Shocks and Spatially Offset Active Galactic Nuclei Produce Velocity Offsets in Emission Lines

For each of the seven velocity-offset AGNs, the host galaxy redshift (based on the stellar absorption features), the LOS velocity offset of the emission lines, and the [O iii] λらむだ5007 luminosity were determined from the SDSS spectrum (Comerford & Greene 2014). Three of the AGNs have emission lines with redshifted velocity offsets and four have emission lines with blueshifted velocity offsets. The absolute values of the velocity offsets range from 50 to 113 km s⁻¹ (Table 1).

Three of the velocity-offset AGNs were observed with Keck Laser Guide Star Adaptive Optics with OSIRIS integral-field spectroscopy (Müller-Sánchez et al. 2016). In each galaxy (SDSS J1055+1520, SDSS J1117+6140, and SDSS J1346+5228), the peak of the line emission (Paαあるふぁ, Paαあるふぁ, and [Fe ii] in each galaxy, respectively) was spatially offset from the galaxy center by $0\buildrel{\prime\prime}\over{.} 1$ (0.2 kpc), $0\buildrel{\prime\prime}\over{.} 2$ (0.5 kpc), and $0\buildrel{\prime\prime}\over{.} 3$ (0.2 kpc), respectively. Based on the kinematics of the gas in the OSIRIS observations, Müller-Sánchez et al. (2016) found that SDSS J1055+1520 and SDSS J1346+5228 host AGN outflows while SDSS J1117+6140 has gas inflow along a bar. They concluded that the spatially offset peaks in line emission are the result of the outflows or inflows driving shocks into off-nuclear gas.

The seven velocity-offset AGNs were observed with Chandra/ACIS for the program GO4-15113X (PI: Comerford). Our exposure times were derived from the observed [O iii] λらむだ5007 flux for each system (Table 1) and the scaling relation between [O iii] λらむだ5007 flux and hard X-ray (2–10 keV) flux for Type 2 AGNs, which has a scatter of 1.06 dex (Heckman et al. 2005). We selected exposure times that would ensure a firm detection of at least 10 counts for each AGN, even in the case of the actual X-ray flux falling in the low end of the 1.06 dex scatter. The galaxies were observed with exposure times of 10–20 ks (Table 2).

The galaxies were observed with the telescope aimpoint on the ACIS S3 chip in "timed exposure" mode and telemetered to the ground in "faint" mode. We reduced the data with the latest Chandra software (CIAO 4.6.1) in combination with the most recent set of calibration files (CALDB 4.6.2).

For each galaxy, we used dmcopy to make a sky image of the field in the rest-frame soft (0.5–2 keV), hard (2–10 keV), and total (0.5–10 keV) energy ranges. Using the modeling facilities in Sherpa, we simultaneously modeled the source as a 2D Lorenztian function (beta2d: $f(r)=A(1+{[r/{r}_{0}]}^{2})-\alpha$) and the background as a fixed count rate estimated using a source-free adjacent circular region of 30'' radius. We used the SDSS galaxy coordinates as the initial position of the beta2d component, and then we allowed the model to fit a region of three times the point spread function (PSF) size (estimated with psfSize) at that location. We determined the best-fit model parameters with Sherpa's implementation of the "Simplex" minimization algorithm (Lagarias et al. 1998) by minimizing the Cash statistic. We also attempted a two-component beta2d model to test for additional sources, but all secondary components were detected with $\lt 1\sigma$ significance. Therefore, none of the systems require a secondary component, and Table 3 and Figure 1 show the best-fit positions of the X-ray source in each galaxy. Table 3 also gives the spatial separations between each X-ray source and the host galaxy's stellar nucleus. The errors on these separations are dominated by the astrometric uncertainties in aligning the Chandra and HST images. These astrometric errors are calculated in Section 3.5, and the median astrometric error is $0\buildrel{\prime\prime}\over{.} 5$.

