A VIEW OF THE NARROW-LINE REGION IN THE INFRARED: ACTIVE GALACTIC NUCLEI WITH RESOLVED FINE-STRUCTURE LINES IN THE SPITZER ARCHIVE

We downloaded the Spitzer S15.0 pipeline basic calibration data (BCD) files. We used both staring and mapping observations, taken on either single-source or cluster mode.

The BCD files of the long-high (LH) wavelength data of each source were processed by the IDL routine DARK SETTLE, which is posted on the Spitzer Science Center (SSC) Web site, to correct for gradations of the dark current along the detector that leads to order tilting and mismatch. Using the short-high (SH) BCD files and the dark-settle corrected LH BCD files, we computed the average frame for each set of on-source observations, namely, for each target, nod position, and module. To identify cosmic ray hits, we also computed the median frame for the same set of observations and compared it to the average frame on a pixel-by-pixel basis. A pixel was flagged if the difference between the median and the average frame value differed by a factor of more than three times the rms noise in the median frame. For this pixel, the average value was replaced by the median value. For sources with available observations on sky,⁷ we also computed the median sky frame, which we subtracted from the on-source frame.

The next step was the removal of bad and rogue (i.e., slowly varying time response) pixels. We used the individual sky frames to create a generic bad pixel mask for all sources observed in a single Spitzer campaign, which we merged with the bad pixel map available at the SSC Web site for the same campaign. We then merged this generic mask with the mask of each individual (on-source and on-sky) exposure to create the mask for each science frame, nod position, and module. We proceeded to further masking of outliers, i.e., pixels that were located a couple of columns away from the edges of each spectral order, and that had a value exceeding the rms noise of the science frame. Their values were replaced with the median value of the frame, computed using only pixels in the useful detector range. A final visual inspection and a manual cleaning of the science frames were performed using the IRSCLEAN routine. All rogue pixels and outliers were flagged in the mask file.

The uncertainty of the average on-source frame was calculated as the square root of the sum of the squares of all individual uncertainty files, divided by the number of exposures. When sky observations were available, we computed the sky frame uncertainty in a similar way and combined it with the on-source frame uncertainty to produce the uncertainty of the final science frame.

We used the science frame, together with its uncertainty and mask files as inputs to the SSC software SPICE, which produces a one-dimensional spectrum from a two-dimensional spectral image. To extract the spectra, we used the regular extraction mode, which equally weighs pixels when collapsing them along each row. We assumed a point-source extraction, since the LH and SH apertures (223 × 111 and 113 × 47, respectively) are likely to include the bulk of the NLR emission for most sources in our sample. The end product of SPICE is the wavelength and flux calibrated spectrum for each individual order.

We merged the spectra of the various orders to a single spectrum for each nod position, clipping noisy edges (between 2 and 25 pixels, depending on the order). This task was performed for both the SH and the LH data sets. The SH and LH spectra were then merged to produce the full-range spectrum per nod position. The final spectrum of each object was produced by averaging the one-dimensional, full-range spectra of the two nod positions. Special care was taken not to merge sky-subtracted and non-sky-subtracted data sets for sources with observations from different programs. At the wavelengths of key atomic/molecular lines, only nod positions without bad pixels were used, when possible. For all other pixels with a bad pixel flag in one nod position, we only kept the value of the second nod position when the two values differed by more than the local rms noise value.

As in Dasyra et al. (2008),⁸ we fitted all lines and their underlying continua using Gaussian and second-order polynomial functions, respectively. Gaussian fitting was preferred over direct FWHM computations which, given the resolution of IRS, can only be reliably performed for few high-velocity systems (e.g., Spoon & Holt 2009). Gaussian fitting also suits best the studies of cloud kinematics on virial, regular, or symmetric motions, instead of clouds that are entrained by asymmetric outflows (Greene & Ho 2005).

To claim a line detection, we required that its signal-to-noise ratio (S/N) was greater than 3. To measure line widths, however, we only used lines with S/N > 5 to avoid studying profiles of barely detected lines. We considered resolved all lines with σ_m − _m > σ_i + _i, where σ_m is the measured velocity dispersion, σ_i is the instrumental resolution at a given wavelength divided by 2.35, and _i is the error of σ_i. The average resolution value in the 12.0–18.0 μm range, which comprises all neon lines for the low z galaxies, is 507 ± 66 km s⁻¹. The 25.0–34.2 μm range, which comprises most of the O iv emission, has an average resolution of 503 ± 63 km s⁻¹. The error of σ_m, _m, encapsulates both measurement and instrumental uncertainties. It was computed as (²_st + _i²)^0.5, where _st is the standard deviation of the different velocity dispersion values that were obtained for each line when using different polynomial functions to describe its underlying continuum. Intrinsic velocity dispersions, σ, were computed as (σ²_m − σ_i²)^0.5, converted to rest frame, and presented in Tables 1 and 2 for key fine-structure lines in all sources.

