A Detailed Kinematic Study of 3C 84 and Its Connection to γ-Rays

This scale (Figures A1 and A2, and Tables A1 and A2) gives the best fits with the least amount of scatter. There are no significant differences between the four- and eight-component fits. Component 24:9, south of the brighter parts of the C3 region, emerges in late 2015 at 0.65c. At a similar time, component 24:1 moves rapidly to the west. No motion or very slow inward motion is found in the C1 region. C2 is quasi-stationary (e.g., component 24:5 at 0.14c).

We now reduce the WISE analysis scale to be the average major axis of the beam (Figures A3 and A4 and Tables A3 and A4). We see broadly consistent results with the 0.48 mas scale. Component 16:17 is the same as component 24:9, with the same speed of 0.47c. Component 16:1 is the same as 24:1, with a similar speed. This component is still detected until the most recent data, continuing on a westerly trajectory. With four-component fits, some motion is detected in the "lane" area, with, for example, component 16:18 having a speed of 0.44c.

This length scale is between the major and minor beam axes, with the results of the analysis in Figures A5 and A6, and Tables A5 and A6. The lanes are clearly detected separately at this scale. Component 12:11 (0.66c) follows an apparently curved path, starting on the western lane, and crossing to the eastern lane in mid-to-late 2012. It then crosses back from the eastern lane to the western lane in early 2014. This coincides with the previous components 16:1 and 24:1, which were one slow-moving component, splitting in two. Now these components are identified as 12:1 until early 2014. Two components were then identified, with component 12:47 being likely the same as 16:17 and 24:9. Another component is detected in the western lane (12:46) with a relatively fast motion of 0.66c although having started in the eastern lane, it then moved across the jet in early-to-mid 2015. In early 2016, an apparently quasi-stationary feature formed (component 12:61) at a separation of ∼2 mas from C1. Additionally in the four-component detection scheme, as with the 0.32 mas scale analysis, some motions are detected in the "laned" region with similar speeds.

The analysis here is performed on the scale of the minor axis of the beam and is likely close to the limit of what could be assumed to be a reliable analysis (Figures A7–A9 and Tables A7–A9). In addition to the four- and eight-component fits, we have included a 12-component fit in order to increase our confidence in the results at this scale. In general, it is consistent with the results seen in the 0.24 mas-scale analysis. The most striking difference is the detection of an additional component in the eastern lane (component 8:8, 0.47c), which although traveling on almost the same trajectory as component 8:31 (cross-identified with component 12:11), is considerably slower than component 8:31's 0.89c. It additionally does not appear to cross from the eastern to western lane. In the 12-component fit, the westerly motion of components 12:36 and 16:1 are not detected although in the eight-component fit it is seen as component 8:78. In the four-component fit plots, we note that almost all components at a separation of ∼0.4–1.2 mas appear to follow a curved trajectory moving from the west to the southeast, although interpreting these should be done with caution, as four-component fits at the smallest length scale tend to be the most unreliable.

From the WISE analysis described in Section 3.2, we have found that the complex kinematic behavior could potentially be associated with γ-ray activity. In order to further explore the association, we have presented CLEAN maps, concentrating on the periods around each of the γ-ray flares. In Figure 5, we found a fast-moving component E2, which was moving southerly along the eastern lane. It then began to interact with the component W1 that had previously been traveling along the western lane. Beginning late 2013, the region containing both components becomes brighter, with both components having comparable brightness, appearing almost as a single large emission region by 2013 December. Flare G1 is observed before the component split into two separate regions and then dissipated quickly. A single region then brightens again, with this component presumed to be component E2 from the WISE analysis. The component E2 is either detected as a single continuous component over the period from ∼G1 until G3, or detected as several components, depending on the length scale of the WISE analysis. We have kept the E2 designation from the larger length scale for the benefit of the reader.

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In Figure 6, component E2 continues to move on a westerly trajectory, consistent with the WISE analysis, becoming brighter, and then in the VLBI images immediately after the γ-ray flare G2 (between the 2014 September 23 and 2014 November 15 maps), the region again is resolved into two separate emission regions, which then dissipate. A similar behavior can be seen in Figure 7, where component E2 continues moving easterly, expanding and becoming brighter before splitting into two components. The "flare-split-dissipate" behavior appears to be common across flares G1, G2, and G3. In the latter two cases, however, the components continue as EB2 and WB1, respectively.

