THE INFRARED NUCLEAR EMISSION OF SEYFERT GALAXIES ON PARSEC SCALES: TESTING THE CLUMPY TORUS MODELS

The unified model for active galaxies (Antonucci 1993; Urry & Padovani 1995) explains the observed differences between Type-1 and Type-2 objects as due to orientation. Although the unification model may not be universally applicable, the most accepted scheme is that there is dust surrounding the central region of active galactic nuclei (AGNs) distributed in a toroidal geometry (Pier & Krolik 1993; Granato & Danese 1994; Efstathiou & Rowan-Robinson 1995; Granato et al. 1997). Thus, the central engines of Type-1 AGNs can be seen directly, resulting in typical spectra with both narrow and broad emission lines coming from the narrow-line region (NLR) and the broad-line region (BLR), respectively. In Type-2 AGNs, the active nucleus and the BLR are obscured by an optically and geometrically thick dusty torus, which explains the lack of broad lines in their observed spectra. The torus dust grains absorb ultraviolet photons from the central engine and re-radiate them in the infrared (IR), peaking at mid-IR wavelengths (7–26 μm).

Pioneering work in modeling dusty tori was performed by Pier & Krolik (1992). They assumed a uniform dust density distribution of a few parsecs radial extent. However, in order to better reproduce the observations, Pier & Krolik (1993) enlarged the torus, e.g., to account for the far-IR emission. Thus, the coolest material in the torus must be located far from the central engine, implying ∼100 pc scale tori. Further investigations with smooth dust distributions were carried out by Granato & Danese (1994), Efstathiou & Rowan-Robinson (1995), Granato et al. (1997), and Siebenmorgen et al. (2004a).

However, recent ground-based mid-IR observations of nearby Seyferts reveal that the torus size is likely restricted to a few parsecs. For example, Packham et al. (2005) and Radomski et al. (2008) established upper limits of 2 and 1.6 pc for the outer radii of the Circinus galaxy and Centaurus A tori, respectively, using data from the Gemini Telescopes. Additionally, interferometric observations obtained with the MID-infrared Interferometric Instrument (MIDI) at the Very Large Telescope Interferometer (VLTI) of Circinus, NGC 1068, and Centaurus A suggest a scenario where the torus emission would only extend out to R = 1 pc (Tristram et al. 2007), R = 1.7–2 pc (Jaffe et al. 2004; Raban et al. 2009), and R = 0.3 pc (Meisenheimer et al. 2007), respectively.

Thus, during the last decade, an intensive search for an alternative geometry to the early homogeneous torus models has been carried out in order to explain the observations. Before Pier & Krolik (1992, 1993) publications, Krolik & Begelman (1988) claimed that smooth dust distributions cannot survive within the AGN vicinity. They proposed that the material in the torus must be distributed in a clumpy structure, in order to prevent the dust grains from being destroyed by the hot surrounding gas. The first results of radiative transfer calculations of a clumpy medium were reported by Nenkova et al. (2002), and further work was done by Dullemond & van Bemmel (2005), Fritz et al. (2006), Elitzur & Shlosman (2006), and Ballantyne et al. (2006).

Thus, the clumpy dusty torus models (Nenkova et al. 2002, 2008a, 2008b; Hönig et al. 2006; Schartmann et al. 2008) propose that the dust is distributed in clumps, instead of homogeneously filling the torus volume. These models are making significant progress in accounting for the mid-IR emission of AGNs. A fundamental difference between clumpy and smooth density distributions of dust is that the former implies that both directly illuminated and shadowed cloud faces may exist at different distances from the central engine. Thus, the dust temperature is not a function of the radius only, as was the case in the homogeneous models, since illuminated and shadowed clouds contribute to the IR emission from all viewing angles. Homogeneous torus models had serious difficulties in predicting the observed differences in the variety of spectral energy distributions (SEDs; Spinoglio & Malkan 1989; Fadda et al. 1998; Kuraszkiewicz et al. 2003; Alonso-Herrero et al. 2003; Rigby et al. 2004) and the strengths of the 10 μm silicate feature in both Seyfert 1 and Seyfert 2 nuclei (Roche et al. 1991; Granato et al. 1997; Mason et al. 2006), and also the large optical depths along the line of sight indicated by X-ray observations (Simpson et al. 1994; Tozzi et al. 2001). Inhomogeneous torus models solve these problems. The clumpy models have been employed in several observational studies, e.g., the first Spitzer analysis of AGN in the GOODS fields (Treister et al. 2004), and in the analysis of the 10 μm spatially resolved spectra of NGC 1068 and NGC 2110 nuclei (Mason et al. 2006, 2009).

Since the reprocessed radiation from the torus is re-emitted in the IR, this range (especially the mid-IR) is key to put constraints on the clumpy dusty torus models. In comparing the predictions of any torus model with observations, the small-scale torus emission must be isolated. Large aperture data (i.e., images with angular resolutions larger than 1–15, such as those provided by ISO, IRAS, or Spitzer) are strongly contaminated with emission from the host galaxy. For example, starburst emission is an important source of IR flux in the majority of AGNs (Netzer et al. 2007; Barmby et al. 2006; Polletta et al. 2007; Ramos Almeida et al. 2009). Mason et al. (2006) found for NGC 1068 that all flux measurements within apertures smaller than 05 were well fitted by the models, whereas larger aperture fluxes were much higher and presented a different spectral shape in the mid-IR. This excess of emission could be due to nearby dust outside the torus, that is also emitting in the IR (see, e.g., Roche et al. 2006). Mason et al. (2006) concluded for NGC 1068 that the torus contributes less than 30% of the 10 μm flux within apertures larger than 1''. The bulk of this large-aperture flux comes from dust in the ionization cone, which occupies a larger volume than the torus dust.

At shorter IR wavelengths (∼1–2.2 μm), the flux contained in apertures of a few arcseconds partly comes from the torus and partly from stellar emission. Alonso-Herrero et al. (1996) found that for Seyfert 2 galaxies (Sy2) the fluxes obtained within a 3'' aperture are dominated by stellar emission in the near-IR, out to ∼2 μm. Indeed, Kotilainen et al. (1992) found for a complete sample of Seyfert galaxies, most of them Seyfert 1 (Sy1), that starlight contributes significantly to the nuclear emission in the near-IR (J, H, and K bands), even within a small projected aperture (of 3''). Consequently, high angular resolution observations at these wavelengths are crucial to separate the pure nuclear emission from that of the host galaxy, which contaminates or hides the AGN emission.

The optimal way to estimate near-IR nuclear fluxes uncontaminated by star formation, in as much as possible, is the use of either subarcsecond spatial resolution data (e.g., from the Hubble Space Telescope (HST) or adaptive optics) or high spatial resolution ground-based data, extracting the nuclear emission in a proper manner (e.g., using point-spread function (PSF) subtraction). In the mid-IR, it is necessary to isolate the torus emission from that produced by dust in the ionization cones or dust heated by intense star formation. With various high-resolution SEDs covering the near- and mid-IR ranges, it is possible to identify SED features that are attributable to the torus.

It is worth mentioning that mid-IR interferometry constitutes the most precise way of characterizing the torus structure using observations and comparing them with the torus models (e.g., Hönig et al. 2006). However, the signal-to-noise ratio (S/N) required for VLTI observations strongly restricts the number of observable sources to the nearest AGN only.

In this work, we report new high-resolution mid-IR imaging data for 18 nearby Seyfert galaxies, for which we have estimated nuclear mid-IR fluxes.⁷ We also compiled near-IR high spatial resolution fluxes from the literature to construct pure-nuclear SEDs. We have fitted these AGN SEDs with the clumpy dusty torus models of Nenkova et al. (2008a, 2008b) to constrain the parameters that describe the clumpy models when applied to Seyfert galaxies. Table 1 summarizes key observational properties of the sources in the sample. Section 2 describes the observations, data reduction, and compilation of near-IR fluxes. Section 3 presents the main observational results, and Section 4 presents the modeling results. We draw conclusions about the clumpy torus models and AGN obscuration in general in Section 5. Finally, Section 6 summarizes the main conclusions of this work.

2.1. Mid-IR Imaging Observations

Ground-based mid-IR high angular resolution observations of 18 nearby active galaxies were carried out over the past years for a variety of science drivers. We make use of this archive of data in this paper. Most of these sources are Type-2 Seyferts, but the sample also includes two Seyfert 1.9 (Sy1.9), one Seyfert 1.8 (Sy1.8), two Seyfert 1.5 (Sy1.5), and one Sy1 galaxy (see Table 1).

