A STRONG RADIO BRIGHTENING AT THE JET BASE OF M 87 DURING THE ELEVATED VERY HIGH ENERGY GAMMA-RAY STATE IN 2012

On 2012 February 24, March 16 and 21, April 5 and 27, and May 17, we made dedicated observations of M 87 with VERA at 22.3 and 43.1 GHz (hereafter we call these sessions Mode-A). All four of the VERA stations participated in good weather conditions. Left-handed circular polarization was received and sampled with a two-bit quantization using the VERA digital filter unit. We employed dual-beam observations to allow astrometric measurements; M 87 and a nearby radio source M 84 (separated by 15 on the sky from M 87) were observed simultaneously. The data were recorded at a rate of 1024 Mbps (a total bandwidth of (128+128) MHz), where each of the two 128 MHz-wide subbands was allocated for each source. In an effort to reduce systematic errors and to achieve similar uv coverage between the two frequencies, each frequency was alternated in turn every 80 minutes. At each epoch, the total on-source time results in about 3 hr at each frequency.

The initial data calibration was performed with the Astronomical Image Processing System (AIPS) developed at the National Radio Astronomy Observatory. First, a priori amplitude calibration was applied using the measured system noise temperature and the elevation-gain curve of each antenna. We then calibrated the amplitude part of bandpass characteristics at each station using the auto-correlation data. Next, we employed the calibration of the fringe phases in the following processes; first, we recalculated delay-tracking solutions for the correlated data using an improved delay-tracking model. Throughout the data analysis, we adopt the delay-tracking center as $\alpha _{\rm J2000}={\rm 12^{\rm h}30^{\rm m}49.^{\rm s}4233830}$ and $\delta _{\rm J2000}={\rm 12^{\circ }23^{\prime }28.^{\prime \prime }043840}$ for M 87, while $\alpha _{\rm J2000}={\rm 12^{h}25^{m}03.^{s}7433330}$ and $\delta _{\rm J2000}={\rm 12^{\circ }53^{\prime }13.^{\prime \prime }139330}$ for M 84. The delay-tracking solutions include delay contributions from the atmosphere, which are estimated using the global positioning system data (Honma et al. 2007). Next, we calibrated the differences due to instrumental delays between the two signal paths in the dual beam, which are measured using artificial noise signals injected at the same time into the two receivers (Honma et al. 2008). After that, we performed fringe fitting to remove residual delays, rates, and phases. Because M 87 is much brighter than M 84, we chose M 87 as a phase calibrator and transferred the derived fringe solutions to the data of M 84. A fringe fitting on M 87 was conducted assuming a point source model. Deviations of the phase/gain solutions from the point source model for M 87 were further corrected using the self-calibrated images, the production process of which is described below. Finally, the corrected phase and gain solutions were applied to M 84 and its phase-referenced images were created, in which the relative position of M 84 with respect to M 87 is conserved. We describe the astrometry results in Section 4.3.

In addition, VERA frequently observed M 87 at 22.2 GHz in the framework of the Gamma-Ray Emitting Notable AGN Monitoring by Japanese VLBI (GENJI) program (Nagai et al. 2013). This is a dense monitoring program of several bright γ-ray AGN jets including M 87 with VERA starting from 2010 October, which takes advantage of the usual calibrator time for VERA's Galactic maser astrometry observations. Between 2011 September and 2012 September, M 87 was routinely monitored with the GENJI mode typically every two to three weeks (hereafter we call these sessions Mode-B). Some of the data were not useful because of the lack of one or two stations, or due to only one or two scans available, preventing us from making reliable images and flux density measurements. Then, we selected the data in which all four of the VERA stations participated and at least three or four scans are available at different hour angles. Through these selection criteria, we eventually obtained the Mode-B data at 18 epochs in total during this period. Total on-source time for this mode is typically ∼30 minutes with an allocated bandwidth of 16 MHz. For more detailed descriptions about the data analysis of the GENJI data, see Nagai et al. (2013).

