Molecular Gas in the Nuclear Region of NGC 6240

To calculate the mass of the dust M_d from the continuum observations we use:

$\begin{eqnarray}&&{M}_{d}={S}_{\nu }{D}_{L}^{2}/{\kappa }_{\nu }{B}_{\nu }(T)\end{eqnarray} \tag{ 1 }$

(Casey 2012), where S_ν is the flux density in the continuum-frequency band, D_L is the luminosity distance of 108 Mpc, κ_ν is the dust mass opacity coefficient, and B_ν (T) is the blackbody emission in the continuum-frequency band for a dust temperature T. For this calculation, we use the 345 GHz as the measure of S_ν because it should have a lower optical depth than the 678 GHz continuum observation. The total S_345GHz for this observation is 27 mJy, 18% of the galaxy-integrated flux density measured at 850 μm by SCUBA of 150 mJy (Klaas et al. 2001). This flux density recovery is comparable to Scoville et al. (2015) who measured 18–24 mJy at 340 GHz for a comparable beam size and sensitivity with ALMA in Cycle 0. The SCUBA beam is as large as our primary beam of the ALMA observations with a diameter of 15'' (Klaas et al. 2001), and as such, we can expect that their measurement includes extended emission that is lost in our high-resolution observations. Therefore, we expect our value of S_ν to be lower than that measured with SCUBA.

For B_ν (T) we choose a dust temperature of 56 K, the dust temperature fit in Kamenetzky et al. (2014), using a graybody fit to Herschel-SPIRE, IRAS, Planck, SCUBA, and ISO photometry for NGC 6240. This dust temperature is a galaxy-averaged property since Kamenetzky et al. (2014) used observations with beam FWHM between ∼17'' and 45'', at least 100 times larger than the ALMA observations. It is likely that the dust temperature in NGC 6240's nuclear region is higher than the galaxy-averaged temperature due to the influences of concentrated star formation and AGN luminosity. However, we do not have flux density measurements across sufficient wavelengths in this central region to independently calculate the dust temperature. From James et al. (2002) we use κ₈₅₀ = 0.07 m²kg⁻¹ and κ_ν ∝ ν² to find κ₈₇₀ = 0.067 m²kg⁻¹.

The calculated masses for the regions outlined in Figure 6 are tabulated in Table 2. The total mass of the dust is calculated to be 1.2 × 10⁷ M_⊙. As a check on this total dust mass we compare to the galaxy-integrated dust mass of 5 × 10⁷ M_⊙ found in Kamenetzky et al. (2014) from their dust SED model described earlier in this section. Our calculated dust mass is 24% of this value, consistent with filtered flux from the ALMA observations.

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Using a gas-to-dust mass ratio of 100, we can convert the dust masses from Table 2 to a total gas mass, 1.2 × 10⁹ M_⊙. The mass values derived from the continuum emission are similar to the values derived from the sub-mm continuum (235 GHz) in Treister et al. (2020) of 2.8 × 10⁹ M_⊙. The gas mass is converted to a column density ${N}_{{{\rm{H}}}_{2}}$ by dividing the gas mass by the mass of molecular hydrogen, the projected size of the region on the sky, and multiplying by the fraction of the total mass assumed to be molecular hydrogen (0.73, assuming solar metallicity; Hollenbach et al. 1987). The average column density for the entire nuclear region is 3 × 10²² cm⁻², while the concentrations around the two nuclei both have higher column densities of 1.5 × 10²³ cm⁻². This value is consistent with the findings of Tacconi et al. (1999) of N(H₂) ∼ 1–2 × 10²³ cm⁻².

A dim trail of gas extending directly north of the central concentration, which we call the "Northern Finger," is observed in the higher sensitivity CO J = 3–2 observation but not in CO J = 6–5 or either continuum observation. It is labeled in the CO J = 3–2 moment 0 map in Figure 2. It is not spatially coincident with observed H₂ V = 1–0 S(1) and S(5) emission (Max et al. 2005, their Figure 12(a)). It dimly appears in Figures 2(a) and (c) of Max et al. (2005), false-color images including the Keck $K^{\prime}$ band, H band, J band, and F814W filter from WFPC2 on the Hubble Space Telescope (HST), and the F450W filter from WFPC2 on HST. Its southern half is spatially coincident with [O III] λ = 5007 and Hα emission (Müller-Sánchez et al. 2018, their Figure 1).

