Off-nuclear H 2 O maser and dense molecular gas in NGC 1068

The results of high-resolution spectral-line observations of dense molecular gas are presented towards the nuclear region of the type 2 Seyfert galaxy NGC 1068. MERLIN observations of the 22 GHz H 2 O maser were made for imaging the known off-nuclear maser emission at radio jet component located about 0.3" north-east of the radio nucleus in the galaxy. High angular resolution ALMA observations have spatially resolved the molecular gas emissions of HCN and HCO + in this region. The off-nuclear maser spots are found to nearly overlap with a ring-like molecular gas structure and are tracing an evolving shock-like structure, which appears to be energized by interaction between the radio jet and circumnuclear medium. A dynamic jet-ISM interaction is further supported by a systematic shift of the centroid velocities of the off-nuclear maser features over a period of 35 years. The integrated flux ratios of the HCO + line emission features at component C suggest a kinetic temperature T k > ∼ 300K and an H 2 density of > ∼ 10 6 cm − 3 , which are conditions where water masers may be formed. The diagnostics of the masering action in this jet-ISM interaction region is exemplary for galaxies hosting off-nuclear H 2 O maser emission.


INTRODUCTION
Highly luminous extragalactic H2O maser in the transition of 616 − 523 (rest frequency: 22.23508 GHz) is a useful tracer of the structure and kinematics of dense molecular gas in interaction regions in galaxies and in clouds on scales of < ∼1 pc from a central engine of active galactic nuclei (AGN).Some fraction of the known H2O megamasers exhibit spectra implying evidence for emission sub-parsec clouds embedded in an edge-on rotating disc surrounding super massive black holes using Very Long Baseline Interferometry (VLBI) at milliarcsecond (mas) angular resolution (e.g., Nakai, Inoue, & Miyoshi 1993;Haschick, Baan, & Peng 1994;Miyoshi et al. 1995;Greenhill et al. 2003;Baan et al. 2022).Many of the H2O megamasers are associated with the radio continuum emission structures resulting from nuclear radio jets, jet-cloud interaction regions or outflows such as TXFS 2226-184, NGC 1052, Mrk 348, and Centaurus A (e.g., Koekemoer et al. 1995;Claussen et al. 1998;Peck et al. 2003;Kameno et al. 2005;Ott et al. 2013;Surcis, Tarchi, & Castangia 2020).These four ⋆ E-mail: yhagiwara@toyo.jp(YH) objects stand out from the other megamasers on the basis of their line profiles.The spectral line profiles of non-nuclear H2O memgamasers consist of single, broad and, relatively smooth emission profiles (FWHM∼100-200 km s −1 ) and are different from profiles found in nuclear masers that consist of narrow components or "high-velocity" components with linewidths of a few to ∼10 km s −1 spread over much wider velocity ranges of ∼100-1000 km s −1 .These non-nuclear masers arise through the shock excitation of ambient gas in circumunuclear regions of galaxies.The masers are associated with the radio continuum emission that believed to be coincident with the nucleus.
Sub-millimetre (sub-mm) telescopes such as Atacama Large millimetre/sub-millimetre Array (ALMA) have opened the possibility to make imaging studies of (sub-)millimetre masers such as H2O maser in the transitions of 313−220 (rest frequency: 183.308GHz) and 1029−936 (rest frequency: 321.226GHz) at high angular resolution to ∼ 20 milliarcsecond (mas), which may serve to diagnose the masering processes in H2O megamaser sources (e.g., Humphreys et al. 2005;Hagiwara et al. 2013Hagiwara et al. , 2021)).The detection of thermally excited molecules such as HCN and HCO + are also reported in these megamaser host galaxies at higher transitions at submillimetre wavelengths.
The galaxy NGC 1068 is a prototypical type 2 Seyfert galaxy hosting an active nucleus obscured by a torus in which broad optical emission lines are seen in polarized optical spectra (e.g.Antonucci & Miller 1985).The galaxy has been investigated extensively at all wavelengths, revealing that various species of molecular gas are abundant in the circumnuclear region, and spiral arms in the galaxy and abundant dense molecular gases related to star-forming activity are in the starburst ring (e.g.Takano et al. 2014;García-Burillo et al. 2019;Sánchez-García et al. 2022).NGC 1068 hosts a nearly one-sided radio jet that may be qualified as a Compact Symmetric Object and luminous and variable 22 GHz H2O maser emission has been detected to be superposed on the radio core-jet structure at lower frequencies (e.g.Gallimore et al. 2001;Gallimore, Baum, & O'Dea 2004).Sub-mm H2O maser action in the 321 GHz transition has not (yet) been detected towards the center of the galaxy using ALMA (Hagiwara et al. 2016;Pesce, Braatz, & Impellizzeri 2016).Very long baseline interferometry (VLBI) observations have revealed that the prominent 22 GHz H2O maser features in NGC 1068 covering a frequency range from VLSR= 800 -1500 km s −1 are distributed along a linear ∼1 pc region and originated in an edge-on (i > 80 • ) molecular gas disc in the nuclear region of the galaxy (e.g.Greenhill et al. 1996;Gallimore et al. 2001).
Recent sub-mm mapping observations of thermally-excited molecular emission lines in the galaxy using ALMA revealed that a parsec-scale torus structure, that surrounds the nuclear region, does not have the simple axisymmetric structure expected in the unified theory (e.g.Impellizzeri et al. 2019;Imanishi et al. 2018Imanishi et al. , 2020)).Gallimore et al. (1996) reported the presence of H2O maser towards radio jet component C (hereafter the "off-nuclear maser"), which is located about 0.3 arcsecond (∼ 30 pc) north-east from the component S1.The off-nuclear maser is peaked at VLSR= 984.1 km s −1 (Gallimore et al. 2001), which is blueshifted ∼140 km s −1 with respect to the systemic velocity of VLSR= 1123 ± 4 km s −1 , estimated from CO emission (Nakai et al. 1995).This off-nuclear maser region traces shocked dense molecular gas coinciding with the radio jet component C, where the jet interacts with the local interstellar medium (ISM) in the galaxy (Gallimore et al. 1996).Off-nuclear masers will thus provide additional diagnostics of the circumnuclear environment of the AGN.Following-up the earlier studies using VLBI for clarifying the origin of the off-nuclear H2O maser in the galaxy is of great interest with different angular resolution and different dense molecular gases at higher frequencies.In this article, the results of high-resolution mapping of 22 GHz H2O maser and HCN and HCO + thermal molecular lines in NGC 1068 using MERLIN and ALMA are presented in order to understand kinematics and conditions of gas in the circumnuclear region of the galaxy.

