ALMA captures feeding and feedback from the active galactic nucleus in NGC613

TL;DR

ALMA observations of NGC613 reveal complex gas dynamics, including nuclear spirals and outflows, indicating active fueling and feedback processes influenced by the central black hole and past AGN activity.

Contribution

This study provides high-resolution ALMA data on gas morphology and kinematics in NGC613, highlighting nuclear inflows and outflows driven by AGN activity and gravitational torques.

Findings

Detection of a nuclear spiral and circumnuclear ring in CO emission.

Identification of a molecular outflow with high energetics.

Evidence of efficient gas inflow towards the central black hole.

Abstract

We report ALMA observations of CO(3-2) emission in the Seyfert galaxy NGC613, at a spatial resolution of 17pc, as part of our NUclei of GAlaxies sample. Our aim is to investigate the morphology and dynamics of the gas inside the central kpc, and to probe nuclear fueling and feedback phenomena. The morphology of CO(3-2) line emission reveals a 2-arm trailing nuclear spiral at $r\lesssim$100pc and a circumnuclear ring at ~350pc radius, that is coincident with the star-forming ring seen in the optical images. The molecular gas in the galaxy disk is in a remarkably regular rotation, however, the kinematics in the nuclear region is very skewed. The nuclear spectrum of CO and dense gas tracers HCN(4-3), HCO+(4-3), and CS(7-6) show broad wings up to $\pm$300km/s, associated with a molecular outflow emanating from the nucleus (r~25pc). We derive a molecular outflow mass $M_{out}$=2x10$^6$M$_\odot$ and a mass outflow rate of $\dot{M}_{out}=$27$\rm M_\odot yr^{-1}$. The molecular outflow energetics exceed the values predicted by AGN feedback models: the kinetic power of the outflow corresponds to 20%L_AGN and the momentum rate is $\dot{M}_{out}v\sim400L_{AGN}/c$. The outflow is mainly boosted by the AGN through entrainment by the radio jet, but given the weak nuclear activity of NGC613, we might be witnessing a fossil outflow, resulted from a strong past AGN that now has already faded. The nuclear trailing spiral observed in CO emission is inside the ILR ring of the bar. We compute the gravitational torques exerted in the gas to estimate the efficiency of the angular momentum exchange. The gravity torques are negative from 25 to 100pc and the gas loses its angular momentum in a rotation period, providing evidence of a highly efficient inflow towards the center. This phenomenon shows that the massive central black hole has a significant dynamical influence on the gas, triggering its fueling.

Tables

Table 1. Table 1: Properties of NGC 613

Parameter	Value	Reference
$\alpha _{J2000}^{}{}_{}{}^a$	01h34m18.23s	(1)
$\delta _{J2000}^{}{}_{}{}^a$	-29d25m06.56s	(1)
Vhel	1481$\pm$5 km$s^{-1}$	(1)
RC3 Type	SB(rs)bc	(1)
Nuclear Activity	Sy/ Starburst	(1,2)
Inclination	41∘	(3)
Position Angle	120∘	(3)
Distanceb	17.2 Mpc	(1)
SFRc	5.3$M_{\odot }{\mathrm{yr}}^{-1}$	(1)
$M_{H\text{i}}$	4.7$\times {10}^9{M}_{\odot }$	(4)
$M_{\ast }$ - Stellar Mass	4.5$\times {10}^{10}{M}_{\odot }$	(5)
$L_{\mathrm{IR}}$	3$\times$10${}_{}{}^{10}L_{\odot }^{}$	(6)
$\alpha _{J2000}^{}{}_{}{}^d$	01h34m18.19s	(7)
$\delta _{J2000}^{}{}_{}{}^d$	-29d25m06.59s	(7)

Table 2. Table 2: Line fluxes

Line	$S_{\mathrm{CO}\left(3-2\right)}$	V	FWHM	$S_{\mathrm{peak}}^{}{}_{}{}^a$
	(Jy.km/s)	(km/s)	(km/s)	(Jy)
C1	541.1$\pm$54.7	-126.3$\pm$1.7	95.0$\pm$3.6	5.4
C2	654.0$\pm$90.7	5.2$\pm$5.0	175.5$\pm$20.8	3.5
C3	109.1$\pm$27.7	146.2$\pm$2.8	68.0$\pm$8.4	1.5

Table 3. Table 3: Line ratios: R HCN / HCO + HCN superscript HCO {}_{\rm HCN/HCO^{+}} and R HCN/CS

Region	R${}_{\mathrm{HCN}/{\mathrm{HCO}}^{+}}$	RHCN/CS
AGN	1.76$\pm$0.26	7.95$\pm$1.19
Clump (3$\sigma$)	0.23$\pm$0.03	3.6$\pm$0.5
Clump (5$\sigma$)	0.034$\pm$0.005	$>$3.7$\pm$0.6

Table 4. Table 4: Gaussian fit in the nuclear spectrum

Component	$S_{\mathrm{CO}}$	Position	FWHM	$S_{\mathrm{peak}}$
	(Jy.km/s)	(km/s)	(km/s)	(mJy)
Corea	68.5 $\pm$ 1.1	-11.8 $\pm$ 0.4	107.2 $\pm$ 0.9	600

Equations

$$\displaystyle v(R,\Psi)=v_{sys}+\leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\ \leavevmode\nobreak\$$

$$\frac{ARcos(\Psi -{\Psi }_0)sin(\theta )co{s}^p(\theta )}{{\left\{R^2\left[si{n}^2(\Psi -{\Psi }_0)+co{s}^2(\theta )co{s}^2(\Psi -{\Psi }_0)\right]+c^{2}co{s}^2(\theta )\right\}}^{p/2}}$$

$${L_{CO}}^{\prime }(K.km/s/p{c}^2)=3.25\times 10^7\frac{S_{CO}\Delta V}{1+z}{\left(\frac{D_L}{{\nu }_{rest}}\right)}^2$$

$${\dot{M}}_{out}=3v_{out}\left(M_{out}/R_{out}\right)$$

$${\dot{M}}_{out}=v_{out}\left(M_{out}/R_{out}\right)$$

$$\log ({\dot{M}}_{out})=1.14\log \left(0.52\frac{SFR}{{\mathrm{M}}_{\odot }\mathrm{y}{\mathrm{r}}^{-1}}+0.51\frac{L_{AGN}}{10^{43}erg.{\mathrm{s}}^{-1}}\right)$$

$$-0.41\log \left(\frac{M_{\ast }}{10^{11}{\mathrm{M}}_{\odot }}\right)$$

$$\Phi (R,\theta )={\Phi }_0(R)+\sum _m{\Phi }_m(R)\cos (m\theta -{\varphi }_m(R))$$

$$t(R)=\frac{{\int }_{\theta }\Sigma (x,y)\times (x\text{leavevmode}{F}_y-y\text{leavevmode}{F}_x)}{{\int }_{\theta }\Sigma (x,y)}$$

Full text

1 Introduction

The energy of active galactic nuclei (AGN) is well interpreted as due to gas accretion onto the supermassive black hole (SMBH) (Antonucci 1993). Gas inflows into the center of galaxies can fuel the SMBH and the energy input by the AGN can trigger subsequent feedback. The feedback can in turn regulate the SMBH growth and suppress star formation (e.g. Croton et al. 2006; Sijacki et al. 2007). Feeding and feedback are key processes to understand the co-evolution of black holes (BH) and their host galaxies, which is now well established by the tight M-$\sigma$ relation (e.g. Magorrian et al. 1998; Gültekin et al. 2009; McConnell & Ma 2013). It is important to study the efficiency of angular momentum transport in galaxy disks in order to understand how the star formation and nuclear activity are fueled and what are the timescales involved, since both feeding processes rely on a common cold gas supply, but in different periods of time ($\sim$105 yr for BH growth and $\sim$107-9 yr for star formation, García-Burillo 2016). These time scales are related to the mechanisms that drive the gas from galactic scales ($\sim$10 kpc) to nuclear scales (a few pc), through removal of angular momentum; large non-axisymmetric perturbations, such as bars or spirals, can do the job, but there is not yet identified a unique physical process associated with inward transport of gas in galaxy disks.

On large scales, cosmological simulations show that mergers and galaxy interactions are able to produce strong non-axisymmetries (e.g. Hopkins et al. 2006; Di Matteo et al. 2008). At kpc scales, bar instabilities, either internally driven by secular evolution or triggered by companions, can first feed a central starburst and then fuel the BH (García-Burillo et al. 2005). On the other hand, gas inflow is impeded by the inner Lindblad resonance (ILR), where the gas is trapped in a nuclear ring (see Piner et al. 1995; Regan & Teuben 2004). At few hundreds of pc scales, the “bars within bars” scenario (e.g. Shlosman et al. 1989), together with m=1 instabilities and nuclear warps (Schinnerer et al. 2000) take over as a dynamical mechanism (see e.g., Hunt et al. 2008). Observations of nearby low luminosity AGN (LLAGN) with the NUGA program have revealed smoking-gun evidence of AGN fueling in one third of the galaxies (García-Burillo & Combes 2012). This result suggests that galaxies alternate periods of fueling and starvation, and might be found in a feeding phase at 300 pc scales only one third of the time.

As we approach the center of galaxies, other mechanisms could contribute to the fueling: viscous torques, from dense gas in regions of large shear, or dynamical friction can drive massive clouds to the nucleus (e.g. Combes 2003; Jogee 2006). Simulations suggest that fueling involves a series of dynamical instabilities (m=2, m=1) at $\sim$10 pc scales, and also predict the formation of a thick gas disk similar to the putative torus invoked to explain obscured AGN (Hopkins & Quataert 2010; Hopkins et al. 2012). These fueling episodes are eventually quenched by either nuclear star formation winds or AGN feedback.