The first set of observations was obtained with the University of Florida mid-IR camera/spectrometer OSCIR, in 1998 December at the 4 m Blanco Telescope at Cerro Tololo Inter-American Observatory (CTIO) and in 2001 May at the Gemini-North Telescope. This instrument employs a Rockwell 128 × 128 pixel Si:As blocked impurity band (BIB) detector array, optimized for the wavelength range between 8 and 25 μm. On CTIO, the pixel scale is 0183, with a field of view (FOV) of 234 × 234, and the resolutions obtained were ∼1'' at both 10.7 and 18.2 μm. On Gemini North, OSCIR has a plate scale of 0089 pixel⁻¹ and a total FOV of 11'' × 11''. The achieved resolutions were ∼05 at 10.7 μm and ∼06 at 18.2 μm. Another set of observations was performed with the mid-IR camera/spectrograph T-ReCS (Thermal-Region Camera Spectrograph; Telesco et al. 1998) on the Gemini-South Telescope. T-ReCS uses a Raytheon 320 × 240 pixel Si:As IBC array, providing a plate scale of 0089 pixel⁻¹, corresponding to an FOV of 285 × 214. The resolutions obtained were 03–04 at 8.8 μm, ∼05 at 10.4 μm, and 05–06 at 18.3 μm. The last set of observations was made with the mid-IR camera/spectrograph Michelle (Glasse et al. 1997) on the Gemini-North Telescope. The Michelle detector is a Si:As IBC array with a format of 320 × 240 pixels. Configured in its imaging mode, Michelle has a 010 pixel⁻¹ plate scale, and the resolutions of our observations were ∼04 at 11.3 μm and ∼05 at 18.1 μm. This plate scale translates to an FOV of 32'' × 24''. A summary of the observations is reported in Table 2.

Table 2. Summary of Mid-IR Observations

					On-Source Time (s)		PSF FWHM
Galaxy	Filters	Instrument	Telescope	Observation Epoch	N Band	Q Band	N Band	Q Band
Centaurus A	Si2, Qa	T-ReCS	Gemini S	2004 Jan	2000	1550	030	053
Circinus	Si2, Qa	T-ReCS	Gemini S	2004 Feb	109	109	033	055
IC 5063	Si2, Qa	T-ReCS	Gemini S	2005 Jul	130	304	040	062
Mrk 573	N, Qa	T-ReCS	Gemini S	2003 Dec	217	217	036	054
NGC 1386	N, Qa	T-ReCS	Gemini S	2003 Dec	217	217	031	054
NGC 1808	N, IHW18	OSCIR	CTIO 4m	1998 Dec	300	300	094	102
NGC 3081	Si2, Qa	T-ReCS	Gemini S	2006 Jan	130	304	030	056
NGC 3281	N, Qa	T-ReCS	Gemini S	2004 Jan	260	455	034	058
NGC 4388	N', Qa	Michelle	Gemini N	2006 May	549	733	034	050
NGC 5728	Si2, Qa	T-ReCS	Gemini S	2005 Jul	130	304	035	056
NGC 7172	N	T-ReCS	Gemini S	2004 May	305	...	051	...
NGC 7582	N, IHW18	OSCIR	CTIO 4m	1998 Dec	250	250	076	099
NGC 1365	N, IHW18	OSCIR	CTIO 4m	1998 Dec	482	482	092	103
NGC 2992	N', Qa	Michelle	Gemini N	2006 May	730	1095	032	053
NGC 5506	N', Qa	Michelle	Gemini N	2006 Apr	546	729	036	051
NGC 3227	N'	Michelle	Gemini N	2006 Apr	300	...	039	...
NGC 4151	N, IHW18	OSCIR	Gemini N	2001 May	360	480	053	058
NGC 1566	Si2, Qa	T-ReCS	Gemini S	2005 Sep	152	304	030	053

Notes. Images were obtained in the 8.74 μm (Si2, Δλ = 0.78 μm at 50% cut-on/off), 10.36 μm (N, Δλ = 5.27 μm), and 18.33 μm (Qa, Δλ = 1.5 μm) filters with T-ReCS; in the 11.29 μm (N', Δλ = 2.4 μm) and 18.11 μm (Qa, Δλ = 1.9 μm) filters with Michelle; and in the 10.75 μm (N, Δλ = 5.2 μm) and 18.17 μm (IHW18, Δλ = 1.7 μm) filters with OSCIR.

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The standard chopping-nodding technique was used to remove the time-variable sky background, the telescope thermal emission, and the so-called 1/f detector noise. The chopping throw was 15'', and the telescope was nodded every 30 s. All data were reduced using in-house-developed IDL routines. The difference for each chopped pair for each given nodding set was calculated, and the nod sets were then differenced and combined until a single image was created. Chopped pairs obviously compromised by cirrus, high electronic noise, or other problems were excluded from any further reduction process.

Observations of flux standard stars were made for the flux calibration of each galaxy through the same filters. The uncertainties in the flux calibration were found to be ∼5%–10% at the N band and ∼15%–20% at the Qa band. PSF star observations were also made immediately prior to or after each galaxy observation to accurately sample the image quality. These images were employed to determine the unresolved (i.e., nuclear) component of each galaxy. The PSF star, scaled to the peak of the galaxy emission, represents the maximum contribution of the unresolved source, where we integrate flux within an aperture of 2'' for the Gemini data, and of 4'' for the CTIO data (NGC 1365, NGC 1808, and NGC 7582). The residual of the total emission minus the scaled PSF represents the host galaxy contribution. A detailed study of the extended near nuclear structures of the galaxies in our sample will be the subject of a forthcoming paper (J. T. Radomski et al. 2010, in preparation). We require a flat profile in the residual (for a realistic galaxy profile) and therefore reduce the scale of the PSF from matching the peak of the galaxy emission (100%) to obtain the unresolved fluxes reported in Table 3. Figure 1 shows an example of PSF subtraction at various levels (in contours) for the Sy2 galaxy NGC 4388 in the N' Michelle filter, performed following Radomski et al. (2002) and Soifer et al. (2003). The residual profiles from the different scales demonstrate the best-fitting result, scaled to 90% of the peak flux. The uncertainty in the unresolved fluxes determination from PSF subtraction is ∼10%–15%. Thus, we estimated the errors in the flux densities reported in Table 3 by adding quadratically the flux calibration and PSF subtraction uncertainties, resulting in errors of ∼15% at the N band and of ∼25% at the Qa band.

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Table 3. Unresolved Mid-IR Fluxes

	Level of PSF Subtraction		Flux Density (mJy)
Galaxy	N Band	Qa Band	N Band	Qa Band
Centaurus A	100%	100%	710	2630
Circinus	90%	90%	5620	12790
IC 5063	100%	100%	399	2790
Mrk 573a	100%	100%	177	415
NGC 1386	70%	70%	147	457
NGC 1808	40%	60%	227	560
NGC 3081	100%	50%	83	231
NGC 3281	80%	100%	355	1110
NGC 4388	90%	100%	195	803
NGC 5728a	100%	100%	25	184
NGC 7172	90%	...	68	...
NGC 7582	70%	50%	195	527
NGC 1365	90%	100%	321	640
NGC 2992	90%	90%	175	521
NGC 5506	100%	100%	873	2200
NGC 3227	100%	...	401	...
NGC 4151	90%	100%	1320	3200
NGC 1566a	100%	100%	29	117

Notes. The percentages of PSF subtraction level are reported in the employed filters (listed in Table 2). Errors in flux densities are dominated in general by uncertainties in the flux calibration and PSF subtraction (∼15% at the N band and ∼25% at the Qa band). ^aFor the galaxies Mrk 573, NGC 1566, and NGC 5728, aperture photometry was performed with the following aperture radii: 089, 045, and 062, respectively. These fluxes include the corresponding aperture corrections.

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For the galaxies that clearly appear spatially unresolved in our mid-IR images (Mrk 573, NGC 1566, and NGC 5728), aperture photometry was employed to derive their nuclear density fluxes (reported in Table 3). The rule for their calculation was to ensure that all the unresolved emission was collected in the chosen aperture, with the minimum contribution of foreground contribution as possible. Aperture correction was applied to these fluxes, employing the images of the corresponding standard stars in both N and Qa filters.

2.2. Compilation of Near-IR High Spatial Resolution Data

3.1. High Versus Low Spatial Resolution SEDs

3.2. Average Seyfert 2 SED

In order to derive general properties of Sy2 galaxies, which constitute the majority of our sample, we constructed an average Sy2 SED, considering only the highest angular resolution data to avoid as much as possible the stellar contamination. This average Sy2 template will be used to compare with the individual SEDs of the Sy2 analyzed in this work, and also with the intermediate-type Seyferts. Out of the 18 galaxies in total (see Table 1), there are 10 "pure" Type-2 Seyferts and two H ii/Sy2 composite objects. The rest of the sample consists of other Seyfert types (Sy1.9, Sy1.8, Sy1.5, and Sy1). For constructing the Sy2 average SED, we first excluded the composite objects and the intermediate-type Seyferts. Second, to ensure that we are collecting the best-measured non-stellar nuclear emission, we exclude galaxies with mid-IR data from the 4 m CTIO, because of their lower spatial resolution compared with that of the 8 m Gemini Telescopes. This restriction excludes NGC 1808 and NGC 7582. Indeed, these two galaxies are undergoing intense episodes of nuclear star formation, making it more difficult to isolate the AGN emission from that of the surrounding host galaxy. Finally, in the construction of the average template, we use only HST (NICMOS) and VLT (NACO) adaptive optics fluxes in the near-IR. This excludes NGC 3281, for which all the compiled data are ground-based, and a few points in the SEDs of some of the other galaxies (e.g., Mrk 573 and NGC 4388).

