The Relationships between Active Galactic Nucleus Power and Molecular Gas Mass within 500 pc of the Center of Elliptical Galaxies

The physical quantity that directly controls the feedback of active galactic nuclei (AGNs) in elliptical galaxies remains to be determined. The discovery of molecular gas around the AGNs suggests that the gas is fueling the AGNs. Therefore, we analyze Atacama Large Millimeter/submillimeter Array data for the CO line (J = 1–0, 2–1, 3–2) emission and estimate the mass of molecular gas within 500 pc of the center of 12 noncentral elliptical galaxies (NCEGs) and 10 of the brightest cluster galaxies. We find that the mass (M mol ∼ 105–109 M ☉) is correlated with the jet power of their AGNs, which is represented by Pcav≈4.1×1042(Mmol/107M☉)1.3ergs−1 , although NCEGs alone do not show the correlation. We also find that M mol is correlated with the AGN continuum luminosities at ∼1.4 GHz (L 1.4) and ∼100–300 GHz (L con). Since P cav reflects galactic-scale, long-term AGN activity, while the continuum luminosities reflect local (≲500 pc), short-term AGN activity, our results suggest that AGN activity depends on the amount of gas, regardless of its timescale. On the other hand, we cannot find a clear correlation between the mass of the black holes in the AGNs (M BH) and P cav. This suggests that M mol, rather than M BH, is the main factor controlling AGN activity. We confirm that the origin of the continuum emission from the AGNs at ∼1.4–300 GHz is mostly synchrotron radiation.


