Observing the Time Evolution of the Multi-Component Nucleus of 3C\,84
Brian Punsly, Hiroshi Nagai, Tuomas Savolainen, Monica Orienti
aa r X i v : . [ a s t r o - ph . GA ] F e b Draft version February 16, 2021
Typeset using L A TEX preprint style in AASTeX63
Observing the Time Evolution of the Multi-Component Nucleus of 3C 84
Brian Punsly,
1, 2, 3
Hiroshi Nagai,
4, 5
Tuomas Savolainen,
6, 7, 8 and Monica Orienti ICRANet, Piazza della Repubblica 10 Pescara 65100, Italy ICRA, Physics Department, University La Sapienza, Roma, Italy National Astronomical Observatory of Japan, Osawa 2-21-1, Mitaka, Tokyo 181-8588, Japan The Graduate University for Advanced Studies, SOKENDAI, Osawa 2-21-1, Mitaka, Tokyo 181-8588, Japan Aalto University Mets¨ahovi Radio Observatory, Mets¨ahovintie 114, 02540 Kylm¨al¨a, Finland Aalto University Department of Electronics and Nanoengineering, PL 15500, 00076 Aalto, Finland Max-Planck-Institut f¨ur Radioastronomie, Auf dem H¨ugel 69, 53121 Bonn, Germany INAF - Istituto di Radioastronomia, Via Gobetti 101, 40129 Bologna, Italy (Received ...; Revised ...; Accepted ...)
Submitted to ApJABSTRACTThe advent of global mm-band Very Long Baseline Interferometry (VLBI) in recentyears has finally revealed the morphology of the base of the two most prominent nearby,bright, extragalactic radio jets in M 87 and 3C 84. The images are quite surprisingconsidering the predictions of jet theory and current numerical modeling. The jetbases are extremely wide compared to expectations and the nucleus of 3C 84 is verycomplicated. It appears as a double in 86 GHz observations with 50 µ as resolution and atriple nucleus with 30 µ as resolution with space-based VLBI by RadioAstron at 22 GHz.What is even odder is that the double and triple are arranged along an east-west linethat is approximately orthogonal to the north-south large scale jet on 150 µ as − ∼ .
08 mas, to track a predominantly east-west separation speedof ≈ . ± .
008 c. We estimate that the observed mildly relativistic speed persistsover a de-projected distance of ∼ − ∼ . − . Keywords: black hole physics — galaxies: jets—galaxies: active — accretion, accretiondisks
Corresponding author: Brian [email protected] INTRODUCTIONThe galaxy, NGC 1275, harbors the radio source 3C 84 with both a parsec scale jet and a kpcscale jet as well as a large low frequency radio halo (Pedlar et al. 1990; Walker et al. 2000). Ithas been the brightest extragalactic radio source at high frequency with flux densities of 45 Jy −
65 Jy in 1980 at 270 GHz and ∼ −
50 Jy at 90 GHz from 1965 − z = 0 . ∼ ◦ and 138 ◦ , respectively and both jets areextremely edge brightened near the base (Kim et al. 2018; Giovannini et al. 2018; Punsly 2019). Thelarge degree of edge brightening and the enormous (the maximum possible geometrically is 180 ◦ )opening angles were not anticipated in seminal works on simple jet theory (Blandford and K¨onigl1979). Numerical models of jet formation have been designed to explain these extreme properties inM 87. It was hoped that choosing lines of sight (LOS) that are nearly aligned with the jet axis andplasma emissivity/plasma enthalpy profiles (injected by numerical researchers) that were specificallydesigned to produce the high resolution radio images would resolve the conflict (Mo´scibrodzka et al.2016; Chael et al. 2019). However, current numerical simulations still produce synthetic jet imagesthat are far too narrow and not nearly edge brightened enough near their bases when compareddirectly to the highest resolution interferometric images of the jet base (Punsly 2019). This widebase seems to abruptly transition to a highly collimated inner jet. The powerlaw fit to the jet width, W ( z ), as a function of axial displacement along the jet, z , is W ( z ) ∝ z k , k = 0 . ± .