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Table 3.  Chandra and HST/F160W Positions of Each Source

SDSS Name	${\rm{R}}.{\rm{A}}{.}_{{HST}/{\rm{F}}160{\rm{W}}}$	$\mathrm{Decl}{.}_{{HST}/{\rm{F}}160{\rm{W}}}$	Chandra Energy	${\rm{R}}.{\rm{A}}{.}_{{Chandra}}$ a	$\mathrm{Decl}{.}_{{Chandra}}$ a	${\rm{\Delta }}\theta (^{\prime\prime} )$ b	${\rm{\Delta }}x$ (kpc)b	Sig.
			Range (keV)
J0132−1027	01:32:58.927	−10:27:07.05	0.5–2	01:32:58.924	−10:27:06.87	0.18 ± 0.33	0.12 ± 0.21	0.6σしぐま
			2–10	01:32:58.917	−10:27:07.05	0.14 ± 0.46	0.09 ± 0.29	0.3σしぐま
			0.5–10	01:32:58.922	−10:27:07.02	0.08 ± 0.43	0.05 ± 0.27	0.2σしぐま
J0839+4707	08:39:02.949	+47:07:55.88	0.5–2	08:39:02.944	+47:07:55.95	0.09 ± 0.29	0.09 ± 0.30	0.3σしぐま
			2–10	08:39:02.961	+47:07:55.84	0.13 ± 0.19	0.13 ± 0.19	0.7σしぐま
			0.5–10	08:39:02.961	+47:07:55.88	0.12 ± 0.18	0.12 ± 0.18	0.7σしぐま
J1055+1520	10:55:53.644	+15:20:27.87	0.5–2	10:55:53.653	+15:20:27.40	0.49 ± 0.84	0.83 ± 1.44	0.6σしぐま
			2–10	10:55:53.682	+15:20:27.16	0.90 ± 0.84	1.54 ± 1.44	1.1σしぐま
			0.5–10	10:55:53.662	+15:20:27.30	0.62 ± 0.84	1.07 ± 1.44	0.7σしぐま
J1117+6140	11:17:29.208	+61:40:15.38	0.5–2	11:17:29.193	+61:40:16.06	0.69 ± 0.73	1.41 ± 1.49	0.9σしぐま
			2–10	11:17:29.287	+61:40:15.63	0.62 ± 0.37	1.26 ± 0.76	1.7σしぐま
			0.5–10	11:17:29.268	+61:40:15.56	0.46 ± 0.36	0.94 ± 0.74	1.3σしぐま
J1346+5228	13:46:40.812	+52:28:36.22	0.5–2	13:46:40.816	+52:28:36.15	0.08 ± 0.36	0.05 ± 0.21	0.2σしぐま
			2–10	13:46:40.821	+52:28:35.76	0.48 ± 0.35	0.28 ± 0.20	1.4σしぐま
			0.5–10	13:46:40.816	+52:28:35.76	0.47 ± 0.35	0.27 ± 0.21	1.3σしぐま
J1654+1946	16:54:30.724	+19:46:15.56	0.5–2	16:54:30.734	+19:46:15.45	0.17 ± 0.48	0.18 ± 0.50	0.4σしぐま
			2–10	16:54:30.806	+19:46:15.78	1.17 ± 0.44	1.22 ± 0.46	2.6σしぐま
			0.5–10	16:54:30.732	+19:46:15.42	0.18 ± 0.44	0.18 ± 0.46	0.4σしぐま
J2323+1405	23:23:28.010	+14:05:30.08	0.5–2	23:23:27.996	+14:05:30.12	0.21 ± 0.26	0.17 ± 0.22	0.8σしぐま
			2–10	23:23:28.008	+14:05:30.12	0.05 ± 0.22	0.04 ± 0.18	0.2σしぐま
			0.5–10	23:23:28.003	+14:05:30.12	0.11 ± 0.21	0.09 ± 0.17	0.5σしぐま

Notes. Columns 2 and 3: coordinates of the host galaxy's stellar nucleus, measured from HST/WFC3/F160W observations. Column 4: rest-frame energy range of Chandra observations. Columns 5 and 6: coordinates of the X-ray AGN source, measured from Chandra/ACIS observations in the energy range given in Column 4. Columns 7 and 8: angular and physical separations between the positions of the host galaxy's stellar nucleus and the X-ray AGN source, where the error includes uncertainties in the positions of the HST and Chandra sources as well as the astrometric uncertainty. Column 9: significance of the separation between the host galaxy's stellar nucleus and the X-ray AGN source.

^aThe astrometric shifts described in Section 3.5 have been applied to the Chandra source positions. ^bThe errors are dominated by the astrometric uncertainties, which range from 02 to 08.

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Then, we used the Bayesian Estimation of Hardness Ratios (BEHR) code (Park et al. 2006) to measure the rest-frame soft, hard, and total counts in each X-ray source. We used calc_data_sum to determine the number of observed soft and hard counts from both the source region and a background region, and then BEHR used a Bayesian approach to estimate the expected values and uncertainties of the rest-frame soft counts, hard counts, total counts, and hardness ratio. Table 4 shows these values; we estimated errors on the counts assuming Poisson noise.

