THE ROLE OF MOLECULAR GAS IN OBSCURING SEYFERT ACTIVE GALACTIC NUCLEI^*,^†

The nine galaxies were observed at the ESO Very Large Telescope (VLT) and the W. M. Keck Observatory. Although the AGNs observed were not selected to comprise a complete sample, both Seyfert 1s and 2s, as well as a low-ionization nuclear emission-line region (LINER), are included. Table 1 lists the full sample of galaxies selected.

The criteria for target selection of the galaxies observed at the VLT were: (1) the nucleus is bright enough to use for an AO correction, (2) the galaxy is close enough that small spatial scales can be resolved (∼20 pc), and (3) the galaxies are well studied such that complementary data can be found in the literature (e.g., radio, submillimeter observations). Although, the first criterion biases the sample to type 1 Seyferts, two of the six galaxies observed are Seyfert 2s.

The sample observed at the Keck Observatory was selected from all AGNs with a black hole mass estimate from reverberation mapping and a redshift such that the 2.1218 μm molecular hydrogen emission and stellar 2.3 μm CO bandheads are observable in the K band. This sample is therefore composed of relatively nearby Seyfert 1 galaxies, all of which have a nucleus that is bright enough for either a correction with the natural guide star (NGS) AO system or as a tip-tilt guide to be used in conjunction with the laser guide star (LGS) AO system. Both the OSIRIS and SINFONI subsamples contain NGC 3227 and NGC 7469, and a comparison of the data from each instrument is presented in the Appendix.

Integral field spectroscopy was obtained for several AGNs at the VLT UT4 with the AO near-IR integral field spectrograph SINFONI (Eisenhauer et al. 2003; Bonnet et al. 2004). The pixel scale of the R ∼ 4300 K-band spectra (approximately 1.95–2.45 μm) is either 0125 × 025 or 005 × 01, which results in a field of view (FOV) of 08 × 08 or 32 × 32, respectively. For each galaxy, the nucleus was used as the reference for a near-diffraction-limited correction by the AO module (Bonnet et al. 2003). The exposure times for Circinus, NGC 3783, and NGC 1068 were 30, 40, and 110 minutes, respectively, and for the remaining galaxies 60 minutes of on-source data were obtained. A summary of the data, including the specific spatial resolution achieved for each galaxy, is given in Table 1.

The data were reduced using the SINFONI custom reduction package SPRED (Abuter et al. 2006), which includes all of the typical reduction steps applied to near-IR spectra with the additional routines necessary to reconstruct the data cube. After background subtraction, which is performed with sky frames obtained interspersed with the on-source exposures, the data are flat-fielded and corrected for dead/hot pixels. Telluric correction and flux calibration are carried out using A- and B-type stars. Residuals from the OH line emission are minimized using the methods outlined in Davies (2007). The flux calibration is confirmed by comparison to 3'' aperture Two Micron All Sky Survey and 1''–3'' aperture NACO or Hubble Space Telescope (HST) NICMOS images and was found to be consistent to within 20%.

The spatial resolution of the SINFONI data (Table 1) is determined from the data themselves rather than from additional point-spread function (PSF) calibration frames. This is done because of the uncertainty involved in using a standard star to recreate the AO performance achieved with an AGN which has spatially extended background galaxy light, as well as to avoid mismatches due to the variability of the ambient seeing. Two methods, outlined in Davies et al. (2004a), are used to determine the PSF directly from the data, which also has the advantage of including all effects associated with the construction of the data cube. The first method makes use of the broad Brγ (λ2.1661 μm) emission assumed to be coming from the broad-line region (BLR), which is expected to be unresolved for the galaxies in this sample (Peterson et al. 2004). The second method applies the fact that the intrinsic equivalent width of the CO 2-0 2.29 μm bandhead is expected to fall within a limited range (Oliva et al. 1995; Förster Schreiber 2000; Davies et al. 2007, hereafter D07), and therefore the observed W_CO2-0 can be used to determine the dilution of the stellar feature due to the AGN continuum emission, which, at this resolution, is also a point source (predicted sizes are less than 2 pc; Jaffe et al. 2004; Tristram et al. 2007).

An analysis of the nuclear star formation properties (star formation rates (SFRs), time since the last star-forming episode, stellar distribution, etc.) in each of the galaxies in this subsample is presented in D07. Detailed studies of a few of the galaxies in the subsample can also be found in the literature: Circinus (Müller Sánchez et al. 2006), NGC 3227 (Davies et al. 2006), and NGC 1068 (Müller Sánchez et al. 2009).

At the W. M. Keck Observatory, the integral field spectrometer OSIRIS (Larkin et al. 2006) on Keck II was used with both the NGS and LGS AO systems (van Dam et al. 2004, 2006; Wizinowich et al. 2006). K-band R ∼ 3000 spectra, covering 1.965–2.381 μm, were obtained with a pixel scale of 0035 pixel⁻¹ over an FOV of 056 × 224 for each of the galaxies. Typically, 10 minute exposures were taken with off-source sky exposures obtained interspersed with the on-source frames. Total on-source exposures vary from 40 minutes for NGC 4051, to 60 minutes for NGC 4151, and 70 minutes for the remaining three galaxies. Of the 70 minutes of on-source exposure for NGC 7469, 20 minutes of this was obtained with the LGS AO system, while the rest of the data for this galaxy, and the others, was obtained with a correction from the NGS AO system using the AGN nucleus as the reference. The spatial resolution achieved for each galaxy, via the methods discussed in the previous section, are given in Table 1. As a consistency check, the PSF full width at half-maxima (FWHMs) estimated using these methods were compared to that of the PSFs determined from observations of standard stars (using the same AO setting as used for the galaxies), and they are found to be consistent to within the uncertainties discussed in Section 2.2 of standard star PSF measurements (e.g., changes in seeing and difficulty in reproducing the AO performance of the galaxy observations).

Reduction of the OSIRIS data was carried out with the OSIRIS final data reduction pipeline (DRP), which performs reduction steps typically applied to near-IR spectra as well as reconstruction of the data cube. These steps include background subtraction, flat-fielding, and correction for dead/hot pixels, as well as correction of detector nonlinearity, removal of detector cross talk, and wavelength calibration. Telluric correction was done using A-type stars and was applied to the data in the DRP. Flux calibration of the OSIRIS data is expected to be accurate to about 30%.

To assess the kinematic properties of the galaxies on a larger scale than is measured here, long-slit data were also obtained with ISAAC on the VLT UT1 for three of the galaxies measured with SINFONI. Seeing-limited data were obtained as part of a service-observing program carried out in 2006. The short wavelength arm of ISAAC was used in the medium resolution mode (R ∼ 3000) with a 0.122 μm narrowband filter centered at 2.144 μm to obtain spectra of the H₂ 1-0 S(1) emission line. Two orthogonal slit positions were obtained for each of the galaxies (see Table 1 for details) with a 2' long and 03 wide slit. The orientations of the two slit positions for each object were selected to align with the major and minor axes as determined from 2.2 μm HST NICMOS images. Exposure times totaled 40 minutes per slit position, and the target was nodded along the slit to perform sky subtraction. The ISAAC data were reduced using standard near-IR reduction techniques, and were carried out with the ESO pipeline software.

As can be seen in the two-dimensional maps of the H₂ flux distribution in Figures 1 and 2, there is a great deal of diversity in the nuclear H₂ flux distributions in the sample galaxies. Although most of the galaxies have a relatively symmetric flux distribution, the two-dimensional maps reveal several nonsymmetric features, particularly in NGC 3227 and NGC 4151. This should not come as a surprise given that H₂ 1-0 S(1) is emitted from warm molecular gas (typically 1000–2000 K), and therefore the local environment will greatly influence the observed luminosity distribution. For this reason, it should be kept in mind that the flux distribution is not necessarily representative of the actual H₂ mass distribution. In fact, particularly in the cases of NGC 3227 and NGC 4151, in addition to the brighter patches of emission, H₂ is also detected at a significant level throughout the measured FOV. The H₂ flux distribution in the individual galaxies observed is discussed in more detail in the Appendix.