049 for0 . < z < . µ as, performed with RadioAstron at22 GHz (Giovannini et al. 2018). The triple is distributed primarily along the east-west directionroughly orthogonal to the jet that is directed towards the south and is defined by two bright ridges,beginning 150 µ as to the south (see the schematic diagram in Figure 1). These circumstances suggestthat there is jet launching physics to be discovered with high resolution of VLBI, and not just theverification of existing theory.Thus motivated, this study explores the nature of the multi-component nucleus that has beenseen with the highest resolution VLBI, ∼ µ as in the east-west direction with RadioAstron onSeptember 21-22, 2013 (Giovannini et al. 2018). Our method is to use the lower resolution 7 mmVery Long Baseline Array (VLBA) data that is created for the purpose of approximately monthlymonitoring by a Boston University based research effort, the VLBA-BU Blazar Monitoring Program (Jorstad et al. 2017). Thus, we can, in principle, detect time evolution of the nuclear region. Apartially resolved double nucleus has appeared in the CLEAN images from August 26, 2018 to April7, 2020. We rely on the publicly available files from the BU website to extract the highest resolutiondata, corresponding to the longest baselines associated with the 43 GHz VLBA. We define the multiplicity of the nucleus, i.e. double or triple, as the apparent number of components that can bediscerned from visual inspection of the image. This designation is a function of the resolution of the telescope. If theresolution were much higher then there could be many small components that could not be seen at lower resolution. EAST - WESTMULTIPLE NUCLEUSEASTERN RIDGE OF PARSEC SCALE JET WESTERN RIDGE OF PARSEC SCALE JET
ELL I PS E H I GH L I GH T S R E G I ON S T UD I E D I N T H I S P A P E R COUNTER JET STATIONARY COMPONENT EMERGED in 2018
Figure 1.
The taxonomy of prominent features in the nuclear region of 3C 84. The position angle of thesoutherly directed jet swings back and forth from east to west by ∼ ◦ over periods of about 5-10 years. We begin with a description of the very complex nuclear inner light year of the jet that has beenrevealed in recent high resolution VLBI campaigns. Figure 1 is a schematic diagram of the numerousnuclear features that have been detected in this nearby very bright radio source. A schematic ismuch clearer than overlaying numerous images made at various frequencies. An approximate scale isindicated at the bottom, both in angular size and physical dimension (projected on the sky plane).The primary feature is the triple nucleus (enclosed by the ellipse) from the 22 GHz RadioAstronobservations (Giovannini et al. 2018). This region is the focus of this study. This nuclear feature isapparently not time stationary. A more recent 86 GHz global VLBI observation on May 16, 2015revealed this region to be a double nucleus along the east-west direction (Kim et al. 2019). With43 GHz VLBA, a double nucleus has never been identified previously. Based on the aforementionedhigher resolution VLBI, the east-west separation is ∼ . − .
15 mas, similar to the nominal east-westrestoring beam of the uniformly weighted 10 station VLBA of 0 .
15 mas. Thus, we expect to seepartially resolved structure in epochs of wide separation.Figure 1 shows other complicating features as well and helps to illustrate the ultimate goal of findinga unifying picture that incorporates all of these important elements. First, there is the faint counter-jet that has been seen at numerous frequencies (Walker et al. 2000; Lister 2001; Fujita and Nagai2017). Then there are the very prominent east and west ridges that frame the jet headed to thesouth. They are of varied prominence from epoch to epoch and observation to observation. Inthe high resolution 22 GHz RadioAstron observation they are significantly brighter than the almosthollow interior of the jet. This “double rail” configuration has also been seen with 43 GHz VLBA(Nagai et al. 2014). A similar double rail configuration has been detected in high resolution VLBIimages of M 87 adjacent to the