MERLIN Observations and Data Reduction
Spectral-line observations at 22 GHz with the five telescopes of Multi-Element Radio-Linked Interferometer Network (MERLIN) 1 , including the Mark 2 telescope.The observations of NGC 1068 were carried out over periods of 6-7 April in 2002 for ∼ 16 hours in total.Phase-tracking position for NGC 1068 was RA 02 h 42 m 40.711 s , Dec. -00 • 00 ′ 47.810 ′′ (J2000).In our observations, a single IF band of 16 MHz width with opposite circular polarizations divided to 64 spectral channels, yielding a frequency resolution (∆ν) of 250 kHz (or 3.4 km s −1 ) was centred at the one frequency setting and changed to other two frequency settings by shifting centre frequency during observations.Using this frequency configuration, we obtained three IF center frequencies, centred at VLSR= 597, 899, and 1092 km s −1 .The resultant velocity coverages are VLSR= 490 -705, 790 -1005, and 985 -1195 km s −1 .The velocity range of VLSR= 705 -790 km s −1 was not covered.Phase-referencing observations were conducted at each frequency set, using a phase-referencing source 0237-027, an ICRF source (RA 02 h 39 m 45. s 4723, Dec. -02 • 34 ′ 40.913 ′′ (J2000)).In earlier MERLIN observations, the position used for 0237-027 in J2000 is RA = 02 h 39 m 45. s 47226, Dec. = -02 • 34 ′ 40.′′ 8984 (± 10 mas) (Muxlow et al. 1996).Note that the differences of these positions are well within the MERLIN synthesized beam.The observations were executed in a sequence of 6 min scans with cycling interval of 250 sec for NGC 1068 and 70 sec for 0237-027.
Amplitude and bandpass calibration were performed by observations of 3C 286 and 3C 273.Data analysis was conducted using the Astronomical Image Processing Software (AIPS).After initial calibration and data editing, the phase reference source 0237-027 was self-calibrated, and the phase solutions obtained from the phase reference source were applied to all IFs containing line emission.In order to make a continuum map, spectral channels without line-emission were averaged.Thus, imaging and CLEANing of the continuum emission was done separately.
The synthesized beam sizes (natural-weighting) used in the CLEAN deconvolution are 0.043 ′′ × 0.021 ′′ in the position angle (P.A.) of 57 • , and the resultant rms noise level per a spectral channel (∆ν = 250 kHz) was about 5-6 mJy beam −1 (A 0.02 arcsec synthesized beam corresponds to 1.2 pc at the galaxy.).The rms noise level of a line-emission-free map made by averaging line-emission-free channels was ∼ 2 mJy beam −1 .In this article, the velocities are calculated with respect to the Local Standard of Rest (LSR).Imaging of the calibrate data was conducted with the NRAO Astronomical Image Processing Software (AIPS) (van Moorsel, Kemball, & Greisen 1996) 2.2 ALMA Data and Data Reduction For analysis of the thermally-excited molecular lines and the sub-millimeter continuum, we used data of ALMA band 6 (211-275 GHz) observations (Project: 2016.1.00052.S, PI: M.Imanishi) conducted at higher spatial resolution.The observations were made from 2016 October to 2017 September.For these Cycle 4 observations, 40-44 12 m antennas were used as a hybrid configuration with baselines ranging from 17 to 7552 m.This configuration results in a largest recoverable scale of ∼1.3" for extended emission and an angular resolution of 0.02".In this analysis, two 1.875 GHz wide spectral windows were used to cover HCO + (J=3-2) and HCN (J=3-2) emission lines at 267.558 GHz and 265.886GHz, respectively.More details of the observations, calibrations, and data analysis are described in (Imanishi et al. 2018).We analyzed HCO + (J=4-3) emission line data at 356.734 GHz (Project: 2016.1.00232.S) obtained from the ALMA Science Archive.The observation was conducted on 2016 September 8.
Imaging of the calibrated data was carried out using the Common Astronomy Software Applications (CASA) 2 (CASA Team et al. 2022).The continuum emission of the galaxy was subtracted from the calibrated spectral line visibility cubes using line-free channels prior to CLEAN deconvolution of line emission.The emission lines were separated out from the continuum emission.Imaging was performed using CASA with Briggs weighting (robust = 0.5).The resultant synthesized beam size in the CLEAN is 0.03"-0.07".

