FRAMEx. IV. Mechanical Feedback from the Active Galactic Nucleus in NGC 3079

Using the Very Long Baseline Array, we observed the active galactic nucleus (AGN) in NGC 3079 over a span of six months to test for variability in the two main parsec-scale radio components, A and B, which lie on either side of the AGN. We found evidence for positional differences in the positions of A and B over the six months consistent with the apparent motion of these components extrapolated from older archival data, finding that their projected rate of separation, (0.040 ± 0.003)c, has remained constant since ∼2004 when a slowdown concurrent with a dramatic brightening of source A occurred. This behavior is consistent with an interaction of source A with the interstellar medium (ISM), as has previously been suggested in the literature. We calculated the amount of mechanical feedback on the ISM for both the scenario in which A is an expulsion of material from the central engine and the scenario in which A is a shock front produced by a relativistic jet, the latter of which is favored by several lines of evidence we discuss. We find that the cumulative mechanical feedback on the ISM is between 2 × 1044 and 1 × 1048 erg for the expulsion scenario or between 3 × 1050 and 1 × 1052 erg for the jet scenario. Integrated over the volume-complete Fundamental Reference AGN Monitoring Experiment (FRAMEx) sample, our results imply that jet-mode mechanical feedback plays a negligible role in the energetics of AGNs in the local Universe.


Introduction
The Fundamental Reference AGN Monitoring Experiment (FRAMEx; Dorland et al. 2020), led by the U.S. Naval Observatory, is an ongoing campaign to better understand the physical mechanisms that can affect the apparent positions and morphologies of active galactic nuclei (AGNs) as a function of wavelength.In FRAMEx I (Fischer et al. 2021), we observed a volume-complete (D < 40 Mpc) sample of 25 nearby AGNs with a snapshot campaign using simultaneous observations with the Very Long Baseline Array (VLBA) and Swift X-ray Telescope (XRT).We found that the "fundamental plane" of black hole activity (e.g., Merloni et al. 2003), which purports to unify the X-ray and radio luminosities of AGNs and X-ray binaries through the black hole mass, breaks down at high physical resolution.Moreover, despite all FRAMEx AGNs having hard X-ray (14-195 keV) luminosities larger than 10 42 erg s −1 by construction, only nine out of the 25 AGNs have detectable 6 GHz radio emission down to a depth of 20 μJy at ∼3 mas (subparsec) spatial scales.To explore the role of variability in the subparsec regime, we followed FRAMEx I with a six month VLBA and Swift-XRT campaign that observed the nine detected sources in a 28 day cadence.FRAMEx II (Fernandez et al. 2022) presented the results for NGC 2992 and found anticorrelated radio and X-ray variability that is consistent with an outburst from the accretion disk simultaneously increasing the free-free absorption depth and the number of electrons available for inverse-Compton scattering of UV photons.The results of the six month campaign for the remaining FRAMEx AGNs are forthcoming.FRAMEx III (Shuvo et al. 2022) explored the radio nondetections from FRAMEx I using the VLBA with longer integration times, expanding the original sample with an additional nine objects that have redshift-independent distances consistent with our volume definition to improve completeness.We found that, despite an observation depth of 8 μJy, the majority of the sample remained undetected at milliarcsecond spatial scales, although five new detections were recorded bringing the total detection fraction to 14/34 (41%).The X-ray-based radioloudness parameter R X ≡ L R /L X of these extremely radio-faint AGNs showed an anticorrelation with Eddington ratio, similar to the behavior found in X-ray binaries.
Continuing with the goals of FRAMEx, a major field of ongoing research is examining how AGN "feedback" affects host galaxies from their immediate surroundings at parsec scales, upwards to kiloparsec scales, and in rare instances megaparsec scales due to jets, outflows, or a combination of both.Quantifying on which scales feedback occurs is critical to understanding the relationship between AGN activity and star formation, heating of the intercluster medium, and the coevolution of supermassive black holes (SMBHs) and their host galaxies more generally.Lister (2008) discusses some of the basic forms of jet interactions with the surrounding medium at parsec scales where the jet is susceptible to external interactions, falling into three classifications: bow shockhotspot interactions, cloud collisions, and entrainment.With a sufficiently long temporal baseline of very long baseline interferometry (VLBI) observations, the generation and evolution of these structures can be seen directly, allowing for quantification of feedback mechanisms on parsec scales.
Since the early 1980s, the AGN in NGC 3079 has been observed multiple times using VLBI (e.g., Hummel et al. 1982; Original content from this work may be used under the terms of the Creative Commons Attribution 4.0 licence.Any further distribution of this work must maintain attribution to the author(s) and the title of the work, journal citation and DOI.Irwin & Seaquist 1988;Haschick et al. 1990), including several multifrequency campaigns to probe the core components of the AGN (e.g., Trotter et al. 1998;Sawada-Satoh et al. 2000;Kondratko et al. 2005).Trotter et al. (1998) observed NGC 3079 with the VLBA at 5 and 8 GHz in 1992 and 22 GHz in 1995 where they observed two compact sources (components A and B).They also detected a third component (C) that lies along the same axis as A and B (their Figure 5) at 22 GHz; unfortunately they were unable to detect component C at 5 or 8 GHz.At 22 GHz, the emission from B is the dominant feature with an integrated flux of ∼16 mJy.Trotter et al. (1998) stated that none of the sources detected appeared to mark the nuclear engine, which was inferred from the presence of water maser emission, and may only represent the features of a nuclear jet.Sawada-Satoh et al. (2000) observed NGC 3079 with the VLBA at 1.4, 8.4, 15, and 22 GHz in 1996.Due to the restoring beam of the VLBA at 1.4 GHz, components A and C appear as a single component, while at 8.4 GHz the components A, B, and C are resolved.Only the B component was detected at 15 and 22 GHz (their Figure 1).In addition to these results, these studies have found the brighter off-nuclear components A and B to be increasing in separation.Middelberg et al. (2007) observed the separating nuclear components from 1999 to 2005 in C-band at 5 GHz.Using their observations with archival data, they found the rate of separation of components A and B to be declining.They attributed the slowdown due to collisions with the interstellar medium (ISM).Helmboldt et al. (2007) observed NGC 3079 in 2006 and suggested the radio knots could be a compact supermassive binary black hole system, but Tremblay et al. (2016) determined this was not the case due to NGC 3079 not having two distinct compact radio cores that have a flat or inverted spectrum.Component A has changed from steep to flat spectrum while component B has remained inverted.
Since 2006, there have been only a few VLBA observations of NGC 3079, most of which have either instrumental effects, limited uv coverage, or low integration times that preclude accurate measurements of the positions and flux densities of components A and B. There were three C-band observations and all three data sets contained issues.The data from an observation in 2016 have a low integration time and limited uv coverage, causing a larger restoring beam where multiple nuclear components appear as a single component.A 2019 observation, from the FRAMEx I snapshot, also suffered from similar issues where the data suffered from instrumental effects and only a single component was observed.We also examined the EVN archive and found two observations, one in 2019 February and one in 2019 October.The observation in October requested time to study the absorption line of OH at 6 GHz and not the continuum.The results from these observations have yet to be published.This means there have not been any accurate measurements of the ongoing separation of the nuclear components A and B for ∼12 yr.Considering that the AGN in NGC 3079 has been observed previously multiple times over ∼40 yr, this provides an opportunity to study the interaction of the AGN with the surrounding medium.In this work, we use the VLBA observations from our six month campaign to dramatically increase the baseline of VLBI observations of the AGN in NGC 3079.From morphological and radio-loudness considerations, we argue that the radio structures in the inner few parsecs of NGC 3079 are jet-powered, although we consider an alternative, outflow scenario, and we estimate the amount of mechanical (kinetic) energy deposited on the ISM by radio-mode feedback in both cases.