For all of the Mode-A and Mode-B data sets, images were created in DIFMAP software with iterative CLEAN and phase/amplitude self-calibration. The resultant amplitude corrections remained stable within ∼10% over time at each station, the level of which is consistent with a typical accuracy of the system temperature measurements for VERA. We thus adopt 10% error for the amplitude uncertainty for the VERA data. The resultant synthesized beams with the naturally weighted scheme were typically 1.3 × 0.8 mas in a position angle (P.A.) =−40° and 0.65 × 0.40 mas in P.A. =−40° at 22 and 43 GHz, respectively. Comparing image qualities at 22 GHz, image rms levels achieved by Mode-A are twice (or more) as good as those obtained by ModeB mainly because of the longer integration time and better uv-coverage. We summarize the information about the VERA data in Table 1.

We observed M 87 with EVN at nine epochs between 2011 March and 2012 October as a continuation of our M 87/HST-1 monitoring project starting from mid-2009 (Giovannini et al. 2011; Giroletti et al. 2012). The observation at each epoch typically lasted 4–8 hr, and the longest baselines were achieved from European stations to Shanghai, Arecibo, and/or Hartebeesthoek. Overall, the data quality is adequate to warrant good signal-to-noise detections of the source structure. For all observations, the sky frequency was centered at 5.013 GHz and divided into eight sub-bands separated by 16 MHz each for an aggregate bit rate of 1024 Mbps. The data were correlated in real time at the Joint Institute for VLBI in Europe (JIVE) and automated data flagging and initial amplitude/phase calibration were also carried out at JIVE using dedicated pipeline scripts. The data were finally averaged in frequency within each subband, but individual subbands were kept separate to minimize bandwidth smearing. Similarly, the data were time-averaged to only 8 s to minimize time smearing. We produced final images in DIFMAP after several cycles of phase and amplitude self-calibration. Various weighting schemes were applied to the data to improve resolution in the core region and enhance the fainter emission in the HST-1 region. For the core region, uniform weights or natural weights were used without uv-tapering, which achieve angular resolutions typically between 1–3 mas. For the HST-1 region, we used natural weights with a Gaussian uv-tapering (typically a factor of 0.3 at a radius of 50 Mλ, which results in a beam size between 5–10 mas. Image rms noise levels estimated in a region far from the core are typically 0.1 mJy beam⁻¹ or less with the natural weights. Regarding uncertainties on flux density measurements, we adopted a 10% error for core flux density based on a typical EVN amplitude calibration accuracy. For HST-1, we conservatively assumed 30% uncertainty because analyses of the HST-1 region could contain a larger amount of deconvolution error due to its weak and extended nature. Details of the EVN data are also summarized in Table 1.

The 230 GHz (1.3 mm) light curve was obtained at the SMA near the summit of Mauna Kea (Hawaii). M 87 is included in an ongoing monitoring program at the SMA to determine the flux densities of compact extragalactic radio sources that can be used as calibrators at millimeter wavelengths (Gurwell et al. 2007). Observations of available potential calibrators are observed for three to five minutes, and the measured source signal strength calibrated against known standards, typically solar system objects (Titan, Uranus, Neptune, or Callisto). Data from this program are updated regularly and are available at the SMA Web site.¹⁸ Most of the SMA measurements were obtained in its compact array configuration and the typical angular resolution is about ∼3''.

Figure 1 shows VLBI images for M 87 during the elevated VHE state in 2012 March. The large-scale jet structure down to HST-1 was clearly detected with EVN, while VERA resolved the innermost region.

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The obtained EVN jet images within several hundreds of mas from the nucleus are in good agreement with the well-known characteristics for this source; the jet is described by the bright radio core at the base with the edge-brightened collimated region (Junor et al. 1999; Ly et al. 2004, 2007; Dodson et al. 2006; Asada & Nakamura 2012; Hada et al. 2013). On the other hand, the VERA array is less sensitive to the extended emission (i.e., mostly resolved out) due to the lack of short baselines (>60 Mλ and >120 Mλ at 22 and 43 GHz, respectively), so the detectable emission is generally concentrated within the central region (i.e., a few mas). Nevertheless, some of brighter features downstream of the core were indeed consistently detected at many of the analyzed epochs. Our preliminary kinematic measurements of these features with VERA suggest an apparent motion around ∼0.4c relative to the radio core (Hada 2013), which is similar to the value obtained in a previous VLBA study (Ly et al. 2007). However, these features have already existed from mid-2011 and we did not find any notable correlations with the 2012 VHE activity. Thus, here we do not describe further details on these features and the more dedicated treatment will be reported in a forthcoming paper.

