THE ORIGIN OF DOUBLE-PEAKED NARROW LINES IN ACTIVE GALACTIC NUCLEI. II. KINEMATIC CLASSIFICATIONS FOR THE POPULATION AT z < 0.1

The 71 galaxies in the uniform sample originate from a full sample of Type 2 AGNs with double-peaked [O iii] emission lines in SDSS (York et al. 2000). Three groups selected catalogs of double-peaked AGNs (Wang et al. 2009; Liu et al. 2010b; Smith et al. 2010).

Wang et al. (2009) selected 87 Type 2 active galaxies using BPT emission-line diagnostics (Baldwin et al. 1981), then made a cut to eliminate galaxies with SDSS r-band magnitudes of r > 17.7. They selected for similar intensity peaks of the double-peaked profiles using a flux ratio cut of 1:10 between the intensity of each peak and required a wavelength separation between these two peaks of Δλ ≥ 1 Å. Smith et al. (2010) visually selected a sample for active galaxies that exhibit double peaks. However, the Type 1 and Type 2 AGNs from Smith et al. (2010) are located at redshifts of 0.1 < z < 0.7, so they are not included in the sample selection for this paper. Since Smith et al. (2010) is the only catalog with Type 1 objects, by excluding these higher redshift objects we also restrict our sample to Type 2 objects. This avoids the influence of broad lines (Δv > 1000 km s⁻¹) on the [O iii] profiles. Liu et al. (2010b) selected 167 Type 2 AGNs by making a signal-to-noise ratio (S/N) > 5 cut for [O iii]λ5007 and requiring that both [O iii]λ5007 and [O iii]λ4959 be best fit by two Gaussians. This excludes AGNs with more complex profiles, wings, and >2 Gaussian components. These three groups selected 340 unique objects. We select the complete sample of 71 double-peaked Type 2 AGNs that are at z < 0.1 to ensure sub-kiloparsec spatial resolution on all optical long-slit instruments used in the follow-up observations.

To determine the nature of these objects and further characterize their properties, we observe them using two complementary follow-up methods: optical long-slit spectroscopy and Jansky Very Large Array (VLA) radio observations.³ We use the long-slit spectroscopy to map the source of the double-peaked emission across the spatial extent of each galaxy; to do so, we observe each galaxy at two position angles in order to constrain the orientation and spatial positioning of the NLR. For most galaxies, these two position angles are orthogonal, with the exception of galaxies that have an intriguing disturbed feature or companion galaxy at a given position angle.

We choose one position angle to be the photometric major axis of the galaxy from the SDSS r-band photometry. This is motivated by one of our science goals, which is to determine if the NLR is rotational in origin. Galaxies in which the NLR is dominated by rotation will demonstrate the most extended emission along the photometric major axis, in the plane of the galaxy.

We use various spectrographs with similar pixelscales (Lick Kast Spectrograph, 078/pixel; Palomar Double Spectrograph, 039/pixel (Oke & Gunn 1982); MMT Blue Channel Spectrograph, 029/pixel (Schmidt et al. 1989); APO Dual Imaging Spectrograph, 042/pixel in the blue channel, 04/pixel in the red channel; and Keck DEep Imaging Multi-Object Spectrograph, 012/pixel (Faber et al. 2003)). We use a 1200 lines mm⁻¹ grating for all spectrographs. Table 1 lists the details of these observations.

The VLA observations are complementary to the optical long-slit data and together they can fully constrain the source of the double peaks for a given galaxy; Müller-Sánchez et al. (2015) focus on this technique for a subsample of 18 double-peaked AGNs. In this paper, we develop a novel technique using only the long-slit data to characterize the NLR of this sample of 71 galaxies. In future work, we will combine our long-slit observations with the VLA data for the full sample of 71 galaxies (O. Müller-Sánchez et al. 2016, in preparation).

We reduce and extract both the two-dimensional (2D) and one-dimensional (1D) spectra at both position angles for each galaxy using the IRAF packages CCDPROC and APALL, respectively. The Keck/DEIMOS data were reduced using the DEEP2 pipeline (Cooper et al. 2012; Newman et al. 2013). We preserve the spatial information in the 2D spectra and use the aperture-extracted 1D spectra for wavelength solutions, which we use to produce the velocity maps. We obtain accurate systemic velocities using extinction corrected stellar absorption features from the OSSY SDSS DR7 value-added catalog (Abazajian et al. 2009; Oh et al. 2011) and the IDL code GANDALF (Sarzi et al. 2006).

With fully reduced data in hand, we use a variety of IDL and Python programs to fit the [O iii]λ5007 line profiles at each spatial position along the slit and extract velocity and dispersion information. We determine the spatial center of emission for each 2D spectrum using the stellar continuum. We fit a 1D continuum in two 10 pixel cutouts on either side of the wavelength center of the [O iii]λ5007 profile, and determine its average center and full width at half maximum (FWHM_cont). We later apply this spatial center and width (FWHM_cont ± 1 row) when we refer to the "resolved center" of the emission. The positive spatial direction shown in all plots of the 2D spectra in this work corresponds to the NE direction on the sky.

We use an information criterion to determine both the extent of the emission and the number of Gaussian components to fit at each spatial position. The Akaike Information Criterion (AIC) is a least squares statistic that introduces a penalty for additional parameters, defined by Akaike (1974). Numerically, $\mathrm{AIC}={\chi }^{2}+2k$, where k is the number of parameters and χ² is the chi-square statistic:

$$\begin{eqnarray*}&&{\chi }^{2}=\displaystyle \sum _{i=1}^{n}\displaystyle \frac{{({y}_{i}-f({x}_{i};\hat{\theta }))}^{2}}{{\hat{\sigma }}_{i}^{2}},\end{eqnarray*}$$

where n is the number of data points in the sample, y_i is the measured flux, $f({x}_{i};\hat{\theta })$ is the Gaussian model for the emission-line flux, x_i is the input wavelength of the Gaussian model, $\hat{\theta }$ are the parameter values of the Gaussians, and ${\hat{\sigma }}_{i}^{2}$ is the measurement uncertainty on the measured flux. We utilize the corrected AIC (AIC_c) due to our finite number of data points: ${\mathrm{AIC}}_{c}=\mathrm{AIC}+2k(k+1)/(n-k-1)$, where n is the sample size and k is the number of parameters. When comparing two models with a different number of parameters, the model that produces the smallest value for the above statistic represents the better fit.

We apply this statistic to each row in the spatial direction to determine the extent of the emission. We establish if the row is better fit with a two parameter linear fit or a five parameter Gaussian + linear fit (Figure 1). This provides what we define as the "Akaike width" of the emission, which is measured in both arcseconds and pixels and encompasses all of the rows that are best fit by a five parameter Gaussian + linear fit. We then derive errors on this measurement from a Monte Carlo simulation. We construct 100 realizations of the spectrum by adding Gaussian noise with flux according to the inverse variance error image, and repeat the measurement of the Akaike width for each realization. The mean value of the Akaike width and its standard deviation are derived from the properties of the resulting distribution (Table 2).