Table 4.  X-Ray Counts and Spectral Fits

SDSS Name	Soft Counts	Hard Counts	Total Counts	Hardness	${n}_{H,\mathrm{exgal}}$	Γがんま	Reduced
	(0.5–2 keV)	(2–10 keV)	(0.5–10 keV)	Ratio	(1022 cm−2)		C-stat
J0132−1027	${14.9}_{-4.2}^{+3.1}$	${8.2}_{-3.4}^{+2.3}$	${23.1}_{-5.2}^{+4.2}$	$-{0.30}_{-0.22}^{+0.19}$	$\lt 0.02$	${1.73}_{-0.38}^{+0.41}$	0.24
J0839+4707	${8.7}_{-3.4}^{+2.1}$	${66.1}_{-8.6}^{+7.4}$	${74.8}_{-9.1}^{+7.9}$	${0.77}_{-0.06}^{+0.09}$	${8.18}_{-0.29}^{+2.21}$	1.70 (fixed)a	0.59
J1055+1520	${15.8}_{-4.5}^{+3.2}$	${6.8}_{-3.3}^{+2.0}$	${22.7}_{-5.3}^{+4.1}$	$-{0.40}_{-0.22}^{+0.19}$	$\lt 0.03$	${1.71}_{-0.47}^{+0.39}$	0.22
J1117+6140	${7.6}_{-3.3}^{+2.0}$	${3.1}_{-2.5}^{+1.1}$	${10.7}_{-4.0}^{+2.6}$	$-{0.43}_{-0.35}^{+0.25}$	$\lt 0.10$	${1.87}_{-0.76}^{+0.78}$	0.12
J1346+5228	${10.8}_{-3.9}^{+2.4}$	${7.2}_{-3.3}^{+1.9}$	${18.0}_{-4.7}^{+3.8}$	$-{0.21}_{-0.25}^{+0.23}$	$\lt 0.12$	${1.35}_{-0.85}^{+0.54}$	0.19
J1654+1946	${23.9}_{-5.3}^{+4.2}$	${4.2}_{-2.7}^{+1.4}$	${28.1}_{-6.0}^{+4.4}$	$-{0.71}_{-0.17}^{+0.11}$	$\lt 0.02$	1.70 (fixed)a	0.20
J2323+1405	${17.4}_{-4.7}^{+3.5}$	${32.5}_{-6.2}^{+5.2}$	${49.9}_{-7.6}^{+6.3}$	${0.30}_{-0.13}^{+0.15}$	${0.41}_{-0.16}^{+0.18}$	1.70 (fixed)a	0.52

Note. Column 2: soft X-ray (rest frame 0.5–2 keV) counts (S). Column 3: hard X-ray (rest frame 2–10 keV) counts (H). Column 4: total X-ray (rest frame 0.5–10 keV) counts. Column 5: hardness ratio HR = (H–S)/(H+S). Column 6: extragalactic column density. Column 7: best-fit spectral index. Column 8: reduced Cash statistic of the fit.

^aThe best-fit spectrum had a spectral index of ${\rm{\Gamma }}\lt 1$ or ${\rm{\Gamma }}\gt 3$, so we redid the fit by freezing the spectral index to ${\rm{\Gamma }}=1.70$.

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To model the energy spectra of the extracted regions over the observed energy range 2–8 keV, we used Sherpa. We fit each unbinned spectrum with a redshifted power law, $F\sim {E}^{-{\rm{\Gamma }}}$ (which represents the intrinsic AGN X-ray emission at the SDSS spectroscopic redshift z). This spectrum is attenuated by passing through two absorbing column densities of neutral hydrogen. One of these is fixed to the Galactic value, ${n}_{H,\mathrm{Gal}}$, and the other is assumed to be intrinsic to the source, ${n}_{H,\mathrm{exgal}}$, at the redshift z. We determined ${n}_{H,\mathrm{Gal}}$ using an all-sky interpolation of the H i in the Galaxy (Dickey & Lockman 1990).

For our first fit to each spectrum, we allowed Γがんま and ${n}_{H,\mathrm{exgal}}$ to vary freely. If the best-fit value of Γがんま was not within the typical range of observed power-law indices, i.e., $1\leqslant {\rm{\Gamma }}\leqslant 3$ (Nandra & Pounds 1994; Reeves & Turner 2000; Piconcelli et al. 2005; Ishibashi & Courvoisier 2010), then we fixed Γがんま at a value of 1.7, which is a typical value for the continuum of Seyfert galaxies, and ran the fit again.

