Resolving the Interstellar Medium in Ultraluminous Infrared QSO Hosts with ALMA

All eight IR QSOs observed in our sample are clearly resolved in the CO(1−0) line emission (i.e., the observed sizes of CO emission are more than two times the synthesized beams; see Figure 1). We detect 3 mm continuum emission in seven (nondetection in IRAS F15069+1808) out of eight IR QSOs, four of which are marginally resolved. The 1σ rms noise level of 3 mm continuum emission in the eight IR QSOs observed is 30−78 μJy, and the total flux of the 3 mm continuum emission measured for each object is summarized in Table 2. The velocity-integrated CO(1−0) line maps and 3 mm continuum maps of the eight IR QSO hosts are presented in Figure 1. The molecular gas in the IR QSO hosts mapped in CO emission is found to distribute in the nuclear regions, and the peaks of CO emission are coincident with the 3 mm continuum emission peaks (the exception is IRAS 06269−0543, where the peak of continuum emission is shifted by ∼019, equivalent to ∼0.4 kpc, with respect to the CO emission¹⁴ ). The CO(1−0) spectra of the QSO hosts (together with the companions we discuss below) are presented in Figure 2.

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High-resolution CO maps reveal a diversity of morphologies for the molecular gas in our sample of IR QSO hosts for the first time. Five of our galaxies show a predominantly compact morphology, while the other three galaxies (IRAS F15069+1808, IRAS F22454−1744, and IRAS F23411+0228) are resolved into multiple distinct objects in the CO emission, showing evidence for a merger with a galaxy accompanying each of the IR QSOs.

Two (I ZW 1 and IRAS F11119+3257) of the eight IR QSOs in our sample have been previously mapped in CO emission. The CO(1−0) imaging observations of I ZW 1 were obtained with the IRAM Plateau de Bure Interferometer (PdBI) and the BIMA millimeter interferometer at 19 and 07 angular resolution (Schinnerer et al. 1998; Staguhn et al. 2004), respectively. Compared with these observations, our ALMA observations at 06 resolution resolve the emission in the nuclear region with improved uv-coverage and angular resolution. In contrast to the BIMA observations, the ALMA observations do not show any particular spatial structure in the nuclear region. This is similar to the spatial distribution of CO(2−1) emission obtained with the PdBI at 09 resolution (Staguhn et al. 2004). We detect two spiral arm–like structures to the west and east of the nucleus in the ALMA CO map, respectively, consistent with that of the PdBI CO(1−0) observations at 19 resolution (Schinnerer et al. 1998). A kinematic analysis of the PdBI CO(1−0) data shows evidence for a circumnuclear molecular ring with a diameter of 15 (∼1.8 kpc; Schinnerer et al. 1998). However, our ALMA observations do not identify this nuclear starburst ring structure. In addition, both optical and near-IR observations reveal that I ZW 1 is likely undergoing a minor merger with a companion galaxy 156 west of the QSO (Hutchings & Crampton 1990; Schinnerer et al. 1998; Canalizo & Stockton 2001). This companion is not detected in our ALMA observations.

With a main objective of detecting the molecular outflow, IRAS F11119+3257 has been observed with ALMA in CO(1−0) emission at about 28 resolution (Veilleux et al. 2017). Compared to these observations that do not spatially resolve the CO morphology, our ALMA observations at 04 resolution clearly resolve the distribution of both CO gas and 3 mm continuum emission in the host galaxy of IRAS F11119+3257 on an ∼1 kpc scale. However, our data are not deep enough for the detection of broad wings in the CO emission.

The CO map of IRAS F15462−0450 exhibits clumpy structures outside the central bright compact source (F15462−0450C). The integrated CO line flux suggests that the detection is significant at the ∼5σ and ∼7σ level for the clumps to the northeast (NE) and southwest (SW), respectively. It is worth noting that these two clumps are almost symmetrically located in a straight line across the CO peak of the central source with a separation of 16 (∼2.9 kpc) between the central peak and the clump in each side. One possibility for the symmetric structure may be related to a massive molecular outflow in the QSO host. Deeper CO observations and higher-resolution imaging in multiwavelength (e.g., radio continuum, optical) are needed to reveal the nature of this feature. The spectra extracted for these two clumps, if associated with a redshifted CO(1−0) transition, show a velocity shift of ∼−60 and ∼40 km s⁻¹ from the CO line of F15462−0450C for the NE and SW, respectively. We detect significant 3 mm continuum emission from the main body of IRAS F15462−0450 at the ∼10σ level with a flux density of 0.645 ± 0.066 mJy (measured from a two-dimensional (2D) Gaussian fit to the continuum image; see Table 2). No 3 mm continuum emission was detected in the clumpy structures NE and SW.

For IRAS F15069+1808, one of the IR QSO systems resolved into multiple distinct CO sources, we identify two bright sources in the CO map, which we denote as northwest (NW) and southeast (SE), and we refer to the overlap region as "overlap" (see Figure 1). Both bright sources show an elongated morphology along the NE–SW axis. It is likely that IRAS F15069+1808 is in the middle stage of a merger when the galaxies have collided and begun to merge. The projected separation between the NW and SE sources is 248, equivalent to a projected physical distance of ∼7.2 kpc. In the continuum image, we do not detect any signal above 3σ, placing a 3σ upper limit on 3 mm continuum emission S_3mm < 0.15 mJy.

Similar to the interacting system IRAS F15069+1808 described above, the CO gas in IRAS F22454−1744 is also resolved into multiple sources with two armlike structures (north (N) and SW arms) originating from the two bright nuclear sources (denoted as NW and SE; Figure 1), which are undergoing merging with a projected separation of 078 (∼1.7 kpc) between the two central CO peaks. The 3 mm continuum emission is detected in the nuclear region of F22454−1744SE at the 4σ–5σ level with a flux density of 0.253 ± 0.078 mJy, whereas it is not detected in the source NW. The SW arm is resolved into two clumps (SW1 and SW2), which form a filamentary structure.

The CO distribution of IRAS F23411+0228 shows that the molecular gas is strongly concentrated in the central region (F23411+0228C) accompanied by an armlike feature to the NE and a clumpy structure outside the main body of the galaxy to the east (F23411+0228E). We detect 3 mm continuum emission in F23411+0228C at the ∼8σ level with flux of 0.433 ± 0.055 mJy. Most importantly, we also tentatively detect 3 mm continuum emission with flux of 86 ± 30 μJy from F23411+0228E, supporting the reality of such a feature. The angular separation between the C and E components in the IRAS F23411+0228 system is 177 (∼3.0 kpc). The spectrum extracted for F23411+0228E demonstrates that the line emission (see Figure 2), if associated with a redshifted CO(1−0) transition, comes from the same redshift as the main galaxy, suggesting that source E is likely physically related to the IRAS F23411+0228 system. However, it is not clear whether this is due to an ongoing merger or interaction or it is a clumpy star-forming region at large radii.