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Table 2.  Measured Luminosities

Galaxy Name	L[O iii] (erg s−1)	${L}_{[{\rm{O}}\,{\rm{III}}]}^{c}$ (erg s−1)	Lbol (erg s−1)	kpc/''	Aik Width (pixels)	R (pc)
J0002+0045	(2.252 ± 0.397) × 1041	(1.516 ± 0.267) × 1042	(6.886 ± 1.216) × 1044	1.62	11 ± 2	6330 ± 980
J0009−0036	(4.813 ± 0.420) × 1041	(4.444 ± 0.388) × 1042	(2.0178 ± 0.1764) × 1045	1.39	19 ± 2	3610 ± 410
J0135+1435	(1.104 ± 0.142) × 1041	(4.52 ± 0.58) × 1041	(6.42 ± 0.82) × 1043	1.37	12 ± 1	6430 ± 800
J0156−0007	(1.420 ± 0.221) × 1041	(5.69 ± 0.88) × 1041	(8.08 ± 1.26) × 1043	1.53	14 ± 1	8330 ± 810

Note. Measured properties for all galaxies. Column 1: galaxy name. Column 2: observed [O iii] luminosity before it is dereddened. Column 3: dereddened [O iii] luminosity. Column 4: bolometric luminosity. Column 5: kiloparsec per arcsecond conversion. Column 6: akaike width of the NLR in pixels. Column 7: the corresponding radius of the NLR in parsecs. This is R_NLR in the size–luminosity relationship.

Only a portion of this table is shown here to demonstrate its form and content. A machine-readable version of the full table is available.

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We also apply the Akaike statistic to determine the appropriate number of Gaussians to fit to each spatial row (Figure 2). We use the AIC_c to determine how many Gaussians are the best fit for each row within the resolved center of the galaxy (FWHM_cont ± 1 row). We classify a galaxy as having >2 Gaussian components only if more than half of these interior rows are better fit by three or more components. This approach is used in the kinematic classification scheme.

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We extract velocity information for each row within the Akaike width by fitting both one and two Gaussians. The velocity offsets of each of the one and two Gaussian profiles are calculated relative to the systemic velocity of the galaxy. The center of each of these Gaussians in velocity space is mapped across the spatial extent of the galaxy. Similarly, we map the dispersion of each of these Gaussian profiles across the galaxy (reported as σ for the one Gaussian fit and σ₁ and σ₂ for the two Gaussian fit). We derive errors on these calculations from the Monte Carlo method described above. The uncertainty on velocity measurements increases as the distance from the galaxy center increases because the S/N for these rows drops dramatically.

Outflows and NLRs with disturbed kinematics have asymmetric emission-line profiles and often blue wings. We utilize a nonparametric diagnostic for profile asymmetry. In order to avoid excluding profiles that have low flux wings or other non-traditional types of asymmetry, we choose not to assign parametric Gaussian metrics of asymmetry. Instead, we employ the nonparametric measurement for line profile asymmetry from Liu et al. (2013b):

$$\begin{eqnarray*}&&A\equiv \displaystyle \frac{({v}_{90}-{v}_{\mathrm{med}})-({v}_{\mathrm{med}}-{v}_{10})}{{W}_{80}},\end{eqnarray*}$$

where v₁₀ and v₉₀ are the velocities that encompass 10% and 90% of the integrated flux across the profile, respectively, v_med is the velocity that corresponds to the median value of the integrated flux profile, and W₈₀ is defined as ${W}_{80}\equiv {v}_{90}-{v}_{10}$. The sign of asymmetry is negative if the profile has a blue wing and positive for red wings.

This statistic (Figure 3) is sensitive to double-peaked profiles that have unequal flux ratios; specifically the absolute value of asymmetry is large if the profile has what can be better described as a shoulder as opposed to an equal flux double-peaked profile. We only use the measurement to classify rotation-dominated profiles as disturbed or obscured. We discuss this aspect of kinematic classification in Section 3.1.

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In addition, we measure the position angle of the NLR [O iii]λ5007 emission (PA_{[O iii]}) on the sky. This allows us to determine if the [O iii] emission is rotational in origin. We fit position centroids at each peak of the double-peaked profile and calculate a separation in spatial position (Figure 4). By iterating at each position angle while introducing Gaussian noise from the inverse variance image, we calculate an angle of maximal separation of these spatial centroids with an associated error.

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Formally, the true position of maximal separation is given by PA_{[O iii]}:

$$\begin{eqnarray*}&&{x}_{1}\cos ({\mathrm{PA}}_{[{\rm{O}}{\rm{III}}]}-{\theta }_{2})={x}_{2}\cos ({\mathrm{PA}}_{[{\rm{O}}{\rm{III}}]}-{\theta }_{1}),\end{eqnarray*}$$

where x₁ and x₂ are the spatial separations at the observed position angles (Figure 4), θ₁ and θ₂, respectively.

To investigate the ionization structure of the NLR, we measure both the size and the [O iii]λ5007 luminosity of the region. To determine the radius (in parsecs) of the NLR, we use half the Akaike width, defined in Section 2.3. We then convert to a physical distance using the Python astropy.cosmology utility.

To determine the luminosity of the NLR, we use the SDSS DR7 OSSY value-added catalog (Oh et al. 2011). We use a dereddened luminosity, ${L}_{[{\rm{O}}\,{\rm{III}}]}^{c}$, which is calculated from the observed [O iii] luminosity, L_{[O iii]}, based upon a two component reddening correction (Oh et al. 2011). This includes a galaxy-wide dust correction as well as a nebular correction using the Hydrogen Balmer decrement:

$$\begin{eqnarray*}&&{L}_{[{\rm{O}}\,{\rm{III}}]}^{c}={L}_{[{\rm{O}}{\rm{III}}]}{\left(\displaystyle \frac{{({\rm{H}}\alpha /{\rm{H}}\beta )}_{\mathrm{obs}}}{3.0}\right)}^{2.94}\end{eqnarray*}$$

where Hα/Hβ is the line ratio for the Balmer lines (Osterbrock & Ferland 2006).

The bolometric luminosity is calculated from ${L}_{[{\rm{O}}\,{\rm{III}}]}^{c}$:

$$\begin{eqnarray*}&&{L}_{\mathrm{bol}}={{CL}}_{[{\rm{O}}\,{\rm{III}}]}^{c}\end{eqnarray*}$$

where the correction, C, depends upon the [O iii] luminosity. C is 87, 142, or 454 for ${L}_{[{\rm{O}}\,{\rm{III}}]}^{c}$ in the respective bins ${L}_{[{\rm{O}}\,{\rm{III}}]}^{c}$ (erg s⁻¹) < 10⁴⁰, ${10}^{40}\lt {L}_{[{\rm{O}}\,{\rm{III}}]}^{c}$ (erg s⁻¹) < 10⁴², and ${10}^{42}\lt {L}_{[{\rm{O}}\,{\rm{III}}]}^{c}$ (erg s⁻¹) < 10⁴⁴ (Heckman et al. 2004; Lamastra et al. 2009). We report L_{[O iii]}, ${L}_{[{\rm{O}}\,{\rm{III}}]}^{c}$, the bolometric luminosity, and the radius of the NLR in parsecs in Table 2 for all galaxies.

