Resolved [C ii] Emission from z > 6 Quasar Host–Companion Galaxy Pairs

From the initial observations discussed in Decarli et al. (2017), we know that quasar J0842+1218 has a bright [C ii]-emitting companion galaxy 47 kpc northwest of the position of the quasar. The higher resolution [C ii] observations detect both the quasar host and this companion galaxy at high significance. The [C ii] spectrum for both sources are shown in Figure 1(A). The integrated [C ii] flux densities of 1.40 ± 0.14 and 1.80 ± 0.24 Jy km s⁻¹ and redshifts of z = 6.0760 and z = 6.0656 for the quasar host and companion galaxy, respectively, are fully consistent with the previous observations (Decarli et al. 2017, 2018). Even in these deeper observations, we see little evidence for any deviation from a Gaussian profile, both the [C ii] spectrum of the quasar host and companion galaxy can be accurately modeled by a single Gaussian fit. However, the deeper observations do reveal an additional [C ii] emitter southeast of the quasar at an impact parameter of 54 (31 kpc). The integrated [C ii] flux density of this emitter is 0.41 ± 0.09 Jy km s⁻¹ and is offset in velocity by −480 km s⁻¹ compared to the quasar host galaxy. This is similar to the velocity offset of the brighter companion galaxy (−460 km s⁻¹).

The 260 GHz continuum image for the field surrounding quasar J0842+1218 yields a dust continuum flux density for the quasar host galaxy of 0.72 ± 0.06 mJy, consistent with the flux measurement from the previous observations. The emission is marginally resolved at this resolution. Using imfit in CASA, we measure the extent of the continuum emission, after deconvolution with the beam, as (028 × 016). We note that since this routine fits a 2D Gaussian to the emission, the size might not capture low-level non-Gaussian extended emission. This is discussed in detail in Section 4.2. These deeper observations further yield a 0.23 ± 0.05 mJy (4.6σ) detection of the continuum of the companion galaxy. However, this faint emission remains unresolved in these observations. The second, weaker [C ii] companion remains undetected in the continuum image.

From the continuum-subtracted, integrated [C ii] flux density (second column in Figure 2), we can measure the extent of the [C ii] emission. As with the continuum emission, the [C ii] line remains very compact with marginally resolved sizes of (057 × 037) and (048 × 030) for the quasar host and companion galaxy, respectively. This corresponds to physical sizes of ≈3 kpc at the redshift of the galaxies. The fainter, second companion is not resolved in these images. Although the extent of the [C ii] emission between quasar host and companion galaxy is similar, when we generate velocity and velocity dispersion maps of the [C ii] emission (third and fourth columns of Figure 2), the companion galaxy shows a velocity gradient along an axis with a position angle of 197° ± 8° east of north (see Section 4.4). Such a velocity gradient could be an indication of rotation. However, the marginally resolved observations cannot rule out other scenarios, such as two merging clumps, which would give a similar velocity gradient. No velocity gradient is seen in the quasar host galaxy.

The discovery [C ii] spectra of quasar PJ167−13 showed no conclusive evidence for a companion in the field (Decarli et al. 2018). However, deeper and better resolution (≈07) observations of the quasar revealed a clear excess of [C ii] and dust emission 092 southeast of the quasar (Willott et al. 2017). This emission was attributed to a close companion at a separation of only 5 kpc from the quasar host galaxy. This companion source remains the only source of our sample that has been detected in the optical/near-infrared (Mazzucchelli et al. 2019). Our higher resolution data confirms the existence of a distinct [C ii] and dust continuum emitter at this position. By extracting [C ii] spectra for both the quasar host and the companion galaxy, individually, we find that both spectra are accurately described by a Gaussian profile (Figure 1(B)). Unlike the results in Willott et al. (2017), the addition of the flux from both the quasar host and the companion galaxy results in an accurate fit of the total flux of the complex (yellow line in Figure 1(B)). No additional source of emission is needed. The discrepancy between the two results is due to the slightly higher redshift determination of the companion galaxy in this work (−140 km s⁻¹, instead of −270 km s⁻¹ relative to the peak [C ii] emission from the quasar host). This more accurate redshift determination was enabled by the improved spatial separation between the sources.