nucleus as well (Hada et al. 2014; Kim et al. 2018). The most curiousaspect of these ridges in the 43 GHz BU VLBA monitoring data is that most of the time one ridgeis much brighter than the other for periods of time that last years. The fundamental question thatwe wish to gain some insight into is: what is the relationship between the multiple east-west nucleusand these vacillating bright ridges of emission that emerge almost orthogonal to the axis of nuclearemission, in the southern direction?Some of these features are evident in the magnified views of the nuclear region from the totalintensity images taken from the BU website in Figure 2. We note one other aspect of the nuclearregion. A modest feature has emerged to the west of the nucleus in 2018, about 0.25 mas away. Itappears to be real because it is persistent and is seen a few contours above the noise level. It alsoseems to be stationary. With all the components emerging in almost every direction, the situationis not well explained by a simple pencil-beam jet. We are actually getting close to the jet launchingregion, so we are starting to uncover some of the messy details of the physical mechanism. We donot attempt to resolve these complexities in the present paper. We take a more modest approachand merely try to establish and quantify the rate of nuclear expansion within the central ellipse ofFigure 1.Section 2 describes our methods of extracting the nuclear separation from the data. In Section 3,we describe how we use the CLEAN component (CC) models from the BU program to extract theeast-west resolution associated with the longest baselines. Section 4 presents our estimate of theapparent speed of separation of the double nucleus. In Section 5, we explore the non-trivial methodsof fitting the nuclear components in the ( u, v ) plane using Gaussian models. In Section 6, we comparethe nuclear configuration observed by the 43 GHz VLBA in 2018-2020 with the nuclear triple observedby RadioAstron in 2013. Throughout this paper, we adopt the following cosmological parameters: H =69.6 km s − Mpc − , Ω Λ = 0 .
714 and Ω m = 0 .
286 and use Ned Wright’s Javascript CosmologyCalculator website (Wright 2006). In our adopted cosmology we use a conversion of 0.360 pc to 1mas. METHOD OF ESTIMATING NUCLEAR EXPANSION
Figure 2.
The nucleus in the 43 GHz image starts elongating in the east-west direction in August 2018. Thenucleus appears almost fully resolved by November 2019. The eastern component seems to veer towards the large scalesoutherly directed jet in the 2020 images. The details of the degree of degradation of many compromised observationsin 2019 can be found in Table 1. The June and July 2019 images reflect the significant degradation indicated in Table1. The contours start from 10 mJy/beam and increase in steps of 2x in all the plots. The restoring beam is indicatedby the cross in the lower left. I n t e n s i t y ( Jy / b ea m ) Milli-arcseconds2018 Aug 26 I n t e n s i t y ( Jy / b ea m ) Milli-arcseconds2018 Oct 15 I n t e n s i t y ( Jy / b ea m ) Milli-arcseconds2018 Dec 8 I n t e n s i t y ( Jy / b ea m ) Milli-arcseconds2019 Jan 10 I n t e n s i t y ( Jy / b ea m ) Milli-arcseconds2019 Mar 31 I n t e n s i t y ( Jy / b ea m ) Milli-arcseconds2019 May 12 I n t e n s i t y ( Jy / b ea m ) Milli-arcseconds2019 Jun 18 I n t e n s i t y ( Jy / b ea m ) Milli-arcseconds2019 JUL 1 I n t e n s i t y ( Jy / b ea m ) Milli-arcseconds2019 Oct 19 I n t e n s i t y ( Jy / b ea m ) Milli-arcseconds2019 Nov 3 I n t e n s i t y ( Jy / b ea m ) Milli-arcseconds2020 Jan 4 I n t e n s i t y ( Jy / b ea m ) Milli-arcseconds2020 Apr 7
Figure 3.
East-west intensity cross sections created from the CLEAN images. They are fixed in the north-southdirection by locating them to pass through the peak intensity. Notice the emergence of a local maximum to the east ofthe peak on August 26, 2018. A double peak is clearly seen on October 15, 2018. A third local maximum emerges inOctober 2019. Notice that January 10, 2019 has a different cross-section with just a single peak. This epoch requiresspecial attention (see Appendix B).