We develop a novel technique for quantitative classification of the double-peaked [O iii]λ5007 profiles using the spatially resolved kinematics of the NLR. Our primary goal is to determine the nature of the double peaks and assess the relative importance of their various spectral features in the kinematic classification scheme. This technique depends on the long-slit data alone. In future papers, the radio data will be independently analyzed and the two data sets will be synthesized.

We design the classification method to isolate rotation-dominated spectra from outflow-dominated spectra. Müller-Sánchez et al. (2015) use a subsample of 18 galaxies to demonstrate that the majority (75%) of double-peaked NLR galaxies are caused by "gas kinematics" (includes 70% outflows and 5% rotating NLR kinematics), 15% are caused by dual AGNs or outflows produced by dual AGNs, and 10% are ambiguous. Shen et al. (2011) and Fu et al. (2011) used resolved spectroscopy to show that the majority of double-peaked NLR galaxies are produced by "gas kinematics" from a single AGN, including extended emission-line nebulae, jet-cloud interactions, or peculiar narrow-line.

Since Müller-Sánchez et al. (2015), Shen et al. (2011), and Fu et al. (2011) identify a statistical majority of outflow-dominated spectra with the double-peaked selection technique, we create a classification technique that classifies a spectrum as outflow-dominated or rotation-dominated and then focuses on the kinematic nature of each broad classification. For instance, we further classify outflows as "Outflow Composite" if they have more than two Gaussian components or "Outflow" if they are best fit by two components. The "Outflow Composite" classification identifies outflows with complicated emission knots observed moving at distinct velocities. We further classify rotation-dominated spectra as containing a disturbance or an obscuration.

Note that dual AGNs may exist in our classification scheme but fall into multiple different categories (Section 5.1).⁴ In this work, we explore the kinematic classifications for the complete sample of z < 0.1 double-peaked AGNs. Within this sample, there are no confirmed dual AGNs from the combination of radio and long-slit data yet.

In this work, we will instead focus on the possible kinematic classifications of dual AGNs that will be confirmed in future work in which we synthesize the VLA radio data and the long-slit kinematic data (F. Müller-Sánchez et al. 2016, in preparation). In Figures 5 and 6, we explore the kinematic properties of a toy model of a dual AGN with no outflow components that is instead dominated by rotating NLR components. Each dual AGN has a rotating disk and both are orbiting in the potential of the host galaxy. We determine that one of the galaxies in the sample matches this observational prediction of a spectral profile of a rotation-dominated dual AGN. This galaxy, J1018+5127, is classified as "Rotation Dominated + Disturbance." Figure 7 shows the spatially resolved profiles at both PAs for this candidate dual AGN. However, since this candidate lacks confirmation of dual radio cores, we do not create a separate kinematic classification for "dual AGNs" and instead allow candidate dual AGNs to fall under different kinematic classifications that describe the nature of the dual AGNs. Additionally, other work has predicted that dual AGNs, such as the toy model presented here, that are characterized purely by rotation-dominated NLRs are not as common as dual AGNs with outflow components (Blecha et al. 2013).

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We find that the most powerful quantitative properties for identifying the kinematic nature of a spectral profile are the velocity dispersion of each of the individual Gaussians in a two Gaussian fit (σ₁ and σ₂), the radial velocity of a one Gaussian fit (V_r), the number of kinematic components, and the alignment of the [O iii]λ5007 emission with the major axis of the galaxy. Figure 8 demonstrates the classification scheme based upon these parameters, Table 3 shows the values of these properties for both observed position angles of each galaxy, and Table 4 produces the final classification for the entire sample of 71 galaxies.

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Using these four properties of the [O iii]λ5007 profiles, we first separate rotation-dominated profiles from outflow-dominated profiles. This elimination-based technique is useful because the observational properties of rotating structure have more stringent constraints. For instance, rotating structure behaves according to Keplerian physics, which places limits on the line-of-sight velocity (V_r < 400 km s⁻¹) and velocity dispersion (σ₁ and σ₂ < 500 km s⁻¹, Osterbrock & Ferland 2006). These observationally defined velocity limits are used to divide outflow-dominated from rotation-dominated kinematics.

We identify outflow-dominated profiles as galaxies with velocity dispersions and line-of-sight velocities that are in excess of the limits given above for rotation-dominated profiles. The presence of a broad component (σ₁ or σ₂ > 500 km s⁻¹) demonstrates the presence of an outflow (Müller-Sánchez et al. 2011). Likewise, line-of-sight velocities that exceed 400 km s⁻¹ (V_r > 400 km s⁻¹) for a single Gaussian fit identify an outflow because discrete knots of emission have been observed at these velocities in outflows (e.g., Das et al. 2006; Fischer et al. 2013; Crenshaw et al. 2015). These outflow-dominated galaxies are then further classified into "Outflow" or "Outflow Composite" according to the number of kinematic components. For instance, a profile with >2 kinematic components is designated as "Outflow Composite" (determined using Akaike statistics described in Section 2). Outflows can show >2 components because they have distinct clouds of gas that move at a variety of discrete velocities dominated by a central engine. For a diagram of an outflow-dominated galaxy, see Figure 9.

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Galaxies that are not classified as outflow-dominated continue along the quantitative classification scheme; we next determine if a galaxy is rotation-dominated or ambiguous according to the alignment. Alignment of the ionized gas with the stellar disk is a property of rotation-dominated galaxies. We measure alignment by comparing PA_gal, the position angle of the photometric major axis of the galaxy from the SDSS r-band, to PA_{[O iii]} (measured in Section 2). As discussed in Comerford et al. (2012), a rotationally dominated double-peaked NLR should be aligned with the plane of the galaxy because the galaxy's potential dominates the kinematics; thus for these galaxies, PA_{[O iii]} ∼ PA_gal within a 20° error (as in Müller-Sánchez et al. 2015). If the [O iii]λ5007 emission is aligned with the plane of the galaxy, the emission is classified as rotation-dominated.

If the emission is not aligned with the plane of the galaxy and the emission has not already been classified as an outflow according to the value of radial velocity or the individual velocity dispersions, the emission could be a counter-rotating disk, an outflow, an inflow, or some combination of these kinematic origins. We could further tie the gas kinematics to an inflow origin if the galaxy were undergoing a merger since mergers funnel gas to the center of the galaxy (e.g., Hopkins et al. 2006). However, these gas kinematics could also be explained by an outflow or counter-rotating disk in a merger. If the galaxy is not undergoing a merger, we can rule out merger-driven inflows for the kinematic origin of the disturbed NLR kinematics. However, it would still be difficult to distinguish between an outflow-dominated kinematic origin to the NLR or a counter-rotating disk. We classify these galaxies as "Ambiguous" since we do not have the ability to fully determine the presence of a merger in these galaxies based upon SDSS imaging alone. Additionally, in either case, this type of galaxy is still ambiguous in its classification.

We use alignment as a classification tool once we have already classified the outflow-dominated galaxies; therefore, galaxies with outflows may also have emission that is aligned with the photometric major axis of the galaxy. This will be important in later work where we discuss the implications of the geometry of the outflow-dominated galaxies (R. Nevin et al. 2016, in preparation). Likewise, the number of Gaussian components is not used to further classify rotation-dominated galaxies. A rotation-dominated galaxy may have more than two Gaussian components, but we do not use this to further classify rotation-dominated galaxies into subcategories.

