The Impact of Low-luminosity AGNs on Their Host Galaxies: A Radio and Optical Investigation of the Kiloparsec-scale Outflow in MaNGA 1-166919

The integrated flux densities of the SE and NW lobes, as measured from the wideband images discussed above, differ significantly between the three observed bands. To better measure how the flux density of these components changes with frequency, we first imaged contiguous subsets of the spectral windows (SPWs) within each band, and then—as in Section 2.1—we fit the resultant image with two Gaussians to measure the integrated flux density of each lobe. The SPWs were grouped such that there would be a ≳ 3σ change in the flux density of the fainter NW lobe assuming that its continuum radio spectrum in this frequency range is well described by a single power law with spectral index α ∼ − 0.9, the value resulting from fitting a power law to the flux densities derived from the wideband images (Table 4). These images were also produced using the casa task tclean, as in Section 2.1, again using natural weighting and the same pixel and image size as before, using the "multiscale" deconvolved algorithm (Cornwell 2008) since the decreased fractional bandwidth of the data set made an additional spectral term unnecessary. We again used the miriad task imfit to fit the central 12'' × 12'' region of each image with two Gaussians. In these fits, the peak flux, size, and orientation of both ellipses were allowed to vary, but the positions of the centers were fixed to the size obtained from wideband images given in Table 4. In general, the morphological properties of the two lobes derived from these fits were consistent with the values derived from the wideband images. The resultant integrated flux densities of both the SE and NW lobes are given in Table 5.

Table 5. Flux Density of SE and NW Lobes Derived from Narrowband Radio Images

Band	SPW a	νb	Δνc	${S}_{\mathrm{int}}^{\mathrm{SE}}$ d	${S}_{\mathrm{int}}^{\mathrm{NW}}$ e
		(GHz)	(GHz)	(mJy)	(mJy)
L	0–5	1.200	0.384	1.76 ± 0.02	1.08 ± 0.02
L	6–9	1.519	0.192	1.70 ± 0.02	0.90 ± 0.02
L	10–15	1.839	0.352	1.60 ± 0.02	0.91 ± 0.02
S	0–3	2.244	0.512	1.02 ± 0.01	0.60 ± 0.01
S	4–6	2.691	0.384	0.96 ± 0.01	0.54 ± 0.01
S	7–10	3.126	0.488	0.97 ± 0.01	0.51 ± 0.01
S	11–15	3.691	0.600	0.92 ± 0.01	0.48 ± 0.01
C	0–3	4.231	0.512	0.59 ± 0.01	0.33 ± 0.01
C	4–9	4.871	0.768	0.61 ± 0.01	0.31 ± 0.01
C	10–16	5.679	0.848	0.62 ± 0.003	0.30 ± 0.003
C	17–23	6.551	0.896	0.56 ± 0.01	0.26 ± 0.01
C	24–31	7.511	1.024	0.55 ± 0.01	0.23 ± 0.01

Notes.

^a Range of spectral windows (SPWs) used in the associated band. ^b Central frequency of subband. ^c Range of frequency within subband. ^d Integrated flux density of the SE lobe. ^e Integrated flux density of the NW lobe.

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The resultant radio spectrum is shown in Figure 5, with the parameters derived from fitting a single power law to the integrated flux densities of both the NW and SE radio lobes given in Table 6. As shown in Figure 5, this model does a good job of reproducing the observed flux densities. We also attempted to fit these flux densities with both a broken power law (as expected if synchrotron cooling is important at higher frequencies) and a power law with exponential cutoff at lower frequencies (as expected from free–free absorption along the line of sight), but these more complicated models did not produce significantly improved fits to the data.

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Table 6. Parameters of Power-law Fits to Integrated Flux Density of NW and SE Radio Lobes

Parameter	SE Lobe	NW Lobe
S1.0 a	${2.35}_{-0.26}^{+0.29}$ mJy	${1.52}_{-0.32}^{+0.40}$ mJy
α	−0.78 ± 0.09	−0.93 ± 0.18

Note.

^a 1 GHz integrated flux density.

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The technique used to get the spectral index maps assumes that the flux density S at a particular frequency ν and sky position (α, δ) can be accurately expressed as

$$\begin{eqnarray}&&{S}_{\nu }(\alpha ,\delta )={S}_{{\nu }_{0}}(\alpha ,\delta )+\frac{{\rm{\Delta }}{S}_{{\nu }_{0}}}{{\rm{\Delta }}\nu }(\nu -{\nu }_{0})\end{eqnarray} \tag{ 1 }$$

and then iteratively solves for the value of ${S}_{{\nu }_{0}}$ and $\tfrac{{\rm{\Delta }}{S}_{{\nu }_{0}}}{{\rm{\Delta }}\nu }$ at each location on the sky. As implemented in the casa command widebandpbcor, the derived value of $\tfrac{{\rm{\Delta }}{S}_{{\nu }_{0}}}{{\rm{\Delta }}\nu }$ is used to calculate the spectral index α within the frequency range of the input data in each pixel of the resultant image.

