# Lack of Correlations between Cold Molecular Gas and AGN Properties in Type 1
AGNs at $z\lesssim 0.5$

Juan Molina Kavli Institute for Astronomy and Astrophysics, Peking University,
Beijing 100871, China  Department of Space, Earth and Environment, Chalmers
University of Technology, Onsala Space Observatory, 439 92 Onsala, Sweden
Jinyi Shangguan Max-Planck-Institut für Extraterrestrische Physik (MPE),
Giessenbachstr., D-85748 Garching, Germany  Ran Wang Kavli Institute for
Astronomy and Astrophysics, Peking University, Beijing 100871, China
Department of Astronomy, School of Physics, Peking University, Beijing 100871,
China  Luis C. Ho Kavli Institute for Astronomy and Astrophysics, Peking
University, Beijing 100871, China  Department of Astronomy, School of Physics,
Peking University, Beijing 100871, China  Franz E. Bauer Instituto de
Astrofísica, Facultad de Física, Pontificia Universidad Católica de Chile,
Campus San Joaquín, Av. Vicuña Mackenna 4860, Macul Santiago, Chile, 7820436
Centro de Astroingeniería, Facultad de Física, Pontificia Universidad Católica
de Chile, Campus San Joaquín, Av. Vicuña Mackenna 4860, Macul Santiago, Chile,
7820436  Millennium Institute of Astrophysics, Nuncio Monseñor Sótero Sanz
100, Of 104, Providencia, Santiago, Chile  Ezequiel Treister Instituto de
Astrofísica, Facultad de Física, Pontificia Universidad Católica de Chile,
Campus San Joaquín, Av. Vicuña Mackenna 4860, Macul Santiago, Chile, 7820436
Centro de Astroingeniería, Facultad de Física, Pontificia Universidad Católica
de Chile, Campus San Joaquín, Av. Vicuña Mackenna 4860, Macul Santiago, Chile,
7820436

###### Abstract

We present new NOrthern Extended Millimeter Array (NOEMA) observations of the
CO(2–1) emission in eight of the brightest Palomar-Green quasars at $z\lesssim
0.5$ to investigate the role of active galactic nuclei (AGN) feedback in
luminous quasars detected at low redshifts. We detect CO(2–1) emission in
three objects, from which we derive CO luminosities, molecular gas masses and
fractions, and gas depletion times. In combination with data available in the
literature, we build a total sample of 138 local type 1 AGNs with CO(2–1)
measurements. We compare the AGN properties with the host galaxy molecular gas
properties, considering the systems non-detected in CO emission. We find that
the CO luminosity does not correlate with AGN luminosity and Eddington ratio,
while the molecular gas fraction is weakly correlated with Eddington ratio.
The type 1 AGNs can be roughly separated into two populations in terms of
infrared-to-CO luminosity ratio, one population presenting values typically
found in normal star-forming systems, while the other have lower ratio values,
comparable to those measured for starbursts. We find no evidence that AGN
feedback rapidly quenches star formation in type 1 AGNs. Our results may imply
an underlying the role of host galaxy gravitational instabilities or the fast
inflow of cold gas in triggering AGN activity.

galaxies: active — galaxies: star formation — quasars: general

††software: Astropy (Astropy Collaboration et al., 2013; Price-Whelan et al.,
2018), matplotlib (Hunter, 2007), numpy (Oliphant, 2006), GILDAS (Guilloteau &
Lucas, 2000).

##  1 Introduction

The evolution of galaxies is tightly correlated with the growth of the
supermassive black holes (BHs) as evidenced by the correlations between the BH
mass and the host galaxy bulge properties (Magorrian et al., 1998; Ferrarese &
Merritt, 2000; Gebhardt et al., 2000). The connection between BH accretion and
the host galaxy growth naturally arises because both depend on the same fuel
reservoir, replenished largely by similar processes that drive gas inward
(Kormendy & Kennicutt, 2004). The co-evolution of the BH and host galaxy
(Kormendy & Ho, 2013) is widely accepted to be regulated by the feedback of
the active galactic nuclei (AGN; Fabian 2012). During the accretion of mass
onto the BH, vast amounts of energy are released, and a merely minor fraction
of this power coupled to the BH surroundings can heat and/or expel the gas
from the host galaxy (e.g., Somerville et al. 2008; Schaye et al. 2015;
Sijacki et al. 2015; Nelson et al. 2018), thereby halting the ongoing star
formation activity (Dubois et al., 2016). The AGN feedback can also affect the
galaxy halo, preventing the condensation of cold and warm gas, and further
hamper the star formation over long timescales (Bower et al., 2006; Croton et
al., 2006; Fabian, 2012; Gaspari et al., 2020).

During the last decade, numerous efforts have been focused to test whether AGN
feedback effectively removes sufficient cold gas from the host galaxy to
curtail ongoing star formation activity. Studies focusing on comparisons with
control samples and/or the main-sequence of star-forming galaxies have
reported no difference between the inactive galaxies and those hosting AGNs
(Rosario et al. 2018; Kirkpatrick et al. 2019; Schulze et al. 2019; Florez et
al. 2020; Koss et al. 2021; Salvestrini et al. 2022; Smirnova-Pinchukova et
al. 2022, but see Vito et al. 2014; Scholtz et al. 2018; Stemo et al. 2020).
Correlations between key host galaxy properties, such as molecular hydrogen
(H2) content, star formation rate (SFR), and/or star formation efficiency,
with AGN luminosity suggest that low-$z$ luminous AGNs are mainly hosted in
typical star-forming galaxies (e.g., Harrison et al. 2012; Rosario et al.
2012, 2013; Zhang et al. 2016; Stanley et al. 2017; Husemann et al. 2017;
Bernhard et al. 2019; Grimmett et al. 2020; Yesuf & Ho 2020; Jarvis et al.
2020; Koss et al. 2021; Vietri et al. 2022), while the more luminous active
systems tend to be found in starbursts (e.g., Young et al. 2014; Bernhard et
al. 2016; Pitchford et al. 2016; Kirkpatrick et al. 2020; Shangguan et al.
2020a; Xie et al. 2021; Zhuang et al. 2021). Only a few studies of high-$z$
AGNs ($z\approx 1-2$) suggest reduced molecular gas content in AGN hosts
(Kakkad et al., 2017; Perna et al., 2018; Circosta et al., 2021; Bischetti et
al., 2021). Whether or how the luminous AGN does efficiently remove or heat
the gas from host galaxy and affect the ongoing star formation is still
uncertain (Harrison et al., 2017).

Optically visible and largely unobscured quasars–the most luminous AGNs–
allows us to study possible effects of AGN feedback on their host galaxies. An
unobscured quasar is thought to arise after the overwhelming release of energy
from the AGN that expels the gas and dust enshrouding the nucleus (e.g.,
Sanders et al. 1988; Hopkins et al. 2008). Strikingly, the study of the global
IR ($\sim 1-500\,\mu$m) spectral energy distribution (SED) emission in a set
of 87 local ($z<0.5$) Palomar-Green (PG) quasars (Boroson & Green, 1992)
suggested that most of these unobscured AGNs have dust-based molecular gas
masses comparable to normal star-forming galaxies with similar stellar mass
(Shangguan et al., 2018). Follow-up Atacama compact array (ACA) observations
targeting the carbon-monoxide molecule (12CO) emission and previous literature
observations confirmed the results from the global IR SED analysis. The
CO$\,J=2\rightarrow 1$ transition [$\nu_{\rm rest}=230.538\,$GHz; hereafter
CO(2–1)] emission was detected in a total 34 out of 40 PG quasars. The global
CO emission line shapes further suggested that the molecular gas appears
kinematically regular within the host galaxies (Shangguan et al. 2020a, b, see
also Molina et al. 2021). However, the PG quasar sample observed in CO is
admittedly biased toward the less luminous local PG quasars ($L_{\rm
bol}\lesssim 10^{45}\,$erg s-1; Figure 1). Luminous AGNs can drive multi-phase
outflows and deposit its energy into the host galaxy interstellar medium (ISM;
Cicone et al. 2014; Feruglio et al. 2015; Perna et al. 2015; Morganti 2017;
Cicone et al. 2018; Fluetsch et al. 2019; Veilleux et al. 2020; Girdhar et al.
2022). The outflow energetics correlate with AGN luminosity (molecular gas
mass outflow rates $\propto L_{\rm bol}^{0.76}$ and kinetic power $\propto
L_{\rm bol}^{2.27}$; Fiore et al. 2017) meaning that the AGN feedback effect
on the host galaxy ISM, if any, should be more easily detected in more
luminous AGNs.