To determine the best-fit model parameters for each spectrum, we used Sherpa's implementation of the Levenberg-Marquardt optimization method (Bevington 1969) to minimize the Cash statistic. Table 4 shows the results of these spectral fits. All fluxes are k-corrected, and we calculated the observed flux values from the model sum (including the absorbing components) and the intrinsic flux values from the unabsorbed power-law component. Finally, we used the redshift to determine the distance to each system and convert the X-ray fluxes to X-ray luminosities (Table 5).

Table 5.  X-Ray Luminosities

SDSS Name	${L}_{X,0.5\mbox{--}2\mathrm{keV}}$ abs (Unabs)	${L}_{X,2\mbox{--}10\mathrm{keV}}$ abs (Unabs)	${L}_{X,0.5\mbox{--}10\mathrm{keV}}$ abs (Unabs)
	(1040 erg s−1)	(1040 erg s−1)	(1040 erg s−1)
J0132–1027	${1.2}_{-0.3}^{+0.4}({1.3}_{-0.4}^{+0.4})$	${2.3}_{-1.2}^{+2.1}({2.3}_{-1.2}^{+2.1})$	${3.3}_{-1.2}^{+2.5}({3.5}_{-1.3}^{+2.6})$
J0839+4707	${0.2}_{-0.1}^{+0.5}({89.7}_{-29.0}^{+29.6})$	${165.0}_{-37.6}^{+44.7}({245.0}_{-59.8}^{+61.2})$	${170.0}_{-40.1}^{+39.6}({338.0}_{-84.3}^{+83.0})$
J1055+1520	${9.7}_{-3.5}^{+3.2}({11.6}_{-3.8}^{+3.3})$	${18.4}_{-8.8}^{+19.2}({18.5}_{-8.8}^{+19.2})$	${30.1}_{-12.7}^{+22.5}({32.3}_{-13.3}^{+21.1})$
J1117+6140	${3.9}_{-1.9}^{+2.4}({6.4}_{-2.9}^{+2.5})$	${7.7}_{-5.1}^{+14.6}({7.8}_{-5.1}^{+14.6})$	${12.3}_{-7.1}^{+15.1}({14.9}_{-8.2}^{+14.0})$
J1346+5228	${0.8}_{-0.3}^{+0.4}({1.0}_{-0.4}^{+0.4})$	${2.7}_{-1.4}^{+3.1}({2.7}_{-1.5}^{+3.1})$	${3.7}_{-1.7}^{+3.5}({3.8}_{-1.7}^{+3.6})$
J1654+1946	${5.5}_{-1.2}^{+1.2}({6.6}_{-1.4}^{+1.2})$	${11.9}_{-2.6}^{+2.1}({12.0}_{-2.7}^{+2.1})$	${17.2}_{-3.2}^{+3.5}({18.2}_{-3.5}^{+3.6})$
J2323+1405	${2.9}_{-0.8}^{+1.2}({7.0}_{-1.4}^{+1.3})$	${12.3}_{-2.6}^{+2.4}({12.7}_{-2.6}^{+2.4})$	${15.4}_{-3.0}^{+3.3}({19.8}_{-3.8}^{+3.9})$

Note. Column 2: absorbed (and unabsorbed) soft X-ray 0.5–2 keV luminosity. Column 3: absorbed (and unabsorbed) hard X-ray 2–10 keV luminosity. Column 4: absorbed (and unabsorbed) total X-ray 0.5–10 keV luminosity.

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The seven velocity-offset AGNs were also observed with HST/WFC3 (GO-13513, PI: Comerford), and the observations covered three bands: UVIS/F438W (B band), UVIS/F606W (V band), and IR/F160W (H band). The exposure times are summarized in Table 2.

Each band revealed different properties of the galaxies. The F438W observations covered ${\rm{H}}\delta$, ${\rm{H}}\gamma$, and [O iii] λらむだ4363 for the $0.02\lt z\lt 0.06$ galaxies and [O ii] λらむだλらむだ3725, 3727 and ${\rm{H}}\delta$ for the $0.09\lt z\lt 0.12$ galaxies. The F606W observations covered Hβべーた, [O iii] λらむだλらむだ4959, 5007; [O i] λらむだλらむだ6300, 6363; [N ii] λらむだλらむだ6548, 6583; Hαあるふぁ, and [S ii] λらむだλらむだ6716, 6730 for the $0.02\lt z\lt 0.06$ galaxies; Hβべーた, [O iii] λらむだλらむだ4959, 5007; and [O i] λらむだλらむだ6300, 6363 for the z = 0.09 galaxy; and ${\rm{H}}\gamma$, [O iii] λらむだ4363, Hβべーた, [O iii] λらむだλらむだ4959, 5007; and [O i] λらむだλらむだ6300, 6363 for the z = 0.11 galaxy. The F160W observations primarily traced the stellar continuum, although they may also have included [Fe ii] 1.6436 μみゅーm emission for the $0.02\lt z\lt 0.04$ galaxies and Paβべーた emission for the $0.09\lt z\lt 0.12$ galaxies.