Introduction
Supermassive black holes are ubiquitous at the centers of galaxies (Kormendy & Ho 2013), and they produce an enormous amount of energy as active galactic nuclei (AGNs).The AGNs in massive elliptical galaxies are in "radio feedback" mode and often show jet activity (Heckman & Best 2014).Since elliptical galaxies are filled with hot gas (Fabbiano 1989), it may be natural to assume that the hot gas is fed into the black holes in the form of the Bondi accretion (Bondi 1952).Allen et al. (2006) showed that there is a strong correlation between the AGN jet power (P cav ), which can be inferred from the size of the X-ray cavities in the host galaxies, and the Bondi accretion rate.However, later studies have disproved such a strong correlation (Russell et al. 2013).
The discovery of a large amount of molecular gas (10 8 M ☉ ) in elliptical galaxies at the center of nearby clusters (Edge 2001;Salomé & Combes 2003;David et al. 2014;McNamara et al. 2014;Russell et al. 2016Russell et al. , 2017Russell et al. , 2019;;Vantyghem et al. 2016Vantyghem et al. , 2017;;Olivares et al. 2019;Rose et al. 2020;Schellenberger et al. 2020;North et al. 2021) suggests that this cold gas is feeding the AGNs.However, the cold gas is often widely distributed on a scale of 10 kpc, and it is unlikely that all of the gas contributes to AGN activity because some of it is consumed in star formation (Fujita et al. 2022).As direct evidence for AGN feeding, many absorption lines have been observed in some AGNs, indicating the presence of dense gas in the vicinity of the AGNs (David et al. 2014;Tremblay et al. 2016;Rose et al. 2019Rose et al. , 2023)).However, it is difficult to estimate the mass of the circumnuclear gas from the absorption.Thus, it is important to focus on the emission from the cold gas in the vicinity (say 500 pc) of the AGNs, which can directly influence the gas accretion onto them.
We note that Russell et al. (2019) compared the mass of the circumnuclear molecular gas obtained with the Atacama Large Millimeter/submillimeter Array (ALMA) with the AGN jet power P cav and showed that there is a correlation (their Figure 7; see also our Figure 4(a)).However, they measured the mass in a single ALMA-synthesized beam centered on the AGNs.Since the physical scale of a given beam is larger for more distant objects (see Section 2 and Figure 1), the mass in that beam is likely to be larger, while distant AGNs are observationally biased to be brighter and more powerful.This could lead to an artifact relationship.
For this reason, we examined the relationship between AGN power and molecular gas mass within a fixed physical radius (M mol ), i.e., within 500 pc of the black holes, for the nine brightest cluster galaxies (BCGs) at the center of clusters (Paper I; Fujita et al. 2023).The nine BCGs are part of the samples of Olivares et al. (2019) and Russell et al. (2019).Since the physical scale of the region is fixed, the above bias should be less likely to occur.
We note that this scale (500 pc) is comparable to the circumnuclear disk around the black hole (Nagai et al. 2019;Fujita et al. 2022).In Paper I we found that M mol is correlated with the AGN jet power (P cav ).Since the timescale of cavity formation is ∼10 7 yr (Bîrzan et al. 2004;Allen et al. 2006;Rafferty et al. 2006), P cav is the power averaged over this timescale.On the other hand, we found that the continuum luminosities of AGNs at 1.4 GHz (L 1.4 ) and ∼100-300 GHz (L con ) are not correlated with M mol (Paper I).The continuum emission is observed as a point source.Considering that the typical beam size is 500 pc and the corresponding light travel time is 1600 yr, the emissions reflect the recent activity of the AGNs.Thus, the lack of correlation between the continuum luminosities and M mol may indicate that AGN activity varies on a short timescale.Indeed, intermittent jet activity and jet-cloud interactions have been observed for NGC 1275, the BCG of the Perseus cluster.This object shows radio luminosity variations on a timescale of decades (e.g., Nagai et al. 2010Nagai et al. , 2017;;Fujita & Nagai 2017;Kino et al. 2021).
In this study, we extend the sample of galaxies studied in Paper I to lower masses by including 12 nearby noncentral elliptical galaxies (NCEGs) that are not at the center of massive clusters. 5We investigate whether the P cav -M mol scaling relation is continuous from less massive NCEGs to giant elliptical galaxies (BCGs).If the relation is well established, it could be used in theoretical models of galaxy formation.For the L 1.4 -M mol and L con -M mol relations, we test for the existence of a correlation for the larger sample.We also investigate whether the mass of the black holes is a key factor in controlling AGN activity.
The paper is structured as follows: Section 2 describes the sample selection.Section 3 describes the reduction of the ALMA data.Section 4 presents the results of the data analysis and the correlation between the mass of molecular gas around black holes and AGN activity.Section 5 explores the implications of these correlations.We also investigate whether the black hole mass affects AGN activity, and discuss the source of the nonthermal emissions.Section 6 is devoted to summarizing our findings.

Sample Selection
We examine CO line emission from cold molecular gas in elliptical galaxies using archival ALMA observations to investigate the correlation between cold gas mass and AGN power.Our sample galaxies are taken from the NCEGs studied by Cavagnolo et al. (2010) andO'Sullivan et al. (2011).For 12 of them, we found ALMA data that may contain CO line emissions (Boizelle et al. 2017(Boizelle et al. , 2021;;Meyer et al. 2018;Temi et al. 2018Temi et al. , 2022;;Morokuma-Matsui et al. 2019;Ruffa et al. 2019;Sawada-Satoh et al. 2022).We also add M 87 (Simionescu et al. 2018), which is a BCG not examined in Paper I. The observational details of the final sample of 13 galaxies are given in Table 1.For the NCEGs, their jet powers P cav were obtained by Cavagnolo et al. (2010).They defined the energy of each to be 4pV, which is the enthalpy of a cavity filled with relativistic gas.The jet P cav was obtained by dividing the energy by the age of the cavity (the buoyant rise time).If there are multiple cavities in a galaxy, their P cav have been summed.Since we have simply selected the targets that have been observed with ALMA and for which P cav has been estimated, they are not a complete sample.
The redshift range of our sample is 0.00313 (NGC 4636; Table 1) to 0.1028 (PKS 0745-191; Paper I) and we focus on the central 500 pc (1 kpc in diameter).In contrast, Russell et al. (2019) studied galaxies with a much wider range of redshifts (z = 0.0093-0.596),and the beam sizes in which they estimated the circumnuclear gas mass varied among the galaxies (Figure 1).The fixed radius (500 pc) and the narrower redshift range (Figure 1) should make our sample less biased.