In the end, we have seven pure Sy2 for constructing the average template: Centaurus A, Circinus, IC 5063, Mrk 573,⁸ NGC 1386, NGC 3081, and NGC 4388. Their IR SEDs are shown in Figure 2. We normalize the SEDs at 8.8 μm in order to emphasize the comparison between the N- and both the H- and Q-band data points that provides useful information about the obscuration (see Section 5.1). The measured N/Q ratio for the average template is 0.23 ± 0.14, which is representative of the Sy2 in our sample.

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Thus, the average template is constructed with near- and mid-IR data having resolutions ≲06, to ensure the isolation of the torus emission. The best-sampled SED, Circinus, defines the wavelength grid, and we interpolated nearby measurements of the other six galaxies onto this scale. We did not interpolate the sparse observations of IC 5063 and NGC 3081. The interpolated fluxes were used solely for the purpose of deriving the average Sy2 SED template, shown in Figure 2. The error bars correspond to the standard deviation of each averaged point, except for the 8.8 μm point (the wavelength chosen for the normalization). In this case, we assigned a 15% error, the nominal percentage considered for the N-band flux measurements.

3.3. Type-2 Seyfert SEDs

3.4. Intermediate-type Seyfert SEDs

The Sy1.5, Sy1.8, and Sy1.9 galaxies were added by Osterbrock (1981) to the Seyfert classification scheme to account for those galaxies with weaker featureless continua, larger broad Balmer decrements, and weaker broad components of the permitted lines than Type-1 Seyferts. Osterbrock (1981) suggested that the observed characteristics of these intermediate Seyferts could be due to the reddening of both the continuum and the BLR by dust. Alonso-Herrero et al. (2003) found for the CfA Seyfert sample that the majority of galaxies optically classified as Sy1.8 and Sy1.9 display either IR spectral indexes and SEDs similar to those of Sy1 or intermediate between Sy1 and Sy2. For the Sy1.5, Alonso-Herrero et al. (2003) found the SEDs to be practically identical to those of Sy1.

Figure 3 shows the SEDs of the five intermediate-type Seyferts considered in this work (two Sy1.5, one Sy1.8, and two Sy1.9), together with the mean Sy2 template for comparison, interpolated onto the mean Sy2 wavelength grid. Spectral indexes are reported in Table 5. The spectral slopes of the intermediate-type Seyferts are shallower than those of the Sy2 (mean slope α_IR = 2.0 ± 0.4 for Sy1.8 and Sy1.9 and α_IR = 1.6 ± 0.3 for Sy1.5, as opposed to 3.1 ± 0.9). Alonso-Herrero et al. (2003) report IR spectral indices (from 1 to 16 μm) of types 1.8 and 1.9 similar to our measurements (α^Alonso_IR = 1.8–2.6), and within the interval α^Alonso_IR = 1.5–1.6 for Sy1 and Sy1.5 galaxies. The steepest SED among the intermediate-type Seyferts is in the Sy1.9 NGC 2992, which is more similar in shape to the Sy2 SEDs. This result could be due to an incorrect or genuinely changed classification of this galaxy, as Trippe et al. (2008) claim (see the Appendix).

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The near-IR slopes of the Sy1.8 and Sy1.9 have intermediate values between those of Sy2 and Sy1.5, with α_NIR > α_MIR. For the Sy1.5 galaxy NGC 4151, α_NIR < α_MIR, indicating the importance of the hot dust contribution in the SEDs of this type of nucleus.

The H/N and N/Q flux ratios show comparable differences among Seyfert types (Table 5). The H/N ratio is larger for Sy1.5 (0.05 ± 0.04) than for Sy2 (0.003 ± 0.002 for the average template). The N/Q ratios of the intermediate-type Seyferts are also larger than those of Sy2 (mean values of 0.41 ± 0.08 for Sy1.8 and Sy1.9 and 0.41 ± 0.06 for Sy1.5, as opposed to 0.23± 0.14).

In summary, the slope of the IR SED is in general correlated with the Seyfert type. Sy2 show steeper SEDs, and intermediate-type Seyferts are flatter. Seyferts 1.8 and 1.9 present intermediate values of the IR slope and H/N ratio between Sy2 and Sy1.5. However, we find a range of spectral shapes among the Sy2 galaxies, and some intermediate-type SEDs have the same slopes as the Sy2. This cannot be reconciled with the predictions of early torus models, since large optical depth homogeneous tori strictly predict steep SEDs for Sy2 and flat SEDs for Sy1. We do not observe such a strong dichotomy (see also Alonso-Herrero et al. 2003). Torus models using lower opacities are observationally discarded (Section 3.3) and models including an extended conical component do not seem adequate for being applied to our high spatial resolution data. Thus, we pursue clumpy torus models of Nenkova et al. (2002) to reproduce the observed SEDs.

4.1. Clumpy Dusty Torus Models

The clumpy dusty torus models of Nenkova et al. (2002, 2008a, 2008b) propose that the dust surrounding the central engine of an AGN is distributed in clumps, instead of homogeneously filling the torus volume. These clumps are distributed with a radial extent characterized by the parameter Y = R_o/R_d, where R_o and R_d are the outer and inner radius of the toroidal distribution, respectively (see Figure 4). The inner radius is defined by the dust sublimation temperature (T_sub ≈ 1500 K), with R_d = 0.4(1500KT⁻¹_sub)^2.6(L/10⁴⁵ erg s^-1)^0.5 pc. Within this geometry, each clump has the same optical depth (τ_V, defined at V). The average number of clouds along a radial equatorial ray is N₀. The radial density profile is a power law (∝r^−q). A width parameter, σ, characterizes the angular distribution, which has a smooth edge. The number of clouds along the line of sight (LOS) at an inclination angle i is $N_{\it LOS}(i) = N_0 e^{(-(i-90)^2/\sigma ^2)}$.

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The radiative transfer equations are solved for each clump using the DUSTY code (Ivezić et al. 1999), with solutions depending mainly on the location of each clump within the torus, its optical depth, and the chosen dust composition. We adopt a dust extinction profile corresponding to the OHMc dust (i.e., the standard cold oxygen-rich ISM dust of Ossenkopf et al. 1992). DUSTY includes dust absorption, emission, and scattering components. The total torus emission is calculated by integrating the source function of the whole number of clumps convolved with the radiation propagation probability along the torus (Nenkova et al. 2002). The direct AGN emission may also be included in the resulting SED, which is appropriate for Type-1 nuclei and some intermediate types.

4.2. BayesClumpy

4.3. Model Results

4.3.1. Seyfert 2 Individual Fits

The results of the fitting process are the marginal posterior distributions for the six free parameters that describe the clumpy models and the vertical shift. These are the probability distribution of each parameter, represented as histograms. Uniform priors have been employed in our analysis of the observational data. Therefore, when the observed data introduce enough information into the fit, the resulting probability distributions will clearly differ from uniform distributions, either showing trends or being centered at certain values within the considered intervals.

We fit the individual Sy2 SEDs with the BayesClumpy code, modeling only the torus emission, assuming no direct AGN continuum is detected. We also assume that foreground extinction from the host galaxy does not significantly modify the IR SEDs of the Seyfert galaxies in the sample. For example, Martini & Pogge (1999) used V–H colors of Sy2 galaxies in the CfA sample to derive levels of optical extinction up to A_V ∼ 5 mag. Based on this, Alonso-Herrero et al. (2003) applied different values of A_V up to 5 mag to a subset of torus models (those of Efstathiou & Rowan-Robinson 1995) to illustrate the effects of dust in the host galaxy, and concluded that moderate amounts of foreground extinction (A_V ≲ 5 mag) will not have a significant effect on the nuclear fluxes at λ≳ 2 μm. Thus, we do not consider foreground extinction in the fits with the clumpy models for the Seyfert galaxies in our sample. The only exception is Centaurus A, since its core is heavily obscured by a dust lane up to A_V ∼ 7–8 mag (Hough et al. 1987; Packham et al. 1996; Marconi et al. 2000). For details on the specific fit of this galaxy, see the Appendix.

The histograms corresponding to the probability distributions of the free parameters are shown in Figure 5 for Circinus, which constitutes the best fit in our sample. It also includes the histogram corresponding to the optical extinction produced by the torus along the LOS, computed as $A_{V}^{\rm LOS} = 1.086 N_0 \tau _{V} e^{(-(i-90)^{2}/\sigma ^{2})}$ mag.