To locate the stellar centroid of each galaxy, we fit a Sérsic profile (plus a fixed, uniform sky component) to each galaxy's F160W image using GALFIT V3.0 (Peng et al. 2010). We ran each fit on a square region of projected physical size 40 kpc on each side, with the angular size scale calculated from z and assuming the cosmology stated in Section 1.

The errors returned by GALFIT are purely statistical in that they are computed directly from the variance of the input images. We note that in reality, the true radial profiles may deviate from the parametric model components used in GALFIT, particularly at large radii. We previously examined this in Comerford et al. (2015) by creating radial profiles of the Sérsic fits to merger-remnant galaxies, where we found that even with significant residuals at large radii, the Sérsic component peaks are excellent tracers of the photometric peaks.

In our fitting procedure, we also attempted a two-Sérsic component fit (over the same fitting region) to test for the presence of secondary nuclei and/or close interacting neighbors. In these cases, we adopted the two-component model if the secondary component is detected at $\gt 3\sigma$ significance above the background. We found one system, SDSS J0839+4707, with a nearby neighbor galaxy. GALFIT returned the positions of the sources and their integrated magnitudes, which we used to determine the spatial separation on the sky between the two galaxies and their merger mass ratio. We approximated the merger mass ratio as the luminosity ratio of the two stellar bulges.

We also measured the centroid of emission for each galaxy, using Source Extractor (Bertin & Arnouts 1996) on the F606W images. According to the SDSS spectra, the [O iii] λらむだ5007 emission line is the dominant line in the F606W image for each galaxy, within the central 3''. Therefore, the centroid of F606W emission within the central 3'' is a proxy for the centroid of [O iii] λらむだ5007 emission. We ran Source Extractor with a detection threshold of $5\sigma$ above the background, and the errors on the positions are statistical.

The positions of the emission centroids, as well as their separations from the stellar centroids, are shown in Table 6 and Figure 2. We determined the spatial separation errors by combining the errors on the GALFIT positions in the F160W data, the Source Extractor positions in the F606W data, and the relative astrometric uncertainties in the F160W (10 mas) and F606W observations (4 mas; Deustua 2016). The relative astrometric uncertainties dominate the errors, so that the spatial separation errors are all $0\buildrel{\prime\prime}\over{.} 01$. We found that all of the spatial separations between the emission centroids and the stellar centroids are greater than $3\sigma$ in significance.

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Table 6.  HST/F606W Positions of Each Source

SDSS Name	${\rm{R}}.{\rm{A}}{.}_{{HST}/{\rm{F}}606{\rm{W}}}$	$\mathrm{Decl}{.}_{{HST}/{\rm{F}}606{\rm{W}}}$	${\rm{\Delta }}\theta (^{\prime\prime} )$ a	${\rm{\Delta }}x$ (kpc)a
J0132−1027	01:32:58.922	−10:27:07.01	0.078 ± 0.011	0.050 ± 0.007
J0839+4707	08:39:02.937	+47:07:56.02	0.193 ± 0.011	0.197 ± 0.011
J1055+1520	10:55:53.638	+15:20:27.96	0.124 ± 0.012	0.212 ± 0.020
J1117+6140	11:17:29.218	+61:40:15.31	0.179 ± 0.011	0.365 ± 0.023
J1346+5228	13:46:40.802	+52:28:36.23	0.252 ± 0.011	0.147 ± 0.006
J1654+1946	16:54:30.734	+19:46:15.48	0.152 ± 0.011	0.159 ± 0.011
J2323+1405	23:23:28.004	+14:05:30.03	0.111 ± 0.011	0.091 ± 0.009

Note. Columns 2 and 3: coordinates of the peak of the emission, measured from HST/WFC3/F606W observations. Columns 4 and 5: angular and physical separations between the positions of the peak of the emission and the host galaxy's stellar nucleus. All separations are $\gt 3\sigma$ in significance.