Data Reduction
The sample galaxies were observed with ALMA at frequencies corresponding to the CO(J = 1-0), CO(J = 2-1), or CO(J = 3-2)6 rotational transition lines, mostly CO(J = 2-1), with additional spectral windows that were used to image the millimeter/ submillimeter (∼100-300 GHz) continuum emission.The observations were single pointing, centered on the AGNs, except for NGC 1316, which was covered with mosaics.The data were calibrated using the appropriate version of the Common Astronomy Software Application (CASA) software (McMullin et al. 2007) and the ALMA Pipeline used for quality assurance.
We subtracted the continuum emission using line-free channels with the CASA task uvcontsub (fitorder = 1) to study the line emissions.We reconstructed the line cubes and the underlying continuum maps using the CASA task tclean with a threshold of 3σ.We used Briggs weighting with a robust parameter of 2 (natural weighting), following previous studies (Olivares et al. 2019;Russell et al. 2019).The synthesized beam size and rms in each final data cube are shown in Table 1.

Results
Using the CASA task immoments, we generate images of the integrated intensity for the AGN neighborhoods in the 13 galaxies that cover each CO line.From six of them (IC 4296, NGC 315, NGC 1316, NGC 4261, NGC 4374, and NGC 4636) we detected Figure 1.Red open triangles show the redshifts and the diameter of the focused region (1 kpc) for our 22 sample galaxies.Black open circles are the redshifts and geometric mean beam sizes for the galaxies studied by Russell et al. (2019).Note that some of these galaxies were observed with different beam sizes and have multiple black open circles for the given redshift.
CO emission around their centers.Their images are shown in Figure 2. The following analysis focuses on these six galaxies.For the other seven sources (six NCEGs + M 87) we could not detect any cold gas, and only the upper limit of the mass is discussed.
Following Paper I, we focus on the central 500 pc region because it is well resolved with ALMA, and the gas in this region is likely to be fed into the black hole (Kawakatu & Wada 2008;Fujita et al. 2022).For all six galaxies in Figure 2, the emission is concentrated on a scale smaller than 500 pc.This is in contrast to the more massive BCGs studied in Paper I, where the CO emission generally extends beyond the central 500 pc region.In the case of NGC 1316 and NGC 4636, the peak of the CO is offset from the location of the AGN (Figure 2), implying that the gas accretion is neither spherically nor axially symmetric.This happens when the accretion is chaotic (Figure 13 in Gaspari et al. 2015).
We extract spectra from the emission regions for the six linedetected galaxies (Figure 3) to check the profiles of the CO lines.Unlike in Paper I, we did not fit the spectra of the six galaxies with one or two Gaussian components, because not all of them are represented by Gaussians.For example, the spectrum of NGC 315 clearly shows the rotation of the gas and is not well fitted by  Gaussians (Figure 3).Instead, we derived the line flux densities from the brightness of the integrated intensity images (Figure 2).The images include channels where line emission is detected.For IC 4296 we ignore the channels corresponding to the prominent absorption (Figure 3).We have confirmed that the two methods (Gaussian fit and intensity image) give consistent results when the spectrum can be well fitted by Gaussians.For the seven galaxies in which we could not detect cold gas, we estimate the 3σ upper limit of the line intensity by assuming that a possible line is within ±500 km s −1 of the galaxy's velocity.
In addition, unlike Paper I, we do not discuss the mass accretion rate due to turbulent viscosity (M  ), where the turbulent velocity is derived from the width of the Gaussian components.While M  is determined by the molecular gas mass (M mol ) and the turbulent velocity, as shown in Paper I, the dependence of the turbulent velocity is not significant.This is because while M mol varies by several orders of magnitude among galaxies, the turbulent velocity varies by only a factor of a few.As a result, M  is approximately proportional to M mol .Moreover, the estimate of M  has a large uncertainty, such as the gas morphology.Therefore, we focus on M mol rather than M  in this study.

