ALMA Multiple-Transition Molecular Line Observations of the Ultraluminous Infrared Galaxy IRAS 20551-4250: Different HCN, HCO+, HNC Excitation and Implications for Infrared Radiative Pumping
Masatoshi Imanishi Kouichiro Nakanishi Takuma Izumi

















National Astronomical Observatory of Japan, National Institutes 
of Natural Sciences (NINS), 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan  
masa.imanishi@nao.ac.jp


National Astronomical Observatory of Japan, National Institutes 
of Natural Sciences (NINS), 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan




National Astronomical Observatory of Japan, National Institutes 
of Natural Sciences (NINS), 2-21-1 Osawa, Mitaka, Tokyo 181-8588, Japan

1Department of Astronomical Science, The Graduate
University for Advanced Studies (SOKENDAI), Mitaka, Tokyo 181-8588,
Japan 

2Institute of Astronomy, School of Science, The
University of Tokyo, 2-21-1 Osawa, Mitaka, Tokyo 181-0015, Japan




We present our ALMA multi-transition molecular line observational
results for the ultraluminous infrared galaxy, IRAS 20551-4250,
which is known to contain a luminous buried AGN and shows detectable
vibrationally excited (v_2=1f) HCN and HNC emission lines. 
The rotational J=1–0, 4–3, and 8–7 of HCN, HCO^+, and HNC
emission lines were clearly detected at a vibrational ground level (v=0). 
Vibrationally excited (v_2=1f) J=4–3 emission lines were detected
for HCN and HNC, but not for HCO^+.
Their observed flux ratios further support our previously obtained
suggestion, based on J=3–2 data, that (1) infrared radiative pumping
plays a role in rotational excitation at v=0, at least for HCN and HNC,
and (2) HCN abundance is higher than HCO^+ and HNC.
The flux measurements of the isotopologue H^13CN, H^13CO^+,
and HN^13C J=3–2 emission lines support the higher HCN abundance
scenario.
Based on modeling with collisional excitation, we constrain the
physical properties of these line-emitting molecular gas, but find that
higher HNC rotational excitation than HCN and HCO^+ is
difficult to explain, due to the higher effective critical density of HNC. 
We consider the effects of infrared radiative pumping using the
available 5–30 μm infrared spectrum and find that our observational
results are well explained if the radiation source is located at
30–100 pc from the molecular gas.  
The simultaneously covered very bright CO J=3–2 emission line displays
a broad emission wing, which we interpret as being due to molecular outflow
activity with the estimated rate of ∼150 M_⊙ yr^-1.  






§ INTRODUCTION


The ubiquity of supermassive black holes (SMBH) at the center of galaxy
stellar spheroidal components and the mass correlation between 
SMBHs and spheroidal stars suggest that SMBHs are an important
ingredient of galaxies <cit.>.  
In the currently widely accepted cold dark matter-based galaxy formation
scenario, small gas-rich galaxies collide and merge, and then grow into
more massive galaxies <cit.>.
Numerical simulations of such merging processes of gas-rich galaxies
containing SMBHs at their centers have been extensively performed, and
it has been argued that active star formation and mass accretion onto
central SMBHs occur in highly obscured regions during an infrared
luminous phase <cit.>.   

Active mass accretion onto SMBHs emits strong radiation and is observed 
as active galactic nucleus (AGN) activity. 
Luminous AGNs deeply buried in gas/dust-rich infrared luminous merging 
galaxies are now thought to play an essential role in galaxy
formation, through feedback to galaxies
<cit.>; however, observational
understanding of such buried AGNs is not easy, due to dust extinction. 
We must establish a method to detect and investigate the
properties of buried AGNs, by separating these from the surrounding starburst
emission.
Observing at wavelengths where the effects of dust extinction are
small is clearly one of the best ways to study dust-obscured energy sources. 

Molecular rotational J-transition emission line flux ratios at the
(sub)millimeter wavelength can be a powerful tool to study buried
energy sources, because (1) dust extinction is typically negligible,
unless the column density of obscuring material is very high (e.g.,
N_ H >> 10^25 cm^-2) and (2) some molecular lines are
argued to become good signatures of AGN activity. 
In particular, high dipole moment molecules, such as HCN, HCO^+,
and HNC, are better suited than the widely used low-J transition CO emission
lines to investigate physical properties around hidden energy sources
because nuclear molecular gas in the vicinity of active star formation
and AGN activity is usually in a dense form with >10^4 cm^-3. 
For example, it was proposed that optically selected AGNs and starbursts
show different molecular line flux ratios, in such a way that in AGNs, 
HCN rotational J-transition emission lines are enhanced, relative to  
HCO^+ <cit.>.
Based on pre-ALMA and ALMA observations of the nuclei of
gas/dust-rich luminous infrared galaxies (LIRGs; infrared luminosity
L_ IR > 10^11 L_⊙), which are diagnosed to contain
optically detectable AGNs or optically elusive, but infrared/X-ray
detectable AGNs or no detectable AGNs, it was demonstrated that
(sub)millimeter molecular emission line flux ratios indeed work to
detect the signs of deeply buried AGNs in these LIRGs 
<cit.>.  
Thus, these (sub)millimeter molecular line observations have potential
in the systematic investigation of buried AGNs in gas/dust-rich LIRGs not
only in the local universe, but also in the distant universe, thanks to
the advent of the highly sensitive ALMA observing facility in this
wavelength range.

However, the physical origin of the strong HCN J-transition line
emission in AGNs remains to be fully understood.
An HCN abundance enhancement in molecular gas in the close vicinity of
a buried AGN is a natural explanation for the strong HCN emission 
<cit.>.
While this high HCN abundance scenario in molecular gas, largely
affected by AGN radiation, is predicted in some parameter range by
chemical calculations <cit.>, it is not necessarily
true that the HCN abundance is always higher than HCO^+
around an AGN <cit.>.
Higher HCN rotational J-excitation in an AGN than a normal
starburst is an alternative explanation because the AGN's higher radiative
energy generation efficiency can increase the temperature of the surrounding
molecular gas and can excite HCN (higher critical density than
HCO^+ under the same line opacity) more than in a normal starburst
<cit.>. 
Multiple rotational J-transition line observations are required to
disentangle the abundance and excitation effects <cit.>.
Flux attenuation by line opacity (not dust extinction) is another
uncertain factor to discuss the hidden energy sources based on 
observed molecular line flux ratios <cit.>.
Optically thin isotopologue molecular line observations will help us
to estimate these line opacity effects for the main bright molecular
emission lines.

Another possible good AGN indicator is vibrationally excited molecular
emission lines whose energy levels are much higher than the widely
investigated rotationally excited emission lines at a vibrational ground
level (v=0).  
The vibrationally excited (v_2=1, l=1f; hereafter v_2=1f)
emission lines of HCN and HNC have recently been detected in several
LIRGs <cit.>.
Since the energy levels of these vibrationally excited states are 
∼1030 K (670 K) for HCN (HNC), it is very difficult to
excite by collision; however, an infrared radiative pumping process can
achieve this, by absorbing ∼14 μm (∼22 μm) infrared photons
<cit.>.
Because an AGN can emit mid-infrared (3–30 μm) continuum emission
more efficiently than a starburst with the same bolometric luminosity
due to AGN-heated hot (>100 K) dust emission, if the vibrationally
excited emission lines are strongly detected in LIRGs, then an obscured 
AGN is a plausible origin as the strong infrared continuum emitting
source to vibrationally excite HCN and HNC <cit.>. 
However, an extreme starburst with a very compact
size remains another possibility <cit.>.

The ultraluminous infrared galaxy (ULIRG), IRAS 20551-4250, 
with infrared luminosity L_ IR ∼ 10^12L_⊙ at 
z=0.043 (Table 1) is one such galaxy, where the vibrationally excited
(v_2=1f) HCN and HNC emission lines have been clearly detected, due to
small observed molecular line widths <cit.>.
The observed HCN-to-HCO^+ flux ratios at J=3–2 and J=4–3 have been
found to be substantially larger than in starburst-dominated regions
<cit.>. 
This galaxy displays a long merging tail in the southern direction
from the main single nucleus <cit.>.
Based on optical emission line flux ratios, it is classified as a
LINER/HII-region <cit.>, whereas <cit.> classified it as a 
starburst-AGN composite or HII-region type, depending on the emission
lines used.   
The presence of a buried AGN, which could explain 20–60% of
the bolometric luminosity, has been suggested, in addition to starburst
activity, based on infrared and X-ray observations 
<cit.>.  
Since IRAS 20551-4250 displays bright molecular rotational
J-transition emission lines <cit.>, this is an
interesting and valuable object to improve our understanding of the
physical origin of observed molecular emission line properties, based on
multiple rotational J-transition lines for multiple molecules. 

In this study, we present our new ALMA observational results in bands 3
(84–116 GHz), 7 (275–373 GHz), and 9 (602–720 GHz) of the ULIRG, IRAS
20551-4250.
The J=1–0, J=4–3, and J=8–7 emission lines of HCN, HCO^+, and
HNC are covered in bands 3, 7, and 9, respectively.
For J=4–3, vibrationally excited (v_2=1f) emission lines
were also observed for HCN, HCO^+, and HNC.   
For J=8–7, vibrationally excited (v_2=1f) HCN and HNC emission
lines were included in our band 9 data

[A vibrationally excited J=1–0 line is not present.].

ALMA band 6 (211–275 GHz) observations of isotopologue lines, 
H^13CN, H^13CO^+, and HN^13C J=3–2, were also conducted
and their results are included. 
We adopt H_0 = 71 km s^-1 Mpc^-1, Ω_ M = 0.27,
and Ω_Λ = 0.73 <cit.>, to be consistent with
our previously published ALMA papers for this galaxy.
The physical scale at z = 0.043 is 0.84 kpc arcsec^-1.
In the absence of a statement about vibrational level, we mean the
vibrational ground level (v=0).



§ OBSERVATIONS AND DATA ANALYSIS


Band 7 (275–373 GHz), 3 (84–116 GHz), 9 (602–720 GHz), and 
6 (211–275 GHz) observations were conducted through our 
ALMA Cycle 2 program 2013.1.00033.S (PI = M. Imanishi), 
Cycle 3 program 2015.1.00028.S (PI = M. Imanishi), 
Cycle 3 program 2015.1.00028.S (PI = M. Imanishi), and 
Cycle 4 program 2016.1.00051.S (PI = M. Imanishi), respectively.
The widest 1.875 GHz band mode and 3840 total channel number were
employed for all observations.
To reduce the data rate, online spectral averaging with a factor of 2
or 4 was applied for some observations. 
Table 2 summarizes these ALMA observations.

For our ALMA band 7 observations, we covered HCO^+ J=4–3 
(rest-frame frequency is ν_ rest = 356.734 GHz), HCN
v_2=1f J=4–3 (ν_ rest = 356.256 GHz), and HCO^+
v_2=1f J=4–3 (ν_ rest = 358.242 GHz), but had to exclude 
the HCN J=4–3 line (ν_ rest = 354.505 GHz), due to the limited
frequency coverage of the ALMA system.  
HCN J=4–3 and HCO^+ J=4–3 (v=0) lines were observed in our ALMA
Cycle 0 observations <cit.>.
The bright HCO^+ J=4–3 (v=0) emission line can be used for
inter-calibration between Cycle 0 and 2 data, by correcting for possible 
absolute flux calibration uncertainty during individual ALMA
observations. 
The very bright CO J=3–2 (ν_ rest = 345.796 GHz) emission line
was also included in our Cycle 2 observations.
HNC J=4–3 emission lines at v=0 (ν_ rest = 362.630 GHz) and
v_2=1f (ν_ rest = 365.147 GHz) were obtained
independently from the HCO^+ J=4–3 observations.

For band 9, HCN J=8–7 (ν_ rest = 708.877 GHz), 
HCO^+ J=8–7 (ν_ rest = 713.341 GHz), and 
HNC J=8–7 (ν_ rest = 725.107 GHz) lines were observed.
The vibrationally-excited 
HCN v_2=1f J=8–7 (ν_ rest = 712.372 GHz) and 
HNC v_2=1f J=8–7 (ν_ rest = 730.131 GHz) lines were also
covered, but HCO^+ v_2=1f J=8–7 (ν_ rest = 716.354
GHz) line was not.
Our scientific aim was to measure the strengths of the vibrational
ground (v=0) J=8–7 emission lines of HCN, HCO^+, HNC;
vibrationally excited (v_2=1f) emission lines were our second
objective. 

In bands 7 and 9, vibrationally excited (v_2=1, l=1e; hereafter 
v_2=1e) J=4–3 and J=8–7 lines, respectively, were covered for
HCN, HCO^+, and HNC. 
However, these frequencies are so close to the bright vibrational ground
(v=0) emission lines for HCN, HCO^+, and HNC that we could not
extract the faint v_2=1e emission line components in a reliable
manner. 
These v_2=1e emission line fluxes will not be discussed in this
paper. 