As shown in Figure 6, in all three bands the spectral index of pixels in the SE and NW is α ≲ − 0.5, consistent with the value derived from the analysis described in Section 2.2.1 (Table 6). However, in all three bands the values of α in the SE lobe are, in general, steeper (more negative) than those in the NW lobe, with a difference in spectral index Δα ∼ 0.1–0.2 (Figure 6), which may not be statistically significant. However, in C band, this analysis indicates the presence of flat-spectrum (α ≳ 0) radio emission. For example, such a spectral index is measured for the ∼ 3σ–5σ peak located W of the two lobes. This suggests that this component has a different physical origin than the two lobes that will be discussed in Section 4.3.

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We used the NBursts full spectral fitting package (Chilingarian et al. 2007a, 2007b) to both derive the properties of the stellar population of this galaxy and determine the stellar contribution to its spectrum. This method uses a χ² minimization algorithm to fit the spectrum in each (spatial) pixel with a model derived from broadening the spectrum predicted from a stellar population model with a Gauss–Hermite parameterized distribution (van der Marel & Franx 1993) of the line-of-sight velocity at this position. To avoid systematically biasing the resultant parameters, we masked wavelengths corresponding to strong emission lines (e.g., Figure 7). The stellar spectra were chosen from a grid of PEGASE.HR high-resolution simple stellar population (SSP) models (Le Borgne et al. 2004) based on the ELODIE3.1 empirical stellar library (Prugniel et al. 2007) assuming a Salpeter initial mass function (Salpeter 1955), pre-convolved with the line-spread function provided within the MaNGA data cube in order to account for instrumental broadening. While the derived properties of the ionized gas do depend on the choice of stellar models, the high signal-to-noise ratio (S/N) of our data suggests that this will be a small effect (Chen et al. 2018). An example of the results of this procedure is shown in Figure 7.

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For each spectrum, this model returns the stellar line-of-sight velocity V_⋆, the velocity dispersion σ_⋆, and the equivalent stellar age T_SSP and metallicity [Fe/H]_SSP of the best-fit SSP. To ensure that the derived parameters are reliable, we binned all spaxels with an S/N > 1 (estimated in the stellar continuum spectrum in a narrow 10 Å spectral window centered on 5100 Å in the galaxy's rest frame) into spatial regions with S/N ≥ 20 using the adaptive Voronoi algorithm developed by Cappellari & Copin (2003). As shown in Figure 8, the spatial distribution of stellar velocity V_⋆ is suggestive of a regularly rotating stellar disk—consistent with the spiral morphology inferred from its optical morphology (e.g., 88% of Galaxy Zoo users classified this source as a spiral galaxy; Lintott et al. 2008, 2011). Furthermore, the increased stellar velocity dispersion σ_⋆ and stellar age T_SSP observed toward the center of a galaxy are indicative of a stellar bulge, with a peak velocity dispersion of σ_⋆ ∼ 170 km s⁻¹ and light-weighted velocity distribution (here we averaged $\sqrt{{v}_{\star }^{2}+{\sigma }_{\star }^{2}}$ values within an elliptical aperture of 4'' size using an ellipticity = 1 − b/a = 0.12 [with b and a minor and major semiaxes, respectively] estimated from the optical image isophotes) within the central 4'' of σ_⋆ = 161.8 ± 0.4 km s⁻¹.

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As shown in Figure 8, the distribution of the stellar line-of-sight velocity of the stellar component V_⋆ is indicative of a regular rotating stellar population. We modeled this stellar velocity field by assuming that, for a spaxel located at a particular (x, y) measured relative to the center of the galaxy, the emitting stars have a line-of-sight velocity

$$\begin{eqnarray}&&{V}_{\mathrm{LOS}}(x,y)={V}_{\mathrm{sys}}+{V}_{\phi }(x,y)\displaystyle \frac{\cos \phi \sin i}{g},\end{eqnarray} \tag{ 2 }$$

where the azimuthal rotational velocity in the center of the disk (its "galactic plane") is

$$\begin{eqnarray}&&\ {V}_{\phi }(R)={V}_{0}\left(\tanh \pi \displaystyle \frac{R}{{R}_{0}}+c\displaystyle \frac{R}{{R}_{0}}\right),\end{eqnarray} \tag{ 3 }$$

where V_sys is the systemic velocity of the galaxy, $g=\sqrt{{\sec }^{2}i-{\cos }^{2}\phi {\tan }^{2}i}$ is a geometrical factor converting the projected sky distance $r\equiv \sqrt{{x}^{2}+{y}^{2}}$ between a spaxel at the center of the galaxy to the distance along the galactic plane R = gr, i is the inclination angle of the disk, R₀ is a radius where velocity reaches a constant maximum value V₀ in the case of c = 0, and c describes the growth (c > 0) or decline (c < 0) of V_ϕ for R > R₀. We then determined the values of V_sys, V₀, R₀, c, i, and the orientation of the galactic disk on the plane of the sky using a χ² minimization routine. This parameterization of a regularly rotating disk is similar to that presented by Chung et al. (2020). As shown in Figure 9, this model is able to reproduce both the observed 1D and 2D stellar velocity distributions.