Molecular Gas Mass
For galaxies in which CO emission is detected, we estimate the masses of the molecular gas from the CO intensities S CO Δv given in Table 2.The table contains the objects studied in Paper I. We take the following relation from Bolatto et al. (2013): where X CO is the conversion factor from CO to H 2 and D L is the luminosity distance.The empirical factor F ul specifies the CO excitation used to estimate the CO(1-0) flux from higher J measurements since we are comparing different transition lines.Specifically, F 21 gives a CO(2-1)/CO(1-0) line ratio on the flux density (Jy) scale of 3.2, and F 32 gives a CO(3-2)/CO (1-0) ratio of 7.2 (Rose et al. 2019;Russell et al. 2019).
Since the conversion factor X CO is not well understood for elliptical galaxies, we adopt a default value of 1 1 measured in the Milky Way, following previous studies (Olivares et al. 2019;Russell et al. 2019 and see their discussion).For galaxies in which no CO emission is detected, we estimate the upper bounds of the mass from the 3σ upper bounds of S CO Δv.The resulting mass M mol is shown in Table 2.

Circumnuclear Gas and Jet Power
Figure 4(a) shows the relationship between the mass of molecular gas within 500 pc of the center (M mol ) and the AGN jet power required to produce all the observed X-ray cavities in the galaxy (P cav ).The red filled squares represent NCEGs, while the black filled circles represent BCGs.While the data of P cav for the NCEGs are taken from Cavagnolo et al. (2010), those for the BCGs are taken from Rafferty et al. (2006) and Pulido et al. (2018).The jet powers for the BCGs were measured in the same manner as for the NCEGs.
The NCEGs analyzed in this paper have lower values of M mol (10 7 M ☉ ; Table 2) compared to the BCGs analyzed in Paper I (M mol  10 7 M ☉ ).The Kendall rank correlation coefficient on the logarithmic scales is τ = 0.472 with a p-value of 1.9 × 10 −3 , which is below the standard threshold of 0.01.Here, the p-value indicates the probability that the quantities are statistically independent.The coefficient and the regression line (Akritas-Theil-Sen line; Helsel 2004) are calculated for all   galaxies including seven galaxies for which only the upper limit of M col was obtained using the R/CRAN package NADA. 7The regression line can be represented by a powerlaw model as follows: where A 1 and B 1 are parameters, and we get A 1 = 1.3 and B 1 = −8.6.Thus, the relation can be written as . The scatter in the relationship between M mol and P cav may be due to physical factors (see Section 5.1).Note that the correlation is mainly influenced by the BCGs.This is because no correlation can be found for the 12 NCEGs alone.
We also checked the molecular gas mass within the radius of 250 pc.Considering the given beam sizes, we include all NCEGs and five BCGs (NGC 5044, A262, A3581, A2052, and M 87).Hydra A is not included due to strong absorption around the center (Paper I).For the molecular gas mass within 250 pc (Figure 4(a)), we examined the P cav -M mol relation and found that the correlation coefficient is τ = 0.25 and the p-value is 0.16.The lack of correlation is partly due to the small number of BCGs that contribute much to the P cav -M mol relationship.