For band 3, HCN J=1–0 (ν_ rest = 88.632 GHz), 
HCO^+  J=1–0 (ν_ rest = 89.189 GHz), and 
HNC J=1–0 (ν_ rest = 90.664 GHz) line data were obtained.

For band 6, we targeted H^13CN (ν_ rest = 259.012 GHz), 
H^13CO^+ (ν_ rest = 260.255 GHz), and HN^13C J=3–2
(ν_ rest = 261.263 GHz), because these isotopologue emission
lines are thought to be optically thin and thus can be used to estimate
possible flux attenuation by line opacity (not dust extinction) for the
previously-obtained HCN, HCO^+, and HNC J=3–2 emission lines 
<cit.>. 
The bright CS J=5–4 line (ν_ rest = 244.936 GHz) was included
in this band 6 observation.

We performed data analysis in the same way as for our
previously obtained ALMA data of IRAS 20551-4250
<cit.>. 
We retrieved data calibrated by ALMA and used CASA
(https://casa.nrao.edu) for further data reduction. 
For the spectral window that includes the very bright CO J=3–2
emission line, we employed self-calibration, using the CO J=3–2 emission
line itself for phase calibration. 
Except for this spectral window, we adopted results produced with a
standard phase calibration using phase calibrators, which were provided
by ALMA.   
We first checked the visibility plots to view the signatures of bright
emission lines.  
To estimate the continuum flux levels, we removed channels that 
contained discernible emission lines.
We then subtracted the derived continuum levels, to extract only molecular
line data.
The task “clean” was then applied for the molecular line data, by
binning spectral channels to make the velocity resolution 
20–40 km s^-1.  
Pixel scale was set as 01 pixel^-1 for band 3 and 7 data,
but was 003 pixel^-1 for band 9 and 6 data, because their
beam sizes were much smaller than those of bands 3 and 7.
The “clean” task was also applied for continuum data. 
We then obtained spectra at the nuclear position defined from the
continuum peaks in individual observations. 
When the flux density levels in the spectra were significantly below
zero at the frequency where no emission and/or absorption lines were
expected to be present, continuum was
over-subtracted, possibly due to the inclusion of weak emission lines for
continuum determination. 
In such cases, we redefined line-free channels and created clean maps
of molecular emission lines and continuum.
After confirming that the extracted spectra at line-free channels at
the continuum peak position show flux density fluctuating around zero
level with noise, we adopted these re-analyzed results as final
products. 



§ RESULT


Continuum-J43a (taken with HCO^+ J=4–3), continuum-J43b 
(taken with HNC J=4–3), continuum-J87 (taken with HCN, HCO^+, HNC
J=8–7),  
continuum-J10 (taken with HCN, HCO^+, HNC J=1–0), and 
continuum-J32 (taken with H^13CN, H^13CO^+, HN^13C J=3–2)
maps are displayed in Figure 1.
In all maps, continuum emission is dominated by a spatially compact
component at the nucleus of IRAS 20551-4250.
Table 3 lists continuum fluxes at the peak position.
We had two continuum measurements in band 7 with
slightly different central frequencies (ν_ cent = 336.7 GHz
and 343.2 GHz; Table 3).
Both of these provided comparable flux levels with 10.5 and 10.3 (mJy
beam^-1) (Table 3). 
Band 7 continuum measurements of IRAS 20551-4250 were made in
ALMA Cycle 0, and the estimated fluxes were 10.1 (mJy beam^-1) 
(ν_ cent = 341.6 GHz) and 9.4 (mJy beam^-1)
(ν_ cent = 346.7 GHz) <cit.>.
These band 7 continuum measurements at similar central frequencies, taken
in ALMA Cycles 0 and 2, agree within ∼10%, supporting the quoted
<10% absolute flux calibration uncertainty in individual ALMA
observations (ALMA Proposer's Guide for Cycles 0 and 2). 

Spectra in bands 7, 9, 3, and 6 at the continuum peak positions within
the beam size of individual data are presented in Figure 2.
The targeted bright emission lines, such as CO J=3–2 line, J=8–7,
J=4–3, and J=1–0 lines of HCN, HCO^+, HNC, and J=3–2 lines of
H^13CN, H^13CO^+, and HN^13C were clearly detected.
Additionally, signatures of several fainter emission lines,
including v_2=1f J=4–3 emission lines of HCN, HCO^+, HNC and
other serendipitously detected emission lines, were observed.
Because gas-rich (U)LIRGs exhibit many faint
emission lines from molecules and the bulk of the observed frequency
range could be occupied by such lines, particularly in band 7
<cit.>, identifying the detected faint emission lines is
not an easy task. 
Our proposed identifications of faint emission lines are indicated with
arrows in Figure 2. 
In Figure 2(m), the isotopologue HC^15N J=3–2 line 
(ν_ rest = 258.157 GHz) is covered and is expected to be
redshifted to the observed frequency of ν_ obs ∼ 247.5
GHz, just lower than the frequency of the SO emission.
However, its signature is not as clear as that of the other isotopologue
line, H^13CN J=3–2.
This is reasonable because, in (U)LIRGs, the
^14N-to-^15N  abundance ratio (∼440) <cit.> is much
higher than the ^12C-to-^13C abundance ratio (50–100)
<cit.>, so that the HC^15N J=3–2
emission line is expected to be weaker than H^13CN J=3–2 by a large
factor. 

For molecular emission lines that are recognizable in the spectra, we 
created integrated intensity (moment 0) maps, by summing spectral
elements displaying discernible signals. 
These maps are shown in Figure 3 for the primarily targeted main emission
lines, and in Appendix A (Figure 17) for serendipitously detected
emission lines. 
All detected molecular lines showed peak positions that agree
with those of the simultaneously taken continuum emission  
within 1 pixel (01 for bands 7 and 3, or 003 for bands 9
and 6) in both RA and DEC directions.
These agreements suggest that the serendipitously detected faint
emission lines are likely to be real features, rather than artifacts,
with the exception of HCO^+ v_2=1f J=4–3 (band 7), HCN
v_2=1f J=8–7 (band 9), and HNC v_2=1f J=8–7 (band 9), which
will be discussed later.  

Figure 4 shows magnified spectra in the vicinity of the primarily targeted
individual molecular emission lines at the continuum peak position
within the beam size, together with the best Gaussian fits. 
The same figures for selected serendipitously detected emission lines
are shown in Appendix A (Figure 18).
Peak flux values in the moment 0 maps and emission line fluxes estimated
from the best Gaussian fits are summarized in Table 4.
Table 5 shows the deconvolved, intrinsic emission sizes of the main
bright molecular lines and continuum, estimated using
the CASA task “imfit”.

HCO^+ J=4–3 and HNC J=4–3 (v=0) fluxes were obtained in both our
ALMA Cycle 0 and 2 observations. 
Our ALMA Cycle 0 data provided HCO^+ J=4–3 and HNC J=4–3 (v=0) 
fluxes of 14±1 and 5.8±0.2 (Jy km s^-1), respectively,
based on Gaussian fit, within 0.6” × 0.4” beam size 
<cit.>.
The estimated fluxes based on Gaussian fit in our ALMA Cycle 2 data were
17±1 and 6.6±0.2 (Jy km s^-1) for HCO^+ J=4–3 (0.9”
× 0.7” beam) and HNC J=4–3 (0.8” × 0.6” beam),
respectively. 
The fluxes in ALMA Cycle 2 data were 10–20% higher than in our ALMA
Cycle 0 data.
This could be partly due to larger beam sizes in the ALMA Cycle 2 data, 
if a significant fraction of these emission lines came from a 
spatially extended region with >05 (>400 pc).
However, the nuclear HCO^+ J=4–3 and HNC J=4–3 emission components
were estimated to be spatially compact (Table 5).
The 10–20% flux discrepancy could be largely accounted for by the
possible absolute flux calibration uncertainty in individual ALMA Cycle
0 and 2 data (maximum ∼10% for each).  

The HCN J=4–3 (v=0) line was not covered in our ALMA Cycle 2 observations.
In ALMA Cycle 0, the HCN J=4–3 and HCO^+ J=4–3 lines were
simultaneously observed.
For the HCO^+ J=4–3 (v=0) line, our Cycle 2 band 7 data
(17±1 Jy km s^-1) provided ∼22% higher absolute
flux than Cycle 0 (14±1 Jy km s^-1).
We thus multiplied the HCN J=4–3 (v=0) flux derived in our Cycle 0
observations (9.5±0.2 Jy km s^-1) <cit.> by
a factor of 1.22, and adopted the re-calibrated HCN J=4–3 flux with
11.6±0.2 (Jy km s^-1) for all subsequent discussion in 
this paper.  

The HCN v_2=1f J=4–3 emission line was also observed in both ALMA Cycles 
0 and 2. 
Its detection significance in the moment 0 map (Figure 3) of our Cycle 2
data was >9σ, which is improved from the ∼5σ
detection in our Cycle 0 moment 0 map <cit.>, and further
confirms the presence of the detectable HCN v_2=1f J=4–3 emission line
in IRAS 20551-4250.  
The estimated HCN v_2=1f J=4–3 emission line flux, based on Gaussian
fit, in the Cycle 0 data was 0.39±0.07 (Jy km s^-1), which is
converted to 0.47±0.08 (Jy km s^-1), after the factor of 1.22
multiplication, because HCN v_2=1f J=4–3 and HCO^+ J=4–3 (v=0) 
line data were taken simultaneously in our ALMA observations. 
That in the Cycle 2 data is 0.60±0.13 (Jy km s^-1).
The flux measurements for the Cycle 0 and 2 data are consistent. 
Given deeper Cycle 2 data than Cycle 0 data, we adopted the 
HCN v_2=1f J=4–3 flux estimated with Gaussian fit in the Cycle 2
data (0.60±0.13 Jy km s^-1). 

The HNC v_2=1f J=4–3 emission line for IRAS 20551-4250 was first
covered in our ALMA Cycle 2 observations, and its signature is shown in
the band 7 spectrum in Figures 2f and 4. 
Based on the moment 0 map (Figure 3) and Gaussian fit (Table 4), we
regard that the HNC v_2=1f J=4–3 emission line was detected.
However, the line width of the HNC v_2=1f J=4–3 emission line (FWHM
∼ 440 km s^-1) is substantially larger than other bright
molecular emission lines with FWHM ∼ 200 km s^-1 (Table
4). Contamination from other faint molecular emission lines is
possible. Thus, the measured HNC v_2=1f J=4–3 
emission line flux should be taken as an upper limit.
If we assume the intrinsic line width of the HNC v_2=1f J=3–2
emission line to be FWHM ∼ 200 km s^-1, then the actual HNC
v_2=1f J=3–2 emission line flux will be about half of that shown in
Table 4. 

For the HCO^+ v_2=1f J=4–3 emission line, we barely see the
3.2σ peak at the nuclear position in the moment 0 map (Figure 3).
However, the contour size at the peak was significantly smaller than the
synthesized beam size and emission with similar 3σ level contours 
was seen at some other off-nuclear regions (Figure 3), making 
the existence of this 3.2σ peak uncertain. 
In Figure 2d, an emission-like feature may be present close to the
expected frequency of the HCO^+ v_2=1f J=4–3 line; however, 
its observed peak seems to be slightly offset from the expected frequency at 
z= 0.043 (shown as a downward arrow). 
Based on Gaussian fit, the peak velocity of this emission-like feature
(v_ opt =  12947±34 km s^-1) was significantly higher
than other bright molecular emission lines detected in band 7 
(v_ opt ∼ 12900 km s^-1), and 
the detection significance was <2σ (Table 4).
Detection of the HCO^+ v_2=1f J=4–3 emission line has never
been reported in any external galaxy. 
We require higher S/N data to improve the constraining of the strength of this
yet-to-be-detected HCO^+ v_2=1f J=4–3 emission line.

The HCN v_2=1f J=8–7 (ν_ rest = 712.372 GHz) and HNC
v_2=1f J=8–7 (ν_ rest = 730.131 GHz) lines were
covered in our ALMA band 9 spectrum, while HCO^+ v_2=1f J=8–7 
(ν_ rest = 716.354 GHz) line was not.
In Figure 2(h) and (i), subtle signatures of emission lines are observed
close to the expected frequencies of redshifted HCN v_2=1f J=8–7
and HNC v_2=1f J=8–7 lines, respectively. 
However, their detection significance, based on Gaussian fit, is
<3σ.
In the moment 0 map of HCN v_2=1f J=8–7, we see a 3.1σ
emission peak at the nuclear position, but the 3σ contour was much
smaller than the synthesized beam size (Figure 3). 
Detection of v_2=1f J=8–7 lines of HCN and HNC was unclear, and we
will need data with higher S/N ratios to discuss their fluxes quantitatively. 