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We adopt a radial extent of Y = 15 as a Gaussian prior with a width of 2.5 because this parameter is otherwise unconstrained and presents no correlation with other parameters. The chosen value of Y=15 is consistent with all current observations of nearby active nuclei, which place the radial extent of the torus within values smaller than ∼20–30 (Jaffe et al. 2004; Packham et al. 2005; Tristram et al. 2007; Meisenheimer et al. 2007; Radomski et al. 2008; Raban et al. 2009), and perhaps even as small as ∼5–10. The lack of restriction of the torus radial extent is in agreement with the findings of Nenkova et al. (2008b), who report that IR SED fitting sets only a poor constraint on the torus size (see Section 5.3).

From Figure 5, it is clear that the Circinus data (eight photometric data points) provide sufficient information to constrain the model parameters. In addition to the above-mentioned prior for the Y parameter, we introduce a Gaussian prior on the inclination angle of the torus i, a Gaussian centered in 85°, with a width of 2°. We make this restriction in the i parameter because of the detection of a water vapor megamaser (Greenhill et al. 2003), which constrains the viewing angle to i ∼ 90°. The optical depth per cloud results in a narrow Gaussian centered at the median value τ_V = 30 ± 2. The number of clouds results in a Gaussian-like distribution of median value N₀ = 10 ± 2, and the width of the angular distribution has a median value of σ = 61° ± 8°. Finally, we establish a lower limit of q > 2.4 at a 68% confidence level. The optical obscuration produced by the torus along the LOS would be of A^LOS_V = 320±⁸⁰₅₅ mag.

Although the solution to the Bayesian inference problem are the probability distributions shown in Figure 5, we translate these results into corresponding spectra (Figure 6). The maximum a posteriori (MAP) values of the parameters (i.e., the modes) represent the "best fit" to the data, since the mode corresponds to the most probable value of each parameter, and we plot the corresponding spectrum as a solid line. The dashed line shows the spectral model obtained using the median value of the probability distribution of each parameter, which is characteristic of the observed SED. Finally, the shaded region indicates the range of models compatible with a 68% confidence interval for each parameter around the median value. The observed Circinus SED is extremely well fitted with the clumpy models, including only the reprocessed torus emission without any stellar contribution. The model fitting to the photometric points makes a spectroscopic prediction: the 10 μm silicate feature appears in shallow absorption in the fitted models, as expected for Sy2 galaxies (Hao et al. 2007; Levenson et al. 2007). In particular, the model prediction for Circinus is in qualitative agreement with spectroscopic observations (Roche et al. 2006; Tristram et al. 2007) that show the silicate feature in absorption, although deeper than the predicted by the models (see the Appendix).

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The excellent fit of the Circinus SED is the result of the combination of the good behavior of the clumpy models and the accuracy of the IR nuclear fluxes. The near-diffraction-limited adaptive optics NACO/VLT near-IR data (providing resolution between 01 and 02) and the T-ReCS/Gemini-South mid-IR data (resolution between 03 and 05), together with the proximity of the galaxy provide the least contaminated (by host galaxy emission) SED of our sample, and consequently the best example of an AGN-dominated SED.

We apply the same technique to all the Sy2 individual galaxy measurements (with the exception of NGC 5728, for which we did not find near-IR nuclear fluxes in the literature, resulting then excluded from any further analysis), and plot the spectral results in Figure 7. The probability distributions of each parameter for all the individual galaxies are summarized in Table 7. Comments on the individual fits of the Sy2 galaxies in our sample are reported in the Appendix. Despite the more limited flux measurements in most individual cases, the resulting model fits are generally good. The fitted parameters are consistent with unified AGN schemes and the requirement that the central engine be hidden from direct view in Type-2 AGNs. The only exceptional cases are NGC 1808 and NGC 7582, as both exhibit intense nuclear star formation and have lower spatial resolution mid-IR measurements (obtained at the CTIO 4 m). Thus, we consider these two model results unreliable, especially that of NGC 7582.

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Table 7. Parameters Derived from the Clumpy Model Fitting

		σ		N0		q		i		τV		ALOSV
Galaxy	Seyfert Type	Median	Mode	Median	Mode	Median	Mode	Median	Mode	Median	Mode	Median	Mode
Centaurus A	2	58±1015	62	2 ± 1	1	<0.2	0.1	>85	89	176±1625	186	300±10080	260
Circinus	2	61 ± 8	59	10 ± 2	9	>2.4	3.0	85 (fix)	85	30 ± 2	30	320±8055	295
IC 5063	2	>57	75	>11	14	<1.5	0.4	>65	89	70±3123	66	780±485345	580
Mrk 573	2	<37	19	6±52	4	<1.4	0.1	85 (fix)	85	30±108	27	185±12075	150
NGC 1386	2	50±1619	51	11 ± 3	12	1.5±0.91.0	2.1	85 (fix)	85	95±6651	51	<1460	410
NGC 1808	2	<35	16	8±54	5	1.2 ± 0.9	0.9	37±1923	44	146±3750	198	<140	10
NGC 3081	2	>52	74	10 ± 3	11	>1.2	2.9	>42	89	47±4223	34	<450	120
NGC 3281	2	>68	75	6±42	5	1.3±1.10.8	0.6	>49	88	<12	10	55±1815	50
NGC 4388	2	>53	74	9±43	7	<1.6	0.2	>38	88	<14	10	<80	50
NGC 7172	2	>54	74	5±31	5	>1.7	2.9	>45	89	<12	10	50 ± 20	50
NGC 7582	2	<29	16	<2	1	>2.5	3.0	41±1928	58	<27	14	<6	1
NGC 1365	1.8	35±2013	31	7±54	3	<1.7	0.1	<42	7	110 ± 60	88	<170	10
NGC 2992	1.9	45±1821	52	7±53	4	<1.0	0.1	>53	85	36±1411	31	160±13080	130
NGC 5506	1.9	25±97	15	<2	1	2.5±0.30.4	2.7	85 (fix)	85	<68	22	<90	30
NGC 3227	1.5	33±2012	23	6±54	3	<2	0.1	<48	14	115 ± 55	77	<210	10
NGC 4151	1.5	<32	16	<3	1	1.7±0.80.9	1.9	41±2328	52	120±5548	93	<65	10

Notes. The Y parameter is fixed to be a Gaussian distribution centered at 15 with a width of 2.5. For the galaxies Circinus, Mrk 573, NGC 1386, and NGC 5506 the i parameter is also introduced as a Gaussian prior into the computations, centered at 85° with a width of 2°, based on other observations. Probability distributions presenting a single tail have been characterized with the mode and upper/lower limits at 68% confidence. Sy1.8 and Sy1.9 have been fitted with the geometry corresponding to torus emission-only. The Sy1.5 models include the intrinsic AGN continuum emission. The Sy2 NGC 5728 and the Sy1 NGC 1566 are not included here because of the lack of near-IR nuclear fluxes for them, preventing the SED fitting.

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From the individual fits with the clumpy models, we infer the following conclusions. (1) For the majority of the Sy2 considered here, the clumpy models reproduce the observed SEDs, suggesting that the high spatial resolution measurements are dominated by the reprocessed emission of the torus. (2) The 10 μm silicate feature appears in absorption in the fitted models for seven out of the eleven Sy2 (Figure 7) and is practically flat in the case of NGC 7172. The unreliable NGC 1808 and NGC 7582 results, and also the Centaurus A fit suggest silicate emission. This is probably related with a characteristic SED shape, characterized by a low N/Q ratio plus L band excess (associated with stellar contamination). See Section 5.2 for details. (3) The average number of clouds along an equatorial ray is typically within the interval N₀ = [5, 15]. The exceptions are Centaurus A (N₀ = 2 ± 1) and NGC 7582 (N₀ < 2). (4) High values of σ are preferred from our fits (σ = [50, 75]). We only find values of σ < 40 for the galaxies Mrk 573, NGC 1808, and NGC 7582. (5) High values of the inclination angle of the torus are preferred, with i > 40°, in general. (6) The combination of i, σ, and N₀ determines the likelihood of encountering a cloud along the line of sight to the central engine. In these cases, such encounters are always likely, which is consistent with having the AGN blocked from direct view, as expected in these Sy2. (7) Relatively low values of τ_V (⩽100) are found. The exception here are Centaurus A and NGC 1808, for which we find τ_V > 100. (8) The radial density profile q does not show any clear trend, and we find both low- and high-values within the considered interval. All the above-mentioned intervals or limits of the parameters correspond to median values. The reason for choosing median values instead of modes is that the median gives a less biased information about the result, since it takes into account degeneracies, while the mode does not.