Effelsberg Observations
22 GHz H2O maser spectrum of the galaxies was obtained using Max-Planck Institute 100-m telescope at Effelsberg.The half-power beam width of the 100-m was ∼40" at 22 GHz.The pointing calibration was made by observing nearby strong continuum sources every 1 to 2 hours, yielding a pointing accuracy of better than ∼ 5".Observations of the maser were conducted using a 22 GHz-band receiver with a 300 MHz bandwidth, 65536 spectral channels, and dual polarization from September 24 to 26 2022 at a spectral resolution of 4.6 kHz or 0.063 km s −1 .Smoothing 16-32 spectral points yields ∼ 1-2 km s −1 velocity resolution at 22 GHz.Accuracy of flux density is estimated to be ∼30%.
Figure 2 shows 22 GHz H2O maser spectrum towards the center of the galaxy that was taken at the Effelsberg 100-m Telescope in September 2022.
Figure 3 shows the maser spectra obtained by MERLIN towards the positions of components S1 and C in the velocity range of VLSR= 800 − 997 km s −1 (the blue-shifted velocity range), VLSR= 994 − 1190 km s −1 (the systemic velocity The H2O maser in the nuclear region of the galaxy was searched within the field of view of 0.768 × 0.768 arcsec 2 , centred on the phase tracking centre of the galaxy and in the velocity range of VLSR= ∼ 800 -1189 km s −1 .We identified possible minor peaks straddling over a few spectral channels centred at VLSR= 980.4 km s −1 .The centre velocity of the peak is similar to the known off-nuclear maser emission at V= 984.1± 1.2 km s −1 (Gallimore et al. 2001).The position of the off-nuclear maser is RA = 02 h 42 m 40.714 s , Dec. = -00 • 00 ′ 47.653 ′′ (J2000), the location of which is located near the radio continuum source C (RA = 02 h 42 m 40.715 s , Dec. = -00 • 00 ′ 47.636 ′′ (J2000)) (Muxlow et al. 1996).Thus, the off-nuclear maser emission is tentatively found at C, despite the fact that the detection level is ∼2-3σ.The upper limit of the isotropic maser luminosity is estimated to be ∼ 0.1 L ⊙ .The coordinates of the nuclear component at 5 GHz and the masers are listed in table 1: A mean position of the detected masers in the blue-shifted and systemic velocity range is RA = 02 h 42 m 40.7087 s , Dec. = -00 • 00 ′ 47.949 ′′ (J2000).Therefore, the positions of the masers in the blue-shifted and systemic velocity range are all confined within ≈ 0.02 ′′ (20 mas) from the mean position, consistent with the results of earlier observations.Fig. 4 displays the centre positions of the nuclear masers detected in an SNR of > ∼ 4 and a tentative position of the offnuclear maser.In this figure, the nuclear maser positions are plotted also as an inset with uncertainties denoted by error bars.These nuclear maser features are peaked at VLSR= 800, 861, and 865 km s −1 in the blue-shifted velocity range and VLSR= 1068, 1105, and 1189 km s −1 in the systemic velocity range.All the detected masers remain unresolved at the angular resolution of ∼ 20 milliarcsecond (mas), or ∼ 4 pc.Considering the position error of the calibrator source (∼5 mas), half the synthesized beam divided by SNR (∼4 mas), the baseline errors (∼10 mas), and an error caused by an offset between the target and phase-reference source, positional accuracy is estimated to be ∼15 mas.In our observations, no 22 GHz continuum has been detected to a 3 σ rms noise of ∼ 6 mJy beam −1 , making it difficult to compare precisely the locations of each maser spot and continuum components in the nuclear region of the galaxy.

