}^{13}\,{\mathrm{cm}}^{-2}$ and ${N}_{{{\rm{H}}}^{13}\mathrm{CN}}=9.2\,\times {10}^{13}\,{\mathrm{cm}}^{-2}$.

The results of the calculations of all four setups are shown in Figure 7. Given that five line intensity ratios are used, there can be 10 intersections, and the quality of the chosen setup was evaluated based on the number of intersections and how close they appear in the investigated parameter space. Figure 7 shows that, although there are intersections in all investigated setups, setup 4 provides the strongest constraints on physical conditions (the line intensity ratios are best confined in the parameter space). There are nine intersections in setup 4, out of which five coincide in the parameter space, yielding a range of densities of ${10}^{4.9}\,{\mathrm{cm}}^{-3}\lesssim {n}_{{{\rm{H}}}_{2}}\lesssim {10}^{5.8}\,{\mathrm{cm}}^{-3}$ and a kinetic temperature range of 20 K ≲ T_k ≲ 100 K (on average T_k ∼ 40 K), where the lower and upper limits are dominated by r_HCN, but also sensitive to R_H and r_H. This result implies the presence of dense and warm molecular gas in the CND. Since ${R}_{{\mathrm{HCO}}^{+}}$ includes the J = 4−3 line, it is possible that the low- and high-transition lines of HCO⁺ arise from somewhat different volumes; selective dissociation may also reduce the emitting volumes of the ¹³C-bearing molecules. If that is the case, the result may be affected to some extent by a difference in beam filling factors. Note that the three most separated intersections in Figure 7 (setup 4) lie on ${R}_{{\mathrm{HCO}}^{+}}$. Increasing the ratio (e.g., correcting for a low beam filling factor of J = 4−3), generally shifts the ratio toward higher values of ${n}_{{{\rm{H}}}_{2}}$ and T_k; for slightly higher ratios of ${R}_{{\mathrm{HCO}}^{+}}\sim 0.5$, all intersections shift closer together near T_k ∼ 45 K and ${n}_{{{\rm{H}}}_{2}}\sim {10}^{5.4}$ cm⁻³.

The analysis is now extended to include the line intensity ratios of CO, which are available throughout the central 1 kpc region (Figure 8(a)). The calculations for the CND were carried out for different parameters as follows (Figure 8(b)): CO column density ranging from ${N}_{\mathrm{CO}}=7\times {10}^{17}\,{\mathrm{cm}}^{-2}$ to ${N}_{\mathrm{CO}}\,=7\times {10}^{19}\,{\mathrm{cm}}^{-2}$, and HCO⁺ column density ranging from ${N}_{{\mathrm{HCO}}^{+}}=7\times {10}^{13}\,{\mathrm{cm}}^{-2}$ to ${N}_{{\mathrm{HCO}}^{+}}=7\times {10}^{15}\,{\mathrm{cm}}^{-2}$ (assuming an abundance ratio of $[{\mathrm{HCO}}^{+}]/[\mathrm{CO}]={10}^{-4}$). A constant velocity width of ΔV = 50 km s⁻¹ was adopted. The results, summarized in the first row of Table 4, where T_k = 40 K was assumed, are generally consistent with Figure 7, indicating gas of ${10}^{4}\mbox{--}{10}^{7}\,{\mathrm{cm}}^{-3}\,{\rm{K}}$ at high pressure, higher than the typical gas pressure in Galactic disk clouds and comparable to the environment in the Galactic center region. Figure 8(b) (dashed arrow) shows that for a larger column density of CO, ${N}_{\mathrm{CO}}=7\times {10}^{19}$ cm⁻² and $[{\mathrm{HCO}}^{+}]/[\mathrm{CO}]={10}^{-5}$, we obtain higher temperatures (50–90 K), also consistent with the derived values in Section 4.2. The distribution of R_CO, indicated by color in panel (b), also shows that, in general, higher values of R_CO result in higher densities and/or temperatures. If the beam filling factor of CO is larger than that of HCO⁺, correcting for this effect would enhance R_CO and shift the solutions toward the regime of higher densities and/or temperatures, consistent with results in the previous section.