The recent discovery of many massive (a few 10$\rm{}^{7}\,M_{\odot}$) molecular outflows in nearby AGN (eg., Fischer et al. 2010; Feruglio et al. 2010, 2017; Alatalo et al. 2011; Sturm et al. 2011; Veilleux et al. 2013; Cicone et al. 2014; Sakamoto et al. 2014; García-Burillo et al. 2014; Dasyra & Combes 2012; Dasyra et al. 2014) has promoted the idea that winds may be major actors in sweeping gas out of galaxies. It has been already established that the mass outflow rates increase with the AGN luminosity, supporting the idea of a luminous AGN pushing away the surrounding gas through a fast wind. Observational works (Cicone et al. 2014; Fiore et al. 2017; Fluetsch et al. 2019) have shown that the molecular outflow properties are correlated with the AGN luminosity, where the outflow kinetic power corresponds to about 5%$\rm L_{AGN}$ and the momentum rate is $\sim$20$\rm L_{AGN}$/c, in agreement with theoretical models of AGN feedback (Faucher-Giguère & Quataert 2012; Zubovas & King 2012, 2014). Outflows have been traced for a long time in ionized or atomic gas (Rupke et al. 2005a; Riffel & Storchi-Bergmann 2011), making it now possible to compare the different gas phases. Carniani et al. (2015) found that ionised gas only traces a small fraction of the total gas mass, suggesting that the molecular phase dominates the outflow mass. This trend is also found by Fiore et al. (2017), but the ratio between molecular to ionised mass outflow rates is reduced at the highest AGN bolometric luminosities.

Probing AGN feeding and feedback phenomena through the kinematic and morphology of the gas inside the central kpc has only recently been possible due to the unprecedented Atacama Large Millimeter/submillimeter Array (ALMA) spatial resolution and sensitivity. Evidence of AGN feeding was found in NGC 1566, where a molecular trailing spiral structure from 50 to 300 pc was detected with ALMA Cycle 0 observations, and according to its negative gravity torques, is contributing to fuel the central BH (Combes et al. 2014). Also with Cycle 0 observations, a molecular outflow is also seen a the LLAGN in the Seyfert 2 NGC 1433. It is the least massive molecular outflow ($\rm\sim 4\times 10^{6}\,M_{\odot}$) ever detected around galaxy nuclei (Combes et al. 2013). A fast and collimated outflow has been detected in HCN(1-0) and CO(1-0) emission in the nucleus of Arp 220, extending up to 120 pc and reaching velocities up to $\pm$840 km/s (Barcos-Muñoz et al. 2018).

In the prototypical Seyfert 2 NGC 1068, a clear molecular ouflow has also been detected, entrained by the AGN radio jets (Krips et al. 2011; García-Burillo et al. 2014). NGC 1068 is also the first case to resolve the molecular torus, using the continuum and the CO(6-5), HCN(3-2) and HCO+(3- 2) emission lines observed with ALMA (Gallimore et al. 2016; García-Burillo et al. 2016; Imanishi et al. 2016). The dynamics of the molecular gas in the NGC 1068 torus revealed strong non-circular motions and enhanced turbulence superposed on a slow rotation pattern of the disk. The AGN is clearly off-center with respect to the torus, implying an m=1 perturbation (García-Burillo et al. 2016). Recently, we have reported observations of molecular tori around massive BHs in a sample of 7 nearby LLAGN (Seyfert/LINER), at the unprecedented spatial resolution of 3-10 pc (Combes et al. 2019, , hereafter Paper I). The ALMA observations bring a wealth of new information on the decoupled molecular tori, which are found to have radii ranging from 6 to 27 pc, unaligned with the orientation of the host galaxy and frequently slightly off-centered to the AGN position. The kinematics of the gas inside the sphere of influence (SoI) of the central BH also allowed us to estimate the BH masses ($\rm M_{BH}\sim 10^{7-8}\,M_{\odot}$).

In this paper, we present the combined ALMA cycle 3 and 4 observations in the CO(3-2) line of the Seyfert galaxy NGC 613, with a spatial resolution of 17 pc. These observations were part of the sample presented in Paper I, but the data analyzed here have more sensitivity in order to detect faint broad wings usually associated to outflows. This object presents a nuclear trailing spiral and we discovered a molecular outflow in its nuclear region. Therefore, NGC 613 is a special case to study the complexity of fuelling and feedback mechanisms in AGN, and the detailed analysis of the gas flow cycle in AGN. In the next subsection, all relevant characteristics of NGC 613 are described. Observations are detailed in Section 2 and results in Section 3. The properties of the nuclear molecular outflow discovered in the very center of NGC 613 are discussed in Section 4. The interpretation of inflowing gas in term of gravitational torques is discussed in Section 5, and conclusions are drawn in Section 6.

1.1 NGC 613

NGC 613 is a nearby barred SB(rs)bc galaxy (de Vaucouleurs et al. 1991) at a distance of 17.2 Mpc (1″=83 pc). It has a large-scale bar of $\rm r_{bar}\sim$90″with a position angle of 127∘ and a secondary nuclear bar with PA=122∘ (Jungwiert et al. 1997; Seigar et al. 2018). Judging from NED, NGC 613 is only moderately inclined, with inclination $\sim\,38^{\circ}$ (see also Section 3.4). Prominent dust lanes are visible along the large-scale bar and the presence of multiple spirals arms gives it a “tentacular” appearance. NGC 613 has a typical inner Lindblad resonance (ILR) nuclear ring, of radius $\sim$3.5″(300 pc), just inside the two characteristic leading dust lanes of the bar (Fig 1).

It hosts a LLAGN, that first was classified as a composite Seyfert/Hii object by Veron-Cetty & Veron (1986) based on its low-resolution optical spectrum, and later confirmed through MIR spectroscopy (Goulding & Alexander 2009) and X-ray observations using the ROSAT and XMM-Newton (Liu & Bregman 2005; Castangia et al. 2013, respectively). Water masers have been detected in the nucleus by Kondratko et al. (2006).

NGC 613 shows clear evidence of star formation, shock excitation and AGN activity (Davies et al. 2017). Radio continuum observations show evidence for a collimated jet from the AGN and a nuclear ring with a moderate inclination of i$\sim$55∘ (Hummel et al. 1987; Hummel & Jorsater 1992). The presence of the outflow has already been suggested by the high velocity dispersion of the [Feii] line along the radio jet (Falcón-Barroso et al. 2014). The ring-like structure in Br$\gamma$ emission in NGC 613, comprising “hot spots” of current massive star formation (Böker et al. 2008; Falcón-Barroso et al. 2014), indicates an ongoing star-forming episode. We collect the main properties of NGC 613 in Table LABEL:tab:prop.

2 Observations

We report the combined ALMA Cycle 3 and Cycle 4 observations of CO(3-2), CS(7-6), HCN(4-3) and HCO+(4-3) and continuum in band 7, at rest frame frequencies $\nu_{rest}$ of 345.8, 342.9, 354.5, 356.7 and 350 GHz, respectively. The observations of the NUGA sample are described in Paper I; here we include additional details for NGC 613.

In Cycle 3, NGC 613 was observed (project ID: #2015.1.00404.S, PI F. Combes) simultaneously in CO(3-2), HCO+(4-3), HCN(4-3) for both the compact (TC, baselines 15 to 630m) and the extended (TE, baselines 15 to 1400m) configurations. The largest recoverable angular scale corresponding to the shortest baseline is about 12″. The TC configuration was observed in April 2016 with 40 antennas and an integration time, including calibration and overheads, of 20 minutes, providing a synthesized beam of $\sim$0$\aas@@fstack{\prime\prime}$38. The TE configuration was observed in August 2016 with 41 antennas, total integration of 40 minutes and a synthesised beam of $\sim$0$\aas@@fstack{\prime\prime}$14. The correlator setup, designed to simultaneously observe three lines, provided a velocity range of 1600 km/s for each line, but did not center the HCO+(4-3) and HCN(4-3) lines (200 km/s on one side and 1400 km/s on the other, which is adequate for a nearly face-on galaxy), and 1800 MHz bandwidth in the continuum.

The Cycle 4 observation were carried out in November 2016 and July 2017 (project ID: #2016.1.00296.S, PI F. Combes) at higher spatial resolution ($\sim$6.5 pc) aiming at resolving the molecular torus. The tuning configuration of Band 7 was in the CO(3-2), HCO+(4-3) and continuum, to avoid a restricted velocity range in the expected broader spectral lines towards the nucleus. The correlator setup was selected to center the CO(3-2) and the HCO+ lines in the 2 GHz bandwidth. The compact configuration (TM2, baselines 19 to 500m) was observed with 44 antennas for an integration time of 14 minutes and a synthesised beam of 0$\aas@@fstack{\prime\prime}$31 and the extended (TM1, baselines 19 to 3100 m) with 43 antennas for 1.2 hours and a synthesised beam of $\sim$0$\aas@@fstack{\prime\prime}$08.

The observations phase center was that of the nucleus (Table LABEL:tab:prop), with a single pointing covering a Field of View (FoV) of 18″. The galaxy was observed in dual polarization mode with 1.875 GHz total bandwidth per spectral window, and a channel spacing of 0.488 MHz corresponding to $\sim$0.8 km/s, after Hanning smoothing. The flux calibration was done with radio quasars close to the position in the sky of the target, which are regularly monitored at ALMA, and resulted in 10% accuracy.

The data from Cycle 3 and 4 were calibrated and concatenated with the CASA software (version from 4.5.3 to 4.7.2, (McMullin et al. 2007), and the imaging and cleaning were performed with the GILDAS software (Guilloteau & Lucas 2000). In Paper I, we have used only the most extended configurations (TM1+TE), but in this work we have combined all the configurations to improve the sensitivity. The analysis were made in GILDAS together with python packages (radio-astro-tools, APLpy, PySpecKit Ginsburg et al. 2015; Robitaille & Bressert 2012; Ginsburg & Mirocha 2011). The CLEANing was performed using the Hogbom method and a natural weighting, in order to achieve the best sensitivity, resulting in a synthesised beam of 0$\aas@@fstack{\prime\prime}$21$\times$0$\aas@@fstack{\prime\prime}$19 for the concatenated data cube. The spectral line maps were obtained after subtraction of the continuum in the $uv$-plane using the tasks uv_continuum and uv_subtract. The data cubes were then smoothed to 10 km/s (11.5 MHz). The total integration time provided an rms of 87$\mu$Jy/beam in the continuum, and in the line channel maps 0.43 mJy/beam per channel of 10 km/s (corresponding to $\sim$1K, at the obtained spatial resolution). The final maps were corrected for primary beam attenuation. Very little CO(3-2) emission was detected outside the full-width half-power (FWHP) primary beam.