In terms of the HST-1 region, we detected the detailed substructure in all of the analyzed EVN data, the characteristics of which are overall consistent with our previous study (Giroletti et al. 2012). We confirmed that the main emission features of HST-1 are still moving constantly at a superluminal speed of ∼4c. While in Giroletti et al. (2012) we identified three main features (called comp1, comp2, and comp3 from the downstream side), in Figure 1 we can only see two main components. These features correspond to comp2 (the downstream, brighter one) and comp3 (the upstream, weaker one), respectively. Comp1, which was identified as the outermost feature in Giroletti et al. (2012), faded gradually and became below the noise limit at the beginning of 2012. While the emergence of new components from the upstream edge of HST-1 (around (R.A., decl.) = (− 780, 350) mas from the core) were seen during the VHE events in 2005 and 2010, we did not find such a structural variation during the 2012 event.

In Figure 2, we show a combined set of light curves of M 87 from radio to MeV/GeV γ-ray between MJD 55400 and MJD 56280. The vertical shaded area over the plots indicates a period between 2012 February and 2012 March, where an elevated VHE state is reported by VERITAS (Beilicke et al. 2012). For the LAT data, we show the light curves produced with one-month and two-month time bins (including 2σ upper limits for the two-month time bins). For the SMA data, we plot a light curve of the total flux densities. For the EVN 5 GHz data, we show the light curves for both the HST-1 region (integrated flux densities) and the core (peak flux densities when convolved by a 1.5 mas circular beam). In terms of the VERA data at 22/43 GHz, the light curves obtained by Modes A and B are combined into a single sequence. At each frequency, we provide both the integrated flux density and the peak flux density when convolved with a 0.6 mas circular Gaussian beam. Additionally, we plot an evolution of the spectral index for the peak flux density between 22 and 43 GHz.

Due to the dense, complementary coverage of VERA and EVN, we revealed the detailed evolutions of the radio light curves for both the core and HST-1. The most remarkable finding in these plots is a strong enhancement of the radio core flux density at VERA 22 and 43 GHz that starts from MJD 55981 (2012 February 24). While the timing of the radio peak is delayed, the onset of the radio flare occurs coincidentally with the enhanced VHE activity. At 22 GHz, we further detected a subsequent decay stage of the brightness at the last three epochs. Also at 43 GHz, we detected a possible saturation of the flux increase near the last epoch. Meanwhile, the EVN monitoring confirmed a constant decrease of the HST-1 luminosity. We also checked the light curve for the peak flux density of HST-1 (with a 10 mas diameter convolving beam), but the overall trend is the same as that of the integrated flux density. We summarize the values of the measured flux with VERA and EVN in Tables 2 and 3.

To better describe the structure of the core region, we created VERA 43 GHz images convolved with a circular Gaussian beam of 0.4 mas diameter (Figure 3), which have ∼30% super resolution along the major axis of the synthesized beam. These images clearly indicate that the flux enhancement occurs within the central spatial resolution of 0.4 mas, corresponding to a linear scale of 0.03 pc or 56 R_s. During the period of the elevated VHE state, the SMA data at 230 GHz also appear to show a local maximum in its light curve, although we note that its angular resolution is significantly large (generally ∼1''–3'', containing both the core and HST-1).

Another notable finding by our monitoring is a frequency-dependent evolution of the radio core flare. Figure 4 summarizes a set of the radio light curves that are normalized by the "baseline level" of the radio flare at each frequency (i.e., the flux values on MJD 55981 at 22/43 GHz and on MJD 55936 at 5 GHz, after which the radio core starts to flare). This figure clearly indicates that the radio core brightens more rapidly with a larger amplitude as frequency increases. At 43 GHz, the flux density increased up to ∼70% for the subsequent two months (between MJD 55981 and MJD 56044) at an average rate of ∼35% month⁻¹, and afterward the growth seems to be saturated. On the other hand, the core flux density at 22 GHz progressively increased up to ∼50% (at least) for the subsequent four months (from MJD 55981 to MJD 56099) at a slower rate of ∼12% month⁻¹. Eventually, the spectral index of the radio core between the two frequencies changed continuously during the flaring event (from α ∼ −0.6 to ∼−0.1 for the peak flux with a 0.6 mas beam; see Figure 2). At 5 GHz, by contrast, the core remained virtually stable within the adopted error of 10%. This is the first time that such a frequency-dependent nature of the radio flare is clearly detected in the M 87 jet.