The H^13CN J=3–2 emission lines were observed in ALMA Cycle 2 (36
min integration) and Cycle 4 (129 min integration).
The flux measurements based on Gaussian fit were 0.37±0.05 
(Jy km s^-1) with 053 ×047
<cit.> and 0.26±0.03 (Jy km s^-1) with
016 × 015 in Cycles 2 and 4, respectively.
The smaller flux measurement in Cycle 4 could be largely explained 
by the smaller beam size and maximum 10% absolute flux calibration
uncertainty in individual ALMA observations. 
We adopted our Cycle 4 measurement for the following two reasons:
(1) The primary aim of our isotopologue observations is to estimate the
flux attenuation by line opacity for HCN, HCO^+, HNC J=3–2 emission.
(2) Our Cycle 4 data contain H^13CN, H^13CO^+, HN^13C
J=3–2 emission line flux measurements with similar beam sizes.
Adopting our Cycle 4 measurement of the H^13CN J=3–2 flux is a more
straightforward way to compare and correct flux attenuation for the HCN,
HCO^+, HNC J=3–2 emission lines.

Figure 5 presents intensity-weighted mean velocity (moment 1)
and intensity-weighted velocity dispersion (moment 2) maps of
selected bright emission lines in band 7, CO J=3–2, HCO^+ J=4–3,
and HNC J=4–3.
The CO J=3–2 emission line was detected not only in the nuclear region,
but also in spatially extended outer regions.
In addition to the much higher flux of CO J=3–2 than other molecular
lines, its lower critical density is likely to contribute 
to the detection of the spatially extended structure because outer
low-density molecular gas can collisionally excite CO J=3–2 more than
HCO^+ J=4–3 and HNC J=4–3.  
Figure 6 shows moment 1 and 2 maps of HCN, HCO^+, HNC J=8–7
emission lines in band 9 for the central zoomed regions.
Velocity information is available only for the nuclear compact regions.
The moment 1 and 2 maps for HCN, HCO^+, HNC J=1–0 emission lines in 
band 3 are presented in Figure 7, where we can obtain velocity
information for spatially extended regions outside the synthesized beam
sizes at least for HCN and HCO^+. 
In Figure 8, the moment 1 and 2 maps of the CS J=5–4 emission line in band
6, the additional dense molecular gas tracer <cit.>, are presented.
Overall, most of the bright emission lines of dense molecular gas
tracers display similar rotational patterns, showing that the
north-eastern region of the nucleus is more redshifted than the
south-western region. 

Table 6 provides the luminosities of the primarily targeted molecular
emission lines. 
In addition to the HCN, HCO^+, HNC emission lines at various
rotational J-transitions at v=0 and v_2=1f, the isotopologue
H^13CN, H^13CO^+, HN^13C J=3–2, CO J=3–2, and CS
J=5–4 emission lines at v=0 are tabulated. 



§ DISCUSSION




 §.§ Molecular gas morphology and dynamics


Continuum and molecular line emission are dominated by a nuclear compact
component; however, in the brightest CO J=3–2 integrated-intensity (moment
0) map in Figure 3, a spatially extended structure is seen in the
south-eastern direction from the nucleus. 
A similar extended structure is seen in the stellar emission probed in
the near-infrared K-band (2.2 μm) image <cit.>, suggesting
that this extended CO J=3–2 emission originates in the host galaxy. 

In the intensity-weighted mean velocity (moment 1) maps of CO
J=3–2, J=1–0, 3–2, 4–3, 8–7 of HCN, HCO^+, HNC, and CS J=5–4
in Figures 5–8 and <cit.>, as well as CO J=1–0 in
<cit.>, the overall dynamics is dominated by rotational motion in
such a way that the north-eastern part is redshifted and the
south-western part is blueshifted, relative to the nucleus.
However, in the moment 1 map of the brightest CO J=3–2 emission line, a
dynamically decoupled component from the overall rotation is seen at the
south-westernmost region (the clump at the lower-right edge in Figure 5).
A plausible explanation is that some type of merger event happened
previously, which is quite reasonable given that IRAS 20551-4250 is a
ULIRG, and ULIRGs are usually driven by gas-rich galaxy mergers
<cit.>.  

In Figure 4, although we fit emission lines with single Gaussian
component, when we examine the line profiles of the very bright CO J=3–2
and HCO^+ J=4–3 emission lines in more detail, skew patterns are
recognizable. 
To investigate the skewed asymmetric line profiles in more detail,
we fit these bright emission lines with a Gaussian
component, only using data points at the red part of the emission peak
(Figures 9a and 9b) and at the blue part of the emission peak (Figure
9c and 9d). 
When we fit the red component, the data in the blue part indicates an 
excess, compared to the best Gaussian fit.
Conversely, when we fit with a Gaussian, using data at the blue
part of the emission peak only, the extrapolation of the best fit
Gaussian to the redder part is higher than the actual data, particularly
for CO J=3–2.
The full-width at half maximum (FWHM) values of the best fit Gaussian 
are 260 km s^-1 and 165 km s^-1 for the blue and red components 
of the CO J=3–2 emission line, respectively. 
These are 205 km s^-1 and 160 km s^-1 for the blue and red
components of the HCO^+ J=4–3 emission line, respectively. 
We thus quantitatively confirm that the line widths are larger for 
the blue components than the red components both for CO J=3–2 and
HCO^+ J=4–3.
Figure 10 displays the contours of the blue and red components
of the CO J=3–2 and HCO^+ J=4–3 emission lines. 
The red component is slightly offset to the north-eastern direction from
the blue component; this could be explained by the overall rotational
motion of IRAS 20551-4250.   
A natural interpretation for this skewed profile is that turbulence is
stronger at the blueshifted molecular gas-emitting region, which
broadens the line width at the blue side.
In the CO J=3–2 moment 1 map in Figure 5, the signature of a
merger-induced distinct emission component is seen at the blueshifted
south-western part of the nucleus.
This possible merger-induced turbulence component may contribute to the
observed broader emission line profile for the blue component.  

In Figure 11(a), we show a zoom-in of the bottom part of the very bright
CO J=3–2 emission line, with the best Gaussian fit of this line (Figure
4 and Table 4) overplotted.
There is a clear excess at both the blue
and red sides of the CO J=3–2 emission line, although at the red side, 
possible contamination from the H^13CN J=4–3 (ν_ rest =
345.340 GHz) emission line makes quantitative discussion of the broad CO
J=3–2 emission component difficult.
This kind of profile is typically interpreted to be due to the broad emission
component by outflow activity <cit.>. 
Figure 11(b) displays the contours of the emission at the blue and red
parts of the broad emission component, defined in Figure 11(a).
The peak position of the red broad component is slightly shifted to the
south-eastern part compared to that of the blue broad component (1 pix
left and 1 pix lower with the pixel scale of 01 pix^-1).  
Considering the peak positional accuracy of the blue and red broad
components with (beam-size)/(signal-to-noise ratio), the significance of 
this positional displacement is marginal. 
However, this pattern is different from the global rotation of IRAS
20551-4250. 
We may be witnessing CO J=3–2 outflow toward (away from) us being
ejected in the north-western (south-eastern) direction from the nucleus.

In Figure 11(a), we added a Gaussian with FWHM = 540 km s^-1 and
velocity peak at 12,886 km s^-1 for the broad outflow component, and
another Gaussian with FWHM = 190 km s^-1 to incorporate the
H^13CN J=4–3 emission line at the red part of the bright CO
J=3–2 emission line. 
The Gaussian fit fluxes of the broad CO J=3–2 emission line
component and the H^13CN J=4–3 emission line at the tail of the
very bright CO J=3–2 emission line are estimated to be 
∼7.7 (Jy km s^-1) and ∼0.9 (Jy km s^-1), 
respectively.  

We here estimate a molecular outflow rate from our CO J=3–2 emission
line data. 
The peak flux value of the blue broad emission component in Figure 11(b)
is ∼0.4 (Jy km s^-1). 
We adopt the value of the blue broad component, because the red broad
component is likely to be contaminated by the H^13CN J=4–3
emission line. 
Assuming that the outflow-origin red broad component is comparable to
the blue broad component, we obtain ∼0.8 (Jy km s^-1) for
outflow-origin CO J=3–2 emission. 
This is a factor of ∼10 smaller than the Gaussian fit flux of the
broad CO J=3–2 emission line component, but we adopt the value of
∼0.8 (Jy km s^-1) to obtain the conservative estimate of a
molecular outflow rate.  
We obtain the CO J=3–2 luminosity with L'_ CO J=3-2 ∼ 7.3
× 10^6 (K km s^-1 pc^2) <cit.>.
Assuming that CO J=3–2 emission is optically thick and thermalized, and
adopting the ULIRG-like CO luminosity to molecular mass (M_ H2)
conversion factor with ∼0.8 M_⊙ (K km s^-1
pc^2)^-1 <cit.>, we obtain a molecular outflow mass of 
M_ outf ∼ 5.8 × 10^6 M_⊙.   
In Figure 11(b), the peak position difference between the blue broad and
red broad emission component is ∼0.14” or ∼120 (pc).
Adopting the outflow peak position offset with R ∼ 60 (pc) from the 
nucleus and outflow velocity with V = 500 km s^-1 (in Figure 
11(a), the broad wing component extends to approximately ±500 km
s^-1 with respect to the systemic velocity of v_ opt = 12900
km s^-1), we obtain a molecular outflow rate with 
Ṁ_ outf ∼ 150 (M_⊙ yr^-1), where we adopt
the relation of Ṁ_ outf = 3 × M_ outf ×
V/R <cit.>. 
Assuming ∼30% AGN contribution to the infrared luminosity of 
IRAS 20551-4250 (i.e., L_ AGN ∼ 1.1 × 10^45 
erg s^-1), the derived molecular outflow rate with Ṁ_ outf
∼ 150 (M_⊙ yr^-1) agrees within a factor of ∼2
with the relation seen in other ULIRGs <cit.>.
The molecular outflow kinetic power is estimated to be P_ outf
≡ 0.5 × Ṁ_ outf × V^2 ∼ 1.2
× 10^43 (erg s^-1), which is ∼1% of the AGN luminosity.
The molecular outflow momentum rate is Ṗ_ outf 
≡ Ṁ_ outf × V ∼ 4.6 × 10^30 
(kg m s^-2), which is ∼12 × L_ AGN/c. 
These values are comparable to those observed in other ULIRGs with
detectable molecular outflow activity <cit.>. 
Note that all of molecular outflow mass (M_ outf), molecular
outflow rate (Ṁ_ outf), molecular outflow kinetic power 
(P_ outf), and molecular outflow momentum rate (Ṗ_ outf)
could increase by an order of magnitude, if we use the Gaussian fit flux
of the broad CO J=3–2 emission line component.    



 §.§ Isotopologue molecular lines and opacity estimate


From Table 4 and <cit.>, we obtained the ratios of
HCN-to-H^13CN J=3–2 flux in (Jy km s^-1) to be ∼22±3, 
HCO^+-to-H^13CO^+ J=3–2 flux in (Jy km s^-1) to be
∼60±9, and HNC-to-HN^13C J=3–2 flux in (Jy km s^-1) to
be ∼45±15.
We must note that the detection significance of HN^13C
J=3–2 is only ∼3σ in both Gaussian fit in the spectrum and
moment 0 map. 
Thus, discussion of HNC could be more uncertain than HCN and HCO^+. 
Adopting the ^12C-to-^13C abundance ratios in ULIRGs with 50–100
<cit.>, we find that 
the flux attenuation by line opacity for HCN J=3–2 is estimated to be a
factor of 2–5, while those of HCO^+ J=3–2 and HNC J=3–2 are 
a factor of ∼1–1.5 and ∼1–2, respectively, where we assume that 
isotopologue emission lines are optically thin <cit.>.

In a geometry where radiation sources and molecular gas are spatially
well mixed, the flux attenuation and optical depth (τ) are related
as τ/1 - exp(-τ). 
From this relationship, we obtain τ = 2–5 for HCN J=3–2. 
Using the estimated H^13CN J=4–3 flux with ∼0.9 (Jy km
s^-1) (4.1), we obtain the ratio of HCN-to-H^13CN J=4–3
flux in (Jy km s^-1) to be ∼13.
The flux attenuation by line opacity for HCN J=4–3 is estimated to be
4–7 or τ=4–7, which is comparable to that for HCN J=3–2
(τ=2–5). 
In summary, our isotopologue observations suggest that the HCN J=3–2 and
J=4–3 emission lines are considerably flux-attenuated by line opacity.

In contrast, the relatively small flux attenuation with <2
suggests that the line opacity for HCO^+ J=3–2 and HNC J=3–2
is τ < 1.5.
Based on the observed HCN, HCO^+, HNC J=3–2 fluxes at
v_2=1f and v=0, and calculation of vibrational excitation by 
infrared radiative pumping, using the available 5–30 μm spectrum of
IRAS 20551-4250, <cit.> argued that HCN abundance is
higher than those of HCO^+ and HNC. 
This higher HCN abundance scenario is a plausible explanation 
for the higher HCN line opacity than HCO^+ and HNC at J=3–2.