To assess possible systematic errors in the wavelength calibration, we normalized and stacked the line profiles of 29 sources with detected but unresolved emission lines of [Ne ii], [S iv], [Ne iii], [O iv], and [Ne v] (Figure 2). The stacking of unresolved lines in different z sources permitted for a finer sampling of the instrumental resolution curve than that determined by the detector pixel size. We only used sources at z < 0.02 to study systematic effects within a few pixels from the rest-frame wavelength of each line. This z cutoff translates to 25 pixels at the center of the SH array range, 14.7 μm. We found that line peak offsets due to such systematics are typically limited to 50 km s⁻¹.

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Of the 304 AGNs in our sample, 300 had spectral coverage at 10.51 μm, and 143 showed [S iv] emission. Similarly, 226 sources had spectral coverage at 25.89 μm, and 135 had [O iv] detections. Thus, the typical line detection rate was of the order of ∼50%.

We plotted the luminosities of the most frequently observed MIR lines against that of [Ne v] to identify fine-structure lines that can be reliably used as tracers of the gas that is photoionized by the AGN (Figure 3). Given that photons of at least 97.12 eV are required to ionize Ne iv to Ne v, its ionization source must be far-ultraviolet or soft X-ray radiation from the AGN. We find that the [Ne v] luminosity is on a tight correlation of 0.2 dex scatter with the [O iv] and [S iv] luminosities (Figure 3; Pereira-Santaella et al. 2010), and we further confirm that the [Ne v] and [Ne iii] luminosities trace each other well (Gorjian et al. 2007). Therefore, the Ne v, O iv, Ne iii, and S iv ions are most likely to be primarily excited by the same mechanism. However, the scatter between the luminosities of [Ne v] and [Ne ii] or [Si ii] is approximately twice as high, of 0.4–0.5 dex. Ne ii and Si ii have low ionization potentials (21.56 and 8.15 eV, respectively), thus, a non-negligible part of their line emission could be tracing star-forming regions in the AGN host galaxy.

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The excellent, almost one-to-one correlation over several orders of magnitude in luminosity that is seen between the [Ne v] 14.32 μm and [S iv] 10.51 μm lines does not include any extinction correction. This result indicates that the bulk of the [S iv] emission is not strongly affected by the silicate absorption feature centered at 9.7 μm, which is seen in several of our targets with moderate or high optical depths, i.e., τ > 0.5. Thus, the geometric distribution of the silicates is likely to be more compact than the size of the NLR (see also Soifer et al. 2002; Tristram et al. 2007; Schweitzer et al. 2008). While obscuration effects do not significantly affect the relative fluxes of MIR lines, the [O iii] 5007 Å emission can suffer from strong extinction primarily in type 2 AGNs (Figure 3).

Our query for sources with resolved [S iv], [Ne iii], [O iv], or [Ne v] lines resulted in 81 AGNs with kinematic information of the NLR gas in the MIR (Figures 4 and 5). The different fine-structure lines that were used as primary tracers of clouds photoionized by the AGN often led to different σ measurements (Figures 4 and 5). Differences in the ionization potential of the various ionic species can play a major role in determining the observed line profiles, alongside with differences in the critical density for collisional de-excitation of the various transitions, and with light extinction by dust particles. We find the [Ne v] line to be often broader than lines from ions of lower ionization potential (e.g., Mrk 590; Figures 4 and 5; Tables 3 and 4). A significant increase in the average velocity dispersion with increasing ionization potential is shown in Figures 6 and 7, as found for 16 sources with resolved profiles in all [Ne ii], [O iii], [S iv], [Ne iii], [O iv], and [Ne v] lines. This result provides evidence for a stratification of the NLR clouds, i.e., for ions of high ionization being located nearer to the BH than ions of low ionization potential (Filippenko & Halpern 1984; Oliva et al. 1994; Ho 2009).

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Table 3. Fluxes and Velocity Dispersions of Ionized Gas Narrow Lines in Type 1 AGNs