Within the category of rotation-dominated spectra, we further classify galaxies as "Rotation Dominated + Obscuration" or "Rotation Dominated + Disturbance" (such as a bar or spiral). If a galaxy has all of the kinematic properties of a rotation-dominated galaxy, the [O iii]λ5007 emission is aligned with the kinematic major axis of the galaxy, and the galaxy has a symmetric profile (compared to both the full sample and the rotation-dominated galaxies), we classify it as Rotation Dominated + Obscuration. Smith et al. (2012) suggest that equal flux double-peaked symmetric profiles are rotating disks. We classify one galaxy (J0736+4759) from the sample of 71 galaxies as Rotation Dominated + Obscuration due to its high degree of symmetry. Radiative transfer effects from a central dust lane could account for a single peaked Gaussian with a decrease in flux at zero velocity at both observed position angles, which would produce a double-peaked profile. Figure 9 shows a diagram of this type of kinematic origin of a double-peaked profile.

Dynamic disturbances in the plane of the galaxy could also account for a rotation-dominated spectrum with a double-peaked profile. We classify asymmetric rotation-dominated profiles where the [O iii]λ5007 emission is aligned with the kinematic major axis as "Rotation Dominated + Disturbance." These galaxies could host nuclear bars, spiral arms, or a kinematically disturbed dual AGN that causes asymmetric double-peaked profiles (Schoenmakers et al. 1997; Davies et al. 2009; Hicks et al. 2009; Blecha et al. 2013). Bars or spirals accelerate the zero velocity gas through infall or chaotic motion (Müller-Sánchez et al. 2009). This enhances the wings of the single peaked rotation-dominated profile and produces a double-peaked profile that is asymmetric in flux. Again, Figure 9 shows a diagram of a disturbed rotation-dominated galaxy. Note that distinguishing between a disturbed and obscured rotation-dominated NLR is the only category of classification that requires the asymmetry parameter. We discuss the quantitative determination of relative asymmetry for the rotation-dominated galaxies in Section 4.1.2.

For each position angle of each galaxy, we measure radial velocity, velocity dispersion, number of kinematic components, and alignment for each spatial row within the Akaike width (Table 3, for PA 1 and PA 2). Then, we calculate the number of rows that have >2 kinematic components within the spatial center (as measured by the stellar continuum) of the galaxy. We classify a galaxy as having >2 kinematic components if more than half of the rows of the Akaike width are best fit with >2 components (Table 4). We record velocity dispersion for both the one Gaussian fit (σ) and the individual components of the two Gaussian fit (σ₁ and σ₂). In Table 4, we determine if the dispersion of the single Gaussian fit is less than or greater than 500 km s⁻¹. We repeat this for each individual velocity dispersion of the two Gaussian fit. Next, in Table 3, we list the position angle of the galaxy (photometric major axis in SDSS r-band) and the position angle of the [O iii]λ5007. The photometric major axis measurements are reported in Müller-Sánchez et al. (2015), originating from Comerford et al. (2012). These position angles each have an error of ∼7° associated with the measurement, thus they are classified as aligned if these position angles are within 3σ (20°). After recording the quantitative measurements, we classify the galaxies in Table 4. We present a cartoon diagram of the kinematic origin of the [O iii]λ5007 double peaks for three of the main classification categories ("Outflow," "Rotation Dominated + Disturbance," and "Rotation Dominated + Obscuration") in Figure 9. We show an example of the profiles of the five main classifications, "Outflow," "Outflow Composite," "Rotation Dominated + Obscuration," "Rotation Dominated + Disturbance," and "Ambiguous" in Figures 10 and 11. We show the SDSS images to demonstrate the power of the alignment classification tool to separate "Ambiguous" from rotation-dominated classifications in Figure 12.

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We take the error on each measured quantity into consideration. We use a superscript to identify galaxies that fall into a given category but based upon the error bars are on the edge of this classification (within 1σ) in Table 4. We include these galaxies in their respective categories for later statistical analysis in Section 4.1.

This quantitative classification system allows us to use the spatial information from long-slit spectra to determine the origin of the disturbed kinematics that produce a double-peaked profile. We track the emission lines across the spatial extent of the galaxy and use the behavior of the ionized gas both at each individual position and across the galaxy as a whole to determine the structure responsible for the integrated double peaks. For the first time, we are able to make a distinction between rotation-dominated spectra and outflow-dominated spectra. Additionally, we are able to separate rotation-dominated and outflow-dominated spectra into further kinematically descriptive categories that explain the origin of the double peaks. After classifying the full sample, we find 26/71 Outflow Composite galaxies, 35/71 Outflow galaxies, 4/71 Rotation Dominated galaxies (1/71 Rotation-Dominated + Obscuration, 3/71 Rotation-Dominated + Disturbance), and 6/71 Ambiguous galaxies in this sample. We comment on the distribution of properties and the success of the classification for our kinematic classification technique in Section 4.1.

We are able to successfully classify 92% of the galaxies as either outflow- or rotation-dominated using our stand-alone long-slit classification technique. This technique utilizes the spatially resolved spectra to probe individual locations in the NLR and successfully identifies the nature of the NLR based upon this spectral information alone. We find from the 71 galaxy sample that 6% of the galaxies (4/71) are Rotation Dominated (1/71 has an obscuration and 3/71 are disturbed), 49% (35/71) are Outflows, 37% (26/71) are Outflow Composites, and 8% (6/71) are Ambiguous (having some combination of outflow, inflow, or rotation-dominated kinematic components).

Shen et al. (2011) conduct a similar classification with optical slit spectroscopy and near-infrared (NIR) imaging of 31 double-peaked AGNs and find that 50% of their sample are classified as having a single NLR, 10% are candidate dual AGNs, and the remaining 40% are ambiguous. Fu et al. (2011) use resolved spectroscopy to show that a single AGN with disturbed "gas kinematics" can produce 70% of the double-peaked profiles. Müller-Sánchez et al. (2015) find that 75% of the double-peaked profiles are produced by "gas kinematics" (including 70% outflows and 5% rotating NLRs), 15% are dual AGNs, and 10% are ambiguous. Blecha et al. (2013) find from their hydrodynamic simulations that only a minority of double-peaked NLRs result directly from two distinct NLRs associated with two AGNs orbiting a central potential. Most are associated with complex gas kinematics or rotating gas disks.

Our results agree with these findings, produce fewer ambiguous cases, and further separate complex gas kinematics into rotation-dominated and outflow-dominated categories. The majority (86%) of our sample is dominated by outflow signatures and only a small minority of the subsample is dominated by rotation. We conclude that selecting Type 2 AGNs by double peaks in integrated SDSS spectra is the most successful at selecting outflows.

We note that we are not fully able to confirm dual AGNs using this technique in isolation without radio data. We discuss the placement of a candidate dual AGN in the Rotation Dominated + Disturbance category in Section 5.1.

We discuss the properties of the galaxies classified as outflow-dominated in Section 4.1.1 and the implications for NLR outflow theory. We analyze the properties of the rotation-dominated galaxies in Section 4.1.2 and compare to predictions from the literature.