Because of lack of very short baselines ($<$15m), extended emission was filtered out at scales larger than 12″  in each channel map. Since the velocity gradients are high in galaxy nuclei, this does not affect significantly the line measurements: indeed, the size in each velocity channel is not expected to be extended.

3 Results

3.1 Continuum emission

Previous ALMA band 3 and 7 observations by Miyamoto et al. (2017) detect continuum emission from both the circumnuclear disk (CND) and the star-forming ring (250$\rm<r<$340 pc). At 95 GHz with a $\sim$0$\aas@@fstack{\prime\prime}$6 resolution, they find a continuum jet with a PA=20∘, which corresponds to the 4.9 GHz and 14.9 GHz jets (Hummel & Jorsater 1992), close to the minor axis of the ring. In the nucleus, the negative spectral index, $\alpha\sim$-0.6, is compatible with synchrotron emission, with a small fraction of free-free, while the index $\alpha\sim-0.2$ along the star-forming ring can be from free-free emission (Miyamoto et al. 2017).

At our resolution of 0$\aas@@fstack{\prime\prime}$2 ($\sim 17$ pc), the central continuum is resolved at 350 GHz, with some compact emission along the star-forming ring, as display in Figure 2. The $\sim$2.2 mJy peak emission is detected at 25$\sigma$ significance. We determine the peak of the continuum emission by fitting a circular Gaussian source in the $uv$-plane using the GILDAS uv_fit task. The fitted results in the central continuum emission for the flux is 2.4$\pm$0.1 mJy and for the RA and DEC relative do the phase center are $\Delta$RA=-0$\aas@@fstack{\prime\prime}$587 and $\Delta$DEC=-0$\aas@@fstack{\prime\prime}$03219, with a relative uncertainty of $\pm$0$\aas@@fstack{\prime\prime}$003. These values are listed as reference of the new adopted center and AGN position in Table LABEL:tab:prop. Within the error bar, the AGN position is consistent with the positions derived by Miyamoto et al. (2017) and from X-ray observations (Liu & Bregman 2005).

3.2 Molecular gas distribution and morphology

Figure 3 displays the CO(3-2) channel maps, with a velocity range of 450 km/s and a velocity resolution of 10 km/s. The channels show evidence of a regular velocity field in a ring at a radius $\sim$3.5″(300 pc), with two winding arms structure coming from the NW and SE directions. These spiral arms coincide with the beginning of the dust lanes along the bar seen in the HST/F814W image (Figure 1): they are the contact points between the tangent dust lanes and the ring.

At small radii, there is a spiral structure in the center channels ($\pm$100 km/s) that can be more clearly seen in Figure 5. The 2-arm nuclear gas spiral at $\rm r\lesssim$100 pc is trailing toward the center, and it will be discussed further in Section 5. Additionally, the velocity distribution is perturbed for channels between $\pm$50-100 km/s for $\rm r\sim$150 pc, and the morphology shows evidence of a filamentary structure connecting the ring and the nuclear spiral. The main morphological features are show in the sketch of the galaxy in Figure 4.

We constructed the moment maps of the CO(3-2) line clipping the emission at $<$5$\rm\sigma_{rms}$. The integrated intensity (zero-moment) map in the left panel of Figure 5 shows that the CO emission follows the $\sim$300 pc star-forming circumnuclear ring. Miyamoto et al. (2017) have mapped the ring in CO(1-0) and CO(3-2) with ALMA at 0$\aas@@fstack{\prime\prime}$7 and 0$\aas@@fstack{\prime\prime}$4 respectively, and found a clumpy ring, globally regular, but with spots of active and efficient star formation. In our maps at higher resolution, we find that the molecular emission in the ring is clumpy and incomplete, and coincides with the same star forming clumps observed in Br $\gamma$ in the near-infrared (NIR) (see Falcón-Barroso et al. 2014, and Sect. 3.6). The CO(3-2) emission peak of 25 Jy.km/s/beam corresponds to the AGN position reported in Table LABEL:tab:prop. Within the CND, there is a clear trailing 2-arm spiral structure. The ring reveals two breaks into two winding spiral arms, at NW and SE.

We superposed in Figure 1 the CO(3-2) contours onto the HST maps in the F814W filter222The HST image was aligned to the ALMA astrometry, the peak emission in the HST image was recentered to the AGN position in Table LABEL:tab:prop.. It shows a remarkable similarity in morphology, the molecular ring seen in the CO emission coincides with the dusty nuclear ring in the HST image, and the winding arms are the beginning of the characteristic dust lanes along the bar. At the very center ($\lesssim$100 pc) though, the stellar and molecular morphologies are dissimilar.

In the middle panel of Figure 5, the intensity-weighted velocity (first-moment) map shows a clear rotation pattern in the galaxy plane, with velocities peaking between $\sim\pm$200 km/s from the systemic velocity ($v_{sys}$1481 km/s, see discussion below). The velocity distribution and morphology in the central 200 pc are more perturbed, due to the filamentary streams and the nuclear spiral. The NW winding arm is mostly blueshifted and the SE redshifted, indicating that rotation and possibly gas pile-up is taking place; this will be discussed further in Section 5.

Close to the AGN, the velocity dispersion is high ($\sigma\sim$130 km/s), as displayed in the right panel of Figure 5 (second-moment map). In the nuclear spiral the velocity dispersion ranges from 70$\sim$120 km/s and the average dispersion along the ring is $\sim$40 km/s, with more elevated values in the clumpy regions. Furthermore, we can distinguish a disturbance in the overdense region in the west part of the ring, with an increased dispersion $\gtrsim$150 km/s. This region also corresponds to an enhanced spot observed in [Feii] with SINFONI, suggesting a strongly shocked medium (see also Sect. 3.6).

3.3 CO luminosity and H2 mass

The mean intensity map is plotted in Fig. 5 (left). Since the galaxy is more extended than the primary beam, it is difficult to quantify the missing flux. We compare it to the central spectrum obtained with the 15-m single dish obtained with the Swedish-ESO Submillimeter Telescope (SEST) in CO(1-0) and CO(2-1) over a 43″  and 22″  FoV, respectively. In Figure 6, we display the total CO(3-2) spectrum integrated over the 18″FoV. Towards the central position, Bajaja et al. (1995) found a CO(2-1) spectrum peaking at T${}_{A}^{*}$= 200 mK with FWHM=300 km/s, yielding a total integrated flux of 1504 Jy km/s, in a beam of 22″. Their beam is very similar to our FoV of 18″. The flux comparison is relevant, since our FoV encompasses the entire nuclear ring, and the emission in this nuclear region corresponds to the strongest surface density at different wavelengths (Comerón et al. 2010; Ho et al. 2011; Li et al. 2011), as already discussed by Combes et al. (2014).

We assume a ratio of $\rm r_{31}=T_{3-2}/T_{1-0}$ of 0.82, typical for Seyfert galaxies (Mao et al. 2010) and a ratio $\rm r_{21}=T_{2-1}/T_{1-0}$ compatible with $1$, within the error bars. The latter is derived from the SEST CO(2-1)/CO(1-0) observations in the galaxy center, by convolving the beam of CO(2-1) to 43″, implying a higher CO excitation at the center of NGC 613. This is expected for thermalized excitation and a dense molecular medium. In that case, the CO(3-2) flux should be higher than the CO(2-1), as we could presume the flux $\rm S_{\nu}\propto\nu^{2}$ in the Rayleigh-Jeans approximation, for gas at temperature larger than 25K and density larger than 104 cm*-3*). Using these values, the expected CO(3-2) intensity is $\sim$2266 Jy.km/s in a 22″ beam. When integrated over the spectral range (FWHM$\sim$250km/s), the integrated emission in our ALMA FoV of 18″  shown in Figure 6, is 1307 Jy.km/s. Therefore, we should expect some missing flux by a factor up to $\sim$40-50%, taking into account the uncertainties of the $r_{31}$ and $r_{21}$ ratios. Hence, we find a molecular mass of 5.6$\times$108M⊙ in our FoV, assuming thermally excited gas, and a Milky-Way like CO-to-H2 conversion factor, of 2$\times$1020cm*-2*/(K.km/s) (e.g. Bolatto et al. 2013).

In comparison, the SEST CO(1-0) observations of Bajaja et al. (1995) give a total molecular mass of 3.8$\times$109 M⊙ integrated over 33 pointing positions covering $\sim$120″along the galaxy, and in the central 43″ beam yields to $\rm M_{H2}\approx$1.5$\times$109 M⊙. In the 22″ beam, the SEST CO(2-1) spectrum, together with the CO(2-1)/CO(1-0) ratio of $1$, gives a mass of 1.2$\times$109 M⊙.

The total CO(3-2) emission line profile integrated over the observed map (FoV of 18″) is shown in Figure 6. We decomposed the spectrum in three components, C1, C2 and C3, and the results of the Gaussian fits for each component are displayed in Table 2. The total flux is $\rm S_{CO(3-2)}=1307\pm 121$ Jy.km/s.

3.4 CO(3-2) kinematics

In Figure 7 we show the rotation velocities deduced from the CO kinematics and the H$\alpha$ rotation curve taken from Burbidge et al. (1964). As already pointed out, the dominant feature in velocity field of the molecular gas appears to be due to circular rotation in the disk (middle panel of Fig. 5), and is consistent with the H$\alpha$ kinematics. We find a good agreement with the PA and inclination from optical studies, in the range of PA=111$\sim$124∘ and i=36$\sim$47∘ (Burbidge et al. 1964; Blackman 1981; de Vaucouleurs et al. 1991), and therefore we adopted the values of PA=120∘ and i=41∘, listed in Table LABEL:tab:prop. We assume a simple model for the rotation curve, proposed by Bertola et al. (1991), assuming the gas is on circular orbits in a plane, $v_{c}=Ar/(r^{2}+c^{2})^{p/2}$, where $A$, $c$, and $p$ are parameters of the model, and for $p=1$ the velocity curve is asymptotically flat and $p=3/2$ the system has a finite total mass, therefore we expect $1\leq p\leq 3/2$. Figure 7 shows the result of fitting the radially averaged velocities to this model; the dotted lines represent the best fit for circular velocity, $v_{c}$.