The Finger's average velocity is 44 km s⁻¹ with an FWHM of ∼300 km s⁻¹, measured with an integrated spectrum of the emission in this region. The low average velocity suggests this gas is unlikely to be an outflow. A nuclear inflow would cause σ_v to be elevated near the nuclei, for which there is no conclusive evidence. The low velocity is consistent with a tidal tail or bridge but the high FWHM does not conform to this idea. The Finger extends from the northern nucleus toward the northern dust lane of the galaxy, which is interpreted as a tidal tail by other authors (Yun & Hibbard 2001; Gerssen et al. 2004). The top edge of the Finger is spatially coincident with the eastern edge of the dust lane, suggesting a possible correspondence. The dust lane is much wider and extends much farther beyond the extent of the Finger—approximately 7'' wide (roughly east/west) and over 20'' long (roughly north/south), beyond the extent of our observations.

There is also extended structure surrounding the two nuclei that align with H₂ V = 1–0 S(1) and S(5) concentrations presented in Max et al. (2005, their Figures 10 and 11, reproduced in our Figure 7): a molecular concentration to the NE of the northern nucleus, a concentration to the SW of the southern nucleus, and dim, diffuse emission extending to the SE of the southern nucleus. The faint arms of H₂ extending SE and SW observed in Max et al. (2005) align with these faint arms extending SE and SW from the central concentration and are also bright in Fe XXV and Hα (Max et al. 2005; Wang et al. 2014). Wang et al. (2014) postulates that these faint molecular arms are molecular gas entrapped and shocked by the superwind caused by a vigorous starburst in the southern nucleus. Similarly, Max et al. (2005) argue that these arms are a thin layer of gas at the edges of soft X-ray bubbles observed in Komossa et al. (2003), where a starburst-driven wind is "driving shocks or ionization fronts into the interstellar medium and surrounding molecular clouds." We therefore conclude that the CO arms to the SE and SW of the southern nucleus are likely associated with the same starburst-driven superwind shocked gas.

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To generate the molecular gas model that tests the validity of the disk interpretation, we use the Line-modeling Engine (LIME; Brinch & Hogerheijde 2010). LIME uses non-local thermodynamic-equilibrium radiative-transfer and molecule-rotational energy level population calculations to predict the line and continuum emission from molecular clouds. The user defines a 3D model describing the density distribution of hydrogen molecules of the source, then assigns 3D temperature and velocity distributions to those molecules. The gas-to-dust mass ratio, the abundance of CO relative to hydrogen, and the 3D distribution of the dust temperature are also set by the user. Finally, the user defines the distance to the source to obtain the proper distance scale per pixel and observed flux density.

The code does not require that the source be in local thermodynamic equilibrium, and instead solves for population levels iteratively until the model populations have converged at all grid points. After convergence, LIME ray-traces photons to obtain an image of the modeled source at a user-defined observing angle. This simulation methodology allows great flexibility in both geometry and kinematics of the simulated source and minimizes the assumptions made about the source to generate the observed line profiles.

To compare the observed data to the simulated model images, we use the CASA package to smooth and continuum-subtract the simulated images. The resulting images have the same beam size as the observations. We must also account for the redshift of the galaxy, which is not included in the LIME simulations. To do this, we measure the central velocity of the galaxy-integrated line profile from the observations of CO J = 3–2 and CO J = 6–5: 7180 ± 20 km s⁻¹ for CO J = 3–2 and 7150 ± 20 km s⁻¹ for CO J = 6–5. These velocities are subtracted from the observed moment 1 maps in Figures 2 and 3, which we can compare to the simulations that are simulated with zero redshift.