4.1.1. Kinematic Properties of the Outflow and Outflow Composite Galaxies

We find that the majority (86%) of the uniform sample of double-peaked NLR galaxies are dominated by outflows. Double-peaked emission lines in SDSS are far more successful at selecting AGN outflows than two kinematically distinct rotating NLRs associated with a dual AGN. Here we discuss the kinematic properties of Outflows and Outflow Composite galaxies and we compare these findings to the current theory of the structure of NLR outflows.

Roughly half of the outflow-dominated galaxies are classified as Outflow. We add the caveat that the classification of Outflow or Outflow Composite is sensitive to S/N; for galaxies with lower S/N, we often do not have enough flux to distinguish the low flux wings of the profiles from the background. We therefore find that these lower S/N galaxies are often better fit with two Gaussians than three. To confirm that the number of Gaussian components is sensitive to S/N, we perform an experiment. We introduce Gaussian noise at a level equivalent to 10% of the flux to spectra that are best fit with a 3 Gaussian component fit. We complete 100 iterations of this random noise introduction and find that 37% of the time we recover a three component fit. The rest of the time we find that a 2 Gaussian component fit is better. Figure 13 shows an example simulation of decreased S/N and its effects on the number of Gaussian components that provide the optimal fit for a spatial row.

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We note that, although using the number of Gaussian components as a classification tool is sensitive to S/N, we still find it useful as a method of constraining the number of emission knots observed in an outflow. Although S/N can influence this classification, galaxies may intrinsically have only two kinematic components and be true Outflows. However, due to the S/N sensitivity, in some cases, the number of component fits is a lower limit, so the galaxies that are classified as Outflow could be classified as Outflow Composites if they were observed with longer integration times. Due to these considerations, we choose to analyze Outflow Composites and Outflows together and refer to this combined category as outflow-dominated in our discussion.

We present the kinematic properties of all of the classification categories in Table 5. We focus here on the properties of the outflow-dominated galaxies. We find that 18% of the outflow-dominated galaxies have a single Gaussian radial velocity in excess of 400 km s⁻¹, 77% have an overall velocity dispersion greater than 500 km s⁻¹, and 100% have a single component with a velocity dispersion in excess of 500 km s⁻¹. Some profiles show the discrepancy where a single Gaussian velocity dispersion is less than the two individual velocity dispersions for the two Gaussian fit. This is because these are double-peaked profiles that are often separated significantly in velocity space. When we fit a single Gaussian component, it sometimes encompasses only one of the two components, while the two Gaussian fit is more sensitive to underlying high velocity dispersion low flux wings.

Table 5.  Kinematic Classification Statistics

Properties	Rotation	Ambiguous	Outflow	Outflow
	Dominated			Composite
>2 Gaussian Components	0/4 (0%)	2/6 (33.3%)	0/35 (0%)	26/26 (100%)
Vr > 400 km s−1	0/4 (0%)	0/6 (0%)	9/35 (25.7%)	2/26 (7.7%)
σ > 500 km s−1	3/4 (75%)	6/6 (100%)	28/35 (80.0%)	19/26 (73.1%)
σ1 or σ2 > 500 km s−1	0/4 (0%)	0/6 (0%)	35/35 (100%)	26/26 (100%)
Aligned? (Disk and [O iii])	4/4 (100%)	0/6 (0%)	17/35 (48.6%)	10/26 (38.5%)

Note. The statistics of the properties for each kinematic classification. Row 1: the fraction of galaxies in each classification that are best fit by more than 2 Gaussian components. Row 2: the fraction of galaxies with a radial velocity of the single Gaussian component fit in excess of 400 km s⁻¹. Row 3: the fraction of galaxies in each classification that have a single Gaussian component velocity dispersion greater than 500 km s⁻¹. Although this property is not used in the classification process, we discuss its value for the different classification categories below. Row 4: velocity dispersion, but for the individual components of the two Gaussian fits. Row 5: the fraction of galaxies where the position angle of the [O iii]λ5007 emission is aligned (within 20°) with the photometric major axis of the galaxy.

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We find that the velocity dispersion of the individual components of the two Gaussian fit, σ₁ or σ₂, is the most powerful tool in identifying outflow-dominated galaxies. In a few galaxies, radial velocity is also important in identifying knots of emission moving at velocities in excess of a rotation-dominated NLR. However, all of the outflow-dominated galaxies that have a radial velocity in excess of 400 km s⁻¹ also have individual components of the two Gaussian fit with velocity dispersions in excess of 500 km s⁻¹. We determine that σ₁ and σ₂ are more useful as a probe of the bulk motion of the outflow than V_r. The knots of emission that achieve velocities in excess of 400 km s⁻¹ could be the faintest components of the outflow, and remain unidentified in our Gaussian fitting and classification method for galaxies with lower S/N. Velocity dispersion is a more consistent identifier of outflow-dominated galaxies because it describes the bulk properties of the walls of the outflow as opposed to being related to extremely low surface brightness knots of fast-moving gas.

We found that, although we did not directly use the velocity dispersion of a single Gaussian fit (σ) in our classification, 77% of the outflow-dominated galaxies had overall velocity dispersions in excess of 500 km s⁻¹. However, 75% of the rotation-dominated galaxies also had this property. This is unsurprising since rotation-dominated galaxies with a disturbance should have an overall velocity dispersion that exceeds the value for an undisturbed rotating disk. The single velocity dispersion σ was not as useful as σ₁ and σ₂ in discriminating between rotation-dominated and outflow-dominated galaxies.

4.1.2. Properties of the Rotation-dominated Galaxies

We identify four galaxies as rotation-dominated. The origin of the double peaks is disturbed kinematics from a bar, spiral, or a possible dual AGN in 3/4 of the cases and an obscuration in 1/4 of the cases. In other words, the category "disturbed" accounts for all kinematic deviations of a rotation-dominated profile from a single rotating disk. We distinguish between an obscured rotation-dominated galaxy and a disturbed rotation-dominated galaxy using the relative nonparametric asymmetry values of the profiles of each galaxy. Although we measure the relative asymmetry parameter for all galaxies, we only use it as a classification tool to distinguish between different kinematic origins of rotation-dominated galaxies.

We use a statistical quantitative method to classify rotation-dominated galaxies as asymmetric or symmetric. We determine the asymmetry values for each galaxy by measuring an asymmetry value for all spatial positions of each position angle. We then take the asymmetry value to be the maximum asymmetry value from either PA. We show this maximum asymmetry value for the four rotation-dominated galaxies in Figure 14. The rotation-dominated galaxies have asymmetry values of 0.12 (J0736+4759), 0.57 (J1018+5127), −0.43 (J1250+0746), and −0.72 (J1516+0517). Note that we compare the absolute value of the asymmetry value because a negative or positive value indicates if the profile has blue or red wings, respectively. Using the values of asymmetry for the rotation-dominated galaxies, we can compare the population mean of the entire sample of 71 galaxies (0.43). Given the sample standard deviation (0.15) for this measurement, we can initially conclude that J0736+4759 is about two standard deviations below the mean and the remaining three rotation-dominated galaxies are consistent with the mean (J1250+0746), one standard deviation greater than the mean asymmetry (J1018+5127) and about two standard deviations above the mean (J1516+0517).