Despite the complexity of the observed flux distributions, the azimuthal average of the H₂ emission is consistent with a half width at half-maximum (HWHM) less than 35 pc in all of the AGN, with a mean HWHM for the sample of ∼30 pc (Figure 6 and Table 2). Of note is that D07 report a nuclear stellar component with similar size scales in the SINFONI subsample based on the excess stellar light beyond that expected from an extrapolation of either a smooth r^1/4 or an exponential function. Fitting a generalized exponential (or Sérsic function; Sérsic 1968) to the azimuthally averaged light profiles of the gas indicates disklike distributions, where the threshold of a disk profile is taken to be n = 2 (Cresci et al. 2005) and n = 1 is an exponential and n = 4 is a de Vaucouleurs profile. Table 2 lists the best-fit n values for each of the galaxies observed, which on average give n = 1.6 ± 0.4.

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In general, the nuclear H₂ kinematics in the sample galaxies exhibits ordered rotation with kinemetry fits that are consistent with co-planar circular rotation (i.e., higher orders of the harmonic expansion are within the velocity and σ measurement errors). Furthermore, kinemetry indicates that both the PA and inclination angle remain constant throughout the nuclear region (to within the measurement error of ∼10°), and residuals of fits with the PA and inclination angle held constant are consistent with the estimated kinematic errors (⩽15 km s⁻¹). This suggests that, in the galaxies observed, the nuclear gas has no significant radial motions (e.g., in/out flows) and that there is no detectable warp down to the smallest scales measured, typically ∼20 pc. Although deviations of up to ∼30 km s⁻¹ from co-planar disk rotation are seen in NGC 1097, NGC 3227, and NGC 4151 (see the Appendix for details), the kinematics in each case is still dominated by disk rotation. We therefore conclude, based on the kinematics and spatial distribution of H₂, that the properties of the nuclear molecular gas in this AGN sample are consistent with a disklike distribution with a radial scale on the order of a few tens of parsecs.

The best-fit PA and inclination angles given by the kinemetry fits to the H₂ gas kinematics are listed Table 2 (see the Appendix for a discussion of the individual galaxies). In all galaxies where a comparison is possible, the best-fit parameters to the gas kinematics are consistent with those determined from the stellar kinematics measured using the CO bandheads detected in the same K-band data (except in NGC 1068, as discussed). Values based on the stellar kinematics for the SINFONI subsample are those reported in D07, and those for the OSIRIS subsample are also determined via kinemetry and are reported for the first time here (the nuclear stellar properties of this subsample will be discussed in more detail in a future publication). As stated, all azimuthally averaged properties are computed with the best-fit PA and inclination angle determined from the stellar kinematics, when possible. However, there is no significant difference in the averages computed using the best-fit values determined from the H₂ kinematics. On larger scales, others have also found that the orientation of the gas disk agrees with that of the stars. For example, Dumas et al. (2007) find agreement between the gas (in this case [O iii] and Hβ) and stellar disk orientation in the central kpc of a sample of local active and inactive galaxies. Moreover, the similarity of the H₂ kinematics and distribution with that of the nuclear stellar component suggests that the gas and stars in the central tens of parsecs are spatially mixed.

While the two-dimensional velocity fields of the nuclear H₂ gas indicate rotating disks, the velocity dispersion suggests that these disks are relatively thick. On average, the rotational velocity to velocity dispersion ratio, V_rot/σ (where V_rot = V_obs/ sin i), is 0.9 ± 0.3 at a radius of 30 pc (Figure 7). This rather low value of V_rot/σ indicates that random motions play a significant role at these scales, despite the general rotation of the gas. This conclusion is drawn from the fact that the kinetic energy of the random motion is of order 3σ² (assuming the dispersion arises from macroscopic motions and that we are observing one dimension of an isotropic distribution), which is significant in comparison to the energy on the order of V²_rot from rotation. Consequently, when determining a dynamical mass, the significant velocity dispersion of the gas must be considered. To achieve this, we estimate the dynamical mass by M_dyn = (V²_rot + 3σ²)r/G, where r is the radius from the nucleus and G is the gravitational constant. The measured kinematics and estimated dynamical masses within the radii of 30 pc and the H₂ light distribution HWHM are given in Table 3 for each galaxy, and the mean σ values within these radii are given in Table 4. The significance and origin of the relatively high nuclear velocity dispersion observed in these galaxies will be discussed in Section 5.

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Table 4. Mean H₂ 1-0 S(1) Velocity Dispersion

	SINFONI and OSIRIS						ISAAC
Galaxy	<σ>30pc (km s−1)	<σ>HWHM (km s−1)	<σ>05 (km s−1)	r (pc)	<σ>D07 (km s−1)	σmax (km s−1)	<σ>$_{20\hbox{$^{\prime \prime }$}}$ (km s−1)	<σ>$_{>5\hbox{$^{\prime \prime }$}}$ (km s−1)	<σ>05 (km s−1)
NGC 1097	61 ± 9	62 ± 10	60 ± 9	22	64 ± 9	74	58 ± 10	47 ± 11	71 ± 1
NGC 3227	95 ± 15	95 ± 15	94 ± 14	32	95 ± 15	108	74 ± 15	43 ± 23	96 ± 5
	78 ± 14	79 ± 14	77 ± 14		79 ± 14	93
NGC 3783	33 ± 1	33 ± 1	34 ± 2	60	33 ± 1	33	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅
NGC 4051	55 ± 8	56 ± 12	56 ± 8	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅
NGC 4151	56 ± 10	54 ± 10	57 ± 11	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅
NGC 6814	48 ± 6	48 ± 5	45 ± 6	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅
NGC 7469	62 ± 2	67 ± 5	71 ± 7	128	70 ± 7	82	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅
	62 ± 6	62 ± 6	79 ± 12		78 ± 13	92
Circinusa	56 ± 3	57 ± 2	56 ± 3	8	56 ± 2	61	54 ± 9	48 ± 10	63 ± 4
NGC 1068	88 ± 42	58 ± 40	88 ± 42	30	88 ± 42	134	⋅⋅⋅	⋅⋅⋅	⋅⋅⋅

Notes. A uniformly weighted mean within a radius given by the subscript, except where it is indicated to be outside of the stated radius. For NGC 3227 and NGC 7469, the first and second lines are based on SINFONI and OSIRIS data, respectively. As discussed in Section 3, NGC 1068 is excluded from the AGN sample. ^aQuantities measured at 9 pc (the edge of the measured FOV) rather than 30 pc.

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Comparing the 20'' FOV ISAAC single-slit spectroscopy with the higher spatial resolution kinematics measured with SINFONI indicates that the velocities measured in the central 05 are consistent with the general galactic rotation (Figure 5). This supports, in at least those galaxies observed with ISAAC, the suggestion that the nuclear gas is distributed in a rotating disk. In addition, the consistency of the nuclear kinematics with the large-scale disk orientation reported in the literature for the sample galaxies indicates that these nuclear disks are well aligned with the host galaxy. In each of the three galaxies measured with ISAAC, the velocity dispersion increases within the central few arcseconds, with the outer disk σ(r > 5'') = 43–48 km s⁻¹ and the inner disk σ(r < 05) = 63–96 km s⁻¹. These elevated σ values are more than can be accounted for by beam smearing of the central velocity gradient, and therefore represent a real increase in σ in comparison to the normal star-forming disk measured at radii outside of 5''. For comparison, Table 4 gives the mean σ measured for each of these galaxies within the outer disk (r > 5'') and inner r < 05 from the seeing-limited single-slit ISAAC data, as well as that from the inner r < 05 of the integral field SINFONI data.