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We noticed a new emission region/component, EB2, in the western lane of the VLBI images at the time of flare G4 (see Figure 8). Then EB2 continues to brighten, producing the radio flare R3, which correlates with the γ-ray flare G4 (see Paper I for the detailed light-curve analysis). This behavior is different from the previous three flares and appears to be coincident with the onset of radio flare R3. Also note that this flaring activity appears to be happening in the western lane, while flares G1 to G3 seem to be associated with the jet activity in the eastern lane.

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In this paper, we have presented evidence for a potential connection between the γ-ray flaring and the kinematic behavior in 3C 84. In order to estimate the significance of these associations, we first determine the significance of individual "split-flare-dissipate" events and then determine the likelihood that these events are randomly associated with γ-ray flaring.

To determine the significance of individual "split-flare-dissipate" events, we first investigated the ridge-line profiles of the region (see Figure 9). We find that in all three cases, the "split" appears significant. To further investigate, we then compared single- and double-Gaussian models to the region in the uv domain.

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3C 84 is a highly complex source and adding more components to the map would have improved the reduced-χ² considerably. However, in this case, we are only interested in the relative change in the reduced-χ² value in order to estimate the degree to which the map prefers a single- or double-component fit to the region in question. For this reason, we only fitted the minimum number of components. In practice, this required a single Gaussian to first be fit to the C1 region, as it dominates the map. Then we fit either one or two components to the region we were analyzing. We then compared the reduced-χ² values of the one- and two-component fits. Table 4 lists the reduced-χ² values. We found that in the cases of Split 1 and Split 2, the model preferred two components. However, in the case of Split 3, the algorithm favors a single Gaussian. Adding a second Gaussian made only a marginal difference. Therefore, we consider Split 1 and 2 to be significant but Split 3 to be marginal. In order to further explore the significance of the associations, we also tested the final model-fitted maps and tested the reduced-χ² values using a single- or double-component fit. The results were consistent with the previous method.

In order to determine the significance of these events being associated with γ-ray flaring, we follow the approach of Rani et al. (2018). From the simulated light-curve analysis in Paper I, we found how often a γ-ray photon flux reached above the flux density, 2.4 × 10⁻⁷ ph cm⁻² s⁻¹, of the weakest flare from the detrended 15 day binned γ-ray light curve. We found that for a given 15 day bin, there were ∼300 photons above this energy within the 5000 simulated light curves. Given the monthly cadence of the VLBI observations, we therefore double this and estimate a 12% chance of random association (∼1.5σ). However, if we assume that the events are independent, the chance of random association for two "split-flare-dissipate" events is 1.4% (∼2.5σ) and 0.17% (∼3σ) for three "split-flare-dissipate" events.

The magnetic reconnection mini-jet scenario, where fast flaring above a slow envelope is predicted, has been analyzed from a theoretical perspective by Giannios (2013), presenting analytical expressions that can be tested in 3C 84. In this paper, the author assumed that the slow envelope emission would be on the order of days; however, we are equating the slow-rising trend with the envelope emission with an envelope timescale of ∼years (e.g., see Figure 12). We have one key observable, the dissipation radius R_diss, where most of the high-energy emission is emitted. This can be directly derived from the data. In the case of 3C 84, this emission could be occurring within the C3 region when it was at ∼2–3 mas from the core, equivalent to a projected distance of ∼1 pc. The difference between the projected and deprojected distances should not be very different if the viewing angle is relatively large (as is suggested in Section 3.5). However, if the viewing angle is smaller, the projected and deprojected distances will vary by a factor of $\sin \theta$. As discussed in the previous section, because 3C 84 is only mildly relativistic, we assume that the Lorentz factor and Doppler factors are ∼1, although a mildly higher Doppler factor should not affect our conclusions significantly. Primed quantities are in the observer frame. The mildly relativistic bulk jet emission may have mini-jets that have their own Doppler factor δ_j . The timescale t_env of the envelope in the jet frame is

$$\begin{eqnarray}&&{t}_{\mathrm{env}}^{\prime} =\displaystyle \frac{(1+z){R}_{\mathrm{diss}}}{{{\rm{\Gamma }}}^{2}\beta },\end{eqnarray} \tag{ 4 }$$

where δ is the relativistic Doppler factor of the jet. We introduce a factor of β here as in the paper of Giannios (2013), who assumed it to be 1. Using cgs units, we set R_diss ∼ 1 pc ∼ 3 × 10¹⁸ cm, giving an envelope timescale of t_env ∼ 1 × 10⁸ s ∼ 3 yr. This matches well with the observed envelope in 3C 84, which began in approximately 2013 and continued until 2015 (see Figure 2 and the sketch in Figure 12). According to this model, when the reconnection timescale, which is directly related to the Schwarzchild radius of the SMBH (R_sch), becomes comparable to the expansion timescale of the jet, much of the high-energy emission is dissipated (i.e., at R_diss). This is because the model assumes that small-scale magnetic field structures are embedded into the jet on the scale of the BH event horizon. It then follows that we can then solve for the magnetic reconnection speed in units of c:

$$\begin{eqnarray}&&\epsilon =\displaystyle \frac{{{\rm{\Gamma }}}^{2}{R}_{\mathrm{sch}}}{{R}_{\mathrm{diss}}}.\end{eqnarray} \tag{ 5 }$$