^aThe errors are dominated by the astrometric uncertainties, which are $0\buildrel{\prime\prime}\over{.} 01$.

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Finally, we measured the spatial separation between the X-ray AGN source and the center of the stellar bulge (Table 3). The error on each spatial separation incorporates the errors from the beta2d model fit to the Chandra data (Section 3.3), the GALFIT fit to the HST/F160W data, and the astrometric uncertainty (Section 3.5). The error budget is dominated by the uncertainty in aligning the Chandra and HST images, where the median astrometric uncertainty is $0\buildrel{\prime\prime}\over{.} 5$. Due in part to these large astrometric uncertainties, all of the spatial separations are less than $3\sigma$ in significance.

To determine if any Chandra sources are significantly spatially offset from the stellar bulges seen in the HST/F160W data, we registered each pair of HST/F160W and Chandra images and estimated their relative astrometric uncertainties. Due to the small number of Chandra/ACIS sources and the relatively small HST/F160W field of view, we registered each image separately to SDSS (u, g, r, i, and z) and the 2MASS point source catalog (Cutri et al. 2003). Then, we combined the two transformations to register the Chandra and HST images.

We used wavdetect with a threshold of sigthresh = 10⁻⁸ to detect sources in Chandra, and Source Extractor with a threshold of $3\sigma$ to detect sources in SDSS, 2MASS, and HST. Then, we matched sources in each pair of images using the xyxymatch task in IRAF. Next, we used the geomap task in IRAF to calculate X and Y linear transformations for each matched pair (${X}_{\mathrm{shift},j}$, ${Y}_{\mathrm{shift},j}$). We took the final linear transformations in X and Y to be the error-weighted averages, $\overline{{X}_{\mathrm{shift}}}={\sum }_{j=1}^{n}{X}_{\mathrm{shift},j}\times {w}_{j,X}$ and $\overline{{Y}_{\mathrm{shift}}}={\sum }_{j=1}^{n}{Y}_{\mathrm{shift},j}\times {w}_{j,Y}$, where n is the number of sources matched between two images and w is the error weighting.

For each dimension, X and Y, we combined in quadrature the errors on the Chandra and SDSS/2MASS source positions in each band. We repeated this procedure to determine the uncertainty of the relative astrometry for the HST and SDSS/2MASS images. Then, we added the relative astrometric errors between Chandra and SDSS/2MASS and between HST and SDSS/2MASS in quadrature to determine the relative astrometric errors between the Chandra and HST images. The final astrometric errors ($\overline{{\rm{\Delta }}X}$, $\overline{{\rm{\Delta }}Y}$) are then the error-weighted averages of these bands, shown in Table 7. These uncertainties range from $0\buildrel{\prime\prime}\over{.} 2$ to $0\buildrel{\prime\prime}\over{.} 8$, and they dominate the errors when we measure the spatial separations between sources in Chandra and HST.

Table 7.  Astrometry Measurements

SDSS Name	nCS	nHS	$\overline{{\rm{\Delta }}X}$ ('')	$\overline{{\rm{\Delta }}Y}$ ('')
J0132−1027	0, 1, 1, 0, 0, 1	0, 0, 1, 0, 0, 0	0.4656	0.2622
J0839+4707	2, 2, 2, 2, 1, 1	0, 2, 2, 2, 2, 1	0.2612	0.2607
J1055+1520	0, 0, 0, 0, 0, 0	0, 0, 0, 1, 0, 0	0.8382	0.8382
J1117+6140	0, 1, 1, 1, 0, 0	0, 1, 1, 1, 0, 0	0.5299	0.7136
J1346+5228	1, 2, 1, 1, 1, 0	0, 1, 1, 1, 1, 0	0.2837	0.3517
J1654+1946	0, 0, 1, 1, 0, 0	1, 2, 3, 3, 2, 1	0.4721	0.4375
J2323+1405	1, 1, 2, 1, 1, 1	0, 0, 1, 0, 0, 0	0.2035	0.2388

Note. Column 2: number of sources matched between Chandra and SDSS u, g, r, i, z, and 2MASS images. Column 3: number of sources matched between HST/F160W and SDSS u, g, r, i, z, and 2MASS images. Columns 4 and 5: astrometric accuracy measurements based on matching these sources, in native X and Y coordinates of the HST/F160W image.