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To measure the properties of emission lines produced by ionized gas in this galaxy, we first subtracted the stellar continuum, as derived in Section 3.1.1, from the observed spectrum in each region, weighting appropriately the contribution of the constituent spaxels. An example of the resulting emission-line spectrum is shown in Figure 10. We then estimate the S/N of the resultant emission-line spectra in each spaxel using the total flux in the Hα+[N ii] lines, and we removed from further analyses all spaxels with S/N < 30. As shown in Figure 11, this requirement primarily excluded spaxels in the outer regions of this galaxy—beyond the observed extent of its radio emission (Figure 3). We then used the Voronoi algorithm developed by Cappellari & Copin (2003) to spatially bin the remaining spaxels into regions with S/N ≥ 50.

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As shown in Figure 10, the profiles of the emission lines in a particular spaxel were not always well described by a single Gaussian. As a result, we modeled the emission-line spectrum in each spaxel assuming two Gaussian components. Unfortunately, using a χ² minimization routine to model the emission-line spectrum in each spaxel with two independent Gaussians yielded unreliable results due—in large part—to the degeneracies inherent in this model. As a result, we developed a procedure to fit the emission-line spectra in all of the spaxels as the sum of two components:

• 1.  
  a "main" component dominated by regularly rotating gas in the disk of this galaxy; and
• 2.  
  an "outflow" component.

In this decomposition, we accounted for the per-locus dispersion and assumed that the spatial distribution of the kinematic properties of gas in the "main" component is well described by the prescription for a regularly rotating disk given in Equations (2) and (3).

Initial parameters were derived assuming that the main component dominated the emission in each spaxels, but final values resulted from simultaneously fitting the emission-line spectra for the "main" and "outflow" component, as described below.

We then refit the emission-line spectrum in every spatial bin, assuming that the profile of each spectral line is described by two Gaussians. The free parameters in this model are as follows for both the "main" and "outflow" components:

• 1.  
  line-of-sight velocity V_los and intrinsic velocity dispersion (the observed velocity dispersion of a line ${\sigma }_{\mathrm{obs}}^{2}\,={\sigma }_{\mathrm{gas}}^{2}+{\sigma }_{\mathrm{inst}}^{2}$, where σ_gas is the intrinsic velocity dispersion and σ_inst is the instrumental resolution) σ_gas of the emitting gas;
• 2.  
  Hα flux;
• 3.  
  Balmer decrement Hα/Hβ;
• 4.  
  log [N ii] λ6584/Hα;
• 5.  
  log ([S ii] λ6717+[S ii] λ6731)/Hα;
• 6.  
  log [O iii] λ5007/Hβ; and
• 7.  
  $\mathrm{log}{n}_{e}$, as determined from the [S ii] λ6717/[S ii] λ6731 ratio using the methods described by Osterbrock & Ferland (2006) and Proxauf et al. (2014).

To determine the values of these quantities in each spatial region, we used the Levenberg–Marquardt minimization method as implemented by the Python-based lmfit package (Newville et al. 2016) to determine the combination of values that minimized the χ². Furthermore, we required that—for both components—our fits returned values within the following ranges:

• 1.  
  $2.75\leqslant \tfrac{{\rm{H}}\alpha }{{\rm{H}}\beta }\leqslant 10$
• 2.  
  $-1.2\leqslant \mathrm{log}\left(\tfrac{[{\rm{O}}\,{\rm\small{III}}]5007}{{\rm{H}}\beta }\right)\leqslant 1.3$
• 3.  
  $-1.0\leqslant \mathrm{log}\left(\tfrac{[{\rm{N}}\,{\rm\small{II}}]6584}{{\rm{H}}\alpha }\right)\leqslant 0.4$
• 4.  
  $-0.9\leqslant \mathrm{log}\left(\tfrac{[{\rm{S}}\,{\rm\small{II}}]6717+[{\rm{S}}\,{\rm\small{II}}]6731}{{\rm{H}}\alpha }\right)\leqslant 0.25$
• 5.  
  $0.475\leqslant \left(\tfrac{[{\rm{S}}\,{\rm\small{II}}]6717}{[{\rm{S}}\,{\rm\small{II}}]6731}\right)\leqslant 1.425$,

as expected from the physical processes governing these emission lines and observations of large samples of other galaxies (e.g., Baldwin et al. 1981; Osterbrock & Ferland 2006; Proxauf et al. 2014). We further required that, for each spatial region, the fitted value V_LOS of the "main" was within 50 km s⁻¹ of the value for the "main" component derived from the initial analysis described above. Using this procedure, we simultaneously fit for the properties of the "main" and "outflow" contribution to the emission-line spectrum in each spaxel. An example of the results from this fitting procedure is shown in Figure 10.