We can refine the above fit of the radially averaged velocities by fitting the entire velocity field with the same model by Bertola et al. (1991). The observed radial velocity at a position $\rm(R,\Psi)$ on the plane of the sky can be described as:

[TABLE]

where $\theta$ is the inclination of the disk (with $\theta$ = 0 for a face-on disk), $\Psi_{0}$ is the position angle of the line of nodes, $v_{sys}$ is the systemic velocity and $R$ is the radius. We used the tilted-ring model (Rogstad et al. 1974), which consists in dividing the velocity field in concentric rings in radii $\Delta r$ and each ring is allowed to have an arbitrary $v_{c}$, $i$ and PA. For each radius, we can independently fit the parameters of Equation 1 to the observed velocity field.

We show the results of the tilted-ring fitting to the velocity map in Figure 8. We adopted a $\Delta r$=0$\aas@@fstack{\prime\prime}$3, that corresponds to the deprojected resolution of our observations in the galaxy plane. In the right panel, we display the residuals after subtracting the Bertola et al. (1991) model to the velocity field. As can be seen, the model represents quite well the observed velocity field, with no significant amplitudes in the residuals along the galaxy disk, except in the west part of the ring, where there is an important contribution from non-circular motions. This region coincides with the contact point between the ring and the SE winding arm, and it is also probably perturbed by shocks, as suggested by the high velocity dispersions in the molecular gas and an enhancement in the [Feii] emission (Fig. 13). This non-circular motions along the minor axis and on the winding spiral indicate streaming motions associated with inflow, if we assume trailing perturbations and that the north side is the far side of the galaxy, as the NW arm is blueshifted and the SE arm is redshifted.

An additional method was used to derive the CO kinematics using the “3D-Based Analysis of Rotating Objects from Line Observations” ( 3DBAROLO) software by Di Teodoro & Fraternali (2015). 3DBAROLO performs a 3D tilted-ring modeling of the emission line data-cubes to derive the parameters that better describe the kinematics of the data. We ran 3DBAROLO on the CO(3-2) data-cube in order to investigate non circular motions, since the code allows us to infer radial velocities in the fit of the rotation curves. We have performed several tests running the code, varying the fixed and free parameters of the disk model, and the results that better reproduce the observed velocity field are found when fixing the PA, inclination and central position to 120∘, 41∘ and AGN position, respectively. The best fit reveals radial components of order $\rm v_{rad}\sim$20 km/s in the nuclear region and $\rm v_{rad}\sim$20–100 km/s from the end of the circumnuclear ring at 4″up to r$\sim$7″, corresponding to the streaming motions of the winding arms. Overall, we find that in the case of high-resolution ALMA observations, the results using 3DBAROLO are quite coherent with the 2D approach described above in the text.

The position-velocity diagrams (PVDs) along the major (PA=120∘) and minor axis (210∘) of NGC 613 are shown in Fig. 9. The best fit obtained with 3DBAROLO including radial velocity components is shown in dashed lines. We notice a highly skewed kinematics in the center, with velocities $\gtrsim$200 km/s, that cannot be described only by co-planar circular motions in the galaxy disk. Since the velocities in the very centre ($\lesssim$0.5″) strongly deviate from the rotation curve pattern, we believe this is a signature of an outflow emanating from the AGN. We discuss the detection and properties of the molecular outflow in Section 4.

3.5 Dense gas: HCO+, HCN and CS emission

In ALMA band 3, dense gas is detected in various lines HCN(1-0), HCO+(1-0) and CS(2-1), while SiO(2-1) was marginally detected at the edges of the radio jets, probably indicating the existence of shock regions related to the jets, as reported by Miyamoto et al. (2017). Along with CO(3-2), our band 7 observations detected the HCO+(4-3), HCN(4-3) and CS(7-6) emission lines. The corresponding maps are displayed in Figure 10, and the integrated spectra in Figure 11. CS(7-6) is mainly detected in the center of the galaxy, while for HCO+(4-3) and HCN(4-3), we detect stronger emission in the center but also some clumps along the star-forming ring. The dense gas tracers detected in the very center are interpreted to be a molecular torus, as discussed in Paper I. The HCN line is about twice brighter than the HCO+ line in the nuclear region, which is the typical value expected for AGN (e.g., Kohno 2005; Krips et al. 2008; Imanishi et al. 2016). The detection of these lines reveals the presence of dense gas, since the critical densities of the HCO$\rm{}^{+}(4-3)$, HCN(4-3) and CS(7-6) transitions are 2.6$\times$106, 1.4$\times$107 and 3.4$\times$106 cm*-3*, respectively.

As already mentioned, NGC 613 exhibits different ionization mechanisms. Recently, spatially resolved Baldwin, Phillips & Terlevich (BPT) diagrams (bpt81), can isolate the contributions from star formation, shock excitation and AGN activity using optical line ratios, as studied with the Siding Spring Observatory Wide-Field Spectrograph (WiFeS) by Davies et al. (2017) and European Southern Observatory Multi-unit Spectroscopic Explorer (MUSE) in Gadotti et al. (2019). Likewise, in the sub-millimeter domain, multi-line observations of higher J transitions are fundamental to derive the chemical conditions of the molecular gas and the heating mechanisms (Viti et al. 2014; Imanishi et al. 2018). One useful extinction-free energy diagnostic tool in the centers of galaxies is the sub-millimeter-HCN diagram (Fig. 12) proposed by Izumi et al. (2016). The diagram uses the HCN(4-3)/HCO+(4-3) and HCN(4-3)/CS(7-6) ratios to distinguish the dominant energy source exciting the molecular gas in galaxies, whether by AGN (XDR or X-ray dominated region) or star formation (PDR or photodissociation region). They suggest enhanced integrated intensity ratios in circumnuclear molecular gas around AGN compared to those in starburst galaxies (sub-millimeter HCN-enhancement).

Thanks to our high-resolution ALMA observations, we are able to disentangle the emission coming from the nuclear region within the spiral trailing feature observed in the central $\sim$100 pc and the contribution from a star-forming clump observed in all three molecular tracers at $\sim$250 pc from the nucleus. The clump is indicated as a circle in Figure 10. We measured the line intensity ratios R${}_{\rm HCN/HCO^{+}}$ and RHCN/CS in these two regions (CND/AGN, for a central aperture of 0$\aas@@fstack{\prime\prime}$3 and clump, listed in Table 3). For a 5$\sigma$ threshold, the clump is barely detected in CS(7-6) emission, and we present the line ratios for a 3$\sigma$ clump detection and a upper limit for the RHCN/CS.

The line ratios are plotted on the sub-millimeter diagram of Izumi et al. (2016), as displayed in Figure 12. We find that the CND region lies in the AGN-dominated part of the diagram, while the clump in the star forming ring of NGC 613 is indeed dominated by star formation. Ultimately, we do find that the nuclear region of NGC 613 presents line ratios that indicate excitation conditions typical of XDRs in the vicinity of AGN.

3.6 Comparison to the warm molecular and ionised gas

In order to compare the CO(3-2) morphology with the ionised material and the warm molecular gas, we superposed the CO contours onto the NIR maps of [Feii], Br$\gamma$ and H$\rm{}_{2}\lambda 2.12\mu m$ presented in Falcón-Barroso et al. (2014), shown in Figure 13. There is a remarkable resemblance between the ionised and warm molecular gas to the CO emission along the star forming ring. The position and ages of the hot spots in the ring suggest a “pearls on a string” scenario of evolution of star formation as proposed by Böker et al. (2008). In this scenario, star formation only occurs in particular overdense regions and the young clusters move along the ring, following the gas movement, and meanwhile age, resulting in an age gradient along the ring. The expected sequence of star formation was indeed observed in the southern part of the ring: the hottest stars are found near the contact point of the dust lanes, and then fewer hot stars are found along the ring (see Fig. 8 of Böker et al. 2008).

At the center, the nuclear spiral corresponds to the massive reservoir of the bright warm H2 and [Feii], while contrasting with the weak emission in Br$\gamma$. Indeed, as discussed by Falcón-Barroso et al. (2014), the high [Feii]/Br$\gamma$ ratio in the center indicates that excitation is dominated by shocks and photoionization in the nucleus, and follows the correlation between the strength of the [Feii] and 6 cm radio emission in Seyfert galaxies (Forbes & Ward 1993).

The high values of the ratio [Feii]/Br$\gamma$=17.7 in the nucleus of NGC 613, are not typical of starburst galaxies, where we expect the ratio in the range 0.5-2 (Colina et al. 2015) and the [Feii] emission originates in supernova-driven shocks. Indeed, the large ratio in the nucleus is similar to those found in AGN, indicating that the most likely mechanism for the production of [Feii] emission in is shock excitation from the radio jets and/or supernova remnants (SNRs), typical for Seyfert galaxies (Rodríguez-Ardila et al. 2004). In fact, X-ray emission, which is dominant in Seyferts, can penetrate deeply into atomic gas and create extended partly ionized regions where [Feii] can be formed. Models presented by Alonso-Herrero et al. (1997) show that X-rays are able to explain [Feii]/Br$\gamma$ ratios up to $\sim$20, in agreement with the values observed in NGC 613 nucleus.