Figure 3 ¹⁵ shows an overlay of the CO(1−0) emission and SDSS u-band (or Pan-STARRS1 (PS1) g-band, if SDSS data are not available) image for the eight IR QSO hosts. The peak of 20 cm radio continuum emission measured from the Very Large Array (VLA) FIRST survey¹⁶ or the VLA 1.4 GHz survey of the ROSAT/IRAS galaxy sample (Condon et al. 1998) is marked as a plus sign in the image. The false-color PS1 yig image is shown in an inset panel. The tidal tails and irregular morphologies shown in the optical images seem to indicate signs of recent and/or ongoing dynamical interactions or mergers in these galaxies.

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Generally, the CO emission peaks roughly coincide with the brightest peaks in the optical images and are consistent with 20 cm continuum peaks within the positional error (∼05 for VLA 20 cm continuum observations). For IRAS F15069+1808, the 20 cm continuum position lies precisely on the nucleus of F15069+1808SE in CO emission, which also coincides with the UV emission peak. This suggests that the AGN is more likely embedded in the nucleus of F15069+1808SE, while the NW source could be a companion galaxy undergoing an interaction with the QSO. The 20 cm continuum emission peak of IRAS F22454−1744 lies between the two central brightest CO sources but closer to the SE source. Combined with the fact that the UV emission peak coincides with the nucleus of the SE source, we speculate that F22454−1744SE is probably the QSO merging with a companion galaxy to the NW that is about to coalesce. The SW molecular tail of IRAS F22454−1744 clearly follows the tidal arm seen in the optical emission of the PS1 image, whereas the NW arm has no counterpart in optical wavelength. For IRAS F23411+0228, the 20 cm continuum emission peaks in the central compact source. In addition, the UV emission is found to peak in the nucleus of the central source, indicating that the AGN is likely located in F23411+0228C. It is clear that the NE armlike structure of CO emission follows the arm seen in the optical image. Higher-resolution Hubble Space Telescope (HST) WFPC2 observations in the F814W band identify a bright peak coincident with F23411+0228C but also a faint peak coincident with the location of the CO peak in F23411+0228E (see the bottom right panel of Figure 3). However, higher-resolution observations (e.g., Chandra, JVLA) of X-ray and radio emission are required to determine the accurate position of the AGN for these merging systems.

The CO line intensity-weighted velocity fields and velocity dispersion of the eight IR QSO hosts are shown in Figure 1. These were made by smoothing the velocity over the emission region and clipping the intensity using the CASA task immoments. The cleaned image cube was smoothed in velocity and clipped at the 3σ level per channel. The zero velocity in the velocity maps corresponds to the CO redshifts listed in Table 2. The kinematics of the molecular gas in the eight IR QSO hosts are also quite varied. The maps of the velocity fields reveal smooth and regular rotation velocities for about half of the galaxies in our sample, while the rest are significantly distorted. Maps of the velocity dispersion show increased velocity dispersion in the centers of almost all CO-emitting systems, with a peak velocity dispersion of about 60−130 km s⁻¹.

For the five IR QSOs that are resolved into an isolated compact CO source, four of the host galaxies (I ZW 1, IRAS 06269−0543, IRAS F11119+3257, and IRAS F15426−0450) show velocity gradients in the velocity maps. The velocity dispersion peaks in these galaxies roughly correspond to the peaks of CO emission, except for IRAS 06269−0543, where there is a shift of the peak between the CO and 3 mm continuum emission. The velocity dispersion map of IRAS 06269−0543 shows an increase in the NW direction with respect to the CO peak, with a peak dispersion of ∼100 km s⁻¹, which is spatially coincident with the location of the 3 mm continuum peak. Given the limited spatial resolution of current data, we are not able to infer whether the 3 mm continuum emission is related to AGN activity, although the velocity dispersion is usually found to increase at the AGN location (e.g., Trakhtenbrot et al. 2017). The complex velocity distribution revealed in IRAS Z11598−0112 shows evidence that the molecular gas is strongly disturbed and has not settled in the galactic plane. For I ZW 1, the velocity gradient is obvious in the SE-to-NW direction, from about +190 to −190 km s⁻¹. This is consistent with the velocity map presented in Schinnerer et al. (1998). A small velocity gradient is present in the east–west direction of IRAS F11119+3257, while the deviation from the regular velocity field seen in the NE region may be indicative of noncircular motion. The CO velocity map of IRAS F15462−0450 shows a clear gradient from the NW to the SE in the main body of the galaxy, while the CO line of the NE clump is too narrow to show a gradient at our spectral resolution, and the SW clump shows a small velocity gradient along the same direction as that of the main body. The SW clump shows a slightly higher velocity dispersion (∼85 km s⁻¹) than that (∼65 km s⁻¹) of the peak in the main galaxy.

The CO kinematics for the remaining three galaxies that are resolved into multiple objects are complex. For the merging system IRAS F15069+1808, the SE source (identified as the possible galaxy-hosting luminous AGN) shows a rotating gas disk with a velocity gradient in the SE–NW direction, whereas the molecular gas in the NW galaxy is kinematically disturbed. The overlap region has the highest velocity dispersion (∼130 km s⁻¹) in CO(1−0) emission, possibly marking the new dynamical center of the merger. This is similar to what is seen in the IR-bright merger VV114, where the large velocity dispersion detected in the overlap region was interpreted as a turbulence-dominated shock region induced by the interaction between the two colliding galaxies (e.g., Saito et al. 2015).

The velocity field in the merging system IRAS F22454−1744 shows a velocity range of ∼230 km s⁻¹ across the galaxy disks, with the largest redshifted velocity in the molecular tail SW1 clump (about +130 km s⁻¹ with respect to the systemic velocity of the merging system). A regular rotating disk with a velocity gradient (ranging from about −100 to +30 km s⁻¹) in the SW–NE direction is clearly seen in the NW galaxy, while the velocity is significantly distorted in the SE source, which is likely to host the QSO, and in the extended CO emission regions. The velocity dispersion map in Figure 1 shows a peak velocity dispersion (∼80 km s⁻¹) in the SE nucleus followed by a large dispersion in the center of the NW source and a quiescent structure along the SW filament.

For IRAS F23411+0228, the central compact source F23411+0228C and the NE arm show complex and distorted velocity fields, whereas source E tends to show a small gradient from north to south. The NE arm has a redshifted velocity of ∼50−150 km s⁻¹ with respect to the main galaxy. The peak of velocity dispersion for F23411+0228C is about 70 km s⁻¹, while a relatively low value (∼10 km s⁻¹) is found in both the NE arm and source E. Deeper observations with higher resolution are needed to accurately constrain the kinematics and morphology of the extended CO structures in these galaxies.

Combining the analysis of CO morphology and gas kinematics, we find that the molecular gas in four (I ZW 1, IRAS 06269−0543, IRAS F11119+3257, and IRAS F15462−0450) out of the eight IR QSO hosts shows signatures of rotating gas disks with an ordered velocity field, one (IRAS Z11598−0112) is a compact CO source with disturbed velocity, and the other three (IRAS F15069+1808, IRAS F22454−1744, and IRAS F23411+0228) are resolved into distinct objects showing evidence for strong interactions and merging.