To assess the statistical significance of the "outflow" component in a given spaxel, we calculated the Bayesian Information Criterion (BIC) statistic (Schwarz 1978; Liddle 2007):

$$\begin{eqnarray}&&\mathrm{BIC}={N}_{\mathrm{data}}\mathrm{ln}\displaystyle \frac{{\chi }^{2}}{{N}_{\mathrm{data}}}+{N}_{\mathrm{vars}}\mathrm{ln}{N}_{\mathrm{data}},\end{eqnarray} \tag{ 4 }$$

where N_data is the number of data points, N_vars is the number of free parameters in the model, and χ² is the result from fitting the data with said model, resulting from fitting the emission-line spectrum of a given region with a single Gaussian (BIC₁) and two Gaussians (BIC₂). As shown in Figure 11, BIC₁ is substantially higher than BIC₂ in the innermost spaxels, strongly implying that the "outflow" component is significant in these regions. These spaxels are also coincident with the radio emission detected from this galaxy, suggesting a physical connection between the ionized gas "outflow" and radio-emitting plasma. In the spaxels beyond the radio emission, BIC₁ is either slightly larger or smaller than BIC₂—implying that the "outflow" component is either not present or a marginal fraction of the ionized gas at these locations. As a result, in 2D maps of the parameters of the "outflow" component, we mask spaxels with BIC₁ < BIC₂, while those with BIC₁ − BIC₂ < 50 are shown in transparent color. Furthermore, in the parameter maps of the main component, we present values from the one-component fit for spaxels with BIC₁ ≤ BIC₂ and values from the two-component fit for those spaxels where BIC₁ > BIC₂.

The differences between the "main" and "outflow" components manifests themselves not only in the statistical significance of the fits but also in the derived properties of the ionized gas. As shown in Figure 12, the velocity dispersion σ_gas of the "outflow" component is in general higher than that of the "main" component—even for spaxels with similar line-of-sight velocities. The "V" shape of the "outflow" component on the V_LOS–σ_gas diagram shown in Figure 12 is suggestive of a biconical geometry (e.g., Bae & Woo 2016). Furthermore, as shown in Figure 13, the line ratios measured for the "main" and "outflow" occupy very different regions on the Baldwin, Phillips, and Terlevich (BPT) diagrams—indicating that they are ionized by different mechanisms (Baldwin et al. 1981). The physical implications of both results will be discussed further in Section 4.1.2.

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As described in Section 2.2, the spectrum of the both the SE and NW radio lobes is well described by a power law with spectral index α ≈ − 0.7, consistent with optically thin synchrotron emission resulting from relativistic electrons (and positrons) interacting with a magnetic field (e.g., Pacholczyk 1970; Condon & Ransom 2016). In this case, the observed radio luminosity L_rad depends on the size R, the relativistic electron u_e, and the magnetic u_B energy density of the emitting region. However, since the synchrotron power P_syn radiated by an electron of energy E in a magnetic field of strength B is (e.g., Pacholczyk 1970; Rybicki & Lightman 1986)

$$\begin{eqnarray}&&{P}_{\mathrm{synch}}(E)=\displaystyle \frac{4{e}^{4}}{9{m}_{e}^{4}{c}^{7}}{B}^{2}{E}^{2},\end{eqnarray} \tag{ 5 }$$

where e and m_e are, respectively, the charge and mass of the electron and c is the speed of light, for a given radio luminosity and size there is not a unique solution for u_e and u_b. However, there is a minimum in the combined (relativistic electron + magnetic field) energy required to power such a source when ${u}_{e}\equiv \tfrac{4}{3}{u}_{{\rm{B}}}$ (e.g., Pacholczyk 1970; Rybicki & Lightman 1986; Condon & Ransom 2016). The magnetic field strength ${B}_{\min }$ is (e.g., Pacholczyk 1970; Condon & Ransom 2016)

$$\begin{eqnarray}&&{B}_{\min }={[4.5(1+\eta ){c}_{12}{L}_{\mathrm{rad}}]}^{\tfrac{2}{7}}{R}^{-\tfrac{6}{7}}\,{\rm{G}},\end{eqnarray} \tag{ 6 }$$

where η is the ion-to-electron energy ratio; c₁₂ is a "constant" whose value depends on ${\nu }_{\min }$, ${\nu }_{\max }$, and α (for ${\nu }_{\min }={10}^{6}\,\mathrm{Hz}$, ${\nu }_{\max }={10}^{10}\,\mathrm{Hz}$, and α ≈ − 0.7 as derived for both the SE and NW radio lobes; Table 6; c₁₂ ≈ 10⁸ in cgs units; Condon & Ransom 2016); R is the radius of the assumed spherical emitting region; and relativistic particle (electrons + ions) energy (e.g., Pacholczyk 1970; Condon & Ransom 2016)

$$\begin{eqnarray}&&{E}_{\min }={c}_{13}{\left[(1+\eta ){L}_{\mathrm{rad}}\right]}^{\tfrac{4}{7}}{R}^{\tfrac{9}{7}}\,\mathrm{erg},\end{eqnarray} \tag{ 7 }$$

where c₁₃ is another constant whose value depends on ${\nu }_{\min }$, ${\nu }_{\max }$, and α (for ${\nu }_{\min }={10}^{6}\,\mathrm{Hz}$, ${\nu }_{\max }={10}^{10}\,\mathrm{Hz}$, and α ≈ − 0.7 as derived for both the SE and NW radio lobes; Table 6; c₁₃ ≈ 3 × 10⁴ in cgs units; Condon & Ransom 2016). Since the 3D geometries of the radio-emitting regions are not known, we assume that R for a particular lobe is between the physical radius inferred by the smallest deconvolved semiminor axis and the largest deconvolved semimajor axis derived from our modeling of the wideband radio images of this source (Section 2.1), as reported in Table 4. The "minimum energy" magnetic field strengths and relativistic particle energies of both the SE and NW lobes inferred from our measurements of their radio morphology (Section 2.1) and spectrum (Section 2.2) are reported in Table 8.