Galaxy	$f_{\rm\, [Ne\,\mathsc{ii}]}$	$f_{\rm\, [S\,\mathsc{iv}]}$	$f_{\rm\, [Ne\,\mathsc{iii}]}$	$f_{\rm\, [O\,\mathsc{iv}]}$	$f_{\rm\, [Ne\,\mathsc{v}]}$	$\sigma _{\rm [Ne\,\mathsc{ii}]}$	$\sigma _{\rm [S\,\mathsc{iv}]}$	$\sigma _{\rm [Ne\,\mathsc{iii}]}$	$\sigma _{\rm [O\,\mathsc{iv}]}$	$\sigma _{\rm [Ne\,\mathsc{v}]}$
	(10−18 W m−2)	(10−18 W m−2)	(10−18 W m−2)	(10−18 W m−2)	(10−18 W m−2)	(km s−1)	(km s−1)	(km s−1)	(km s−1)	(km s−1)
2MASSJ09184900+2117170	<3.61	<10.86	15.65 ± 2.39	...	<25.07	...	...	206 ± 35	...	...
2MASSiJ1659397+183436	<10.67	<10.16	26.79 ± 2.95	...	<10.15	...	...	277 ± 52	...	...
2MASXJ10514428+3539304	<6.21	9.97 ± 1.98	19.45 ± 2.11	...	<5.20	...	325 ± 48	...	...	...
3C249.1	4.37 ± 0.40	8.85 ± 0.43	...	...	5.05 ± 0.59	370 ± 65	286 ± 33	...	...	329 ± 36
3C273	11.42 ± 1.67	36.04 ± 3.33	41.58 ± 2.61	85.45 ± 6.42	21.20 ± 4.21	230 ± 39	470 ± 87	402 ± 47	450 ± 67	495 ± 57
Ark120	28.97 ± 2.53	<13.56	35.23 ± 2.71	36.84 ± 3.70	10.04 ± 1.61	202 ± 32	...	213 ± 38	190 ± 39	...
CGCG121-075	24.88 ± 1.44	24.39 ± 2.00	47.28 ± 1.96	85.25 ± 1.86	16.36 ± 1.25	...	209 ± 50	238 ± 42	220 ± 27	223 ± 43
ESO140-G043	96.32 ± 2.92	87.41 ± 2.95	139.5 ± 2.2	247.6 ± 4.9	79.10 ± 2.19	...	...	...	...	203 ± 29
FAIRALL9	21.50 ± 1.85	28.59 ± 3.86	44.80 ± 3.44	63.73 ± 3.68	20.79 ± 3.77	...	296 ± 45	197 ± 36	258 ± 48	231 ± 42
IC4329A	241.5 ± 6.2	245.7 ± 9.5	535.0 ± 6.8	1009 ± 14	286.1 ± 8.4	227 ± 32	235 ± 29	256 ± 30	275 ± 31	282 ± 34
IRAS13342+3932	53.68 ± 1.11	19.74 ± 1.27	<28.42	98.54 ± 1.72	33.98 ± 0.98	...	310 ± 48	...	324 ± 29	403 ± 38
IRAS13451+1232	45.66 ± 1.82	<5.59	<70.31	27.87 ± 5.24	<7.86	311 ± 37	...	...	479 ± 54	...
IRAS18216+6418	27.52 ± 2.06	58.26 ± 1.23	104.5 ± 3.5	240.1 ± 12.3	50.79 ± 1.69	214 ± 34	304 ± 31	237 ± 31	343 ± 36	390 ± 34
MCG-2-58-22	74.71 ± 1.86	<33.31	87.08 ± 3.79	126.3 ± 3.6	28.26 ± 2.63	...	...	183 ± 33	187 ± 32	204 ± 43
Mrk 1014	58.26 ± 1.42	33.20 ± 1.67	93.20 ± 2.96	119.9 ± 5.8	46.01 ± 2.39	253 ± 37	376 ± 36	379 ± 41	379 ± 39	380 ± 48
Mrk 279	81.42 ± 2.88	26.48 ± 2.04	80.35 ± 3.97	102.8 ± 3.6	34.80 ± 2.19	215 ± 34	237 ± 36	222 ± 35	...	248 ± 42
Mrk 335	10.54 ± 0.90	<25.80	22.56 ± 1.75	130.0 ± 3.7	12.88 ± 1.86	...	...	...	155 ± 17	247 ± 64
Mrk 493	62.69 ± 1.31	<23.47	27.09 ± 1.53	28.42 ± 4.76	9.59 ± 1.27	...	...	280 ± 39	267 ± 46	280 ± 38
Mrk 590	32.81 ± 2.12	<16.58	21.14 ± 2.54	31.04 ± 3.06	9.57 ± 1.64	...	...	197 ± 33	200 ± 33	206 ± 40
Mrk 704	<10.05	<61.44	<50.82	<151.67	51.08 ± 3.04	...	...	...	...	249 ± 37
Mrk 705	52.30 ± 1.90	<23.26	49.59 ± 2.11	57.82 ± 2.19	30.18 ± 1.66	...	...	192 ± 31	210 ± 35	280 ± 39
NGC 3227	708.7 ± 25.2	220.9 ± 5.5	725.8 ± 6.2	668.0 ± 17.6	231.2 ± 7.5	...	241 ± 32	228 ± 30	216 ± 29	209 ± 34
NGC 3516	74.01 ± 2.29	128.9 ± 4.4	164.4 ± 2.9	458.4 ± 5.5	67.57 ± 2.18	...	...	198 ± 30	229 ± 28	...
NGC 4051	172.6 ± 4.9	<47.59	162.0 ± 2.9	347.6 ± 7.1	107.7 ± 3.9	...	...	172 ± 29	295 ± 27	...
NGC 4235	34.85 ± 1.62	<6.03	33.29 ± 1.77	33.60 ± 3.04	<5.28	...	...	214 ± 34	286 ± 43	...
NGC 5548	83.08 ± 3.32	42.90 ± 2.55	81.76 ± 2.77	124.7 ± 8.6	31.50 ± 2.16	...	...	177 ± 30	...	206 ± 38
NGC 7469	1915 ± 27	90.00 ± 7.88	357.9 ± 7.5	340.0 ± 38.0	154.4 ± 10.0	...	158 ± 12	196 ± 29	196 ± 45	240 ± 44
PG0026+129	2.56 ± 0.33	4.94 ± 0.43	<7.72	20.16 ± 4.01	<5.07	...	...	...	305 ± 40	...
PG0804+761	<4.44	15.53 ± 2.28	20.89 ± 1.70	20.74 ± 2.87	<11.13	...	292 ± 111	323 ± 47	342 ± 66	...
PG1119+120	<4.00	20.63 ± 2.55	28.41 ± 2.01	60.00 ± 2.37	16.16 ± 2.33	...	...	...	...	193 ± 47
PG1229+204	5.84 ± 0.59	<20.90	12.05 ± 1.37	26.74 ± 3.55	11.48 ± 1.13	...	...	...	...	218 ± 50
PG1351+640	21.92 ± 0.99	<10.26	29.39 ± 1.73	<12.38	<3.83	...	...	200 ± 43	...	...
PG1411+442	4.54 ± 0.79	7.79 ± 1.00	9.24 ± 0.62	13.99 ± 2.31	6.49 ± 0.58	...	...	...	212 ± 45	316 ± 63
PG1426+015	13.46 ± 1.08	13.67 ± 2.28	25.55 ± 1.09	29.51 ± 4.38	8.47 ± 1.09	226 ± 38	...	258 ± 36	292 ± 57	289 ± 57
PG1440+356	42.72 ± 0.96	15.55 ± 1.70	38.57 ± 1.26	50.22 ± 2.37	14.26 ± 0.86	193 ± 34	211 ± 39	253 ± 35	253 ± 38	304 ± 107
PG1613+658	37.66 ± 1.23	13.25 ± 1.01	30.90 ± 1.02	66.49 ± 3.15	<7.92	226 ± 30	269 ± 33	289 ± 33	225 ± 29	...
PG2130+099	16.14 ± 1.22	32.54 ± 1.53	55.73 ± 2.88	100.8 ± 3.7	45.16 ± 3.01	...	...	187 ± 30	...	287 ± 45
PG2349−014	15.95 ± 0.71	<6.36	20.51 ± 1.01	34.73 ± 3.82	<6.83	273 ± 48	...	259 ± 34	308 ± 35	...
3C120	78.86 ± 3.72	225.7 ± 3.3	271.6 ± 3.7	1129 ± 7	163.8 ± 2.7	...	...	...	114 ± 8	111 ± 16
Mrk 509	118.0 ± 4.1	73.19 ± 3.92	153.0 ± 3.4	180.0 ± 5.1	54.04 ± 2.63	173 ± 35	...	...	165 ± 30	...
NGC 3783	197.0 ± 3.3	128.8 ± 5.1	255.9 ± 5.0	380.0 ± 8.5	152.0 ± 5.2	...	...	244 ± 12	141 ± 24	133 ± 21
NGC 4151	1180 ± 12	1130 ± 22	350.0 ± 13.9	2030 ± 33	560.0 ± 11.0	...	207 ± 16	155 ± 7	169 ± 12	139 ± 25