4.3.2. Intermediate-type Seyfert Individual Fits

We fit the Sy1.8 and Sy1.9 nuclei the same way we fit the Sy2 SEDs, namely considering only the reprocessed torus emission. The optically broad lines and the relatively strong near-IR fluxes of the Sy1.5, however, suggest that some direct AGN contribution is also present in these cases. Thus, we include the intrinsic AGN emission as a broken power law in these models. The AGN scales self-consistently with the torus flux, and additional extinction (separate from the clumpy torus) is a free parameter. The resulting fits are plotted in Figure 8. The Sy1 NGC 1566 is not included in the following because of the lack of near-IR nuclear fluxes in the literature for it.

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From the individual fits of the intermediate-type Seyfert galaxies with the clumpy models, we find similarities and differences with the Sy2 results. (1) Compared with the Sy2, lower values of σ are preferred in the fits of both the Sy1.8 and Sy1.9 (σ = [25, 45]) and Sy1.5 (σ < 35). (2) All the intermediate-type Seyferts result in a low number of clouds along the equatorial plane (N₀ = [1,7]). (3) Low values of the inclination angle of the torus are found for Sy1.5 (i < 50°) and also for the Sy1.8 NGC 1365. (4) q does not show any clear trend for intermediate-type Seyferts, and both low- and high-values within the considered interval are found, as for Sy2. (5) Low values of the optical depth per cloud are found for the two Sy1.9 galaxies (τ_V < 70), while for the Sy1.8 and Sy1.5, high values (τ_V > 100) are preferred. (6) In contrast with the wide range of values of the optical extinction produced by the torus for Sy2, all the intermediate-type Seyferts show A_V ≲ 200 mag. (7) Including some obscured AGN contribution fits the near-IR excess of the observed SEDs of the Sy1.5 NGC 4151 and NGC 3227. The AGN is obscured by up to a few magnitudes at V in each case. (8) Except for the case of NGC 2992, for which both the data and the fit are very similar to those of Sy2 galaxies, the 10 μm silicate feature appears either in weak emission or is absent in the intermediate-type Seyfert fits. As in Section 4.3.1, the values of the parameters above mentioned correspond to the median. Although the results from the modeling of Sy2 and intermediate-type Seyfert SEDs seem to point to different trends in their torus parameters, a larger set of objects is needed to clarify if these differences are really significant.

The results of our SED modeling of Seyfert galaxies are generally in good agreement with the findings of Nenkova et al. (2008b), who reproduce IR observations of both Type-1 and Type-2 Seyferts from the literature (Sanders et al. 1989; Elvis et al. 1994; Alonso-Herrero et al. 2003; Prieto et al. 2004; Mason et al. 2006; Hao et al. 2007; Netzer et al. 2007) using clumpy torus models. They find N₀ ∼ 5–15 clouds, τ_V ∼ 30–100, σ ∼ 30°–50°, and the angular distribution of the clouds having a soft edge (the only distribution we consider here), with q = 1 or 2. They reproduce the observational data with compact torus sizes (Y ∼ 5–10), although they claim that the radial extent of the torus is poorly constrained from SED fitting.

5.1. NIR Flux and Torus Inclination

5.2. Stellar Contamination in the Near-IR?

5.3. Torus Size

5.4. 10 μm Silicate Feature and Column Density Estimates

5.5. AGN Luminosities

We report subarcsecond resolution mid-IR fluxes for 18 Seyfert galaxies. These nuclear fluxes, in combination with published near-IR measurements at comparable resolution are used to construct SEDs corresponding to torus emission. We analyze and fit these SEDs with the clumpy dusty torus models of Nenkova et al. (2002, 2008a, 2008b). The main results are summarized in the following.

• 1.  
  The high spatial resolution mid-IR nuclear fluxes reported in this work provide a spectral shape of the individual SEDs that is different from that of large aperture data SEDs (on scales of a few arcseconds).
• 2.  
  The shape of the average Sy2 SED, constructed using only pure Sy2 galaxies and either diffraction- or near-diffraction-limited data, rises steeply toward the mid-IR, with an IR slope (from ∼1 μm to 18 μm), α_IR = 3.1 ± 0.9.
• 3.  
  The individual Sy2 SEDs are typically steep through the IR, with α_IR ranging from 1.8 to 3.8. Considering separately the near-IR (from ∼1 to ∼9 μm) and the mid-IR (∼10 to ∼18 μm) slopes, we find α_NIR ≳ α_MIR, with α_NIR = 3.6 ± 0.8 and α_MIR = 2.0 ± 0.2 measured from the average Sy2 SED.
• 4.  
  The IR SEDs of the intermediate-type Seyferts in the sample are flatter (α_IR = 2.0 ± 0.4 for Sy1.8 and 1.9 and α_IR = 1.6 ± 0.3 for Sy1.5) and present larger N/Q band ratios than those of Seyfert 2 galaxies. The near-IR excess that flattens the SED of all intermediate-type Seyferts is due to the contribution of hot dust from the illuminated faces of the clouds, while direct AGN emission is also important in the case of Sy1.5.
• 5.  
  The clumpy models of Nenkova et al. (2008a, 2008b) successfully reproduce the SEDs of both the Seyfert 2 and the intermediate-type Seyferts. The models accommodate the range of α_IR observed in the former, while providing optically thick obscuration along the line of sight.
• 6.  
  The IR SEDs do not constrain the radial extent of the torus, Y, and this parameter remains uncorrelated with the other parameters. Because the outer torus contains the coolest material, high angular resolution measurements at wavelengths longer than 15 μm are needed to reveal significant variations in the torus size.
• 7.  
  In the individual Sy2 fits, we generally find the number of clouds within the interval N₀ = [5, 15], the width of the angular distribution of clouds within σ = [50°, 75°], high values of the inclination angle of the torus (i = [40°, 90°]), and optical depths per cloud τ_V < 100. The radial density profile q does not show any clear trend within the considered interval ([0, 3]).
• 8.  
  We find small number of clouds in the individual intermediate-type Seyfert fits (N₀ = [1,7]). Low values of σ are preferred from the fits of Sy1.8 and Sy1.9 (σ = [25°, 50°]) and even lower for Sy1.5 (σ < 35°). We require direct (though extinguished) emission of the AGN to reproduce the near-IR excess observed in the SEDs of Sy1.5.
• 9.  
  Views of Sy2 are more inclined than those of the Sy1.5 galaxies. More importantly, the larger values of N₀ and σ in the Sy2 models suggest that these central engines are blocked from direct view along more lines of sight, in contrast to the intermediate-type Seyferts, which present more clear views of the AGN. Due to the limited size of the analyzed sample, these differences are not significant.
• 10.  
  Although the fits are based on photometric data, the models predict the behavior of the 10 μm silicate spectral feature. Most of the individual Sy2 galaxies show shallow silicate absorption. In all but one of the intermediate-type Seyferts, the feature is either in shallow emission or absent.
• 11.  
  The columns of material responsible for the X-ray absorption are larger than those inferred from the model fits for most of the galaxies in the sample, which is consistent with X-ray absorbing gas located within the dust sublimation radius, whereas the mid-IR flux arises from an area farther from the accretion disk.
• 12.  
  The combination of large number of clouds and high values of σ results in tori that more efficiently reprocess the incident nuclear radiation than those with lower values of these parameters.
• 13.  
  In the models, the outer radial extent of the torus scales with the AGN luminosity, and we find the tori to be confined to scales less than 5 pc.

C.R.A. and J.R.E. acknowledge the Spanish Ministry of Education and Science through projects PN AYA2007-67965-C03-01 and Consolider-Ingenio 2010 Program grant CSD2006-00070: First Science with the GTC (http://www.iac.es/consolider-ingenio-gtc/). C.R.A. thanks the University of Florida Astronomy Department, the Gemini Observatory Northern Operations Center, and the University of Kentucky Department of Physics and Astronomy for their hospitality during part of this project. N.A.L. acknowledges the work supported by the NSF under grant 0237291 and thanks the University of Florida Astronomy Department and the IAC for their hospitality during this project. A.A.H. acknowledges support from the Spanish Plan Nacional del Espacio under grant ESP2007-65475-C02-01 and from the Spanish Ministry of Science and Innovation under grant Proyecto Intramural Especial 200850I003. C.P. acknowledges support of the NSF through grant number 0704095. A.A.R. acknowledges the Spanish Ministry of Education and Science through project AYA2007-63881.

This work is based on observations obtained at the Gemini Observatory, which is operated by the Association of Universities for Research in Astronomy, Inc., under a cooperative agreement with the NSF on behalf of the Gemini partnership: the National Science Foundation (United States), the Science and Technology Facilities Council (United Kingdom), the National Research Council (Canada), CONICYT (Chile), the Australian Research Council (Australia), Ministério da Ciência e Tecnologia (Brazil), and Ministerio de Ciencia, Tecnología e Innovación Productiva (Argentina). The Gemini programs under which the data were obtained are GS-2003B-DD-4, GS-2004A-DD-4, GS-2005B-DD, GS-2005A-Q-6, GN-2006A-Q-11, and GS-2006A-Q-30.