Methodology
As in Fischer et al. (2021), we used a redshift of z = 0.0037 and a distance D = 15.9Mpc for NGC 3079, which translates to an angular scale of 0.077 pc mas −1 .

VLBA Observations
Through the U.S. Naval Observatory's 50% timeshare, we received observation time on the VLBA at 5 cm (6 GHz) every 28 days (PI: T. Fischer).This began on 2019 December 31 and provided a total of six observations.We followed the same phase referencing method described in Fischer et al. (2021) and Fernandez et al. (2022).For our time-series observations, we requested an integration time of 1 hr with all 10 antennas for NGC 3079.Unfortunately, on 2019 December 31 and 2020 April 21 not all 10 antennas were used.On 2019 December 31 antennas HN and OV did not participate and on 2020 April 21 antenna MK did not participate.From previous measurements (Middelberg et al. 2007), the separation rate of the nuclear components A and B indicates that the observable separation will be difficult to distinguish at our cadence.Therefore, we present only the first and last observations from the time series that utilized all 10 antennas to obtain the highest flux sensitivity and consistent angular resolution between epochs.Table 1 summarizes these observations.

Calibration and Imaging
We followed the same steps described in Fernandez et al. (2022) to calibrate and image the VLBA data of NGC 3079 using NRAO's software package, Astronomical Image Processing System (AIPS; Greisen 2003), release 31DEC19.These steps corrected for ionospheric delays, Earth orientation parameters, sample threshold errors, instrument delays, bandpass, amplitude, and parallactic angle.We flagged radio frequency interference in both time and by frequency using the tasks EDITR and WIPER, respectively.Next, we calibrated the phase and absolute astrometry of our data to the accuracy of the phase calibrator's position using a two-point interpolation function.The phase calibrator used for NGC 3079 is ICRF J095622.6+575355, which has an R.A. and decl. of α = 149°.09431037(8) and δ = 57°.89886214(3), respectively, in ICRF3 (Charlot et al. 2020), where the parentheses denote the uncertainties (on the order of 100 μas).
To image the calibrated data, we followed the same steps outlined in Fernandez et al. (2022) using the AIPS task IMAGR.Since the data have a high signal-to-noise ratio, we were able to apply self-calibration to the images by first self-calibrating on phase only, and then on a combination of phase and amplitude using the AIPS task CALIB.This was an iterative process where we used the new image as a model for the subsequent calibration until the thermal rms noise could not be improved any further without introducing artifacts and falling below the theoretical rms.The final self-calibrated images were then used to analyze the flux densities of components A and B (we also include the results for component C).