With regard to the MeV/GeV regime, the LAT light curves were stable up to 2012 February (both one- and two-month time bins), and we did not find any significant flux enhancement during the period of the VHE activity. The observed HE flux level was consistent with that seen in the earlier epochs (Abdo et al. 2009; Abramowski et al. 2012) within the adopted uncertainty. After 2012 March, however, no significant emission was detected for the subsequent six months in the one- and two-month binned data, suggesting a change in the HE state after the VHE event. To quantify this, we analyzed the LAT data in two six-month intervals, 2011 October–2012 March and 2012 April–September, following the same procedure described in Section 3. The fits resulted in 0.1–100 GeV fluxes of (2.6 ± 0.5) × 10⁻⁸ photons cm⁻² s⁻¹ (TS = 56) and (1.1 ± 0.5) × 10⁻⁸ photons cm⁻² s⁻¹ (TS = 10), respectively. This indicates a decrease in the HE flux by a factor of ∼2 after the VHE event, in agreement with the level of decrease observed at VHE in 2012 April–May (Beilicke et al. 2012).

Since the VERA Mode-A performed astrometry observations at both 22 and 43 GHz, these data enable us to examine the core shift effect during the VHE activity in 2012. The core-shift effect is expected as a natural consequence of the nuclear opacity effect if the radio core at each frequency corresponds to a surface of synchrotron-self-absorption (SSA) τ_ssa(ν) ∼ 1 (Blandford & Königl 1979; Königl 1981; Lobanov 1998; Hada et al. 2011).

In Figure 5, we show the result of our VERA astrometry for the M 87 radio core at 22 and 43 GHz, which are measured relative to the radio core of M 84 at each frequency. For each data, we defined the core position as follows. For M 87, we convolved the self-calibrated images by a 0.6 mas/0.4 mas circular Gaussian beam at 22/43 GHz, the length of which is virtually equal to that of the minor axis of synthesized beam at each frequency. Then, we determined a brightness centroid of the image by fitting a Gaussian model with the AIPS task JMFIT. For M 84, we used its phase-referenced images instead of self-calibrated ones. Regarding position errors adopted for each data point in Figure 5, here we considered a root-sum-square of individual errors from the peak-to-noise ratio of the M 84 phase-referenced image, tropospheric residuals, ionospheric residuals, and geometrical errors.

Although the position uncertainty estimated for each data point is not sufficiently small (a level of 0.1–0.15 mas), our multi-epoch collective data set reveals a noticeable trend that the 22 GHz core of M 87 tends to be located northeast of the 43 GHz core. At each frequency, we derived a weighted-mean position of the M 87 core over the analyzed epochs to be (x₄₃, y₄₃) = (− 199 ± 41, 25 ± 41) μas (red square in Figure 5) and (x₂₂, y₂₂) = (− 263 ± 44, 120 ± 45) μas (blue square in Figure 5) relative to the nominal phase-tracking center of M 87. These values yield a time-averaged separation of the core between 22 and 43 GHz to be (Δx_22–43, Δy_22–43) = (64, 95) μas, corresponding to a projected distance of (0.005, 0.008) pc or (9, 13) R_s. This results in a P.A. of the core shift of 326°, which is well within a wide opening angle (between P.A. ∼255° and ∼340°) observed at the M 87 jet base with higher angular resolution studies (Junor et al. 1999; Hada et al. 2013).