Notes. No data for the line fluxes indicate no spectral coverage at the observed-frame wavelengths of these lines. No data for the velocity dispersion of detected lines indicate that their signal-to-noise ratio was between 3 and 5, or that their profiles were unresolved.

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Table 4. Fluxes and Velocity Dispersions of Ionized Gas Narrow Lines in Type 2 AGNs

Galaxy	$f_{\rm\, [Ne\,\mathsc{ii}]}$	$f_{\rm\, [S\,\mathsc{iv}]}$	$f_{\rm\, [Ne\,\mathsc{iii}]}$	$f_{\rm\, [O\,\mathsc{iv}]}$	$f_{\rm\, [Ne\,\mathsc{v}]}$	$\sigma _{\rm [Ne\,\mathsc{ii}]}$	$\sigma _{\rm [S\,\mathsc{iv}]}$	$\sigma _{\rm [Ne\,\mathsc{iii}]}$	$\sigma _{\rm [O\,\mathsc{iv}]}$	$\sigma _{\rm [Ne\,\mathsc{v}]}$
	(10−18 W m−2)	(10−18 W m−2)	(10−18 W m−2)	(10−18 W m−2)	(10−18 W m−2)	(km s−1)	(km s−1)	(km s−1)	(km s−1)	(km s−1)
2MASXJ08035923+2345201	<6.39	<5.50	18.78 ± 2.08	28.45 ± 1.59	<4.75	...	...	203 ± 42	...	...
2MASXJ08244333+2959238	33.17 ± 2.04	<20.88	49.47 ± 3.44	83.64 ± 2.13	36.14 ± 2.78	207 ± 39	...	...	...	264 ± 30
2MASXJ10181928+3722419	8.67 ± 1.53	<6.35	14.69 ± 1.87	28.81 ± 1.60	16.59 ± 2.80	...	...	...	...	200 ± 32
2MASXJ12384342+0927362	<8.33	20.09 ± 2.25	27.85 ± 2.15	58.83 ± 2.38	12.94 ± 2.35	...	232 ± 42	260 ± 42	261 ± 36	265 ± 73
2MASXJ16164729+3716209	<5.34	16.53 ± 1.49	22.55 ± 2.52	90.14 ± 2.28	17.88 ± 2.23	...	...	...	...	211 ± 37
CGCG218-007	102.6 ± 3.1	35.72 ± 2.64	86.07 ± 2.69	166.7 ± 2.3	46.59 ± 1.98	...	...	...	...	215 ± 33
ESO103-G035	294.0 ± 7.6	115.1 ± 10.1	414.0 ± 9.4	311.7 ± 13.9	172.9 ± 10.5	223 ± 37	232 ± 34	276 ± 31	240 ± 35	346 ± 52
IRAS05189−2524	191.8 ± 8.9	65.30 ± 6.26	186.1 ± 7.1	261.2 ± 37.2	152.6 ± 12.0	253 ± 42	335 ± 55	392 ± 41	444 ± 63	404 ± 43
IRAS15001+1433	66.48 ± 1.36	4.74 ± 0.82	27.97 ± 0.69	21.78 ± 3.21	15.89 ± 1.97	247 ± 34	388 ± 36	348 ± 38	558 ± 96	422 ± 81
IRAS18325−5926	367.9 ± 7.8	114.9 ± 8.2	436.0 ± 5.3	390.7 ± 12.2	262.6 ± 9.6	181 ± 31	265 ± 39	367 ± 32	300 ± 34	404 ± 64
IRAS23060+0505	32.26 ± 2.40	19.65 ± 2.34	25.61 ± 2.10	35.31 ± 5.45	20.12 ± 2.69	278 ± 59	366 ± 127	285 ± 62	343 ± 57	419 ± 62
MCG-03-34-064	514.9 ± 8.2	476.1 ± 8.3	1150 ± 13	1053 ± 22	615.6 ± 8.2	344 ± 34	298 ± 33	361 ± 28	273 ± 30	435 ± 36
Mrk 1066	1094 ± 21	102.0 ± 7.4	469.1 ± 7.6	418.1 ± 22.1	92.38 ± 8.31	...	...	216 ± 32	284 ± 41	246 ± 48
Mrk 1457	91.99 ± 2.39	<14.09	38.13 ± 4.09	28.10 ± 2.54	22.09 ± 3.04	...	...	...	228 ± 43	310 ± 60