Using LIME, we model the 3D central gas concentration with density and velocity distributions with exponentially decaying density and velocity profiles. Our 3D model for the disk density follows the function:

$\begin{eqnarray}&&{n}_{{\rm{H}}2}={n}_{{{\rm{H}}}_{2},0}\exp (-r/{r}_{{sh}})\exp (-| z| /{z}_{{sh}}),\end{eqnarray} \tag{ 2 }$

where $r=\sqrt{{x}^{2}+{y}^{2}}$, r_sh is the radial scale height of the density, z_sh is the vertical scale height, and ${n}_{{{\rm{H}}}_{2},0}$ is the central H₂ number density of the gas concentration. The total gas mass within the extent of our ALMA observations is set to a simulation parameter g_mass, from which ${n}_{{{\rm{H}}}_{2},0}$ is calculated based on the simulation geometry. We also allow an overall density asymmetry by multiplying the density on one half of the gas concentration (x > 0) by a model parameter a_n . For the CO J = 3–2 model we also allow the extent of the gas to differ for x > 0 and x < 0 by varying the scale height on either side of the modeled concentration.

We model the velocity with:

$\begin{eqnarray}&&v(r)={v}_{\mathrm{circ}}(1-\exp (-r/{r}_{\mathrm{circ}})),\end{eqnarray} \tag{ 3 }$

where v_circ is the circular velocity and r_circ is the radial scale length of the circular velocity. We use the exponential profile because aside from the high-velocity gas component, we find no sufficient justification for deviation from a rotation curve that rapidly becomes flat with radius (which would be appropriate in the case of a self-gravitating disk).

In Equations (2) and (3), parameters except r and z are fit parameters that can be tuned to match the resultant modeled line profiles to the observed data. In addition to those parameters, the LIME model requires a gas inclination, position angle, dust temperature T_dust, turbulent velocity v_turb, gas temperature T, and gas-to-dust mass ratio (set to 100). All available parameters, fiducial fit results, and acceptable ranges of fiducial fit parameters can be found in Table 3 and are discussed in Section 4.3.

The position angle of the gas concentration is modeled as 34°, the angle between the maximum of the highly blueshifted gas and that of the highly redshifted gas from Figure 8. This is close to the position angle used by Tacconi et al. (1999) of 40° for their disk models. Thirty-four degrees was chosen following methodologies laid out in Cicone et al. (2018) and Tacconi et al. (1999). Following the methodology presented in Cicone et al. (2018), we separate the observations into "quiescent" [−200, 250] km s⁻¹ gas and high-velocity gas. Figure 8 shows the contours of the observed highly redshifted (CO J = 3–2: [250, 700] km s⁻¹, CO J = 6–5: [250, 740] km s⁻¹) and highly blueshifted (CO J = 3–2: [−500, −200] km s⁻¹, CO J = 6–5: [−420, −200] km s⁻¹) gas in panels a and b. The centroids between these two velocity extremes (34°) is at a steeper angle than between the two nuclei (∼19°). The contours of moderate velocity, or "quiescent" gases of velocity [−200, 250] km s⁻¹ are shown in in panels (c) and (d). The velocity gradient observed in moment 1 for CO J = 3–2 and J = 6–5 remains clearly present in the high-velocity gas, with distinct centroids of emission at a PA of ≈34°. The lower velocity gas has much more overlap between the redshifted and blueshifted components, without as clear of a separation between centroids of emission. This lower velocity gas aligns approximately with the semimajor axis of the central gas concentration at a PA of ≈0°, along the north/south axis. Due to the distinct gradient present in the high-velocity gas that more closely resembles a traditional disk, we choose the position angle based on the highest-velocity gas. However, we find during modeling that the position angle does not influence the fit parameters outside of acceptable ranges already incorporated into the model.

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The center of the modeled gas concentration is placed at the maximum of the observed integrated line emission, following the methodology of Tacconi et al. (1999). If the gas were a simple disk, the maximum of the line emission would be expected to align closely with the turnover point of the velocity gradient. As noted in Tacconi et al. (1999) and confirmed in this paper's observations, this is not the case. This offset could be caused by a number of phenomena, including that the gas is not a simple disk. The offset could also be explained by a gas concentration with a highly asymmetric mass distribution leading to an offset in the maximum line emission. Optical depth effects could also displace the velocity gradient turnover point from the maximum of the line emission.