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We build upon these initial conclusions using the Analysis of Means (ANOM) statistical test. ANOM allows us to set a confidence interval and test for differences in means between subsamples. We plan to group J1018+5127, J1250+0746, and J1516+0517 together and prove that the mean asymmetry of this group is statistically different than the asymmetry of the galaxy J0736+4759, which we have preliminarily demonstrated has a relatively symmetric profile when compared to the other rotation-dominated galaxies. We define the confidence interval and population mean used in ANOM as

$$\begin{eqnarray*}&&\bar{X}\pm {h}_{c,{n}_{j}}\sqrt{\displaystyle \frac{{\sigma }_{p}^{2}(c-1)}{n}},\end{eqnarray*}$$

where $\bar{X}$ is the mean of the full sample (71), c is the number of groups between which we wish to compare means (2), n_j is the sample size for group j, ${h}_{c,{n}_{j}}$ is the critical value for Nelson's h statistic with c groups and n_j observations per group, ${\sigma }_{p}^{2}$ is the pooled variance of the overall sample, and n is the total number of observations. Note that n_j is set by the smallest sample size of the groups (1). The smallest group sample size is set by J0736+4759 with one measurement. Thus, in our case, ${h}_{\mathrm{2,1}}=12.7$ for a 95% confidence value.

We obtain a 95% confidence interval around the sample mean of [0.19, 0.66]. We find that the A value of J0736+4759 (0.12) is significantly less than the mean of the overall sample and that the mean of the A values for the group including J1018+5127, J1250+0746, and J1516+0517 (0.58) is consistent with the mean of the overall sample. J1018+5127, J1250+0746, and J1516+0517 are classified as asymmetric rotation-dominated galaxies quantitatively according to sample statistics. We classify them as Rotation Dominated + Disturbance. We classify J0736+4759 as Rotation Dominated + Obscuration.

Liu et al. (2013b) use an identical definition of nonparametric asymmetry and find values of asymmetry with a maximum around 0.4 for their energetic outflows. Therefore, our quantitative asymmetry cut is even higher, meaning that our rotation-dominated galaxies with a disturbance are even more asymmetric when compared to other work.

We can also confirm that the three galaxies that we classify as asymmetric under our nonparametric measurement would be classified as asymmetric by Smith et al. (2012) using an alternate definition of asymmetry. Smith et al. (2012) use a ratio of the red and blue flux components of their double-peaked profile fits to quantify asymmetry for their sample of "equal-peaked" AGNs (EPAGNs). Specifically, they classify a symmetric EPAGN as one with a value of $0.75\leqslant {F}_{r}/{F}_{b}\leqslant 1.25$, where F_r is the flux of the redder Gaussian component and F_b is the flux of the bluer component. Their quantitative classification involves fitting two Gaussians. We prefer the nonparametric method of asymmetry quantification because it accounts for features such as low flux wings in complicated profiles that are best fit by more than two Gaussians.

Smith et al. (2012) conclude that symmetric EPAGNs from the double-peaked sample are most likely to originate from a single rotation-dominated NLR. Our clearest example of this type of a rotation-dominated galaxy is the galaxy J0736+4759, which is rotation-dominated with a central obscuration due to its high degree of symmetry. The peaks are of equal flux for both position angles across the entire slit. This galaxy is consistent with the EPAGNs discussed in Smith et al. (2012). However, the results of our classification reveal that rotation-dominated objects with double-peaked profiles are more likely to be asymmetric due to disturbances such as spirals, bars, or dual AGNs. Three of our four rotation-dominated galaxies have asymmetric peaks.

We also investigate the Hα kinematics of the four rotation-dominated galaxies. We refrain from investigating the Hα kinematics of all the galaxies in this sample because it is beyond the scope of this work. However, it is a useful exercise to compare the Hα kinematics to the [O iii]λ5007 kinematics for the rotation-dominated profiles because ionized gas dominated by rotation should exhibit gas kinematics that are identical to the stellar kinematics of the stars in the disk. Note that, although Hα traces both the NLR and stellar kinematics, in the case of a rotation-dominated NLR both the stellar kinematics and gas ionized by the AGN should be consistent with rotation. In other words, if the ionized gas is coincident with the stellar disk, the Hα and [O iii]λ5007 kinematics should be identical.

We find for the four rotation-dominated galaxies that the Hα emission is aligned with the [O iii]λ5007 emission and that the velocity offsets, velocity dispersions, and relative asymmetry values of the profiles are consistent within the errors (to 3σ). We present velocity separations (ΔV) between the red and blue Gaussian components of each profile in Table 6 and demonstrate the consistency of the profiles visually in Figure 15 for J1018+5127. The results verify that the kinematics of these galaxies are indeed dominated by rotation.

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Table 6.  ΔV for [O iii]λ5007 and Hα

SDSS ID	[O iii]λ5007	[O iii]λ5007	Hα	Hα
	ΔV (km s−1)	ΔV (km s−1)	ΔV (km s−1)	ΔV (km s−1)
	PA 1	PA 2	PA 1	PA 2
J0736+4759a	274 ± 6	283 ± 6	289 ± 118	273 ± 190
J1018+5127	298 ± 4	285 ± 4	312 ± 79	312 ± 79
J1250+0746	211 ± 8	218 ± 4	184 ± 2	158 ± 58
J1516+0517	292 ± 30	285 ± 50	320 ± 81	309 ± 61

Note. Table of the separation in velocity space (ΔV) between the blue and red Gaussian component fits for the four rotation-dominated galaxies. Column 1: galaxy name. Columns 2 and 3: the velocity separation in [O iii]λ5007 in km s⁻¹ for PA 1 and PA 2 for each galaxy. Columns 4 and 5: the velocity separation in Hα in km s⁻¹ for PA 1 and PA 2.

^aDue to a restricted wavelength coverage from the observations of J0736+4759, we lack a Hα profile and instead compare to the Hβ profile.

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This kinematic long-slit technique was originally conceived as a method for positively identifying candidate dual AGNs. We cannot exclude dual AGNs from any of the classification categories with this work, but we can offer insight into which categories they could fall.

A compelling candidate dual AGN could be classified as Outflow or Outflow Composite. Both NLRs will only be visible during the latest kiloparsec and sub-kiloparsec separation stages of dual AGN evolution while both AGNs are accreting simultaneously (Van Wassenhove et al. 2012; Blecha et al. 2013; Steinborn et al. 2016). Since observable dual AGNs are by definition in an actively accreting phase of evolution, they can drive outflows and be classified as outflow-dominated. Observationally, past work has found that the optical spectra of confirmed dual AGNs have signatures of disturbed kinematics (outflows and shocks, e.g., Engel et al. 2010; Mazzarella et al. 2012). Even if one or both distinct NLRs can be described as rotation-dominated, the two AGNs might have unequal luminosities. We would observe this type of galaxy as one narrow component with an associated outflow that dominates a smaller flux second narrow rotation-dominated component from the second AGN. This case of a fainter NLR would be categorized as Outflow Composite or Outflow based upon the number of kinematic components in the outflow and the brightness of the dimmer AGN.