Mrk 273	444.9 ± 7.9	101.7 ± 2.3	338.1 ± 2.5	550.1 ± 17.8	112.3 ± 3.7	252 ± 30	357 ± 34	332 ± 30	357 ± 38	406 ± 32
Mrk 3	979.8 ± 10.2	592.7 ± 6.2	1749 ± 11	1964 ± 24	632.5 ± 7.5	276 ± 29	322 ± 29	314 ± 29	263 ± 28	327 ± 31
Mrk 463E	108.2 ± 3.5	275.0 ± 5.4	404.6 ± 7.3	641.8 ± 11.3	193.9 ± 4.7	308 ± 35	284 ± 30	235 ± 29	295 ± 29	287 ± 31
Mrk 609	213.5 ± 6.2	<22.18	56.71 ± 2.53	82.43 ± 25.69	38.69 ± 4.28	...	...	202 ± 36	...	488 ± 60
Mrk 622	97.29 ± 13.80	<8.61	49.29 ± 2.82	<37.42	<38.06	...	...	333 ± 34	...	...
NGC 1068	4988 ± 183	6199 ± 336	13781 ± 246	20406 ± 473	8974 ± 221	359 ± 52	414 ± 44	383 ± 31	364 ± 48	363 ± 39
NGC 1275	461.5 ± 8.0	<16.26	223.7 ± 5.6	<84.37	<11.65	299 ± 31	...	260 ± 31	...	...
NGC 2622	62.02 ± 2.63	<18.46	80.41 ± 2.93	89.29 ± 3.58	24.73 ± 2.08	...	...	213 ± 33	...	289 ± 39
NGC 2623	550.1 ± 9.7	11.20 ± 1.36	147.2 ± 1.7	117.4 ± 18.2	37.55 ± 2.97	...	...	213 ± 31	357 ± 52	222 ± 39
NGC 2639	86.23 ± 2.66	<6.90	48.88 ± 1.95	<23.82	<7.51	346 ± 43	...	336 ± 49	...	...
NGC 3079	1310 ± 60	<14.61	238.3 ± 3.3	<94.19	<38.79	198 ± 33	...	285 ± 29	...	...
NGC 4258	123.5 ± 7.3	<15.61	70.61 ± 5.61	79.40 ± 8.03	<13.67	193 ± 42	...	191 ± 36	204 ± 53	...
NGC 4507	307.8 ± 6.9	93.08 ± 6.84	287.8 ± 6.3	354.1 ± 11.6	125.7 ± 6.4	...	...	220 ± 35	318 ± 42	345 ± 81
NGC 5256	160.6 ± 3.1	27.06 ± 1.56	94.40 ± 1.45	569.8 ± 10.3	20.54 ± 1.37	227 ± 29	239 ± 37	227 ± 30	191 ± 28	202 ± 40
NGC 5506	850.6 ± 14.3	735.4 ± 15.6	1537 ± 11	2262 ± 40	568.0 ± 10.6	...	239 ± 33	207 ± 28	...	208 ± 32
NGC 5728	366.2 ± 7.7	317.2 ± 8.2	536.5 ± 6.7	1155 ± 12	217.1 ± 3.4	...	272 ± 41	263 ± 29	306 ± 30	314 ± 32
NGC 5929	104.8 ± 2.2	12.41 ± 1.98	95.07 ± 1.40	43.67 ± 6.18	<6.09	...	...	210 ± 28	...	...
NGC 6240	1872 ± 29	38.7 ± 2.9	599.9 ± 4.2	374.0 ± 35.9	90.24 ± 9.02	362 ± 37	279 ± 52	341 ± 29	...	...
NGC 7172	334.6 ± 8.1	55.74 ± 4.43	168.1 ± 4.0	384.4 ± 5.3	90.23 ± 3.49	256 ± 30	...	204 ± 30	...	...
NGC 7674	215.7 ± 5.2	152.6 ± 5.9	346.0 ± 6.5	442.9 ± 12.1	184.4 ± 7.0	...	267 ± 34	253 ± 32	242 ± 32	267 ± 39
SBS1133+572	108.3 ± 2.9	42.01 ± 3.62	105.3 ± 3.8	168.7 ± 2.8	69.89 ± 2.87	...	248 ± 40	...	...	...
UGC 02608	566.5 ± 9.4	292.8 ± 9.5	706.3 ± 6.1	1378 ± 17	312.9 ± 5.1	...	213 ± 31	...	...	...
UGC 5101	379.7 ± 9.0	<7.34	146.2 ± 2.1	57.18 ± 9.66	34.19 ± 3.73	254 ± 40	...	350 ± 34	285 ± 41	385 ± 40
Centaurus A	2210 ± 45	140.0 ± 9.6	1400 ± 12	980.0 ± 42.2	200.0 ± 8.5	220 ± 31	...	134 ± 21	127 ± 9	132 ± 21
Circinus	4536 ± 145	1270 ± 58	4000 ± 90	6793 ± 420	2180 ± 101	...	91 ± 6	86 ± 4	113 ± 3	90 ± 8