Circumnuclear Gas and Continuum Emission
While P cav depends on AGN activity on a timescale of ∼10 7 yr, the radio continuum emission is associated with recent (10 3 yr) AGN activity (Section 1).Thus, the presence or absence of the correlation between M mol and the continuum luminosity reflects the time variability of the gas supply and/or AGN activity on the shorter timescale.
Figure 4(b) shows the relation between M mol and L con , which is the continuum luminosity in the millimeter/submillimeter band.The luminosity is calculated from the continuum flux in the line-free ALMA channels.Fluxes observed at different frequencies are converted to those at the rest-frame CO(1-0) line frequency (ν 10 = 115.3GHz), assuming that the continuum emission is represented by a power law of n n µ n g 10 , where ν is the frequency.A typical spectral index of γ = − 0.75 is assumed, following Paper I. In fact, the contribution of dust emission is not significant (see Section 5.3) and the results do not depend much on γ.For an object observed at the frequency ν con and located at the redshift z, we estimate the radio continuum luminosity at the frequency ν 10 to be where F con is the observed flux (mJy), and η is the line frequency ratios (η = 1 for CO(1-0), η ≈ 2 for CO(2-1), and η ≈ 3 for CO(3-2)), which is needed to convert the flux between different line frequencies.The redshift dependence of (1 + z) −(1+γ) comes from the K-correction (e.g., Runburg et al. 2022).The values of ν con , F con , and L con are listed in Table 2.
The relationship between L con and M mol is shown in Figure 4(b).There is a correlation between M mol and L col with a correlation coefficient of τ = 0.515 and a p-value of 6.8 × 10 −4 .The regression line can be represented by a power-law model of the form: where A 2 and B 2 are fit parameters and we obtain A 2 = 1.4 and B 2 = −11.5.
We also calculate the continuum luminosity at 1.4 GHz (L 1.4 ) from the observed flux at 1.4 GHz taken from the literature: where ν 1.4 is 1.4 GHz and F 1.4 is the observed flux at 1.4 GHz (Table 2), and γ = −0.75.The derived luminosities L 1.4 are shown in Table 2 and compared to M mol in Figure 4(c).The correlation coefficient is τ = 0.437 and the p-value is 4.0 × 10 −3 , indicating the existence of a correlation between M mol and L 1.4 , which can be represented by a power-law model of the form: where A 3 and B 3 are fit parameters and we obtain A 3 = 2.0 and The presence of the correlations (Equations ( 4) and ( 6)) indicates that the short-term variability in gas supply and/or AGN activity is not strong enough to break the correlations.In Paper I we concluded that there were no correlations between M mol and L col and between M mol and L 1.4 . 8The results of the current paper suggest that the lack of correlations is simply due to the small number of sample galaxies and the narrow range of M mol .

Correlations and Scatter
The results shown in Section 4 indicate that the mass of the circumnuclear molecular gas (M mol ) is correlated not only with the jet power (P cav ), but also with the continuum luminosities (L con and L 1.4 ).
The power P cav depends on the averaged AGN activity on a timescale of ∼10 7 yr, while the luminosities L con and L 1.4 are associated with recent (10 3 yr) AGN activity (Section 1). 9he correlations shown in Figure 4 exhibit a scatter of about ±0.5 dex.This may indicate that the actual accretion of the cold gas is intermittent due to turbulence in the gas (Pizzolato & Soker 2010;Gaspari et al. 2017) or precipitation (Voit et al. 2015).
We note that the actual mass accretion rate (M  ) or the AGN power depends not only on the mass of the circumnuclear gas (M mol ) but also on other factors such as the dynamical stability of the gas around the black hole (Kawakatu & Wada 2008;Fujita et al. 2022).The cycle of variation for each factor is likely to be different.For example, in the model of Fujita et al. (2022), the circumnuclear gas lifetime is 10 8 yr, while the timescale of dynamical stability is 10 7 yr.Smaller timescales can also affect AGN activity.For example, if the circumnuclear gas is very clumpy on a scale much smaller than the resolution of ALMA, M  could fluctuate on a timescale of <10 7 yr.Indeed, recent observations by Ubertosi et al. (2023) have shown that while the overall properties of the cool gas do not appear to change on timescales of 10 7 yr, AGN activity has shorter variability timescales.If this difference changes M M mol  by a factor of 3 ( ∼ 10 0.5 ), the scatter of the correlations in Figure 4 could be explained.Moreover, the difference in the conversion factor X CO among galaxies could be another cause of the scatter.
The difference in black hole spin among our sample galaxies may also contribute to the scatter in the relations in Figure 4. Sikora et al. (2007) showed that elliptical galaxies are systematically more radio-loud than spiral galaxies, probably because of a larger black hole spin.The angular momentum brought by the accreted cold gas can spin-up the black holes.In fact, some of our sample galaxies appear to have a disk (NGC 315 and NGC 4261 in Figures 2 and 3), showing that the gas has angular momentum.Other galaxies may also have unresolved small disks.It will be interesting to study the relationship between disk properties and AGN power in the future.
The relationship between the amount of molecular gas around the black hole and the activity of the AGN10 is also known in disk galaxies (Izumi et al. 2016).Therefore, the mechanism that fuels the AGN in elliptical galaxies may be similar to that in disk galaxies.
The NCEGs alone do not form a correlation in Figure 4(a) (Section 4.2).Thus, it is not clear whether the P cav -M mol relationship extends from the BCGs to the NCEGs.We need more samples to infer the correlation among the NCEGs.Although the number of NCEGs is small, the wide distribution of NCEGs in Figure 4(a) suggests that the potential scatter of the possible correlation is large.