This work is based on observations made with the NASA/ESA Hubble Space Telescope, and obtained from the Hubble Legacy Archive, which is a collaboration between the Space Telescope Science Institute (STScI/NASA), the Space Telescope European Coordinating Facility (ST-ECF/ESA), and the Canadian Astronomy Data Centre (CADC/NRC/CSA).

This research has made use of the NASA/IPAC Extragalactic Database (NED) which is operated by the Jet Propulsion Laboratory, California Institute of Technology, under contract with the National Aeronautics and Space Administration.

This research has made use of data obtained from the High Energy Astrophysics Science Archive Research Center (HEASARC), provided by NASA's Goddard Space Flight Center.

The authors acknowledge Ana M. Pérez García, Rachel Mason, Itziar Aretxaga, and Tanio Díaz Santos for their valuable help and thank the anonymous referee for useful suggestions.

Below, we comment on the individual fits of the galaxies in our sample, including Type-2 Seyferts and intermediate types. Unless the opposite is indicated, all the reported values from the fits correspond to or are calculated from the median values.

Centaurus A. Centaurus A (NGC 5128) is a nearby Sy2 nucleus, with its core heavily obscured by a dust lane. This makes it visible only at wavelengths longwards ∼1 μm (Schreier et al. 1998; Marconi et al. 2000). Indeed, Hough et al. (1987), Packham et al. (1996), and Marconi et al. (2000) determined a value for the extinction caused by the dust lane of A_V ∼ 7–8 mag. However, the total obscuration on our LOS to the core was estimated by Meisenheimer et al. (2007) to be A_V ∼ 14 mag, including the torus material. Due to the existence of the dust lane, that is probably affecting our nuclear fluxes (specially the near-IR ones), we exceptionally have taken this foreground extinction into account for the fit of Centaurus A with the clumpy models (Figure 7), by fixing A_V = 8 mag and applying the Calzetti et al. (2000) law to the fitted models.

The clumpy models reproduce the observed photometry very accurately, but not the broad absorption silicate feature detected in mid-IR spectroscopy and interferometry (Siebenmorgen et al. 2004a; Meisenheimer et al. 2007). This mismatch in the fitted model could be due to the synchrotron radiation contribution to the IR fluxes claimed by Bailey et al. (1986), Turner et al. (1992), Chiaberge et al. (2001), and Meisenheimer et al. (2007). Indeed, Meisenheimer et al. (2007) find from mid-IR interferometric observations that the contribution of synchrotron emission to the nuclear emission of Centaurus A is of ∼80% at ∼8 μm and ∼60% at ∼13 μm. However, the results of Radomski et al. (2008), including the lack of variability at ∼10 μm (see Radomski et al. 2008 and references therein) and zero polarization at ∼1 mm (although low millimeter polarization may be associated with low-luminosity sources; Packham et al. 1996) are inconsistent with a synchrotron source as that suggested by Meisenheimer et al. (2007). A more detailed analysis of the SED of this galaxy, e.g., including an optically thin power law in the fits to account for the synchrotron radiation can be done. However, this kind of detailed analysis of an individual galaxy is beyond the scope of this work.

The probability distributions derived from the fit of the Centaurus A SED with the clumpy models clearly constrain the number of clouds N₀, the optical depth of each cloud τ_V, and the width of the angular distribution σ. N₀ resembles a Gaussian distribution centered at the median value N₀ = 2 ± 1. The τ_V histogram shows an asymmetric shape, with a tail toward low values and of median τ_V = 176 at a 68% confidence level. High-σ values are more probable than others (median value of 58° ± ¹⁰₁₅), and the same for the inclination angle of the torus (i > 85°). In contrast, low values of q are preferred (q < 0.2). The radial thickness of the torus Y has been introduced to the code as a Gaussian prior centered in 15 with a width of 2.5, as explained in Section 4.2. Indeed, the preliminary fit of Centaurus A without restrictions in any of the model parameters was the only one that constrained the radial thickness of the torus, with a median value of its probability distribution of Y∼ 15. The calculated median value of the optical extinction produced by the torus is A^LOS_V = 300±¹⁰⁰₈₀ mag for this galaxy.

Circinus. The Circinus galaxy is a nearby Sy2 with a prominent cone-shaped region revealed in the [O iii] images (Wilson et al. 2000). Both the accuracy of the eight high spatial resolution flux measurements and the proximity of the galaxy make the resulting fit excellent. Water vapor megamasers (Greenhill et al. 2003) constrain the viewing angle to i ∼ 90°. Thus, in addition to the Gaussian prior for the Y parameter, we introduce a prior on i, a Gaussian centered in 85°, with a width of 2°.¹⁰ The resulting fit constrains most model parameters. The optical depth per cloud results in a narrow Gaussian centered at the median value τ_V = 30 ± 2. The number of clouds results in a Gaussian-like distribution (median value of N₀ = 10 ± 2), and the width of the angular distribution has a median value of σ = 61° ± 8°. Finally, we establish a lower limit of q < 2.3 at a 68% confidence level. The optical obscuration produced by the torus would be A^LOS_V = 320±⁸⁰₅₅ mag. Roche et al. (2006) found the core of Circinus compact and obscured by a substantial column of silicate dust from T-ReCS/Gemini-South spectroscopy. They obtained a value for the silicate absorption depth of τ_{10 μm} = 1.6. Our fitted models reproduce the silicate feature in absorption (see Table 8), in qualitative agreement with the observations, but shallower (τ^app_{10 μm} = 0.86) than that reported by Roche et al. (2006). We find that the absorption column density inferred from X-ray measurements (N^X-rays_H = 4 × 10²⁴ cm⁻²) is larger than that responsible for the mid-IR absorption (N^LOS_H ∼ 6 × 10²³ cm⁻²). This is consistent with the X-ray obscuring region being closer to the central engine than the mid-IR emitting dust.

IC 5063. This Sy2 nucleus is hosted by a merger remnant classified as an elliptical galaxy (Colina et al. 1991). An obscuring dust lane partially covers the eastern side of the galaxy. A peculiarity of this source is its strong radio luminosity, which is 2 orders of magnitude larger than the typical values for Seyfert galaxies (Colina et al. 1991). From an N-band acquisition image of IC 5063 obtained with T-ReCS/Gemini-South, Young et al. (2007) tentatively found the nucleus of this galaxy slightly resolved. However, from our T-ReCS Si2 and Qa band imaging the nucleus appears unresolved, and consequently, we subtracted the corresponding PSF at the 100% level to derive the nuclear fluxes. From the fit with the clumpy models, we establish lower limits for three of the parameters (σ>57°, N₀ > 11, and i > 65°) and an upper limit for the index of the radial density profile (q < 1.5). The only Gaussian-like distribution resulting from the fit corresponds to τ_V (median value of 70±³¹₂₃). A^LOS_V is calculated to be 780±⁴⁸⁵₃₄₅ mag. The galaxy presents one of the highest L^AGN_bol of the sample (2.4 × 10⁴⁴ erg s⁻¹, see Table 9), and also a high reprocessing efficiency (87%), consistent with the large values of N₀ and σ we find. X-ray observations with the ASCA satellite allow us to infer an intrinsic 2–10 keV luminosity of ∼10⁴³ erg s⁻¹, that is within the range expected for Seyfert 1 galaxies (Turner et al. 1997). The silicate feature appears in absorption in the fitted models, in qualitative agreement with mid-IR spectroscopic observations obtained with T-ReCS/Gemini-South (Young et al. 2007). However, the absorption band appears deeper in our models (τ^app_{10 μm} = 0.94) than in the mid-IR spectrum (τ_{10 μm} = 0.33).

Mrk 573. Mrk 573 is optically classified as a classical Sy2 nucleus (Tsvetanov & Walsh 1992), and Ramos Almeida et al. (2008) recently re-classify it as an obscured NLSy1 galaxy, based on near-IR spectroscopy and X-ray archival data. The X-ray observations of Mrk 573 do not straightforwardly reveal the intrinsic luminosity of this AGN because it suffers from Compton thick obscuration (Guainazzi et al. 2005). The strong soft X-ray emission is likely photoionized line emission. It is not the AGN continuum in any case, so previous simplified fits of power-law models over a broad energy range (e.g., Guainazzi et al. 2005; Shu et al. 2007) fail to accurately measure the AGN. We determine the intrinsic AGN luminosity from the XMM-Newton observation of Mrk 573 with the pn detector, which offers a high S/N. We use the reduced data and associated background and calibration files from XAssist pipeline processing (Ptak & Griffiths 2003). We fit only the data at energies greater than 3 keV, to avoid confusion from the separate soft emission sources. The observed continuum is flat and the Fe Kα line equivalent width (EW) is large, which are characteristic of a purely reflected (not direct) AGN continuum. We fix the photon index Γ = 0 and find EW = 2.0 ± 0.7 keV. The results are similar if a typical AGN continuum slope is adopted (Γ = 1.9). We follow the technique of Levenson et al. (2006), using the Fe line luminosity and EW and to determine the intrinsic AGN luminosity, finding L^AGN_X = 2.2 × 10⁴³ erg s^-1 in the 2–10 keV bandpass. We note that the fitted hard continuum directly corresponds to an intrinsic luminosity that is a factor of 100 smaller.