The dust continuum and [C ii] integrated flux map for PJ167−13 show that the companion galaxy can be clearly distinguished as a separate density peak (Figure 2). There is also evidence for significant emission arising from gas that lies between the quasar host and companion galaxy. This gas has a mean velocity between the systemic velocity of the quasar host and companion galaxies, resulting in a smooth velocity gradient for the quasar host–companion galaxy pair. This indicates that the excess gas is smoothly distributed between the two galaxies, likely the result of tidal interactions between the two interacting galaxies. The high velocity dispersion throughout the system indicates the emitting gas is turbulent, which is expected for gas inside a merging system.

Previous ∼1'' [C ii] observations of the host galaxy of quasar J1306+0356 revealed that the [C ii] emission is extended over a 143 × 074 region (Decarli et al. 2018). No significant velocity gradient was evident in these observations. The current higher resolution observations reveal that the [C ii] emission arises from two spatially and spectrally distinct sources with a physical separation of 5.4 kpc and velocity separation of 60 km s⁻¹. Both [C ii] emission features can be accurately described by a Gaussian fit (Figure 1(C)). We interpret this emission as arising from two distinct galaxies with integrated fluxes of 1.80 ± 0.15 and 0.86 ± 0.11 Jy km s⁻¹ for the quasar host and companion galaxy, respectively. Both sources are also detected in the 263 GHz continuum observations (0.92 ± 0.09 and 0.30 ± 0.09 mJy). As with PJ167−13, excess gas is observed between the companion and quasar host, suggesting that these galaxies are actively interacting.

The [C ii] emission from both galaxies appears compact, with deconvolved sizes for the quasar host and companion galaxy of 056 × 042 and 064 × 049, respectively. In addition, the velocity field of the two galaxies suggests little coherent motion in either source, although the companion galaxy shows a possible velocity gradient along the northeast to southwest direction. The excess gas between the galaxies has a velocity that is most similar to the companion galaxy, suggestive of a gaseous tidal feature associated with the companion galaxy due to an interaction with the quasar host. Velocity dispersions in the quasar host and companion galaxy are similar.

The [C ii] discovery spectra taken of the field surrounding PJ231−20 revealed a strong [C ii] emitter at 9.1 kpc distance from the quasar host. The new observations yield continuum and integrated line fluxes that are consistent with the results previously obtained (Decarli et al. 2018). In addition to these two sources, the deeper observations reveal an additional, weaker, [C ii] emitter 14 kpc south–southeast of the quasar, 6 kpc from the companion galaxy. It has an integrated flux of 0.26 ± 0.07 Jy km s⁻¹, and is redshifted by 400 km s⁻¹ compared to the redshift of the quasar host. A slight continuum excess is also seen at this position, resulting in a far-infrared continuum flux measurement for this source of 0.19 ± 0.04 mJy (Figure 1(D)).

The continuum emission, integrated [C ii] flux, velocity, and velocity dispersion maps of this galaxy pair are shown in the fourth row of Figure 2. Unlike the lower resolution data, the emission from the quasar host and companion galaxies are clearly separated into two distinct sources without significant overlap. A Gaussian 2D fit to the data reveals that the emission from both sources is compact. However, faint, much more extended, emission surrounds both sources. This suggests some gas has already been stripped from the galaxy due to gravitational interactions. It is therefore very likely that these galaxies are in the beginning stages of actively interacting with each other. In this scenario, the second [C ii] emitter east of the companion galaxy could be dense gas stripped from the companion by tidal forces.

In addition to the similar velocity fields, we also see little difference between the extent of the continuum and/or [C ii] line emission between quasar host and companion galaxy. Both objects have roughly equal sizes (see Section 4.2), providing no obvious clues why one of the galaxies hosts an unobscured quasar and the other does not.