In NGC 6240 the CO J = 6–5 emission has been found to be dominated by relatively hot gas while the CO J = 3–2 emission is dominated by cool/warm gas (Kamenetzky et al. 2014). The upper levels of the CO J = 6–5 and J = 3–2 CO lines are at very different energies, with the J = 6 level at ∼116 K and the J = 3 level at ∼33 K; it is clear that the J = 6–5 line will arise in warmer gas than does the J = 3–2. The true excitation picture is of course more complicated than a simple model of "warm" and "cool" components. The J = 3–2 line is to some extent sensitive to warm and hot gas: it is observed in quite hot regions (e.g., Consiglio et al. 2017) and in starburst galaxies is usually in excess of what the true "cold" gas component predicts (Kamenetzky et al. 2014). But although there is probably some overlap between the J = 6–5 and J = 3–2 emitting gas, in bulk, they preferentially probe two different temperature regimes.

We therefore generate separate models for a "warm" component matching the J = 6–5 profile and a "cool" component matching the J = 3–2 line. Models of the two temperature components have the same velocity structure, gas inclination, dust temperature, and position angle. The gas mass, density, and temperature distribution are different for the two models. In effect, we require the cool and warm gas to have the same morphology, but permit the gas' extent and density to vary within that morphology.

Due to the simpler nature of the CO J = 6–5 line profiles compared to those of CO J = 3–2, we first use CO J = 6–5 observations to constrain the velocity structure, inclination and position angle, and dust temperature. We then applied the fiducial fit parameters from the CO J = 6–5 model to find the gas density distribution and gas temperature of CO J = 3–2.

The model parameters are found by eye due to the complexity of the nuclear gas structure and dynamics, the large parameter space, and the number of fit parameters available to the model. The parameters are chosen to minimize the apparent differences between the modeled line profiles and the observed line profiles extracted at points separated by a beam FWHM along the major and minor axes of the modeled gas. Once a fiducial fit is found, ranges on acceptable fit parameters are found by varying one parameter at a time until the model's line profiles are no longer acceptably close to the observed line profiles. "Acceptable" fits are determined by a combination of factors: first, the modeled line profiles on average cannot appear to differ from the observed line profiles by more than ∼25% in height, width, or central velocity. The fits focus on the brightest region along the gas' major axis. Second, the shape of the modeled line profiles should approximately match that of the observed line profiles.

Many of the parameters can be well constrained by the observed line profiles, for example, r_sh by the rate of decay of the line profile heights with radius and v_turb by their widths. The singly peaked profiles and lack of gradient in their central velocities constrains the inclination to nearly face-on models. Inclinations between 45° and 135° are strongly disfavored because they showed doubly peaked profiles. Other parameters are more difficult to constrain. v_circ and r_circ are the least constrained because they are anti-correlated (see Equation (3)) leading to large fit ranges as they trade off against each other. However, v_circ is not wholly unconstrained. It cannot be so high as to shift the line centers, but must be high enough to create the singly peaked profiles. The temperature T is constrained by the brightness of the lines, with higher temperatures (and therefore higher CO rotational excitation) corresponding to brighter lines.

All available parameters, fit values, and acceptable ranges of model parameters are reported in Table 3. The fiducial fit model whose emission profiles most closely match the observed profiles is a nearly face-on pancake-like distribution of gas, with a scale height z_sh of 20-60 pc and a radial scale length of 390 pc at an inclination of 22.5° from face-on. The line profiles extracted from these models along the semimajor axis of the gas concentration for CO J = 6–5 and J = 3–2 are compared to those from the data in Figure 9.

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A wide range of parameter space resulted in fits of similar quality to our fiducial model. As an example, we include a thicker-disk model with the parameters in Table 4 with the corresponding modeled line profiles in Figure 10. This model is thicker than the models presented in Table 3, with a vertical scale height z_sh of 60 pc instead of 20 pc, a gas concentration that is more horizontally concentrated (r_sh = 270 pc instead of 390 pc), and with a lower ratio of turbulent to circular velocity (v_turb/v_circ = 0.44 instead of 1.4). While this thicker model's parameters are all within the thin disk's acceptable ranges and still capture the majority of the observed emission (line profile width, intensity, and in some cases, line-profile shape), the line profiles are more doubly peaked and less representative of the observed line profiles.