Black Hole Mass
Since the region we focused on (500 pc) is much smaller than the effective radii of the galaxies (10 kpc; Samir et al. 2016), it is unlikely that the overall properties of the galaxies directly affect M mol and AGN activity.Instead, local properties, such as the mass of the central black hole, M BH , may play some role in AGN activity.In fact, Figure 4(a) shows that BCGs (black marks) tend to have larger P cav , and one might think that this is a result of their larger black hole masses.Here we check this possibility.
In Figure 5 we plot the jet power against the black hole masses M BH , which are taken from the literature and adjusted to our cosmological parameters.The masses are listed in Table 2.For all 22 galaxies, the correlation coefficient is τ = 0.234, and the p-value is 0.13, indicating a lack of correlation.This is because some galaxies have significant uncertainties in M BH and P cav (Figure 5).Thus, there is no conclusive evidence that the mass of a black hole is a primary factor in the activity of an AGN, at least within our sample of galaxies.Of course, we do not deny a possible correlation between M BH and P cav for more precise data that would be obtained in the future.Since the mass of the black hole reflects the mass and velocity dispersion of the host galaxy (e.g., Magorrian et al. 1998;Ferrarese & Merritt 2000), the fact that our sample galaxies have similar M BH (∼10 9 M ☉ ) suggests that the host galaxies also have similar properties.
For AGNs not restricted to those in elliptical galaxies, a correlation between jet power and black hole mass has been reported (Liu et al. 2006).However, the correlation has a large scatter (±1 dex), while M BH spans 3 orders of magnitude.In addition, Chen et al. (2015) pointed out that the correlation between jet power and black hole mass is unclear for AGNs with low gas accretion rates (small Eddington ratios), while the correlation between jet power and accretion rate is prominent for these AGNs.This may be consistent with our results because the accretion rates to AGNs in nearby elliptical galaxies are generally small (Rafferty et al. 2006).

The Origin of the Millimeter/submillimeter Continuum Emission
We found the correlation between M mol and continuum emission in Section 4.3.The origin of the continuum emission reflects what kind of matter is present around the AGNs.In Figure 6 we show the ratio of F con /F 1.4 .With the exception of NGC 5044, the ratio is less than 1, indicating that most of the continuum emission is synchrotron emission from relativistic electrons.In addition, we show a possible continuum spectrum (solid line), which is assumed to be represented by a combination of power-law (synchrotron) and modified blackbody (dust) components: AGN BB b 0 where γ = −0.75,ν 0 = 1.5 THz, b = 1.5, and B ν (ν, T) is a blackbody distribution (e.g., Falkendal et al. 2019).The dust temperature is assumed to be T = 10 K (Fogarty et al. 2019; see Paper I).The values for N AGN and N BB are adjusted to match the observations of NGC 5044. Figure 6 shows that, except for NGC 5044, the effect of the dust component is minimal at frequencies around 100-300 GHz, in agreement with local AGN observations (Kawamuro et al. 2022).A t-test shows that the ratios of F con /F 1.4 for the NCEGs are statistically indistinguishable from those for the BCGs.In Paper I we discussed that galaxies with smaller L 1.4 may have a larger contribution from dust emission at ∼100-300 GHz, because , and the trend disappears.