The largest separation quasar host–companion galaxy pair of the sample, the quasar host of quasar J2100−1715 and its companion galaxy have a separation of 108 (61 kpc). As Figure 1(E) shows, both the quasar host and the companion galaxy are bright, with fluxes of 2.26 ± 0.22 and 4.15 ± 0.52 Jy km s⁻¹, respectively. These fluxes are consistent with the previous observations after taking into account the extent of the emission (Decarli et al. 2018). The [C ii] spectra of the companion galaxy is the only spectrum in our sample that shows a deviation from a Gaussian profile, the emission is flattened compared to the best-fit Gaussian shown in Figure 1(E). We also confirm the detection of the continuum emission for both sources, which have fluxes of 0.88 ± 0.09 and 2.25 ± 0.21 mJy.

In addition to the non-Gaussian [C ii] profile, the companion galaxy shows a strong velocity gradient along an axis with a position angle of 13°. This is in contrast with the quasar host galaxy, which shows little ordered motion. The non-Gaussianity of the companion galaxy's [C ii] profile is likely driven by this strong velocity gradient. Such a velocity gradient is consistent with the [C ii] emission arising from gas rotating in a disk. This is further corroborated by the elongated extent of the [C ii] emission (066 × 031) and the kinematic modeling (Section 4.4). However, the resolution is insufficient to rule out other possible scenarios. The [C ii] emission and dust continuum extent of the quasar host are similar to the companion galaxy, both are listed in Table 2.

Galaxies that are interacting are expected to show gas distributions that are more extended and perturbed due to tidal forces during the encounter. This is seen at low redshift in abundance, and has also been observed at high redshift in dust continuum (Díaz-Santos et al. 2018). In the two closest-separation quasar host–companion galaxy pairs discussed in this manuscript, a clear excess of gas, which is detected both in continuum and in [C ii] emission, can be seen connecting both galaxies (Figure 2 second and third row). The third-closest galaxy pair (PJ231−20) shows a perturbed gas distribution with significant faint, extended [C ii] emission both between the galaxies and in the immediate environs. To highlight the gas between the galaxies, we generate a position–velocity (p–v) diagram that is oriented such that it intersects both galaxies for these three galaxy pairs in Figure 3.

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This figure shows that the gas connecting the host of QSO PJ167−13 and its companion galaxy in projection, also shows a smooth velocity gradient from one galaxy to the other. This is reminiscent of the smooth velocity gradient of the nearby galaxy merger between M81 and M82 (e.g., de Blok et al. 2018). The emission between the galaxy pair toward J1306+0356 is more tenuous, and seems to have a kinematic profile that is more consistent with the companion galaxy than the quasar host. For PJ231−20, no direct gas connection is detected. However, both the quasar host and companion galaxies show perturbed gas distributions that are both more extended (see Section 4.2) and irregular compared to the gas distributions of the galaxies forming the two wide separation pairs. This suggests gravity has already perturbed the gas distribution in this galaxy pair.

The size estimates in Table 2 are based on the assumption that the emission can be accurately described by a 2D Gaussian. For resolved observations of objects with non-Gaussian surface brightness profiles, this might not be a valid assumption. If, for instance, there exists low-level extended emission around a compact bright source, the fitting routine might not accurately describe the extent of the low-level emission as the fit is dominated by the compact source. To ascertain if such low-level flux exists in these resolved observations, we fit a 2D Gaussian to the total emission for each of our sources. We then compare the area of the emission for this 2D Gaussian (A_Gauss) to the area of the observed emission (A_obs) for a range of different flux values. Here, both areas remain convolved with the ALMA beam. The results are plotted in Figure 4. If the shape of the emission was a pure 2D Gaussian, each line would have a constant value of 1 independent of the flux cut.