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We use the Chandra observations to pinpoint the location of the AGN in each galaxy, and we find that each AGN's position is consistent with the host galaxy center to within $3\sigma$ (Table 3). Some of the AGNs may have small, but real, spatial offsets from the galaxy center, but the HST/F160W images do not show evidence of secondary stellar cores that would accompany these offset AGNs. This leads us to conclude that each galaxy in our sample most likely hosts a central AGN, and not an offset AGN.

The emission-line maps for each galaxy are probed by the HST/F606W observations, which are dominated by [O iii] λらむだ5007. We find that the emission-line centroids are spatially offset from the host galaxy centers by 0.05–0.4 kpc, and that all of the spatial separations are greater than $3\sigma$ in significance (Table 6). For the three galaxies that were also observed with Keck/OSIRIS, in all three galaxies the spatial offsets of the emission in the OSIRIS data are consistent with those measured in the F606W data.

Such spatially offset peaks in emission could be produced by photoionization of an off-nuclear cloud of gas. Outflows and inflows can drive gas into off-nuclear dense regions, but this gas need not necessarily be excited by shocks (e.g., Rosario et al. 2004, 2010b). Spatially offset peaks in emission can also be a signature of shocks. Interacting gas clouds shock the gas, enhancing the ionized gas emission and producing an off-nuclear peak of emission within the narrow line region (e.g., Mazzalay et al. 2013).

To search for further evidence of shocks, we examine the optical line flux ratios [O iii] λらむだ4363/[O iii] λらむだ5007, [O iii] λらむだ5007/Hβべーた, and [O i] λらむだ6300/[O iii] λらむだ5007 measured from the SDSS spectrum of each galaxy. Shocks driven into the surrounding gas clouds compress the gas, increasing its density and temperature. The [O iii] λらむだ4363 emission line indicates a very high kinetic temperature, which is produced by shock wave excitation and is inconsistent with photoionized low-density clouds. Consequently, the [O iii] λらむだ4363/[O iii] λらむだ5007 line ratio is temperature sensitive and a good indicator of shock activity. Shock heating can also be probed by the [O iii] λらむだ5007/Hβべーた line flux ratio (e.g., Shull & McKee 1979). The [O i] λらむだ6300 emission line is another indicator of shocks (e.g., Dopita 1976), and [O i] λらむだ6300/[O iii] λらむだ5007 is an ionization level-sensitive line flux ratio.

We compare the [O iii] λらむだ5007/Hβべーた versus [O iii] λらむだ4363/[O iii] λらむだ5007 line flux ratios, as well as the [O i] λらむだ6300/[O iii] λらむだ5007 versus [O iii] λらむだ4363/[O iii] λらむだ5007 line flux ratios, to models of pure AGN photoionization and combined AGN photoionization and shocks (Moy & Rocca-Volmerange 2002). The pure photoionization models are computed with CLOUDY (Ferland 1996) and use a spectral index $\alpha =-1$ of the ionizing continuum and an ionization parameter ranging from $-4\leqslant \mathrm{log}U\leqslant -1$. The hydrogen density is 100 cm⁻³, which is typical for extended emission-line regions (McCarthy et al. 1990), and the metallicity is solar. The shock models are computed with MAPPINGSIII (Dopita & Sutherland 1996), and have a range of shock velocities $100\lt {v}_{s}$(km ${{\rm{s}}}^{-1})\lt 1000$. We find that none of the velocity-offset AGNs have line flux ratios consistent with pure photoionization, and that instead their spectra are explained by a combination of photoionization and shocks (Figure 3).

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To further explore the role of photoionization and shocks in these galaxies, we compare our data with the radiative shock models of Allen et al. (2008). They assume solar abundance, a preshock density 1 cm⁻³, magnetic parameters ranging from 10⁻⁴ to 10 μみゅーG cm^3/2, and shock velocities ranging from 200 to 1000 km s⁻¹, and they use MAPPINGSIII to model both the shock and its photoionized precursor. For shocks with velocities $\gtrsim 170$ km s⁻¹, the ionizing front is moving faster than the shock itself, and the ionizing front dissociates and spreads out to form a precursor H ii region in front of the shock. Hence, a shocked region can have both shocked gas and photoionized gas. We find that the line flux ratios of our seven velocity-offset AGNs are consistent with the shock plus precursor models of Allen et al. (2008).

We conclude that all seven of the galaxies host both shocked gas and photoionized gas. In the three galaxies observed with Keck/OSIRIS, the OSIRIS data show that the velocity-offset emission lines in the SDSS integrated spectra originate from the shocked off-nuclear emission peak in the gas (Müller-Sánchez et al. 2016). The same is most likely true for the other four galaxies in our sample, and spatially resolved spectra would show it definitively.