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We place the model parameters in a physical context by comparing them to the findings of Kamenetzky et al. (2014) who use the Herschel Space Observatory and other supplementary observations (see their Table 16) of CO J = 1–0 to 13–12 to model gas temperatures, H₂ column densities, gas masses, and H₂ number densities for NGC 6240. We find our CO J = 3–2 model has a temperature and mass consistent with their calculations. The CO J = 6–5 model is on the high end of both temperature and mass, but the total modeled mass of the gas is consistent with other findings for NGC 6240.

Our models indicate the CO J = 6–5 emission is dominated by relatively hot (T = 2000 K) gas, and the CO J = 3–2 emission by warm (T = 600 K) gas. Kamenetzky et al. (2014) modeled the CO emission as a combination of cold (16 K with 1σ range [5, 50] K) and hot (1260 K with 1σ range [790, 2000] K) gas. They found the CO J = 3–2 emission is dominated by a mixture of both cold and hot gas, while the CO J = 6–5 emission is produced primarily by the hot gas component. Our CO J = 3–2 fiducial model temperature of 600 K lies between the temperatures of Kamenetzky et al. (2014)'s cool and hot components, supporting the argument that the CO J = 3–2 emission is created by a combination of gas temperatures. Also in line with their model, our model finds the CO J = 6–5 emission to be dominated by hot (2000 K) gas, at the upper bound of their modeled 1σ range on gas temperature. Our model temperatures may be on the higher end due to the much smaller ALMA beam sizes that probe the nuclear region while Kamenetzky et al. (2014)'s models incorporate Herschel data that combines emission from both nuclear and extended regions. The nuclear region is likely to be much warmer than the extended gas due to star formation and AGN activity concentrated in the central kpcs. The high gas temperatures are supported by the presence of prominent H₂1 − 0S(1) emission that requires temperatures >1,000 K to be excited (Max et al. 2005; Meijerink & Kristensen 2013).

The model fit dust temperature range of [20, 100] contains Kamenetzky et al. (2014)'s best-fit dust temperature of 56 K that we used in our continuum mass calculations (Section 3.1).

Kamenetzky et al. (2014) also models the masses of these cool and warm components, finding a cool gas mass of 2 × 10⁹ ± 5 × 10⁸ M_⊙ and a warm gas mass of 4 × 10⁸ ± 10⁸ M_⊙. Our total modeled mass for CO J = 3–2 is 7.6 × 10⁸ M_⊙, higher than Kamenetzky et al. (2014)'s modeled warm gas mass but lower than their cool gas mass. This is again consistent with the theory that CO J = 3–2 is a mixture of cool and warm gas components. The ranges of CO J = 6–5 gas mass modeled by LIME spans a factor of two (Table 3) that contain Kamenetzky et al. (2014)'s masses. However, our modeled hot gas mass (captured by simulations of CO J = 6–5) is 6–7 × 10⁸ M_⊙, higher than their best-fit warm gas mass by around 50%. Despite the high mass of the hot gas in the model, the total modeled mass of ∼1.4 × 10⁹ M_⊙ (CO J = 3–2 plus CO J = 6–5) is close to the nuclear region's mass calculated from the continuum in Section 3.1 (1.2×10⁹ M_⊙, region 1, Figure 6). This presents a possible conundrum: the dust-continuum observations in Section 3.1 suggest that much of the dust emission is not captured by these observations, while the modeled gas masses do appear to capture the majority of the gas mass. It is possible that this discrepancy comes down to the high L_CO/L_FIR ratio in NGC 6240, around 10 times higher than other nearby galaxies (Kamenetzky et al. 2014). The CO emission could be dominated by the shocked gas observed with ALMA, while there is more dust and cold (less luminous) gas outside of the ALMA observations that would included in Herschel observations. In other words, due to the concentrated nuclear excitation of CO in NGC 6240, the ALMA observations efficiently captured CO emission, but not the extended dust emission.