Off-nuclear maser
In our MERLIN observations, the off-nuclear H2O maser at component C was not distinctly detected.It is likely that the flux density of the maser was weaker when observed or it was resolved out by our MERLIN synthesized beam that is by a factor of 5 smaller than that for earlier detection with the Very Large Array (VLA) (Gallimore et al. 1996).However, the latter is less likely since the masers lying in the blue-shifted and systemic velocity ranges were detected in our MERLIN maps.Moreover, according to the recent research using a global VLBI network including the National Radio Astronomy Observatory (NRAO) VLBA, the phased-VLA, and the Effelsberg 100-m, which was observed on 2000 February 23-24, the H2O masers at C were detected at an even smaller 1.3 × 1.0 mas angular resolution (see Figure 9)(Morishima et al. 2023).The off-nuclear masers at C were previously detected in velocities of VLSR≃ 950-1050 km s −1 by the VLA in 1987, and the flux density of the maser was ∼ 50 mJy (Gallimore et al. 1996).If the strength of the maser was as strong as that observed by the VLA, the maser should have been clearly detected in our observations.Nevertheless, a minor 2.5σ peak at VLSR= 980.4 km s −1 seen with MERLIN near component C in the Figures 3 and 4 would represent the location of the off-nuclear maser.The observed intensity variability of the off-nuclear maser (Gallimore et al. 2001) may indeed account for the reduced flux density of the maser at component C below ∼20 mJy at the time of our MERLIN observations.

Nuclear H2O masers at the continuum nucleus (S1,N)
One important result in our observations is that the positions of the nuclear masers in NGC 1068 obtained at the angular resolution of ∼ 20 mas have been estimated with respect to the radio nuclear component N (S1) in Figures 1 and 5 from earlier 5 GHz MERLIN data and has not been well established by VLBI observation.Earlier VLBI observations at 22 GHz (Greenhill et al. 1996) did not detect the nuclear continuum components, which makes astrometric registration difficult for the masers and the radio nucleus.An attempt has been made to register the relative positions of all maser emissions extending to ±300 km s −1 below systemic and the radio continuum components using VLBI data at 5 GHz (Gallimore, Baum, & O'Dea 2004).The positional uncertainties resulting from the not precisely known position of the radio nucleus S1 are comparable with those of the masers.The positions of the blueshifted masers presented in Greenhill et al. (1996) were not obtained with phase-referencing observations and their positions were estimated relative to the brightest maser spot in the galaxy Gallimore et al. (2001).In our observations, the 22 GHz continuum was not detected and the positions of the nuclear masers have been determined with respect to the phase-referencing source used in both our observations and earlier MERLIN observations (Muxlow et al. 1996).The coordinates of the nuclear component at 5 and 22 GHz and the masers are listed in Table 1.The positions of the unresolved maser sources and the continuum nucleus at 5 GHz are co-located within the uncertainties.It should be noted that the maser positions are offset south-west or south with respect to the 5 GHz or 22 GHz continuum nucleus and some systematic position shifts between the maser spots and the 5 GHz S1 continuum source could not be removed in our data analysis.Nevertheless, we conclude that the detected blue-shifted and systemic masers arise near from the central engine of the galaxy, which is consistent with the results of earlier VLBI measurements.