In this work, we report new NOrthern Extended Millimeter Array (NOEMA)
observations targeting the CO(2–1) for a sub-sample of eight $z\approx
0.3-0.5$ PG quasars selected from Shangguan et al. (2018). Those targets
correspond to the more luminous PG quasars at $z\lesssim 0.5$. By using
complementary data taken from the literature, we build a total sample of 138
unobscured local AGNs covering the $L_{\rm bol}\approx 10^{43}-10^{47}\,$erg
s-1 range to study the relation between the host galaxy molecular gas content
and AGN activity, and to explore whether AGN feedback is effectively operating
in those sources. The paper is organized as follows. Section 2 presents our
sample, observation strategy and data reduction. The data analysis is
described in Section 3, and the subsequent results are described in Section 4.
We further discuss our findings in Section 5. Section 6 is the conclusion. We
adopt a $\Lambda$CDM cosmology with $\Omega_{m}=0.308$,
$\Omega_{\Lambda}=0.692$, and $H_{0}=67.8\,$km s${}^{-1}\,$Mpc-1 (Planck
Collaboration et al., 2016).

Figure 1:  Black hole mass as a function of the AGN monochromatic luminosity
at 5100 Å for the PG quasar host galaxies. The red-filled circles present the
8 targets observed by NOEMA and analyzed in this work. The open circles show
the PG quasars with previous CO observations (Shangguan et al., 2020b), while
the blue circles correspond to the parent sample of $z\lesssim 0.5$ PG quasars
observed by Herschel (Shangguan et al., 2018). The dashed lines represent
constant Eddington ratio values. We target a sub-sample of PG quasars with
more massive BHs and luminous AGNs, complementing the previous CO
observations. Table 1:  Basic Parameters of the Sample

Object | R.A. | Decl. | $z$ | Morphology | $\log M_{\star}$ | $\log\lambda L_{\rm 5100}$ | $\log M_{\rm BH}$ | $L_{\rm bol}/L_{\rm Edd}$
---|---|---|---|---|---|---|---|---
| (J2000.0) | (J2000.0) |  |  | ($M_{\odot}$) | (erg s-1) | ($M_{\odot}$) |
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9)
PG 1049$-$005 | 10:51:51.45 |  $-$00:51:17.7 | 0.357 | Merger | 11.1∗ | 45.60 | 9.34 | 0.14
PG 1100$+$772 | 11:04:13.86 |  $+$76:58:58.2 | 0.313 | Elliptical | 11.27 | 45.55 | 9.44 | 0.10
PG 1259$+$593 | 13:01:12.96 |  $+$59:02:06.7 | 0.472 | Elliptical | 10.99 | 45.88 | 9.09 | 0.49
PG 1425$+$267 | 14:19:03.82 |  $+$26:32:14.5 | 0.366 | Elliptical | 11.15 | 45.73 | 9.90 | 0.05
PG 1512$+$370 | 15:14:43.07 |  $+$36:50:50.3 | 0.371 | Elliptical | 11.01 | 45.57 | 9.53 | 0.09
PG 1704$+$608 | 17:04:41.37 |  $+$60:44:30.5 | 0.371 | Elliptical | 11.52 | 45.67 | 9.55 | 0.10
PG 2112$+$059 | 21:14:52.58 |  $+$06:07:42.4 | 0.466 | Elliptical | 10.8∗ | 46.16 | 9.18 | 0.76
PG 2251$+$113 | 22:54:10.42 |  $+$11:36:38.7 | 0.323 | Elliptical | 11.05 | 45.66 | 9.15 | 0.26

Note— (1) Source name. (2) Right ascension. (3) Declination. (4) Redshift. (5)
Morphology of the host galaxy (Zhang et al., 2016; Zhao et al., 2021) (6)
Stellar mass; the $1\,\sigma$ uncertainty is 0.3 dex (Shangguan et al., 2018).
(7) AGN monochromatic luminosity at 5100 Å. We assume a $1\sigma$ error of
0.05 dex (Vestergaard & Peterson, 2006). (8) Black hole mass, estimated by
applying the calibration of Ho & Kim (2015) and taken from Shangguan et al.
(2018); the $1\sigma$ uncertainty is 0.3 dex. (9) Eddington ratio, where
$L_{\rm bol}=10\,L_{\rm 5100}$ (Richards et al., 2006) is the bolometric
luminosity, and $L_{\rm Edd}=1.26\times 10^{38}(M_{\rm BH}/M_{\odot})$ erg s-1
is the Eddington luminosity. (∗) The stellar mass values are taken from Zhao
et al. (2021), but carry large uncertainty ($\sim 0.7-0.9\,$dex).

Table 2:  NOEMA Observational Setup

Object | Observation | Bandpass & |  Amplitude & | PWV | Observing | Beam Size | Beam Position | Half-power | Maximum Recoverable
---|---|---|---|---|---|---|---|---|---
| Date | Flux Calibrator |  Phase Calibrator | (mm) |  Time∗ (h) |  ($\arcsec\times\arcsec$) |  Angle (∘) |  Beamwidth ($\arcsec$) |  Scale∗∗ ($\arcsec$)
(1) | (2) |  (3) |  (4) | (5) | (6) | (7) | (8) | (9) | (10)
PG 1049$-$005 | 10 Apr. 2022 | 3C84 |  1044+018 / J1028$-$0236 | 3 | 1.5 | $3.3\times 1.0$ | 11 | 29.7 | 9.9
PG 1100$+$772 | 6/14 Apr. 2022 | 3C345 | 1039+811 / 1044+719 | 4 | 4.1 | $2.8\times 1.1$ | 40 | 28.7 | 12.1
PG 1259$+$593 | 13 Apr. 2022 | 3C279 | 1300+580 / J1259+516 | 5–6 | 2.6 | $2.4\times 1.5$ | 127 | 32.2 | 12.8
PG 1425$+$267 | 6 Apr. 2022 | 3C273 | 1417+273 / J1422+323 | 4 | 1.1 | $2.4\times 1.3$ | 110 | 29.9 | 14.5
PG 1512$+$370 | 10 Apr. 2022 | 3C279 | 3C345 / 1504+377 / 1505+428 | 2 | 2.6 | $2.4\times 1.0$ | 71 | 30.0 | 11.3
PG 1704$+$608 | 14/15 Apr. 2022 | 0851+202 / 2013+370 | 1637+574 / 1645+635 | 3–6 | 2.2 | $3.0\times 1.3$ | 98 | 30.0 | 11.7
PG 2112$+$059 | 6 Apr. 2022 | 3C345 | 2059+034 / 2121+053 | 4 | 1.5 | $3.5\times 1.4$ | 18 | 32.0 | 13.8
PG 2251$+$113 | 17/18 Apr. 2022 | 2013+270 / 2230+114 | 3C454.3 / 2230+114 | 1–3 | 6.4 | $3.7\times 1.4$ | 12 | 29\. 5 | 14.5

Note— (*) Including overheads.

##  2 Sample and Observations

We focus on observing 8 PG quasars taken from the broader sample of 87 $z<0.5$
quasars belonging to the PG survey (Boroson & Green, 1992). The PG quasars
were selected by their optical/ultraviolet colors, and correspond to luminous,
broad-lined (type 1) AGNs. Multi-wavelength data are available across the
entire electromagnetic spectrum range, from X-ray (Reeves & Turner, 2000;
Bianchi et al., 2009) through optical (Boroson & Green, 1992; Ho & Kim, 2009),
mid-IR (Shi et al., 2014; Xie et al., 2021; Xie & Ho, 2022), far-IR (Petric et
al., 2015; Shangguan et al., 2018; Zhuang et al., 2018), mm (Shangguan et al.,
2020a, b), and radio (Kellermann et al., 1989, 1994; Silpa et al., 2020)
wavelengths, allowing detailed SED characterization and accurate estimation of
the global SFR and gas content of the host galaxies (Shangguan et al., 2018).
A major fraction of the sample has been already observed in the optical and
near-IR by the Hubble Space Telescope (HST) at $\sim 0.1\arcsec$ resolution
(Kim et al., 2008; Zhang et al., 2016; Kim & Ho, 2019; Zhao et al., 2021),
while arcsecond resolution interferometric and integral field unit data are
accessible for a few of these (Molina et al., 2021, 2022a).

Shangguan et al. (2020a) presented CO(2–1) observations for a representative
sample of 40 $z<0.3$ PG quasars, 23 newly observed host galaxies using ACA
(synthesized beam FWHM $\sim 6\,\arcsec$). They reported line emission
detection in 34 host galaxies, 21 sources detected from their ACA campaign.
For the ACA data, Shangguan et al. (2020a) computed the global CO velocity
integrated fluxes by spatially collapsing the spectra over the $2\,\sigma$
contour region of the imaged data, to then fit the emission line using a
single Gaussian or double-horn profile functions.

We selected the 8 PG quasar host galaxies to complement and expand the sample
already observed in CO(2–1) emission, specially at high AGN luminosity
($\lambda L_{5100}\gtrsim 10^{45.5}\,$ erg s-1) where Shangguan et al. (2020a)
only reported CO(2–1) measurements for 3 host galaxies (Figure 1). Our
selection was based on requiring: (1) PG quasars with AGN monochromatic
luminosities at 5100 Å ($\lambda L_{5100}$) higher than $10^{45.5}\,$ erg s-1;
and (2) targets with robust AGN/host galaxy far-IR SED decomposition performed
by Shangguan et al. (2018). The first criterion implies that we build a
combined sample of PG quasars spanning $\sim 2$ orders of magnitude in terms
of $\lambda L_{5100}$ and BH masses (Figure 1). The second criterion ensures
that the host galaxies have accurate estimates for the dust 8 to 1000$\mu$m
far-IR luminosity, so that their SFR could be reliably computed. We show the
properties of our targets in Table 2.