Conclusion
Cold molecular gas has been observed in elliptical galaxies, and it is likely that this gas fuels their AGNs.To confirm this speculation, we measured the masses of the gas around the AGNs and discussed their relation to AGN activity.In this study, we extend the sample of galaxies studied in Paper I to lower masses.
Using ALMA data, we studied the CO line emission within 500 pc of the center of 12 NCEGs plus 1 BCG, and detected the emission in 6 of them.We estimated the mass of the molecular gas M mol from the emission and combined the results with those of nine BCGs studied in Paper I. We found that M mol is correlated with the jet power of the central AGN (P cav ), which is given by » ´ 1 , although NCEGs alone do not show the correlation.This suggests that AGNs are powered by molecular gas.Moreover, M mol is also correlated with the continuum luminosity of AGNs at ∼1.4 GHz and ∼100-300 GHz.Since P cav reflects long-term AGN activity, while the luminosity of the continuum indicates short-term AGN activity, our findings suggest that the amount of gas is a critical factor that affects AGN activity, regardless of the temporal scale.
On the other hand, we cannot find a clear relationship between the mass of black holes in AGNs (M BH ) and P cav .This may be due to the large uncertainties in the data, but it suggests that M mol , rather than M BH , is the primary factor influencing AGN activity.We confirm that synchrotron radiation is mostly responsible for the continuum emission from AGNs at ∼1.4-300 GHz.
In galaxy formation studies, different models of gas accretion onto black holes have been adopted.For example, the Bondi accretion model is used in the Illustris simulations (e.g., Sijacki et al. 2015).Some semianalytical models of galaxy formation use an empirical model of cold gas accretion (e.g., Enoki et al. 2014).The simple correlation we found between M mol and P cav could be used instead of these models.), and open squares (NCEGs + BCGs) show ((1 + z)ν 1.4 , 1); the latter is almost independent of galaxies.The solid line represents a power-law + modified blackbody spectrum reproducing the observations for NGC 5044 (see the main text).The observational errors and the effects of 1 + z are negligible.

Figure 2 .
Figure 2. Close-up CO integrated intensity (moment 0) map.The AGNs are located in the center of the figures and are indicated by the crosses.The beam is shown in white at the bottom left of each panel.

Figure 3 .
Figure 3. CO line spectra within 500 pc from the AGNs.

Figure 4 .
Figure 4. Molecular gas mass within 500 pc of the AGN compared to (a) jet power estimated from X-ray cavities, (b) continuum luminosity in the millimeter/ submillimeter band, and (c) continuum luminosity at 1.4 GHz.Red filled squares represent NCEGs, while black filled circles represent BCGs.Galaxies for which only the upper bounds of M mol are determined are represented by the left-pointing open triangles (red denotes NCEGs and black denotes BCGs).The thick solid line shows the regression line (Akritas-Theil-Sen line).In (a), the cyan crosses are the objects for which molecular gas masses within 250 pc of the AGN are obtained, and the green dots are the values obtained byRussell et al. (2019); uncertainties are not shown.For the former, objects for which only the upper limit is obtained are omitted.For the latter, the correlation found byRussell et al. (2019) is shown by the thin dotted line.

Figure 5 .
Figure5.Jet power vs. black hole mass.Red squares are the NCEGs and black circles are the BCGs.Filled marks are the galaxies for which M mol is determined, while open marks are those for which only the upper limit of M mol is obtained.

Table 2
Target and Observation Details