Analysis
Similar to Fernandez et al. (2022), we used AIPS to calculate the rms noise with the task IMEAN, then used the task JMFIT to calculate the peak and integrated flux for components A, B, and C. Table 2 lists our measurements.
To determine the separation between components A and B and minimize the uncertainty in their position, we needed to create additional images that had a convolved beam with equal major and minor axes, similar to what was done in Middelberg et al. (2007).This is due to detecting complex source structures that are resolved, making it problematic to accurately measure the source positions and their separation (see the top of Figure 1).To account for source extent we used a taper of 48 Mλ in the uv plane to obtain a nearly circular convolved beam while making sure to use as much of the data as possible and avoiding source confusion.To measure the separation, we constructed Monte Carlo simulations to estimate the posterior distribution of the distance between components A and B. This was done by performing an initial fit of a two-dimensional, elliptical Gaussian function to each component (Figure 1).With this fit as a source model, we produced background images with correlated noise by convolving an elliptical Gaussian beam kernel with uncorrelated noise and adjusting the rms of this noise to match that of the data after convolution.We first compared the separation of A and B based on our initial fit from the elliptical Gaussian with that of the measured separation between the peak brightnesses of A and B. For both observations, we obtained a difference of <0.3 pixels (<0.24 mas).
While the source positions from the elliptical Gaussian fits are therefore consistent with the peak positions within the uncertainties of the latter, we nonetheless considered pixel-topixel position uncertainties in our Monte Carlo simulations by adding an independent random value between −0.5 and 0.5 to the x-position and to the y-position of the modeled fit.We repeated this 10 5 times, at each iteration adding correlated noise to the source model and refitting each source.We also found an archival image from the VLBA Imaging and Polarimetry Survey (VIPS; Helmboldt et al. 2007) in which NGC 3079 was observed on 2006 June 19 at 5 GHz.We repeated our Monte Carlo method using this image and found that the difference between the source separation using the fit model and that using the peak-to-peak separation was also <0.5 pixel, which Note.The calibrator J0956+5753 was used for phase referencing.Tapered measurements are from a uv coverage of equal distance of 48 Mλ.Note.Measured peak and integrated flux values with 1σ uncertainties calculated using the task JMFIT, which uses an elliptical Gaussian fitting algorithm.There is an additional uncertainty of 5% of the measured flux added in quadrature to the 1σ uncertainty to account for the absolute flux uncertainty of the VLBA.Tapered measurements are from a uv coverage of equal distance of 48 Mλ.
was consistent with our tapered data.We list our source separation measurements, along with their 90% confidence intervals (CIs), in Section 3.1.

X-Ray Observations
We requested observation time using Swift-XRT with Target of Opportunity (ToO) observations (PI: N. Secrest) to be simultaneous with our VLBA observations.The XRT has a point-spread function (PSF) with a half-power diameter of 18″ at 1.5 keV with a positional accuracy of 3″ and observes at an energy range from 0.2 to 10 keV.We requested an integration time of 1.8 ks using photon counting (PC) mode and generated the X-ray spectra using the online XRT product generator (Evans et al. 2009), setting the source extraction coordinates to the location of the VLBA sources.As described in FRAMEx II, we were unable to obtain observations for 2020 February and 2020 April.In any case, we were not able to extract enough counts for X-ray spectral fitting, likely because the AGN in NGC 3079 is Compton-thick.Fortunately, we found a 24 ks NuSTAR observation taken serendipitously within a month of our 2020 May 19 VLBA observation, providing a quasisimultaneous constraint on the 3-79 keV X-ray luminosity of NGC 3079.

X-Ray Analysis
As in Fernandez et al. (2022), we used the XSPEC v.12.11.1 (Arnaud 1996) software to perform the spectral analysis.Since the AGN in NGC 3079 is Compton-thick, we used a physically self-consistent fitting model instead of a phenomenological combination of different spectral components.Specifically, we used MYTorus (Murphy & Yaqoob 2009) to fit the X-ray spectrum.To robustly estimate the model errors and covariances, the command chain was used to produce Monte Carlo Markov Chains (MCMCs), allowing us to obtain 90% CIs for our model's free parameters.Using the MCMCs to estimate the posterior distributions of the constituent model components (e.g., the power-law continuum), we calculated the intrinsic X-ray flux and its uncertainty.Our results are given in Section 3.2.

Separation of Radio Components A and B
The results for the observation on 2006 June 19 from VIPS gave a separation between the nuclear components A and B of 28.13 ± 0.09 mas, where the uncertainty is the 90% CI and derived from the posterior distribution.In our recent 2020 January 27 observation, the separation is 30.1 ± 0.2 mas, while in our 2020 May 19 data it is 30.4 ± 0.2 mas.We show the posteriors from these latter two observations in Figure 2. We plot the separation over time, including the 5 GHz separation measurements from Irwin & Seaquist (1988) Middelberg et al. (2007), where they measured projected velocities of (0.12 ± 0.02)c, (0.08 ± 0.01)c, and (0.01 ± 0.02)c corresponding to two periods of slowdown, has continued to the present day, and that there are step-like jumps in the brightness of component A contemporaneous with this slowdown.Given the sampling of the data and their uncertainties, a polynomial fit is not statistically justified, so we instead use a broken linear fit, with a linear component for each jump in the brightness of source A. The components of the this linear fit have projected velocities of (0.13 ± 0.01)c, (0.08 ± 0.03)c, and (0.040 ± 0.003)c (alternatively, (0.52 ± 0.02) mas yr −1 , (0.3 ± 0.1) mas yr −1 , and (0.16 ± 0.01) mas yr −1 ), corresponding to the periods before 2000, 2000-2004, and 2004-present, respectively.If we only examined the angular separation over time, there is a possibility that only one slowdown took place and fitting a two-component broken