For those galaxies in which the cold molecular gas has been measured through millimeter interferometric CO observations on scales similar to those measured here, the kinematics of the relatively hot H₂ and cold gas are found to be qualitatively similar. This indicates that nongravitational forces do not significantly influence the hot gas traced by H₂ and that it does indeed follow the mass distribution in the nuclear region. The best-fit PA and inclination angles of the H₂ gas disks agree with those of the CO gas disks reported in the literature (see Table 5 for references), with differences of ≲10 km s⁻¹ and thus within the measurement errors. In addition, similar to the hot molecular gas, the velocity dispersion of the cold gas is significant with respect to its rotational velocity (Table 5). For example, in NGC 7469 the velocity dispersion measured (after taking into account beam smearing of the velocity gradient) is as high as 60 km s⁻¹ compared to a rotational velocity of ∼100 km s⁻¹. Although the velocity dispersion of the cold molecular gas is generally lower than that of the hotter H₂ gas, its relatively high value indicates that the cold gas, similar to the hot gas, has a significant component of random motion.

With a velocity dispersion that is greater than the inclination-corrected rotational velocity out to radii of tens of parsecs (Figure 7), a simple thin disk of H₂ gas can be ruled out. As discussed in Section 3.2, this is because, in this case, the kinetic energy of the random motion is greater than that from the ordered rotation. In addition, the kinematics of the sample galaxies is consistent with co-planar circular rotation, suggesting that disk warps are not the cause of the high velocity dispersion. Therefore, although the molecular gas exhibits bulk rotation, on these scales it must be in a more spherical-like distribution (e.g., a geometrically thick disk).

As discussed in Section 3.2, the σ measured in the extended stellar disks (r > 5'') of the galaxies measured with ISAAC indicates that processes associated with typical disk star formation are capable of producing an H₂ velocity dispersion of σ ∼ 45 km s⁻¹ (comparable to the σ of the cold molecular gas; Table 5). An additional velocity dispersion of ∼30 km s⁻¹ is then needed to produce the higher H₂ nuclear velocity dispersions observed in the AGNs at a radius of 30 pc (this is found by subtracting, in quadrature, the σ observed in the outer galactic disk). A similar conclusion is reached when considering the mean σ within a radius of 30 pc (Table 4). The excess H₂ velocity dispersion is greater than 25 km s⁻¹ in five of the eight galaxies, with values ranging from 26–87 km s⁻¹ at a radius of 30 pc (9 pc in Circinus). In the remaining three galaxies (NGC 3783, NGC 4051, and NGC 6814) the measured σ is comparable to the value seen in the outer star-forming disks.

Models have shown that strong H₂ 1-0 S(1) emission can be produced via shocks of speeds 20–40 km s⁻¹ (e.g., Hollenbach & McKee 1989; Burton 1992). However, when the shock exceeds 40 km s⁻¹ the molecular hydrogen is dissociated, and thus emission is no longer produced. Even if the excitation of H₂ is dominated by shocks at the maximum speed of 40 km s⁻¹, and these shocks are randomly oriented, it is only possible to produce σ ∼ 40 km s⁻¹ (including instrumental dispersion). It is, however, possible to produce a higher H₂ velocity dispersion with bow shocks, where the angle between the shock front and the propagation direction of the bow is highly oblique and the resulting shock does not dissociate the H₂ (examples include the Orion bullets and Herbig–Haro object HH99B; Tedds et al. 1999; Giannini et al. 2008, respectively). In this scenario, the H₂ 1-0 S(1) velocity dispersion measured when integrating over the molecular cloud corresponds to the cloud's bulk motion. Therefore, the high gas velocity dispersion measured is likely to be the result of bulk motion of the molecular clouds.

Although it is not straightforward to derive the disk scale height from the nuclear velocity dispersions measured, we attempt to get a rough estimate via two methods. The first is to assume that the gas and stars are self gravitating, in which case the scale height of the gas disk can be estimated with the relationship z_o = σ²/2πGΣ, where G is the gravitational constant and Σ is the surface density of the disk assuming a gas mass determined from the M_dyn estimates derived in Section 3.2 and the gas mass fraction of 10% estimated in the following section, i.e., Section 3.4.1. Strictly speaking this relationship should only be applied to a thin isothermal disk and consequently the relationship breaks down at the smallest radii where V_rot/σ is significantly less than unity (r ≲ 20 pc). Taking the measured σ at a radius of 30 pc, where V_rot/σ ∼ 1, the implied scale height is on average z_o = 40 ± 6 pc for the galaxies observed (excluding Circinus, which was measured out to a radius of only 9 pc where the disk height is 13 pc). At the HWHM radius of the light distribution, which is on average 23 ± 11 pc, the average height is z_o = 33 ± 16 pc. Estimates of the disk heights for the individual galaxies are given in Table 3.

The second method used to determine the height of the gas disk assumes vertical hydrostatic equilibrium, which implies V_rot/σ ∼ r/z_o. For each galaxy, the estimated z_o at a radius of 30 pc and at the HWHM radii are consistent, to within 10 pc, with that derived above under the assumption of a thin isothermal disk. The average disk height given by this method is z_o = 38 ± 13 pc at a radius of 30 pc, again consistent with that derived above. We therefore estimate that the heights of the molecular gas disks in the observed AGNs are on the order of tens of parsecs at the radii considered, with typical values of z_o ∼ 30–40 pc at a radius of 30 pc.

3.4.1. Column Density Derived from Dynamical Mass

An order of magnitude estimate of the gas mass, and thus the column density, within the nuclear regions of the galaxies can be derived by assuming that the nuclear gas masses are a fixed fraction of the dynamical masses. In addition, we make the simplifying assumption that the H₂ gas mass at a given radius is distributed uniformly. The derived column densities are thus the average values within a given a radius, and provide a measure of the maximum extinction. As will be shown in the following section, a significant fraction of the gas within the thick disks observed is in a clumpy distribution and the actual column densities are consequently lower than derived here.

This method of estimating the column densities requires that the gas masses are distributed as implied by H₂ 1-0 S(1) and are not in a denser component such as the H₂O maser disks seen on parsec scales (e.g., Greenhill et al. 2003). We argue that this is indeed the case based on evidence that the nuclear stellar component is spatially mixed with the thick gas disk observed (Section 3.2). The thick stellar disk indicates that the cold component of gas from which the stars formed must also be in a similarly thick disk, which is supported by the high velocity dispersion measured in CO observations (e.g., Schinnerer et al. 2000a; Davies et al. 2004b; Table 5). Therefore, while evidence exists of dense thin disks on scales smaller than observed here, the distribution and kinematics of the stars and molecular gas (both hot and cold) suggests that, on scales of tens of parsecs, the mass is distributed in a thick disk consistent with the disk traced by H₂ 1-0 S(1).

Although the gas mass fraction (f_g) is not accurately known in the nuclear regions of AGNs, we attempt to constrain this value via several methods discussed below.