Colina et al. (2015) developed a 2D diagnostic diagram using integral field spectrograph spectrograph data to characterize line emitting regions. The diagnostic uses the line ratios H2(1- 0)S(1)$\lambda$2.122 $\mu$m/Br$\gamma$ and[Fe ii] $\lambda$1.644$\mu$m/Br$\gamma$. By this method, they found that young star-forming regions, older supernova dominated regions, and the compact AGN dominated region occupy different areas in the line-ratio space. We show the NIR diagnostic diagram proposed by Colina et al. (2015) in Figure 14. We use the line emission listed in Tables 1 and 2 of Falcón-Barroso et al. (2014) for different apertures: one in the nucleus, 7 along the circumnuclear ring (spots 1 to 7) and 1 aperture between the ring and the nucleus (“spot 8”, see Fig.1 of Falcón-Barroso et al. 2014). Placing the line ratios for the different apertures in the diagrams, we note that all spots in the circumnuclear ring are located in the regions of young star formation or SNe-dominated stellar populations. The spot in the intermediate region has higher line ratios, and it is shifted into the compact AGN region. On the other hand, the nucleus of NGC 613 takes its place in the shock ionized LINER regime, where we expect H2/Br$\gamma$ ratios larger than 6 (Mazzalay et al. 2013; Riffel et al. 2013). As suggested by Falcón-Barroso et al. (2014), the enhancement of the H2 emission in the nucleus is possibly due to the interaction with the radio jet. The high value of H2/Br$\gamma$ measured in the nucleus of NGC 613 is consistent with a LLAGN Seyfert/LINER composite, which is strongly influenced from shock heating.

4 The molecular outflow

4.1 The CO(3-2) kinematics of the outflow

The PVDs along the major and minor axes of the galaxy shown in Fig. 9 illustrate the highly skewed kinematics in the central part of NGC 613. The nuclear region contains gas reaching velocities up to $\sim\pm$300 km/s in projection, which is much higher than the rest of the nuclear disk gas, as we can notice in the middle panel of Fig. 5.

An examination of the individual spectra at pixels around the AGN position reveals conspicuous blue and redshifted wings in all the spectra within a radius of $r\sim$0.3″. These broad line wings are characteristic of gas ejection out of equilibrium, in this case, an indication of a molecular outflow. The integrated spectrum extracted in a central circular aperture of 0.28″ ($\sim$23 pc) is shown in Figure 15. We can notice a bump in the emission around $\rm v\sim$400 km/s, which corresponds to the isotope H13CN(4-3).

One might question whether the outflow signature could arise by a central mass able to induce such a high rotation in the centre. If we assume that these high-velocity components are within the SoI, in a radius equivalent to our nuclear aperture of $\sim$0.3″=25 pc, or about r=38 pc in the galaxy plane, a massive black hole located in the centre should have a mass of at least $M_{BH}$=$\rm v^{2}$R/G for the rotational velocity in the galaxy plane $v$=460 km/s (corresponding to $\pm$300 km/s projected velocities), or MBH=1.9$\times$109 M⊙. This value is about 2 orders of magnitude higher than the values reported in the literature, e.g. MBH=7.4$\times$106 M⊙ derived by Davis et al. (2014) using the spiral pitch angle and MBH=4$\times$107 M⊙ using the central stellar velocity dispersion by van den Bosch (2016). In Paper I, we have derived a black hole mass of $M_{BH}=3.7\times 10^{7}M_{\odot}$ within the SoI of 50 pc, and for all the NUGA sample the values derived tend to follow the pseudo-bulge region in the M${}_{BH}-\sigma$ plane (Ho & Kim 2014).

Furthermore, if these high-velocity features were due to the rotation, they should not be observed along the minor axis of the galaxy; however, the PVDs in Figure 9 clearly show a gradient of the high-velocity emission along the minor axis that cannot be explain as due to co-planar rotation. Could these features be signature of inflowing gas? We cannot exclude a priori that the high-velocity components are due to a coplanar inflow, since the blueshifted gas is observed in the north and the redshifted gas is the south. If the far side of the galaxy is the north side, this gradient could be explained as an inflow. However, the deprojected velocities onto the galaxy disk would be about $v\sim$300/sin(i)$\sim$460 km/s. The order of magnitude of the co-planar inflow would be too large, and therefore we can exclude this hypothesis.

Additionally, in Figure 16 we show the contours for the blue and red wing emission, and we see that the contours overlap and the blue component arises in the northern part of the nucleus and the red in the south. Due to the small size of the outflow, we can barely resolve each wing contribution, however, there is an indication that they do not follow the rotation pattern of the mean velocity field. The direction of velocities are also opposite to what is found in the molecular torus (cf Paper I).

We compare the molecular to the radio emission observed with the Karl G. Jansky Very Large Array (VLA) at 4.86 GHz (Hummel & Jorsater 1992) in Figure 16. The VLA radio jet emission is shown in the right panel with the molecular outflow blue and red wings emission contours overlaid. The molecular outflow emission coincides with the central blob of the radio jet and appears to be aligned with the orientation of the radio jet at PA=12∘.

In order to derive conservative values for the flux related to the outflow in the broad emission, instead of fitting one Gaussian component for the “core” and one broad component for the outflow (including some low-velocity emission that might not be associated with the outflowing material), we have taken two different approaches. First, we fit a Gaussian to the nuclear spectrum to take into account the contribution of the main rotating disk (black line in Fig. 15). After subtracting the core contribution to the CO spectrum, we have the residuals, as shown by the gray line. We then integrated the contribution of the blue and red regions in the residual spectrum. The results of the fit of the main core and blue and red wings in the residuals are listed in Table 4. The derived molecular mass corresponding to the main disk component inside the radius of 23 pc is $\rm 4.8\times 10^{7}M_{\odot}$, which agrees with the mass of the 14 pc molecular torus of $\rm 3.9\times 10^{7}M_{\odot}$ found in Paper I (using the same conversion factor and $\rm r_{31}$ as in Paper I).

The second approach consists in creating moment maps only taking the velocity channels from -400 to -120 km/s for the blue component and from +120 km/s to 300 km/s for the red wing. We try to avoid the contribution from the H13CN by limiting the velocity channels up to 300 km/s. We display the blue and red wings contour maps in Figure 16, superposed to the intensity weighted velocity map of the original CO map, which represents the mean velocity pattern. The integrated fluxes corresponding to velocity intervals of the red and blue maps are also listed in Table 4. The peak temperatures of the blue and red wings represent $\sim$5% of the peak of the main core component, however they are still detected with a 50$\sigma$ significance in the case of the residuals wings.

The maximal velocities of the red and blue components are up to about $\pm$300 km/s in projection ($\sim$460 km/s if in the galaxy plane, $i$=41∘). Given their location near the nucleus, we tentatively interpret these high-velocity features as the two sides of an outflow. Globally, these features represent as much as $\lesssim$8% of the total molecular emission in the nuclear ring region.

4.2 CO-to-$H_{2}$ conversion in the nuclear region of NGC613

From the integrated flux $\rm S_{CO}\Delta V$(Jy km/s) listed in Table 4, we can derive the molecular mass involved in the outflow using the equation from Solomon & Vanden Bout (2005):

[TABLE]

where $\rm\nu_{rest}=345.796$ GHz, and $\rm D_{L}$ is the luminosity distance in Mpc. The molecular mass, including helium, is then derived from $\rm M(H_{2})=\alpha_{CO}{L_{CO}}^{\prime}r_{13}$ (Tacconi et al. 2013). This implies a molecular mass of $M_{out}$=1.9-2.2$\times$106M⊙. This mass was obtained using $r_{31}$=0.82, a luminosity distance of 17.2 Mpc and the standard Galactic CO-to-H2, conversion factor ($\rm\alpha_{CO,MW}=4.36\,M_{\odot}(K.km/spc^{2})^{-1}$ Dame et al. 2001; Bolatto et al. 2013). However, this mass could be an upper limit if the flow is made of more diffuse optically thin gas.

The standard $\rm\alpha_{CO}=4.36$ for the Milky Way is the recommended value to use in the inner disk of galaxies. However, several observational works (e.g., Israel 2009b, a; Sandstrom et al. 2013) found that in the center of galaxies (R$\lesssim$1 Kpc) the conversion $X_{CO}$ can be a factor up to 3-10 times lower than $X_{CO,MW}$. As pointed out by Bolatto et al. (2013), the recommended value to be applied in galaxy centers is $\alpha_{CO,cen}\sim\frac{1}{4}\alpha_{CO,MW}$, with a 0.3 dex uncertainty. In our case, the masses involved in the outflow would be four times lower, i.e., in the range of $\rm M_{out}=4.8-5.5\times 10^{5}M_{\odot}$, providing a more conservative estimative of the mass.

The assumption of a smaller $\rm\alpha_{CO}$ has been already discussed in the literature. In the case of the outflow in NGC 1068, the $\frac{1}{4}\alpha_{CO,MW}$ factor was also assumed (García-Burillo et al. 2014), in agreement with LVG analysis of the CO line ratios in the central region of this galaxy (Usero et al. 2004). Another example is the molecular outflow detected in M 51, where the authors assumed $\rm\alpha_{CO}=\frac{1}{2}\alpha_{CO,MW}$ (Querejeta et al. 2016; Matsushita et al. 2007). In a study of molecular gas excitation in the jet-driven winds of IC 5063, Dasyra et al. (2016) found that the outflowing molecular gas is partly optically thin, implying a $\rm\alpha_{CO}$ one order of magnitude smaller than the Galactic.

Most molecular outflows are detected in ultra-luminous infrared galaxies (ULIRGs) (Cicone et al. 2014). Therefore, the CO-to-H2 conversion factor usually assumed in the literature is $\rm\alpha_{CO}=0.8$, a factor $\sim$5 times lower than the Milky Way factor $\alpha_{CO,MW}$. Since NGC 613 has a rather moderate infrared luminosity ($L_{IR}=3\times 10^{10}L_{\odot}$), there is no reason a priori to adopt the lower factor of applied to ULIRGs. In fact, we would like to highlight that uncertainties in $\alpha_{\rm CO}$ impact the comparison of scaling factors between outflows and host galaxies propertie (e.g., Fiore et al. 2017; Fluetsch et al. 2019) by a factor of $\sim$5.