In this section, we examine the modeled velocity dispersion and circular velocities in the context of the model geometry, finding that the model suggests a transient structure that is stable against collapse.

The ratio of our average rotational velocity to our modeled velocity dispersion is 〈v〉 / σ ∼ 0.7 for the thin fiducial models presented in Figure 9. According to Tacconi et al. (1999) this is in the range that indicates a disk that must be geometrically thick. However, the fiducial models are quite thin, with z_sh of only 20 pc and r_sh of 250–390 pc. This aspect ratio is unlikely for a self-gravitating structure with such high-velocity dispersion since the dispersion would have the effect of "puffing up" the disk. It is also possible that with such a thin concentration of gas, the modeled high-velocity dispersion could partially be accounted for by shear. That is, the gas concentration could be undergoing tidal disruption in the plane of the sky.

The thicker fiducial model presented in Table 4 and Figure 10 has a higher ratio of 〈v〉/ σ ∼ 2.3 and a thicker geometry (z_sh = 60 pc, r_sh = 270 pc). In both senses this model is less extreme than the thinner model, though it visibly does not fit the observed line profiles as well. That the thicker model would correspond to a lower velocity dispersion may seem counterintuitive, as we would expect that higher velocity dispersions would "puff up" the gas. However, if one invokes shear in the plane of the sky this would artificially inflate the velocity dispersion for thinner and more optically thin gas concentrations.

We can also conduct a back-of-the-envelope calculation to determine the lifetime of the gas concentration given its modeled velocity dispersion and vertical extent. For the thin model, the velocity dispersion is 140 km s⁻¹ (assuming no contribution from shear) and the vertical extent of the concentration is ∼40 pc (two vertical scale heights). Gas moving at 140 km s⁻¹ would travel this distance after 300,000 yr. This is an extremely short timescale in the context of galaxy mergers that occur over timescales of Gyr, suggesting the model represents a highly transient structure. For the thicker model, gas traveling at a speed equal to the velocity dispersion of 110 km s⁻¹ would travel two scale heights' distance (120 pc) in ∼1 Myr, still a short timescale in the context of galaxy mergers. Such short lifetimes are unlikely for a self-gravitating structure.

As a further test of the models in the context of a self-gravitating structure, we can compare the velocity dispersion and circular velocities to the escape velocity from the modeled gas concentration. For this calculation, we use the escape velocity of $\sqrt{2{GM}/r}$ for the entire gas concentration with M = 1.4 × 10⁹ M_⊙. At the radial scale height of the thinner model r_sh = 390 pc, v_esc is 170 km s⁻¹. This value is similar to the thin models' velocity dispersion of 140 km s⁻¹, and is less than the circular velocity (100 km s⁻¹) added to the modeled dispersion. At the radial scale height of the thicker model r_sh = 270 pc, v_esc is 210 km s⁻¹. This exceeds the thicker model's turbulent velocity of 110 km s⁻¹ but is less than its circular velocity alone (v_circ = 250 km s⁻¹). This means both models' gas velocity can exceed the escape velocity of the gas concentration, indicating it is extremely unlikely this gas is a self-gravitating disk.

Given the fiducial LIME model, we can also check the stability of the gas concentration by calculating the Toomre parameter Q = σ_r κ/π G Σ_gas. Here κ=$\sqrt{3}$ v_max/R is the epicyclic frequency, σ_r is the line-of-sight velocity dispersion, and Σ_gas is the mass surface density of the gas (Toomre 1964). Q for the thinner LIME model is 2.3 for CO J = 6–5 and 2.5 for the CO J = 3–2 model. A Q > 1 means the gas is stable against collapse at this time, with the majority of models within the acceptable parameter ranges fitting into this category. These high values of Q are consistent with this highly turbulent system. The majority of the luminosity being generated in this central mass concentration is then unlikely to be due to star formation, consistent with other papers that argue for heating from shocks and superwinds originating in starbursts around the nuclei, not in the central region between the two nuclei (e.g., Tecza et al. 2000; Max et al. 2005; Engel et al. 2010).