Note. Same as in Table 3.

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Radially dependent line widths will also be produced if the NLR has a gas density gradient increasing with proximity to the BH (Filippenko & Halpern 1984; Ferguson et al. 1997), which is not connected to a mean ionization level gradient. The line widths will be affected as the line fluxes from transitions of low critical density for collisional de-excitation, n_c, will be preferentially suppressed at dense environments. We observe no trend of σ with n_c (Figure 6), suggesting that the typical NLR gas densities are below n_c for the MIR transitions that we examined. The lack of dependence of the average σ on n_c demonstrates the power of MIR lines in probing the NLR kinematics. One counter example to this statistical finding could be MCG-03-34-064. Because all of its neon lines have higher velocity dispersions than [O iv] and [S iv], its NLR density could be of the order of 10⁴ hydrogen atoms per cubic centimeter.

Dust either mixed or outside the NLR gas clouds can lead to different extinction of lines at different λ (Groves et al. 2004; Winter et al. 2010). Because MIR lines are less affected by obscuration than optical lines, they could be probing clouds that are nearer to the BH, where obscuration is often higher. In this case, their widths could be broader than those of optical lines, in particular in type 2 AGNs. Mrk 273, NGC 2623, and IRAS15001+1433 do have larger [O iv] than [O iii] widths and low [O iii]/[O iv] flux ratios (see Figure 3), but their [O iii] and [S iv] or [Ne iii] widths are in good agreement with each other. The comparable ionization potentials of O iii, S iv, and Ne iii, i.e., 35.12, 34.79, and 40.96 eV, respectively, ascribe again any profile differences to ionization effects. We conclude that obscuration is not a common driver of differences in the profiles of optical and IR lines. The nuclear obscuration could be high enough to hide blue wings, associated with outflows moving away from the observer, even in IR wavelengths.

A simple comparison of the NLR gas velocity dispersion to that of the stars in the host galaxy shows that σ is not identical to σ_* (Figure 8). The gas velocity dispersion systematically exceeds that of the stars, with a large scatter between the two quantities. The average velocity dispersion excess is in the range 50–100 km s⁻¹ for all lines. The excess could be intrinsically higher, given that the optical observations had a slit width that was often an order of magnitude narrower than the IRS slit width. The origin of this excess could be related to either gas clouds that are accelerated by AGN-feedback mechanisms (Ho 2009) or to virialized gas clouds with a more compact spatial distribution than that of the stars when probed by emission lines from ions of ionization potential ≳ 35 eV. High spatial resolution MIR spectroscopy of eight local AGNs indicated that the [S iv] emission is unresolved at a scale of 100 pc (Hönig et al. 2008), while near-IR integral-field-unit data of Circinus showed that most of the [Si vi] and [Ca viii] emission is unresolved at 4 pc (Müller Sánchez et al. 2006). This velocity dispersion excess is seen even for the [O iii] 5007 Å line, which is resolved for all systems in our sample. Greene & Ho (2005) also reported such an excess in a large flux-limited sample of AGNs observed with SDSS.

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Another trend known from optical NLR studies is that the widths of the lines increase with their own luminosities (Phillips et al. 1983; Whittle 1985, 1992b). We reproduce this result for the MIR fine-structure lines that we examined in Figure 9. The velocity dispersion correlates roughly as L^0.15 based on, e.g., the [Ne v] measurements. A higher dependence of σ on L is plausible when taking into account the upper limits of σ. An exact determination of this slope will require the use of a flux-limited sample of AGNs in the local universe.