The CO(2–1) emission line was observed with NOEMA on 6–18 April, 2022, as part
of the program W21CI (PI: J. Molina). The observations were carried out using
10 or 11 antennas in compact array (D) configuration, dual polarization, and
for total sample observing time of 22 h. We used the autocorrelator PolyFix,
which covers a total bandwidth of 15.5 GHz in each linear polarization, and
split between the lower sideband (LSB) and the upper sideband (USB). The
channel width is 2 MHz, namely 3.4 km s-1 at the tuning frequency (set in the
USB) of our observations. The synthesized beam FWHM size is
$1.0-3.7\,\arcsec$, corresponding to scales between 5 and 21 kpc at the
redshift of our sources. The observational setup for each source is detailed
in Table 2.

###  2.1 Data Reduction

We reduced the data following the standard procedure using the GILDAS software
(Guilloteau & Lucas, 2000). The data were calibrated using the Institute for
Radio Astronomy in the Millimeter Range (IRAM) package Continuum and Line
Interferometer Calibration (CLIC). The standard pipeline reduction and
calibration was implemented to a large extent, but some minor fraction of data
scans were flagged following the astronomer on duty
report.111https://www.iram.fr/IRAMFR/GILDAS/doc/pdf/pdbi-cookbook.pdf We
imaged the data using the MAPPING software of GILDAS. We used the uv_cont task
to combine all the line-free channels in both sidebands (we also avoided the
noisy channels), and then we merged those using uv_merge to produce the
continuum $uv$ table for each source. To produce the emission line $uv$ table
we subtracted the continuum using uv_base from the calibrated $uv$ tables in
the USB. Then, we used the task uv_compress to set the data spectral
resolution. For PG 1049$-$005 and PG 1259$+$593 we set the channel width $\sim
40\,$km s-1 as both were detected in CO emission at high signal-to-noise. For
the rest of the sample we set a channel width $\sim 100\,$km s-1 after
exploring different spectral setup aiming to maximize CO line detection.222The
target PG 2251+113 was found offset by $2.2\arcsec$ and $-2.7\arcsec$ in right
ascension and declination, respectively, from the expected location. We
corrected the observation pointing by this offset using uv_shift before
proceeding with the continuum and emission line $uv$ tables construction. For
both, the continuum and the emission line $uv$ tables, we produced the dirty
images using the task uvmap and estimated the data rms level (Table 3). Those
values broadly correspond to our observation sensitivity requirements. The
image pixel size is set to $0.2\arcsec$ following uvmap task recommendation.
We used the CLEAN algorithm in the version of Högbom (1974) to do the data
deconvolution. We use natural weighting to maximize the observation
sensitivity. We set CLEAN down to the data rms level by doing many iterations
as needed. After doing the cleaning, we visually checked the residual maps,
finding no emission higher than the noise level in any target. The data are
corrected for primary beam. Finally, the imaged data was converted to the
usual FITS format using the task vector$\backslash$fits. We consider a
conservative systematic NOEMA flux calibration uncertainty of 20 % at 2 mm.1

###  2.2 IR Spectral Energy Distribution

To estimate the IR luminosity decontaminated from AGN effects for our targets,
we benefit from the panchromatic IR SED from $\sim 1$ to 500 $\mu$m,
complemented by mid-IR ($5-38\,\mu$m) spectra from the Spitzer Infrared
Spectrometer (IRS), and available radio data collated in Shangguan et al.
(2018). Briefly, in the near-IR the fluxes were re-derived by Shangguan et al.
(2018) from the 2MASS (Skrutskie et al., 2006) $J$, $H$ and $K_{s}$ bands
(Cohen et al., 2003) images using $7\,\arcsec$ aperture radius with the sky
annulus set to a radius of 25 to $35\,\arcsec$. Shangguan et al. (2018) also
re-estimated the mid-IR WISE (Wright et al., 2010; Jarrett et al., 2011) $W1$
($3.353\,\mu$m) and $W2$ ($4.603\,\mu$m) fluxes for the PG quasars, but
avoided to include the $W3$ ($11.561\,\mu$m) and $W4$ ($22.088\,\mu$m) data
due to known systematic uncertainties associated to the red color of the
targets, plus the bands wavelength overlap with the bandpass of the Spitzer
IRS spectra. The WISE $W1$ and $W2$ fluxes were computed using a similar
method to that used for the 2MASS images. An aperture radius of
$8.25\,\arcsec$, plus a sky annulus of $50-70\,\arcsec$ were adopted. Coadded
PSFs for the WISE bands were used to compute the aperture correction factors.
The Herschel Photodetector Array Camera and Spectrometer (PACS, Poglitsch et
al. 2010) and Spectral and Photometric Imaging Receiver (SPIRE; Griffin et al.
2010) observations were formally presented in Shangguan et al. (2018) for the
PG quasars. For the PACS data, point-source aperture photometry were performed
using 12, 12, and $22\,\arcsec$ aperture radius for the 70, 100, and
$160\,\mu$m bands. Sky annulus radius were set to $35-45\,\arcsec$ to minimize
PSF wing contamination, and aperture corrections were also applied. From the
SPIRE data, the sources flux density values or upper limits were computed
following Savage & Oliver (2007). The Spitzer data were processed by Shi et
al. (2014), who scaled the short-low ($5-14\,\mu$m) spectrum, the long-low
($14-40\,\mu$m) spectrum, and the overall flux of the spectrum to match the
Spitzer MIPS $24\,\mu$m photometry. Shangguan et al. (2018) also found that
the density flux scale of the Spitzer spectra were well-matched with respect
to the WISE data. The radio data were updated from that presented in Shangguan
et al. (2018) considering newer literature data. We present the radio data in
Appendix A.

Figure 2:  Comparison between our target sample (red) with the sample of PG
quasars with previously detected CO emission (black; Shangguan et al. 2020b),
the BASS type 1 AGN sub-sample (grey), and the CARS survey (brown), in terms
of the (a) redshift, (b) host galaxy stellar mass, (c) 5100 Å AGN luminosity,
and (d) BH mass. Our target sample is presented over the “PG quasar–ACA”
sample data to improve figure visualization.

###  2.3 Complementary AGN Sample

We complement our PG quasar CO survey with literature data taken from two main
surveys, the BAT-AGN Spectroscopic Survey (BASS) sample presented in Koss et
al. (2022) and the Close AGN Reference Survey (CARS; Husemann et al. 2022). In
their data-release 2, the BASS AGNs consist of 858 nearby ($z\lesssim 0.24$)
AGNs selected by their ultrahard (14–195 keV) X-ray emission. We select a sub-
sample of BASS AGNs presenting H$\alpha$ and H$\beta$ broad-lines,333Mejía-
Restrepo et al. (2022) refer to those systems as Seyfert 1, 1.2, 1.5, and 1.8,
based on the ratio between the broad H$\beta$ and [O iii] line luminosity.
Here, we only refer to those BASS AGNs as “Sy1–1.8”. but we discard all the
BASS AGNs with poor optical spectra models following Mejía-Restrepo et al.
(2022). From this sub-sample, we further select the host galaxies with CO(2–1)
line emission detection or upper limit. Those BASS AGN host galaxies were
observed with the Atacama Pathfinder Experiment telescope (APEX; 46 sources),
the James Clerk Maxwell Telescope (JCMT; 7 sources) and the Caltech
Submillimeter Observatory (CSO; 3 sources). At the observed frequencies ($\sim
220-229\,$GHz), the APEX, JCMT, and CSO observations have effective primary
beam size of $26.3-27.5\,\arcsec$, $20.4\,\arcsec$, and $32\,\arcsec$,
respectively, corresponding to scales of $\sim 6-27\,$kpc at the sources
redshift (Koss et al., 2021). Specifically, we adopt the CO velocity
integrated fluxes computed by fitting the line profiles with a single Gaussian
or double-horn functions. We note that Koss et al. (2021) show that those
values are in good agreement with estimates computed by simply summing the CO
emission over the line spectral range (see their Appendix D). The BASS AGN
measurement uncertainties are 10 % and 15 % for flux calibration and aperture
correction, respectively. We take the BASS AGN host galaxy properties from
Koss et al. (2021). For the CARS survey, we take the AGN and host galaxy
properties from Husemann et al. (2022) and Smirnova-Pinchukova et al. (2022),
respectively. We note that the CO(2–1) line flux measurements were carried out
using the IRAM 30–m telescope (Bertram et al., 2007). The IRAM 30–m telescope
primary beam size is $\sim 10.9-11.4\,\arcsec$ at the observed frequencies
($\sim 217-227\,$GHz), and correspond to a physical scale $\sim 3-11\,$kpc.
Bertram et al. (2007) estimate the CO line velocity integrated fluxes by
simply summing the flux density over the full velocity range of the emission
line. The IRAM 30–m telescope flux calibration uncertainty is $\sim 10$ %.