Table 8. Physical Properties of SE and NW Radio Lobes

Property	SE Lobe a	NW Lobe a
${L}_{\mathrm{rad}}\,\left[\tfrac{\mathrm{erg}}{{\rm{s}}}\right]$ b	(2.0 ± 0.3) × 1039	${1.6}_{-0.5}^{+0.9}\times {10}^{39}$
R (kpc)	0.45−0.82	0.49−0.85
${B}_{\min }$ (μG) c	∼ 20–40	∼ 20–40
${E}_{\min }$ (erg) c	∼ (1–3) × 1054	∼ (1–3) × 1054

Notes.

^a Calculated using spectral properties given in Table 6 and morphological properties given in Table 4. ^b Calculated for ${\nu }_{\min }\equiv {10}^{6}\,\mathrm{Hz}$, ${\nu }_{\max }\equiv {10}^{10}\,\mathrm{Hz}$, and the value of d_L given in Table 1. ^c Calculated assuming η = 0, i.e., the emitting plasma is composed solely of electrons (no ions).

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With this information, we can estimate the energy of the radio-emitting electrons. The synchrotron emission from an electron with energy E in a magnetic field of strength B peaks at a frequency (e.g., Pacholczyk 1970; Rybicki & Lightman 1986)

$$\begin{eqnarray}&&{\nu }_{\mathrm{peak}}=0.29\times \displaystyle \frac{3}{2}{\left(\displaystyle \frac{E}{{m}_{e}{c}^{2}}\right)}^{2}\displaystyle \frac{{eB}}{{m}_{e}c}.\end{eqnarray} \tag{ 8 }$$

As a result, for a particular ν_peak and B, the energy of the emitting electron is

$$\begin{eqnarray}&&E\sim 6{\left(\displaystyle \frac{{\nu }_{\mathrm{peak}}}{{10}^{9}\,\mathrm{Hz}}\right)}^{\tfrac{1}{2}}{\left(\displaystyle \frac{B}{1\,\mu {\rm{G}}}\right)}^{-\tfrac{1}{2}}\,\mathrm{GeV}.\end{eqnarray} \tag{ 9 }$$

For the observed frequency range of ν = 1–8 GHz and range of ${B}_{\min }$ given in Table 8, for both lobes the radio emission is dominated by E ∼ 1–4 GeV electrons. The synchrotron cooling time for such particles t_cool is ${t}_{\mathrm{cool}}\equiv \tfrac{E}{{P}_{\mathrm{synch}}}\sim 100\mbox{--}200\,\mathrm{Gyr}$ in both lobes for the estimated particle energies and magnetic field strengths. This suggests that radiative cooling plays a minor role in the evolution of the radio emission from the relativistic particles in this outflow.

Furthermore, the synchrotron spectrum of the observed radio emission can be used to determine the spectrum and origin of the GeV-emitting electrons. Optically thin synchrotron radiation with a power-law spectrum S_ν ∝ ν^α is the result of emission from particles with a power-law energy spectrum:

$$\begin{eqnarray}&&\displaystyle \frac{{dN}}{{dE}}(E)\propto {E}^{-p},\end{eqnarray} \tag{ 10 }$$

where $\tfrac{{dN}}{{dE}}(E)$ is the number of particles per unit energy at particle energy E and p is the particle index (p = 1–2α) (e.g., Rybicki & Lightman 1986; Condon & Ransom 2016). For the spectral index α ∼ − 0.85 measured for both the SE and NW lobes (Section 2.2, Table 6), this suggests p ∼ 2.7—the value expected from first-order Fermi or diffusive shock acceleration (DSA; e.g., Fermi 1949, 1954). DSA requires that particles cross a shock multiple times (e.g., Bell 1978a, 1978b; Blandford & Ostriker 1978), gaining energy in each shock crossing. The particle spectrum, as well as the spectral index α of its resultant synchrotron emission, generated from this process is dependent on the Mach number ${ \mathcal M }$ of the shock, where (e.g., Berezhko & Ellison 1999; Guo et al. 2014; Di Gennaro et al. 2018)

$$\begin{eqnarray}&&{ \mathcal M }=\sqrt{\displaystyle \frac{2\alpha -3}{2\alpha +1}}.\end{eqnarray} \tag{ 11 }$$

The spectral index α ∼ − 0.8 to − 0.9 observed from both the SE and NW lobes (Section 2.2, Table 6) suggests that the emitting particles in both components are accelerated in shocks with ${ \mathcal M }\sim 2\mbox{--}3.5$.

However, such shocks should also efficiently accelerate ions to high energies (e.g., Guo et al. 2014). Recent simulations (e.g., Park et al. 2015) and observations of particles accelerated in shocks with similar Mach numbers ${ \mathcal M }$ (e.g., S/N 5.7–0.1; Joubert et al. 2016) suggest the ion-to-electron energy ratio η > 100. If that also occurs in this galaxy, then minimum total relativistic particle energies in the SE and NW lobes are ∼ 10× higher than the values given in Table 8, or on the order of ∼ 10⁵⁵ erg. Regardless of the true value of α, the larger energy in the relativistic component of this outflow suggests that it can have a significant impact on the host galaxy (e.g., Mao & Ostriker 2018; Hopkins et al. 2020).