Blecha et al. (2013) demonstrate that either rotation-dominated NLR of the pair of AGNs could be disturbed by the secondary AGN and appear rotation-dominated with a disturbance. In fact, dual AGNs are more likely to appear observationally as NLRs characterized by disturbed kinematics rather than kinematics dominated by the motion of two SMBHs. We would classify this type of profile as Rotation Dominated + Disturbance. Returning to the picture of the toy model of a dual AGN with two rotation-dominated NLRs, recall that even a theoretical dual AGN with no disturbed kinematics would be classified as Rotation Dominated + Disturbance (e.g., J1018+5127). This theoretical dual AGN would have NLRs that alternate in flux at the position angle of maximum spatial separation (Figure 5). This causes the profile of this type of dual AGNs to appear asymmetric for at least one position angle. Lastly, dual AGNs could be classified as Ambiguous because they may demonstrate a lower velocity offset or dispersion, which are properties that are consistent with either an inflow or a less energetic outflow (σ₁ or σ₂ < 500 km s⁻¹ or V_r < 400 km s⁻¹).

Even if both rotation-dominated NLRs are visible, Blecha et al. (2013) show that these NLRs would most likely demonstrate a large velocity separation between individual components of the order of ΔV > 500 km s⁻¹ due to enhanced velocity separation during pericentric passage. These objects would most likely be classified as outflow-dominated by our kinematic classification because the velocity offset between the individual components is so large. This large velocity offset would cause the single Gaussian V_r to be greater than 400 km s⁻¹ and this type of galaxy would be classified as an outflow. While the velocity offset limits were derived with the purpose of identifying fast-moving outflow components, narrower dual components could also fall into this category. At present, we have no galaxies that fall into this category of being classified as an Outflow due to the velocity offset of two narrow lines with a large velocity separation.

The only category that is unlikely to include dual AGNs is Rotation Dominated + Obscuration. The high degree of symmetry required for this classification is statistically unlikely to be associated with two NLRs producing an outflow or either rotating NLR being disrupted by a secondary AGN. Blecha et al. (2013) predict that equal flux symmetric profiles are most likely associated with an obscured rotating disk, and Smith et al. (2012) support this prediction observationally.

None of the galaxies in this sample are yet confirmed as radio-detected dual AGN, but one galaxy presents a compelling long-slit spectrum, where each NLR appears to be rotation-dominated. This galaxy, J1018+5127, is undetected in the VLA radio data, so we can place an upper limit on the radio luminosity but cannot reject the presence of a double radio core (F. Müller-Sánchez et al. 2016, in preparation). The long-slit [O iii]λ5007 profiles of J1018+5127 (Figure 16) are consistent with two distinct rotation-dominated NLRs, and this galaxy is classified as Rotation Dominated + Disturbance. One of the rotation-dominated NLRs is centered at zero velocity and one has a blueshift of ∼450 km s⁻¹ at all spatial positions. The flux ratio of the NLRs switches along the first PA and the NLRs are roughly equal in flux at the second PA. This is consistent with a dual NLR system with maximal separation nearest the first PA; we measure PA_{[O iii]} = 22°, which is nearly aligned with PA_gal = 27°. This object is most extended in the plane of the galaxy, and this is consistent with a dual AGN interpretation (Comerford et al. 2012). Although we can conclude that the long-slit kinematic information is consistent with a dual AGN explanation, we stress that this is not a confirmed dual AGN without the complementary double radio core confirmation.

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In the study of the structure of AGNs, the nature of the NLR is still uncertain. In this work, we investigate how the extent of the NLR scales with the luminosity of the central source (R${}_{\mathrm{NLR}}\propto {L}_{[{\rm{O}}\,{\rm{III}}]}^{\alpha }$). If we can investigate this relationship over a large range of AGN luminosities (by combining our sample with other studies), we can use the strength of this correlation to constrain the ionization structure (ionization parameter) and density structure of the NLR.

The [O iii] luminosity is an accurate probe of the ionization structure and density of the NLR because it is a collisionally excited transition; the line emissivity of [O iii]λ5007 is set by the electron density n_e and ionization state. Note that, although [O iii]λ5007 can also be produced by stars, BPT diagnostics suggest an AGN origin for the emission in this sample. We use the observed [O iii] luminosity (L_{[O iii]}; Section 2.4) in this work as a probe of the intrinsic luminosity of the NLR.⁵

A positive slope is expected in the size–luminosity relationship if the AGN's radiation is responsible for the photoionization of the NLR. The slope of the relationship, α, is influenced by the density structure of the NLR and the ionization parameter, U, which is defined as the ratio of the number density of ionizing photons to the number density of electrons:

$$\begin{eqnarray*}&&U=\displaystyle \frac{{n}_{\gamma }}{{n}_{e}}=\displaystyle \frac{1}{4\pi {R}_{\mathrm{NLR}}^{2}{{cn}}_{e}}{\int }_{{\nu }_{0}}^{\infty }\displaystyle \frac{{L}_{\nu }}{h\nu }d\nu \end{eqnarray*}$$

where n_γ is the number density of ionizing photons, R_NLR is the radius of illumination by a central source (Section 2.4), L_ν integrated is the bolometric luminosity of the central source over all frequencies, ν is frequency, and ν₀ is the ionization edge.

Therefore, the relationship between the estimated integrated ionizing luminosity (L_ion, in this work, we use L_{[O iii]} as a proxy for L_ion) and radius can be written as

$$\begin{eqnarray*}&&{R}_{\mathrm{NLR}}={{KL}}_{[{\rm{O}}\,{\rm{III}}]}^{0.5}{({{Un}}_{e})}^{-0.5},\end{eqnarray*}$$

where $K={(4\pi c\langle h\nu \rangle )}^{-0.5}$. Determining the slope of the size–luminosity relationship is a direct investigation of both the ionization structure U and the density structure n_e of the NLR, both of which are poorly determined.

Our sample of 71 moderate-luminosity ($40\lt \mathrm{log}\ {L}_{[{\rm{O}}{\rm{III}}]}$ (erg s⁻¹) < 43) AGNs represents a unique opportunity to investigate this size–luminosity relationship for a uniform sample of moderate-luminosity AGNs with resolved NLRs. Our measurement of R_NLR (Section 2.4) is a lower limit since we only have spatial data along two dimensions of the galaxy. If neither position angle is exactly aligned with the position angle of maximal extent of the NLR, we are unable to measure the true extent of the NLR (R_NLR; Section 2.4). However, we note that other studies of the size–luminosity relationship are also limited by resolution and surface brightness considerations (Fraquelli et al. 2000; Bennert et al. 2002; Schmitt et al. 2003; Hainline et al. 2013; Liu et al. 2013a).

Here we review the slope of the size–luminosity relationship measured by other studies. In a simplistic one-zone model of the NLR, the NLR is described by an isotropic distribution of gas where n_e and U are constant. In this case, the size–luminosity relationship will have a positive correlation and slope of α = 0.5 (Basin & Laor 2005). Bennert et al. (2002) find a slope of α = 0.52 ± 0.06 for their sample of seven Seyfert 2 galaxies and seven quasars (41 < log L_{[O iii]} (erg s⁻¹) < 43) and conclude that a constant density law and a constant value for the ionization parameter describe the NLR. Hainline et al. (2013) predict a limit to the correlation at the higher luminosity extreme of AGNs (42 < log L_{[O iii]} (erg s⁻¹) < 43). This is confirmed by Hainline et al. (2014); they observe quasars at the high-luminosity limit of AGNs and observe a flattening in the size–luminosity relationship. They attribute this flattening to a limit in the amount of gas in the gas reservoir of the NLR that is available for ionization. Liu et al. (2013a) confirm this effect and find a flatter slope of 0.25 ± 0.02 for a sample of 11 luminous obscured quasars (42 < log L_{[O iii]} (erg s⁻¹) < 44).