Figure 4 shows position–velocity (PV) diagrams of the CO(1−0) emission line for the four isolated QSO host galaxies (I ZW 1, IRAS 06269−0543, IRAS F11119+3257, and IRAS F15462−0450) with signatures of disklike rotation in their CO velocity fields along the velocity gradient through the peak CO position. For IRAS F11119+3257, we combined our high-resolution CO data with the archival ALMA CO data (∼28 resolution) observed by Veilleux et al. (2017) to produce the PV diagram. The PV plots show that the rotation curve rises steeply in the inner region, becoming flat at radius ∼05−08 (∼0.9–1.3 kpc) for I ZW 1, IRAS 06269−0543, and IRAS F15462−0450. However, for IRAS F11119+3257, the rotation curve is much less prominent. We calculated the inclination angle (between the polar axis of the disk and the line of sight) based on the axis ratio, i = cos⁻¹(a_min/a_maj), where a_min and a_maj are the semiminor and semimajor axes of the CO-emitting regions (assuming a thin-disk geometry; see Section 3.4 and Table 3). We then assumed the gas to be in a rotating disk and studied the kinematic properties by fitting 3D tilted-ring models to emission line data cubes with the ^3DBAROLO code (Di Teodoro & Fraternali 2015). The red circles in Figure 4 denote the best-fit values for the projected rotation velocity derived from ^3DBAROLO. We adopt values of the rotation velocity and velocity dispersion derived at the turnover radius, i.e., the transitional point between the rising and flat parts of the rotation curve, as the intrinsic rotation velocity and local velocity dispersion for each galaxy. Except for IRAS F11119+3257, which is poorly fit by models, the kinematics for the remaining three galaxies can be well fitted by models. The derived rotation velocity and velocity dispersion range from 157 to 273 km s⁻¹ and 42 to 45 km s⁻¹ (see Table 4), respectively, and the corresponding ratio of the rotation velocity to the velocity dispersion, V_rot/σ, is in the range of 4−6 for the three galaxies, somewhat smaller than the values of present-day disks (Sofue & Rubin 2001).

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Table 3.  Derived Properties

Source	${L}_{\mathrm{CO}(1-0)}^{{\prime} }$	${M}_{{{\rm{H}}}_{2}}$	CO Size	Cont. Size	Inclination i	Mdynsin2i	Mdyn	MBH	SFRCO	Lbol
	(109 Ll)a	(109 M⊙)	(kpc)	(kpc)	(deg)	(1010 M⊙)	(1010 M⊙)	(107 M⊙)	(M⊙ yr−1)	(1012 L⊙)
(1)	(2)	(3)	(4)	(5)	(6)	(7)	(8)	(9)	(10)	(11)
I ZW 1	5.50 ± 0.26	4.40 ± 0.21	3.2 ± 0.2	⋯	38 ± 11	1.6 ± 0.3	4.1 ± 0.7	2.1	117	1.0
IRAS 06269−0543	6.91 ± 0.44	5.53 ± 0.35	2.3 ± 0.3	0.6 ± 0.1	51 ± 10	0.7 ± 0.1	1.1 ± 0.2	3.2	183	1.8
IRAS F11119+3257	11.36 ± 0.90	9.09 ± 0.72	4.8 ± 0.8	1.0 ± 0.2	48 ± 15	2.4 ± 0.4	4.3 ± 0.8	15.7	312	11.0
IRAS Z11598−0112	11.99 ± 0.68	9.59 ± 0.54	4.7 ± 0.6	⋯	37 ± 19	⋯	1.6 ± 0.2	0.4	378	0.4
IRAS F15069+1808NW	5.57 ± 0.31	4.45 ± 0.25	3.3 ± 0.4	⋯	48 ± 12	⋯	2.0 ± 0.3	⋯	130	⋯
IRAS F15069+1808SE	4.35 ± 0.40	3.48 ± 0.32	7.0 ± 1.0	⋯	64 ± 8	5.5 ± 1.4	6.9 ± 1.8	1.0	96	0.5
IRAS F15462−0450C	3.64 ± 0.10	2.91 ± 0.08	2.0 ± 0.3	0.4 ± 0.1	25 ± 21	0.15 ± 0.03	0.9 ± 0.2	0.8	70	0.2
IRAS F22454−1744NW	3.07 ± 0.09	2.46 ± 0.07	2.9 ± 0.2	⋯	31 ± 17	0.7 ± 0.1	2.8 ± 0.3	⋯	62	⋯
IRAS F22454−1744SE	2.43 ± 0.10	1.94 ± 0.08	1.2 ± 0.2	⋯	31 ± 24	⋯	0.7 ± 0.2	0.5	47	0.6
IRAS F23411+0228C	1.75 ± 0.06	1.40 ± 0.05	2.4 ± 0.6	0.4 ± 0.2	28 ± 31	⋯	1.3 ± 0.3	1.0	55	1.3

Note. Column (1): galaxy name. Column (2): CO(1−0) luminosity derived with the integrated flux density listed in Table 2. Column (3): molecular gas masses derived with ${L}_{\mathrm{CO}(1-0)}^{{\prime} }$ by assuming a CO luminosity-to-molecular gas mass conversion factor of α_CO = 0.8 M_⊙ (K km s⁻¹ pc²)⁻¹. Column (4): CO FWHM major-axis size of the extended component, derived from visibility fitting (see Table 2). Column (5): 3 mm continuum FWHM size. We take the source as an unresolved point source if the size measurement is only significant at <2σ. Column (6): disk inclination angle estimated from the ratio of CO(1−0) minor and major axes as i = cos⁻¹(a_min/a_maj). Column (7): dynamical mass without inclination angle correction for the galaxies with kinematical signatures of rotating molecular gas disks, estimated from the CO(1−0) line width and source size (see Section 3.5 for details). Column (8): inclination angle–corrected dynamical mass within the CO-emitting region. The uncertainty in these dynamical masses does not include the uncertainties in the inclination angle. For the galaxies without a velocity gradient in the CO map, we adopt the virial relation to estimate dynamical mass. Column (9): virial BH masses from Hao et al. (2005) using Hβ broad emission line and λL_{λ,5100 Å} measurements. For I ZW 1, we take the average of the measurements derived in Hao et al. (2005) and Vestergaard & Peterson (2006). Column (10): SFR derived from IR luminosity, which is predicted from CO(1−0) luminosity based on the correlation between ${L}_{\mathrm{CO}(1-0)}^{{\prime} }$ and L_IR observed for starburst galaxies (see Section 4.2 for details). Column (11): AGN-associated bolometric luminosities from Hao et al. (2005) using the bolometric correction of L_bol ≈ 9λL_{λ,5100 Å}.

^a ${L}_{l}\equiv {\rm{K}}\,\mathrm{km}\,{{\rm{s}}}^{-1}\,{\mathrm{pc}}^{2}$.