To be accurate, however, we should be cautious about the following additional position uncertainties. As described in Hada et al. (2011), the structure of the reference source M 84 is elongated in the north–south direction. This may produce a core shift of M 84 itself in declination (although its amount should be less than 10 μas between 22 and 43 GHz; see Hada et al. 2011). Also, it is empirically suggested that astrometric measurements with VERA tend to leave slightly larger position errors in declination than in right ascension due to the residuals of zenith tropospheric delay estimations (e.g., Honma et al. 2007; Hirota et al. 2007). Thus, the actual position uncertainties of the M 87 core in declination could be somewhat larger than those adopted in Figure 5.

Another concern is that the amount of the core shift obtained with VERA (Δx_22–43, Δy_22–43) could be slightly larger than that of the true core shift, since the "radio core" defined by VERA, a beam size of which is typically ∼2–3 times larger than that of VLBA, would contain more amounts of the optically thin jet emission beyond the τ_ssa(ν) ∼ 1 surface. Such a blending of the optically thin jet should be more significant at 22 GHz as hinted by the result that the core spectra obtained by VERA tend to be steeper than those of VLBA. Then, in order to estimate a potential (artificial) increase of the core position shift due to the blending of the optically thin jet, we performed the following test; at 22 GHz, we convolved the M 87 structure by many different beam sizes with diameters ranging from 0.6 to 2.4 mas in incremental steps of 0.2 mas. Then, we plotted systematic changes of brightness-peak position (i.e., effective core position at each resolution) as a function of beam size. Using this plot, we found a progressive position shift of the brightness peak (toward the downstream side) to be (∼ 6, ∼ 3) μas per 0.2 mas (in (x, y) directions) for a range of beam size from 0.6 to 2.4 mas. This implies that a core shift of (∼ 6, ∼ 3) × (0.6 mas/0.2 mas) = (∼ 18, ∼ 9) μas can be artificially caused by the blending effect of the unresolved optically thin jet within a beam size of 0.6 mas.

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Therefore, we conclude that the true core shift of M 87 should be a level of 40–50 μas in the right ascension, while in declination 80–90 μas is estimated with a slightly larger uncertainty. In terms of the component in right ascension, a quite similar level of core shift is obtained in the previous measurements with VLBA (∼30 μas between 22 and 43 GHz; Hada et al. 2011).

In principle, our multi-epoch astrometry allows us to investigate a time evolution of the core position, which is particularly interesting to explore during a radio flaring stage. However, the observed small position changes relative to the errors make a reliable examination difficult among individual epochs. Conservatively, in this paper we believe that the core position is stable within a scale of 0.3 mas (corresponding to ∼40 R_s or ∼0.02 pc) during the radio flare by taking into account the maximum extent of the core position scatters in these data.

The location and the origin of the γ-ray emission up to VHE from M 87 have been under active debate in recent years. In the 2005 episode, the VHE flare was accompanied by radio-to-X-ray flares from HST-1 (Harris et al. 2006) with the ejections of superluminal radio features (Cheung et al. 2007), leading to a scenario that the VHE emission originates in HST-1 (Stawarz et al. 2006; Cheung et al. 2007; Harris et al. 2008, 2009). In contrast, contemporaneous flux increases at VHE, from the X-ray core and from the 43 GHz core during the 2008 episode, suggest that the VHE flare originates in the jet base (Acciari et al. 2009). A coincident enhancement of the X-ray core flux also occurred during the VHE flare in 2010 (Harris et al. 2011; Abramowski et al. 2012) together with a possible flux density increase from the radio core (Hada et al. 2012). These results also tend to favor the scenario in which the VHE emission originates in the jet base. However, the detection of the new component emergence from HST-1 near the VHE event again evoked the possibility that the HST-1 region is related to the active event in 2010 (Giroletti et al. 2012).

During the period of the elevated VHE activity in 2012 (Beilicke et al. 2012), we detected a significant flux density increase from the radio core at both 43 and 22 GHz. Following the 2008 episode, this is the second time where a VHE event accompanied a remarkable radio flare from the core. Meanwhile, the radio luminosity of the HST-1 region was continuously decreasing, and we did not find any hints of the emergence of new components from HST-1 as seen in 2005 and 2010. These results strongly suggest that the VHE activity in 2012 is associated with the core at the jet base, while HST-1 is an unlikely source. We should note that these remarkable flares are also very rare in radio bands (see the supporting material in Acciari et al. 2009), so it is unlikely that an observed joint radio/VHE correlation is a chance coincidence, while the low statistics of the LAT light curves still do not allow conclusive results on the HE–VHE connection. Moreover, we also emphasize the clear detection of a progressive change of the radio core spectral index after the VHE high state using three frequencies. This was not revealed in the previous radio flare during the 2008 VHE event, where there was only single radio coverage at 43 GHz.