4.3 Mass outflow rate

To estimate the mass outflow rate, along with the observational quantities (outflow mass $M_{out}$, size $\rm R_{out}$ and velocity $\rm v_{out}$), we need to assume a certain geometry. Following Fiore et al. (2017) and Cicone et al. (2014), for a spherical or multi-conical geometry, in which the outflowing clouds are uniformly distributed along the flow, the mass outflow rate $\dot{M}_{out}$ can be calculated as:

[TABLE]

If instead we assume a time-averaged thin expelled shell geometry (Rupke et al. 2005b), also adopted in the study of molecular outflows in the local Universe (Veilleux et al. 2017; Fluetsch et al. 2019), we have

[TABLE]

which corresponds to the outflow mass averaged over the flow timescale, $t_{flow}=\frac{R_{out}}{v_{out}}$. The difference in the mass loading factor between the two proposed scenarios for the outflow geometry is a factor 3 times larger in the multi-conical/spherical description.

In the following estimates, we use Eq. 3 to derive more conservative outflow energetics, since the observations cannot constrain the geometry, and thus favour one scenario over the other.

As discussed in Section 4.1, the outflow is found in a region of $R_{out}$=0$\aas@@fstack{\prime\prime}$28 ($\sim$23 pc) and here we will consider the maximum projected velocity of the wings, $v_{out}$=300 km/s. If the outflow direction is between the observer line of sight and the galaxy plane, even assuming the maxima projected velocities, the de-projected velocities would encompass the adopted value, therefore, $v_{out}$=300 km/s is a conservative value. The flow timescale is then $t_{flow}\sim 10^{4}$ yr, which is comparable to the timescales of the BH growth bursts episodes of nuclear activity, with a duration of $10^{4-5}$ yr (Wada 2004).

For an outflow mass of $M_{out}$=(1.9-2.2)$\times$106 M⊙ (assuming the standard $\rm\alpha_{CO,MW}$), we find a mass outflow rate of $\dot{M}_{out}$=(25-29) $\rm M_{\odot}yr^{-1}$. If instead, we use the mass derived assuming the typical values for galaxy centers, $\rm\alpha_{CO}=\frac{1}{4}\alpha_{CO,MW}$, we find that the mass load rate is $\dot{M}_{out}\sim 7\,M_{\odot}yr^{-1}$.

4.4 The nuclear molecular outflow in dense gas tracers

We also detected the presence of broad wings in the nuclear spectrum of dense gas tracers $\rm HCN(4-3)$, $\rm HCO^{+}(4-3)$ and $\rm CS(7-6)$, as indicated in Figure 17. We also show the CO nuclear spectrum for comparison, and the high-velocity components cover the same velocity width of the CO wings ($\pm$300 km/s). We find that the ratio between the peak fluxes for the main core in the dense gas and CO are $\sim$5, $\sim$8.5, $\sim$36, for $\rm HCN(4-3)$, $\rm HCO^{+}(4-3)$ and $\rm CS(7-6)$, respectively. We also can notice in Fig. 17, there is some indication that, at least for HCN(4-3) and CS(7-6), the line ratios of the blue wings tend to be higher than the core.

In order to quantify the line ratio in the core and wings, we show the $\rm HCN(4-3)/CO(3-2)$ along the nuclear spectra in Figure 18. The ratio is shown up to velocities +200 km/s due to the tuning of Cycle 3 described in Section 2. The core component, define by the disk rotation with velocities up to $\pm$100 km/s, has a ratio of $\sim$0.2 and the ratio increases for the high-velocities towards the wings, up to values of $\sim$0.6, suggesting and enhancement of HCN in the outflow. As discussed in Section 3.5, the nuclear region of NGC 613 presents excitation conditions typical of XDRs in the vicinity of AGN, when analysing the dense gas ratios in the sub-millimeter-HCN diagram (Izumi et al. 2016) in Figure 12. Yet, we find evidence that the HCN in the outflow can be a factor 3 times higher than the values found in the nuclear CND.

A similar trend was also reported in the molecular outflow of the QSO galaxy Mrk 231. The detection of the outflow in HCN(1-0) by Aalto et al. (2012) covers the same velocity range ($\pm 750\,km/s$) of the CO(1-0) outflow (Feruglio et al. 2010), and they found a high ratio of the HCN/CO$\sim$0.3-1 in the outflow, higher than in the line core. The HCN is enhanced in the line wings by factors of 2-5, and they suggest that the outflow is mostly entrained in dense gas $n\gtrsim 10^{4}cm^{-3}$, which is consistent with the molecular gas being compressed and fragmented by shocks (Aalto et al. 2012). High resolution observations of HCN and HCO+ in the higher J=3$\rightarrow$2 transition exhibit prominent, spatially extended line wings for HCN(3-2) in Mrk 231 (Aalto et al. 2015). In Mrk 231 there were no line wings detected in HCO+(3-2), while in NGC 613, there is some indication of high-velocity gas. Aalto et al. (2015) claimed that the elevated HCN abundance in the outflow is possibly caused by high temperatures in the X-ray irradiated gas regions surrounding AGN (Harada et al. 2013).

Another possibility to explain the HCN enhancement in the outflow of NGC 613, is that the HCN emission stems from shocks potentially originated from the interaction of the ouflowing gas with the radio jet. The fact that the molecular outflow is spatially aligned with the central blob of the radio jet detected by Hummel & Jorsater (1992) (see Fig. 16), region where there is evidence of shock excitation as discussed in Section 3.6, corroborates this scenario. A further detailed analysis of the line ratios for all the NUGA sample will be discussed in a future paper.

4.5 The driving mechanism: AGN or star formation?

The origin of the outflow might be related to star formation, which is concentrated in the nuclear ring region. The star formation rate (SFR) can be estimated from the IR luminosity and the calibration from Kennicutt (1998). From the IRAS fluxes, the IR luminosity is $L_{IR}$=3$\times$109 L⊙ (Table LABEL:tab:prop, Sturm et al. 2002), and the total SFR equals to 5.3 M⊙/yr. Based on the H$\alpha$ luminosity associated with star formation in the central 3$\times$3 kpc measured by Davies et al. (2017), $\rm L(H\alpha)_{SF}=5.28\times 10^{41}$ erg/s, we can also deduce from Kennicutt’s calibration a SFR=4.1 M⊙/yr, which is consistent with the estimate from IR luminosity. If we isolate the contribution only coming from circumnuclear star-forming ring, the SFR estimated is SFR=2.2 M⊙/yr in the ring of r$\lesssim$400 pc (Mazzuca et al. 2008). Evidence of young star-forming regions in the “hotspots” along the ring has been recently found by Falcón-Barroso et al. (2014). However, the value reported for NGC 613 in the nuclear region of aperture of $r\sim$40 pc is very low, SFR$\sim$0.015 M⊙/yr (Falcón-Barroso et al. 2014). This low value can be due to extinction factors or a a possible AGN contribution. The same nuclear region has a large reservoir of warm molecular gas (e.g., see Fig.13), also found in other Seyfert galaxies (Hicks et al. 2013). Falcón-Barroso et al. (2014) suggest a cyclical episode of starburst about $\sim$10 Myr ago, followed by another episode of nuclear activity.

We estimate for the nuclear molecular outflow a mass rate of $\rm\dot{M}_{out}\sim 27\,M_{\odot}yr^{-1}$. Although this estimate is uncertain by a factor of a few, given the unknown projection and the assumptions previously discussed in the text, the SFR in the nuclear region is about 3 orders of magnitude lower than $\rm\dot{M}_{out}$. In general, galactic winds driven by starbursts correspond to mass outflows rates of the same order as the SFR (e.g., Veilleux et al. 2005). Given the discrepancy between the SFR in the nuclear region of and the mass load rate of the outflow, we conclude that star formation alone is not able to drive the nuclear molecular outflow in NGC 613.

It has been already established that the mass outflow rate increases with the AGN luminosity, supporting the idea of a luminous AGN pushing away the surrounding gas through a fast wind. Previous observational works (Cicone et al. 2014; Carniani et al. 2015; Fiore et al. 2017) have shown that the molecular outflow properties are correlated with the AGN luminosity, where the outflow kinetic power corresponds to about 5%$\rm L_{AGN}$ and the momentum rate is $\sim$20$\rm L_{AGN}$/c, in agreement with theoretical models of AGN feedback (Faucher-Giguère & Quataert 2012; Zubovas & King 2012). For a sample of molecular and ionised outflows, Carniani et al. (2015) found that the ionised gas only traces a small fraction of the total gas mass, suggesting that the molecular phase dominates the outflow mass. This trend is also found by Fiore et al. (2017), but the ratio between molecular to ionised mass outflow rates is reduced at the highest AGN bolometric luminosities. However, the authors have analysed different samples of galaxies, and this conclusion could be affected by selection bias.

From XMM-Newton observations of NGC 613, Castangia et al. (2013) reported a X-ray luminosity of log$L_{X}(2-10keV)=$41.3 erg/s. Applying a bolometric correction from Marconi et al. (2004) gives an AGN bolometric luminosity of $\rm L_{AGN,X}=1.7\times 10^{42}$ erg/s. The bolometric luminosity derived by Davies et al. (2017) using the [Oiii] emission associated only with the AGN contribution, traced as an extended ionization cone aligned with the radio jet, is $\rm L_{AGN,[OIII]}=4\times 10^{42}$ erg/s. If we include the shock and star forming contributions of the total O [iii] emission, it gives $\rm L_{bol,[OIII]}=3.75\times 10^{43}$ erg/s. The shock contribution most likely arises from the radio jet launched by the AGN, but here we cannot disentangle the contribution from star formation; the latter probably overestimates the bolometric AGN luminosity, while the former probably sets a lower limit.

In a recent study, Fluetsch et al. (2019) have identified 45 molecular outflows in the local Universe using previous results from the literature and new detections from ALMA archive. They propose an even tighter empirical relation between the mass outflow rate and the SFR, stellar mass, $M_{*}$, and the bolometric $L_{AGN}$:

[TABLE]

where the SFR is calculated from the total IR luminosity and $\dot{M}_{out}$ is in $\mathrm{M_{\odot}yr^{-1}}$. We adopt the bolometric AGN luminosity derived from the O [iii] emission line, $L_{AGN}=4\times 10^{42}$ erg/s (Davies et al. 2017), the total SFR inferred from the IRAS fluxes, SFR=5.3$\rm M_{\odot}yr^{-1}$ and the stellar mass of $M_{*}=4.5\times 10^{10}M_{\odot}$ calculated in Paper I, derived from the S4G3.6 $\mu$m IR image and the GALFIT decomposition (Salo et al. 2015). Hence, according to Eq. 4, we should expect an outflow mass rate of $4.8\,M_{\odot}yr^{-1}$ in NGC 613, which corresponds to a factor of 6 times lower than our estimate.