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We measured the CO fluxes based on the spectra extracted from a circular aperture, of which the CO peak fluxes are consistent with single-dish IRAM 30 m measurements (see the spectra in Figure 2 and the corresponding apertures used for spectra extraction shown in Figure 1), and found that both the CO integrated fluxes and the line profiles are in good agreement with the IRAM 30 m data for the galaxies in our sample.

In Figure 2, we plot the CO spectra extracted from the ALMA cube using a mask that encompasses the ≥2σ region in the velocity-integrated CO(1−0) map for comparison. In this work, we define a detection if the velocity-integrated line intensity is higher than or equal to 3σ, but we use the 2σ cutoff for data analysis as a comparison. It is clear that in most cases, apart from I ZW 1 and IRAS 06269−0543, both the CO peak flux and the line profile of the spectra extracted from the ≥2σ region agree well with IRAM 30 m measurements, suggesting that little emission is filtered out by long baselines and the molecular gas is centrally concentrated.

In the cases of I ZW 1 and IRAS 06269−0543, the spectra extracted from the 2σ CO-emitting regions show an ∼30%–40% smaller CO peak flux. The CO spectra of these two galaxies are best described by a double-horned velocity profile, with a separation of 225 ± 10 and 165 ± 8 km s⁻¹ between the red and blue peaks, respectively, consistent with the CO spectra measured with the IRAM 30 m (Evans et al. 2006; Xia et al. 2012). In comparison, the 30 m spectra (beam size ≈25'') have more flux in the horns, indicative of an extended disk component in the host galaxies. For the ALMA data that were extracted from a circular aperture with peak CO fluxes consistent with the single-dish measurements, the diameter of the circular aperture is 10'' and 8'' for I ZW 1 and IRAS 06269−0543, respectively. This may indicate that the molecular gas is extended to a radius of about 6 and 8 kpc for these two galaxies, respectively. For I ZW 1, our estimate agrees well with previous PdBI observations that show an extent of about 10 kpc for the molecular disk size of the host galaxy (Schinnerer et al. 1998). By comparison, the ≥2σ CO-emitting region extends to a size with a radius of about 20 and 11 (both equivalent to ∼2.4 kpc) for I ZW 1 and IRAS 06269−0543, respectively, suggesting that a substantial amount of molecular gas is concentrated in the central few kpc. Given that the flux extracted from a larger aperture is found to be comparable to that measured with the IRAM 30 m, it is likely that the flux not recovered within the 2σ region for these two galaxies is due to the emission from the extended disk undetected in our ALMA observations.

For the remaining six galaxies, the CO line profiles are well described by a single Gaussian fit. Similarly, the CO molecular gas is found to be within an extent of about 4–8 kpc (∼2''–3'') in radius for these galaxies, based on the spectra extracted from a circular aperture with the diameter shown in Figure 2. It can be seen from Figure 1 that these apertures are typically larger than the 2σ CO-emitting regions for the galaxies in our sample. A comparison of the CO(1−0) integrated fluxes measured based on the ALMA spectra extracted from the ≥2σ region with the fluxes seen by the IRAM 30 m (Xia et al. 2012) shows that our interferometric data typically recover ∼80% of the observed single-dish flux. The consistency of the flux measured from a larger-aperture ALMA spectrum with the single-dish observations (Figure 2) is likely to indicate that the flux not recovered in the 2σ CO-emitting region is attributed to the insufficient sensitivity of our ALMA observations for the detection of more extended lower surface brightness CO emission. However, it should be noted that the systematic uncertainties in the flux calibration would also affect the comparison of flux measured with different observations.

To make a consistent flux measurement with the IRAM 30 m data, the total CO integrated flux was measured from the spectrum extracted from a circular aperture (with the diameter shown in Figure 2 for each source) by integrating the intensity over the line-emitting region in each channel, except for the galaxies spatially resolved into interacting systems and/or clumpy structures, IRAS F15069+1808, IRAS F15462−0450, IRAS F22454−1744, and IRAS F23411+0228, for which the integrated flux derived for each component was measured from the spectrum extracted from the ≥2σ region in the CO intensity map (see the spectra in Figure 5). The redshift and line width were measured from a Gaussian fit to the CO line. The ALMA CO line properties measured for the galaxies in our sample are summarized in Table 2.

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The CO luminosity can be derived from the line integrated intensity listed in Table 2, following Solomon et al. (1997),

$$\begin{eqnarray}\begin{array}{rcl}{L}_{\mathrm{CO}}^{{\prime} } & = & 3.25\times {10}^{7}\left(\displaystyle \frac{{S}_{\mathrm{CO}}{\rm{\Delta }}v}{1\ \mathrm{Jy}\ \mathrm{km}\ {{\rm{s}}}^{-1}}\right){\left(\displaystyle \frac{{\nu }_{\mathrm{obs}}}{1\mathrm{GHz}}\right)}^{-2}\\ & & \times \,{\left(\displaystyle \frac{{D}_{{\rm{L}}}}{1\mathrm{Mpc}}\right)}^{2}{\left(1+z\right)}^{-3}\ {\rm{K}}\ \mathrm{km}\ {{\rm{s}}}^{-1}\,{\mathrm{pc}}^{2},\end{array}\end{eqnarray} \tag{ 1 }$$

where S_COΔv is the velocity-integrated flux density, ν_obs is the observed line frequency, and D_L is the luminosity distance. Similar to the measurements in Xia et al. (2012), the CO(1−0) luminosity ranges from several times 10⁹ to 10¹⁰ K km s⁻¹ pc² for our sample of IR QSO hosts (see Table 3). The molecular gas mass derived by ${M}_{{{\rm{H}}}_{2}}={\alpha }_{\mathrm{CO}}{L}_{\mathrm{CO}}^{{\prime} }$ corresponds to a few times 10⁹ M_⊙ if we adopt a ULIRG-like CO luminosity-to-H₂ mass conversion factor, α_CO, of 0.8 M_⊙ pc⁻² (K km s⁻¹)⁻¹ (e.g., Downes & Solomon 1998). We note that α_CO is uncertain and varies significantly from source to source, and possibly from region to region, within a galaxy (e.g., Bolatto et al. 2013). For simplicity, we adopt a constant α_CO to estimate the molecular gas mass for all of the galaxies in our sample.

For the systems that are resolved into multiple separate objects in CO images, the ALMA data enable us to estimate the molecular gas mass for each component for the first time (see Table 3). The molecular gas mass derived for the two brightest sources NW and SE in the merging system IRAS F15069+1808 are found to be comparable, implying that these two galaxies are likely undergoing a major merger. Similarly, the approximate equivalent mass derived for the NW and SE sources in IRAS F22454−1744 is probably indicative of a major merger. In the case of IRAS F23411+0228, the molecular gas mass estimated for the E source (∼3.8 × 10⁷ M_⊙) is much lower compared to that of the central bright galaxy (∼1.4 × 10⁹ M_⊙). Combined with the observed properties discussed above, i.e., multiwavelength identification and gas kinematics, this may suggest that IRAS F23411+0228 would be a minor merger if the faint E source is indeed an interacting companion.