Note that the highest measured excitation of HCO⁺ molecules, reflected in the elevated ratio ${R}_{{\mathrm{HCO}}^{+}}\sim 0.6$, is found toward the core inside the CND (the high-velocity component shown in Figure 9(b)). The core also exhibits an elevated ratio of HCO⁺ (4–3) to CO (3–2) compared to the rest of the CND (panel (a)), and it is spatially coincident with the 93 GHz continuum (Figure 5(a)). The continuum has been carefully subtracted so that it does not affect the HCO⁺ (4–3) spectrum significantly; this is also supported by the absence of emission in the HCO⁺ (4–3) spectrum at velocities ${V}_{\mathrm{LSR}}\,\lt 900$ km s⁻¹ and ${V}_{\mathrm{LSR}}\gt 1120$ km s⁻¹ in the PVD diagram in Figure 4 (middle panel in the bottom row). The same plot also shows enhanced HCO⁺ (4–3) emission in the "core" component relative to the surrounding gas torus. The behavior is clearly different from that of HCO⁺ (1–0) shown in the second row. For the ratios of R_CO = 1.50 ± 0.50 and ${R}_{{\mathrm{HCO}}^{+}}=0.50\pm 0.12$ and the same column densities as adopted above for the CND, RADEX calculations yield a temperature range of 40–70 K and gas densities of $\mathrm{log}({n}_{{{\rm{H}}}_{2}}/{\mathrm{cm}}^{-3})=5.0\mbox{--}5.6$, within uncertainties. Here, we have assumed that 1 < R_CO < 2 and that R_CO and ${R}_{{\mathrm{HCO}}^{+}}$ trace the same volumes.

The CMC consists of regions R1 and R2, which represent giant molecular clouds where all gas tracers are firmly detected (Figure 8). RADEX calculations based on ${R}_{{\mathrm{HCO}}^{+}}$ yield gas densities comparable to those in the CND for an assumed temperature of 30 K. On the other hand, a derivation based on R_CO for the same temperature results in densities lower by two orders of magnitude (Table 4). R_CO and ${R}_{{\mathrm{HCO}}^{+}}$ cross at a point that corresponds to a relatively high density of ∼10⁶ cm⁻³ and a low temperature of ∼15 K. Considering the results for the CND in Section 4.2, we note that the intersection of R_CO and ${R}_{{\mathrm{HCO}}^{+}}$ may be an artificial solution produced by a difference in beam filling factors (emitting volumes). If that is the case, the excitation of the dense gas tracers HCN and HCO⁺ reflects the inner cloud regions, whereas CO, whose optical depth is larger and critical density lower, traces the conditions in the outer regions and envelopes.

The investigated part of the 500 pc ring consists of regions R3 and regions R4 and R5. These are further classified based on their location with respect to the ring rotation about the galactic center (see panel (a) in Figure 8): R3 is located "upstream," whereas R4 and R5 (whose average is used in calculations) are "downstream." The results in Figure 8 and Table 4 suggest that either gas density or temperature rises inside the ring from the upstream to the downstream side; this can be explained as a result of enhanced star formation activity within the ring, as discussed in Salak et al. (2017) in terms of cloud evolution. The clouds enter the 500 pc ring from the large-scale bar (upstream side) and engage in starburst activity as they revolve around the galactic center. The downstream regions R4 and R5 are located at the point of highest star-forming activity in the ring, as revealed by 93 GHz continuum tracing free–free emission.