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Changes in the profile moments of different lines can also be seen when the emission originates from gas out of dynamical equilibrium. Several of the 81 sources in our sample show signatures of outflowing (or inflowing) gas motions, such as an offset from systemic velocity. This offset often depends on the ionization potential of each ionic species. With increasing ionization potential, the lines trace clouds that are nearer to the BH, and therefore more susceptible to outflows. We identified six sources in which the offset between the peak of the lowest ionization line available and the highest ionization line available exceeds Nyquist sampling of the resolution element, ≳250 km s⁻¹. Namely, these are the type 1 AGNs 3C273 and IRAS13342+3932, and the type 2 AGNs IRAS05189−2524, IRAS15001+1433, IRAS23060+0505, and Mrk 609 (see also Spoon et al. 2009; Spoon & Holt 2009). Line shifts below Nyquist sampling of the instrumental resolution, yet above the wavelength calibration uncertainty (50 km s⁻¹), could also be theoretically observed. They could be considered real if they systematically increased as a function of the ionization potential of the ionic species. Only one source⁹ satisfies this criterion, Mrk 1457. Its [Ne v] and [Ne ii] lines are offset by 100 km s⁻¹.

Asymmetric wings are found in ∼1/5th of the sources with resolved profiles. We consider such wings to be reliable only when they are detected in two or more lines. Similar [O iii] 5007 Å and [Ne iii] or [Ne v] wings are observed, for example, in PG1351+640, PG1411+442, and PG1440+356. Likewise, an agreement of the [O iii] and [O iv] 25.89 μm line profiles is found for 3C273, IRAS13451+1232, IRAS15001+1433, Mrk 1014, NGC 4235, and NGC 7674. Specifically, IRAS13451+1232 is a merging system with two nuclei separated by ∼5 kpc (e.g., Axon et al. 2000; Dasyra et al. 2006a). The velocity of the secondary [O iv] peak, at ∼−1000 km s⁻¹, is comparable to the velocities of the outflowing [O i] and [O iii] gas components that are seen in optical spectroscopy and that are associated with the nucleus responsible for the radio-jet emission (Holt et al. 2003).

By performing a similar profile analysis of the [Ne v] and [O iv] lines, restricted only to AGNs with direct M_BH measurements from reverberation experiments (Peterson et al. 2004), we previously demonstrated that the NLR velocity dispersion correlates with the mass of its central BH (Dasyra et al. 2008). We now further populate this relation using data from the full Spitzer archive, complementing them with ISO SWS data to cover the parameter space σ ≲ 200 km s⁻¹. The M_BH values for this expanded sample include single-epoch optical spectroscopic estimates for type 1 AGNs, as well as direct M_BH measurements for a few type 2 AGNs (see Section 2; Tables 3 and 4).

The fit to these data (Figure 10) was performed with the IDL routine MPFITFUN. Given the sparsity of data at the low σ end, we opted for a linear fit of fixed slope in logarithmic space. The slope was set to 4.24, which is identical to that of the stellar relation (Ferrarese & Merritt 2000; Gebhardt et al. 2000) as recently revised by Gültekin et al. (2009). While the rms scatter was computed using all available data points, the best-fit solution was computed using only Spitzer observations of sources with $\hbox{$M_{\rm BH}$}> 10^7$ M_☉ or ISO observations, as in Dasyra et al. (2008). The reason why we excluded Spitzer data sets for $\hbox{$M_{\rm BH}$}<10^7$ M_☉ is that they would introduce a bias toward high intercept values: the resolution of IRS is insufficient to resolve lines on the left-hand side of the M_BH–σ relation below this threshold. This excludes the type 2 AGNs NGC 1068, and the narrow-line Seyfert 1 galaxies (NLS1s) Mrk 493 and NGC 4051 that have high σ values for their BH masses. The existence of such outliers nonetheless suggests that σ could fail as a proxy of M_BH, as it is also known for the BLR gas (e.g., Vestergaard & Peterson 2006). On the other hand, such sources are not outliers in the relation connecting M_BH to the luminosity of the NLR lines (Figure 11).

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The multiple relations between M_BH and σ, σ and L, and M_BH and L could be suggestive of a plane connecting these three parameters (Figure 12), which we fit using the equation

$$\begin{equation} \log (\hbox{$M_{\rm BH}$}) = \alpha \log (\sigma) + \beta \log (L) + \gamma, \end{equation} \tag{ 1 }$$

where α, β, and γ are constants. We find that the best-fit-solution coefficients correspond to α = 0.9 and β = 0.5, when averaged over all MIR lines. Given the L and σ^∼7 proportionality shown in Figure 9, this result roughly reproduces the $\hbox{$M_{\rm BH}$}\sim \sigma ^{4}$ relation. In Figure 13, we present the plane equation for each line, when fixing the log (σ) and log (L) slopes to their average values for simplicity.¹⁰ We find that the use of a plane equation minimizes the scatter of the NLR-based M_BH estimates from their actual values. The improvement primarily originates from the correction of the M_BH–σ relation outliers at its low-M_BH and high-σ end.