 §.§ Infrared radiative pumping and independent molecular 
abundance estimate
 

Based on the fluxes of vibrationally excited (v_2=1f) and
vibrational ground (v=0) HCN, HCO^+, HNC emission lines at J=3–2,
it has been estimated that the infrared radiative pumping mechanism
plays a role in rotational excitation at v=0 in IRAS 20551-4250 at
least for HCN and HNC <cit.>. 
Namely, once HCN and HNC are vibrationally excited to v_2=1 by
absorbing infrared ∼14 μm and ∼22 μm photons,
respectively, they are decayed back to v=0 and their rotational
J-transition fluxes at v=0 can be higher than those for collisional
excitation alone <cit.>. 
We here attempt to confirm this result, based on our newly collected ALMA
data.
The J=1–0 line is not present at the vibrationally excited level
(v_2=1).  
For J=8–7, v_2=1f emission lines are not clearly detected, mainly due to
large background noise at this high ALMA frequency range. 
We thus focus on J=4–3 data, and follow the same logical steps as those
made by <cit.> for J=3–2 data. 

Infrared radiative pumping is estimated to play a significant role
if the following condition is met:  

    T_ex-vib > T_0/lnA_v2=1-0,vib/A_J=4-3,rot.
 
where T_ex-vib is the v_2=1f vibrational excitation temperature,
T_0 is the energy level at v_2=1f J=4, A_v2=1-0,vib is the
Einstein A coefficient from v_2=1f to v=0, and A_J=4-3,rot is
the Einstein A coefficient from J=4 to J=3 at v=0 <cit.>. 

Adopting the values in Table 7, and A_v2=1-0,vib = ∼1.7 s^-1,  
∼3.0 s^-1, and ∼5.2 s^-1 for HCN, HCO^+, and HNC,
respectively <cit.>, we obtain ∼160 (K),
∼185 (K), and ∼210 (K) in the right-hand column of
Eqn. (1) for HCN, HCO^+, and HNC, respectively. 
The observed T_ ex-vib values in the left-hand column of
Eqn. (1), derived based on e.g., Eqn. (2) of <cit.>, 
are ∼360 (K), <280 (K), and ∼360 (K) for HCN, HCO^+, and HNC,
respectively (Table 8).
For HCN and HNC, the condition is fulfilled. 
If the HNC v_2=1f J=4–3 flux is approximately half that shown in Table 4
(3), the left-hand column of Eqn. (1) for HNC is ∼260 (K),
which is still higher than the right-hand column.
For HCO^+, the upper limit of T_ ex-vib still allows the
condition to be met.

The left-hand column of Eqn. (1) will decrease if flux attenuation by
line opacity is significant for some v=0 lines and the intrinsic
line opacity-corrected flux at v=0 and v_2=1f is used for the
calculation.   
From our isotopologue observations, we see that HCN J=4–3 flux is
estimated to be attenuated by line opacity with a factor of 4–7.
Adopting a factor of 5 flux attenuation for HCN J=4–3, the T_ ex
value of HCN decreases only to ∼230 (K). 
Eqn. (1) is still fulfilled for HCN, not changing the above conclusion.
For HCO^+ and HNC, flux attenuation by line opacity is not
significant at J=3–2 <cit.>.
Assuming that this is also the case for J=4–3, the condition in
Eqn. (1) is still valid for HNC J=4–3.
Thus, it is confirmed from our new ALMA J=4–3 data that the role of 
infrared radiative pumping is significant in IRAS 20551-4250 at least
for HCN and HNC. 

As discussed in <cit.>, if the column density at v=0 is the
same for HCN, HCO^+, and HNC, and if all molecular lines are emitted
from the same regions, the ratio of the infrared radiative pumping rate
among HCN, HCO^+, and HNC in IRAS 20551-4250 is calculated to be  

    HCN:HCO^+:HNC (P_IR)     =     1:0.9:27,

and the v_2=1 to v=0 column density ratio among HCN, HCO^+,
and HNC is calculated to be  

    HCN:HCO^+:HNC (N_v_2=1/N_v=0)     =     1:0.5:9, 
    
    based on the Einstein A coefficients of
    HCN, HCO^+, HNC in Table 7 and the infrared 5–35 μm spectrum of
    IRAS 20551-4250 obtained with Spitzer IRS <cit.>.
    In essence, the number of infrared photons at ∼22 μm 
    (corresponding to the vibrational-rotational transitions for HNC) is
    higher than at 12–14 μm (corresponding to the
    vibrational-rotational transitions of HCN and HCO^+), such that it is
    naively expected that HNC is more vibrationally excited by infrared
    radiative pumping than HCN and HCO^+.
    
    The ratio of the column density at the 
    v_2=1f J=4 level (N_v_2=1f, J=4) among HCN, HCO^+, and HNC
    is derived with ∝flux/A_ul, where the line flux
    from the upper (u) to lower (l) transition level is in units of 
    (Jy km s^-1) and  A_ul is the Einstein A coefficient for
    spontaneous emission from the upper (u) to lower (l) level
    <cit.>. 
    From observational fluxes in Table 4 and Einstein A coefficients in
    Table 7, we obtain the column density ratio at J=4 at v_2=1 
    
        HCN:HCO^+:HNC (N_v_2=1f, J=4)     =     1:<0.2:0.7,
    
    where we adopt that the actual flux of HNC v_2=1f J=3–2 emission
    line is half of the Gaussian fitted result from Table 4 (see 3).
    
    Assuming that the fraction of J=4 level, relative to all J-levels at
    v=0, does not differ significantly among HCN, HCO^+, and HNC 
    
    [The J=4–3 to J=3–2 flux ratios for HCN, HCO^+, and HNC 
    are all comparable to each other <cit.>.
    Given that the molecular population is typically dominated by low J levels at
    J < 5, this assumption is reasonable for IRAS 20551-4250. 
    ],
    
    and that v_2=1f J-transition emission is optically thin
    <cit.>, Equations (3) (prediction) and (4) (observation) can be
    reconciled if the column density at v=0 (N_v=0) (and thereby
    abundance) for HCN is higher than HCO^+ and HNC by factors of
    >2.5 and ∼10, respectively.  
    Thus, we obtain an abundance ratio of 
    
        HCN:HCO^+:HNC (abundance)     =     1:<0.4:0.1.
    
    The HCN-to-HCO^+ abundance ratio with >2.5 and 
    HCN-to-HNC abundance ratio with ∼10 are comparable to those derived
    from J=3–2 data <cit.>. 
    The HCN-to-HNC abundance ratios derived in this manner at J=4–3 and J=3–2
    (∼10) appear to be larger than that from isotopologue observations 
    (∼2).
    This discrepancy could be partly explained by the possibly large
    ambiguity of the HN^13C J=3–2 flux, due to its marginal
    (∼3σ) detection (4.2).
    Although a quantitatively accurate estimate of the actual HCN-to-HNC
    abundance ratio is subject to further investigation, two independent
    methods consistently suggest that HCN abundance is higher than 
    HCO^+ and HNC, by at least a few times.
    
    
    
     §.§ Molecular gas properties
    
    
    To obtain a better understanding of the physical properties of these
    line-emitting molecular gas, we use the RADEX software <cit.>,
    which treats the non-LTE analysis and predicts molecular line flux
    ratios at v=0, by solving the excitation of rotational transitions at
    v=0 by collision, based on the large velocity gradient (LVG) approximation.
    Free parameters are the number density of hydrogen molecule
    (n_ H2), kinetic temperature of H_2 (T_ kin), column
    density of a particular molecule divided by its line width 
    (N_ mol/Δv), and background radiation temperature 
    (T_ bak), which is set as ∼3 K.  
    
    Infrared radiative pumping to v_2=1 should play a
    role for molecular rotational excitation at v=0, in addition to
    collision, in IRAS 20551-4250 (4.3). 
    However, with the limited amount of available molecular rotational
    J-transition line data in our study, separating the contributions from
    collisional excitation and infrared radiative pumping with sufficient
    reliability is not easy. 
    Even for collisional excitation alone, it is sometimes argued that 
    (1) HCN and HCO^+ probe substantially different phases of molecular
    gas, and 
    (2) there exist multiple temperature components for
    HCN-, HCO^+-, HNC-emitting molecular gas in LIRGs <cit.>. 
    These collisional excitation models with increased numbers of parameters
    and infrared radiative pumping effects are virtually
    indistinguishable.  
    <cit.> estimated that, in LIRGs, the infrared radiative pumping
    has a measurable, but relatively small (20–30%), effect of enhancing the
    HCN J=1–0 flux, when compared to collisional excitation alone, 
    although the effect for higher-J was not estimated and could be higher.  
    This 20–30% level of flux alternation is comparable to the uncertainty
    of different J-transition line flux ratios, coming from ALMA's absolute 
    flux calibration uncertainty in individual observations in each
    band (maximum ∼10%). 
    Thus, we first derive rough values of the molecular gas parameters based
    on collisional excitation, and will later investigate how they change by
    including the infrared radiative pumping.
    
    We vary the H_2 number density (n_ H2) between 10^3
    and 10^8 cm^-3, because HCN, HCO^+, and HNC are well
    known to be dense (>10^3 cm^-3) molecular gas tracers, due to
    their high dipole moments and resulting high critical densities. 
    The kinetic temperature range (T_ kin) is set from 10 K to 500 K,
    where the lowest kinetic temperature of 10 K corresponds to cool
    molecular gas far from energy sources, whereas the highest kinetic
    temperature of 500 K reflects compact (<10 pc), warm molecular gas in
    the close vicinity of the putative AGN. 
    Since the molecular line widths of HCN, HCO^+, and HNC at J=1–0,
    3–2, 4–3, and 8–7 are ∼300 km s^-1 at 10% of the peak
    intensity <cit.>, we adopt Δv = 300 km s^-1
    for the line width in our RADEX calculation. 
    We include T_ bak∼ 3 K cosmic microwave background radiation
    in the calculations. 
    The column density of individual molecular gas is not directly derived
    from observations. 
    The XMM-Newton 2–10 keV X-ray observation of IRAS 20551-4250 shows
    that the hydrogen column density toward the putative X-ray-emitting
    obscured AGN is estimated to be N_ H = 7.9^+6.9_-1.9× 10^23 cm^-2<cit.>. 
    Since the abundance ratios of HCN, HCO^+ and HNC, relative to H, 
    in warm molecular gas in LIRGs are estimated to be ∼10^-8<cit.>, we first set the column density (N_ mol) of
    HCN, HCO^+, and HNC to be 1 × 10^16 cm^-2. 
    
    We summarize our RADEX calculation results in Figure 12, where the
    ratios are derived from the comparison of observed fluxes in (Jy km
    s^-1) (Table 9).
    The parameter ranges that can reproduce the observed flux ratios
    of individual J-transitions are shown as thick lines.
    For n_ H2 = a few ×10^5 cm^-3, 
    T_ kin = 70–100 K, Δv = 300 km s^-1, and 
    HCN column density N_ HCN = 1 × 10^16 cm^-2, 
    which can reproduce the observed HCN J=3–2 to J=1–0 flux ratio in
    Figure 12, our RADEX calculations show that the HCN J=3–2 and J=4–3
    line optical depths are τ∼ 3, roughly comparable to
    the observationally derived values from isotopologue line data (4.2). 
    Thus, the choice of N_ HCN = 1 × 10^16 cm^-2 is
    regarded as appropriate. 
    
    Since HCO^+ and HNC abundance are estimated to be at least a few
    times lower than HCN in IRAS 20551-4250 (4.3), we show the same 
    RADEX calculation results in Appendix A (Figure 19) for the HCO^+
    and HNC column density of 3 × 10^15 cm^-2.
    The overall trends change little.  
    In interpreting these results, we must consider two possible
    caveats. 
    
    First, the line-emitting volume can differ between the high-J and
    low-J transition lines.
    AGNs are typically located at galactic center regions where typical
    molecular gas density is expected to be higher, due to nuclear molecular
    gas concentration, than that in outer off-nuclear regions.
    Additionally, in an AGN, the surrounding molecular gas and dust has a
    strong temperature gradient such that the temperature at the inner
    part is higher than that at the outer part.
    Consequently, dense and warm molecular gas is concentrated in the inner
    part of the nuclear region from where high-J transition lines can be
    efficiently emitted. 
    More diffuse, low-density cool gas is distributed in more spatially
    extended regions, which can strongly emit low-J transition lines, but 
    high-J transition line emission is relatively limited.
    Thus, the probed effective molecular gas volume is very likely to be
    smaller at higher-J than lower-J transition lines, whereas we assume that
    both lines come from the same volume in the RADEX calculations.
    If we focus on the volume of high-J line-emitting molecular gas and 
    compare flux ratios  within that volume, then the actual high-J to
    low-J line flux ratios will be higher than the observed ratios.
    Thus, the derived temperature and density from the observed flux ratios
    and RADEX calculations are taken as  lower limits for the actual
    values for the high-J line-emitting molecular gas.
    