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To estimate the physical conditions in the nuclear outflow (labeled "stream" in Figure 8(a)), we derived the ratios of R_CO and ${R}_{{\mathrm{HCO}}^{+}}$ in position–velocity space along the minor galactic axis, which is assumed to be the direction of the outflow (Salak et al. 2016). The R_CO ratio was presented in Salak et al. (2017), while in Figure 10 (bottom-right panel) we present the ${R}_{{\mathrm{HCO}}^{+}}$ ratio derived at a comparable angular resolution of ∼2''. For low column densities of ${N}_{\mathrm{CO}}=1\times {10}^{18}\,{\mathrm{cm}}^{-2}$ (equivalent to optically thin CO (1–0) emission; see Section 4.1) and ${N}_{{\mathrm{HCO}}^{+}}=1\times {10}^{14}\,{\mathrm{cm}}^{-2}$, assumed temperature of ${T}_{{\rm{k}}}\gt 30$ K, and a velocity width of ${\rm{\Delta }}V=50\,\mathrm{km}\,{{\rm{s}}}^{-1}$, corresponding to the velocity of the extraplanar stream, RADEX calculations yielded relatively low densities as listed in Table 4 and plotted in Figure 8(e). However, since HCO⁺ (4–3) is not clearly detected in the outflow, the ratio ${R}_{{\mathrm{HCO}}^{+}}$ is not well constrained; we plot the results in the range $0.025\lt {R}_{{\mathrm{HCO}}^{+}}\lt 0.05$. The resulting parameters are notably different from those in other investigated regions in the starburst disk. In particular, the density, which is better constrained by R_CO than the temperature, is lower than in the massive molecular clouds in the starburst disk. Since the density was derived over 100 pc regions, smaller structures are not resolved. If the physical conditions of the outflow gas are uniform, then the result reflects diffuse (${n}_{{{\rm{H}}}_{2}}\sim {10}^{2}\mbox{--}{10}^{3}\,{\mathrm{cm}}^{-3}$) and warm (${T}_{{\rm{k}}}\gtrsim 20\,{\rm{K}}$) medium, comparable to the conditions in the superbubble in M82 (Chisholm & Matsushita 2016). On the other hand, the same result can also imply a clumpy gas, where the clumps of dense gas are unresolved within the probed aperture. The clumpy nature is likely given the detection of other dense gas tracers in the stream, namely, HCN, CS, and C₂H presented below. All of these tracers have critical densities of the order ${n}_{\mathrm{cr}}\gtrsim {10}^{3}\,{\mathrm{cm}}^{-3}$ in the regime of the most likely kinetic temperatures. Salak et al. (2017) also showed that R_CO is decreasing with galactocentric distance in extraplanar gas, from 0.5 near the CND to 0.2 at the farthermost point. Figure 8(e) implies that, for a constant column density, such trend reflects a decrease in gas density (divergence of mass flux or molecule destruction) and/or temperature in the outflow direction.

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Also shown in Figure 10 are the PVDs along the minor galactic axis for HCN (1–0), HCO⁺ (1–0), CS (2–1), and C₂H (1–0). Dense gas tracers such as these were recently detected in the molecular outflow in the starburst galaxy NGC 253 (Walter et al. 2017), providing evidence that starburst-driven outflows can include dense gas. The line intensity ratio of HCN (1–0) to HCO⁺ (1–0), R_H, in position–velocity space is shown on the bottom-left panel of the figure. The PVDs of these lines show evidence of dense molecular gas in the outflow with kinematics similar to that of CO. In particular, the PVDs exhibit an outward velocity gradient reported earlier by Salak et al. (2017) as a possible evidence of outflow acceleration. Note that R_H > 1 in the CND, and decreases to ∼1 at a radius r ≳ 5'' (260 pc). There are signatures of local enhancements (${R}_{{\rm{H}}}\gt 1$) in some regions of the outflow, especially at the high-velocity end between offset = −4'' and 0'', and between V_LSR =850 km s⁻¹ and 900 km s⁻¹, but the ratio is close to unity (the mean ratio in the region defined by offset <−2'' and ${V}_{\mathrm{LSR}}\lt 950\,\mathrm{km}\,{{\rm{s}}}^{-1}$ is ${R}_{{\rm{H}}}^{\mathrm{stream}}=1.1\pm 0.8$), implying that the HCN (1–0) to HCO⁺ (1–0) ratio in the outflow is similar to the average value in the starburst disk and lower than the ratio in the CND. If the stream gas is ejected from the CND, the decrease of R_H along the outflow direction can imply that the electron densities in the outflow are significantly lower than in the CND, yielding a decreased effect of electron excitation and hence smaller R_H.