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We can see that for the strongest emission of the continuum flux density (flux cuts >0.1 mJy) the ratio of the Gaussian size to the observed size is ∼1. This implies that this emission must come from a compact source that can be accurately described by a 2D Gaussian. However, at lower continuum flux cuts, the emission is more extended than what is predicted from a Gaussian shape. This deviation from a Gaussian shape could be caused by calibration issues, or it could be actual low-level emission that is not modeled by the Gaussian fitting routine. As the largest deviations occur for PJ231−20, two close, interacting galaxies, we posit that, at least for this system, the low-level emission arises from more extended gas, and the size/area estimates from the Gaussian routine could be off by as much as a factor of two.

The same analysis can be done on the integrated [C ii] line emission map. The results are shown in Figure 4(B). Again the two largest deviators in the plot are the quasar host and companion galaxy of PJ231−20, indicative of low-level [C ii] emission from gas on more extended scales around these galaxies. The remaining systems show observed sizes that are roughly consistent with the Gaussian estimates, although with substantial scatter. This suggests that, unlike the continuum observations, the emission is less centrally concentrated and the Gaussian fit fully captures the extended [C ii] emission. Indeed, for some emitters—such as the quasar host galaxy of PJ167−13—the Gaussian sizes are actually larger than the observed sizes, suggesting that these emitters have a surface brightness profile that is flatter than a 2D Gaussian.

A well-known property of both low- and high-redshift galaxies, is the decrease in [C ii] to total infrared (TIR) luminosity as the TIR luminosity of the galaxy increases. The cause for this deficit in [C ii] luminosity for more TIR-luminous systems is still debated. One possibility is that the TIR luminosity is enhanced in TIR-luminous galaxies, because of an increased UV radiation field, either due to the presence of an active galactic nucleus (AGN) or due to increased star formation (Malhotra et al. 1997). Other possibilities suggest that [C ii] emission is suppressed in TIR-luminous systems, either because of dust absorption of the [C ii] line (Riechers et al. 2013, 2014), or because of intrinsic properties of the gas responsible for the [C ii] emission (Muñoz & Oh 2016; Narayanan & Krumholz 2017). Observationally, galaxies hosting an AGN or actively interacting have the highest [C ii] deficits (e.g., Sargsyan et al. 2012; Carilli & Walter 2013; Farrah et al. 2013). Apportioning our sample by type and impact parameter allows us to see if these observational trends hold for our current sample as well. In addition, we can observe for a spatial variation in the [C ii] deficit for the individual sources, as most sources are resolved.

Figure 5 shows the spatial extent of the [C ii] deficit for all sources. This figure highlights that brighter sources have lower [C ii]-to-TIR luminosity ratios, L_{[C ii]}/L_TIR. This is further exemplified by plotting the [C ii] deficit as a function of TIR luminosity surface density, Σ_TIR for the sources (Figure 6). The yellow symbols mark the values for the central pixel of each source. If quasars (i.e., AGNs) are the dominant cause of the [C ii] deficit, we would expect to see a difference between the quasar host and companion galaxies. However, the central pixels for both quasars host and companion galaxies show remarkable agreement with a compilation of [C ii] deficit measurements from local infrared-bright galaxies (LIRGs; Díaz-Santos et al. 2017). Unless all of the companion galaxies host an obscured AGN, which we consider unlikely (see Section 4.5), the presence of an AGN in the quasar host galaxies does not add to the [C ii] deficit. Similarly, we find no evidence for a decreased L_{[C ii]}/L_TIR in actively interacting galaxy pairs. Although the scatter in L_{[C ii]}/L_TIR does seem to increase in these systems, the average is comparable to the average of the large impact parameter galaxy pairs.