    Second, since vibrational transition is not included in our RADEX
    calculations, infrared radiative pumping is not properly taken into
    account. 
    For IRAS 20551-4250, it is quantitatively demonstrated by
    <cit.> and this study (4.3) that infrared radiative
    pumping plays a role in rotational excitation at v=0, through the decay
    from v_2=1 to v=0, at least for HCN and HNC, and 
    could realize higher rotational excitation at v=0 than collisional
    excitation alone, for a given H_2 number density and kinetic
    temperature. 
    Owing to infrared radiative pumping, lower values of H_2 number
    density and kinetic temperature may suffice to reproduce the observed
    flux ratios.
    Thus, the H_2 number density and kinetic temperature should be taken
    as  upper limits. 
    This second ambiguity works in opposition to the first, 
    and it is not easy to disentangle the two in a quantitatively reliable
    manner.
    
    Regarding the first issue, the derived number density and kinetic
    temperature using low-J lines largely reflect a large volume of
    spatially extended low-density, low-temperature molecular gas,
    resulting in low values.    
    If we compare the flux ratios at high-J transitions only, a small volume 
    of dense and high-temperature molecular gas is preferentially probed,
    and the derived density and temperature can be high.
    In Figure 12, we find that the density and kinetic temperature that
    reproduce the observed flux ratios increase from “J=3–2 to J=1–0” 
    to “J=4–3 to J=3–2” or “J=8–7 to J=4–3” or “J=8–7 to J=3–2” 
    for HCN, HCO^+, HNC, namely, the thick curved line moves from the
    lower-left to upper-right regions.
    This is a natural consequence, that higher-J lines selectively
    probe dense and warm molecular gas with a small emitting volume. 
    
    In Figure 12, the J=3–2 to J=1–0 flux comparison is expected to
    reflect the largest molecular gas volume, including outer low-density and
    low-temperature gas.
    For the kinetic temperature of T_ kin> 25 K, H_2 number
    density of n_ H2 = 10^5–10^6 cm^-3 
    (10^4–10^5 cm^-3) seems required for HCN and HNC
    (HCO^+).
    The lower required density for HCO^+ is reasonable, given the
    lower critical density of HCO^+ than HCN and HNC, under similar
    line opacity <cit.>. 
    
    This possible difference of the probed molecular line-emitting volumes
    can be small, if we compare the flux ratios between adjacent
    J-transitions, such as J=4–3 and J=3–2.  
    The typical density and temperature of molecular gas that emits J=4–3
    and J=3–2 lines are >10^6 cm^-3 and >50 K for HCN,
    HCO^+, and HNC (Figure 12).
    We thus quantitatively confirm that these J=4–3 and J=3–2 emission
    lines selectively probe dense and warm molecular gas in the close
    vicinity of energy sources. 
    
    The derived density and kinetic temperature that reproduce the observed  
    “J=8–7 to J=3–2” and “J=8–7 to J=4–3” flux ratios are lower
    than those for “J=4–3 to J=3–2” flux ratios for HCN, HCO^+, and
    HNC. 
    This is opposite to the expected trend that the derived density becomes
    higher when we compare flux ratios at higher-J transition. 
    A plausible explanation for this is that the J=8–7 emitting volume is
    substantially smaller than those of J=4–3 and J=3–2. 
    This can result in much smaller “J=8–7 to J=3–2” and “J=8–7 to
    J=4–3” flux ratios than expected from the same emitting volume
    assumption, and thereby smaller derived density and kinetic temperature. 
    
    The dense molecular mass, derived from the observed HCN J=1–0
    luminosity (Table 6), is estimated to be ∼2 × 10^9 M_⊙,
    where we adopt the relationship between dense molecular mass and HCN J=1–0
    luminosity, M_ dense = 10 × HCN J=1–0 luminosity 
    [M_⊙ (K km s^-1 pc^2)^-1] <cit.>.
    Conversely, the hydrogen column density toward the X-ray emitting
    AGN in IRAS 20551-4250 is N_ H∼ 8 × 10^23
    cm^-2<cit.>. 
    We here assume that molecular gas distributes spherically and the AGN is
    located at the center.
    If all X-ray-obscuring material is in a dense molecular form that is
    probed with HCN J=1–0, we obtain the following two relations:  
    
        r (pc) × n (cm^-3) ∼ 8 × 10^23 (cm^-2), 
        
        4/3 ×π× r^3 (pc^3) × n (cm^-3) ×
        m_H2∼ 2 × 10^9 M_⊙,
    
    where r (pc) is the radius of the sphere, n (cm^-3) is volume
    averaged gas number density, and m_ H2 is the mass of molecular 
    hydrogen (=3.3 × 10^-24 g).
    From Equations (6) and (7), we obtain r ∼ 200 (pc) and n ∼
    10^3 (cm^-3). 
    However, if the kinetic temperature is >30 (K), 
    the typical number density of HCN J=1–0 emitting gas, derived from 
    the observed HCN J=3–2 to J=1–0 flux ratio and RADEX calculation, 
    is 10^5–10^6 cm^-3 (Figure 12).
    These results can be reconciled if nuclear molecular clouds in IRAS
    20551-4250 consist of dense (10^5–10^6 cm^-3) clumps
    with a small volume filling factor of 0.1–1%, as argued by
    <cit.>.
    The slightly low estimated density of 10^4–10^5 cm^-3
    from HCO^+ observations (Figure 12) could be reconciled if
    HCO^+ probes more extended lower-density envelopes of each clump
    <cit.>, because HCO^+ emission is observationally found to
    be more diffuse than HCN <cit.>.
    This kind of clumpy molecular structure can naturally explain similar
    profiles of various molecular emission lines with different line opacity 
    <cit.>, as observed in IRAS 20551-4250 <cit.>.  
    
    
    
     §.§ Molecular line flux ratio
    
    
    Figure 13 plots the observed HCN-to-HNC and HCN-to-HCO^+ flux ratios
    at J=1–0, J=3–2, J=4–3, and J=8–7.
    For J=3–2 and J=4–3, line-opacity corrected intrinsic flux ratios are
    also shown. 
    In the intrinsic flux ratios, IRAS 20551-4250 deviates even farther
    away from starburst-dominated regions, suggesting that the line opacity
    correction, particularly for high-HCN-abundance AGN-containing
    objects, makes our HCN-based molecular line flux ratio method even more
    powerful in distinguishing AGNs from starbursts.
    
    On the ordinate, the observed HCN-to-HCO^+ flux ratios are comparable 
    at J=1–0, J=3–2, and J=4–3, but are slightly lower than that at J=8–7.
    Since the critical density of HCN is higher than HCO^+ at individual
    J-transitions, the higher HCN-to-HCO^+ flux ratio at higher
    J-transition is difficult to explain with collisional excitation under
    the same line opacity.
    However, the estimated higher line opacity of HCN reduces its effective 
    critical density with 1/τ.
    Furthermore, due to higher HCN abundance than HCO^+,
    line-opacity-corrected intrinsic HCN-to-HCO^+ flux ratios will be
    higher than those observed. 
    The intrinsic HCN-to-HCO^+ flux ratios at J=3–2 and J=4–3 are 
    at least higher than the observed ratio at J=8–7.
    Since the line opacity at J=1–0 is estimated to be higher than J=8–7
    with RADEX under the parameter range of 
    n_ H2 = 10^5 cm^-3, 
    T_ kin = 50–100 K, 
    N_ HCN = 1 × 10^16 cm^-2, 
    and Δv = 300 km s^-1, the intrinsic HCN-to-HCO^+ flux
    ratio at J=1–0 will move to the upper side more than at J=8–7.
    Both of these factors could help to explain the result. 
    
    On the abscissa, the observed HCN-to-HNC flux ratio at J=1–0 is
    higher than those at J=3–2, J=4–3, and J=8–7. 
    Figure 14 is the plot of the “high-J to low-J” flux ratios for HCN,
    HCO^+, and HNC, where the combination of “J=3–2 to J=1–0”, 
    “J=4–3 to J=1–0”, “J=8–7 to J=1–0”, “J=4–3 to J=3–2”, 
    “J=8–7 to J=3–2”, and “J=8–7 to J=4–3” are selected. 
    The actual ratios are summarized in Table 9.
    We see a trend that the ratios are a factor of ∼2 higher for HNC
    than HCN and HCO^+ for the first three combinations (including 
    J=1–0 as the low-J transition), but comparable for the latter three 
    combinations (not including J=1–0).
    HCN and HNC have comparable critical densities at individual J-transition 
    under a similar line opacity <cit.>.
    The derived higher HCN opacity (4.2 and 4.3) will make the effective
    HCN critical density lower than HNC, in which case the 
    “high-J to low-J” flux ratios for HNC are expected to be lower than
    those for HCN, when collisional excitation is considered.
    This is opposite to the trends observed in Figure 14.
    
    The excitation temperatures of rotational J-transition at v=0 are
    summarized in Table 8, where the differences of beam sizes are not
    considered, to be consistent with our previous calculations
    <cit.>. 
    This assumes that the intrinsic emission size is the same among 
    HCN, HCO^+, HNC and is smaller than the beam sizes in all
    observations.     
    The rotational excitation temperatures within v=0 are slightly
    higher for HNC than for HCN (Table 8).
    
    We suggest that the following two mechanisms could help reduce the
    discrepancy between observations and predictions.
    First, we find from our RADEX calculations that at high density 
    (n_ H2> 3 × 10^5 cm^-3) and high temperature
    (T_ kin = 50–100 K),  
    a maser phenomenon occurs at J=1–0 first for HCN and HCO^+, and
    then later for HNC. 
    For example, for the column density of 1 × 10^16 cm^-2, 
    Δv = 300 km s^-1, and n_ H2 = 1–3 × 10^6
    cm^-3, the maser phenomenon is predicted to occur at T_ kin> 30 K for HCN J=1–0, but only at T_ kin> 70 K for HNC
    J=1–0.  
    Also with n_ H2 = 3 × 10^5 cm^-3, HCN J=1–0 shows
    the maser phenomenon at T_ kin = 50–100 K, but HNC J=1–0 does
    not. 
    The maser phenomenon could boost J=1–0 emission.
    If the maser occurs only for HCN J=1–0, but not for HNC J=1–0,
    under some parameter range, the “high-J to J=1–0” flux ratios for HCN
    could be smaller than HNC.   
    HCO^+ J=1–0 also starts to show the maser phenomenon earlier than
    HNC from lower density and temperature.
    The higher values of “high-J to J=1–0” flux ratios for HNC than
    HCO^+ could also be explained by the maser phenomenon in some
    parameter range. 
    
    Our second scenario is infrared radiative pumping.
    In IRAS 20551-4250, it is calculated that the infrared radiative
    pumping rate is higher for HNC than for HCN and HCO^+ 
    (4.3 and <cit.>).
    This could boost high-J HNC emission more than HCN and HCO^+,
    through decay back from v_2=1 to v=0.
    Given that this infrared radiative pumping is estimated to play a role
    in IRAS 20551-4250 at least for HCN and HNC (4.3), its effect
    must be evaluated in an appropriate manner. 
    
    
    
     §.§ Inclusion of infrared radiative pumping
    
    
    Our ultimate goal is to quantitatively estimate (1) how much
    fraction of molecular excitation at individual J-transition levels is 
    due to collision and infrared radiative pumping, and (2) the increase of 
    molecular line fluxes at individual J-transitions, brought by infrared
    radiative pumping, when compared to collisional excitation alone.
    However, this is difficult to achieve with currently available data,
    because of a large freedom of parameters for collisional excitation.
    First, the possibly different emitting volumes at different
    J-transitions (4.4) are not constrained in a meaningful manner. 
    Next, the typical temperature and density probed by different
    J-transition lines are different (4.4), so that different number of
    multiple temperature and density components needs to be taken into
    account when we compare flux ratios among different J-transition lines.
    We thus investigate quantitatively how infrared radiative pumping
    reproduces the observed trend of higher values of “high-J to 
    low-J” flux ratios for HNC than HCN shown in Figure 14, by fixing molecular
    gas physical parameters to canonical values. 
    We use MOLPOP <cit.>, which handles the exact solution of
    radiative transfer problem in multi-level atomic systems. 
    The ∼3 K cosmic microwave background radiation is always included
    in MOLPOP.  
    The large velocity gradient (LVG) method is prepared as an option, and
    we adopt it to compare the output with our RADEX calculation results.
    We have quantitatively confirmed that, under LVG, both MOLPOP and RADEX 
    outputs about molecular line flux ratios among J=1–0, J=3–2, J=4–3,
    and J=8–7 agree within 20–30% for various H_2 number density,
    H_2 kinetic temperature, and molecular column density divided by
    line width.  
    
    To calculate the role of infrared radiative pumping, we require Einstein A
    coefficient values for vibrational (v)-rotational (J) transitions between 
    (v_2,J) = (1,J) and (0, J±1 or J).
    We find the required information for HCN and HNC, but not for HCO^+, in
    the GEISA database <cit.>.
    We thus perform this calculation for HCN and HNC.
    Collision rates between J-transition levels at v_2=1 are not
    available, so we tentatively adopt the same values as v=0. 
    Since vibrational-rotational transitions are much faster than the
    transitions between J-levels within v_2=1 <cit.>, possible 
    small ambiguities in the collision rates at v_2=1 do not significantly
    affect our final results. 
    Collisional transitions between v_2=1 and v=0 are also not taken
    into account, due to their very large energy gaps. 
    