In consistency with the estimates presented for the PG quasars (Table 1), for
both BASS and CARS AGN surveys we use the AGN monochromatic luminosity at 5100
Å and broad H$\beta$ line width values to estimate $L_{\rm bol}$ and $M_{\rm
BH}$ following Richards et al. (2006) and Shangguan et al. (2018),
respectively. The host galaxy CO luminosity and SFR values are estimated by
using the conventions adopted in this work, and the stellar masses are scaled
assuming the Kroupa (2001) initial mass function (IMF; see Section 3). The BH
masses estimated by us and the values reported by Mejía-Restrepo et al. (2022)
for the BASS AGNs are in good agreement with an average BH mass ratio of $\sim
0.9$ and 0.25 dex scatter. For the CARS sample there are several systems with
fewer than two SED data points at $\lambda\gtrsim 60\mu$m, implying inaccurate
far-IR emission luminosity estimates. Those correspond to 19 out of 38 host
galaxies that were excluded whenever $L_{\rm IR}$ was involved in our
analysis. On average, the discarded systems have slightly lower stellar mass
($-0.2$ dex) and CO(2–1) luminosity ($-0.1$ dex) compared to the full CARS
sample, but present no systematic offset in terms of average molecular gas
fraction, bolometric luminosity, BH mass, and Eddington ratio estimates
(offset $\lesssim 0.05$ dex in terms of absolute value). However, we caution
that by discarding those CARS host galaxies we may result with a sub-sample
biased toward the most IR luminous systems. The excluded CARS AGNs tend to be
found at slightly higher redshifts ($z\approx 0.05-0.06$) compared to the
sample average ($\langle z\rangle\approx 0.04$). We further exclude few
duplicated objects among the BASS, CARS and PG quasar surveys.

Figure 2 presents the properties of our sample, the PG quasars with previous
CO line measurements (Shangguan et al., 2020b), the sub-sample of broad-lined
BASS AGNs, and the CARS targets. The BASS sub-sample correspond 56 $z\lesssim
0.05$ host galaxies (21 upper-limit estimates) . The CARS sub-sample consists
of 34 $z\lesssim 0.06$ systems (9 upper-limit estimates). The PG quasars and
BASS AGNs cover similar host galaxy stellar mass range, while the CARS host
galaxies tend to be less massive. Compared to those three AGN samples, our
targets tend to be slightly biased toward the more massive systems in terms of
stellar mass, expected as we selected the local quasars with the most massive
BHs, hence the host galaxies presenting the most massive bulges. The sample of
8 PG quasars presented here probes the high BH mass and AGN luminosity tail of
the $z\lesssim 0.5$ AGN population.

Table 3:  Flux Density and Derived Properties of the Sample.

Object | $S_{\rm cont}$ | $\sigma_{\rm cont}$ | $S_{\rm CO}\Delta v$ | $\nu_{\rm obs}$ | FWHM | $\sigma_{\rm CO}$ | $\log L_{\rm IR}$ | $\log L^{\prime}_{\rm CO(2-1)}$ | $\log M_{\rm H_{2}}$
---|---|---|---|---|---|---|---|---|---
| (mJy) | (mJy beam-1) | (Jy km s-1) | GHz | km s-1 | (mJy) | (erg s-1) | (K km s-1 pc2) | $M_{\odot}$
(1) | (2) | (3) | (4) | (5) | (6) | (7) | (8) | (9) | (10)
PG 1049$-$005 | $0.52\pm 0.11$ | 0.04 | $2.53\pm 0.51$ | 170.300 | $181\pm 5$ | 0.52 | 45.4 | 9.64$\pm$0.09 | 10.13
PG 1100$+$772 | $22.37\pm 4.47$ | 0.24 | $\lesssim 2.09$ |  $\cdots$ |  $\cdots$ | 2.00 | 44.8 |  $\cdots$ |  $\cdots$
PG 1259$+$593 | $\lesssim 1.78$ | 0.03 | $0.73\pm 0.16$ | 157.403 | $111\pm 10$ | 0.75 | 44.7 | 9.35$\pm$0.10 | 9.85
PG 1425$+$267 | $4.69\pm 0.94$ | 0.06 | $\lesssim 0.59$ |  $\cdots$ |  $\cdots$ | 0.54 | 44.9 |  $\cdots$ |  $\cdots$
PG 1512$+$370 | $5.75\pm 1.15$ | 0.04 | $\lesssim 0.39$ |  $\cdots$ |  $\cdots$ | 0.36 | 44.6 |  $\cdots$ |  $\cdots$
PG 1704$+$608 | $3.34\pm 0.67$ | 0.07 | $\lesssim 0.83$ |  $\cdots$ |  $\cdots$ | 0.77 | 45.1 |  $\cdots$ |  $\cdots$
PG 2112$+$059 | $\lesssim 2.40$ | 0.05 | $0.75\pm 0.33$ | 157.093 | $398\pm 169$ | 0.68 | 45.2 | 9.35$\pm$0.17 | 9.85
PG 2251$+$113 | $8.98\pm 1.80$ | 0.13 | $\lesssim 0.52$ |  $\cdots$ |  $\cdots$ | 0.49 | 44.6 |  $\cdots$ |  $\cdots$

Note— (1) Source name. (2) Millimeter continuum flux density at restframe 230
GHz. (3) Noise level of the continuum image. (4) CO(2–1) velocity integrated
intensity. (5) CO(2–1) emission line observed frequency. (6) Full width at
half maximum. (7) Noise level of the cleaned data cube. (8) Total infrared
luminosity of the host galaxy calculated following Shangguan et al. (2018).
The typical uncertainty is $\sim 0.2-0.3$ dex. (9) CO(2–1) line luminosity.
(10) Molecular gas mass derived from the CO luminosity, assuming $\alpha_{\rm
CO}=3.1\,M_{\odot}\,($K km s-1 pc${}^{2})^{-1}$. The 1$\sigma$ errors are
dominated by the CO-to-$H_{2}$ conversion factor uncertainty ($\sim$0.3 dex).
We note that the error estimates of the mm continuum flux density, the CO(2–1)
line velocity integrated intensity, and line luminosity consider a
conservative NOEMA flux calibration uncertainty of $20$ % at 2 mm.

##  3 Methods

###  3.1 CO(2–1) Emission-line and Millimeter Continuum Characterization

To estimate the CO(2–1) velocity integrated intensity, first, we get a
spectrum by spatially collapsing the data cube within a beam-sized region
centered at the expected target location (Figure 3). This aperture selection
was set after exploring different values aiming to maximize the CO line S/N
detection, and roughly corresponds to the host galaxy stellar component size
reported by Zhao et al. (2021). Then, we fit the line emission by simply using
a Gaussian function deriving the line velocity integrated intensity ($S_{\rm
CO}\Delta v$), center ($\nu_{\rm obs}$) and FWHM. We quantify the total
continuum flux density ($S_{\rm cont}$) by simply fitting a two-dimensional
Gaussian model to the continuum image (Figure 4). We found a good agreement
between $S_{\rm cont}$ and the continuum flux density values estimated by
summing the individual pixel values within an aperture of $20\arcsec$ (similar
to that used for the Herschel data) centered on the continuum peak location
(average ratio $\sim 1.08$, scatter $\sim 0.23\,$dex). In both cases, we
estimate the uncertainties by re-sampling the data in 1000 iterations using
the rms of the residuals as the noise level. The 1$\sigma$ errors are obtained
from the distributions build for each parameter. In the case of non-detection,
the CO(2–1) emission line and continuum 3$\sigma$ upper limits were calculated
as

$S_{\rm CO}\Delta v<3\,\sigma_{\rm CO}\,\delta v\,\sqrt{N_{\rm ch}\frac{N_{\rm
A}}{N_{\rm B}}},$ (1)

and

$S_{\rm cont}<3\,\sigma_{\rm cont}\,\sqrt{\frac{N_{\rm A}}{N_{\rm B}}}$ (2)

respectively, where $\sigma_{\rm CO}$ is the RMS level of the data cube,
$\delta v$ is the velocity resolution, $N_{\rm ch}$ is the number of channels
sampling the CO line FWHM (assumed to be 400 km s-1 given the stellar masses
of our targets and the $M_{\star}$–FWHM trend reported by Shangguan et al.
2020b for the local PG quasars), $N_{\rm A}$ is the aperture size in pixel
units, and $N_{\rm B}$ is the number of pixels for the synthesized beam. We
assume $N_{\rm A}=3N_{\rm B}$ for estimating the CO flux density upper limits
(Hainline et al., 2004; Michiyama et al., 2021), while $N_{\rm A}=20\arcsec$
for the continuum. We list the estimates (or upper limits) for each source in
Table 3.