Our high-resolution CO imaging reveals the detailed structure of the molecular gas distribution for IR QSO hosts, which is crucial for placing constraints on the dynamical states of the sources. To avoid possible uncertainties produced by the image reconstruction process that will be introduced into the size measurement, we directly fit models to the interferometric observables (i.e., the visibilities) in the uv-plane, which is preferable for the cases of simple source structure, by using the UVMULTIFIT tool (Martí-Vidal et al. 2014).

Based on the centroid of the surface brightness distribution inferred from 2D Gaussian fitting (Table 2), we shift the phase center of both the line and continuum data sets used for the size measurement to match the centroid of each source. Assuming that the surface brightness distribution of the CO line and continuum follow a symmetric Gaussian profile, we performed fits of the visibilities that were spectrally averaged with different source models (i.e., a single Gaussian profile, a combination of a point-source model and an elliptical Gaussian model, and a combination of a compact circular Gaussian model and an extended elliptical Gaussian model to investigate the possibility of having compact CO emission embedded in an extended, low surface brightness component) and found that all of the CO sources are well resolved and the best fit is given by a combination of circular and elliptical Gaussian components. For the continuum, a single circular Gaussian component model is preferred due to the relatively low S/N of the detection. The best fit is determined by χ² minimization. For IRAS F15069+1808 and IRAS F22454−1744, which are resolved into two separate galaxies with comparable gas mass, the CO sources are best fit with two elliptical Gaussians with positions centered on the QSO host and the companion galaxy, respectively. The best-fitting values of the double Gaussian models for the line and the one-component model for the continuum are reported in Table 2. Figure 6 shows the visibility function for the CO and 3 mm continuum and the corresponding best-fitting profiles.

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For the double Gaussian models fit to the CO data, the source size of the compact component (FWHM measured from circular Gaussian profile) ranges from 022 to 037 (∼0.4−1.0 kpc with a median of 0.8 kpc), and the size of the extended component (major-axis FWHM from elliptical Gaussian profile) ranges from 055 to 275 (∼1.2−7.0 kpc with a median of 3.2 kpc). The largest CO source size (241, equivalent to a physical scale of 7.0 kpc) is seen in IRAS F15069+1808SE. For the rest of the galaxies in our sample, the major-axis size of the CO source ranges from 1.2 to 4.9 kpc. For the continuum emission, four of the sources are marginally resolved with observed sizes comparable to the synthesized beams, while the remaining detections are pointlike sources in our observations. The continuum source sizes are estimated to be 022−031 (∼0.4−1.0 kpc with a median of 0.6 kpc) for the four sources with size measurements at ≳2σ significance, which is more than a factor of 3 smaller than their CO sizes, suggesting that the continuum emission is more concentrated than that of molecular gas. Compared to the full CO flux distribution (∼4−8 kpc in radius) discussed in Section 3.3, the 2D Gaussian visibility fitting gives a smaller CO size, which represents the distribution of the relatively dominant central component.

As described in the previous section, large-scale systematic velocity gradients are seen for six galaxies (I Zw 1, IRAS 06269−0543, IRAS F11119+3257, IRAS F15069+1808SE, IRAS 15462−0450, and IRAS F22454−1744NW) in our sample, whereas for the remaining four CO sources, the molecular gas is found to be highly disturbed with complex velocity structure (see Figure 1).

For the six galaxies exhibiting CO velocity gradients across the source, we estimate the dynamical mass within the CO-emitting region by assuming that the bulk of the emission in these sources can be well described by a rotating disk. In this case, the dynamical mass is given by applying the relation ${M}_{\mathrm{dyn}}\approx 2.3\times {10}^{5}{v}_{\mathrm{cir}}^{2}R$ (e.g., Wang et al. 2010), where R is the disk radius in kpc, which we assume is equal to 0.75 times the CO FWHM major axis of the extended component measured from visibility fitting (i.e., half of the full width at 20% of the peak intensity for a Gaussian profile of CO emission; Wang et al. 2013), and v_cir is the maximum circular velocity of the gas disk in km s⁻¹. For the three galaxies that are well fitted by our rotating kinematic models (see Figure 4), the circular velocity is equal to the rotation velocities reported in Table 4. For the remaining three galaxies, one (IRAS F11119+3257) is not consistent with our model, and the other two (IRAS F15069+1808SE and IRAS F22454−1744NW) are undergoing a major-merger interaction. For these galaxies, their circular velocities were estimated by v_cir = 0.75 Δv_FWHM/sin i (Ho 2007a, 2007b; Wang et al. 2010), assuming the gas is distributed in an inclined disk. Adopting the inclination angle listed in Table 3, the derived inclination-corrected dynamical masses range from 9.0 × 10⁹ to 6.9 × 10¹⁰ M_⊙. These estimates of M_dyn can be significantly affected by the uncertainty of inclination, and the assumption of a rotating disk as part of the emitting gas might be associated with noncircular motion, especially in interacting systems with perturbations. For the three galaxies with v_cir derived from model fitting, we also calculated the circular velocity using the aforementioned equation and found that the v_cir inferred by the FWHM of the CO line is roughly twice as high as that derived from model fitting. This is suggestive that the likely presence of nonrotating gas components also contributes to the CO line width, which would affect the determination of circular velocity. If true, this would result in lower v_cir and therefore lower M_dyn for IRAS F11119+3257, IRAS F15069+1808SE, and IRAS F22454−1744NW.

For the galaxies with irregular velocity fields, we assumed that the galaxy is supported by random motions and estimated the dynamical mass using the virial theorem, assuming that the distribution of molecular gas is spherical with uniform density and has an isotropic velocity dispersion. Under these assumptions, the dynamical mass can be estimated as M_dyn = 5σ²R/G (e.g., Pettini et al. 2001), where R is the gas disk radius, σ = Δv_FWHM/2.35 is the one-dimensional velocity dispersion, and G is the gravitational constant. The derived dynamical masses range from 7.4 × 10⁹ to 2.0 × 10¹⁰ M_⊙ for these four galaxies. We found that the virial estimator leads to a smaller M_dyn compared to that derived from a rotating disk estimator. Note that the virial mass estimates are also affected by large systematic errors, e.g., the unverified assumption that the system is virialized and the source size is likely underestimated due to the possibly more extended, low surface brightness CO-emitting regions missed by our high-resolution ALMA observations. As discussed in Section 3.4, the CO size inferred from visibility fitting is more likely to represent the distribution of a relatively central component. Detailed modeling of spatially resolved gas kinematics is needed to obtain a more accurate estimate of the dynamical mass for the IR QSO hosts in our sample.