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Figure 5 further shows that the [C ii] deficit is relatively constant within the inner part of the galaxies. This is similar to the spatially resolved mergers observed at high redshift (e.g., Neri et al. 2014; Litke et al. 2019; Rybak et al. 2019). The constant ratio can be explained if the bulk of [C ii] and TIR emission arises from a compact source, which is consistent with the result in Section 4.2. For nearly all galaxies the [C ii] deficit gets smaller toward the edges of the galaxy. However, as Figure 6 shows, the outer edges still follow the global trend of larger [C ii] deficits for increasing TIR luminosity surface densities. The offset between the central and outer parts of the galaxies in this trend could be due to varying physical conditions within these regions, which would corroborate the assertion that L_{[C ii]}/L_TIR is set by local ISM conditions (Muñoz & Oh 2016; Smith et al. 2017; Gullberg et al. 2018; Herrera-Camus et al. 2018). We note two important caveats to these results: (i) these results hold at the resolution of the observations. Any variations in L_{[C ii]}/L_TIR at the subkiloparsec scale is not resolved by these observations (see e.g., Venemans et al. 2019). (ii) To calculate the TIR luminosity, we assume that the physical conditions of the gas do not vary across the galaxy and are equal to the fiducial values (see Section 3). This is likely an oversimplification on small scales.

Several estimators are used in the literature to obtain the dynamical mass of galaxies with unresolved or marginally resolved far-infrared lines. Under the assumption that the gas is rotationally supported, the enclosed mass (in M_⊙) within an emission region is ${M}_{\mathrm{dyn}}=1.16\times {10}^{5}\,{v}_{\mathrm{circ}}^{2}\,D$ (e.g., Walter et al. 2003; Wang et al. 2013). Here, D is the size (diameter) of the emission in kiloparsecs and v_circ is the circular velocity in kilometers per second. The circular velocity estimate relies on an additional assumption on the kinematics and distribution of the gas. If the gas is virialized but shows nonordered, dispersion-dominated motion, then v_circ is best characterized by the velocity dispersion (σ_v) of the gas ($\sqrt{3/2}{\sigma }_{v};$ e.g., Decarli et al. 2018). However, if the gas shows order motion, then the FWHM of the [C ii] line can be used as a proxy for the velocity of the system: ${v}_{\mathrm{circ}}=0.75\times {\mathrm{FWHM}}_{[{\rm{C}}{\rm{II}}]}/\sin i$, where the inclination is often taken to be 55° (e.g., Wang et al. 2013; Decarli et al. 2018). The range of dynamical mass estimates inferred from applying these two methods are given in Table 3.

The higher resolution of the observations presented here allows us to better constrain the dynamical properties of the gas. To accomplish this, we use a custom, python-based code which fits the three-dimensional data cube to a model data cube generated from a user-defined model. The code generates a model data cube with the same spectral and spatial resolution as the data from the user-defined model. It then convolves this data cube with the ALMA synthesized beam, which is compared with the observed data cube using a simple χ² statistic. To account for the large spatial correlation between adjacent pixels, the comparison is done using a bootstrap method. Finally, the full parameter space is sampled through a Markov Chain Monte Carlo method by employing the emcee package (Foreman-Mackey et al. 2013).

In this paper, we model the emission with two different models, one in which the [C ii] emission is due to a purely dispersion-dominated gas, and one in which the [C ii] is emitted from gas in a thin disk with constant circular velocity and constant velocity dispersion. Both models assume that the intensity of the [C ii] line can be modeled by an exponential function, and are describe in more detail in Appendix C. Results from the fitting procedure are shown in Table 4.