The CO(2–1) line luminosity is calculated following (Solomon & Vanden Bout,
2005)

$L^{\prime}_{\rm CO(2-1)}=3.25\times 10^{7}\,\frac{S_{\rm CO(2-1)}\Delta
v\,D^{2}_{L}}{\nu_{\rm
obs}^{2}\,(1+z)^{3}}\,\,\,{\rm[K\,km\,s^{-1}\,pc^{2}]},$ (3)

where $S_{\rm CO(2-1)}\Delta v$ is in units of Jy km s-1, $D_{L}$ is the
luminosity distance in Mpc, $\nu_{\rm obs}$ is the observed frequency of the
line in GHz, and $z$ is the redshift. We estimate the luminosity of the
CO(1–0) line transition ($L^{\prime}_{\rm CO(1-0)}$) by adopting the median
luminosity ratio $r_{21}\equiv L^{\prime}_{\rm CO(2-1)}/L^{\prime}_{\rm
CO(1-0)}=0.62$ found by Shangguan et al. (2020b) for PG quasars at
$z<0.3$.444For the BASS AGNs Lamperti et al. (2020) report an average
$r_{21}=0.72$ value, with a median absolute deviation of 0.17. For the CARS
sample, we use the CO(1–0) and CO(2–1) velocity integrated intensity values
provided by Bertram et al. (2007) for 25 sources and estimate a median
$r_{21}=0.61^{+0.34}_{-0.17}$ value.  The molecular gas masses are estimated
under the assumption of $\alpha_{\rm CO}=3.1$ $M_{\odot}$ (K km s-1 pc2)-1, as
suggested by the comparison of $L^{\prime}_{\rm CO(1-0)}$ and the dust-based
gas masses for the $z<0.3$ PG quasars (Shangguan et al., 2020b), and in
consistency with the recommendation by Sandstrom et al. (2013) for nearby
star-forming galaxies.

Figure 3:  Spectra at restframe $\sim 1.3\,$mm of the eight PG quasar host
galaxies. The red curve corresponds to the best-fit Gaussian model. The grey
shade highlights the spectrum $\pm 1\sigma$ level, with $\sigma$ representing
the rms of emission line-free channels. In the cases where no CO(2–1) emission
is detected, the spectrum is centered at the expected line location following
the redshift derived from optical light.

Figure 4:  Continuum images at restframe $\sim 1.3\,$mm for the PG quasar
hosts. The contours indicate $-3$ (dashed), 3, 5, 10, 20$\sigma$ levels, with
$\sigma$ being the RMS value of the source-free pixels and indicated in each
map. The synthesized beam is shown in the lower left corner of each image.

Figure 5:  Far-IR SED of the eight PG quasar host galaxies. The orange diamond
indicates the NOEMA $\sim 2\,$mm continuum. The open circles show the IR data
from 2MASS, WISE, and Herschel collated in Shangguan et al. (2018, see Section
2.2), along with the GHz radio data taken from the literature. Upper limits
are indicated by downward arrows (Appendix A). The black solid line represents
the available IRS spectrum in the $\sim 5-40\mu$m wavelength range. The far-IR
SED model is in grey band, and it is composed by five sub-components:
starlight (red), hot dust (yellow), AGN torus (green), cold dust (blue) and
jet (purple; Section 3.2).

###  3.2 Far-IR SED modeling and IR-based SFRs

We use our $S_{\rm cont}$ estimates to complement the far-IR SED (Section 2.2)
and update the AGN-decontaminated IR luminosity values previously estimated by
Shangguan et al. (2018) for our targets. Our $S_{\rm cont}$ measurements
provide key information for constraining the targets far-IR SED flux density
at low frequencies.

Shangguan et al. (2018) modeled the far-IR SED by adopting physically
motivated emission components for the AGN dusty torus, host galaxy cold dust,
and starlight. The torus emission is modeled by using the CLUMPY model
(Nenkova et al., 2008a, b), plus a complementary blackbody component that
accounts for emission from the torus very hot dust (Zhuang et al., 2018). The
far-IR models adopt a fixed dust emissivity index ($\beta$) within the Draine
& Li (2007) models (roughly $\beta\approx 2.08$). The far-IR modeling also
handle a synchrotron emission component, but its addition to the SED is
optional to the radio data availability. The synchrotron emission is modeled
as a power-law spectrum with fixed spectral index
($S_{\nu}\propto\nu^{\alpha_{\rm R}}$). A 5 Gyr stellar population with a
Kroupa (2001) IMF from Bruzual & Charlot (2003) is assumed for the starlight
component. We refer to Shangguan et al. (2018), for more details. The SED data
and models are presented in Figure 5.

We compute the IR luminosity by integrating the host galaxy far-IR SED sub-
component corresponding to the cold dust emission and over $8-1000\,\mu$m
(Table 3). To estimate SFRs, we use Kennicutt (1998)’s calibration, re-
normalized to a Kroupa (2001) IMF,

${\rm SFR}(M_{\odot}\,{\rm yr}^{-1})=3\times 10^{-44}\,L_{\rm IR}({\rm
erg\,s}^{-1}).$ (4)

We note that the systematic uncertainties of the far-IR SED model
decomposition dominate the SFR errors. Xie et al. (2021) found that the IR-
based SFRs correlate with the estimates from the mid-IR neon emission lines
within $\sim 0.2-0.3\,$dex scatter for the $z<0.3$ PG quasar hosts.555While
Xie et al. (2021) analyzed the full sample of $z<0.5$ PG quasars with Herschel
data (Shangguan et al., 2018), the most distant host galaxy detected in mid-IR
neon emission is at $z\approx 0.32$ (PG 2251+113). Hereafter, we assume this
scatter value as the 1$\sigma$ error of our SFR estimates.

##  4 Results

Our main goal is to study whether the AGN may affect the cold molecular gas
content in a sample of the most powerful unobscured quasars observed at
low-$z$. From the sub-sample of 8 quasars presented in this work, we detect
the CO(2–1) emission coming from 3 host galaxies (Figure 3). Those 3 systems
tend to have the less massive BHs and higher Eddington ratios among the sample
of 8 objects. Considering both the NOEMA and ACA campaigns, we detect line
emission in 36 out of 48 host galaxies. All 17 disk-like host galaxies are
detected in CO, while we detect CO emission in 7 out of 9 merger systems, and
in 5 ellipticals from a total of 12 (5 non-detections from this campaign). We
detect the CO emission in 7/10 host galaxies with uncertain morphology
classification. Using the qualitative radio spectra classification for the PG
quasars (Shangguan et al., 2018), we find that 33/38 radio-quiet systems are
detected in CO, 3 out of 4 PG quasars with flat radio spectra present line
detection, and no CO emission was detected in systems with steep radio spectra
(6 in total).

Thanks to the large frequency coverage of NOEMA, we detect the restframe $\sim
1.3\,$mm continuum in 6 systems (Figure 4). The modeling of the global far-IR
SEDs (Figure 5) suggests that the restframe $\sim 1.3\,$mm continuum can be
associated with synchrotron emission from a jet in 5 sources. We now proceed
to analyze the data in detail.

Figure 6:  CO-based molecular gas mass compared to the total gas mass
predicted from cold dust emission and subtracted for extended atomic gas (H i)
content. In the bottom right corner we present the typical $1\sigma$
uncertainty of the data. The arrows denote to $3\sigma$ upper limits.

###  4.1 Total Gas Mass Content Estimated from Cold Dust Emission

The far-IR SED of galaxies can be used to predict the dust masses, which are
closely related to their total gas content (Draine et al., 2007; Leroy et al.,
2011). Shangguan et al. (2018) provided total gas mass ($M_{\rm gas}$)
estimates for the PG quasar host galaxies, finding that those closely
correlate with direct measurements from CO emission plus atomic gas (H i) for
the closer systems. Here, we extend their analysis by comparing both the
molecular gas masses estimated from the CO(2–1) emission-line luminosity and
$M_{\rm gas}$ values for the $z<0.5$ PG quasar host galaxy sample. The latter
quantity is computed by converting the dust masses to $M_{\rm gas}$ using the
dust-to-gas ratio values derived by Shangguan et al. (2018), but avoiding the
correction factor ($\sim 0.23$ dex) for extended atomic hydrogen gas content
($M_{\rm gas,sub}$). Hence, the $M_{\rm gas,sub}$ estimates correspond to the
atomic plus molecular gas mass within roughly the same host galaxy area where
the dust emission comes from (Shangguan et al., 2018). The $M_{\rm gas}$
values have a systematic uncertainty of $\sim 0.2\,$dex, while the CO-based
estimates have a typical uncertainty of $\sim 0.32\,$dex inherent to
$\alpha_{\rm CO}$ ($\sim 0.3\,$dex), and $R_{21}$ ($\sim 0.1\,$dex). We remind
that the $L^{\prime}_{\rm CO(2-1)}$ uncertainty is dominated by the flux
calibration uncertainties.

Figure 7:  The dependence of CO luminosity on (a) $\lambda L_{5100}$ and (b)
Eddington ratio. In both panels, the blue squares correspond to median
$L^{\prime}_{\rm CO(2-1)}$ values computed in $0.6\,$dex $\lambda L_{5100}$
and $0.3\,$dex $L_{\rm bol}/L_{\rm Edd}$ bins. The arrows correspond to
$3\sigma$ upper limits.