• 1.  
  Typical Galaxies. Normal spiral galaxies, similar to the galaxies hosting the Seyfert AGNs observed, have typical gas mass fractions of ∼10%, with values ranging from 4% for Sab to 25% for Scd galaxies (e.g., Young & Scoville 1991). Given the evidence reported by D07 for recent nuclear star formation in the SINFONI galaxy subsample, the gas mass fraction measured in starburst and ULIRG galaxies may also be applicable to the nuclear regions of these AGNs. Local starburst and ULIRG galaxies are typically found to have f_g = 10%–20% (e.g., Young & Scoville 1984; Downes & Solomon 1998; Genzel et al. 2001; Greve et al. 2005; Tacconi et al. 2006). Therefore, a gas mass fraction similar to that in spiral, starburst, or ULIRG galaxies suggests f_g ∼ 10% with a range from 4% up to 20%–25%.
• 2.  
  Cold Molecular Gas. Measurements of the cold molecular gas within the nuclear region exist in the literature for four of the galaxies in this sample: NGC 1097, NGC 3227, NGC 1068, and NGC 7469. The standard galactic CO-to-H₂ conversion factor is not assumed since evidence indicates that this conversion factor is lower in intense star-forming environments such as the nuclei observed here (e.g., Downes & Solomon 1998; Papadopoulos & Allen 2000). We therefore use the conversion factor of (1.38 ± 0.46) × 10²⁰ cm⁻² (K km s⁻¹)⁻¹ found by Davies et al. (2004b) for the central 800 pc in NGC 7469, which is 0.4–0.8 times the Galactic conversion measured by Strong et al. (1988). The total gas mass is then determined from the H₂ gas mass implied by the CO luminosity by assuming a mass correction for helium of 40% and that the masses of H i and H ii are negligible at these radii. As can be seen in Table 5, the gas fractions derived from the CO 2-1 integrated intensity vary significantly from source to source, with values of f_g = 1%–29%. To date, there are no higher spatial resolution CO 2-1 observations of NGC 7469 than those of Davies et al. (2004b), but over this relatively large region of 1.6 kpc, the independently determined H₂ mass (used to estimate the CO-to-H₂ conversion factor above) and the CO dynamical mass imply f_g = 58%.
• 3.  
  Sample Wide Average for Active Galaxies. There now exist in the literature several studies of the cold molecular gas in the central hundreds of parsecs of galaxies of various activity levels, including Seyfert galaxies. Taking a sample of five active galaxies that have been observed in CO 2-1 as part of the NUGA Survey (NGC 4321, NGC 4579, NGC 4826, NGC 6574, and NGC 6951), we use the reported gas and dynamical masses to derive a gas mass fraction (Lindt-Krieg et al. 2008; García-Burillo et al. 2003, 2005; Krips et al. 2007). In several cases, no dynamical mass is given in the literature at the small radii considered here, in which case it is estimated from the reported CO 2-1 kinematics. Based on this sample we find a typical gas mass fraction of ∼10%, with f_g = 1%–15% within the central ∼200 pc of four galaxies and f_g = 10% out to a radius of 300 pc in the fifth galaxy.
• 4.  
  H₂ 1-0 S(1) Luminosity. The gas mass can also be determined (to within a 1σ uncertainty of a factor of about 2) from the luminosity of H₂ 1-0 S(1) using the relationship reported by Müller Sánchez et al. (2006), which has a conversion factor of 4000 M_☉/L_☉ (also see Dale et al. 2005). A lower limit on the gas mass is estimated from the most extreme case in their sample, NGC 6240, which is known to be over luminous in H₂ 1-0 S(1)(e.g., Sugai et al. 1997; Tecza et al. 2000), and has an order of magnitude lower conversion factor of 430 M_☉/L_☉. Based on this extreme conversion factor, the median gas mass fraction for the sample is f_g ∼ 13%, with values ranging from 5% to 53% (individual gas mass estimates are given in Table 6). In each of the individual galaxies, the gas mass fraction derived from the H₂ luminosity is consistent with that determined from the CO observations discussed above. The typical conversion factor gives significantly higher gas masses and the lowest value in the sample is f_g = 47%. In some cases the typical conversion factor implies a gas mass fraction greater than 100%, suggesting that these galaxies may also be over luminous in H₂ compared to the sample of galaxies studied by Müller Sánchez et al. (2006), and that a conversion similar to that found for NGC 6240 is more appropriate. We therefore deduce from this method that f_g is greater than a few percent, with no constraint on the upper limit.

Table 6. Gas Mass Estimates as Derived in Section 3.4.1

			LH2 Conversiona
Galaxy	Mdyn (107 M☉)	fg = 10% Mgas (107 M☉)	Mgas (107 M☉)	fg (%)
NGC 1097	9.5	1.0	0.5–4.5	5–47
NGC 3227	22.6	2.3	2.4–22.2	11–98
	17.7	1.8	2.2–20.2	⩾12
NGC 3783	2.8	0.3	1.1–10.6	⩾39
NGC 4051	5.0	0.5	0.7–6.6	⩾14
NGC 4151	14.0	1.4	1.2–10.8	9–77
NGC 6814	4.2	0.4	0.6–5.5	⩾14
NGC 7469	9.3	0.9	4.9–45.5	⩾53
	10.1	1.0	4.7–43.3	⩾47
Circinus	1.9	0.2	0.2–1.5	11–79
NGC 1068	22.5	2.3	4.2–39.3	⩾19

Notes. Dynamical masses are based on the H₂ kinematics as discussed in Section 3.2. All masses are derived for a radius of 30 pc, with the exception of Circinus, for which the radius is 9 pc. For NGC 3227 and NGC 7469, the first and second lines are based on SINFONI and OSIRIS data, respectively. As discussed in Section 3, NGC 1068 is excluded from the AGN sample. ^aFor cases where the typical conversion from H₂ luminosity to M_gas results in a mass higher than M_dyn, only the f_g lower limit derived from the more extreme conversion factor is given (see the discussion in Section 3.4.1).

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To summarize, typical galaxies have f_g ∼ 10% (ranging from 4% to 25%), CO measurements of active galaxies also suggest f_g ∼ 10% (with a range from 1% to 15%), CO measurements of three Seyferts in this sample on scales comparable to those measured here imply f_g = 1%–29%, and a conversion of the nuclear H₂ luminosity observed in the sample galaxies gives a lower limit on f_g of a few percent. We therefore conclude that for the nuclear regions of the Seyfert galaxies observed that typically f_g ∼ 10% with a range of f_g ∼ 1%–20%. If the gas is uniformly distributed, then f_g ∼ 10% gives an average column density within a radius of 30 pc of N_H ∼ (4.9 ± 3.3) × 10²³ cm⁻² for the galaxy sample, with values ranging from 1.3 to 10.0 × 10²³ cm⁻² (Figure 8). The column densities within a radius of 30 pc and the HWHM light radius are listed for each galaxy in Table 3. Taking f_g ∼ 1% still results in column density estimates greater than 10²² cm⁻² in all galaxies, which is sufficient to obscure an AGN, and f_g ∼ 20% gives an average N_H ∼ 10²⁴ cm⁻². However, as will be shown in the following section, the gas is unlikely to be uniformly distributed within the nuclear region, and the actual clumpy distribution results in significantly less obscuration of the AGN (as well as the nuclear star formation).

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3.4.2. Column Density Derived from Extinction

In summary, based on the kinematics of H₂ 1-0 S(1), the molecular gas within the central ∼100 pc of the Seyferts is in a rotating, thick (z_o/r ∼ 1) disklike distribution that is spatially mixed with the nuclear stellar population. This gas/stellar disk has spatial scales of less than 35 pc in all cases, with a typical HWHM of ∼30 pc. Within the central ∼60 pc the dynamical mass is ∼10⁸ M_☉, which suggests M_gas∼ 10⁷ M_☉ based on the typical gas mass fraction of 10% (M_gas = (0.1–2.0) × 10⁷ M_☉ assuming f_g = 1%–20%). If a uniform gas distribution is assumed, then this typical gas mass fraction implies an average column density at a radius of 30 pc of ∼5 × 10²³ cm⁻². However, the average column density implied by the extinction of the nuclear stellar continua is over an order of magnitude lower than this estimate (N_H ∼ 2 × 10²² cm⁻²), suggesting that the nuclear gas in these galaxies is actually in a clumpy distribution. The disklike distribution of gas on ∼10 pc scales in Seyfert galaxies is therefore relatively transparent and does not heavily obscure the nuclear stellar population or the central AGN.