Velocity fields in HCN and HCO + at C
The velocity gradients in both the HCN (3-2) and HCO + (3-2) emission at the radio component C have been resolved at the ∼0.03 ′′ spatial resolution of ALMA in Figure 6.As is evident in the first moment maps of Figure 6 (upper), the velocity gradients in the HCN and HCO + lines are spanning VLSR= ∼ 1050 to 1150 km s −1 and VLSR= ∼1000 to 1100 km s −1 , respectively.However, the directions of the gradients are seen to be opposite: the HCN gradient appears increasing towards north-west with red-shifted by ∼ 100 km s −1 , while the HCO + gradient decreases westward with blue-shifted by HCO + 100 km s −1 .The latter seems to trace outflowing materials in the local circumnuclear medium that would be with the velocity distribution of the H2O maser emission imaged at C with milliarcsec VLBI observations as discussed below.However, there is no straightforward interpretation for this discrepancy except for the possibility that the HCN samples a much larger emission component.
Figure 6 (lower) shows the second moment maps for the two molecular emissions.In the figures, we find a high velocity dispersion region with a velocity dispersion of σv = ∼ 30-40 km s −1 in HCN and σv = ∼30-60 km s −1 in HCO + .The HCO + dispersion also shows a small gradient from nearly south to north along the assumed trajectory of the jet.The high-dispersion region in HCO + appears offset about 0.05" or 3pc north of the center of C, and the high-dispersion regions in both HCN and HCO + are located at the edges of the line emission regions.This may indicate that the jet-ISM interaction creates a cavity that forces gases to accumulate at the edges of the gaseous regions.The difference between the optical and radio velocity conventions is ≈ 5 km s −1 .

Systematic velocity shift of the off-nuclear maser
Figure 8 shows time-series of the centre velocity of the offnuclear maser at six epochs spanning from 1987 to 2022 covering a period of 35 years.The values of the velocities at each epoch are taken from H2O maser spectra in the literature listed in Fig. 8 caption.It should be noted that the flux density of the off-nuclear masers are very variable and that the maser features at C at around VLSR=∼980 km s −1 were not always distinctly seen in the single-dish spectra (e.g., Braatz et al. 2003).Despite the fact that the measured velocity-shift shows such ambiguities, the plot does suggest a systematic velocity shift of about 0.85 km s −1 yr −1 in velocity in time towards the blue.
Figure 9 shows the distribution of the H2O maser spots at component C obtained by VLBI that is superposed on the HCO + (3-2) emission in Figure 5, assuming that the centre of the maser distribution largely corresponds to that of the HCO + (3-2) ring-like structure.The maser image has been obtained with a high-sensitivity array consisting of the VLBA, the phased-VLA, and the Effelsberg 100-m telescope on 2000 February 23-24 (Morishima et al. 2023).This figure places the maser component structure around the cavity found in HCO + (3-2), although there are no absolute coordinates registered for the maser distribution map presented as compared with the HCO + map in Morishima et al. (2023).Note that the 22 GHz position of component C (marked by a cross in Figure 5) lies nearly south of the group of the maser spots.
Indeed, the overall distribution of the masers at component C shows a ring-like structure with a hole or cavity at its centre, which may indicate that the presence of a strong shock in the jet-ISM interaction causes a ring-like HCO + emission structure.The blue-shifted maser features spanning VLSR=900-1100 km s −1 depicted in Figure 9 provide evidence that the shock front between the jet and the intervening molecular gas is steadily moving towards the observer.(1996), Nakai et al. (1995), Gallimore et al. (2001), Braatz et al. (2003).and this article.The horizontal axis is time scaled in year.
The enhanced line intensity ratio of the HCN (3-2) and HCO + (3-2) lines at C (1.35 in Table 2) could be explained under conditions of T k ≥ 300 K, nH 2 > ∼ 10 8 cm −3 if we take the molecular abundance ratio of HCN to HCO + to be about 2 (Fig. 10).Enhancement of the HCN to HCO + abundance ratio by a factor of three or even larger than 10 has indeed been found in nuclear AGN environments, although this may not be representative for the off-nuclear region C in NGC 1068 (e.g.Izumi et al. 2016).On the other hand, studies of the molecular abundance ratio in Ultra-luminous infrared galaxies (ULIRGs) show that the HCN to HCO + flux ratio also increases with changes of the HCN/HCO + abundance ratio as a function of kinetic temperature and hydrogen density (Baan, Loenen, & Spaans 2010;Imanishi et al. 2023).Similar conditions are likely to prevail in Region C as well.