Radio-Loudness
After fitting the NuSTAR data using the physical MYTorus model and obtaining the MCMCs, the best-fit normalization of the intrinsic power-law is 6 10 When it comes to determining the ratio for the radioloudness parameter, there is a source of ambiguity.The radioloudness parameter was derived using AGN core radio luminosities at different spatial scales.The C-band observations with the Very Large Array (VLA) are at a resolution of 1″, which is unable to resolve any of the core nuclear components, while the VLBA observations are at a resolution of ∼2 mas, which resolves any extended emission and may contain multiple nuclear radio components.Additionally, there is ambiguity as to what constitutes the radio core, where at milliarcsecond scales the apparent position of the core is frequency dependent because of synchrotron self-absorption (Plavin et al. 2019), which appears as a "core shift."Therefore, depending on which spatial scale is used, this can drastically change the result of R X .A majority of the sources used in determining the radio-loudness parameter of −4.5 in Terashima & Wilson (2003) were from VLA observations (11 objects) and a small minority were from VLBA observations (four objects) where all sources are within 60 Mpc.In other words, at these distances, the VLA is probing both parsec-scale (compact) and kiloparsec-scale (extended) radio emission.This means that if there are multiple nuclear compact radio sources, the VLA is unable to resolve them and is therefore observing the sum of all radio emission that can be detected by the VLA's convolved beam.Since a large statistical representation of the sources used in determining the radio-loudness parameter log (R X ) > −4.5 is from VLA observations, we therefore summed the luminosities from each nuclear component observed by the VLBA (A and B from our tapered images) and find log (R X ) = −4.0.By the log (R X ) > −4.5 radio-loudness threshold established in Terashima & Wilson (2003), NGC 3079 is therefore radio-loud.Similarly, using a VLA observation, Chiaraluce et al. (2019) found the ratio log (R X ) = −4.4,which would also imply that NGC 3079 is radio-loud given the delineation of −4.5.For the purpose of this analysis, the exact demarcation of what is considered radio-loud versus radioquiet is not as important as the relative differences between R X (measured in the same way) for the full FRAMEx sample.In other words, those objects with a higher R X are more likely to be jet-powered than those with lower R X value even if R X is biased or ambiguous in some way.
There is evidence that suggests, based on the presence of water maser emission, that the true position of the central engine lies between components C and B (Trotter et al. 1998;Kondratko et al. 2005), suggesting that the radio emission is due to the presence of a jet. Figure 6 in Kondratko et al. (2005) shows what is described as maser emission tracing a nearly edge-on molecular disk at the position of the AGN.In Middelberg et al. (2007), they found the 5-15 GHz spectral index of component A changed from steep spectrum to flat spectrum over three observations from 1999 to 2000 (α = 1.07, 0.90, and 0.27, respectively, with S ν ∝ ν − α ) while component B remained inverted (−1.02, −0.97, and −1.00, respectively).
It is therefore likely that the central engine lies somewhere between radio knot A and B, which are currently separated by a projected distance of ∼2 pc.If NGC 3079 were at a higher redshift or observed at a lower spatial resolution, such as with the VLA, it would be indistinguishable from that of an AGN core.This means the radio emission in radio-loud AGNs may not correspond solely to the central engine (true core) and be mostly due to the effect it has on the surrounding medium due to feedback mechanisms.This would mean the radio emission observed in NGC 3079 does not correspond to the central engine and also does not preclude it from being validly classified as radio-loud.However, Chiaraluce et al. (2019) suggests that the log (R X ) > −4.5 criterion is too low and a better parameter to follow is the ratio log (R X ) = −2.755found by Panessa et al. (2007).Additional evidence that suggests this may be the case is presented in Shuvo et al. (2022).In general, the radio-loudness of an object can be used to estimate if its radio emission is powered by a relativistic jet if the jet itself is difficult to distinguish, due to distance, lack of resolution, or a lack of beaming.As the hard X-ray emission is produced nearest to the SMBH in the compact corona, the VLBA probes a spatial scale more causally connected to the immediate accretion rate inferred from the hard X-rays.Radio emission within the subparsec to parsec scales resolved by the VLBA therefore provides a more cotemporal picture of the ratio between the mechanical output of the AGN and its radiative output.Regardless of which R X criterion is used, the radioloudness of NGC 3079 compared to the rest of the volumecomplete FRAMEx sample suggests that its nuclear radio emission is jet-driven.

Discussion
When we compared our measured separation rate of NGC 3079ʼs nuclear core components A and B with Middelberg et al. (2007), we find the slowdown is not as extensive as previously measured.Their measured separations from 2004 to 2006 are within each other's uncertainty, meaning their measured separation rate was limited by the short spacing between observations.This caused their calculated separation rate to appear slower than the actual separation.Since our new observations took place over 10 yr after the previously measured observations, we provide a more accurate depiction of how components A and B are separating.It is clear based on the changes in luminosity and the spectral index of component A to a more flat spectrum (Middelberg et al. 2007), A has impacted a more dense region of the surrounding ISM.Meanwhile, component B has retained an inverted spectrum while its luminosity has reduced over time.This indicates only A has undergone a recent change in its interaction with the ISM.