The middle rows of Figure 10 show that the emission of CS (2–1) and C₂H (1–0) arises primarily from the clouds in the galactic plane rotating at velocities close to the systemic velocity V_sys, denoted by "disk." However, the line splitting into "disk" and "stream" (outflow) in the figure indicates the presence of CS and C₂H in the extraplanar gas. While CS (2–1) is detected at 4σ at $(\mathrm{offset},{V}_{\mathrm{LSR}})=(-7^{\prime\prime} ,900\,\mathrm{km}\,{{\rm{s}}}^{-1})$, the emission of C₂H (1–0) in the stream component is detected at 3σ. Figure 11 shows that the intensity projections of the dense gas tracers in the outflow direction are similar to those of CO (3–2); the major differences are observed in the HCN (1–0) to HCO⁺ (1–0) ratio, which decreases from ∼1.4 in the CND to ∼1 in the stream, and in the intensity of CS (2–1), which is enhanced at the radius of r ∼ 2'' and is relatively low at r ∼ 5'', though within the uncertainty of 20%.

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There are several causes of systematic errors that dominate the overall uncertainty of the non-LTE analysis presented above. First, the emission from the investigated regions is regarded as an average within an aperture size of 2'' (100 pc). Since this is probably larger than the size of individual giant molecular clouds (e.g., Sanders et al. 1985), the line intensity reflects an average over a cloud/envelope/intercloud region. The physical conditions and chemical composition may vary from the cloud to the intercloud medium.

Second, in one part of the analysis (Section 4.3), some solutions were based on the assumption that CO and HCO⁺ emission arises from the same cloud volumes. However, as mentioned above, even the lines of the same species may be tracing somewhat different regions. For example, while HCO⁺ (4–3) may be tracing the cloud interior, HCO⁺ (1–0) can be more prominent in the outer layers (e.g., Hogerheijde et al. 1997). In other words, the beam filling factor may vary among the tracers. In general, the solutions of the physical conditions based on mixed R_CO and ${R}_{{\mathrm{HCO}}^{+}}$ ratios produce lower kinetic temperatures (10–20 K). When the ratios are considered separately and ¹³C-bearing molecular species are included, the dense gas is found to be warmer (CND; Section 4.2). Considering that the CND and CMCs are dominated by vigorous star formation and its feedback (e.g., shock heating), higher temperatures are plausible.

Also, the column densities of CO and HCO⁺ were estimated from indirect methods (CO luminosity converted to H₂ column density by using a constant conversion factor, and then converted to CO and HCO⁺ column densities by assuming abundance ratios). For this purpose, we estimated the CO column density in the case of optically thin CO (1–0) emission to obtain a lower limit. The column density of HCO⁺ was also derived by assuming LTE. The uncertainty of the column density is estimated to be a factor of a few.

The results obtained in the analysis are generally consistent with previous studies of gas conditions in NGC 1808 based on single-pointing data from single-dish telescopes (Aalto et al. 1994; Salak et al. 2014). Measuring the intensity ratios from additional CO lines, including optically thin lines of ¹³CO and C¹⁸O, as well as other dense gas tracers with comparable critical densities throughout the starburst disk (compact and diffuse components) would be a next step of the analysis to obtain a more detailed picture of the physical conditions of the molecular medium.