Table 4.  Parameters of the Kinematic Modeling

Name	R.A. (xc)	Decl. (yc)	zkin	vcirca	σvb	ic	αd	I0e	Rdf
	(J2000)	(J2000)		(km s−1)	(km s−1)	(°)	(°)	(mJy beam−1)	(kpc)
Thin disk model
J0842+1218Q	08:42:29.4376(8)	+12:18:50.437(14)	${6.07639}_{-0.00022}^{+0.00020}$	⋯g	${157}_{-8}^{+9}$	<46	${174}_{-24}^{+25}$	${3.9}_{-0.5}^{+0.6}$	${0.83}_{-0.09}^{+0.12}$
J0842+1218C	08:42:28.9743(7)	+12:18:54.966(11)	${6.06655}_{-0.00017}^{+0.00018}$	>220	${129}_{-9}^{+10}$	<28	${197}_{-7}^{+8}$	${5.9}_{-0.7}^{+0.9}$	${0.73}_{-0.06}^{+0.06}$
PJ167−13Q	11:10:33.9829(6)	−13:29:45.863(6)	${6.51625}_{-0.00010}^{+0.00010}$	${114}_{-10}^{+9}$	${170}_{-4}^{+5}$	${57}_{-2}^{+2}$	${303}_{-2}^{+2}$	${5.1}_{-0.3}^{+0.3}$	${1.61}_{-0.07}^{+0.07}$
PJ167−13C	11:10:34.031(2)	−13:29:46.278(18)	${6.5125}_{-0.0003}^{+0.0003}$	⋯g	${181}_{-12}^{+14}$	<55	${340}_{-40}^{+50}$	${2.7}_{-0.3}^{+0.4}$	${1.17}_{-0.15}^{+0.19}$
J1306+0356Q	13:06:08.2648(11)	+03:56:26.233(13)	${6.03386}_{-0.00014}^{+0.00013}$	⋯g	${106}_{-6}^{+7}$	<55	⋯g	${7.3}_{-0.9}^{+1.0}$	${1.01}_{-0.11}^{+0.17}$
J1306+0356C	13:06:08.3271(14)	+03:56:26.128(21)	${6.03519}_{-0.00012}^{+0.00013}$	⋯g	${72}_{-6}^{+6}$	<38	${206}_{-15}^{+16}$	${5.8}_{-0.9}^{+1.0}$	${1.07}_{-0.12}^{+0.14}$
PJ231−20Q	15:26:37.8403(2)	−20:50:00.790(3)	${6.58734}_{-0.00008}^{+0.00008}$	<120	${150}_{-3}^{+3}$	${33}_{-7}^{+5}$	${111}_{-12}^{+9}$	${11.3}_{-0.7}^{+0.7}$	${0.54}_{-0.03}^{+0.03}$
PJ231−20C	15:26:37.8721(5)	−20:50:02.425(6)	${6.59074}_{-0.00015}^{+0.00015}$	>210	${203}_{-7}^{+7}$	<22	${250}_{-9}^{+9}$	${3.57}_{-0.21}^{+0.22}$	${0.82}_{-0.04}^{+0.04}$
J2100−1715Q	21:00:54.6996(11)	−17:15:22.008(15)	${6.08142}_{-0.00025}^{+0.00024}$	⋯g	${147}_{-10}^{+11}$	<40	${30}_{-40}^{+30}$	${4.3}_{-0.5}^{+0.6}$	${0.90}_{-0.09}^{+0.10}$
J2100−1715C	21:00:55.4197(8)	−17:-15:-22.124(19)	${6.0806}_{-0.0004}^{+0.0004}$	${206}_{-28}^{+26}$	${189}_{-18}^{+19}$	${67}_{-5}^{+4}$	${13}_{-4}^{+4}$	${5.5}_{-0.9}^{+1.1}$	${1.15}_{-0.12}^{+0.13}$
Dispersion-dominated model
J0842+1218Q	08:42:29.4380(7)	+12:18:50.434(12)	${6.07638}_{-0.00021}^{+0.00021}$		${163}_{-8}^{+10}$			${4.2}_{-0.6}^{+0.7}$	${0.88}_{-0.09}^{+0.10}$
J0842+1218C	08:42:28.9743(7)	+12:18:54.965(11)	${6.06664}_{-0.00017}^{+0.00018}$		${148}_{-8}^{+8}$			${5.2}_{-0.6}^{+0.7}$	${0.82}_{-0.06}^{+0.07}$
PJ167−13Q	11:10:33.9822(6)	−13:29:45.865(7)	${6.51635}_{-0.00011}^{+0.00010}$		${184}_{-4}^{+4}$			${4.7}_{-0.3}^{+0.2}$	${1.43}_{-0.05}^{+0.07}$
PJ167−13C	11:10:34.031(2)	−13:29:46.27(2)	${6.5123}_{-0.0002}^{+0.0002}$		${185}_{-11}^{+14}$			${2.9}_{-0.3}^{+0.4}$	${1.24}_{-0.14}^{+0.17}$
J1306+0356Q	13:06:08.2645(10)	+03:56:26.227(14)	${6.03383}_{-0.00013}^{+0.00014}$		${107}_{-6}^{+7}$			${8.0}_{-1.0}^{+1.0}$	${1.03}_{-0.09}^{+0.10}$
J1306+0356C	13:06:08.3268(15)	+03:56:26.127(21)	${6.03517}_{-0.00013}^{+0.00013}$		${76}_{-5}^{+6}$			${5.2}_{-0.8}^{+1.0}$	${1.27}_{-0.15}^{+0.17}$
PJ231−20Q	15:26:37.8404(2)	−20:50:00.789(3)	${6.58736}_{-0.00007}^{+0.00007}$		${148}_{-3}^{+3}$			${13.9}_{-0.8}^{+0.8}$	${0.519}_{-0.017}^{+0.018}$
PJ231−20C	15:26:37.8724(4)	−20:50:02.423(6)	${6.59065}_{-0.00015}^{+0.00016}$		${212}_{-7}^{+8}$			${3.71}_{-0.24}^{+0.27}$	${0.90}_{-0.05}^{+0.05}$
J2100−1715Q	21:00:54.6990(11)	−17:15:22.011(13)	${6.08143}_{-0.00023}^{+0.00022}$		${150}_{-10}^{+11}$			${4.5}_{-0.6}^{+0.7}$	${0.99}_{-0.09}^{+0.10}$
J2100−1715C	21:00:55.4199(9)	−17:15:22.105(20)	${6.0809}_{-0.0004}^{+0.0004}$		${245}_{-17}^{+21}$			${4.0}_{-0.5}^{+0.6}$	${0.88}_{-0.08}^{+0.08}$