In addition to theoretical models and hydrodynamical simulations indicating that the gas on ∼10 pc scales is distributed in discrete clouds rather than evenly throughout the nuclear region (e.g., Elitzur 2006; Schartmann et al. 2009), additional support for this conclusion comes from spectroscopic observations of 10 μm silicate in Seyfert galaxies. It is understood that significant silicate absorption requires the radiation source be deeply embedded in dust that is both optically and geometrically thick (e.g., Levenson et al. 2007). Strong silicate absorption therefore suggests that a fairly uniform thick shell of gas and dust surrounds a compact starburst or AGN. On the other hand a medium that consists of clouds illuminated from the outside will not produce silicate absorption since there is no strong temperature gradient across the clouds leading to a relatively constant dust temperature. Hao et al. (2007) and Deo et al. (2007) found that only a small fraction of Seyferts have deep silicate absorption (seven out of 61 Seyfert galaxies, six of which are type 2s). The lack of silicate absorption in most Seyfert galaxies (Shi et al. 2006; Spoon et al. 2007; Uddin et al. 2007; Thompson et al. 2007) is interpreted to mean that the gas and dust is clumpy. Moreover, Deo et al. (2007) find that the few Seyfert with deep silicate absorption are either highly inclined or merging systems, suggesting that the spectral feature arises in a cool dusty region on scales of tens of parsecs or greater.

Marr et al. (1993) find that in our own Galaxy the molecular gas in the central tens of parsecs is confined to virial clumps with sizes of order 0.1 pc and densities of 10⁶ cm⁻³. Similarly, Christopher et al. (2005) find numerous dense cores with typical diameters of 0.25 pc, densities of 3–4 × 10⁷ cm⁻³, and masses of ∼2 × 10⁴ M_☉. With such high densities, these clouds are stable against tidal disruption and have long lifetimes (∼10⁷ yr). In addition to these virial estimates, similar cloud densities are also derived from multitransition modeling (Jackson et al. 1993) and are also found for clouds in the central 30 pc of Seyferts using analytical modeling (Vollmer et al. 2008). If we assume that all of the molecular gas in the observed Seyfert galaxies is composed of clouds with properties similar to those seen in the Galactic Center (0.25 pc diameter, ∼2 × 10⁴ M_☉), then there must be about 500 clouds within a radius of 30 pc for a gas mass of ∼10⁷ M_☉. This results in only a ∼1% chance that a given line of sight will be blocked by a cloud, and considering the full range of f_g values of 1%–20%, the chance of obscuration by a cloud is 0.1%–2%. These results are qualitatively in agreement with the small fraction of Seyferts that show deep silicate absorption. However, this is an extreme case in which all of the gas is assumed to be within dense clumps. Since the reddened stellar continuum in these galaxies implies significant extinction, it is likely that in addition to dense clouds of gas there is a nonnegligible fraction of the nuclear gas in a diffuse component.

In half of the sample galaxies (four of eight), the extinction of the nuclear star formation derived in Section 3.4.2 implies gas column densities greater than the 10²² cm⁻² required to obscure the optical and UV emission from the AGN and its associated BLR (Risaliti et al. 1999; Treister et al. 2004). Of note is that the Seyfert 2 galaxy Circinus (and NGC 1068, which has been excluded from the analysis of H₂; see Section 3) falls within this group of obscured AGNs. In another two galaxies, the derived column densities are N_H ∼ 10²² cm⁻², but considering the estimated errors it is uncertain if the densities are enough to obscure AGN emission. The column densities of the remaining two galaxies are below the threshold for obscuring the AGN. The additional clumpy component of dense gas implied by the high gas masses derived from the H₂ kinematics (Section 3.4) is, as discussed in Section 3.5, unlikely to significantly contribute to obscuration of the AGN since only a few percent of the lines of sight will encounter a gas clump. We therefore conclude that in approximately half of the Seyfert galaxies observed the column density along lines of sight that pass through the molecular gas detected on scales of tens of parsecs will be great enough to obscure the central AGN.

As discussed in Sections 3.3 and 5, the high velocity dispersion and radial profile of the molecular gas on the scales observed suggests that the molecular gas disk in Seyfert galaxies is vertically thick due to bulk motion of the gas, and thus some fraction of the lines of sight will pass through this disk. Observations of the space density of Seyfert 1s (unobscured) versus Seyfert 2s (obscured) suggest that the half-opening angle of the torus predicted by popular AGN unification schemes is 39°–48° (Osterbrock & Martel 1993; Rush et al. 1996; Schmitt et al. 2001; Hao et al. 2005), implying that z_o/r ∼ 0.9–1.3. The disk heights derived in Section 3.3 are consistent with this prediction with an estimated average z_o/r of 1.3 ± 0.2. This fraction is unchanged if only those galaxies for which N_H > 10²² cm⁻² are considered. Therefore, if the molecular disks observed on scales of tens of parsecs are capable of obscuring AGN emission (as half of the galaxies observed suggest), then the derived disk heights imply the fraction of Seyferts observed through the thick obscuring disk is consistent with the observed space densities of Seyfert 1s and 2s.

Since the observed properties of the nuclear molecular gas suggest a rotating, geometrically thick, clumpy, gas disk, we conclude that in Seyfert galaxies the gas on scales of tens of parsecs is likely to be associated with the smaller scale torus invoked in AGN unification models. This clumpy disklike structure is consistent with the radii predicted by models of clumpy tori (e.g., Cameron et al. 1993; Schartmann et al. 2005, 2008, 2009; Honig et al. 2006; Fritz et al. 2006). Given the estimated column densities, it is also possible that the gas on these scales plays a role in obscuring the AGN. While there is evidence that obscuring material exists at smaller scales than the ∼20 pc scales probed here (e.g., Greenhill et al. 2003; Jaffe et al. 2004; Tristram et al. 2007), we would argue that the molecular gas measured reveals the larger scale extended structure of the nuclear obscuring material. Although it is most likely that the smaller scale torus component is largely responsible for obscuring the AGN, and other functions such as collimation of ionization cones, the contribution of the extended structure to AGN obscuration can be significant. Furthermore, clumpy torus models predict similar additional larger scale structures. For example, Schartmann et al. (2009) find that a clumpy torus consisting of a dense compact (∼5 pc) component embedded in a more extended and diffuse component (∼50 pc) is required to match the observed spectral energy distributions of Seyfert galaxies. In addition, the alignment of the clumpy disklike structure with the large-scale orientation of the host galaxy disk is consistent with evidence that Seyfert galaxies are likely to fuel their AGN via secular processes rather than by the major mergers that are thought to trigger the fueling of higher luminosity quasars (e.g., De Robertis et al. 1998; García-Burillo et al. 2005).

As shown by a detailed analysis of the SINFONI subsample of Seyfert galaxies in D07, as well as by other studies of mostly Seyfert 2 galaxies (e.g., González Delgado et al. 2001; Cid Fernandes et al. 2004; Riffel et al. 2007), recent nuclear star formation is associated with the AGN activity. Since the star formation measured on scales similar to the H₂ distribution is likely to have been Eddington limited (D07), it is inevitably short-lived. This implies that the star formation may be episodic in nature with multiple short bursts, the frequency of which would be dependent on the variability of the inflow of gas to the nuclear region (central ∼100 pc). With the typical velocity, velocity dispersion, and M_gas values observed (e.g., 75 km s⁻¹, 50 km s⁻¹, and 10⁷ M_☉, respectively), an inflow rate of ∼10 M_☉ yr⁻¹ is expected (Förster Schreiber et al. 2006). This is reasonable for a short time period, but is certainly not likely to be sustainable.

The correlation of the gas velocity dispersion with star formation that is shown in Figure 9 suggests that the height of the molecular gas disk is related to the state of the nuclear star formation. As discussed in Section 5, the disk height may be maintained by stellar radiation pressure (Thompson et al. 2005). It is also possible that the nuclear star formation and disk height are both dictated by the inflow rate into the nuclear region (Vollmer et al. 2008) and that stellar radiation pressure is a secondary effect. This later scenario is consistent with the clumpy nature of the gas (Section 3.5), since on these scales the gas is predicted to be in a geometrically thick, collisional disk that is dominated by compact clouds rather than a diffuse medium, and is thus transparent. Only immediately after a short, massive inflow of material into the central ∼100 pc would the structure be opaque, and this phase lasts for only ∼10 Myr. García-Burillo et al. (2008) suggest a possible triggering mechanism for this inflow event via the dynamical decoupling of a nuclear bar with respect to an outer bar, which results in significant gas inflow. In addition, they find in numerical simulations that gravitational torques combined with viscosity can result in recurrent episodes of inflow.