Figure 6 shows $M_{\rm H_{2}}$ against $M_{\rm gas,sub}$ for the full sample
of PG quasars (NOEMA plus ACA campaigns). Both quantities closely match, in
agreement with the previous finding of Shangguan et al. (2018, their Figure
10). We compute a mean $M_{\rm H_{2}}/M_{\rm gas,sub}$ ratio of 0.93 with
scatter $\sim 0.40\,$dex. The scatter is consistent with the mass ratio
systematic uncertainty ($\sim 0.38\,$dex), but we note that it may be larger
considering the $M_{\rm H_{2}}$ upper limits. Among the PG quasars, the disk-
like host galaxies present an average $M_{\rm H_{2}}/M_{\rm gas,sub}\approx
0.95$ and scatter slightly reduced to $0.32\,$dex. $M_{\rm gas,sub}$ tends to
be larger than $M_{\rm H_{2}}$ in mergers. For such systems, the data average
ratio and scatter is 0.80 and $0.23\,$dex, respectively; however, we caution
the low statistics (7 host galaxies). We only detect the CO emission in 5
elliptical host galaxies, so we do not provide any statistical measurement.
For the PG quasar hosts with uncertain morphological classification, we find
an average mass ratio of $0.77$, with scatter $\sim 0.51$ dex. Our sample is
too small to statistically characterize the sub-sample of PG quasar host
galaxies presenting a flat or steep radio spectra. The radio-quiet quasars are
characterized by an average $M_{\rm H_{2}}/M_{\rm gas,sub}\approx 0.92$, with
scatter of $0.37\,$dex. Our observations suggest low atomic gas content inside
the stellar disks of the PG quasar host galaxies, but this result sensibly
depends on the correction factor applied to the dust-to-gas ratio, namely the
extended H i mass value subtracted to $M_{\rm gas}$. Only 13 PG quasars hosts
have H i global measurements from literature, most of these host galaxies are
ongoing mergers where the emission line exhibit complex profiles and suggest
dynamical disturbance, or have neighboring companions (e.g., PG 0007+106 and
PG 1119+120) inducing signal confusion (Shangguan et al., 2018). Detailed
observations resolving the H i content in PG quasars hosts are needed to draw
deeper conclusions.

###  4.2 AGN Properties Compared to $L^{\prime}_{\rm CO(2-1)}$

We compare the CO(2–1) luminosity with respect to $\lambda L_{5100}$ and the
Eddington ratio in Figure 7 for the PG, BASS, and CARS type 1 AGNs. We use
pymccorrelation (Privon et al., 2020) to compute the generalized Kendall’s
rank correlation coefficient ($\tau$) considering the censored data (Isobe et
al., 1986). We assume $p\leq 0.05$ to determine if the quantities are
correlated. We find that the CO luminosity does not correlate with the
Eddington ratio with $\tau=0.09$ and a $p$-value of $0.10$. This is consistent
with the results from the previous ACA campaign targeting the PG quasar hosts
(Shangguan et al., 2020a), but inconsistent with the findings of Koss et al.
(2021), who found a tentative increase of molecular gas mass (hence,
$L^{\prime}_{\rm CO(2-1)}$) with Eddington ratio for the full BASS AGN sample
(their Figure 15). Nevertheless, Koss et al. (2021) analyzed type 1 and type 2
AGNs, while we only analyze type 1 AGNs. We find that $L^{\prime}_{\rm
CO(2-1)}$ and $\lambda L_{5100}$ are weakly correlated ($\tau=0.18$,
$p<0.01$). This result agrees with that reported by Shangguan et al. (2020a),
but the correlation coefficient is $\sim 2$ times lower due to the inclusion
of the less luminous BASS and CARS AGNs.

We also provide median trends by computing median values over bins of 1.0 dex
in $\lambda L_{5100}$ and 0.6 dex in $L_{\rm bol}/L_{\rm Edd}$ using the
Kaplan-Meier estimator implemented in the Python package
lifelines,666https://lifelines.readthedocs.io/en/latest/index.html# including
CO(2–1) upper limits. The median trend between $L^{\prime}_{\rm CO(2-1)}$ and
$L_{\rm bol}/L_{\rm Edd}$ is nearly constant, as expected because both
quantities are not correlated. In terms of $L^{\prime}_{\rm CO(2-1)}$ and
$\lambda L_{5100}$, the median trend suggests an $\sim 0.4\,$dex increase of
$L^{\prime}_{\rm CO(2-1)}$ for AGNs with $\lambda L_{5100}\gtrsim 10^{44}$ erg
s-1. Such an increase of $L^{\prime}_{\rm CO(2-1)}$ with $\lambda L_{5100}$ is
not artificially produced by host galaxy mass selection bias as most of these
AGNs tend to be hosted in galaxies with $M_{\star}\approx
10^{10.75}-10^{11.5}\,M_{\odot}$. We note that, the AGNs with $\lambda
L_{5100}\lesssim 10^{44}$ erg s-1 tend to be observed in the nearby Universe
($z\lesssim 0.1$), while the more luminous quasars with $\lambda
L_{5100}\approx 10^{46}$ erg s-1 tend to be found at higher redshifts
($\langle z\rangle\approx 0.35$) where galaxies have molecular gas fractions
($f_{\rm H_{2}}\equiv M_{\rm H_{2}}/M_{\star}$) about twice higher than the
local ones (Tacconi et al., 2018),meaning that the possible increase of
$L^{\prime}_{\rm CO(2-1)}$ with $\lambda L_{5100}$ could be due to the cosmic
evolution of the molecular gas content in galaxies.777There is no significant
bias with host galaxy redshift when considering the Eddington ratio estimates.
To test this possibility, we correct the host galaxy CO(2–1) luminosity by
adopting the parametrization of Tacconi et al. (2018) for the cosmic evolution
of $f_{\rm H_{2}}$ for main-sequence galaxies and a constant $\alpha_{\rm CO}$
value. In this case, we find no correlation between the corrected
$L^{\prime}_{\rm CO(2-1)}$ and $\lambda L_{5100}$ ($\tau=0.11$, $p=0.06$).

###  4.3 The $L_{\rm IR}-L^{\prime}_{\rm CO(2-1)}$ relation

In Figure 8 we show the relation between $L_{\rm IR}$ and $L^{\prime}_{\rm
CO(2-1)}$ for the AGNs in our sample. We find that the more powerful quasars
observed in this work ($\lambda L_{5100}\gtrsim 10^{45.5}\,$ erg s-1) follow
the best-fit relation of Shangguan et al. (2020a, their Equation 4, after
correcting by $R_{21}$). The five systems with $L^{\prime}_{\rm CO(2-1)}$
upper limits provided by NOEMA tend to be on or above the best-fit relation of
Shangguan et al. (2020a), suggesting even lower $L^{\prime}_{\rm CO(2-1)}$
values. However, we caution that due to the presence of strong synchrotron
emission and Herschel photometry upper limits, their $L_{\rm IR}$ estimates
are somewhat more uncertain than for the rest of our targets.

Figure 8:  Infrared luminosity as a function of the CO(2–1) line luminosity.
The arrows denote $3\sigma$ upper limits. The best-fit of Shangguan et al.
(2020b) has a slope consistent with unity and an intrinsic scatter of $\sim
0.3\,$dex. The trends for inactive systems correspond to those reported in
Genzel et al. (2010) for normal star-forming systems (0.33 dex scatter) and
starbursts (0.21 dex scatter).  Figure 9:  Host galaxy molecular gas
properties as a function of AGN properties. The molecular gas fraction
($M_{\rm H_{2}}\,/\,M_{\star}$) dependence with (a) $\lambda L_{5100}$ and (b)
Eddington ratio. Panels (c) and (d) show similar dependence on AGN properties,
but for the molecular gas depletion time ($M_{\rm H_{2}}\,/\,$SFR). In all
panels, the data are colored by host galaxy morphology, and the blue squares
correspond to median $M_{\rm H_{2}}\,/\,M_{\star}$ or $t_{\rm dep}$ values
computed in $0.6\,$dex $\lambda L_{5100}$ and $0.3\,$dex $L_{\rm bol}/L_{\rm
Edd}$ bins, respectively. The arrows correspond to $3\sigma$ upper limits.