However, the flattening at the high-luminosity end of the relationship is not the only interesting conclusion from previous work. Schmitt et al. (2003) find a slope of 0.33 ± 0.04 for their sample of moderate-luminosity (39 < log L_{[O iii]} (erg s⁻¹) < 42) Seyfert 1 and Seyfert 2 galaxies, which is much shallower than the slope of α = 0.5 predicted for a constant density law and ionization parameter. They conclude that a single-zone model with a constant density and ionization parameter is not an appropriate representation of the NLR and that a two-zone ionization model for the NLR is a better explanation (Dopita et al. 2002; Basin & Laor 2005).

In a two-zone ionization model, the NLR can be described by both a matter-bound zone and an ionization-bound zone, where the ionizing photons are pre-processed by passing through an ionization-bound zone. The ionization-bound zone is characterized by a lower ionization parameter and a higher density. The ionization-bound regime is thus optically thick to ionizing radiation. In the most simplistic two-zone models, the ionization-bound zone is confined to a smaller radius and the matter-bound zone exists at spatial positions exterior to this. We will also discuss a more complicated two-zone model where these two zones exist in a clumpier and/or mixed state, but note that Basin & Laor (2005) model the radially confined case where denser NLR clouds are confined to a smaller radii and all NLR material is distributed continuously. Most work deals with this simplistic model. Basin & Laor (2005) assume that the majority of emission originates from the outer matter-bound zone where the size–luminosity relationship can be modeled with a slope of α = 0.34. Thus, an NLR with mixed matter-bound and ionization-bound zones could be described by a slope between the extremes of α = 0.34 and α = 0.5. Likewise, an NLR with a clumpier distribution of matter-bound material than the continuous assumption would have a slope shallower than α = 0.34.

Observations support this idea of a changing ionization parameter; the ionization parameter can decrease with radius (e.g., Fraquelli et al. 2000), which could be a signature of a matter-bound region at a larger radius of a galaxy. Liu et al. (2013a) confirm that beyond 7 kpc for their quasars sample, the ionization diagnostic [O iii]/Hβ declines. They argue that the NLR is entering a matter-bound regime at these radii, which explains the shallower slope they fit to their size–luminosity relationship (0.25 ± 0.02). Consequently, arguing for a two-zone ionization model where an outer matter-bound zone is characterized by a lower density is similar to arguing that the gas reservoir is depleted at these extreme radii.

Shocks may also influence the size–luminosity relationship for AGNs. Müller-Sánchez et al. (2015) find a steeper slope of 0.52 ± 0.14 for a sample of 18 double-peaked AGNs that includes three confirmed dual AGNs. We note that shocks may steepen this slope by introducing higher-ionization zones. Dual AGNs, which host two interacting NLRs, are most likely to produce shocks that are enhancing this relationship, thus enhancing the [O iii]λ5007 emissivity.

From our sample of moderate-luminosity AGNs, we confirm a linear correlation with a Pearson correlation coefficient of 0.48 and find a log–log slope⁶ of 0.21 ± 0.05. We can reject the null hypothesis that α = 0 to a 1% confidence level. We plot the results of our linear fit in Figure 17 with the slopes of the one-zone and two-zone ionization models for comparison. We discuss our linear correlation coefficient, fitted slope, and confidence interval on this value both in the context of the one- and two-zone ionization models.

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Our results for a fitted slope are inconsistent with the predicted slope of α = 0.5 for a one-zone ionization model to 3σ confidence. Our results cannot be explained by a constant density profile with a constant ionization parameter. Our slope is closer to the predicted slope of 0.34 (within 3σ confidence) for the two-zone ionization model of the NLR (Basin & Laor 2005). However, our slope is still shallower than α = 0.34 at a confidence level of 1σ. We suggest two possible explanations for this discrepancy.

First, the filling factor of the NLR is not well determined, so if the clouds are sparsely distributed, this would flatten the relationship to values less than the α = 0.34 slope derived for a simple two-zone ionization model. This simple model assumes a smooth density distribution of the NLR gas and a radial distribution of the two zones. This implies that the simplistic two-zone model may not be adequate to explain our data and we may require a clumpier or mixed NLR that is not well described by a simplistic radial density profile, as in Basin & Laor (2005).

Alternatively, we measure larger than average NLR extents when compared to NLR size measurements for AGNs with a similar luminosity range (40 < log L_{[O iii]} (erg s⁻¹) < 43); see Hainline et al. (2013) and references therein. We find a mean R_NLR of 4.3 kpc, which is comparable to studies of more luminous AGNs (e.g., Bennert et al. 2002 find a mean R_NLR of 4.3 kpc for their 41 < log L_{[O iii]} (erg s⁻¹) < 43 AGNs and Hainline et al. 2013 find a mean R_NLR of 3.8 kpc for their 42 < log L_{[O iii]} (erg s⁻¹) < 43 AGNs) and our value of R_NLR is greater than studies of AGNs with similar luminosity ranges (e.g., Schmitt et al. 2003 find a maximum R_NLR of 1.6 kpc for their 39 < log L_{[O iii]} (erg s⁻¹) < 42 AGNs).

Although we refer to our sample as moderate-luminosity AGNs, note that some of them have observed luminosities in a range described as higher luminosity (42 < log L_{[O iii]} (erg s⁻¹) < 43). We may be probing regions of the NLR where the gas reservoirs available for ionization are limited and the material is better characterized as matter-bound. Basin & Laor (2005) derive the expected slope of 0.34 for a two-zone ionization model for galaxies with a maximum spatial extent of the NLR of 1.3–1.7 kpc and a constant density. Our sample of galaxies may have a relatively larger and/or sparsely populated (less dense) matter-bound region. These effects could lead to a shallower slope for the relationship. We note that, while we cannot fully distinguish between these two scenarios, our results are more consistent with a two-zone rather than a one-zone picture of the NLR. We refer to some combination of a non-constant density or non-radially distributed matter-bound region as a "clumpy two-zone model."

The positive correlation of this relationship indicates that the AGN itself is the mechanism responsible for ionization of the NLR. The Pearson correlation coefficient for the data (0.48) reflects scatter in the data. This could be a consequence of the lower limit nature of the R_NLR measurement. The error bars show significant uncertainty in both the luminosity measurement and the spatial extent measurement for some galaxies in the sample. Another source of the scatter in our data could be the nature of a two-zone ionizing model for the NLR. While studies mostly describe the matter-bound zone as the outer zone of a galaxy, the matter-bound and ionization-bound zones could exist at different locations in a galaxy, forming a "clumpier" picture of an intermixed two-zone NLR. Therefore, individual galaxies in our large sample could have different ionization structures and this could intrinsically produce the scatter.