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The physical interpretation of the suggested plane linking the NLR line luminosity, velocity dispersion, and the BH mass, varies depending upon the assumed kinematics and distribution of the gas clouds. A plane equation can be meaningful for clouds on accelerated motions powered directly by the AGN via radiation pressure (Murayama & Taniguchi 1998) acting mostly upon dust particles due to their high opacity (Dopita et al. 2002), magnetic fields related to jets (Whittle 1992c), and AGN-related winds. The winds can lead to either asymmetric outflows, identified in 7% of the systems in this sample, or to symmetric outflows that can be related to the AGN accretion disk (Crenshaw et al. 2003; Ho 2009). In this scenario, the measured gas velocity would be related to the fraction of the energy generated by the AGN that is deposited into the NLR gas. The luminosity would be a probe of the AGN accretion rate, since the luminosities of MIR NLR lines are known to be correlated with the optical, X-ray, and bolometric AGN luminosities (Schweitzer et al. 2006; Dasyra et al. 2008; Meléndez et al. 2008; Rigby et al. 2009; R. Mor et al. 2011, in preparation). A plane connecting σ, L, and M_BH would then suggest that the kinetic energy of the interstellar medium (ISM), as measured from the MIR lines, is directly related to the amount of material that is accreted onto the BH for a given M_BH value. An analogous idea was introduced by Merloni et al. (2003), who found a correlation between the mass of an accreting BH with its X-ray and radio luminosities.

Instead of responding to AGN feedback mechanisms, the gas clouds could be in virial motions that are dictated by the enclosed mass at the NLR radius R. For a geometric factor f converting this total mass to the BH mass, the virial equation can be written as

$$\begin{equation} \log (\hbox{$M_{\rm BH}$})= 2 \log (\sigma) + \log (R) +\log (f) - \log (G), \end{equation} \tag{ 2 }$$

where G is the gravitational constant. In this model, the NLR radius depends on the AGN luminosity alongside with the stellar mass and distribution in the AGN host galaxy. Equation (2) will take the form of Equation (1) if R scales with the AGN luminosity as a power law of L, as found for the [O iii] 5007 Å line (Bennert et al. 2002; Schmitt et al. 2003). The hardness of the ionizing radiation together with the ionization fraction, the covering factor, and the density distribution of the clouds can also determine how far the AGN radiation reaches, illuminates, and photoionizes gas clouds. For example, the observed increase of σ with L can be driven either by a tendency for more massive BHs to reside in larger galaxies (Ho 2009) or by the ionization state of the NLR. Lines from ions of high ionization potential are thought to be tracing matter-bound clouds that are partially ionized (Murayama et al. 1998; Wilson et al. 1997). In the case of partially ionized clouds, an increase of the AGN luminosity can lead to an overall expansion of the NLR, while most of the ionization can still occur for clouds at small radii. The exact relation between σ, L, and M_BH will depend on the gas density distribution, which is encapsulated in the scaling factor f. The coefficients of the best-fit plane solution, α = 0.9 and β = 0.5, suggest that f is dropping with σ, corresponding to a lower scaling factor for denser gas within a fixed radius. If, however, the scaling factor f was constant, α would be equal to 2, and the best-fit plane solution would correspond to β = 0.4. Such a solution could also be plausible. It would increase the rms scatter by a small amount, i.e., by only 0.01–0.02 dex for the MIR lines and by 0.07 dex for [O iii].

If the cloud kinematics cannot be approximated by either feedback-driven motions or by virial motions, Equation (1) might not provide a good means of estimating M_BH. For cloud kinematics that are described by a combination of virial and accelerated motions, e.g., in a virialized NLR where radiation pressure is significant, M_BH is proportional to σ²RG⁻¹ + a'L, where a' is a constant that depends on the column density and level of ionization of the clouds (Marconi et al. 2008; but see also Netzer & Marziani 2010). Further investigation of the optimal description of M_BH from narrow-line properties will be tested on large, flux-limited samples of AGNs with multiwavelength data sets. This will be the focus of a forthcoming paper using SDSS data.

Given that we see no significant difference in the NLR properties of type 1 and type 2 AGNs at a given L or σ_* (see also Pereira-Santaella et al. 2010), we applied the relations presented earlier in this work to type 2 AGNs for which such an analysis is presently possible from Spitzer data. Only four of these sources have other, direct M_BH measurements (Table 2). The comparison between the M_BH estimates from the stellar $\hbox{$M_{\rm BH}\hbox{--}\sigma $}_*$ relation, the M_BH–σ relation for the NLR gas, and the best-fit linear combination of log (σ) and log (L) are presented in Table 5. For either computation based on the NLR gas, the result is averaged over all available MIR lines. We find that the median ratio of M_BH as estimated from the plane equation over M_BH as estimated from the stellar velocity dispersion is 1.8. On the other hand, the median ratio of M_BH as estimated from the NLR gas velocity dispersion over M_BH as estimated from the stellar velocity dispersion is much higher, 6.5. The difference seen when folding a luminosity dependence on the computation of M_BH is largest for the IR-bright galaxies IRAS05189-2524, IRAS15001+1433, and Mrk 609, which have gas motions that are predominantly out of dynamical equilibrium.