Non-detection of the sub-mm maser and continuum emission
Figure 7 shows that the submillimetre continuum emission at 266 GHz towards the nuclear region of the galaxy, in which the Component C is peaked north of the nuclear continuum peak S1(N).The Spectral Energy Distribution of the galaxy suggests that the continuum at 266 GHz is dominated by dust emission (using the photometric data points of NGC 1068 from NED) and the continuum component traces the dust emission from foreground material and heated by the obscured active nucleus.
Water maser emission at both 183 and 321 GHz would serve as a further diagnostic of the local environments but these emissions have not been detected towards the nuclear region and component C in NGC 1068 (Hagiwara et al. 2016;Pesce, Braatz, & Impellizzeri 2016).The energy level of H2O in the 183 GHz transition (Eu/k=205 K) is lower than those of the 22 GHz (644 K) and 321 GHz (1862 K) transitions.Assuming that emissions in these higher transitions also result from maser amplification of the background dust emission by fore-ground material, recent ALMA observations at ∼0.6" angular resolution have not detected the 183 GHz maser transition at a 5σ upper limit of 37 mJy above a detected background continuum flux of 128 mJy arcsec −2 (Pesce et al. 2023).Considering the small ratio of the upper limit of the maser flux and the continuum, low-gain amplification could indeed result in observable maser emission.

SUMMARY
MERLIN observation of the 22 GHz H2O maser emission in NGC 1068 at ∼ 20 mas angular resolution has been conducted to resolve the maser and to understand the kinematics of the dense molecular gas at the shock front between the radio jet and intervening gas in the galaxy.The nuclear masers at blueshifted and systemic velocities were detected at the location of the 22 GHz continuum nucleus of the galaxy within uncertainties.Only a minor maser peak was seen at VLSR= 980.4 km s −1 at the known off-nuclear maser position at component C, which would be consistent with the earlier results obtained by the VLA in 1983 and 1987.This maser may have faded during our observing period in 2002.
Molecular emission lines of HCO + at 257 GHz and HCN at 255 GHz show an enhanced dispersion at C and weak velocity gradients in the roughly southeast to northwest direction.However, the direction of the velocity gradients of HCO + and HCN is almost opposite, which may suggests that each of the emission lines probe different molecular structures.The HCO + velocity gradient is largely consistent with the weak velocity gradient traced by the 22 GHz H2O masers at component C as seen by VLBI results at mas resolution.
Analysis of published maser spectra shows that the velocity of the off-nuclear masers has shifted towards the blue during the 35 years covering six observing epochs (Fig. 8).Since component C results from the shock front between the jet and the ambient molecular materials, this velocity drift towards the observer confirms that the jet points in front of the plane of the sky.Thus, the blue-shifted velocity of both the local HCO + emission at C and the off-nuclear H2O maser probe the jet-ISM interaction region in the nuclear outflow.
The ring-like structure imaged both at high resolution in the H2O maser and HCO + (3-2) molecular gas emission may suggest an shock-driven (cylindrical) expansion of the dense gas triggered by the heating from the decelerating shock in the radio jet.The 22 GHz off-nuclear H2O maser components trace velocity coherent column density regions at the edges of this shock-driven expansion.
The non-LTE radiative transfer model calculation explains the observed molecular line intensity ratios obtained by the sub-millimeter ALMA observations.The results of our calculations using RADEX are largely consistent with conditions where 22 GHz H2O maser excitation occurs.Thus, the data obtained from ALMA enabled us to diagnose the gas conditions required for excitation of sub-mm molecular line as well as for the H2O maser emission.
Further observations at higher angular resolution using interferometry with VLBI and ALMA would reveal more details of the gas dynamics and conditions at component C.  (n H 2 in cm −3 ) for three different kinetic temperatures: T kin =100, 300, 500, and 700 K, assuming the cosmic microwave background temperature(T bg )=2.73 K, hydrogen column density(N H ) = 10 13 cm −2 , and a line velocity-width(∆V)=100 km s −1 .(Right): The HCN (3-2)/HCO + (3-2) integrated flux density ratio as a function of n H 2 for T kin =100, 300, 500, and 700 K, assuming the HCN to HCO + molecular abundance ratio of 2. For other parameters, the same values as those in the left figure are adopted.The results in these plots are calculated using the RADEX program (van der Tak et al. 2007).