As described in Section 4.1.1, the radio emission observed from MaNGA 1-166919 is believed to be produced by electrons accelerated by a shock propagating through this galaxy. However, theoretical work suggests that ≲ 10% of the shocked material is accelerated to relativistic energies (e.g., Caprioli & Spitkovsky 2014; Caprioli et al. 2015), with the bulk of the material heated to a temperature T_shock (e.g., Faucher-Giguère & Quataert 2012; Caprioli & Spitkovsky 2014):

$$\begin{eqnarray}&&{T}_{\mathrm{shock}}\sim \displaystyle \frac{1}{2}\displaystyle \frac{{{mv}}_{\mathrm{shock}}^{2}}{k},\end{eqnarray} \tag{ 12 }$$

where m is the mass of the particle, k is Boltzmann's constant, and v_shock is the velocity of the shock relative to the surroundings. If v_shock is high enough, a copious amount of UV and soft X-ray photons will be generated at the shock front (e.g., Raymond 1976; Allen et al. 2008). The spectra from material photoionized by this radiation are expected to have emission-line ratios (e.g., Dopita & Sutherland 1995; Allen et al. 2008) that lie within the LIER of the [S ii] BPT diagram (Kewley et al. 2006). (In the literature, this emission is often referred to arise from a "low-ionization nuclear emission-line region" [LINER] since they were first and primarily identified in the centers of galaxies; e.g., Heckman 1980; Heckman et al. 1981. However, subsequent work has found that such emission can be detected throughout a galaxy, e.g., Belfiore et al. 2016, and therefore we use the more general term.) Indeed, as shown in Figures 13 and 18, the emission-line ratios of the "outflow" material largely fall within the LIER region of such a diagram. Furthermore, as shown in Figure 18, LIER-like emission is only detected in the center of this galaxy and predominantly found in the "outflow" component of the ionized gas. Therefore, it seems likely that the ionized gas "outflow," as inferred from our analysis of the MaNGA (Section 3.1.2) and GMOS (Section 3.2) data, is dominated by material photoionized by the shock that also accelerates the relativistic electrons responsible for the observed radio emission. However, in many galaxies, such line ratios are instead thought to result from photoionization by post-AGB stars (e.g., Yan & Blanton 2012; Singh et al. 2013; Belfiore et al. 2016). Such stars are expected to be prevalent in older (≳1 Gyr) stellar populations—as inferred for the central regions of this galaxy (T_SSP ∼ 3 Gyr; Figure 8) from our derivation of its stellar population as described in Section 3.1.1.

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It is possible to distinguish between these models by measuring the kinematics of the putative "outflow" component of the ionized gas in this galaxy, which we identify through deviations from a regularly rotating disk (as derived in Section 3.1.2). For the GMOS data, we estimated this by subtracting the line-of-sight velocity measured in a particular spaxel (left panel of Figure 15) with that predicted by our model for the regular rotating gas in this galaxy (right panel of Figure 17), while for the MaNGA data we calculated the difference in line-of-sight velocity between the "main" and "outflow" components (ΔV_{gas, OF}) as derived from the modeling described in Section 3.1.2. As shown in Figure 19, the relative line-of-sight velocities show a clear spatial separation of "red" and "blue" components—strongly suggesting a biconical "outflow." This geometry is consistent with the V_LOS − σ_gas of the "outflow" component (Figure 12). Furthermore, the correspondence between the kinematics of the "outflow" ionized gas and the SE and NW radio "lobes," which is particularly evident in the higher angular resolution GMOS data (left panel of Figure 19), strongly suggests a physical connection between the two. Since the radio emission is produced by shock-accelerated particles, we therefore conclude that these shocks are indeed responsible for producing the LIER-like emission observed from the ionized gas. This conclusion is further supported by the observed dependence between ∣ΔV_gas,OF∣ and the line ratios of the "outflow" gas. As shown in Figure 18, spaxels with higher values of ∣ΔV_gas,OF∣ typically fall above and to the right of spaxels with lower ∣ΔV_gas,OF∣ on the [S ii] BPT diagram. This trend is similar to that predicted by models for the emission of material photoionized by shock-heated gas, which find that their location on the [S ii] BPT diagrams moves up and to right as the shock velocity v_shock increases (e.g., Allen et al. 2008).

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If correct, then the relative line-of-sight velocity between the "main" and "outflow" component provides a lower limit on v_shock, since this quantity is not sensitive to differences in velocity between these components in the plane of the sky. As a result, we estimate v_shock ≳ 100 km s⁻¹ for the NW lobe and v_shock ≳ 200 km s⁻¹ for the SE lobe—sufficient to photoionize substantial amounts of material both "downstream" (postshock) and "upstream" (preshock) of the shock (e.g., Raymond 1976; Dopita & Sutherland 1995; Dopita et al. 1996; Wilson & Raymond 1999). Furthermore, the observed geometry and differences in extent and shock velocity between the two components of the outflow are consistent with those expected from outflows resulting from high-velocity material ejected from an AGN interacting with a clumpy interstellar medium (ISM; e.g., Mukherjee et al. 2018; Nelson et al. 2019). In fact, simulations suggest that the biconical geometry of this outflow is the natural consequence of a central outflow being confined by the disk of a galaxy (e.g., Wagner et al. 2012). In summary, both the relativistic and ionized components of this outflow appear to be the result of shocks driven into the surrounding ISM by a central engine.