Mechanical Feedback
The apparent motion of source A, indicated both by the increasing A−B separation and the dramatic brightening of A associated with a slowing of the A−B separation, implies AGN-driven kinematics, in which kinetic energy from a jet or wind is deposited into the ISM.There are generally two modes of mechanical feedback: jet-mode and wind-mode, the latter being the uncollimated deposition of kinetic energy from an energetic particle accretion disk wind, but the degree of collimation varies and there may be large, relatively compact masses of material ejected from the AGN accretion disk in discrete events, analogous to the coronal mass ejections seen in stars (e.g., Fernandez et al. 2022).
Given the compact nature of A, we quantitatively assess the jet and compact wind-driven mass scenarios here.In the jet scenario, source A is a shock front propagating away from the AGN as the jet drills into the ISM.The collimated jet itself, not being highly beamed, is much less luminous, although there is a faint possibly linear feature connecting source C to source A visible in the residual image of Figure 1 that supports the existence of a jet, as is predicted if radio-loudness is a hallmark of jet activity.The synchrotron emission in source A is generated from the in situ production of relativistic electrons by the jet shocking the ISM, unlike the compact mass scenario in which a specific blob of material is physically propagating away from the AGN.
The average power in synchrotron radiation emitted by a single, relativistic electron with an isotropic pitch angle distribution is (as reviewed in Condon & Ransom 2016): where U B B 8 2 = p is the magnetic energy density, σ T is the electron Thompson cross section, γ is the Lorentz factor, and v c b º .For synchrotron emission from an electron, we estimated γ using: where ν is the observed frequency (Condon & Ransom 2016).Sebastian et al. (2019) calculated the minimum magnetic field strength of the host disk of NGC 3079 by fitting models with different volume filling factors to their observational data.They found a magnetic field strength of 35.9 μG for a filling factor of 1, 43.8 μG for a filling factor of 0.5, and 500 μG for a filling factor of 10 −4 .Using these magnetic field strength estimates in Equation (2), in order for an electron to produce synchrotron emission, γ must be approximately equal to 7600, 6880, and 2040, respectively.These values appear to be appropriate given relativistic simulations that reproduce synchrotron emission at radio frequencies where the electron Lorentz factors used are between 10 and 10 5 (γ ∼ 10 4 used in Nolting et al. 2019;Yates-Jones et al. 2021).After combining Equations (1) and (2) with the estimated magnetic field strengths, we found the power from each electron to be 7.9 × 10 −17 erg s −1 , 9.6 × 10 −17 erg s −1 , and 1.1 × 10 −15 erg s −1 , respectively.Taking the ratio of the observed luminosity with the calculated power for an electron gives an estimate to the number of electrons needed in order to produce the luminosity observed.With the estimated number of electrons for different magnetic field strengths, we are able to estimate a range of mass of the shocked electrons in component A to be between M e = 4 × 10 −8 M e and M e = 5 × 10 −7 M e .
Using the estimated total electron mass, we calculated the mechanical energy deposited into the ISM by the jet acting on component A. As the shocks act on in situ electrons, the initial average net velocity of the electrons can be assumed to be ∼0, so the relativistic motions of the electrons along magnetic field lines are powered by the mechanical energy deposited on the ISM by the jet.Then, the total kinetic energy, expressed as mechanical power is: where M e is the total mass of shocked electrons as calculated above and γ is their Lorentz factor.We treat the ISM as having an equal number of protons and electrons in bulk, where the protons absorb as much kinetic energy from the jet on average, giving the factor of 2. Given the range of mass from the magnetic field estimates, the mechanical power is between 3 × 10 50 and 1 × 10 52 erg.This is within an order of magnitude of the total average kinetic energy from a supernova (∼10 51 erg).Based on the magnetic field estimates, the lifetime of synchrotron radiation is larger than >10 4 yr (Condon 1992), which implies that the energy calculated here is the cumulative amount of kinetic feedback from the AGN given the apparent motion of the shock and its proximity to the AGN.Because we are probing the AGN with the VLBA there is undoubtedly some larger-scale emission that is resolved out.This can be seen when we compared the luminosity of previous VLA A-configuration observations at 5 GHz from the literature (provided in Table 4 of Fischer et al. 2021) with the total luminosity from all nuclear components added together from our VLBA observations; the ratio between the two is 1.25.As mentioned earlier, there is also the possibility that component A is hot plasma ejected from the AGN that has been continuously propagating away from the central engine and collided with a denser region of the ISM during the ∼2000-2006 slowdown/brightening period (Figure 3).In this picture, the faint possibly linear feature could be the trail of the ejected hot plasma from previous shocks, and the kinetic energy difference ΔKE captures how much energy is being dumped into the surrounding ISM.We calculated the relativistic ΔKE by using the projected separation velocity from before and after the collision, with the mass estimates of component A assuming that it is composed purely of electrons.This resulted in a range of ΔKE between 2 × 10 44 and 1 × 10 45 erg.In reality, component A is most likely composed of both electrons and protons, but only the electrons are responsible for synchrotron emission.These numbers are therefore a lower limit on the total amount of kinetic feedback component A is having on the surrounding ISM.For the case where there is an equal number of protons and electrons that make up component A, the ΔKE range is from 3 × 10 47 to 1 × 10 48 erg.Since determining the exact composition of component A is difficult, there is also the possibility component A contains more protons than electrons.If this is the case, the range 2 × 10 44 -1 × 10 48 erg is a better lower limit to the total amount of kinetic feedback A could be having on the surrounding medium.