Notes.

^aCircular velocity. ^bVelocity dispersion. ^cInclination. ^dPosition angle. ^eCentral flux density. ^fExponential scale length. ^gThese parameters are not well determined because either the galaxy is viewed face-on and/or there is not enough evidence for rotation. For these systems the dispersion model provides a similar fit to the data.

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From this analysis, we conclude that three of the companion galaxies (J0842+1218, PJ231−20, and J2100−1715) and one quasar host galaxy (PJ167−13) have [C ii] emission that is consistent with arising from a rotating disk. However, in nearly all cases the emission is highly turbulent, with dispersion velocities roughly equal to the circular velocities. This could indicate that the assumed constant velocity profile is incorrect, because the [C ii] emission is still probing the rising part of the rotation curve (de Blok & Walter 2014). To assess how this affects the circular velocity estimate, we also run a model where the velocity is described by a linearly increasing function. We find that for this model the resulting circular velocity estimates at the maximal extent of the emission are similar to the previous estimates. Therefore the choice of velocity profile does not significantly affect the results of the fitting. For the remaining objects, either the circular velocity must be substantially smaller than the dispersion (e.g., the quasar host galaxy toward PJ231−20), and/or the inclination of the galaxies is small.

The large velocity dispersion estimates provide an explanation for the remarkable near-Gaussian shape of the total integrated [C ii] flux spectra (see Figure 1 and Decarli et al. 2018). Even for clearly distinct [C ii] emitters (i.e., PJ167−13 and J1306+0356), the combined [C ii] spectrum of the two sources remains nearly Gaussian, since the large velocity dispersion, compared to the small offset in central frequency, hinders spectral separation. The high velocity dispersions could be caused by turbulent ISM conditions (e.g., De Breuck et al. 2014), but could also be the result of sampling the [C ii] emission from the rising part of the rotation curve (de Blok & Walter 2014). In either case, these velocity dispersions are comparable to the velocity dispersions found for z ∼ 2 compact star-forming galaxies (Barro et al. 2014). An important caveat to these results is that velocity structures on subkiloparsec scales, below the resolution of the observations, are smoothed out, causing an increase in the velocity dispersion. In addition, the resolution is insufficient to rule out other possible scenarios, such as merging clumps.