In Section 4.1.1, we presented our measurements for the energy contained in the relativistic component of this outflow. However, this outflow also consists of several nonrelativistic components, including ionized gas, atomic gas, and molecular material. In this section, we use the emission-line spectra derived from MaNGA (Section 3.1.2) and GMOS (Section 3.2) to measure the properties of its ionized component. While studies of similar outflows in other galaxies suggest that atomic and molecular material may constitute the bulk of the entrained mass (e.g., Oosterloo et al. 2017), currently the observational data needed to measure the properties of these components in this galaxy are not available.

The mass of the ionized gas in this outflow M_out, can be estimated as (e.g., Soto et al. 2012; Baron et al. 2017)

$$\begin{eqnarray}&&{M}_{\mathrm{out}}=\mu {m}_{{\rm{H}}}{{Vn}}_{e}f,\end{eqnarray} \tag{ 13 }$$

where m_H is mass of the hydrogen atom, μ is the average atomic number of the emitting material (assumed to be solar, such that μ ≡ 1.4), V is volume of the emitting region, f is the filling factor, and n_e is the number density of electrons. The Hα luminosity of this region is equal to (e.g., Baron et al. 2017)

$$\begin{eqnarray}&&{L}_{{\rm{H}}\alpha }={\gamma }_{{\rm{H}}\alpha }{n}_{{\rm{e}}}^{2}{fV},\end{eqnarray} \tag{ 14 }$$

where γ_Hα is the Hα emissivity of the ionized plasma. In the case of highly ionized material with an electron temperature T_e ≈ 10⁴ K and optically thick to Lyman line emission ("Case B"; e.g., Baker & Menzel 1938; Burgess 1958), γ = 3.56 × 10⁻²⁵ erg cm³ s⁻¹ (Osterbrock & Ferland 2006). As a result, we can calculate M_out by evaluating

$$\begin{eqnarray}&&{M}_{\mathrm{out}}=\displaystyle \frac{\mu {m}_{{\rm{H}}}{L}_{{\rm{H}}\alpha }}{{\gamma }_{{\rm{H}}\alpha }{n}_{{\rm{e}}}}.\end{eqnarray} \tag{ 15 }$$

Therefore, to calculate this quantity, we first need to determine n_e in the outflow, as well as correct the observed Hα emission for extinction along the line of sight.

We estimate n_e using the observed ratio of the [S ii] λ6717/[S ii] λ6731 emission lines (Osterbrock & Ferland 2006; Proxauf et al. 2014) separately for the "outflow" component of the MaNGA emission-line spectrum and the GMOS data. As shown in Figure 20 for the MaNGA "outflow," there are considerable variations in this parameter between adjacent spaxels due to the weakness of these lines and/or complexity of the line decomposition in many spaxels. We therefore calculated an average n_e for the outflow in each data set, weighting the value in each spaxel by the total Hα+[N ii] flux of its outflow component. This yields a weighted average of $\mathrm{log}{n}_{e}\approx 1.9$ ( ≈ 80 cm⁻³) in the MaNGA data and $\mathrm{log}{n}_{e}\approx 2.0$ ( ≈ 100 cm⁻³) in the GMOS data, similar to the value inferred for outflows in other galaxies (e.g., Harrison et al. 2014; Karouzos et al. 2016), as well as in the previous analysis of this galaxy by Wylezalek et al. (2017) (Table 9). However, this method for estimating the electron density preferentially returns values in the range of 10 cm⁻³ ≲ n_e ≲ 10⁴ cm⁻³ (e.g., Proxauf et al. 2014). Therefore, the central regions of the outflow where we estimate n_e ∼ 10 cm⁻³ may have a true density below this value. Furthermore, the low ionization of the emitting gas suggests that there is a significant neutral component to this material, whose density is not measured using this technique. As a result, the total (neutral and ionized) gas density is likely to be significantly higher than the estimated value of n_e (e.g., Dempsey & Zakamska 2018). Lastly, recent results suggest that the electron densities estimated using [S ii] are systematically lower than those using other emission lines (e.g., Davies et al. 2020) unfortunately not detected with sufficient spectral resolution or low S/N in our data.