Surprisingly, we find that the BASS sample of type 1 AGNs is in offset with
respect to the $L_{\rm IR}-L^{\prime}_{\rm CO(2-1)}$ best-fit provided by
Shangguan et al. (2020a) for the PG quasars. We quantify this offset
$=-0.54\,$dex in terms of $L_{\rm IR}$. We report a similar result when
including the BASS type 2 AGN data (not shown). The CARS host galaxies follow
a trend similar to that reported for the PG quasars, but this result could be
the affected by IR luminosity bias induced when discarding the systems with
poorly sampled far-IR SED. The redshift difference between the BASS AGN and PG
quasar samples is not high enough to explain this offset. Among the PG quasar
sample, 13 out of 48 host galaxies are at $z\sim 0.05$, similarly as the BASS
AGN systems, while 27 PG quasar host galaxies are at $z\lesssim 0.1$, making
these practically immune to any cosmic evolutionary effect. We also note that
the offset for the BASS type 1 AGNs cannot be explained by incorrect aperture
correction when deriving the CO(2–1) luminosity (Koss et al., 2021). The
NOEMA- and ACA-based CO(2–1) emission-line measurements for the PG quasars do
not suffer from any systematics in aperture (Shangguan et al., 2020a). Nor
does the offset arise from the use of different far-IR SED models when
estimating $L_{\rm IR}$. The PG quasar far-IR modeling is detailed in Section
3.2, and here we only highlight that this method is consistent with fitting a
modified black-body (MBB) to the far-IR SED (see Appendix of Shangguan et al.
2018). For the BASS sample, the far-IR luminosity was computed mainly by
Shimizu et al. (2017), with some few systems taken from Ichikawa et al.
(2019). Both methods are consistent between each other (see Appendix of
Shimizu et al. 2017). We fitted the far-IR SED of our targets following the
method outlined in Shimizu et al. (2017), namely by considering a MBB plus an
additional sub-component modeling the emission from the warm dust heated by
the AGN and intense star formation activity. We found no significant
discrepancy between the $L_{\rm IR}$ values provided by those fits and the
estimates reported in Table 3, notwithstanding a scatter of $0.2\,$dex. For
the CARS sample, we obtain similar results when comparing the IR luminosity
reported by Smirnova-Pinchukova et al. (2022) and the result of our MBB fits.
Therefore, we find that the BASS AGNs tend to be offset with respect to the PG
sample in the $L_{\rm IR}-L^{\prime}_{\rm CO(2-1)}$ plane.

Compared to the non-active systems, represented by the fits for normal star-
forming galaxies and starbursts (Genzel et al., 2010), the less-luminous PG
quasars follow the relation of starbursts (Shangguan et al., 2020a, b). The
same picture holds for the most luminous PG quasars at $z\lesssim 0.5$. The
sub-sample of BASS type 1 AGNs follows the relation of normal star-forming
galaxies.

###  4.4 Molecular Gas Fraction and Depletion time

Figure 9 shows the molecular gas fraction as a function of $\lambda L_{5100}$
and Eddington ratio. We find no significant correlation between $f_{\rm
H_{2}}$ and $\lambda L_{5100}$ ($\tau=0.05$, $p$-value = 0.37). This result
does not change after taking into account the host galaxy redshift bias with
$\lambda L_{5100}$ ($\tau=-0.07$, $p$-value = 0.21). The constant $f_{\rm
H_{2}}$–$\lambda L_{5100}$ median trend further highlights this. On the other
hand, we find a weak correlation between $f_{\rm H_{2}}$ with Eddington ratio
($\tau=0.14$, $p$-value = 0.02), but the corresponding $f_{\rm
H_{2}}$–Eddington ratio median trend does not suggest any significant
correlated increase.

Figure 9 also presents the depletion time ($t_{\rm dep}\equiv M_{\rm
H_{2}}/$SFR) as a function of $\lambda L_{5100}$ and Eddington ratio. We find
no correlations with $\lambda L_{5100}$ ($\tau=-0.08$, $p$-value = 0.18) or
Eddington ratio ($\tau=-0.06$, $p$-value = 0.30). Considering the depletion
time cosmic evolution (Tacconi et al., 2018) has a negligible effect on the
correlation coefficient values. If anything, the $t_{\rm dep}-L_{\rm
bol}/L_{\rm Edd}$ median trend suggests a somewhat minor $t_{\rm dep}$
decrease from $\sim$1.0 Gyr to $\sim$0.4 Gyr at $L_{\rm bol}/L_{\rm
Edd}\gtrsim 0.1$, but note that the median trend may only reflect the
Eddington ratio range at which the CARS and PG quasar sample dominate the
median bin statistics.

##  5 Discussion

The properties of the molecular gas in AGN host galaxies provide important
clues regarding the role of BH accretion in shaping the evolution of galaxies.
Early studies already suggested that the local luminous quasars are hosted in
galaxies with significant gas reservoirs (Scoville et al., 2003; Evans et al.,
2006; Bertram et al., 2007). These findings were subsequently supported by the
many new observations detecting CO emission for broader samples of local type
1 and type 2 AGNs (Husemann et al., 2017; Rosario et al., 2018; Shangguan et
al., 2020b; Koss et al., 2021; Ramos Almeida et al., 2022; Salvestrini et al.,
2022). The large amounts of cold gas content detected in type 1 AGN hosts are
at odds with the idea of negative AGN feedback affecting the host galaxies
globally (e.g., Husemann et al. 2017; Jarvis et al. 2020; Shangguan et al.
2020a, but see Ellison et al. 2021; Ward et al. 2022), with conflicting
results regarding how the AGN properties correlate with the molecular gas
properties in the AGN host galaxies. Koss et al. (2021) reported that the BASS
AGNs with higher Eddington ratio tend to have on average larger molecular gas
reservoir, which disagrees with the findings of Shangguan et al. (2020a) who
report that the CO luminosity does not correlate with Eddington ratio for the
local PG quasars (see also Husemann et al. 2017). This disagreement seems to
arise because both samples are complementary in terms of AGN luminosity, with
the PG quasars representative of more luminous AGNs (Figure 2). It should be
noted that Shimizu et al. (2016) already suggested that the BASS AGN sample
may not extend to high enough AGN luminosity to reveal correlations with the
host galaxy properties. Conversely, artificial correlations between host
galaxy and AGN properties could also arise because of sample selection bias,
with targets covering a narrow range in terms of AGN properties (Zhuang & Ho,
2020). When combining the BASS type 1 AGNs, CARS, and the PG quasar samples,
including our observations, we further confirm the lack of correlation between
CO luminosity (i.e., molecular gas mass) with Eddington ratio, in agreement
with Husemann et al. (2017) and Shangguan et al. (2020a). On the other hand,
we find a weaker correlation between CO emission and AGN luminosity than that
reported by Shangguan et al. (2020a), mainly because the inclusion of the less
luminous BASS and CARS AGN data to the analysis. This correlation is mainly
driven by the more luminous AGNs ($\lambda L_{5100}\gtrsim 10^{45}\,$erg s-1)
observed at higher redshift, and it vanishes when correcting the CO luminosity
by the cosmic evolution of the molecular gas content in galaxies. The observed
trends suggest the lack of negative AGN feedback effects on the molecular gas
content of the host galaxies.

Even though we report a lack of correlation between $L^{\prime}_{\rm CO(2-1)}$
and $\lambda L_{5100}$ for the full sample of type 1 AGNs (after correcting by
redshift), we note that there is still a stronger link remaining for the PG
quasar sample alone (Shangguan et al., 2020a). Such trend is reminiscent of
that found between AGN luminosity and SFR for local AGNs, where the processes
that drive and regulate most of the star formation in low-luminosity AGN hosts
presumably do not strongly affect the BH fueling, while in high luminosity
AGNs it may be the opposite (Rosario et al., 2012). If there is any
correspondence between the global SFR and BH accretion events in high
luminosity AGNs, it should occur over timescales short compared to the AGN
duty cycle ($\sim 10-100$ Myr; Hopkins et al. 2005), requiring that most of
the star formation activity being triggered on the central region of the host
galaxies. Under this scenario, the $L^{\prime}_{\rm CO(2-1)}-\lambda L_{5100}$
trends reported for the full sample of type 1 AGNs and PG quasar sample alone
may reflect how differently the gas is distributed within the PG quasar hosts
compared with the BASS AGN host galaxies, in addition to a closer connection
between the AGN properties and the molecular gas content on the central scales
of the quasar hosts. Note that the more gas-rich PG quasars have compact
molecular gas distributions (Molina et al., 2021). In AGN hosts, the cold dust
emission mainly arises from compact nuclear scales (Mushotzky et al., 2014;
Lutz et al., 2018; Molina et al., 2023). Additionally, our $L_{\rm
IR}/L^{\prime}_{\rm CO}$ measurements for the BASS AGNs and PG quasars presume
a difference in the gas distribution between both type 1 AGN samples.
Similarly to Bertram et al. (2007), we find that type 1 AGNs can be roughly
separated into two populations in terms of $L_{\rm IR}/L^{\prime}_{\rm CO}$
(proxy of the star formation efficiency or $t_{\rm dep}$), with one
population, most of the BASS AGNs, following the typical $L_{\rm
IR}/L^{\prime}_{\rm CO}$ ratio found in normal star-forming galaxies, and a
second population, the PG quasars, and some CARS AGNs, presenting $L_{\rm
IR}/L^{\prime}_{\rm CO}$ values comparable to those measured for luminous
infrared galaxies (Figure 8). It is well known that luminous infrared galaxies
have molecular gas distributions mainly concentrated in their central kpc and
sub-kpc regions (e.g., Downes & Solomon 1998; Iono et al. 2009; Bellocchi et
al. 2022), while normal star-forming galaxies have more extended gas
distributions (e.g., Bolatto et al. 2017). Accounting for the difference in
gas distribution for both type 1 AGN samples would imply adopting different
$r_{21}$ and CO-to-H2 conversion factor values when estimating the host galaxy
molecular gas masses, further decreasing the $M_{\rm H_{2}}$ values for the PG
quasars, and amplifying both AGN sample differences in terms of $t_{\rm dep}$
or star formation efficiency.