Using M_BH ∼ 3 × 10⁸ M_⊙, leading to R_sch ∼ 1 × 10¹⁴ cm, this gives ∼ 3 × 10⁻⁵. This value is several orders of magnitude lower than the expected value of ∼0.1 used in Giannios (2013). Nevertheless, we can use this value with the envelope timescale to estimate the size of the reconnection region in the jet frame, $l^{\prime}$:

$$\begin{eqnarray}&&l^{\prime} ={t}_{\mathrm{env}}{\rm{\Gamma }}\epsilon c,\end{eqnarray} \tag{ 6 }$$

and therefore the jet frame flare timescale ${t}_{\mathrm{flare}}$:

$$\begin{eqnarray}&&{t}_{\mathrm{flare}}^{\prime} =\displaystyle \frac{0.1l^{\prime} }{{\delta }_{p}c},\end{eqnarray} \tag{ 7 }$$

where δ_p is the Doppler factor of a mini-jet plasmoid. This leads to a jet frame reconnection region size of $l^{\prime} \sim 9\times {10}^{14}\,\mathrm{cm}\sim 3\times {10}^{-4}$ pc and a flare timescale of ${t}_{\mathrm{flare}}\sim 60$ minutes. Because relativistic effects are only mild in 3C 84, the observer and jet frame emission will be quite similar. Even if we assume that the Doppler factor of a plasmoid is also of ∼1, the predicted flare timescale is somewhat shorter than the observed timescale of ∼hours to days. However, it is likely that mini-jets oriented toward the line of sight of the observer would have Doppler factors greater than unity.

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While the picture fits in a broad sense, there are also large inconsistencies, for example, the size of the reconnection region, which should be related to the SMBH size by $l^{\prime} \simeq {\rm{\Gamma }}{R}_{\mathrm{sch}}$ and is an order of magnitude larger than the size estimated via the location of the dissipation region. Similarly, the estimated flare timescale is roughly an order of magnitude faster than what is seen. The reconnection rate is two orders of magnitude lower than expected. In our calculations, we assumed an SMBH mass of ∼ 3 × 10⁷ M_⊙ (Onori et al. 2017). If the mass of the SMBH were higher than this, it could resolve the discrepancy. For example, an SMBH mass of ∼ 10¹⁰ M_⊙ would reconcile the values. However, it is possible that the mass is lower, of order 10⁶–10⁷ M_⊙ in 3C 84, which would make the inconsistencies worse (see Sani et al. 2018 for a discussion about the SMBH mass in 3C 84). Another possibility is that other physics is involved such as radiation (e.g., Uzdensky 2016). The presence of a spine–sheath structure could also potentially create the conditions for magnetic reconnections if the current sheets are opposed in the regions where the spine and sheath meet.

We consider it more likely that the reconnection length scale would not scale directly with R_sch. The turbulence scenario described at the start of Section 4.2 would naturally explain such a discrepancy, as randomly aligned "cells" of plasma could easily have opposing magnetic field directions (Marscher 2014). We can then estimate the number of "cells" within a volume (Burn 1966):

$$\begin{eqnarray}&&{n}_{\mathrm{cells}}\sim {\left(\displaystyle \frac{70 \% }{P \% }\right)}^{2},\end{eqnarray} \tag{ 8 }$$

where P% is the polarization degree of the emitting region. The size of a "cell," R_cell, which should be equivalent to the reconnection size $l^{\prime}$, would then simply be the third root of the volume of the region divided by the number of cells:

$$\begin{eqnarray}&&{R}_{\mathrm{cell}}\sim \displaystyle \frac{{R}_{\mathrm{region}}}{{n}_{\mathrm{cells}}^{1/3}},\end{eqnarray} \tag{ 9 }$$

where R_region is the size of the region. This assumes that the emitting region is roughly spherical. If the emitting region is disk like, the area of the region should be divided by the number of cells. Thus, for a polarization degree of ∼2%, which was localized within the C3 region (Nagai et al. 2017), this leads to n_cells ∼ 1000 and to a cell size (equivalent to a reconnection size) of ∼0.02 pc ∼ 6 × 10¹⁶ cm. Setting $l^{\prime} ={R}_{\mathrm{cell}}$ in Equations (6) and (7) allows us to estimate ∼ 0.02, which is closer to the expected value of 0.1 and ${t}_{\mathrm{flare}}\sim 2$ days, which better matches the observations. Including a Doppler factor for the mini-jets (δ_j ) would further match the model with the observed behavior.