The IR SED shape of Mrk 573 is practically the same as those of the rest of Sy2 galaxies in the sample, so we consider it equivalent to the other Sy2. This galaxy presents a strong symmetric double radio lobe (Nagar et al. 1999), suggesting that it contains an edge-on torus; the radio lobes would be asymmetric if the jets were out of the plane of the sky. The SED fit reproduces all seven data points and also constrains the majority of the parameters. As for the case of Circinus, we have introduced the inclination angle of the torus as a Gaussian prior, centered in 85° with a width of 2°. The probability distribution of N₀ present a Gaussian shape, with median value N₀ = 6 ± ⁵₂ (there is a tail toward large values that enlarges the error). The σ and q distributions allow us to establish upper limits of σ < 37° and q < 1.4. The optical depth of each cloud shows a Gaussian distribution with a median value of τ_V = 30±¹⁰₈. The optical extinction produced by this clumpy torus is A^LOS_V = 185±¹²⁰₇₅ mag. Mrk 573 has the highest L^AGN_bol of the Sy2 subset (4.3 × 10⁴⁴ erg s⁻¹; Table 9), but due to the low values of N₀ and σ derived from its fit, its reprocessing efficiency is low (∼15%). The 10 μm silicate feature appears in shallow absorption in the median-fitted model (τ^app_{10 μm} = 0.44; see Table 8), producing an estimated value of the optical extinction A^app_V = 11 mag. The hydrogen column density obtained from the modeling along the LOS (N^LOS_H ∼ 3 × 10²³ cm⁻²) is much lower than the one that obscures the X-ray emission (N^X-rays_H > 1 × 10²⁴ cm⁻²).

NGC 1386. NGC 1386 is one of the nearest Sy2 galaxies and therefore extensively studied. Mauder et al. (1992) resolved its NLR on a 03 scale (∼15 pc) using speckle interferometry, detecting individual NLR clouds and claiming a clumpy structure. The detection of a water vapor megamaser in NGC 1386 (Braatz et al. 1997) constrains the inclination angle of the torus to be i ∼ 90°, as in the case of Circinus and Mrk 573. The fit with the clumpy models reproduces the observed SED; we find N₀ = 11 ± 3, σ = 50° ± ¹⁶₁₉, τ_V = 95 ± ⁶⁶₅₁, and q = 1.5±^0.9_1.0 at a 68% confidence level. The optical extinction produced by the clumpy torus is A^LOS_V < 1460 mag. The fitted models show a shallow silicate absorption feature (τ^app_{10 μm} = 0.41) from which we derived an optical extinction of A^app_V = 11 mag. As for most of the galaxies in the sample, we find N^LOS_H < N^X-rays_H, indicating that the X-ray obscuring region must be closer to the central engine than the torus material.

NGC 1808. The Sy2 galaxy NGC 1808 is undergoing an intense episode of star formation in its central 750 pc (Tacconi-Garman et al. 1996, 2005; Galliano & Alloin 2008). The near-IR fluxes were obtained using ISAAC/VLT, and we measured the mid-IR flux from 10.7 and 18.2 μm OSCIR/CTIO images. Consequently, NGC 1808 has relatively low spatial resolution for our sample (the angular resolution of the ISAAC images is ∼06 and that of the OSCIR image at CTIO is ∼09–1''). The near-IR SED shape is flat and peculiar, and star formation may contaminate these measurements (according to the argument of Section 5.2), making the fit not very reliable. Low values of σ and i are preferred (<35° and 37° ± ¹⁹₂₃, respectively), contrary to the general trend for the Sy2 galaxies in our sample. The median value of the number of clouds is N₀ = 8 ± ⁵₄, the optical depth per cloud τ_V > 122, and q = 1.2 ± 0.9. The calculated optical extinction produced by the torus is A^LOS_V < 140 mag. From the bolometric luminosities derived from the fit, we derive the reprocessing efficiency of the modeled torus that results on ∼45%. The 10 μm silicate feature appears in weak emission in the fitted spectrum (τ^app_{10 μm} = −0.21). Summarizing, due to the intense stellar formation that is taking place in the nuclear region of this galaxy, and to the lower spatial resolution near- and mid-IR measurements that we have for it (all from 3 or 4 m telescopes), the IR SED of NGC 1808 is very likely contaminated with starlight. This is probably producing its peculiar shape and the different trends in the fitted parameters, in comparison with the rest of Sy2 in the sample. For these reasons, we consider the NGC 1808 SED fit unreliable.

NGC 3081. NGC 3081 is a Sy2 galaxy with intense stellar formation located in a series of nested ringlike features (Buta et al. 2004). As in the case of NGC 1386, the SED of NGC 3081 is formed with only three data points, and the model results are similar, with the probability distributions of the parameters presenting the same shapes. The N₀ and τ_V histograms have median values of N₀ = 10 ± 3 and τ_V = 47±⁴²₂₃, respectively. We determine lower limits of σ>52°, q > 1.2, and i > 42°. A^LOS_V is estimated to be lower than 450 mag. According to the calculated luminosities for this galaxy, the fraction of reprocessed radiation (L^tor_bol/L^AGN_bol) is among the highest in the sample (∼90%). The 10 μm silicate feature is reproduced in absorption by the models (τ^app_{10 μm} = 0.91), from which we inferred an optical obscuration A^app_V ∼ 23 mag.

NGC 3281. This Sy2 galaxy suffers large extinction (A_V = 22 ± 11 mag to the IR-emitting and N_H = 2 × 10²⁴ cm^-2 to the X-ray-emitting regions; Simpson 1998; Vignali & Comastri 2002). The clumpy models fit the data well, except for the 18.3 μm point, which the models underestimate slightly. The probability distributions resulting from the fit show that large values of σ and i are more probable than others (>68° and >49°, respectively) and establish an upper limit for the optical depth per cloud of τ_V < 12 at a 68% confidence level. The number of clumps N₀ presents a Gaussian distribution with a tail toward large values, with median value N₀ = 6 ± ⁴₂, as the q histogram (median value of q = 1.3±^1.1_0.8). The optical extinction produced by the clumpy torus corresponds to a Gaussian distribution of median value A^LOS_V = 55 ± ¹⁸₁₅ mag. The models predict the 10 μm silicate feature in shallow absorption (τ^app_{10 μm} = 0.21), resulting in an apparent optical obscuration of A^app_V = 5 mag. N^LOS_H < N^X-rays_H, indicating a closer X-ray obscuring region to the central engine than the torus material.

NGC 4388. This highly inclined disk galaxy is spectroscopically classified as a Sy2 nucleus (Phillips & Malin 1982). However, Shields et al. (1996) report the detection of weak, broad Hα emission. The ground-based L-band point introduces a bump in the SED around 3–4 μm, which likely represents starlight contamination (Section 5.2). Indeed, the galaxy appears very extended in the L band (Alonso-Herrero et al. 2003), making difficult to isolate the nuclear emission. Thus, the fit correctly reproduces the near-IR and the N-band points but severely underestimates the Q-band measurement. The probability distributions establish lower limits of σ>53° and i > 38°, and upper limits of q < 1.6 and τ_V < 14 at a 68% confidence level. The median value of the number of clouds is N₀ = 9±⁴₃. Along the line of sight, A_V < 80 mag. The silicate feature appears in shallow absorption in the fitted models (τ^app_{10 μm} = 0.51), allowing us to estimate an optical obscuration of A^app_V = 13 mag. As for most of the galaxies in the sample, we found N^LOS_H < N^X-rays_H.

NGC 7172. NGC 7172 is a Type-2 Seyfert nucleus in a nearly edge-on spiral galaxy. A prominent dust lane in the east–west direction crosses the galaxy. Similar to the case of NGC 4388, we observe a near-IR bump of emission in the SED of NGC 7172, which stellar contamination of the seeing-limited fluxes likely produces (Section 5.2). The N₀ histogram shows a Gaussian shape, with median value N₀ = 5 ± ³₁. High values of i, σ, and q are more probable (i > 45°, σ>54°, and q > 1.7, respectively), while low values of τ_V are preferred (τ_V < 12). The torus produces optical extinction A^LOS_V = 50 ± 20 mag. The reprocessing efficiency of this galaxy is high (∼80%), according to the derived values of the AGN and torus bolometric luminosities. T-ReCS mid-IR spectroscopy shows a substantial silicate absorption feature (Roche et al. 2007) that is not reproduced by the fitted models, that predict it in very extremely emission (and self-absorbed). This could be due to the above-mentioned stellar contamination of the near-IR fluxes, that in addition to the lack of Q-band data point for this galaxy, make it difficult the correct reproduction of the silicate feature in absorption.