Comparing Feedback Mechanisms
In order to better understand and contextualize the effects of AGN-driven, jet-mode feedback on host galaxies, we can leverage the fact that NGC 3079 is part of a volume-complete sample to roughly assess the overall importance of jet-mode, wind-mode, and radiative-mode feedback in the interactions between AGNs and their host galaxies, at least in the local Universe.Given the considerations previously discussed, we favor the jet interpretation for the radio emission in NGC 3079.This being the case, NGC 3079 joins NGC 1052 as the jetdriven, radio-loud members of the FRAMEx sample.For NGC 1052, we scaled the KE of NGC 3079 (KE from weakest magnetic field strength estimate of 35.9 μG) by the ratio of their 6 GHz radio luminosities, a factor of 17. Applying this to the mechanical power in component A, we find the value for NGC 1052 to be ∼10 53 erg, which is within an order of magnitude of the value (1.3 ± 0.9) × 10 53 erg recently found by Cazzoli et al. (2022) using MUSE data.Then, the mean mechanical energy from jet-mode feedback across the FRAMEx sample is ∼10 51 erg.This is equivalent to the total average KE from a supernova.
The energetics of wind-mode and radiative feedback can be estimated from the bolometric luminosities of the full FRAMEx sample, which can in turn can be estimated from the hard X-ray luminosities.We used Equation (1) in Temple et al. (2023) with the 14-195 keV luminosities listed in Fischer et al. (2021) to estimate the bolometric luminosities of the FRAMEx sample.With the estimates of the jet-mode mechanical feedback from NGC 3079 and NGC 1052 in hand, we can exploit the volume completeness of the FRAMEx sample to assess the relative importance of jet-mode feedback in the local Universe.As we have seen, NGC 1052 dominates the jet-mode energy budget, with a total feedback of ∼10 53 erg.While this amount of energy would take ∼500 yr to reach given the bolometric luminosity of NGC 1052, if we compare the summed jet-mode feedback energy from NGC 1052 and NGC 3079, the only two radio-loud objects in this volume, with the summed bolometric luminosities of all the AGNs in the volume (∼10 45 erg s −1 ), we find that it only requires ∼3 yr for the total, nonjet bolometric output of the AGNs to reach the same amount of energy as their total, jet-mode output.We have seen that, at least for NGC 3079, the energy from the jet has taken ∼70 yr to build in the ISM, given the much longer synchrotron cooling times (>10 4 yr; Condon 1992).As the radio source in NGC 1052 is obviously much older than ∼3 yr, and likely at least as old as the source in NGC 3079, this implies that, on average, the jet-mode energy feedback from AGNs in the local Universe is of order a few percent of their total bolometric output, indicating that jet-mode feedback is relatively unimportant.A potential caveat of this statement is that there could be older radio lobes and shock relics on larger scales than what our VLBA observations are sensitive to.However, given the relatively compact radio morphologies seen in archival VLA data (Figure 3 in Fischer et al. 2021), this appears not to be the case.Defining a volume-complete sample has allowed us to integrate over a statistically representative sample of AGNs, allowing for detailed single-object studies such as our study of NGC 3079 to directly inform our understanding of the wider role of AGNs in their environments and host galaxies.
We also examined the amount of wind power that is generated to compare with our results from jet-mode feedback in order to probe the total mechanical feedback of NGC 3079.In order to estimate this, we started from first principles of accretion disks from Shakura & Sunyaev (1973) and created a surface temperature profile using a M BH = 10 6.38 M e (provided in Table 1 of Fischer et al. 2021).Using this temperature profile, we calculated a range of specific luminosities L ν for a range of frequencies.L ν was then normalized using the intrinsic 2500 Å luminosity estimated from the 2 keV luminosity using the α OX relationship from Lusso et al. (2010).The normalized L ν was then used to calculate the amount of kinetic energy imparted on outer-disk protons and electrons via Compton scattering, accounting for relativistic effects using conservation of energy.Examining the difference in the amount of power lost due to a final scattering off of either a proton or electron, yields the total amount of power of the wind (P wind ∼ 4 × 10 38 erg s −1 ).Using the initial projected separation velocity of components A and B, we estimated the amount of time elapsed since the separation began with that of our most recent observation (∼70 yr).Therefore the amount of energy released from wind-mode feedback since the separation began is ∼9 × 10 47 erg.This is in line with the wind-driven scenario discussed toward the end of Section 4.1.