Figures 11 and 12 show the moment 0 and 1 normalized residuals (upper panels) and moment 1 absolute residual (lower panel) between ALMA data and the thinner fiducial LIME models for CO J = 6–5 and J = 3–2 (presented in Table 3 and Figure 9). The normalized fractional residuals are calculated by subtracting the model from the observation and dividing by the observation for each pixel. We present the residuals for the thinner and not the thicker models because they most closely represent the observed line profiles.

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The residuals for each moment take a similar shape for both emission lines. The low values of the moment 0 fractional residual in the brightest central region indicate that the test model captures the majority of the line emission in this central region. However, the model misses the northernmost portion of the observed gas concentration, especially apparent in the CO J = 6–5 residual. The test model does not accurately describe the 〈v〉 data, as evidenced by the large values and amount of structure that remains in the fractional residuals of moment 1 for both CO J = 6–5 and J = 3–2. The non-normalized residual of 〈v〉 (observed—model), shown in the bottom panel of each figure, remains largely unchanged from the observed values. This indicates that the model does not reproduce the velocity structure well at all, and explains why the normalized residuals are all close to one.

The residuals shed light on what components of NGC 6240's molecular gas are captured by the test model, if any. There are aspects of the gas that are clearly not captured, for example, the modeled line profiles in Figure 9 miss a shoulder of highly redshifted emission (>300 km s⁻¹) in the northeast, plotted therein as dark brown and black line profiles. This emission corresponds to the highly redshifted gas visible in the average velocity maps (∼300 km s⁻¹ in Figure 2 and ∼400 km s⁻¹ in Figure 3) and in the channel maps (up to 665 km s⁻¹ in Figure 4 and up to 724 km s⁻¹ in Figure 5). It also corresponds to the highly redshifted gas in Figure 8 with an average velocity of ∼400 km s⁻¹ when isolated from the quiescent gas or ∼250 km s⁻¹ when including the quiescent gas. This gas is dim compared to the majority of the line emission, and as such does not augment the normalized fractional residual moment 0 maps above ∼0 despite not being described by the models.

Despite missing this high-velocity gas, the low values for the integrated line emission residuals in the central/southern portion of the central gas concentration indicate that the models capture the majority of the CO emission in this, the brightest and most massive part of the ALMA observations. We calculate that the model captures 96% of the observed emission, a value found by dividing the sum of the modeled CO J = 6–5 emission divided by the sum of the observed emission within the 5σ contour area. Capturing the majority of the emission indicates we accurately model the gas mass and gas temperature, which are degenerate parameters that each increase the total emission when increased. Constraints on gas mass and temperature are provided by the modeled line profile shapes with exceedingly high masses or low temperatures resulting in doubly peaked profiles. Accurate models of mass and temperature do not directly imply accurate models of gas distribution. The other parameters important for this are r_sh, well constrained by the visible extent of the gas, and z_sh. z_sh is somewhat difficult to constrain because the gas is nearly face-on, but thick gas results in doubly peaked profiles constraining z_sh to small values (tens of parsecs). Density is directly calculated from the gas mass, r_sh, and z_sh. Our constraints on these values and the gas temperature indicate we have successfully modeled the physical distribution and density of the gas. Our models found that this central gas region is pancake-like: quite thin (tens of pc) with respect to its extent (hundreds of pc).

While the fractional residuals of the line emission appear to accurately capture the distribution of the gas, the velocity residuals tell a different story. The normalized fractional velocity residuals (upper right panel of each figure) are composed almost entirely of values close to one, with absolute residuals (lower panel of each figure) close to the average velocities of the observed gas. These large residuals suggest a simple exponentially decaying velocity profile (like that of a disk) does not accurately capture the kinematics of the gas. When taken with the arguments in Section 4.4 that the modeled velocity dispersion indicates a transient structure whose velocities can exceed the escape velocity of the gas concentration, we suggest that the nuclear molecular gas emission is dominated by a thin pancake-like gas concentration that is not rotating like a disk. This conclusion is also consistent with the findings of Section 4.4, finding our masses and temperatures fit within current observations but the high-velocity dispersion relative to the circular velocity is unlikely for such a thin geometry if the gas were to be a self-gravitating disk.