In the case of the HCO⁺ molecule, Equation (3) can be expressed in terms of intensities as

$$\begin{eqnarray}&&\displaystyle \frac{{{ \mathcal S }}_{13}}{{{ \mathcal S }}_{12}}=\displaystyle \frac{1-{e}^{-{\tau }_{12}/{ \mathcal R }}}{1-{e}^{-{\tau }_{12}}},\end{eqnarray} \tag{ 5 }$$

where "12" and "13" denote the isotopologues H¹²CO⁺ and H¹³CO⁺, respectively. In the above equation, we have taken ν₁₂ ≈ ν₁₃ and ${T}_{\mathrm{ex},12}\approx {T}_{\mathrm{ex},13}$. Note that we also consider that the beam filling factors of the two lines are identical. The optical depth ratio is approximately the abundance ratio ${{ \mathcal R }}_{{\mathrm{HCO}}^{+}}\approx [{\mathrm{HCO}}^{+}]/[{{\rm{H}}}^{13}{\mathrm{CO}}^{+}]$; we adopt the values of 50, following Sanhueza et al. (2012), and 25, estimated in Section 4.2. The intensities of the two lines, derived by Gaussian fitting of the line profiles within a circle of diameter 2'' centered at the galactic center, are ${{ \mathcal S }}_{12}=21.6\,\pm 0.9\,\mathrm{Jy}\,{\mathrm{beam}}^{-1}$ and ${{ \mathcal S }}_{13}=1.2\pm 0.5\,\mathrm{Jy}\,{\mathrm{beam}}^{-1}$. Solving Equation (5) numerically yields the optical depths of τ₁₂ = 2.65 and τ₁₃ = 0.05 for ${ \mathcal R }=50$ and τ₁₂ = 0.73 and τ₁₃ = 0.03 for ${ \mathcal R }=25$: the HCO⁺ (1–0) line is moderately optically thick, whereas H¹³CO⁺ (1–0) can be regarded as optically thin.

The total column density of HCO⁺ molecules is calculated from Equation (4) as

$$\begin{eqnarray}&&{N}_{{\mathrm{HCO}}^{+}}=\displaystyle \frac{3k}{8{\pi }^{3}B{\mu }^{2}}\displaystyle \frac{{T}_{\mathrm{ex}}+{hB}/3k}{1-\exp (-h\nu /{{kT}}_{\mathrm{ex}})}\tau {\rm{\Delta }}V,\end{eqnarray} \tag{ 6 }$$

where we have used E_J = 0 (ground state). For the adopted values of B = 44.5944 GHz, μ = 3.89 D, T_ex = 31 K, τ = 2.65, and ΔV = 136 ± 4 km s⁻¹, where B and μ are taken from the Splatalogue database, we find ${N}_{{\mathrm{HCO}}^{+}}\,=(2.19\pm 0.06)\times {10}^{16}$ cm⁻², where the uncertainty is estimated only from the uncertainty of the velocity width. A lower excitation temperature of T_ex = 10 K, e.g., yields one order of magnitude smaller column density (Table 5). On the other hand, applying ΔV = 50 km s⁻¹ and using the derived lower optical depth would result in one order of magnitude lower ${N}_{{\mathrm{HCO}}^{+}}$, in agreement with the value applied in Section 4.2, which was based on $[{\mathrm{HCO}}^{+}]/[{{\rm{H}}}_{2}]={10}^{-8}$.

Table 5.  Dense Gas Parameters in the CND Derived Under LTE

Parameter	HCN	HCO+
μ[D]	2.984	3.888
B [GHz]	44.31597	44.59442
ΔV [km s−1]	137 ±  4	136 ±  4
τ	3.76	2.65
N [cm−2] (${T}_{\mathrm{ex}}=31$ K)	$(5.39\pm 0.16)\times {10}^{16}$	$(2.19\pm 0.06)\times {10}^{16}$
N [cm−2] (${T}_{\mathrm{ex}}=10$ K)	(6.74 ± 0.20) × 1015	(2.75 ± 0.08) × 1015