The combined analysis of CO morphology and gas kinematics of the IR QSO hosts in our sample reveals the diversity of host galaxy properties. Three of IR QSO systems in our sample are identified as interacting systems, one galaxy accompanying each of these QSOs. The companion galaxies are located between roughly 2 and 7 kpc in projection from the QSOs, with small velocity offsets (Δv < 60 km s⁻¹). Two of these interacting QSO systems (IRAS F15069+1808 and IRAS F22454−1744) are interpreted as major mergers, while the other one (IRAS F23411+0228) shows evidence for a minor merger, although higher-resolution multiwavelength data are needed for further confirmation. Our ALMA data for the first time provide evidence for significant major-merger interactions in some of the local IR QSO systems. Observations toward high-z have also revealed companion galaxies interacting with the central luminous QSOs, suggesting that merger activity may be a dominant mechanism for the most luminous galaxies (Hu et al. 1996; Omont et al. 1996; Decarli et al. 2017; Trakhtenbrot et al. 2017; Díaz-Santos et al. 2018). The velocity fields of the molecular gas in QSO hosts IRAS F23411+0228 and IRAS F22454−1744 are significantly disturbed and show complex structure, while the gas in the QSO host of the IRAS F15069+1808 system shows a velocity gradient. Simulations of gas-rich mergers have shown that the coalesced nuclei of mergers can rapidly relax into smooth disks (e.g., Springel & Hernquist 2005; Robertson et al. 2006; Hopkins et al. 2009), which has also been shown observationally (Ueda et al. 2014). We therefore caution that our ALMA data cannot disprove the possibility that the interacting QSO hosts may have already experienced a merging process with other galaxies if all of the QSOs are triggered by major mergers.

For the other five IR QSO systems in our sample, of which the QSO hosts are found to be isolated without any interacting companion, most of these sources show evidence for ordered rotation, suggesting that these systems are likely observed in the final coalescence stage. For the three galaxies that can be well fitted by a rotating kinematic model, I ZW 1, IRAS 06269−0543, and IRAS F15462−0450, the ratio of the rotation velocity to the local velocity dispersion of V_rot/σ is in the range 4−6, indicating that the molecular gas in these galaxies is dominated by rotation. Similar rotating disks with V_rot/σ > 3 have also been revealed in massive star-forming galaxies at z ∼ 2, which were observed at the transition stage from extended disks to compact spheroids with rapid dense core buildup (Tadaki et al. 2017a, 2017b). In addition, the line-of-sight velocities are found to flatten at ≳1 kpc for the three galaxies in our sample, implying that these galaxies may not yet have a significant bulge component, as a dominant bulge would cause the rotation curve to rise steeply at the center and flatten on scales of <500 pc (e.g., Sofue et al. 1999). However, higher spatially resolved data are necessary to draw a firm conclusion. For IRAS F11119+3257, the complex velocity field becomes disturbed in the NE region, probably affected by a turbulent component (see Figure 1). Its kinematic properties reveal the likely presence of a disturbed disk with turbulent molecular gas. This is consistent with the large-scale (a few kpc) molecular outflow observed in this galaxy, which is interpreted as likely driven by the strong feedback from the central AGN (Veilleux et al. 2017).

High-resolution millimeter observations of Mrk 231, the only well-studied local IR QSO so far, have revealed that the molecular gas traced by both CO and dense molecules is dominated by rotation with a disk size of ∼1 kpc FWHM (Downes & Solomon 1998; Aalto et al. 2012; Feruglio et al. 2015). Together with the eight IR QSOs observed in this study, the combined analysis of the CO morphologies and kinematic properties allows us to roughly classify the local IR QSO hosts into three categories: (1) rotating gas disk with ordered velocity gradient, (2) compact CO peak with disturbed velocity indicative of unsettled molecular gas in the galactic plane, and (3) multiple CO distinct sources undergoing a merger between a luminous QSO and a companion galaxy separated by a few kpc. The diverse host galaxy properties revealed in our observations show evidence that the merging between luminous QSOs and companion galaxies is still ongoing in some of the IR QSO systems. This is unexpected, since the objects in the IR QSO phase are typically characterized by the final coalescence of the galaxies, according to the theoretical models of the merger-driven evolutionary sequence (e.g., Sanders et al. 1988; Barnes & Hernquist 1992; Hopkins et al. 2008; Narayanan et al. 2010), but consistent with the recent discovery of a population of late-stage nuclear mergers with separation <3 kpc in obscured luminous BHs by high-resolution near-IR observations (Koss et al. 2018). We caution, however, given that our classification of IR QSOs is based on a small sample with only nine CO-mapped sources, it is a first-order kinematic classification and may be too simplistic. A larger sample of local IR QSOs mapped in gas emission with high resolution is needed to reach a meaningful statistical study for galaxy classification.

Table 3 summarizes the size measurements for the IR QSOs spatially resolved in CO(1−0) and 3 mm continuum emission. It is clear that the 3 mm continuum sizes are substantially (a factor of >3) smaller than the CO sizes, indicative of a more compact structure of continuum emission compared to that of molecular gas, which is related to the star formation in host galaxies. With a physical size of 3.2 ± 0.2 kpc, I ZW 1 is spatially resolved in CO emission but unresolved in 3 mm continuum in our observations with an angular resolution of about 06 (∼0.7 kpc). The ALMA HCN (3−2) and HCO⁺ (3−2) imaging of I ZW 1 with a comparable angular resolution (069 × 0 63) to that of our CO observations shows that the source is marginally resolved in dense molecular gas emission with a deconvolved size of ∼04 (Imanishi et al. 2016). Compared to the total molecular gas as traced by CO emission, both HCN and HCO⁺ lines with high critical densities probe the dense molecular gas (i.e., $n({{\rm{H}}}_{2})\geqslant {10}^{4}\ {\mathrm{cm}}^{-3}$), of which the mass is observed to have a tight linear correlation with the star formation rate (SFR) in galaxies, suggesting that the dense gas is likely the direct fuel for star formation (e.g., Gao & Solomon 2004). The significantly smaller size of the dense gas observed compared to the CO size may indicate that the star formation is concentrated in subkiloparsec-scale structure for I ZW 1. At the same time, ALMA observations performed by Imanishi et al. (2016) also marginally resolved the continuum emission at 1.2 mm that is usually dominated by dust thermal radiation, with an intrinsic size of about 06 (∼0.8 kpc). This is roughly equal to the dense gas size but larger than that of 3 mm continuum emission, which is unresolved in our ALMA observations with a slightly higher angular resolution (see Table 1).

In addition, VLA snapshot observations (beam size ≈031) of I ZW 1 at 8.4 GHz show a pointlike structure in the map (Kukula et al. 1995). Based on this, we collected and processed the A configuration 8.4 GHz radio data (project ID: AB0670) from the VLA data archive that was observed much deeper and with a higher resolution of 027. A 2D Gaussian fit to the 8.4 GHz continuum image obtains a deconvolved size of 021 ± 006. This is obviously smaller than the size of 1.2 mm continuum emission that is mainly related to the star formation in host galaxies. Combining the analysis that the 3 mm continuum size is smaller than that of 1.2 mm but could be close to the 8.4 GHz radio size, we speculate that the 3 mm continuum emission of I ZW 1 may be partially related to the compact synchrotron radiation arising from plasma accelerated by the central AGN (Panessa et al. 2019).