Recent findings suggest the more luminous and more efficiently growing BHs
tend to be hosted in starbursts (Bernhard et al., 2016; Shangguan et al.,
2020a; Xie et al., 2021). The position of an AGN host relative to the main-
sequence of star-forming galaxies seems to be correlated with Eddington ratio
(e.g., Shimizu et al. 2016; Ellison et al. 2016; Woo et al. 2020; Zhuang & Ho
2020; Torbaniuk et al. 2021; Zhuang & Ho 2022). How does BH accretion connect
to the galaxy’s star formation activity on much larger scales? A
straightforward possibility is the common dependence of BH growth and star
formation on the molecular gas supply (Jarvis et al., 2020; Shangguan et al.,
2020b), replenished by the gravitational instabilities that drive the gas
inward (Kormendy & Kennicutt, 2004; Romeo & Fathi, 2016). Another possibility
could be triggering of star formation due to positive AGN feedback, with in-
situ star formation in AGN-driven outflows (Maiolino et al., 2017; Gallagher
et al., 2019), and more luminous AGNs producing more frequent and stronger
outflows (Fiore et al. 2017; Rakshit & Woo 2018; Fluetsch et al. 2019; but see
Baron & Netzer 2019; Davies et al. 2020; Shangguan et al. 2020a; Molina et al.
2022a; Ramos Almeida et al. 2022). The role of gas-rich major mergers cannot
be overlooked, as they offer a natural explanation for the triggering of an
AGN (e.g., Hopkins et al. 2008), specially for more luminous active galaxies
(Treister et al., 2012). However, not all the galaxies hosting a luminous AGN
present evidence of merger activity (e.g., Koss et al. 2011; Kim et al. 2017;
Zhao et al. 2019, 2021). The relative fraction of early-type and late-type
low-$z$ quasar hosts depends only on stellar mass, and not on bolometric
luminosity or Eddington ratio (Zhuang & Ho, 2022). We highlight this in Figure
9 where, apart from the mergers likely presenting shorter depletion times, we
find no trend between $t_{\rm dep}$ and the AGN properties with galaxy
morphology. The only clue that remains is the weak correlation between the
Eddington ratio and the host galaxy molecular gas fraction, possibly implying
an underlying role of gravitational instabilities or the fast inflow of cold
gas in producing nuclear starbursts and the fueling of the BHs.

##  6 Conclusions

We present new NOEMA observations of the CO(2–1) line for the most luminous
eight Palomar-Green quasar host galaxies at $z\lesssim 0.5$. We detect CO(2–1)
emission in three objects, doubling the number of most luminous PG quasar host
galaxy with line emission detection. Combined with already published
observations for active galaxies, we assemble CO measurements for a broad
sample of $z\lesssim 0.5$ type 1 AGNs covering $\sim 3$ decades in AGN
luminosity. This sample is used to investigate the relations between AGN
properties, molecular gas properties, and star formation efficiency of the
host galaxies. The systems with non-detected CO emission are treated as
censored data. We summarize our conclusions as follows:

  * •

The luminous AGNs ($\lambda L_{5100}\gtrsim 10^{45.5}$ erg s-1) observed by
NOEMA possesses CO emission consistent with the expectations from the far-IR
emission. Overall, the total gas mass predicted from the cold dust emission,
and after subtracting the extended atomic gas content, is well-matched with
the molecular gas mass within an accuracy of $\sim 0.40\,$dex, with some small
variation depending on the host galaxy morphological type.

  * •

The PG quasar and CARS AGN host galaxies follow a tight, linear $L_{\rm
IR}-L^{\prime}_{\rm CO}$ correlation consistent with that found for starbursts
galaxies (Shangguan et al., 2020b). The BASS AGNs follow a similar
correlation, but they show a zero-point offset placing them on the relation
for normal star-forming galaxies.

  * •

We find a weak correlation between CO(2–1) line luminosity and AGN luminosity,
as well as between molecular gas fraction and Eddington ratio. The former
correlation vanishes when considering the cosmic evolution of the gas content
in galaxies and that the more luminous AGN hosts are found at higher
redshifts, meaning that the AGN luminosity is not correlated with host galaxy
global molecular gas content. The second correlation points to the role of
host galaxy gravitational instabilities or the fast inflow of cold gas in
triggering AGN activity. Both findings suggest an ineffective role of negative
AGN feedback.

We thank the anonymous referee for helpful comments and suggestions. We
acknowledge support from the National Science Foundation of China (11721303,
11991052, 12011540375, 12233001) and the China Manned Space Project (CMS-
CSST-2021-A04, CMS-CSST-2021-A06). R.W. acknowledges support from the National
Science Foundation of China grants No. 12173002. This work was funded by ANID
- Millennium Science Initiative Program - ICN12_009 (FEB), CATA-BASAL -
FB210003 (FEB, ET), and FONDECYT Regular - 1190818 (ET, FEB) and 1200495 (FEB,
ET). We thank to Stefano Antonellini for his support during the NOEMA data
reduction process. This work is based on observations carried out under
project number W21CI with the IRAM NOEMA Interferometer. IRAM is supported by
INSU/CNRS (France), MPG (Germany) and IGN (Spain)

##  Appendix A Radio Continuum Measurements

Radio continuum measurements collated from the literature for the eight
sources presented in this work.

Table 4:  Radio Continuum Measurements

Object | Frequency | $S_{\nu}$ | Reference
---|---|---|---
| (GHz) | (mJy) |
(1) | (2) | (3) | (4)
PG 1049$-$005 | 1.4 | $0.82\pm 0.14$ | Becker et al. (1995)
| 5.0 | $0.48\pm 0.03$ | Kellermann et al. (1989)
| 8.5 | $0.37\pm 0.07$ | Baldi et al. (2022)
| 45 | $<0.18^{*}$ | Baldi et al. (2022)
PG 1100+772 | 1.4 | $2341\pm 79$ | Condon et al. (1998)
| 2.7 | $1415\pm 40$ | Laing & Peacock (1980)
| 5.0 | $775\pm 30$ | Laing & Peacock (1980)
| 10.7 | $375\pm 19$ | Laing & Peacock (1980)
| 14.9 | $310\pm 20$ | Laing & Peacock (1980)
| 31.4 | $330\pm 130$ | Geldzahler & Kuhr (1983)
PG 1259+593 | 1.4 | $<0.45$ | Condon et al. (1998)
| 5.0 | $<0.3^{*}$ | Baldi et al. (2022)
| 45 | $<0.15^{*}$ | Baldi et al. (2022)
PG 1425+267 | 0.074 | $2710\pm 360$ | Cohen et al. (2007)
| 0.151 | $2260\pm 158$ | Waldram et al. (1996)
| 0.365 | $572\pm 64$ | Douglas et al. (1996)
| 1.4 | $108\pm 4$ | Condon et al. (1998)
| 4.85 | $112\pm 16$ | Gregory & Condon (1991)
PG 1512+370 | 0.074 | $9860\pm 1010$ | Cohen et al. (2007)
| 0.365 | $3003\pm 49$ | Douglas et al. (1996)
| 1.4 | $990\pm 31$ | Condon et al. (1998)
| 4.85 | $361\pm 45$ | Gregory & Condon (1991)
PG 1704+608 | 1.49 | $1258\pm 123$ | Kuehr et al. (1981)
| 4.85 | $590\pm 30$ | Gregory & Condon (1991)
| 10.7 | $420\pm 20$ | Kuehr et al. (1981)
PG 2112+059 | 1.4 | $3.0\pm 0.4$ | Condon et al. (1998)
| 1.49 | $2.93\pm 0.38$ | Barvainis et al. (1996)
| 4.89 | $0.89\pm 0.09$ | Barvainis et al. (1996)
| 4.9 | $0.89\pm 0.07$ | Kellermann et al. (1989)
| 8.4 | $0.52\pm 0.05$ | Barvainis et al. (2005)
| 8.48 | $0.56\pm 0.07$ | Barvainis et al. (1996)
| 14.9 | $<0.48$ | Barvainis et al. (1996)
PG 2251+113 | 0.074 | $11840\pm 1240$ | Cohen et al. (2007)
| 0.365 | $4387\pm 89$ | Douglas et al. (1996)
| 1.4 | $1436\pm 43$ | Condon et al. (1998)
| 2.7 | $700$ | Wright & Otrupcek (1990)
| 4.85 | $615\pm 85$ | Gregory & Condon (1991)

Note— (1) Source name. (2) Restframe frequency. (3) Flux density. (4)
Reference. If available, we provide a $3\sigma$ flux density upper limit. (∗)
Upper limit values were calculated by using the observation rms as input to
Equation 2 and assuming an aperture size equal to 3 times the observation
synthesized beam size ($N_{\rm A}/N_{\rm B}=3$).

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