    In MOLPOP, we first set n_ H2 = 10^5 cm^-3, 
    T_ kin = 100 (K), Δv = 300 km s^-1, and the HCN and
    HNC column density of 10^16 cm^-2 to calculate molecular line
    fluxes by collisional excitation. 
    We confirm that the maser phenomenon does not happen at J=1–0.
    We choose the small side of the estimated density range for HCN and HNC,
    n_ H2 = 10^5 cm^-3 for our calculations, because the maser
    phenomenon happens at higher n_ H2 values, which complicates
    interpretations. 
    We then add infrared radiation at 5–30 μm in the power-law form of 
    F_ν (Jy) = 0.0024 ×λ(μm) ^2.0 (the dashed
    straight line in <cit.>).
    In this form, the number of infrared photons at ∼22 μm is
    larger than at 12–14 μm.
    The integrated luminosity between 5–30 μm is estimated to be 
    ∼2 × 10^11L_⊙ at a distance of 187 Mpc 
    (z = 0.043).
    Plane-parallel geometry is adopted, and the infrared 5–30 μm
    radiation source is placed at 30 pc and 100 pc from the
    molecular gas. 
    We then investigate if the high-J to low-J flux ratios of HNC are
    higher than HCN, particularly for “J=3–2 to J=1–0”, 
    “J=4–3 to J=1–0”, and “J=8–7 to J=1–0”, as observed in Figure
    14.
    Figure 15(a) plots the values of “high-J to low-J flux ratio of HNC,
    divided by the same ratio of HCN” in the ordinate.
    Since the infrared radiative pumping effects are calculated to be higher
    for HNC than HCN, the high-J to low-J flux ratios for HNC are expected
    to increase more than those for HCN, by the inclusion of infrared
    radiation. 
    Namely, the values in the ordinate are expected to be higher in the case
    of stronger infrared radiation than the case with no infrared radiation
    (i.e., collisional excitation only).
    We find that the inclusion of infrared radiative pumping 
    better reproduces the observed trend of higher values of 
    “high-J to low-J flux ratios” for HNC than HCN, for the combinations  
    of “J=3–2 to J=1–0”, “J=4–3 to J=1–0”, and “J=8–7 to
    J=1–0” observed in Figure 14.
    
    In Figure 15(b), we display a similar plot, but with a factor of 
    ∼3 smaller HNC column density than HCN, as indicated in 4.3.
    Since an additional parameter is introduced, the behavior becomes
    complicated, but the general trend of enhanced high-J to J=1–0 flux
    ratios for HNC than HCN is observed.
    We thus argue that the observed trend in IRAS 20551-4250 can be
    largely accounted for by infrared radiative pumping.
    
    Although collisional excitation is usually adopted to interpret the 
    observed molecular J-transition emission line fluxes in galaxies, it has
    been widely argued that the infrared radiative pumping mechanism can
    play an important role in AGN-containing galaxies, because AGNs can emit
    strong mid-infrared 5–30 μm continuum photons, due to AGN-heated
    hot dust grains.  
    In this AGN-containing ULIRG, IRAS 20551-4250, we have demonstrated 
    that the infrared radiative pumping indeed plays a role for molecular
    rotational J-level excitation at least for HCN and HNC, which
    suggests that this is the case in other AGN-containing ULIRGs as well.  
    However, in general ULIRGs, the similar estimates of the infrared
    radiative pumping effects, through the v_2=1f emission line flux
    measurements, are prohibitively difficult because HCN J=3–2 and J=4–3
    emission lines at the v_2=1 level are spectrally highly overlapped
    with the nearby, much brighter HCO^+ J=3–2 and J=4–3 emission
    lines at the v=0 level, respectively <cit.>. 
    IRAS 20551-4250 is unique in that, thanks to its small observed 
    molecular emission line widths, the flux estimates of the HCN v_2=1f 
    J=3–2 and J=4–3 emission lines are possible, by clearly separating
    from the bright HCO^+ (v=0) emission lines.
    Further detailed investigations of IRAS 20551-4250 with additional
    emission lines at v=0 and v_2=1 will help better constrain the
    quantitative role of infrared radiative pumping in this
    ULIRG as well as other AGN-containing ULIRGs.
    
    
    
     §.§ Infrared to radio spectral energy distribution
    
    
    Figure 16 shows the spectral energy distribution (SED) of IRAS
    20551-4250 in the infrared and radio.
    The q-value, defined as the far-infrared-to-radio flux ratio, is q
    ∼ 2.7 (Table 1).
    This is not smaller than for starburst-dominated galaxies and many
    radio-quiet AGNs (q ∼ 2.3–2.4) <cit.>,
    suggesting that the infrared-to-radio SED of IRAS 20551-4250 is an
    example of a radio-quiet AGN and starburst composite. 
    
    Continuum data points in ALMA bands 7 (275–373 GHz) and 9 (602–720 GHz)
    are well fitted to the extrapolation from the infrared dust thermal
    radiation at 2000–7500 GHz (40–150 μm).
    ALMA band 3 (84–116 GHz) continuum data points roughly agree with 
    the extrapolation from lower-frequency synchrotron emission. 
    The thermal free-free emission from starburst regions in IRAS
    20551-4250 is also present <cit.>, but mainly
    contributes to the frequency range at the minimum flux density
    (∼200 GHz), due to its relatively flat spectral shape.
    Overall, continuum flux measurements with our ALMA data in the
    (sub)millimeter wavelength range are consistent with those at other
    wavelengths taken with other observing facilities, further confirming
    that most activity (AGN and/or starburst) in IRAS 20551-4250 is 
    spatially compact, and their emission is well recovered with our ALMA 
    interferometric data.
    
    
    
    § SUMMARY
    
    
    We conducted ALMA band 3, 6, 7, and 9 observations of the
    buried-AGN-hosting ULIRG, IRAS 20551-4250, in Cycles 2, 3, and 4.
    When our new data were combined with our previously collected ALMA data, we
    obtained information on flux and its sensitive upper limit for
    J=1–0, J=3–2, J=4–3, and J=8–7 emission lines of HCN, HCO^+, HNC,
    CO J=3–2, vibrationally excited (v_2=1f) J=3–2 and J=4–3 emission
    lines of HCN, HCO^+, HNC, v_2=1f J=8–7 emission lines of HCN
    and HNC, J=3–2 emission lines of isotopologue H^13CN,
    H^13CO^+, HN^13C, and some other serendipitously detected
    emission lines.    
    From our previous ALMA observations of HCN, HCO^+, HNC at J=3–2 and
    calculations of infrared radiative pumping, it had been argued that HCN
    abundance was higher than HCO^+ and HNC, and that an infrared
    radiative pumping played a role in molecular gas rotational (J)
    excitation at the vibrational ground level (v=0) in IRAS 20551-4250. 
    By adding our new ALMA data, we found the following main results. 
    
    
      *  We detected v_2=1f emission lines at J=4–3 for HCN and HNC,
    but not for HCO^+, in the same manner as our previous J=3–2
    observations.
    HCO^+ v_2=1f fluxes are smaller than HCN v_2=1f and HNC
    v_2=1f fluxes at both J=3–2 and J=4–3. 
    The estimated vibrational excitation temperature from J=4–3 supported 
    our previous argument based on J=3–2 data that the infrared radiative
    pumping plays a role in rotational excitation at v=0, at least for HCN
    and HNC.
    
    
      *  There are possible signatures of v_2=1f J=8–7 emission lines
    of HCN and HNC in our ALMA band 9 spectrum; however, their detection
    significance is at most ∼3σ, in both their integrated
    intensity (moment 0) maps and Gaussian fits in the spectra.
    Confirmation with deeper data will be necessary for further discussion
    of these lines. 
    
    
      *  The J=4–3 fluxes of HCN, HCO^+, and HNC at v_2=1f and
    v=0 can be explained by a higher HCN abundance than HCO^+ and
    HNC, as was previously argued from J=3–2 data.   
    
    
      *  The comparison of fluxes between HCN, HCO^+, HNC and their 
    isotopologues (H^13CN, H^13CO, HN^13C) at J=3–2 also suggests
    higher flux attenuation by line opacity for HCN than for HCO^+ and HNC,
    supporting the above higher HCN abundance scenario than 
    HCO^+ and HNC.
    
    
      *  Line-opacity-corrected intrinsic molecular line flux ratios among 
    HCN, HCO^+, and HNC were derived at J=3–2 and J=4–3. 
    We confirmed that IRAS 20551-4250 has higher intrinsic 
    HCN-to-HCO^+ and HCN-to-HNC flux ratios than the observed 
    ratios. The difference from starburst-dominated regions was even larger
    if the intrinsic ratios are used for IRAS 20551-4250.
    
    
      *  The bright CO J=3–2 emission line enabled us to probe the
    dynamical properties of spatially extended molecular gas in detail, and
    showed a dynamically distinct region at the south-western part of the
    nucleus, compared to overall rotational motion.
    Our molecular observations support the scenario that some merger event
    occurred in the past in IRAS 20551-4250.  
    
    
      *  A broad (FWHM ∼ 500 km s^-1) emission line component was
    detected in the bright CO J=3–2 emission line, which we interpret to
    be caused by molecular outflow activity in this galaxy. 
    We estimate a molecular outflow mass M_ outf∼ 5.8 ×
    10^6 M_⊙, a molecular outflow rate Ṁ_ outf∼
    150 (M_⊙ yr^-1), a molecular outflow kinetic power 
    P_ outf∼ 1% of AGN luminosity (L_ AGN), and 
    a molecular outflow momentum rate Ṗ_ outf∼ 12 
    × L_ AGN/c.
    
    
      *  We conducted RADEX calculations and derived H_2 number density 
    and kinetic temperature that reproduce the observed flux ratios at
    different rotational J-transition lines of HCN, HCO^+, HNC at v=0,
    by collisional excitation.
    The derived number density and kinetic temperature tend to be higher
    when we use higher-J transition lines, supporting the expectation that
    higher-J transition lines preferentially probe higher-density and
    higher-temperature molecular gas in more compact areas.
    The comparison between J=3–2 and J=1–0 suggests that the typical
    molecular gas density that emits the HCN J=1–0 emission line is
    ∼10^5–10^6 (cm^-3). 
    The X-ray-absorbing hydrogen column density and 
    estimated mass of dense molecular gas from HCN J=1–0 luminosity suggest
    that the volume averaged number density and size of HCN J=1–0 emitting
    molecular gas are ∼10^3 (cm^-3) and ∼200 (pc),
    respectively. 
    We infer that the molecular clouds in the IRAS 20551-4250 nucleus are
    in a clumpy form in which dense clumps with ∼10^5–10^6
    (cm^-3) occupy 0.1–1% of the total volume of the nuclear molecular
    gas.  
    
    
      *  From our J=8–7, J=4–3, J=3–2, and J=1–0 data of
    HCN, HCO^+, and HNC, higher rotatioal excitation was seen for
    HNC than for HCN and HCO^+.
    This is difficult to explain with collisional excitation alone, due to
    the estimated higher effective critical density of HNC than HCN and 
    HCO^+.
    Infrared radiative pumping could explain this result because of
    higher infrared pumping efficiency for HNC than for HCN and HCO^+, due
    to a larger amount of infrared photons at ∼22 μm (wavelength for
    vibrational-rotational transitions between v=0 and v_2=1 for HNC) 
    than at 12–14 μm (those for HCN and HCO^+).
    Besides the vibrational excitation temperature, this is another 
    indication that infrared radiative pumping is at work in IRAS
    20551-4250.
    Given that Einstein A coefficients for vibrational-rotational
    transitions are available for HCN and HNC, we performed quantitative 
    calculations of the effects of the infrared radiative pumping process 
    for HCN and HNC, using the MOLPOP software.
    We found that the observed higher HNC rotational excitation was
    largely reproduced if an energy source with observationally constrained
    infrared spectral shape was placed at 30–100 pc from the molecular gas.
    
    
    
    IRAS 20551-4250 is a unique ULIRG in that the small observed 
    molecular emission line widths allow us to clearly separate the HCN
    v_2=1f J=3–2 and J=4–3 emission lines from the nearby, much
    brighter HCO^+ (v=0) J=3–2 and J=4–3 emission lines.
    Thus, molecular line fluxes at the v_2=1 level and the effects of 
    infrared radiative pumping can be investigated with small quantitative
    uncertainty.   
    Given that the infrared radiative pumping can have a significant effect
    to other AGN-containing ULIRGs, but that its quantitative estimate is
    more difficult due to the spectral overlap between HCN v_2=1f and
    HCO^+ v=0 emission lines at J=3–2 and J=4–3, further detailed
    investigations of IRAS 20551-4250 will provide an important clue to
    understand how the infrared radiative pumping contributes to molecular
    rotational J-transition line fluxes at v=0, in addition to the usually
    assumed collisional excitation, in AGN-containing ULIRGs.
    