The kinetic power of the nuclear outflow can be estimated as $P_{K,out}=0.5v^{2}\dot{M}_{out}$. For the $\alpha_{CO,MW}$ assumption, $\rm\dot{M}_{out}\sim 27\,M_{\odot}yr^{-1}$, and we find $P_{K,out}=8\times 10^{41}$ erg/s, which corresponds to 20%$L_{AGN}$. This value exceeds the predictions from AGN feedback models and cosmological simulations that require that a fraction of the radiated luminosity should be coupled to the surrounding gas $\sim 5\%L_{AGN}$ (Di Matteo et al. 2005; Zubovas & King 2012). However, these predictions are based on powerful AGN, accreting close to the Eddington limit and we hypothesise that the coupling efficiency between AGN-driven outflows and $L_{AGN}$ should be outweighed in LLAGN. The Eddington luminosity derived from the BH mass ($M_{BH}$=3.7$\times 10^{7}M_{\odot}$, Paper I) is $L_{Edd}=4.6\times 10^{45}$erg/s, leading to a low accretion rate $L_{AGN}/L_{Edd}\lesssim 1\times 10^{-3}$. If we assume the lower $\alpha_{CO}=1/4\alpha_{CO,MW}$, the kinetic power of the outflow is $P_{K,out}\sim 2\times 10^{41}$ erg/s, and the coupling is 5%$L_{AGN}$. In both assumptions, the results indicate that the AGN can power the nuclear outflow in NGC 613, but the former requires a higher coupling efficiency.

The momentum flux of the outflow can be computed from $P_{out}=\dot{M}_{out}v\sim 5\times 10^{34}$ dynes. Compared to the momentum provided by the AGN photons, $L_{AGN}/c$=1.3$\times 10^{32}$ dynes, it is higher by a factor of $\dot{M}_{out}v\sim 400L_{AGN}/c$. In case of energy-conserved winds, AGN feedback models predict a momentum boost by factors up to 50 (e.g. Faucher-Giguère & Quataert 2012). Even assuming the lower $\alpha_{CO}$, the value would exceed the predictions ($\sim 100L_{AGN}/c$). One possibility to explain the high apparent energetics of the outflow in NGC 613 is that the AGN activity was stronger in the past. As discussed by Fluetsch et al. (2019), they found that 10% present outflows that exceed the theoretical predictions. They suggest these galaxies could have fossil outflows, resulting from a strong past AGN that now has already faded. In the case of the LLAGN NGC 1377, a collimated molecular outflow is detected at 150 pc scales (Aalto et al. 2016), possibly entrained by a faint radio jet, and the authors suggested that the nuclear activity of NGC 1377 may also be fading.

Alternatively, it is possible that the outflow is driven through the AGN radio jets. The radio power of the jet can be estimated from the 1.4 GHz luminosity, $P_{1.4}$, using the relation of Bîrzan et al. (2008). If we compute the $P_{1.4}$ luminosity using the NRAO VLA Sky Survey (NVSS) flux measurement of 179.6 mJy at $\nu$=1.4 GHz(Condon et al. 1998), we find a radio power $P_{jet}=1.2\times 10^{43}$ erg/s. Since this value is very elevated, it might include emission from the circumnuclear star-forming ring. To avoid this contribution, we used only the flux of the linear component of the radio jet at 4.86 GHz by Hummel & Jorsater (1992). At 4.86 GHz, the flux associated to the jet is $S_{\nu}$=7.2 mJy, and using a spectral index of $\alpha$=-0.8 to derive the flux at 1.4 GHz, we find $P_{jet}=5.5\times 10^{42}$ erg/s. Hydrodynamical simulations of the interaction of the jet with a clumpy interstellar medium has shown that the jet is able to drive a flow efficiently as soon as the Eddington ratio of the jet Pjet/LEdd is larger than 10*-4* (Wagner et al. 2012). This condition is required for the jet-driven outflow velocity to exceed the velocity dispersion of the $M-\sigma$ relation but it also depends on the cloud sizes in the ISM. In NGC 613, this ratio is about 1.2$\times$10*-3*, and the jet power is about one or two orders of magnitudes higher than the kinetic luminosity of the outflow. We conclude that the jet is able to drive the molecular outflow, even with low coupling.

The molecular outflow in NGC 613 is an intriguing case where a very powerful molecular outflow is detected in a LLAGN. The SFR is very weak in the nuclear region, and therefore, not able to drive the flow. Radio jets are found to play a role in the driven mechanism to accelerate the molecular gas in other LLAGN. This is the case for the LINERs NGC 1266 and NGC 6764, as suggested by Alatalo et al. (2011) and Leon et al. (2007), respectively, and the Seyfert 2 NGC 1433 (Combes et al. 2013). The properties of the flow require the contribution of the AGN through the entrainment of its radio jets.

5 Torques and AGN fueling

In Paper I, we reported the ALMA observations of the CO(3-2) line for all the galaxies in the NUGA sample. In three cases, NGC 613, NGC 1566 and NGC 1808, the CO emission has revealed a nuclear trailing spiral, as the large-scale one. Inside the nuclear ring at the ILR of the bar, usually a leading spiral is expected, developing transiently, and generating positive torques, which drive the inner gas onto the ring. However, when the gravitational impact of the black hole is significant, the spiral can then be trailing, and the torques negative, to fuel the nucleus (Buta & Combes 1996; Fukuda et al. 1998).

We find filamentary structures in NGC 613, pointing to a radial gas transport from the circumnuclear star forming ring into the core region dominated by the AGN, as displayed in Figure 5. The ring morphology appears disturbed by a radial outflow of material from the AGN, which is confirmed by the existence of a weak jet in archival radio maps. However, the radio jet does not seem to have any significant effect on the morphology of the large reservoir of molecular gas that has accumulated inside the central 100 pc.

If gas is inflowing from the bar dust lanes into the ring, as expected from gravity torques (García-Burillo et al. 2005), there is also an inflow in the CND, due to the nuclear trailing spiral, as already observed for NGC 1566 (Combes et al. 2014). Inside the nuclear spiral structure, there is a very dense and compact (radius $\sim$ 14 pc) rotating component, which might be interpreted as the molecular torus (Paper I).

In order to explore the efficiency of feeding in NGC 613, we have estimated the gravitational torques exerted by the stellar potential on the molecular gas, following the methodology described by García-Burillo et al. (2005). The gravitational potential is computed in the plane of the galaxy using a red image (F814W) from HST, since 2MASS images have insufficient angular resolution. We have not separated the bulge from the disk contribution since NGC 613 is a late type (Sbc) galaxy. This means that the bulge was effectively assumed to be flattened. Dark matter can be safely neglected inside the central kpc. The image has been rotated and deprojected according to PA=120∘ and i=41∘, and then Fourier transformed to compute the gravitational potential and forces. A stellar exponential disk thickness of $\sim$1/12th of the radial scale-length of the galaxy (hr=3.8kpc) has been assumed, giving hz=317pc. This is the average scale ratio for galaxies of this type (e.g., Barnaby & Thronson 1992; Bizyaev & Mitronova 2009). The potential has been obtained assuming a constant mass-to-light ratio of M/L=0.5 in the I-band over the considered portion of the image of 1 kpc in size. This value is realistic in view of what is found statistically for spiral galaxies (Bell & de Jong 2001). The pixel size of the map is 0.06″=5 pc, the average value between the ALMA and HST resolutions. The stellar M/L value was fit to reproduce the observed CO rotation curve.

The potential $\Phi(R,\theta)$ can be decomposed into its different Fourier components:

[TABLE]

where $\Phi_{m}(R)$ and $\phi_{m}(R)$ are the amplitude and the phase of the $m-$mode, respectively. The strength of the $m$-Fourier component, $Q_{m}(R)$ is defined as $Q_{m}(R)=m\Phi_{m}/R|F_{0}(R)|$, i.e. by the ratio between tangential and radial forces (Combes & Sanders 1981). The strength of the total non-axisymmetric perturbation $Q_{T}(R)$ is defined similarly with the maximum amplitude of the tangential force $F_{T}^{max}(R)$. Their radial distributions and the radial phase variations are displayed in Fig. 19.

The derivatives of the potential yield the forces per unit mass ($F_{x}$ and $F_{y}$) at each pixel, and the torques per unit mass $t(x,y)$ are then computed by $t(x,y)=x\leavevmode\nobreak\ F_{y}-y\leavevmode\nobreak\ F_{x}$. The sign of the torque is determined relative to the sense of rotation in the plane of the galaxy. The product of the torque and the gas density $\Sigma$ at each pixel allows one then to derive the net effect on the gas, at each radius. This quantity $t(x,y)\times\Sigma(x,y)$, is shown in Fig. 20, together with the deprojected CO map.

The torque weighted by the gas density $\Sigma(x,y)$ is then averaged over azimuth, i.e.

[TABLE]

The quantity $t(R)$ represents the time derivative of the specific angular momentum $L$ of the gas averaged azimuthally (García-Burillo et al. 2005). Normalising at each radius by the angular momentum and rotation period ($\rm T_{rot}$) allows us to estimate the efficiency of the gas flow, as shown in Fig. 21. The torques are negative in the winding arms at r$\sim$500 pc (corresponding to the dust lanes) and are indeed contributing to drive the outer gas into the star-forming ring at $\sim$350 pc. The observations of nuclear rings are more common among barred galaxies (Kormendy & Kennicutt 2004; Peeples & Martini 2006; Jogee 2006), and can be explain by the gas slowing down as it crosses the ILR, consequently weakening the gravitational torques, and the gas piles up in rings (Combes & Gerin 1985; Byrd et al. 1994). We can see in Fig. 21 that the efficiency certainly drops in the inner ILR region. The filaments within the nuclear region, between 100 and 200 pc, show that the gas gains angular momentum in one rotation, which is $\rm T_{rot}\sim$12 Myr.