Moreover, the 3 mm flux density we measured for I ZW 1 is found to exceed the interpolation of the low-frequency steep-slope power law (see Figure 11 in Pasetto et al. 2019), which may indicate a significant contribution from additional AGN-related synchrotron emission and thermal free–free emission. In addition, theoretical calculations using Clumpy models, together with the MIR to X-ray and radio fundamental plane scaling relations, provide evidence for a nonnegligible contribution of synchrotron emission to the 3 mm band for bright AGNs (Pasetto et al. 2019).

According to the above analysis, the different radiation components contributing to the 3 mm band of I ZW 1 seems to be a plausible explanation for the compact structure of 3 mm continuum emission compared to the CO morphology observed for this source, as well as for the remaining local IR QSOs in our sample. However, deeper observations with higher angular resolution at (sub)millimeter wavelengths, together with a spectral energy distribution (SED) analysis including radio data, are necessary to explore the different radiation structures and mechanisms from the galaxy to the nuclear regions and their connections for IR QSOs.

The CO-based dynamical mass we derived for each of the QSO hosts is the sum of all of the mass (contributed by various galaxy components, i.e., stars, gas, dust, central BH, and dark matter) inside the central few kpc of the galaxies. Given that both the dust and BH masses make up a substantially small fraction compared to the total mass, we assumed that the molecular gas fraction can be approximated as the ratio of gas to dynamical mass and found that the gas fraction of M_gas/M_dyn ranges from 0.05 ± 0.01 to 0.60 ± 0.08 with a median value of 0.22 ± 0.04 for IR QSOs, in line with that of local ULIRGs (e.g., Downes & Solomon 1998). However, it should be noted that the gas fractions derived for the IR QSOs in our sample are largely affected by the uncertainties of dynamical mass; e.g., the relatively smaller CO size compared to the full CO flux distribution adopted for the dynamical mass estimates would lead to an overestimation of the gas fraction (see Section 3.5). Similar results have been obtained for z ∼ 6 QSOs detected in CO emission, with a median value of M_gas/M_dyn = 0.16 (e.g., Wang et al. 2010, 2016; Feruglio et al. 2018). For comparison, the gas fraction of molecular gas to total baryonic mass of M_gas/(M_⋆ + M_gas) is found to have a mean value of about 0.3 in z = 1 main-sequence galaxies, and the fraction increases with look-back time (e.g., Tan et al. 2013; Schinnerer et al. 2016; Magdis et al. 2017; Tacconi et al. 2018).

As the SMBH grows primarily through mass accretion during the AGN phase and the bulge of the host galaxy builds up from star formation, a comparison of the mass accretion rate of the SMBH with the SFR will be useful to understand how the BHs and their host galaxies grow in the IR QSO phase, under the assumption that the object is caught in the phase with ongoing processes of galaxy assembly.

Figure 7 shows the BH mass accretion rate ${\dot{M}}_{\mathrm{acc}}$ as a function of the SFR for low-z IR QSOs (circles) compared to a compilation of high-z QSOs (squares) for which both the far-IR and AGN bolometric luminosities have been measured (see caption of Figure 7 for details). The colored and gray circles represent the local IR QSOs mapped in CO emission and the remaining sample in Xia et al. (2012) without CO images.

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The BH accretion rate is derived as ${\dot{M}}_{\mathrm{acc}}={L}_{\mathrm{bol}}/\eta {c}^{2}$ assuming an accretion efficiency η = 0.1. For the IR QSOs, the AGN bolometric luminosities L_bol were estimated from the extinction-corrected continuum emission at 5100 Å and using a bolometric correction, i.e., L_bol ≈ $9\lambda {L}_{\lambda ,5100\mathring{\rm A} }$ (Hao et al. 2005). For the high-z QSOs, L_bol was taken from the literature, when available, and generally derived from the continuum luminosity at 1450 Å, while for sources with no L_bol reported in the literature, we estimated the ${\dot{M}}_{\mathrm{acc}}$ by assuming Eddington accretion, i.e., ${\dot{M}}_{\mathrm{Edd}}\approx 2.2\times {10}^{-8}{M}_{\mathrm{BH}}$ ${M}_{\odot }{\mathrm{yr}}^{-1}$. For both low- and high-z QSOs, we computed the SFR from the far-IR emission that is dominated by the cold dust component tracing the star formation–related IR luminosity following the scaling relation found in the local universe: SFR/${M}_{\odot }\ {\mathrm{yr}}^{-1}=1.49\,\times {10}^{-10}{L}_{\mathrm{IR}}/{L}_{\odot }$ (Kennicutt & Evans 2012). Here we converted the far-IR luminosity to the total IR luminosity (in the range of 3–1100 μm) by adopting L_IR = 1.3 L_FIR (Decarli et al. 2018), which is derived for bright QSOs by modeling the dust continuum emission as a modified blackbody. Note that the SFR measured for the hyperluminous (L_bol > 10¹³ L_⊙) QSOs may be overestimated due to the possible contribution from AGNs to the far-IR emission (Dai et al. 2012; Duras et al. 2017).

For the low-z IR QSOs, the far-IR luminosities were calculated based on the flux densities measured at IRAS 60 and 100 μm (see Xia et al. 2012). However, for the two IR QSOs that are identified as interacting systems in our resolved CO maps, IRAS F15069+1808 and IRAS F22454–1744, the SFRs were estimated from IR luminosities that are predicted by the CO(1−0) emission based on the correlation between ${L}_{\mathrm{CO}(1-0)}^{{\prime} }$ and L_IR, i.e., log $\left(\tfrac{{L}_{\mathrm{CO}(1-0)}^{{\prime} }}{{\rm{K}}\ \mathrm{km}\ {{\rm{s}}}^{-1}\,{\mathrm{pc}}^{2}}\right)$ = ${0.08}_{-0.08}^{+0.15}$ + 0.81 log $\left(\tfrac{{L}_{\mathrm{IR}}}{{L}_{\odot }}\right)$, observed for starburst galaxies (Sargent et al. 2014). The CO-based SFRs estimated for IRAS F15069+1808SE and IRAS F22454–1744SE, both of which are likely galaxies hosting the luminous AGN, are found to be lower than the dust-based SFR estimates, which are global measurements for the whole systems. We also calculated the CO-based SFR for the remaining local IR QSOs with CO(1−0) luminosities derived from the single-dish data in Xia et al. (2012) and found a median and a mean value of the SFR_CO-to-SFR_dust ratio of 0.86 and 1.06, respectively, with a 1σ dispersion of 0.57. This suggests that the two estimates are comparable, although with substantial scatter. Given that the CO distribution of IR QSOs in our sample is found to be composed of a compact component and an extended component by model fitting (see Section 3.4), as well as the much compact 3 mm continuum emission compared to the CO source observed for these galaxies, we speculate that the excitation of a compact component of the CO emission is likely related to the X-ray-dominated regions in the AGN torus. In this case, the CO-based SFR estimates for IR QSOs might be overestimated. We will investigate this topic by performing an SED analysis including multiwavelength data for more details in a future work.