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The intensities of the HCN (1–0) and H¹³CN (1–0) lines are ${{ \mathcal S }}_{12}=31.0\pm 0.9\,\mathrm{Jy}\,{\mathrm{beam}}^{-1}$ and ${{ \mathcal S }}_{13}=2.3\pm 0.3\,\mathrm{Jy}\,{\mathrm{beam}}^{-1}$, respectively, and the corresponding optical depths are τ₁₂ = 3.76 and τ₁₃ = 0.07 for the abundance ratio of ${{ \mathcal R }}_{\mathrm{HCN}}\approx [\mathrm{HCN}]/[{{\rm{H}}}^{13}\mathrm{CN}]=50$ and τ₁₂ = 1.47 and τ₁₃ = 0.06 for the abundance ratio of ${{ \mathcal R }}_{\mathrm{HCN}}\approx [\mathrm{HCN}]/[{{\rm{H}}}^{13}\mathrm{CN}]=25$. The same abundance ratio is applied for HCN and HCO⁺, because it is largely determined by the abundance ratio of ${[}^{12}{\rm{C}}]/{[}^{13}{\rm{C}}]$. The HCN (1–0) line too is moderately optically thick toward the galactic center. Since this is the only region where H¹³CN (1–0) is detected, the calculation using isotopes is limited to the CND.

Finally, the column density is calculated from Equation (6). Inserting B = 44.31597 GHz, μ = 2.984 D (from Splatalogue), T_ex = 31 K, τ = 3.76, and ΔV = 137 ± 4 km s⁻¹, the column density of HCN molecules becomes ${N}_{\mathrm{HCN}}=(5.39\,\pm 0.15)\times {10}^{16}$ cm⁻².

The result yields a column density ratio (equivalent to the abundance ratio) of ${N}_{\mathrm{HCN}}/{N}_{{\mathrm{HCO}}^{+}}=2.46\pm 0.10$ averaged over the central 100 pc. The derived parameters are summarized in Table 5. Note that μ² is about two times larger for HCO⁺ than for HCN. This means that, under the conditions of similar excitation temperatures, velocity widths, and column densities of HCN (1–0) and HCO⁺ (1–0), the opacity of the HCO⁺ (1–0) line would be about two times larger than that of HCN (1–0), which is not observed in the isotope ratios (Table 5). The derived moderate opacities of HCN (1–0) and HCO⁺ (1–0) are similar to those in the central region of the starburst galaxy NGC 253 (Meier et al. 2015).

The intensity ratio of the triplets of the C₂H (1–0) line in LTE is expected to be ${R}_{{{\rm{C}}}_{2}{\rm{H}}}\equiv {{ \mathcal S }}_{\max }(J=3/2\mbox{--}1/2)/{{ \mathcal S }}_{\max }(J=1/2\mbox{--}1/2)=2$ in the optically thin case and ${R}_{{{\rm{C}}}_{2}{\rm{H}}}=1$ in the optically thick case (Tucker et al. 1974). From Table 1, the intensity ratio in the CND is measured to be ${R}_{{{\rm{C}}}_{2}{\rm{H}}}=2.26\pm 0.19$, close to the LTE expectation, suggesting that the line is optically thin. Similar intensity ratios are also obtained toward the other regions from Table 2, indicating optically thin (or moderately optically thick) medium: 2.07 ± 0.46 (R1), 1.90 ± 0.41 (R2), 1.65 ± 0.30 (R3), 1.57 ± 0.22 (R4), and 1.36 ± 0.31 (R5). Applying Equation (3), where ${ \mathcal R }=2$, and assuming that a single excitation temperature T_ex holds for all hyperfine components, the optical depths of the J = 3/2–1/2 components in regions R1–R5 are <1.0, 0.24 (<1.4), 0.89 (within 0.1–2.1), 1.1 (within 0.5–2.1), and 2.0 (within 0.8–5.9), respectively, where the values in brackets are uncertainties that arise from the ratio uncertainties.