    We thank the anonymous referee for his/her useful comment 
    which helped a lot to improve the clarity of this manuscript.
    We are grateful to Dr. H. Nagai, A. Kawamura, F. Egusa for their kind help
    regarding ALMA data retrieval and reduction.
    We are thankful to Dr. M. Elitzur and A. Asensio Ramos for their kind
    advice about the use of the MOLPOP code.  
    M.I. was supported by JSPS KAKENHI Grant Number 23540273, 15K05030 and
    the ALMA Japan Research Grant of the NAOJ Chile Observatory,
    NAOJ-ALMA-0001, 0023, 0072. 
    T.I. was thankful for the fellowship received from the Japan Society for
    the Promotion of Science (JSPS).
    This paper makes use of the following ALMA data:
    ADS/JAO.ALMA#2013.1.00033.S, #2015.1.00028.S, and #2016.1.00051.S. 
    ALMA is a partnership of ESO (representing
    its member states), NSF (USA) and NINS (Japan), together with NRC
    (Canada), NSC and ASIAA (Taiwan), and KASI (Republic of Korea), in
    cooperation with the Republic of Chile. The Joint ALMA Observatory is
    operated by ESO, AUI/NRAO, and NAOJ.
    Data analysis was in part carried out on the open use data analysis
    computer system at the Astronomy Data Center, ADC, of the National
    Astronomical Observatory of Japan. 
    This research has made use of NASA's Astrophysics Data System and the
    NASA/IPAC Extragalactic Database (NED) which is operated by the Jet
    Propulsion Laboratory, California Institute of Technology, under
    contract with the National Aeronautics and Space Administration. 
    
    
    
    
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    lcrrrrcccl[!bht]
    
    Observed properties of IRAS 20551-4250 0ptObject   Redshift   f_ 12   f_ 25   f_ 60   f_ 100   log L_ IR   log L_ FIR   S_ 1.4 GHz   q
          (Jy)   (Jy)   (Jy)   (Jy)   (L_⊙)   (L_⊙)   (mJy)   
    (1)   (2)   (3)   (4)   (5)   (6)   (7)   (8)   (9)   (10)
    IRAS 20551-4250     0.043     0.28     1.91     12.78     9.95      12.0     11.9     31.0     2.7 
    
    Col.(1): Object name. 
    Col.(2): Redshift. 
    Col.(3)–(6): f_12, f_25, f_60, and f_100 are 
     IRAS fluxes at 12 μm, 25 μm, 60 μm, and 100 μm,
    respectively, taken from the IRAS  FSC catalog. 
    Col.(7): Decimal logarithm of infrared (8-1000 μm) luminosity
    in units of solar luminosity (L_⊙), calculated with
    L_ IR = 2.1 × 10^39× D(Mpc)^2× (13.48 ×f_12 + 5.16 ×f_25 +
    2.58 × f_60 + f_100) (ergs s^-1) <cit.>.
    Col.(8): Decimal logarithm of far-infrared (40-500 μm) luminosity
    in units of solar luminosity (L_⊙), calculated with
    L_ FIR = 2.1 × 10^39× D(Mpc)^2× (2.58 × f_60 + f_100) (ergs s^-1) <cit.>.
    Col.(9): Radio 1.4 GHz flux in (mJy) <cit.>.
    Col.(10): Decimal logarithm of the far-infrared-to-radio flux ratio,
    defined as a q-value <cit.>.
    
    llccc|ccc[!bht]
    
    
    Log of our ALMA observations 0ptBand   Date   Antenna   Baseline   Integration   3cCalibrator
       (UT)   Number   (m)   (min)   Bandpass   Flux   Phase
    (1)   (2)   (3)   (4)   (5)   (6)   (7)   (8) 
    Band-7a (HCO^+ J=4–3)     2014 June 8     34     28–646     15     J1924-2914     Titan     J2056-4714 
        2015 April 3     37     15–328     15     J1924-2914     Titan     J2056-4714 
       
    Band-7b (HNC J=4–3)     2014 June 8     34     28–646     39     J1924-2914     J2056-4714     J2056-4714 
        2015 April 29     39     15–349     39     J2056-4714     Titan     J2056-4714 
       
    Band 9 (HCN, HCO^+, HNC J=8–7)     2016 May 18     42     15–640     39    
    J2253+1608     Pallas     J2056-4714 
       
    Band-3 (HCN, HCO^+, HNC J=1–0)     2016 May 27     41     15–784     39    
    J2056-4714     J2056-4714     J2049-4020 
        2016 August 15     38     15–1462     47     J2056-4714     J2056-4714     J2049-4020 
       
    Band-6 (H^13CN, H^13CO^+, HN^13C J=3–2)     2016 October 1
        41     15–3248     40     J1924-2914     J2056-4714     J2056-4714 
        2016 October 5     44     19–3248     40    
    J2056-4714     J2056-4714     J2056-4714 
        2016 October 5–6     44     19–3248     40     J2056-4714     J2056-4714     J2056-4714 
     
    Col.(1): Observed band and primarily targeted emission lines.
    Col.(2): Observing date in UT. 
    Col.(3): Number of antennas used for observations. 
    Col.(4): Baseline length in meters. Minimum and maximum baseline lengths are shown.  
    Col.(5): Net on-source integration time in min.
    Cols.(6), (7), and (8): Bandpass, flux, and phase calibrators for the 
    target source, respectively.
    
    ccrccl[!bht]
    
    Continuum emission properties 0ptContinuum   Frequency   Flux   Peak Coordinate   rms   Synthesized beam
       (GHz)   (mJy beam^-1)   (RA,DEC)J2000   (mJy beam^-1)   (arcsec × arcsec) (^∘)
    (1)   (2)   (3)   (4)   (5)   (6) 
    J10     84.1–87.9, 96.1–99.9     2.3 (61σ)     
    (20 58 26.80, -42 39 00.3)     0.038     1.1×0.9 (68^∘) 
    
    J32     232.1–235.7, 247.3–250.9     1.8 (68σ)     
    (20 58 26.80, -42 39 00.3)     0.027     0.18×0.17 (46^∘) 
    
    J43a     329–332.5, 340.7–344.4      10.5 (59σ)     (20 58 26.80, -42 39 00.3)     0.18
        0.84×0.68 (82^∘) 
    
    
    J43b     335.3–338.9, 347.2–351.0      10.3 (81σ)     (20 58 26.80,
    -42 39 00.3)     0.13     0.66×0.53 (-81^∘) 
       
    J87     678.7–684.4, 694.2–701.0      75.7 (29σ)     
    (20 58 26.80, -42 39 00.3)     2.6     0.23×0.21 (89^∘) 
    
    Col.(1): Continuum. J10, J32, J43a, J43b, and J87 were taken with
    “HCN, HCO^+, HNC J=1–0”, “H^13CN, H^13CO^+, HN^13C
    J=3–2”, “HCO^+ J=4–3”, “HNC J=4–3”, and “HCN, HCO^+,
    HNC J=8–7”, respectively. 
    Col.(2): Observed frequency in (GHz).
    Col.(3): Flux in (mJy beam^-1) at the emission peak. 
    The detection significance relative to the rms noise is shown in
    parentheses. 
    Possible systematic ambiguity, coming from ALMA absolute flux
    calibration uncertainty and choice of frequency range for continuum
    determination, is not included.  
    Col.(4): The coordinate of the continuum emission peak in J2000.
    Col.(5): The rms noise level (1σ) in (mJy beam^-1).
    Col.(6): Synthesized beam in (arcsec × arcsec) and position angle
    in (^∘). 
    The position angle is 0^∘ in the north–south direction
    and increases in the counterclockwise direction.
    
    ll|lll|cccc
    
    Molecular Line Flux 0ptLine   ν_ rest   3cIntegrated intensity (moment 0) map   4cGaussian line fit
       (GHz)   Peak   rms   Beam   Velocity   Peak   FWHM   Flux
          2c(Jy beam^-1 km s^-1)   (”×”) (^∘)   (km s^-1)   (mJy)   (km s^-1)   (Jy km s^-1)
    (1)   (2)   (3)   (4)   (5)   (6)   (7)   (8)   (9) 
    CO J=3–2     345.796    156.9 (64σ)     2.46     0.83×0.65
    (-84^∘)     12886±1     717±7     221±3     162±3 
    
    HCO^+ J=4–3     356.734     16.1 (70σ)     0.23    
    0.85×0.67 (74^∘)     12884±1     85±1     194±2    
    16.9±0.2 
      
    HCN J=4–3 v_2=1f     356.256     0.49 (9.5σ)     0.052    
    0.86×0.67 (74^∘)     12915±12     2.9±0.4    
    200±32     0.60±0.13 
         
    HCO^+ J=4–3 v_2=1f a    358.242     0.20
    (3.2σ)     0.062     0.81×0.66 (84^∘)     12947±34    
    1.4±0.6     146±58     0.21±0.13 
      
    SO 8(8)–7(7) b    344.311     0.55 (9.8σ)     0.056    
    0.85×0.70 (84^∘)     12908±10     4.3±0.7    
    148±24     0.64±0.15 
         
    SO_2+SO c    346.524–528 c   
    0.96 (14σ)     0.068     0.83×0.65 (-84^∘)    —   —   —   —
     
    HOC^+ J=4–3 d    357.922     0.46 (6.9σ)     0.067    
    0.86×0.69 (82^∘)     12875±21     3.0±0.5    
    213±62     0.66±0.22 
        
    CH_3CCH     358.709–818 e    0.45 (7.0σ)     0.065    
    0.81×0.66 (84^∘)     12900±16     2.6±0.5    
    185±39     0.49±0.14 
    
    HNC J=4–3     362.630     6.4 (70σ)     0.091     0.75×0.58
    (-78^∘)     12890±2     37±1     177±4     6.6±0.2 
      
    HNC J=4–3 v_2=1f f    365.147     
    0.64 (11.5σ)f    0.056f   
    0.66×0.53 (-83^∘)     12890 (fix)     2.2±0.4     443
    (fix)     0.98±0.19 
      
    H_2CO 5(1,5)–4(1,4)     351.769     1.2 (24σ)     0.051    
    0.63×0.52 (-81^∘)     12879±4     6.8±0.2    
    213±9     1.5±0.1 
     
    HOCO^+ 17(1,16)–16(1,15)g    364.804     2.5
    (42σ)     0.059     0.81×0.64 (-83^∘)     12898±2
        13±1     181±4     2.5±0.1 
    
    HCN J=8–7     708.877     12.9 (7.1σ)     1.8     
    0.24×0.21 (88^∘)     12930±9     51±3     262±19    
    13.7±1.3 
       
    HCO^+ J=8–7     713.341     11.9 (9.9σ)     1.2    
    0.23×0.21 (-88^∘)     12884±4     77±4     159±10
        12.5±1.0 
       
    HNC J=8–7     725.107     6.9 (4.8σ)     1.4     0.23×0.20
    (90^∘)     12904±10     43±5     164±21     7.2±1.3 
     
    HCN J=8–7 v_2=1f     712.372     1.0 (3.1σ)     0.32
    h    0.23×0.21 (-88^∘)     12918±12    
    15±5     61±25     1.0±0.5 
       
    HNC J=8–7 v_2=1f     730.131     0.88 (1.7σ)     0.52
    h    0.23×0.20 (88^∘)     12871±30     11
    (fix)     67 (fix)     0.7 
      
    HCN J=1–0     88.632     1.4 (33σ)     0.041     1.2×0.9
    (69^∘)     12881±2     7.1±0.2     195±5     1.4±0.1 
      
    HCO^+ J=1–0     89.189     2.2 (40σ)     0.054     1.2×0.9
    (72^∘)     12888±1     11±1     202±3     2.2±0.1 
       
    HNC J=1–0     90.664     0.36 (11σ)     0.034     1.0×0.7
    (61^∘)     12878±5     2.2±0.1     169±13     0.37±0.04
    
    
    H^13CN J=3–2     259.012     0.25 (6.8σ)     0.036    
    0.16×0.15 (35^∘)     12903±6     1.4±0.1     181±16
        0.26±0.03 
    
    H^13CO^+ J=3–2     260.255     0.13 (5.2σ)     0.024    
    0.16×0.16 (59^∘)     12901±8     0.86±0.09    
    159±18     0.14±0.02 
    
    HN^13C J=3–2     261.263     0.066 (2.8σ)    0.024    
    0.16×0.16 (59^∘)     12911±20     0.34±0.07    
    204±51     0.071±0.023 
    
    CS J=5–4     244.936     1.2 (40σ)     0.030     0.19×0.17
    (38^∘)     12901±2     7.5±0.1     167±4     1.3±0.1 
     
    SO 6(6)–5(5)     258.256     0.34 (10σ)     0.034     0.16×0.15
    (35^∘)     12909±4     1.9±0.1     187±10     
    0.37±0.03 
    
    SiO J=6–5     260.518     0.22 (5.8σ)     0.037     0.16×0.16
    (59^∘)     12902±7     1.2±0.1     188±15     0.24±0.03 
     