If the disk height is related to the state of the nuclear star formation and/or the inflow rate to the central ∼100 pc, we may expect that the thick molecular gas disks detected in the observed Seyferts is a dynamic structure. Each burst of gas inflow or star formation could increase the σ of the gas, resulting in a thickening of the disk. In contrast, when the inflow rate decreases and nuclear star formation is in a low intensity state, the σ of the gas would quickly decrease, allowing the gas to settle into a thin disk. In cases where the gas disk on these scales is capable of obscuring the AGN, as is the case in at least half of the observed Seyferts, a high state of inflow or star formation would result in an obscuring torus-like structure on scales of tens of parsecs and in a low state no obscuring medium on these scales would be present. In this case, the fraction of Seyfert 1s versus 2s would depend not only on orientation but also on the nuclear inflow rate and the level of star formation. This would imply that on average type 2 Seyferts have a higher rate of inflow into the nuclear region and/or a higher SFR per unit area out to radii of tens of parsecs. Unfortunately, it is not possible to rigorously test either of these predictions with the data currently available. The star formation properties on scales of tens of parsecs have been investigated in only a small number of Seyferts (e.g., D07), and the inflow rate into the nuclear region has been determined in even fewer AGNs, the majority of which are at most low luminosity Seyfert galaxies (e.g., García-Burillo et al. 2008). HST imaging studies have however, found that the central kpc of Seyfert 2 galaxies exhibit a more disturbed morphology (more twisting of the isophotes) than is seen in Seyfert 1 galaxies, which can be interpreted as a sign of a greater inflow rate (Hunt & Malkan 2004). It is important to note that obscuration of the AGN is also likely to occur on scales smaller than those probed here. Therefore, even if a state of low inflow and/or star formation leads to a thin disk on scales of tens of parsecs, and thus less probability of obscuration of the AGN, it is still possible for Seyfert 2-like properties to be observed.

NGC 1097 has an H₂ flux distribution that is centrally concentrated with an elongation in a roughly north–south direction and a peak flux coincident with both the K-band continuum and nonstellar emission. The distribution has an HWHM of 28.5 pc, which is resolved based on a spatial resolution determined from the nonstellar emission of 025, or 22 pc at the distance of NGC 1097. A Sérsic fit to the azimuthal average of the flux distribution gives a disklike fit with n = 1.5. The smoothness of the H₂ velocity field indicates there is no significant warp in the gas disk down to the smallest scales measured. The best-fit kinematic parameters to the gas velocity field are consistent with that of the stars, with a best-fit PA of −52° and an inclination of 42° given by the gas and PA of −49° and an inclination of 43° by the stars. The kinemetry fit to the gas velocity field reveal deviations from co-planar disk rotation of the order of 30 km s⁻¹ (greater than the ∼10 km s⁻¹ error of the velocity measurements) and outline a spiral structure. An investigation of the detailed kinematics in NGC 1097 will be presented in a future paper.

As reported by D07, the central stellar velocity dispersion decreases significantly, displaying what has become known as a "sigma-drop." Within the central 1'', the dispersion drops to 100 km s⁻¹ compared to a relatively constant value of 150 km s⁻¹ beyond this radius. Based on this sigma-drop, and evidence of recent star formation, the presence of a dynamically cold nuclear disk is suggested. The kinematics of the gas supports this in that the central σ and rotational velocity change within the central 1'' to more closely match that measured for the stars. The gas σ increases from an average of 45 km s⁻¹ outside of r = 05 to an average of 63 km s⁻¹ and a maximum of 74 km s⁻¹ at the nucleus (Figure 5 and Table 4). The offset of about 10 km s⁻¹ higher σ measured by ISAAC compared to that measured with SINFONI is due to blurring of the steep velocity gradient (∼300 km s⁻¹ in the central 2'') in the lower spatial resolution seeing-limited ISAAC data.

The dynamical mass derived from the gas kinematics is M_dyn = 9.5 × 10⁷ M_☉ at 30 pc, and is similar to the HWHM radius of 28.5 pc. This mass is lower by a factor of 1.4 than the dynamical mass determined from the stellar kinematics (D07), but is consistent when the velocity and σ errors of ± 10 km s⁻¹ are considered. The kinematics within this region is therefore dominated by the BH mass, which is estimated to be within the range of 4–12 × 10⁷ M_☉ (Lewis & Eracleous 2006). Although the H₂ velocity dispersion is not as significant in comparison to the rotational velocity as is seen in other galaxies in the sample (V_rot/σ reaches unity at a radius of 24 pc, only slightly greater that the spatial resolution), the disk height at a radius of 30 pc is still estimated to be comparable to the radial scale. The gas column density based on the M_dyn and the adopted f_g = 10% is above 10²³ cm⁻² out to over 150 pc, with N_H = 4.2 × 10²³ cm⁻² at 30 pc. Based on the cold molecular gas measured in CO (Hsieh et al. 2008), the gas mass fraction may be as low as 1.3% (Table 5), which lowers the column density to N_H = 5.5 × 10²² cm⁻² at 30 pc. The column density implied by the extinction of the stellar continuum based on the mixed model is 1.7 × 10²² cm⁻²  which is just above the 10²² cm⁻² limit of obscuring the AGN.

The flux distribution of the hot molecular gas in NGC 3227 is relatively complex compared to the other galaxies in the sample. The strongest H₂ 1-0 S(1) emission is not found at the location of the nucleus, but is instead distributed along a PA of −45° with peaks of emission 024 northwest and 035 and 081 southeast of the nucleus. Schinnerer et al. (2000a) also report that the strongest emission from the cold molecular gas, measured by CO on a larger scale of 06, is not coincident with the nucleus. The azimuthal average of this complex emission structure peaks at a radius of about 013. The azimuthal average of the OSIRIS data differs from that measured with SINFONI because of the FOV coverage (Figure 11). The OSIRIS data only covers east of the nucleus, and therefore does not include the northwest emission knot, which largely is responsible for the off-center emission peak of the full FOV azimuthal average measured with SINFONI. For this reason, the properties derived from the SINFONI data are taken to be more representative of the full nuclear region in NGC 3227.

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With an azimuthal average, it is of course not possible to represent the complex emission structure seen in NGC 3227, and a Sérsic fit to the averaged distribution at the radii of the nonsymmetric emission is thus of limited value. We therefore fit a Sérsic function to the azimuthally averaged flux distribution beyond the radii effected by the knots of emission, and the HWHM of the observed distribution can then be estimated from an extrapolation of this fit. For the SINFNOI data a fit is preformed to the fall in emission beyond the peak at 013 (10 pc), and a best fit is found with n = 1.76. The OSIRIS data are fit outside a radius of 039 (30 pc), which is beyond the majority of the bright emission knots and most likely represents the more extended emission. The best fit in this case is found with a n = 1.16 Sérsic function. The HWHMs of the extrapolated Sérsic fits are 29.3 pc and 34.9 pc for the SINFONI and OSIRIS data, respectively. For comparison, the HWHM of the azimuthally averaged observed distribution measured with OSIRIS is 60.9 pc with respect to the nucleus and 28.1 pc with respect to the peak of the distribution. These HWHM estimates, both the observed values and those determined from the Sérsic fits, are well resolved based on the spatial resolution given by the broad Brγ emission, which for the SINFONI data is 0085 (7 pc) and for the OSIRIS data is 007 (6 pc).