Currently, a variety of mechanisms have been proposed for the VHE γ-ray production from the jet base of M 87 based on both leptonic and hadronic origins. In what follows, we will briefly discuss the compatibility of these models with the VHE activity in 2012, specifically from the point of view of high-resolution radio observations. On the basis of VLBI data, we can summarize some of the key observational constraints as follows; first, the VERA 43 GHz images indicate the size of the radio flaring region to be smaller than the central spatial resolution of ∼0.4 mas (56 R_s or 0.03 pc), which is consistent with a source size implied by the observed month scale VHE variability in 2012 (R_var ∼ cδt_var ∼ 7.5 × 10¹⁶δ cm or 42δR_s for t_var ∼ 30 days, where δ is the Doppler factor); second, M 87 has a very short BH-to-core distance (∼a few tens of R_s; Hada et al. 2011) and the jet launch/collimation region is beginning to be resolved at its base (Junor et al. 1999; Asada & Nakamura 2012; Hada et al. 2013); third, while the maximum of the radio flare is delayed, the onset of the radio brightening in 2012 occurs simultaneously with the VHE enhancement, indicating that the two emission regions are not spatially separated. Therefore, any compatible scenarios with the 2012 VHE activity should satisfy these conditions obtained by the radio observations.

Some of the existing models ascribe the VHE production to extremely compact regions (BH magnetosphere; Neronov & Aharonian 2007; Rieger & Aharonian 2008; Levinson & Rieger 2011: multi-blob in jet launch/formation region; Lenain et al. 2008: mini-jets in the main jet; Giannios et al. 2010: or red-giant-stars/jet-base interactions; Barkov et al. 2010). These models well explain the rapid (a few days) variability observed in the previous VHE flares in 2005, 2008, and 2010. Also, these models are able to avoid the internal γ (VHE) – γ (IR) absorption problem near the BH since M 87 has only a weak infrared (IR) nucleus (Neronov & Aharonian 2007; Brodatzki et al. 2011). However, as far as we consider the case in 2012, the size of the associated region expected from these models (typically of the order of R_s but as small as ∼0.01 R_s in Lenain et al. 2008) seems to be significantly smaller than that suggested by VLBI and the observed longer timescale of the VHE variability. Note that a contemporaneous millimeter-VLBI observation at 230 GHz during the 2012 event also suggests possible constraint on the associated size to be a similar spatial scale (≳0.3 mas; K. Akiyama et al., in preparation).

On a larger scale (but still unresolved with centimeter-VLBI), Georganopoulos et al. (2005) proposed a blazar-type, two-zone emission model where the VHE emission is produced in the upstream, faster jet while the lower-energy emission originates in the downstream, decelerating part of the jet. This model can reproduce the VHE data of M 87 if the jet decelerates its bulk Lorentz factor from Γ_j ∼ 20 to Γ_j ∼ 5 over a length of ∼0.1 pc at the jet base. However, the previous VLBA monitoring studies as well as our VERA monitor often show sub-relativistic motions and do not support such a very fast speed near the jet base (Reid et al. 1989; Dodson et al. 2006; Ly et al. 2007; Kovalev et al. 2007), although one cannot completely rule out faster motions in the jet base region that cannot be resolved with current centimeter-VLBI. The application of this model for the jet base of M 87 (i.e., jet launch region within ≲ 100 R_s from the BH) seems to also be incompatible with the current theoretical paradigm on the jet production, where the launched jet is expected to start acceleration on this scale (e.g., McKinney 2006; Komissarov et al. 2007).