    HC_3N J=27–26     245.606     0.15 (6.4σ)    0.023    
    0.19×0.17 (38^∘)     12900±5     0.99±0.07     154±13    
    0.16±0.02 
    a
    SO_2 20(0,20)–19(1,19) emission line (ν_ rest = 358.216 GHz) 
    might contaminate.b
    HC^15N J=4–3 emission line (ν_ rest = 344.200 GHz) might
    contaminate.c
    Combination of SO_2 16(4,12)–16(3,13) (ν_ rest = 346.524
    GHz) and SO 9(8)–8(7) (ν_ rest = 346.528 GHz).d
    SO_2 6(4,2)–6(3,3) emission line (ν_ rest = 357.926 GHz) 
    might contaminate.e
    Combination of 
    CH_3CCH 21(4)–20(4) (ν_ rest = 358.709 GHz), 
    CH_3CCH 21(3)–20(3) (ν_ rest = 358.757 GHz), 
    CH_3CCH 21(2)–20(2) (ν_ rest = 358.791 GHz), 
    CH_3CCH 21(1)–20(1) (ν_ rest = 358.811 GHz), and 
    CH_3CCH 21(0)–20(0) (ν_ rest = 358.818 GHz).f
    All emission line components with FWHM ∼ 443 km s^-1 are
    integrated.g
    H_3O^+ 3(2)–2(2) emission line (ν_ rest = 364.797 GHz) 
    might contaminate.h
    The rms noise level was determined from the 40–100 pixels annular region
    around the center of the moment 0 map. 
    Col.(1): Observed molecular line. 
    Primarily targeted lines are listed first, followed by serendipitously detected
    lines.
    Col.(2): Rest-frame frequency of each molecular line in (GHz). 
    Col.(3): Integrated intensity in (Jy beam^-1 km s^-1) at the 
    emission peak. 
    Detection significance relative to the rms noise (1σ) in the 
    moment 0 map is shown in parentheses. 
    Possible systematic uncertainty is not included. 
    Col.(4): rms noise (1σ) level in the moment 0 map in 
    (Jy beam^-1 km s^-1), derived from the standard deviation 
    of sky signals in each moment 0 map. 
    Col.(5): Synthesized beam in (arcsec × arcsec) and position angle
    in (^∘).
    Position angle is 0^∘ in the north-south direction, 
    and increases in the counterclockwise direction. 
    Cols.(6)–(9): Gaussian fits of emission lines in the spectra at the 
    continuum peak position, within the beam size. 
    Col.(6): Optical LSR velocity (v_ opt) of emission peak in (km
    s^-1).  
    Col.(7): Peak flux in (mJy). 
    Col.(8): Observed FWHM in (km s^-1) in Figure 4.  
    Col.(9): Flux in (Jy km s^-1). The observed FWHM in 
    (km s^-1) in column 8 is divided by (1+z) to obtain the
    intrinsic FWHM in (km s^-1).
    
    lcc
    
    Intrinsic emission size after deconvolution for selected 
    bright emission lines and continuum 0ptLine   (mas × mas) (^∘)   Beam (arcsec × arcsec) 
    (1)   (2)   (3)
    CO J=3–2     828±123, 561±127 (131±23)     0.83 × 0.65 
    
    HCO^+ J=4–3     306±35, 275±37 (96±76)     0.85 × 0.67 
    
    cont43a     348±52, 336±63 (136±88)     0.84 × 0.68 
    
    HNC J=4–3     206±30, 105±55 (152±17)     0.75 × 0.58 
    
    
    
    
    cont43b     326±26, 284±22 (89±48)     0.66 × 0.53 
    
    HCN J=8–7     218±44, 135±43 (84±38)     0.24 × 0.21
    
    HCO^+ J=8–7     246±36, 179±34 (70±34)     0.23 × 0.21 
    
    HNC J=8–7     141±57, 65±50 (72±74)     0.23 × 0.20 
    
    cont87     261±16, 225±15 (56±23)     0.23 × 0.21 
    
    HCN J=1–0     711±138, 655±170 (108±82)     1.19 × 0.95 
    
    HCO^+ J=1–0     763±136, 609±221 (142±83)     
    1.22 × 0.95 
    
    HNC J=1–0     320±222, 45±186 (71±22)     1.02 × 0.73 
    
    cont10     510±81, 468±87 (84±87)     1.09 × 0.87 
    
    CS J=5–4     201±13, 152±13 (80±13)     0.19 × 0.17 
    
    cont32     198±13, 170±12 (60±28)     0.18 × 0.17
    
    Col.(1): Emission line or continuum.
    Col.(2): Intrinsic emission size in mas, after deconvolution using
    the CASA task “imfit”. 
    The position angle in (^∘) is shown in parentheses.
    Col.(3): Synthesized beam size in arcsec × arcsec, shown for
    reference.
    
    lccc
    
    Luminosity of selected molecular emission lines 0ptLine   Flux (Jy km s^-1)   10^4 (L_⊙)   10^7 (K km s^-1 pc^2)
    HCN J=1–0     1.4±0.1     0.44±0.03     19.6±1.4 
    
    HCN J=3–2     5.9±0.1 a    5.5±0.1 a   
    9.2±0.2 a
    
    HCN J=4–3     11.6±0.2 b    14.5±0.3
    b    10.1±0.2 b
     
    HCN J=8–7     13.7±1.3     34.1±3.2     3.0±0.3 
     
    HCN v_2=1f J=3–2     0.25±0.07 a    0.23±0.07
    a    0.35±0.10 a
     
    HCN v_2=1f J=4–3     0.60±0.13     0.75±0.16     0.52±0.11 
    
    HCO^+ J=1–0     2.2±0.1     0.69±0.03     30.4±1.4 
    
    HCO^+ J=3–2     8.4±0.1 a    7.9±0.1 a    12.9±0.2 a
    
    HCO^+ J=4–3     16.9±0.2     21.2±0.3     14.6±0.2 
    
    HCO^+ J=8–7     12.5±1.0     31.3±2.5     2.7±0.2 
     
    HCO^+ v_2=1f J=3–2    <0.088 a   <0.084
    a   <0.13 a
     
    HCO^+ v_2=1f J=4–3    <0.20    <0.26    <0.18 
     
    HNC J=1–0     0.37±0.04     0.12±0.01     4.9±0.5 
    
    HNC J=3–2     3.2±0.1 a    3.1±0.1
    a    4.7±0.1 a
     
    HNC J=4–3     6.6±0.2     8.4±0.3     5.5±0.2 
    
    HNC J=8–7     7.2±1.3     18.3±3.3     1.5±0.3 
     
    HNC v_2=1f J=3–2     0.20±0.07 a    0.19±0.07
    a    0.27±0.09 a
    
    HNC v_2=1f J=4–3     0.98±0.19     1.3±0.2     0.81±0.16 
    
    H^13CN J=3–2     0.26±0.03     0.24±0.03     0.43±0.05 
    
    H^13CO^+ J=3–2     0.14±0.02     0.13±0.02     0.23±0.03 
    
    HN^13C J=3–2     0.071±0.023     0.065±0.021     0.11±0.04 
    
    CO J=3–2     162±3     197±4     149±3 
    
    CS J=5–4     1.3±0.1     1.1±0.1     2.4±0.2 
    aTaken from <cit.>.bOriginally taken from ALMA Cycle 0 data by
    <cit.> and multiplied by a factor of 1.22 to correct for the
    flux difference between Cycle 0 and 2 data. 
    See 3 for more detail.
    Col.(1): Emission line.
    Col.(2): Adopted values for the observed flux in (Jy km s^-1) shown
    for reference.  
    Col.(3): Luminosity in units of (L_⊙), calculated with
    Equation (1) of <cit.>.
    Col.(4): Luminosity in units of (K km s^-1 pc^2), 
    calculated with Equation (3) of <cit.>.
    
    lcrcc
    Parameters for molecular transition lines 0ptLine   Frequency   E_ u/k_ B   A_ ul   Flux
       (GHz)   (K)   (10^-3 s^-1)   (Jy km s^-1)
    (1)   (2)   (3)   (4)   (5) 
    HCN J=1–0     88.632     4.3     0.024     1.4±0.1 
    
    HCN J=3–2     265.886     25.5     0.84     5.9±0.1 
    
    HCN J=4–3     354.505     42.5     2.1     11.6±0.2 
      
    HCN J=8–7     708.877     153.1     17.4     13.7±1.3 
    
    HCN J=3–2, v_2=1f     267.199     1050.0     0.73     0.25±0.07 
    
    HCN J=4–3, v_2=1f     356.256     1067.1     1.9     0.60±0.13 
    
    HCO^+ J=1–0     89.189     4.3     0.042     2.2±0.1 
    
    HCO^+ J=3–2     267.558     25.7     1.5     8.4±0.1 
    
    HCO^+ J=4–3     356.734     42.8     3.6     16.9±0.2 
      
    HCO^+ J=8–7     713.341     154.1     30.2     12.5±1.0 
    
    HCO^+ J=3–2, v_2=1f     268.689     1217.4     1.3    <0.088 
    
    HCO^+ J=4–3, v_2=1f     358.242     1234.6     3.4    <0.20 
    
    HNC J=1–0     90.664     4.4     0.027     0.37±0.04 
    
    HNC J=3–2     271.981     26.1     0.93     3.2±0.1 
    
    HNC J=4–3      362.630     43.5     2.3     6.6±0.2 
      
    HNC J=8–7     725.107     156.6     19.4     7.2±1.3 
    
    HNC J=3–2, v_2=1f     273.870     692.0     0.85     0.20±0.07 
    
    HNC J=4–3, v_2=1f     365.147     709.6     2.2     0.98±0.19 
    
    Col.(1): Molecular transition line.
    Col.(2): Rest-frame frequency in (GHz).
    Col.(3): Upper energy level in (K).
    Col.(4): Einstein A coefficient for spontaneous emission in 
    (10^-3 s^-1). 
    Values in Cols. (3) and (4) are from the Cologne Database of
    Molecular Spectroscopy (CDMS) <cit.> via Splatalogue
    (http://www.splatalogue.net).
    Col.(5): Flux in (Jy km s^-1) estimated based on Gaussian fit 
    (Table 4, column 9 of this paper; Imanishi & Nakanishi 2013b; Imanishi
    et al. 2016b). 
    For the undetected HCO^+ v_2=1f J=3–2 and J=4–3 emission
    lines, upper limits based on the integrated intensity (moment 0) maps
    are adopted.
    
    
    lcc
    
    Excitation temperature for IRAS 20551-4250 0ptMolecule   (v_2,J; v, J)   T_ ex (K)
    (1)   (2)   (3) 
    HCN     (1f,4; 0,4)     360  
      
    HCO^+    (1f,4; 0,4)    <280 
     
    HNC     (1f,4; 0,4)     360  
    
    HCN     (0,3; 0,1)     7  
        (0,4; 0,3)     36 
        (0,8; 0,4)     42 
    
    HCO^+    (0,3; 0,1)     7 
        (0,4; 0,3)     38 
        (0,8; 0,4)     36 
    
    HNC     (0,3; 0,1)     10 
        (0,4; 0,3)     41 
        (0,8; 0,4)     42 
    
    Col.(1): Molecule.
    Col.(2): Transition.
    Col.(3): Excitation temperature (T_ ex) in (K), derived from
    observed fluxes.
    Different beam sizes among different J-transition lines are not
    considered, to be consistent with our previous estimates <cit.>.
    
    
    cccc
    
    Flux ratios for HCN, HCO^+, and HNC 0ptJ-transition   HCN   HCO^+   HNC
    (1)   (2)   (3)   (4)
    3–2/1–0     4.2±0.6     3.8±0.5     8.6±1.2 
    
    4–3/1–0     8.3±1.2     7.6±1.1     17.8±2.5 
    
    8–7/1–0     9.8±1.4     5.6±0.8     19.3±4.0 
    
    4–3/3–2     2.0±0.3     2.0±0.3     2.1±0.3 
    
    8–7/3–2     2.3±0.3     1.5±0.2     2.2±0.5 
    
    8–7/4–3     1.2±0.2     0.74±0.10     1.1±0.2 
    
    Ratios of flux in (Jy km s^-1).
    Col.(1): J-transition. 
    Col.(2): HCN.
    Col.(3): HCO^+.
    Col.(4): HNC.
    For all flux ratios, 10% absolute calibration uncertainty in
    individual ALMA observations is included.
    
    
    
    
    
    
    
    
    
    
    
    
      
    
    
    
    
    
    § APPENDIX
    
    
    Integrated intensity (moment 0) maps of selected serendipitously
    detected faint emission lines are displayed in Figure 17.
    Figure 18 shows spectra around these lines and best Gaussian fits, 
    except for “SO_2+ SO” in Figure 17, because two lines
    overlap at close frequency (Figure 2c). 
    Figure 19 shows our RADEX calculations to reproduce the observed molecular
    line flux ratios, in the case of HCO^+ and HNC column density of 3
    × 10^15 cm^-2.