Despite the complexity of the H₂ flux distribution, the kinematics of the molecular gas is fairly regular. The best-fit inclination and PAs of the gas disk determined from the SINFONI and OSIRIS data are consistent, with i = 50°–60° and PA = −30 to −45°. These disk parameters are in agreement with the best fit to the stellar kinematics of i = 55°–60° and PA = −45°, as well as with the large-scale galactic disk (de Vaucouleurs et al. 1991). As discussed in Davies et al. (2006), the majority of the gas is in uniform rotation, with only the weak emission along the minor axis showing signs of nonrotational motions, possibly an outflow. The kinemetry fit shows deviations from co-planar disk rotation along the minor axis on the order of ∼30 km s⁻¹ (compared to the ∼10 km s⁻¹ error of the velocity measurements). The velocity dispersion is rather high, with an average value of ∼86 km s⁻¹ within r = 05 (94 km s⁻¹ measured with SINFONI and 77 km s⁻¹ measured with OSIRIS). The velocity field, as well as the velocity dispersion, is comparable to that measured for the stars in the nuclear region, with a maximum difference of 25 km s⁻¹ along the minor axis. A comparison of the azimuthally averaged velocity and velocity dispersion as measured with SINFONI and OSIRIS is shown in Figure 11.

The gas kinematics indicate that M_dyn = 20 × 10⁷ M_☉ at a radius of 30 pc. Modeling of the H₂ 1-0 S(1) kinematics suggests that NGC 3227 has a BH of 2.0^+1.0_−0.4 × 10⁷ M_☉ (Hicks & Malkan 2008), and modeling of the stellar kinematics gives a mass estimate of 0.7–2.0 × 10⁷ M_☉ (Davies et al. 2006), therefore the BH is not a significant fraction of the dynamical mass measured. The H₂ velocity dispersion is greater than the inclination-corrected rotational speed out beyond 30 pc, suggesting that the gas is in a thick disk ∼45 pc high at 30 pc from the nucleus. Although measurements of the cold molecular gas detected with CO (2-1) show that V_rot/σ greater than one outside of 1'', even the cold gas has a significant velocity dispersion of 60 km s⁻¹ inside of this radius (Table 5; Schinnerer et al. 2000a). Assuming f_g = 10% (which is consistent with estimates derived from CO observations; Table 5), and that this gas is uniformly distributed, the average gas column density inside of 30 pc is estimated to be ∼9 × 10²³ cm⁻². Based on the stellar extinction a mixed model suggests that the column density is 1.9 × 10²² cm⁻², which is well over an order of magnitude lower than that derived from the dynamical mass, suggesting that the majority of the nuclear gas is in a clumpy distribution.

A more detailed analysis of the stellar and gas kinematics in NGC 3227 is presented in Davies et al. (2006) and Hicks & Malkan (2008).

The H₂ 1-0 S(1) flux distribution in NGC 3783 is centrally concentrated and the strongest emission is consistent with the nucleus location. The observations of NGC 3783 have a spatial resolution (based on both the nonstellar emission and the broad Brγ emission) of 018, which is equivalent to 36 pc at the galaxy distance. A Sérsic fit to the azimuthally averaged light distribution gives a best fit with n = 1.85 and the azimuthally averaged light profile has an observed HWHM of 20.2 pc.

The H₂ kinematics can reliably be measured out to only about 1'' (equivalent to 200 pc). The velocity field is relatively regular, with a best-fit PA of −15°, and inclination of 35°. Over the central 05 less than 4% of the K-band continuum is stellar (D07), which prevents a reliable measurement of the stellar kinematics, and thus no comparison with the gas kinematics is possible. A comparison to the K-band photometry (Mulchaey et al. 1997) indicates that the gas kinematics is consistent with the large-scale isophotes, suggesting that there is no warp in the gas disk.

At a radius of 30 pc, a dynamical mass of M_dyn = 2.8 × 10⁷ M_☉ is derived from the gas kinematics, and at the observed HWHM of 20.2 pc M_dyn = 1.6 × 10⁷ M_☉. Based on the mass estimated from reverberation mapping (Peterson et al. 2004), the central BH has a mass comparable to the dynamical mass within a radius of 30 pc and therefore it likely dominates the kinematics. The disk height is estimated to be similar to the radial scale, with a vertical scale of 40 pc at a 30 pc radius. The gas column density in NGC 3783 (assuming f_g = 10%) is a bit lower than estimated for the other galaxies in the sample, but is still above 10²³ cm⁻² out to a radius of ∼70 pc and is 1.3 × 10²³ cm⁻² at 30 pc. The stellar extinction implies N_H = 5.3 × 10²² cm⁻², which is still high enough to obscure the AGN.

In NGC 4051, the H₂ flux distribution is symmetric and centrally concentrated at a location coincident with the nonstellar emission. The observed azimuthally averaged HWHM is 7.6 pc, which is just barely resolved based on the spatial resolution determined from the nonstellar emission of 012, or 6 pc at the distance of NGC 4015. The best fit to the azimuthally averaged flux distribution is a n = 1.8 Sérsic function.

The measured velocity field is consistent with uniform disk rotation without any indication of a warp down to the smallest scales measured, but the limited FOV and relatively low signal-to-noise ratio of these data do not constrain the kinematics as well as in the other galaxies. The best fit to the H₂ kinematics suggests a disk with i = 50° and PA = 5°. At a radius of 30 pc the V_rot/σ ratio is 0.83 and a disk height of z_o = 41 pc is derived from the kinematics. The dynamical mass within this radius is 5.0 × 10⁷ M_☉  and, based on the reverberation mapped M_BH estimate of 0.2 × 10⁷ M_☉ (Peterson et al. 2004), the M_BH does not dominate the kinematics on these scales. The derived gas column density within r = 30 pc (assuming f_g = 10%) is then 2.2 × 10²³ cm⁻² and remains above 10²³ cm⁻² within the measured FOV. Unlike all other galaxies in the sample, there is very little extinction of the nuclear stars with a mixed extinction model predicting at most A_V = 1 mag.

The H₂ flux distribution in the nuclear region of NGC 4151 is relatively complex due to knots of emission along a PA of roughly 90°. As noted by Hicks & Malkan (2008), several of these knots are coincident with radio emission associated with a nuclear jet (e.g., Mundell et al. 2003). Underlying these knots of emission is a component of extended H₂ emission that is centrally peaked at the location of the nonstellar emission. We do not attempt to examine the bright knots of emission further in this paper, and exclude them from the azimuthal average by only considering flux below 25% of the peak. Furthermore, H₂ is not well detected in the central 02, and this region is binned to obtain a reliable measure of the central flux and kinematics. Unfortunately, a treatment of the bright emission knots such as that carried out for NGC 3227 is not possible because the knots extent throughout the measured FOV. The azimuthally averaged flux distribution of the extended H₂ emission has an observed HWHM of 28.1 pc and is best fit with an n = 1.3 Sérsic function. If instead all of the emission is considered in the azimuthal average, then there are two additional peaks at ∼04 and 07 due to knots of emission on either side of the nucleus at these radii. In Figure 4, this radial profile (smaller diamonds with dashed error bars) can be compared with that of the diffuse emission (solid diamonds and error bars). Based on the nonstellar emission, the spatial resolution of these NGC 4151 data is 011, or 7.5 pc at the distance of NGC 4151.

The underlying H₂ emission has a velocity field suggestive of uniform disk rotation with a best-fit of PA = 10° and i = 45°, which is consistent with the kinematics of the stars in the nuclear region and roughly consistent with the large-scale galactic rotation (de Vaucouleurs et al. 1991). Coincident with the knots of bright emission mentioned above are patches of velocity inconsistent with co-planar circular rotation, with residuals on the order of ∼30 km s⁻¹. This deviation from rotation is not surprising if indeed the knots of emission are associated with the radio jet. The velocity dispersion throughout the measured FOV is ∼55 km s⁻¹, and is greater than the inclination-corrected rotational velocity out to a radius of about 20 pc, beyond which V_rot/σ rises steadily above unity. The kinematics at this radius implies a disk height of z_o = 33 pc and a dynamical mass of 14.0 × 10⁷ M_☉, suggesting that the central BH does not dominate the kinematics at this radius based on the estimated BH mass (Hicks & Malkan 2008; Peterson et al. 2004). The gas column density remains above 10²³ cm⁻² out to the edge of the FOV and is estimated to be 6.2 × 10²³ cm⁻² at a radius of 30 pc, assuming f_g = 10%. A column density of an order of magnitude less is predicted by fitting a mixed extinction model to the stellar continuum. The extinction suggests that N_H = 2.8 × 10²² cm⁻², which is still high enough to obscure the AGN.