Another blazar-type scenario in the sub-parsec jet is proposed by Tavecchio & Ghisellini (2008), where the radio-to-GeV emission of M 87 originates in the interior spine part of the jet while the VHE emission is produced in the surrounding layer. However, in their steady state model, whether or not the model can explain the observed simultaneous radio/VHE correlation has not yet been well investigated because the emission regions associated with radio and VHE are spatially separated from each other.

Similarly, the existing hadronic-based VHE emission models (e.g., Reimer et al. 2004; Barkov et al. 2010; Reynoso et al. 2011) do not necessarily expect obvious radio/VHE correlations because the radio emission is usually ascribed to be the synchrotron emission from the electrons that are not responsible for the VHE production. To test the viability of these (both multi-zone and multi-particle) models, more detailed considerations including their time-dependent behaviors through radio to VHE γ-ray would be necessary.

Interestingly, Abdo et al. (2009) showed that a broadband spectral energy distribution (SED) of M 87 through radio to VHE (at a relatively moderate state) can be reasonably reproduced by a simple, homogeneous one-zone synchrotron self-Compton (SSC) jet model using a roughly comparable source size (≲0.1 mas) to the one suggested in the 2012 case. In principle, one can also accept coincident radio/VHE correlations in this context. One-zone SSC models also explain the broadband SEDs in the other known γ-ray-detected Fanaroff–Riley I (FR I) radio galaxies 3C 84/NGC 1275 (up to TeV; MAGIC Collaboration et al. 2014) and Centaurus A (up to GeV; Chiaberge et al. 2001; Abdo et al. 2010), implying that these sources are misaligned counterparts of BL Lac objects. However, such single-zone approaches to misaligned objects derive systematically smaller bulk Lorentz factors (Γ_j < 5) than those generally required in BL Lacs (Γ_j > 10), which may pose a conflict with the radio-loud AGN unification paradigm (Urry & Padovani 1995). This caveat, along with limb-brightened jet structures observed in some radio galaxies (e.g., Junor et al. 1999; Nagai et al. 2014), indeed led to the preferable use of more sophisticated models with multiple jet parts at different velocities (e.g., Georganopoulos et al. 2005; Tavecchio & Ghisellini 2008) or with multiple substructures (e.g., Lenain et al. 2008; Giannios et al. 2010). For M 87, such multi-zone models also should be viable, but more extended theoretical consideration would be needed (e.g., ways to produce the joint radio/VHE correlation).

Our multi-frequency radio monitoring revealed a frequency-dependent property of the radio light curves for the M 87 core; as frequency decreases, the luminosity slowly increases with a smaller amplitude enhancement, resulting in a larger time delay/lag until reaching its peak. While this type of behavior is often seen in blazars (e.g., Orienti et al. 2013), the present study is the first clear confirmation for the M 87 jet. Such behavior is often explained by the creation of a plasma condensation (presumably induced by the VHE event at the jet base), which subsequently expands and propagates down the jet under the effect of SSA (Marscher & Gear 1985; Valtaoja et al. 1992). In this idea, the stronger SSA opacity at the jet base causes a delayed brightening of the radio flux density at lower frequencies. The light curve at each frequency reaches its maximum when the newborn component passes through the τ_ssa(ν) ∼ 1 surface (i.e., the radio core at the corresponding frequency). Afterward, the light curve enters a decay phase due to the adiabatic expansion loss (plus additional cooling effects, if any). A self-absorbed synchrotron response of radio core light curve in M 87 is also suggested for the 2008 episode (Acciari et al. 2009), where the delayed increase of the 43 GHz core flux relative to the VHE peak was reasonably reproduced by a phenomenological modeling of a self-absorbed plasma at the jet base.

On the other hand, we did not see any flux enhancement from the 5 GHz core of M 87. This implies that the newborn component was short-lived and incorporated into the uniform (underlying) jet before reaching the τ_ssa(5 GHz) ∼ 1 surface, resulting in the absence of any explicit emergences of knots or notable features from the core during this period. We note that the inner jet region of M 87 shows a relatively smooth brightness distribution, in agreement with low power (FR Is and BL Lacs) jet properties, while jets in high power sources (FR IIs and quasars) show clear evidence of complex substructures (Giovannini et al. 2001).