In order to determine the possible mechanisms at work in NGC 3079, we then examined the Eddington ratio (λ Edd = L bol /L Edd ).First, in order to calculate the bolometric luminosity of the AGN in NGC 3079, we used the bolometric estimate equation from Temple et al. (2023)  , we found λ Edd = 0.136.This means even on the upper end, λ Edd < 0.2 for the AGN in NGC 3079.Giustini & Proga (2019) suggests an AGN with λ Edd at this regime (10 −3  λ Edd  10 −1 ) is dominated by an optically thick and geometrically thin accretion disk where a radiation-driven disk wind is unable to form, feedback is mainly radiative, and jet emission is suppressed compared to lower Eddington ratios.Those AGNs with 10 −6  λ Edd  10 −3 are expected to be magnetically dominated with high-velocity collimated radio jets with a low-velocity outer wind, while AGNs with λ Edd  0.25 are said to be wind dominated.Zhu et al. (2022) also come to a similar conclusion through twodimensional simulations, where they studied large-scale dynamics of accretion disk winds driven by line force.They found that for black hole masses < 10 7 M e and a λ Edd = 0.3, the strength of the wind's kinetic energy is substantially weaker at larger radii and unable to provide a sufficient amount of feedback to affect the host galaxy.Marziani et al. (2018) suggest outflow velocities are related more to the Eddington ratio than black hole mass or luminosity.Where at low accretion rates (<0.2), they propose there is a partly failed wind with a geometrically thin accretion disk.This appears to be consistent with what is observed in NGC 3079 given λ Edd ∼ 0.02.Due to the nature of the volume-complete sample, this would indicate all AGNs in the local Universe with similar Eddington ratios may also be dominated by other forms of feedback (i.e., radiative feedback).
There is another object in the FRAMEx I volume-complete sample that has similar characteristics to NGC 3079.The AGN in NGC 1068, at a distance similar to NGC 3079, is also a Compton-thick source, also contains multiple nuclear radio components, and has a similar bolometric luminosity (Fischer et al. 2021).In a recent publication, Fischer et al. (2023) explore apparent motion in some of the radio knots in NGC 1068, but unlike NGC 3079 they conclude that the radio knots are most likely pseudomotions due to changes in the densest regions in a much larger, extended radio structure that is otherwise resolved out by the VLBA.This behavior is more likely to be due to AGN winds or radiative feedback, instead of jet-mode feedback as we infer for NGC 3079.The reasons why we do not conclude that a similar process is occurring in NGC 3079 are as follows.First, NGC 3079 has been observed at milliarcsecond scales multiple times over a span of ∼40 yr and only radial, linear motion away from the maser-inferred position of the AGN has been seen.This is not the expected behavior for pseudomotion, in which regions dense enough to be detected by VLBI observations randomly condense out of the extended radio emission, leading to nonradial or tangential motions.Second, we know a priori that NGC 3079 is much more radio compact on larger scales than NGC 1068.In FRAMEx I, we found that, while the ratio of VLA (Aconfiguration) to VLBA C-band at 5 GHz integrated fluxes is ∼3 (and around 1.25 using the 6 GHz data from this work), the same ratio for NGC 1068 is ∼400.In other words, NGC 1068 is over two orders of magnitude more radio extended than NGC 3079, given that they are at nearly the same distance (∼16 Mpc), consistent with radio emission in NGC 1068 being primarily driven by an uncollimated wind.Additionally, while we find a faint, potentially linear feature along historical trajectory of source A, no such feature is present in NGC 1068.Finally, only NGC 1068 has a source detected at C-band with the VLBA coincident with its assumed AGN core position, while NGC 3079 is undetected at the AGN position inferred from maser emission, implying different core radio production mechanisms.If NGC 3079 is indeed producing a jet as the evidence suggests, then the apparent radio silence of the core may be due to synchrotron self-absorption, free-free absorption, or a combination of both.Nonetheless, NGC 1068 and NGC 3079 also have similar bolometric luminosities (estimated using their hard X-ray luminosities) and SMBH masses, which mean they have similar Eddington ratios.Given the differences discussed above regarding the possible physical mechanisms at play with NGC 1068 and NGC 3079, this is somewhat surprising.One explanation is that the SMBH mass of NGC 3079 is actually larger than we have assumed.Indeed, there is considerable variance in literature estimates of NGC 3079ʼs SMBH mass, ranging between 10 6 and 10 8 M e (10 6 , 10 8 , 10 6 , 10 7.2 , 10 8.2 ; Kondratko et al. 2005;Lamperti et al. 2017;Gliozzi et al. 2021;Osorio-Clavijo et al. 2022;Tanimoto et al. 2022).Given this range of masses, the Eddington ratio could be two orders of magnitude less than that of NGC 1068.If this is the case, it could help explain the differences in physical mechanisms inferred for the two objects and add to the evidence in favor of a jet-mode feedback scenario for the AGN in NGC 3079.