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Table 9. Properties of the Ionized Gas Outflow and AGN

Property	This Work		Wylezalek et al. (2017)
	MaNGA	GMOS a
ne	≈ 80 cm−3	≈ 100 cm−3	≡ 100 cm−3
Mout	2.4 × 107 M⊙	(2.2–3.9) × 107 M⊙
Kion	2.4 × 1055 erg	(4.6–8) × 1054 erg
tage	≈ 6 Myr	6.2 Myr	2–3 Myr
${\dot{M}}_{\mathrm{out}}$	$\approx 4\,\tfrac{{M}_{\odot }}{\mathrm{yr}}$	$(3.5\mbox{--}6.3)\,\tfrac{{M}_{\odot }}{\mathrm{yr}}$	$66\,\tfrac{{M}_{\odot }}{\mathrm{yr}}$
${\dot{E}}_{\mathrm{kin}}$	$\approx 1.3\times {10}^{41}\,\tfrac{\mathrm{erg}}{{\rm{s}}}$	$(2.4\mbox{--}4.1)\times {10}^{40}\,\tfrac{\mathrm{erg}}{{\rm{s}}}$	$1.4\times {10}^{42}\,\tfrac{\mathrm{erg}}{{\rm{s}}}$
Lbol	$(0.3\mbox{--}9.1)\times {10}^{43}\,\tfrac{\mathrm{erg}}{{\rm{s}}}$		$(6\mbox{--}7.1)\times {10}^{43}\,\tfrac{\mathrm{erg}}{{\rm{s}}}$

Note.

^a Ranges reflect the difference resulting from the two ways of estimating the extinction along the line of sight, as described in Section 4.1.3.

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To estimate the extinction along the line of sight toward the outflowing material in both data sets, we use the Balmer decrement (the Hα/Hβ flux ratio) of the outflow component measured in the MaNGA data. This is because, as described in Section 3.2, Hβ is not detected in the GMOS data. As shown in Figure 20, this quantity varies significantly, and for the MaNGA outflow we corrected the Hα flux of the outflow in each spaxel with the corresponding Balmer decrement measured for this component. The differing angular resolutions of the MaNGA and GMOS data preclude us from making a similar spaxel-by-spaxel correction. As a result, we estimate the average extinction toward the outflow in the GMOS data from the MaNGA data in two ways: the mean value, 〈Hα/Hβ〉 = 6.8, and the Hα+[N ii] flux weighted averaged value 〈Hα/Hβ〉_{Hα+N II} = 8.6. In all cases, we use the Balmer decrement to correct the Hα flux using the extinction law derived by Cardelli et al. (1989), with the results shown in Figure 21.

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With these measurements of $\mathrm{log}{n}_{e}$ and extinction-corrected Hα flux in hand, it is now possible to measure the total mass of outflowing ionized gas in this galaxy. For the MaNGA data, we do so by adding together the mass estimated in each spaxel (Figure 20), deriving a total mass of M_out ∼ 2.4 × 10⁷ M_⊙. For the GMOS data, we use the total Hα flux measured in the "outflow" region—which, as described in Section 3.2, corresponds to those spaxels with σ_gas > 100 km s⁻¹, or the central r_OF ≈ 1'' ≈ 1.4 kpc (Figure 15) of this galaxy. In this case, we estimate M_out ∼ (2.2–3.9) × 10⁷ M_⊙—in good agreement with the value derived from the MaNGA data alone.

Furthermore, we can estimate the total velocity of the outflow v_out as (e.g., Karouzos et al. 2016)

$$\begin{eqnarray}&&{v}_{\mathrm{out}}=\sqrt{{v}_{\mathrm{los}}^{2}+{\sigma }_{\mathrm{gas}}^{2}},\end{eqnarray} \tag{ 16 }$$

where the value of these quantities as measured from the GMOS data is shown in Figure 15 and that as derived for the "outflow" component in the MaNGA emission-line spectrum is shown in Figure 22. Both data sets give similar values of v_out, with the ionized gas moving near ∼400 km s⁻¹ near the center of the galaxy and slowing to values of ∼200–300 km s⁻¹ near the edge of the radio emission.

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With this velocity information, we can calculate the kinetic energy and "age" of the ionized gas in this outflow. We determine the kinetic energy K_ion of the ionized gas in the MaNGA data by evaluating $K=\tfrac{1}{2}{M}_{\mathrm{ion}}{v}_{\mathrm{out}}^{2}$ in each spaxel (Figure 23), and we add together the values to measure a total K_ion = 2.4 × 10⁵⁵ erg in the MaNGA data and K_ion = (4.6–8) × 10⁵⁴ erg for the GMOS data. These energies are comparable to the minimum energy estimated for the relativistic content of this outflow (Table 8, Section 4.1.1), suggesting that these two components are in rough equipartition. Furthermore, we estimate the age of the MaNGA outflow in each spaxel as

$$\begin{eqnarray}&&{t}_{\mathrm{age}}=\displaystyle \frac{R}{{v}_{\mathrm{out}}},\end{eqnarray} \tag{ 17 }$$

where R is the projected physical separation between the spaxel and the center of the galaxy. As shown in Figure 23, this suggests that the outflow is ∼6 Myr old. For the GMOS data, the ∼1.4 kpc extent of the outflow coupled with the Hα+[N ii] flux weighted average outflow velocity v_out value of 222 km s⁻¹ suggests t_age = 6.2 Myr—consistent with the results derived from the MaNGA data. As shown in Table 9, this suggests a mass outflow rate of ∼ 4 M_⊙ yr⁻¹ and a kinetic power of ${\dot{E}}_{\mathrm{kin}}\sim (0.2\mbox{--}1)\times {10}^{41}\,\mathrm{erg}\,{{\rm{s}}}^{-1}$.

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