Figure 1 .
Figure 1.MERLIN 5 GHz continuum contour map by Gallimore, Baum, & O'Dea (2004) overlaid the ALMA HCO (3-2) total intensity map appearing in Figure 5.The four major radio components NE,C,N(S1),and S2 are indicated in on the map.Location B, C, and N are HCO + and HCN emission peaks defined in Figure 5.The synthesized beams of MERLIN (smaller) and ALMA (larger) are plotted at the bottom left.

FluxFigure 3 .Figure 4 .
Figure 3. Spectra of the 22 GHz H 2 O maser with Gaussian weighting, obtained with the MERLIN.These spectra show the nuclear masers towards S1 (N) in the blue-shifted velocity range (top) and those in the systemic velocity range (middle).A vertical bar indicates the systemic velocity of the galaxy.A spectrum of H 2 O maser towards the radio jet component C (bottom) shows a few minor peaks (denoted by a horizontal bar) centred at V LSR = 980.4km s −1 .

Figure 6 .
Figure 6.Moment maps in HCN (3-2) and HCO + (3-2) towards the nuclear region of NGC 1068, obtained from the ALMA Cycle 4 observations.Mean velocity (first moment) maps (upper), and velocity dispersion (second moment) maps (lower) in HCN (3-2) and HCO + (3-2) are presented.A 22 GHz radio continuum peak position of component C is marked by a cross in each pannel.The synthesized beam sizes (∼0.04") are shown in the bottom left of each panel.In these maps, the optical convention for Doppler velocities are adopted.The difference between the optical and radio velocity conventions is ≈ 5 km s −1 .

Figure 9 .
Figure 9. (Lef t:)The off-nuclear maser spots superposed on the HCO + (3-2) total intensity map (Figure 5) (Sudou, H., private communication).The picture assumes that the centre of the maser distribution corresponds approximately with the centre of the HCO + (3-2) map having a hole or a cavity in the middle.The 22 GHz radio peak position measured in component C measured by VLA is marked by a cross (Mutie, Beswick et al. in preparation).(Right:) Zoom-up map of the off-nuclear maser spots obtained by VLBI(Morishima et al. 2023).The V LSR =980 km s −1 off-nuclear maser feature in Fig.4could be found in a group of the features lying at V LSR =901-1000 km s −1 (green squares).

Table 1 .
Positions of radio continuum and water maser emissions in NGC 1068.
a Position errors.The errors in Dec are larger due to the low declination of the galaxy.b5-GHznuclearcontinuum position and errors are from Muxlow et al. (1996).cMeasuredat22 GHz in 2015 by VLA (Mutie, Beswick et al. in preparation).dTentativedetectionTable2.HCO + and HCN Line integrated intensity (in Jy km s −1 ) ratios at Components A, B, C, and N are listed.*The HCO + (4-3) emission data from Figure5 + (3-2) at component C show values that are very different from those at components A and B in Figure 1.A non-LTE radiative transfer calculation based on the RADEX program (van der Tak et al. 2007) indicates that the observed integrated flux ratio of HCO + (3-2) to HCO + (4-3) (0.87) in Table 2 can be explained by a hydrogen number density (nH 2 ) of ≈10 6 cm −3

Table 3 .
Gallimore et al. (2001) of the off-nuclear masers as a function of time are presented.The relative velocities are estimated from the difference between the systemic velocity of the galaxy and the centre velocity of the maser emission at each epoch.The value at the 1996.0epoch is from the integrated spectra spanning 1995-1998 as stated inGallimore et al. (2001).Data points appearing in Figure8are from this table.