The nuclear bar strength is moderate, however, the BH has a strong influence on the nuclear molecular gas, as shown in Fig. 21, the fueling efficiency is high in the nuclear spiral. Between 25 and 100 pc, the gas loses its angular momentum in one rotation, which is $T_{rot}(100pc)\sim$9.5 Myr. Inside 25 pc, the torques are positive and correspond to the region where we detect the molecular outflow. Since the gas in this region is not in quasi-stationary orbits, but rather ejected from the galaxy plane, the computation cannot be interpreted in terms of the average torque here.

As shown in Fig. 20, the nuclear spiral structure inside the ILR ring of the bar is of a trailing nature and is located inside the negative torque quadrants. This might appear surprising, since in many cases the spiral structure is predicted to be leading in this region, and the torque positive, maintaining the gas in the ILR ring (Buta & Combes 1996). However, in the presence of a sufficiently massive black hole, this behaviour can be reversed: the spiral becomes trailing, and the torque negative. Indeed, the indicator of the precession rate of elliptical orbits in the frame of the epicyclic approximation, $\Omega-\kappa/2$, is significantly modified by a central massive body. Instead of decreasing regularly towards zero at the center, the $\Omega-\kappa/2$ curve increases steeply as r*-3/2*. The gas undergoes collisions, loses energy and spirals progressively towards the center. When the precession rate decreases, the series of elliptical orbits precess more and more slowly, and then lag at smaller radii, forming a leading structure. When the precession rate increases, they form a trailing structure (Combes et al. 2014).

One way to detect spiral structure in the nuclear gas is to amplify the dust extinction features in the HST images. However, we would like to stress that observations of spiral dust lanes interior to the star-formation rings are not very common (Martini et al. 2003; Peeples & Martini 2006). Notwithstanding, a clear case is seen in NGC 2207, where dusty spirals extend from $\sim$50 to 300 pc, suggesting that the gas continues to sink inside the ILR and might be promoting gas accretion into the nucleus (Elmegreen et al. 1998). Multiple spiral arms were also detected inside the star-forming ring ($r\sim$700 pc) in the LINER/Sy 1 galaxy NGC 1097 by Prieto et al. (2005). They compared their results with hydrodynamic models of Maciejewski (2004), concluding that inflows were occurring along the nuclear spirals. Although nuclear star forming rings are common, their interior structure is difficult to distinguish in dust maps, making the molecular gas emission a better tracer. The NUGA maps show clear evidence of trailing spirals in three objects of the sample, highlighting the importance of the high resolution ALMA observations.

NGC 613 is therefore an example of a trailing spiral inside the nuclear ring of a bar i.e., the case described in Buta & Combes (1996). This means that the mass of the black hole should be sufficiently high to have an influence on the gas dynamics on a 100 pc scale. In summary, the gravity torques are negative in the winding spirals, and the gas accumulates in the star forming ring at the inner ILR of the nuclear bar. The filamentary structure gains angular momentum and then the nuclear spiral at $\lesssim$100 pc present a very high efficiency in fuelling the central BH.

6 Conclusions

We have presented the combined ALMA cycle 3 and 4 observations for the Seyfert/nuclear starburst galaxy NGC 613. The combined observations in CO(3-2) reach a spatial resolution of 0.2″$\sim$17 pc. We study the morphology and the kinematics of the molecular gas in the central 1 kpc and our main findings are summarized below:

$\bullet$ The 350 GHz continuum map shows a compact, barely resolved, emission peak at the position of the AGN, surrounded by a patchy ring, matching the star-forming ring seen on optical images.

$\bullet$ The morphology of CO(3-2) line emission reveals several components: a 2-arm nuclear spiral at $\rm r\lesssim$100 pc trailing the gas toward the center, a circumnuclear ring $\sim$350 pc, that correspond to the star-forming ring. Also, we find evidence of a filamentary structure connecting the ring and the nuclear spiral. The ring reveals two breaks into two winding spiral arms, at NW and SE, corresponding to the dust lanes in the HST images.

$\bullet$ The kinematics of the CO emission show a rather regular rotational velocity field in the inner kpc disk. We applied a tilted-ring model to fit the velocity map and the residuals show indeed the bulk of the molecular gas in circular motion except in the west part of the ring, which perturbations are due to the contact point between the ring and the SE winding arm.

$\bullet$ There is a remarkable coincidence between the molecular gas and the warm H2 and ionised gas, traced by the [Feii] and Br$\gamma$ emission lines, in the star-forming ring. Line diagnostics in the NIR indicate that the clumps in the ring are in agreement with young star-forming excitation. On the other hand, the nucleus of NGC 613 presents an excitation mechanism typical of Seyfert or LINER.

$\bullet$ We measured the line intensity ratios R${}_{\rm HCN/HCO^{+}}$ and RHCN/CS in the nuclear region and in a clump along the ring. We find that the ratio for the nuclear region points to the AGN-dominated part of the HCN-submillimeter diagram, while the ratio for the clump is located in the starburst-dominated part. These results indicate that the nuclear region of NGC 613 presents line ratios in agreement with excitation conditions typical of XDRs in the vicinity of AGN.

$\bullet$ In the PV diagrams, we find skewed kinematics in the nuclear region of r$\sim$25 pc. This feature is seen as broad wings ($v\pm$300 km/s) in the CO nuclear spectrum, and the wings are also present in the dense gas tracers. We identify this feature as a molecular outflow emanating from the nucleus. The molecular outflow is co-spatial with the central blob detected in the radio jet.

$\bullet$ We derive the molecular mass associated to the outflow as $M_{out}$=2$\times$106 M⊙. The mass outflow rate is $\dot{M}_{out}=$27 $\rm M_{\odot}yr^{-1}$. If instead, we use the mass derived assuming the typical values for galaxy centers, $\rm\alpha_{CO}=\frac{1}{4}\alpha_{CO,MW}$, we find that the mass load rate is $\dot{M}_{out}\sim 7\,M_{\odot}yr^{-1}$.

$\bullet$ We find a HCN enhancement in the outflow, probed by an increasing of the HCN(4-3)/CO(3-2) ratio along the wings in the nuclear spectra. While the core has ratios of about $\sim$0.2, this value increases in the wings up to $\sim$0.6, indicating that the outflow is entrained mostly in a dense gas ($\rm n\gtrsim 10^{4}\,cm^{-3}$). Another possibility is that the HCN emission stems from shocks potentially originated from the interaction of the ouflowing gas with the radio jet.

$\bullet$ The molecular outflow energetics exceed the values predicted by AGN feedback models. The kinetic power of the nuclear outflow corresponds to $P_{K,out}=$20%$L_{AGN}$ and the momentum rate is $\dot{M}_{out}v\sim 400L_{AGN/c}$. We speculate that, given its current weak nuclear activity, NGC 613 might be a case of fossil outflows, resulted from a strong past AGN that now has already faded.

$\bullet$ The outflow can be entrained by its radio jet. We find that Pjet/L${}_{Edd}\sim$10*-3* and the jet power is about one or two orders of magnitudes higher than the kinetic luminosity of the outflow. In these conditions, the jet is able to drive the molecular outflow.

$\bullet$ The trailing spiral observed in CO emission is inside the ILR ring of the bar. We have computed the gravitational potential from the stars within the central kpc, from the I-band HST image. Weighting the torques on each pixel by the gas surface density observed in the CO(3-2) line has allowed us to estimate the sense of the angular momentum exchange and its efficiency. The gravity torques are negative from 25 to 100 pc. Between 50 pc and 100 pc, the gas loses its angular momentum in a rotation period, providing evidence of fueling the AGN.

The molecular outflow in NGC 613 is an intriguing case where a very powerful molecular outflow is detected in a LLAGN. The SFR is very weak in the nuclear region, and therefore, not able to drive the flow. The properties of the flow require the contribution of the AGN through the entrainment of its radio jets. On the other hand, there is a clear trailing spiral observed in molecular gas inside the ILR ring of a bar, indicating that the super-massive black hole is influencing the gas dynamics. Instead of maintaining the ILR ring density, the torques are then driving gas towards the nucleus, a first step towards possibly fueling the AGN. NGC 613 is a remarkable example of the complexity of fuelling and feedback mechanisms in AGN, and reinforce the importance of detailed analysis of nearby galaxies with ALMA capabilities to shed light on the gas flow cycle in AGN.

Acknowledgements.

The ALMA staff in Chile and ARC-people at IRAM are gratefully acknowledged for their help in the data reduction. We particularly thank Philippe Salomé for useful advice and Jesús Falcón-Barroso for the SINFONI and VLA data. AA would like to thank the Brazilian scholarship program Science without Borders - CNPq (reference [234043/2014-8]) for financial support. SGB acknowledges support from the Spanish MINECO grant AYA2016-76682-C3-2-P. LH is grateful to INAF PRIN-SKA funding program 1.05.01.88.04. This paper makes use of the following ALMA data: ADS/JAO.ALMA#2015.0.00404.S, and ADS/JAO.ALMA#2016.0.00296.S. ALMA is a partnership of ESO (representing its member states), NSF (USA) and NINS (Japan), together with NRC (Canada) and NSC and ASIAA (Taiwan), in cooperation with the Republic of Chile. The Joint ALMA Observatory is operated by ESO, AUI/NRAO and NAOJ. The National Radio Astronomy Observatory is a facility of the National Science Foundation operated under cooperative agreement by Associated Universities, Inc. We used observations made with the NASA/ESA Hubble Space Telescope, and obtained from the Hubble Legacy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESA), and the Canadian Astronomy Data Centre (CADC/NRC/CSA). We made use of the NASA/IPAC Extragalactic Database (NED), and of the HyperLeda database. This research made use of Astropy, a community developed core Python package for Astronomy. This work was supported by the Programme National Cosmology et Galaxies (PNCG) of CNRS/INSU with INP and IN2P3, co-funded by CEA and CNES.