To estimate the dynamical mass for the four systems that have a kinematic signature consistent with a rotating disk, we take the circular velocity estimate from the model, and add in quadrature $\sqrt{3/2}$ times the velocity dispersion estimate. This accounts for part of the velocity dispersion arising from the simplified assumption that the gas is constrained to a thin disk. For the remaining systems, we approximate the circular velocity by $\sqrt{3/2}$ times the velocity dispersion as given by dispersion-dominated model. This will give a lower limit to the dynamical mass. The dynamical masses for all systems range between (0.3 − >5.4) × 10¹⁰ M_⊙ (Table 3).

The dynamical mass estimates obtained through kinematic modeling are in rough agreement with the estimates obtained using the [C ii] line profile. For the two systems with well constrained dynamical mass estimates (PJ167−13Q and J2100−1715C), the kinematics modeling estimates are on the lower end of the dynamical range estimate obtained from the [C ii] line profile. This is due to the the large velocity dispersion in these systems, which widens the line profile. Thus, for systems with large velocity dispersions, using the FWHM of the [C ii] line as a proxy for the circular velocity could overestimate their dynamical mass estimate. Finally we note that standard practice has been to assume an inclination angle of 55° for quasar host galaxies (Wang et al. 2013; Willott et al. 2015; Decarli et al. 2018). We can rule out this inclination for four out of the six quasar hosts, and derive a mean inclination of <39°.

One of the primary aims of this study is to compare the far-infrared properties of the quasar host galaxies to the far-infrared properties of the brightest companion host galaxies in order to examine the effect, if any, that the central accreting supermassive black hole has on these properties. As shown in the previous sections, we find no evidence that the quasar affects the strength or extent of either the [C ii] or continuum emission. In addition, the L_{[C ii]}/L_TIR ratio of both galaxy populations is similar (Figure 6). These observations therefore corroborate the assertion that the central accreting supermassive black holes in quasars do not significantly alter the observed [C ii] and dust continuum emission, instead this emission originates predominantly from heating of the ISM by stars (e.g., Venemans et al. 2017). This is in agreement with the [O iii] 88 μm observations of one of the galaxy pairs (J2100−1715), which revealed little difference in the far-infrared emission properties of the ionized gas (Walter et al. 2018).

A possible caveat to this result is that the companion galaxies could host an obscured AGN. If some fraction of companion galaxies host an obscured AGN that significantly alters their far-infrared properties, we would expect to see a bimodal distribution within the companion galaxies' far-infrared properties. The lack of such a bimodality implies that either none or all of the companion galaxies host an obscured AGN. If we assume the latter and assume an AGN obscuration factor of ∼50% (Merloni et al. 2014), then the likelihood of not detecting any quasar–quasar pairs (i.e., where both AGNs are optically unobscured) is 3%. Formally this is an upper limit, as no close quasar–quasar pairs are known at z > 6, whereas several nonquasar host, far-infrared luminous galaxy pairs are known at high redshift (Oteo et al. 2016; Riechers et al. 2017; Marrone et al. 2018). We therefore disfavor this scenario, and conclude that quasars do not significantly alter the [C ii] and far-infrared continuum emission measurements of high-redshift galaxies.

In these resolved [C ii] observations, there is a possible hint that the kinematics or orientation of the companion hosts are slightly different, as three out of five companion galaxies show signs of rotation, compared to only one out of five quasar host galaxies. One possible explanation for such a difference is that the gas kinematics in the quasar hosts are more disturbed due to previous mergers unrelated to the current merger. In this scenario, the quasar hosts are still in a post-merger state characterized by perturbed gas kinematics, whereas the companion galaxies have not experienced a recent merger, and show more ordered rotation. Another possibility is that we are preferentially observing the quasar host galaxies face-on, thereby minimizing any velocity gradient caused by rotation. Such an orientation is at least consistent with the observation of a bright luminous quasar in a dusty galaxy. However, the sample remains too small to confirm potential differences of this magnitude in the kinematics of the gas.