In Figure 7, we find a trend between ${\dot{M}}_{\mathrm{acc}}$ and SFR over about 3 orders of magnitude in far-IR luminosity/SFR. The solid line shows the best-fit (a logarithmic linear least-squares bisector fit) correlation for the whole sample of QSOs, with a power law of ${\dot{M}}_{\mathrm{acc}}\propto {\mathrm{SFR}}^{(1.68\pm 0.17)}$. The Spearman rank correlation coefficient for this correlation is 0.77 with a high significance (P < 10⁻⁵) but substantial scatter. Our result is in general agreement with the correlation found between AGN activity and star formation, i.e., ${L}_{\mathrm{AGN}}\propto {L}_{\mathrm{IR},\mathrm{SF}}^{\alpha }$ (α ∼ 1.1–1.7; see Netzer 2009; Chen et al. 2013; Hickox et al. 2014; Duras et al. 2017; Dai et al. 2018; Izumi et al. 2019 and references therein). As noted in previous works (see e.g., Dai et al. 2018), the variation of slope might be attributed to different sample compositions and/or methods of analysis. However, all of these studies, including our own, reveal a significant trend between the SFR and BH accretion spanning a wide range of luminosity, implying that there may be a direct connection between the AGN and star formation activities over galaxy evolution timescales. In addition, there is evidence that SMBHs have grown in step with their host galaxies since z ∼ 2 (Daddi et al. 2007; Mullaney et al. 2012). The median value of ${\dot{M}}_{\mathrm{acc}}$/SFR is 6.0 × 10⁻³ for IR QSOs, consistent with the value derived in Xia et al. (2012). In contrast, the ${\dot{M}}_{\mathrm{acc}}$/SFR values for high-z QSOs are found to be about a factor of 10 higher (a median of 7.3 × 10⁻²) than the local IR QSOs. This is consistent with the "overmassive" BH revealed for z > 5 QSOs (Walter et al. 2004; Wang et al. 2010, 2013, 2016), for which a plausible interpretation is likely related to the different efficiency of gas accretion to the central SMBHs, i.e., faster gas consumption in the most massive SMBHs. Similar results have been reported by Hao et al. (2008), who found a trend that the SFR increases with the accretion rate for both low- and high-redshift IR-luminous QSOs, and the relative growth of BHs and their host spheroids may depend on the intensity of QSO activities.

Based on the CO-based dynamical mass estimates and the SMBH mass taken from the literature (see Table 3; Hao et al. 2005), we also investigated the possible constraints of the relationship between the BH and the host galaxy in IR QSO systems and found that almost all local IR QSOs in our sample are located on or below the local BH–bulge mass relation (equating M_dyn to M_bulge) with a mass ratio of M_BH/M_dyn ranging from 0.02% to 0.36% with a median value of 0.08%, about three to four times lower than the local BH-to-bulge mass ratio at M_BH = 10⁷ M_⊙ (Kormendy & Ho 2013). This is similar to the IBISCO hard X-ray-selected AGN sample galaxies at z < 0.05, most of which are found to show large offsets with BH masses below the local relationship (Feruglio et al. 2018), as well as low-luminosity QSOs at z > 6 (Izumi et al. 2019). As hypothesized by Xia et al. (2012), the low ratio of M_BH/M_dyn is likely to imply that the star formation and AGN activities are not necessarily synchronized and the SMBH may grow faster after the short IR QSO phase, even though they are intimately connected. It should be noted, however, that there are significant uncertainties in the estimates of both M_dyn and M_BH, although the high spatial resolution and sensitivity CO observations toward low-z IR QSOs allow us to better constrain the gas geometry and dynamical properties of host galaxies compared to those of high-z QSOs. Recent reverberation mapping observations show evidence that the empirical scaling relation between the size of the broad-line region and the continuum luminosity of the AGN for M_BH estimates may depend tightly on accretion rates; i.e., AGNs with extremely high accretion rates tend to have shorter Hβ time lags and hence be overestimated in their BH mass, if adopting correlations inferred based on the low accretion rate sources (see Du et al. 2016; Wang et al. 2017 and references therein). In addition, it remains unclear whether a significant bulge component has formed in the IR QSO phase. It has been found that bulges are less common at high redshift (e.g., Cassata et al. 2011). Therefore, we may not expect the growth of the bulge and central SMBH to follow the local BH–bulge mass relationship for IR-luminous QSOs.

According to the major-merger evolutionary scenario first proposed by Sanders et al. (1988), IR QSOs are likely short-lived ULIRG-to-QSO transition objects. A comparison of local CO-detected IR QSOs with ULIRGs revealed similar cold molecular gas properties, e.g., molecular gas mass, CO line width, and star formation efficiency (SFE; ${L}_{\mathrm{FIR}}/{L}_{\mathrm{CO}}^{{\prime} }$), between these two populations (Xia et al. 2012). Moreover, the CO source sizes we measured for IR QSOs are found to be comparable to those of ULIRGs (radius ≲2 kpc; e.g., Downes & Solomon 1998; Iono et al. 2009; Ueda et al. 2014) but slightly smaller than those of less IR-bright luminous infrared galaxies (LIRGs; ${10}^{11}\ {L}_{\odot }\leqslant {L}_{\mathrm{IR}}\lt {10}^{12}\ {L}_{\odot }$), indicative of more compact molecular gas reservoirs and star formation regions in ULIRGs and IR QSOs. Gao & Solomon (2004) showed that the SFE indicated by ${L}_{\mathrm{FIR}}/{L}_{\mathrm{CO}}^{{\prime} }$ reflects the dense molecular gas fraction and starburst activity in galaxies, since a tight linear correlation is observed between the far-IR and the HCN molecule (a tracer of dense molecular gas) luminosities. The comparable SFE found for ULIRGs and IR QSOs and a smaller value for PG QSOs (Xia et al. 2012) suggests that there are much stronger and massive starburst activities in ULIRGs and IR QSOs than in PG QSOs. Similarly, the SFE is lower in LIRGs compared to ULIRGs (e.g., Iono et al. 2009). These are consistent with the gas-rich merger models (Di Matteo et al. 2005; Hopkins et al. 2008), which predict that these objects represent different phases in an evolutionary sequence, where the most intense star formation activity is seen in stages of ULIRGs and IR QSOs due to massive gas inflows to the galaxy center. As molecular gas is consumed by starbursts, as well as the central BH, a buried AGN continues to grow an SMBH and evolves into an IR-luminous QSO during the final stages of the coalescence.

Overall, the data of local IR QSOs in this study are broadly consistent with the AGN–galaxy coevolution scenario, although some of the IR QSOs are found to undergo mergers with companion galaxies by our resolved CO images. However, we must emphasize that, combined with extensive multiwavelength data, a systematic analysis of the molecular ISM properties, such as the gas content, morphology, excitation, dynamics, and dust properties, for a complete sample of local IR-luminous galaxies/QSOs is necessary for comprehensively testing the evolutionary hypothesis. We will focus on these issues in future work.