NGC 7582. NGC 7582 is a Sy2 galaxy that harbors a nuclear starburst surrounding the active nucleus (Cid Fernandes et al. 2001; Sosa-Brito et al. 2001; Wold & Galliano 2006; Bianchi et al. 2007) and presents a nuclear outflow (Morris et al. 1985). The fit with the clumpy models shown in Figure 7 does not reproduce the 18.2 μm point, and the resulting probability distributions of the parameters are very different compared with the rest of Sy2 galaxies discussed here (except for NGC 1808). Low values of σ are more probable (<29°), as are extremely small numbers of clouds (N₀< 2). High values of q (>2.5) and low values of the τ_V (<27) are preferred. The i probability distribution has a Gaussian shape whose median value is i = 41° ± ¹⁹₂₈. The optical obscuration produced by the torus results in an unrealistic value of A^LOS_V < 6 mag. The reprocessing efficiency fraction of this galaxy is among the lowest in the sample (∼10%), a consequence of the low values of N₀ and σ. The 10 μm silicate feature appears in emission in the fitted models, in contradiction with TIMMI2 mid-IR observations (Siebenmorgen et al. 2004a) that show a strong absorption band characterized by τ_{10 μm} = 1.1. All these results are probably due to stellar contamination of our mid-IR data (obtained at the 4 m CTIO). The intense circumnuclear star formation present in this galaxy makes it more difficult to isolate the torus emission from that of the host galaxy. Consequently, as for the case of NGC 1808, we consider the model fit of NGC 7582 unreliable.

NGC 1365. This Sy1.8 nucleus is hosted in a galaxy with intense nuclear star formation. The X-ray emission of NGC 1365 is also remarkable, showing the most dramatic spectral changes observed in an AGN (Risaliti et al. 2005, 2007). The rapid X-ray variability is attributable to variations in the LOS density, which is compatible with a low number of clouds along the LOS. The clumpy models fit the SED of NGC 1365 well, but the model parameters are not well constrained. The number of clouds has a median value of 7 ± ⁵₄ (which is consistent with the rapid X-ray variability), σ = 35° ± ²⁰₁₃, and τ_V = 111 ± ⁵⁸₅₆. Low values of q and i (q < 1.7 and i < 42°) are more probable. The optical obscuration due to the torus is A^LOS_V < 170 mag. The silicate feature is completely absent in the fitted models.

NGC 2992. This galaxy is optically classified as a Sy1.9 nucleus, based on early published spectra (Ward et al. 1980), which showed a weak broad Hα component, but no broad Hβ. In a later observation (Allen et al. 1999), the broad component of Hα disappeared, leading to a new classification of the galaxy as a Sy2. Gilli et al. (2000) reported that the spectrum regained the broad wings of Hα coinciding with a period of intense X-ray activity, contrary to the low stage that was taking place during Allen's observations. Trippe et al. (2008) report the re-classification of NGC 2992 as a Sy2 nucleus again, as of 2006. The near-IR ground-based data were taken in 1998 April, coinciding with the epoch of Gilli's observations, and thus with the classification as intermediate-type Seyfert. On the other hand, our mid-IR measurements from Michelle were obtained in 2006 May, coinciding with the Sy2 state. Thus, our IR SED includes fluxes taken during different periods of activity of NGC 2992. This can explain its similarity with a typical Sy2 SED. The clumpy models that include only torus emission (and no direct AGN component) fit the observed data well. The probability distributions are Gaussians for σ, N₀, and τ_V, with median values σ = 45° ± ¹⁸₂₁, N₀ = 7 ± ⁵₃, and τ_V = 36±¹⁴₁₁. High values of i (>53°) and low values of q (<1.0) are preferred. The calculated optical extinction due to the torus is A_V < 160 mag. NGC 2992 is the only intermediate-type Seyfert with the 10 μm silicate feature in absorption in the fitted models (τ^app_{10 μm} = 0.74). The derived apparent optical extinction from the measurement of the band is A^app_V ∼ 19 mag. The hydrogen column density along the LOS results in N^LOS_H = 2.5 × 10²³ cm⁻². This value results unrealistic when compared with that inferred from X-ray measurements (N^X-rays_H = 8 × 10²¹ cm⁻²). This could be due to the intrinsic X-ray variability observed in NGC 2992 (Trippe et al. 2008).

NGC 5506. The nucleus of this galaxy is classified as a Sy1.9 based on the detection of broad wings of the Paβ profile in the near-IR (Blanco et al. 1990). However, more recently, Nagar et al. (2002) presented evidence that NGC 5506 is an obscured narrow-line Sy1, as a result of the finding of the permitted O i λ1.129 μm line, together with a broad pedestal of Paβ and rapid X-ray variability. The clumpy models reproduce the near-IR and the N-band data points well, while slightly underestimating the Q-band flux. The discrepancy between the spectral observations and the model fit along with the poor mid-IR fit together suggest either that additional emission contaminates the near-IR measurements or that the models cannot produce this observed SED shape (Section 5.2). Based on the detection of a water vapor megamaser (Raluy et al. 1998), we have introduced the inclination angle to the code as a Gaussian-prior centered in 85° with a width of 2°. In the resulting probability distributions, we find σ = 25° ± ⁹₇, q = 2.5±^0.3_0.4, and the average number of clouds along an equatorial ray to be less than 2. The optical depth per cloud τ_V < 68, and the calculated torus optical extinction is A_V < 90 mag. NGC 5506 has the highest L^AGN_bol of the sample (7.3 × 10⁴⁴ erg s⁻¹; Table 9). As a consequence of the low values of N₀ and σ derived from its fit, the reprocessing efficiency is low (7%). The galaxy nucleus is very compact in the mid-IR, with an apparent optical depth of τ^app_{10 μm} ∼ 1.4 (Roche et al. 1991, 2007; Siebenmorgen et al. 2004b), although NGC 5506 also shows variations in its silicate absorption depth on parsec scales (Roche et al. 2007). Unfortunately, the fitted models reproduce the silicate feature in emission (τ^app_{10 μm} = −0.21), contrary to the spectroscopic observations. This galaxy has comparable X-ray and mid-IR absorbing columns, indicating that the dust-free absorption in this galaxy is lower than for the Sy2 reported here.

NGC 3227. This active nucleus is usually classified as a Sy1.5. XMM-Newton observations show short-term hard X-ray variability likely related to variation in the intrinsic continuum emission (Gondoin et al. 2003). The clumpy models reproduce the SED well, including the direct though extinguished AGN emission (using the Calzetti et al. (2000) law), as in the case of NGC 4151. The resulting histograms show broad Gaussian distributions of the σ, N₀, and τ_V parameters, with median values of 33° ± ²⁰₁₂, 6 ± ⁵₄, and 116 ± ⁵⁶₅₅, respectively. Low values of i (<48°) are more probable than others, and the q parameter results unconstrained. The optical depth calculated using the fitted model parameters is A^LOS_V < 210 mag. On the other hand, the extinction that obscures the direct AGN emission is A_V = 2.7 ± ^2.0_1.5 mag (not related with the torus). This value is intermediate among those reported in the literature of A_V = 1.2–1.7 mag (Cohen 1983; González-Delgado & Pérez 1997) and A_V = 4.5–4.9 mag (Mundell et al. 1995). The 10 μm silicate feature is practically absent from the fitted models (τ^app_{10 μm} = −0.1).

NGC 4151. The nucleus of this well-known Sy1.5 galaxy shows flux variability in a wide wavelength range, with timescales ranging from a few hours in the hard X-rays (Yaqoob et al. 1993) to several months in the IR (Oknyanskij et al. 1999). Shapovalova et al. (2008) reported changes in the spectral type of the nucleus from a Sy1.5 to a Sy1.8, coinciding with maximum and minimum activity states, respectively. The SED of NGC 4151 is one of the flattest in our sample, with the near-IR excess likely due to direct AGN emission, which is absent in the Sy2 galaxies. We include this power-law contribution and allow for some extinction to account for the observed reddening of the active nucleus. The fit correctly reproduces the observed SED, especially in the near-IR. The probability distributions establish a median value of q = 1.7±^0.8_0.9, i = 41°±²³₂₈, and τ_V = 120±⁵⁵₄₈. Low values for the number of clouds along equatorial rays (N₀ < 3) and for the width of the angular distribution (σ < 32°) are more probable. The optical extinction derived from the fitted model parameters is A^LOS_V < 65 mag. On the other hand, the optical obscuration of the direct AGN emission (not produced by the torus) is another free parameter of the fit, and we find A_V = 2.5 ± ^1.4_1.6 mag. The 10 μm silicate feature appears in weak emission (τ^app_{10 μm} = −0.31) in the fitted models, in qualitative agreement with Spitzer observations of this galaxy (Weedman et al. 2005).