Alternatively, we consider the case of the high-energy emission originating from the C1 region. In this case, we set R_diss to be the beam size of ∼0.15 mas. This leads to R_diss ∼ 0.05 pc ∼ 1.5 × 10¹⁷ cm, which must be emphasized is an upper limit. Using this limit, we find the envelope timescale to be t_env ∼ 8 weeks and the reconnection speed to be ∼ 7 × 10⁻⁴. We then estimate the size of the reconnection region to be $l^{\prime} \sim 1\times {10}^{14}\,\mathrm{cm}\sim 3.3\times {10}^{-5}$ pc and a flare timescale of ${t}_{\mathrm{flare}}\sim 5$ minutes, which is inconsistent with the observations (the fastest flare observed from the source has a timescale of ∼10 hr). Faint polarized emission of ∼0.5% was found by Nagai et al. (2017), which would lead to n_cells ∼ 20,000 and a cell size of ~2.4 × 10⁻⁶ pc. Using Equation (7) we find ${t}_{\mathrm{flare}}\sim 30$ s. Thus, we find that if the emission is originating from within the C1 region, it is highly unlikely to be due to magnetic reconnections.

We can also use the observed jet and γ-ray luminosity to further constrain possible models. Using a peak γ-ray flux density of ∼ 8 × 10⁻⁷ ph cm⁻² s⁻¹, from the period before flare G4, we estimate the isotropic γ-ray luminosity to be ∼9 × 10³⁷ W (9 × 10⁴⁴ erg s⁻¹). This is less luminous than the flaring period that was also analyzed by Baghmanyan et al. (2017). Aharonian et al. (2017) set lower limits for the jet luminosity in the mini-jet scenario with MAGIC Collaboration et al. (2018), finding that this lower limit is ∼4 × 10³⁷ W (4 × 10⁴⁴ erg s⁻¹), using a more luminous flare. The less luminous flaring analyzed in this paper should further lower this limit. This would make the mini-jets scenario compatible with the jet luminosity estimated to be of the order ∼0.3–5 × 10³⁷ W (0.3–5 × 10⁴⁴ erg s⁻¹), found by Abdo et al. (2009) and Dunn & Fabian (2004).

It is presumed that the specific mechanism to produce the γ-rays is via the inverse-Compton mechanism in the leptonic scenario; however, the hadronic process is equally probable. It is possible that the mini-jets themselves would have their own Doppler factor (δ_j ; Marscher 2014), although it is not necessary to describe the observed behavior. The acceleration of high-energy electrons could occur in very small regions or these small regions experienced short Doppler boosts (i.e., mini-jets, see Section 4.2.1 and Giannios 2013). Both of these conditions can occur in magnetic reconnections arising in turbulent regions. In addition to such a Doppler factor, in order to produce the γ-rays, seed photons are required.

The two main sources for the seed photons are thought to be either the jet itself (synchrotron self-Compton, SSC) or the external environment (external Compton, EC) (e.g., Sokolov & Marscher 2005). The nature of the circumnuclear gas, which could provide the seed photons near the core of 3C 84, has also been actively studied, with much of this gas inflowing to the central kiloparsec (Salomé et al. 2006; Lim et al. 2008). In the region closest to the SMBH, it is thought that free–free absorption suppresses counter-jet emission in VLBI images (Dhawan et al. 1998; Walker et al. 2000). Nagai et al. (2017) has suggested from rotation measure measurements that this emission, if it is related to the accretion flow, must be highly inhomogeneous, consistent with an analysis of the free–free absorption opacity, suggested by Fujita et al. (2016). Many previous studies have found evidence for a dense ionized plasma in the central regions of 3C 84 (O'Dea et al. 1984; Walker et al. 2000), with the C3 region itself likely to be within the broad-line region (BLR). Punsly et al. (2018) recently found evidence for broad Hβ emission lines within the system. Krabbe et al. (2000) investigated the near-infrared emission and found ionized gas, molecular gas, and hot dust in the central regions of 3C 84. These sources could all potentially provide seed photons that are external to the jet. Seed photons from the jet do the job equally well (Kino et al. 2017).