One of the important results of our observations is that we independently obtained both the core shift and the time-lag of the multi-frequency flare simultaneously. As examined by Kudryavtseva et al. (2011), the time-lag of the radio flare is directly related to the amount of core shift divided by the speed of the propagating shock or component. In turn, this means that we can now estimate the speed of the propagating component in the following way using the core shift and the time-lag:

$$\begin{eqnarray*} \beta _{\rm app, 43 \rightarrow 22} &=& \frac{\Delta r_{\rm proj, 43\hbox{--}22}}{c \Delta t_{\rm 43\hbox{--}22}} \\ &=& 0.97 \left(\frac{\Delta \theta _{\rm 43\hbox{--}22}}{\rm 0.1\, mas}\right) \left(\frac{\Delta t_{\rm 43\hbox{--}22}}{\rm 10\ days}\right)^{-1} \left(\frac{D_{\rm source}}{\rm 16.7\ Mpc}\right), \end{eqnarray*}$$

where β_{app, 43 → 22}, Δr_{proj, 43–22}, Δθ_43–22, Δt_43–22 and D_source represent a proper (projected) motion of the propagating component from the 43 GHz core to that of the 22 GHz, a projected separation of the 43 and 22 GHz cores (in physical unit/in angular unit), a time-lag of the light curve peaks between 43 and 22 GHz, and a source distance, respectively. For Δθ_43–22, our VERA astrometry obtained a level of Δθ_43–22 ∼ 0.04–0.09 mas during the radio flare. Regarding Δt_43–22, although the obtained light curves are not adequate to specify the exact date of the peak at both 22 and 43 GHz, we can still reasonably constrain a likely range of the peak date to be between MJD 56044 and MJD 56064 at 43 GHz, and between MJD 56099 and MJD 56168 at 22 GHz, respectively. This results in the maximum allowed range of Δt_43–22 to be 35 days ≲ Δt_43–22 ≲ 124 days. Therefore, we finally derive a likely range of β_{app, 43 → 22} to be ∼0.04c–0.22c. This indicates that the newborn component propagating through the cores between 43 and 22 GHz is not highly relativistic. Notably, many previous kinematic observations of M 87 obtained a similar speed (≲ 0.05c; Kovalev et al. 2007) or a slightly higher value (0.25–0.4c; Ly et al. 2007) in the jet a few mas (subparsec) downstream of the core. A value around ∼0.4c (relative to the core) at a few mas beyond the core was also measured in our VERA data (Hada 2013), suggesting a possible acceleration process in the jet flow on this scale. On the other hand, the derived sub-luminal speed of the newborn component is significantly smaller than the super-luminal features that appeared from the core during the previous VHE event in 2008 (∼1.1c; Acciari et al. 2009), where the peak VHE flux is >5 times higher than that in 2012. If we assume that propagating shocks or component motions traced by radio observations reflect the bulk velocity flow, this may suggest that the stronger VHE activity is associated with the (episodic) production of the higher Lorentz factor jet. We note that the M 87 jet is misaligned (i ∼ 15°–25°; Acciari et al. 2009), but such a positive correlation between the jet speed and the observed VHE flux is plausible because the jet emission is still "beamed" toward us (δ ∼ a few) for such mildly relativistic speeds (Γ ≲ 2) in the suggested i range.

We note that the above discussion applies to a thin-shock case where the thickness (i.e., the size along the jet) of the propagating feature is smaller than the (de-projected) separation between the 43 and 22 GHz cores in order to allow a non-zero time delay (Δt_43–22) in their light curve peaks. Also, here we considered only a time-averaged value for the core shift for simplicity. However, the amount of core shift can be variable especially during the radio flaring event (Kovalev et al. 2008), because the creation of such features may locally change the particle number density, the magnetic field strength and thus the SSA optical depth at the jet base. The position accuracies in the present study are still not enough to explore the core-shift variations among the individual epochs, but this effect should be of interest to test with a more suitable astrometry technique (e.g., Korean VLBI Network (KVN); Lee et al. 2014 : or KVN+VERA joint array; Sawada-Satoh 2013). This will enable us to bring further insights into the nature of the flaring core as well as the γ-ray production in the formation and collimation region of the M 87 jet.