Possible Scenarios for the Nuclear Component B
The balance of the evidence is that source A is propagating through the ISM, brightening or dimming as the density of the intervening material changes, driven by a likely jet seen as a faint linear structure connecting A to the position of the AGN somewhere near C.In this scenario, component B does not appear to be moving, a conclusion supported by the relative stability of its luminosity (see the bottom of Figure 3).We note, however, that B has an inverted spectrum (Middelberg et al. 2007), which argues against it being relic emission from an earlier accretion event or supernova.One possible explanation is that B is the termination point of a frustrated jet.A second, less likely scenario is based on the recent work of Baczko et al. (2022), who examined NGC 1052 and found that the emission gap between the base of the jet had a highly inverted radio spectral index and indicated this was due to an obscuring molecular torus causing free-free absorption.In this case, component B may be at or near the base of the jet and is being obscured by the torus.Source A would therefore be material from an older ejection from the central engine.We view this scenario as less likely because of the position of the water maser emission between A and B, which suggests that the AGN core lies between these two sources.This was shown in Kondratko et al. (2005) where they found blueshifted and redshifted maser emission that trace a nearly edge-on molecular disk about a parsec in radius and aligned with the kiloparsecscale molecular disk.

Conclusions
In this work, we have presented an analysis of the radio knot kinematics in NGC 3079, one of two radio-loud members of the volume-complete FRAMEx sample.Using new VLBA observations, we found the current projected rate of separation between the two main knots A and B to be (0.040 ± 0.003)c.This is consistent with previous work, but our observations significantly increase the temporal baseline of VLBI monitoring of NGC 3079.The brightening of component A cotemporal with an apparent reduction in its velocity suggests that A marks an interaction of the AGN with a more dense ISM.We have considered two scenarios for the nature of the radio knot kinematics: shocking of the ISM by an otherwise radio-faint jet, and bulk motion of radio-emitting plasma ejected from the AGN.Our primary conclusions are as follows: 1.If the radio knots are jet-powered then the cumulative amount of kinetic feedback on the surrounding medium is between 3 × 10 50 and 1 × 10 52 erg.This scenario is supported by the presence of a faint linear feature seen in our VLBA observations connecting component A to the inferred position of the AGN, and is also predicted by the physical picture in which radio-loudness is a consequence of relativistic jets.If the radio knots are ejected plasma, then the cumulative kinetic feedback is between 2 × 10 44 and 1 × 10 48 erg, depending on the composition of component A, vastly lower than in the jet scenario.2. Since the projected separation velocity was initially ∼0.13c, the appearance of a possible linear feature in the residual image from the model subtracted from the data in Figure 1, a log (R X ) = −4.0suggests that NGC 3079 is radio-loud, the scaled total KE from the jet-mode feedback scenario of the AGN in NGC 3079 to the AGN in NGC 1052 (a well known radio-loud jetted AGN) is consistent with the KE found in the literature, and a λ Edd ∼ 0.02 suggests a failed or weak wind that is insufficient to produce the amount of mechanical feedback needed to affect the host galaxy, therefore the evidence points toward the jet-mode scenario.3.As NGC 3079 is the only member of the volumecomplete FRAMEx sample of local AGNs other than the radio-loud NGC 1052 to exhibit the likely jet-powered radio knot kinematics shown here, our results indicate that the amount of mechanical energy produced by jetmode feedback and wind-mode feedback with Eddington ratio ∼ 0.02, appears to not be as significant as other modes of feedback (i.e., radiative feedback) for AGNs in the local Universe.
Further understanding the effects of mechanical feedback from AGNs can inform the overall importance of feedback and its role on galaxy formation and bulges.This can also inform what role mechanical feedback has on ISM/intergalactic medium heating in AGNs.For wind-mode feedback, King & Pounds (2015) suggest small-scale momentum-driven outflows (thermal energy is lost to cooling and only ram pressure is conserved) that interact with a small central part of the bulge sets the critical M-σ black hole mass.Where energy-driven outflows (wind shock energy is conserved and shocked wind is expanding adiabatically) are global and expand out to greater scales to produce large-scale molecular outflows that can sweep up and clear the galaxy of gas.As for jet-mode feedback, Fabian (2012) reviewed different types of AGN feedback, where jet-mode feedback can create bubbles of relativistic plasma on either side of the nucleus and affect the surrounding ISM.As part of a volume-complete sample, NGC 3079, along with NGC 1052, therefore provide a direct view into mechanical feedback from AGNs in the local Universe.

Figure 1 .
Figure 1.From our 6 GHz VLBA observations using our model fitting of radio core components A and B. Images are 64 × 64 mas, centered on the core component A. The color bar is in units of mJy beam −1 .The green ellipse is the convolved beam.Top row: untapered observation on 2020 May 19 with included 15× rms contours.Both the middle and bottom row images are tapered to 48 Mλ in the uv plane to constrain the data as close to a circular convolved beam with included 10× rms contours.Middle row: observation on 2020 January 27.Bottom row: observation on 2020 May 19.

,
Trotter et al. (1998), Kondratko et al. (2005), and Middelberg et al. (2007), in the top panel of Figure 3, along with their corresponding integrated flux values in the bottom panel.It is immediately clear that the slowdown of the A−B separation reported in

Figure 2 .
Figure 2. Posterior distribution of the projected offset between the nuclear components A and B in NGC 3079.Top: for our analysis of the data from Helmboldt et al. (2007).Middle: for our observation on 2020 January 27.Bottom: for our observation on 2020 May 19.

Figure 3 .
Figure 3. 5 GHz archival data points are hollow markers while our 6 GHz data are filled circles.Top: separation of the core components A and B from NGC 3079.Black dashed line indicates a broken linear fit with three slopes corresponding to the separate brightening.Bottom: integrated flux over time.

Table 2 6
GHz VLBA Measurements of NGC 3079 and the 14-195 keV luminosity from FRAMEx I. Then we calculated the