Here, we explore the nature of the shocks in each of the seven galaxies individually.

4.2.1. Four AGN Outflows

4.2.2. Two Inflows of Gas Along a Bar

SDSS J0839+4707. This galaxy has a stellar bar that is visible in Figure 1, and the peak of emission is spatially offset along the bar (Figure 2). SDSS J0839+4707 is also the only galaxy in our sample that has a close companion. The companion galaxy, SDSS J083902.50+470813.9, is located 18.8 kpc ($18\buildrel{\prime\prime}\over{.} 4$) to the northwest and has a redshift of $z=0.053454\pm 0.000045$ (Figure 4). This corresponds to a velocity difference of 311.9 ± 21.4 km s⁻¹ redshifted away from the primary galaxy. Emission-line diagnostics of the companion's SDSS spectrum show that it is a star-forming galaxy (Brinchmann et al. 2004). Using the ratio of the stellar bulge luminosities as a proxy for the merger mass ratio, the merger ratio is 3.59:1 (SDSS J0839+4707 is the more massive galaxy). There is no morphological evidence that SDSS J0839+4707 and its companion are interacting, though a future interaction may trigger new accretion onto the central AGN.

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SDSS J1117+6140. The OSIRIS observations of this galaxy reveal two kinematic components: a disturbed rotating disk on large scales and a counterrotating nuclear disk on the small scales of the central kpc (Müller-Sánchez et al. 2016). The galaxy's stellar bar is apparent in Figure 1, and the peak of emission is spatially offset along the bar (Figure 2). Based on the model of the counterrotating disk (Müller-Sánchez et al. 2016), the emission peak is located where the nuclear disk and the bar intersect.

4.2.3. One Ambiguous System

We determined that the velocity offsets in our seven targets are produced by shocks and not offset AGNs. Now, for comparison, we consider a velocity-offset AGN that has been confirmed as an offset AGN: SDSS J111519.98+542316.65. SDSS J1115+5423 is z = 0.07 galaxy that is in the velocity-offset AGN catalog (Comerford & Greene 2014) from which we selected the seven targets in this paper, and it is the only galaxy in that catalog that has been shown to be an offset AGN so far. The emission lines in SDSS J1115+5423 are offset −68.5 ± 11.9 km s⁻¹ from systemic. By analyzing archival Chandra observations of this galaxy, Barrows et al. (2016) found that it has a hard X-ray source with ${L}_{2\mbox{--}10\mathrm{keV}}=4\times {10}^{43}$ erg s⁻¹ that is located 0.8 ± 0.1 kpc ($0\buildrel{\prime\prime}\over{.} 64\pm 0\buildrel{\prime\prime}\over{.} 05$) from the host galaxy center. This offset AGN is located within the 3'' SDSS fiber and presumably is the source of the velocity-offset emission lines in the SDSS spectrum, which could be confirmed with a spatially resolved spectrum of the system.

Interestingly, SDSS J1115+5423's [O iii] λらむだ5007/Hβべーた versus [O iii] λらむだ4363/[O iii] λらむだ5007 line flux ratios, as well as its [O i] λらむだ6300/[O iii] λらむだ5007 versus [O iii] λらむだ4363/[O iii] λらむだ5007 line flux ratios, are consistent with models of pure photoionization, in contrast to the seven velocity-offset AGNs studied here (Figure 3). In the case of the offset AGN (SDSS J1115+5423), the emission lines are produced by photoionization from an AGN that is off-nuclear from the galaxy center but still within the SDSS fiber; this explains the velocity-offset emission lines observed in the SDSS spectrum. On the other hand, in each of the seven velocity-offset AGNs studied here, the emission lines originate from a central (not offset) AGN. Inflowing or outflowing gas is shocked, producing off-nuclear peaks in emission (still within the SDSS fiber) that result in the velocity-offset emission lines in the SDSS spectrum.

Consequently, we suggest that it is possible to separate a sample of velocity-offset AGNs into offset AGNs and central AGNs (which have shocks resulting from inflows or outflows of gas) using the shocks versus photoionization diagnostic line flux ratios [O iii] λらむだ5007/Hβべーた versus [O iii] λらむだ4363/[O iii] λらむだ5007, or [O i]λらむだ6300/[O iii] λらむだ5007 versus [O iii] λらむだ4363/[O iii] λらむだ5007. These line flux ratios are measurable with the SDSS spectrum alone; no follow-up observations are required.