The H₂ emission detected in NGC 6814 is nearly symmetric and peaks at the AGN location of the nonstellar emission. With a spatial resolution of 017 (18 pc), the observed HWHM of the azimuthally averaged distribution is measured to be 34.8 pc. Fitting a Sérsic function indicates a disklike distribution with n = 1.04.

Like the other galaxies in the sample, NGC 6814 exhibits regular rotation indicative of uniform disk rotation. The best fit to the gas kinematics suggests a disk with i = −40° and PA = 55°, which is consistent with results from fitting the stellar kinematics. The velocity dispersion is greater than the inclination-corrected rotational velocity out to the point where a reliable fit can no longer be obtained at about 05. At a radius of 30 pc, the disk height based on the kinematics is estimated to be comparable to the radial distance with z_o = 46 pc. The dynamical mass at this radius is 4.2 × 10⁷ M_☉, a quarter of which is estimated to be mass attributable to the central BH (Wandel 2002). The derived gas column density is greater than 10²³ cm⁻² to a radius of 40 pc, with N_H = 1.9 × 10²³ cm⁻² at 30 pc assuming f_g = 10%. The stellar extinction in this galaxy is relatively low, with an implied column density of only N_H = 5.7 × 10²¹ cm⁻². This estimate is well over an order of magnitude lower than derived from the dynamical mass, suggesting that the majority of the gas in this galaxy, on scales of tens of parsecs, is in a clumpy distribution.

The H₂ 1-0 S(1) flux distribution in NGC 7469 is very symmetric with a peak coincident with both the nonstellar and stellar emission. The spatial resolution of the SINFONI data is estimated from the nonstellar continuum to be 015, which is 48 pc at the distance of NGC 7469. The azimuthal average of the SINFONI observed distribution has an HWHM of 77.4 pc, and a fit to the azimuthal average finds a Sérsic n = 1.3 distribution. The OSIRIS data have a higher spatial resolution of 011, equivalent to 35 pc, and for this reason the properties measured from the OSIRIS data are taken to be more accurate, although, with the exception of the observed flux HWHM, the measured and derived properties from both data sets are consistent. The observed HWHM of the azimuthally averaged flux distribution measured with OSIRIS is 30.8 pc and a best fit to the flux profile is found with a Sérsic n = 1.98 distribution. A comparison of the azimuthally averaged flux distribution measured with OSIRIS and SINFONI, as well as that of the velocity and velocity dispersion, is shown in Figure 12.

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The H₂ velocity field is suggestive of uniform rotation, with no indication of a significant warp in the gas disk down to the smallest scales measured. The gas kinematics is best fit with i = 50° and PA = −40° in the SINFONI data, in comparison to i = 30° and PA = −48° in the higher spatial resolution OSIRIS data. These results just barely agree to within the expected ± 10° errors of the measurements, and both agree with the fit to the nuclear stellar kinematics and with the larger scale gas disk measured in CO (Davies et al. 2004b). The velocity dispersion is about 60 km s⁻¹ in the center and rises as high as 89 km s⁻¹ at r = 05. This dispersion in velocity is greater than the (inclination-corrected) rotational velocity in the central 029, and V_rot/σ remains near unity out to at least 1''. The kinematics implies a disk height of about 43 pc at a radius of 30 pc. The dynamical mass derived from the gas kinematics gives M_dyn = 10.1 × 10⁷ M_☉ within r = 30 pc, and assuming f_g = 10%, the derived gas column density within 30 pc is 4.2 × 10²³ cm⁻². Based on CO observations of the cold molecular gas (Table 5; Davies et al. 2004b), the gas mass fraction is likely to have a significantly higher value of ∼60%, suggesting an average gas column density of 2.4 × 10²⁴ cm⁻² out to a radius of 30 pc. A mixed extinction model also suggests column densities high enough to obscure the AGN, with N_H ∼ 5 × 10²² cm⁻². This column density is still an order of magnitude or more lower than implied by the dynamical mass, suggesting that a significant fraction of the nuclear gas is distributed in clumps rather than uniformly.

The H₂ 1-0 S(1) emission in Circinus is symmetric with a peak coincident with that of the K-band continuum. The HWHM of the azimuthally averaged light profile is 7.4 pc, observed with a spatial resolution of 022, or 4.2 pc at the galaxy distance. The light profile is best fit with a n = 1.1 Sérsic function. The H₂ velocity field suggests uniform rotation, with the exception of a region at the western edge of the FOV at 9 pc, which is most likely associated with the ionization cone. A gas disk is best fit to the kinematics with a PA of 30° and an inclination of 55°. Within the errors, these parameters agree with the large-scale optical photometry (PA = 20° and inclination of 65°; Freeman et al. 1977), suggesting that there is no warp down to at least a few parsecs (there is evidence of a warp on much smaller scales of 0.1–0.4 pc; Greenhill et al. 2003).

The dynamical mass is estimated to be M_dyn = 1.9 × 10⁷ M_☉ within 9 pc, and M_dyn = 1.8 × 10⁷ M_☉ within the HWHM radius of 7.4 pc. Based on this M_dyn and assuming a gas fraction of 10%, the gas column density within 9 pc is 9.4 × 10²³ cm⁻², and increases to 1.3 × 10²⁴ cm⁻² within the HWHM radius. The stellar continuum is heavily obscured in this galaxy, consistent with its classification as a Seyfert 2. A mixed extinction model implies column densities of N_H = 4.3 × 10²² cm⁻², which is high enough to obscure the AGN. This estimate is still over an order of magnitude lower than that derived from the dynamical mass, suggesting a clumpy medium. The velocity dispersion is relatively constant throughout the FOV measured (σ ∼ 56 ± 3 km s⁻¹ for r < 05; Table 4) and the rotational velocity to σ ratio is relatively low with V_rot/σ only reaching 0.7 at the edge of the FOV. At this radius, the disk height is estimated to be 13 pc, and a height of 11 pc is estimated at the HWHM radius.

A detailed analysis of the nuclear region of Circinus, including the H₂ properties as measured with SINFONI, is presented in Müller Sánchez et al. (2006).

NGC 1068 has the most complex H₂ 1-0 S(1) properties of any of the galaxies in the sample and is discussed in detail in Müller Sánchez et al. (2009). Within the central 1'', there are two knots of H₂ emission, one coincident with the nucleus and another to the north, and there is no detectable H₂ emission in the southwest. An azimuthal average of this distribution gives an observed HWHM of 13.2 pc and a Sérsic fit finds n = 2.09, although, like in NGC 3227, these values obviously do not reflect the two-dimensional nature of the nuclear H₂ distribution. The nuclear stars are heavily obscured in this galaxy, and even after correcting for contamination from the nonstellar continuum, the extinction is so great that it is beyond the saturation limit of a mixed extinction model (which is at an optical depth of a few). The spatial resolution based on the nonstellar emission is 008, equivalent to 5 pc at the distance of NGC 1068.

Noncircular motions dominate the H₂ kinematics, and Müller Sánchez et al. (2009) argue that streaming of the gas toward the nucleus is suggested. This should therefore be kept in mind when evaluating the azimuthally averaged rotational velocity and σ shown in Figure 3. Because the H₂ properties in NGC 1068 so greatly differ from the disk rotation seen in the stars, unlike the consistency seen in the other sample galaxies, this galaxy is not included in the analysis of general H₂ properties in AGNs. This galaxy therefore represents an exception to the general conclusions presented.