It is fortuitous that the nucleus expands primarily in the east-west direction, this is also the di-rection of maximum resolution of the VLBA at 43 GHz (the major axis of the restoring beam hasa position angle of − ◦ ). The full width at half maximum (FWHM) of the beam is approximately0.28 mas × u, v ) data. However, when the data have sufficiently highsignal-to-noise ratio, the interferometer can resolve structures significantly smaller than the nominalbeam size. In our case the longest baselines provide a typical resolution of approximately 0.08 mas inthe east-west direction. The resolution of the interferometer is defined here as the FWHM of a circularGaussian brightness distribution that gives a visibility amplitude of 50% times the zero-baseline value.Mathematically, this is expressed as resolution = (91M λ/ baseline-length) mas (Marscher 1985). Itis known that higher resolution can be achieved by analyzing the visibility domain and these reso-lution limits depend on the noise in the ( u, v ) plane (Marti-Vidal et al. 2012). However, working inthe image plane has the advantage of less ambiguity as to whether the model chosen for the sourceis appropriate (Fomalont 1999). Since we are measuring small changes to a small separation on a -0.150-0.100-0.0500.0000.0500.100 -0.150-0.100-0.0500.0000.0500.1000.1500.200 R e l a v e D e c li n a o n ( m a s ) Real ve Right Ascension (mas)
CLEAN Components August 26, 2018
WN Centroid EN Centroid 567 mJy 322 mJy 133 mJy75 - 100 mJy 50 - 75 mJy 35 - 50 mJy 20 - 35 mJy -0.150-0.100-0.0500.0000.0500.1000.150 -0.150-0.100-0.0500.0000.0500.1000.1500.2000.250 R e l a v e D e c li n a o n ( m a s ) Real ve Right Ascension (mas)
CLEAN Components May 12, 2019
WN Centroid EN Centroid 718 mJy 249 mJy 100 - 150 mJy75 - 100 mJy 50 - 75 mJy 35 - 50 mJy 20 - 35 mJy
894 mJy 1613 mJy -0.200-0.150-0.100-0.0500.0000.0500.100 -0.150-0.100-0.0500.0000.0500.1000.1500.2000.2500.300 R e l a v e D e c li n a o n ( m a s ) Real ve Right Ascension (mas)
CLEAN Components November 3, 2019
WN Centroid EN Centroid 322 mJy 200 - 250 mJy 100 - 200 mJy75 - 100 mJy 50 - 75 mJy 35 - 50 mJy 20 - 35 mJy Ejection B mas
988 mJy 973 mJy532 mJy -0.250-0.200-0.150-0.100-0.0500.0000.0500.100 -0.150-0.100-0.0500.0000.0500.1000.1500.2000.2500.3000.350 R e l a v e D e c li n a o n ( m a s ) Real ve Right Ascension (mas)
CLEAN Components January 4, 2020
WN Centroid EN Centroid 366 mJy 200 - 300 mJy 100 - 150 mJy75 - 100 mJy 50 - 75 mJy 35 - 50 mJy 20 - 35 mJy Ejection B mas
Figure 4.
The location of the nuclear CCs in four epochs. The two examples in the top row are used toillustrate our methods of defining which CCs determine the WN and EN. The WN and EN are defined bythe CCs enclosed within red and blue ellipses, respectively. The red and blue triangles are the correspondingcentroids of the flux density for each physical component. The details of these constructions are provided inthe text. Note that the CCs outside the solid ellipses are weak (20 −
35 mJy) and do not affect the centroidestimates, but we cut the CC distribution off once it approaches 0.1 mas in east-west width as motivatedin the text. The two examples in the bottom row show the emergence of a weaker (green) component inthe fall of 2019. We consider EN as the first ejection, ejection A, and the green cluster of CCs as a secondejection, ejection B. complex background, the ambiguities in the models can cause a significant degradation of accuracy.In Appendix A, we provide simulations in the visibility domain to motivate the Marscher (1985)resolution limit as appropriate to this study. These simulations incorporate all the details of theobservations that degrade the very high resolution limits achievable with model-fitting the visibilitydata with near perfect circumstances. We incorporate the ( u, v ) coverage, SNR, and the complexityof the source structure. Even though this analysis is in the ( u, v ) plane,“analysis of a properly madeCLEAN image via good analysis techniques should produce values and errors which are equal to thoseof model fitting visibility data”(Fomalont 1999). The CLEAN component based method utilized inthis paper will be shown to be an example of a “good analysis technique” in the image plane. We areable to find Gaussian fitting methods in Section 5 that yield similar resolution limits to our CLEAN
Table 1.
Compromised Observations in 2019Date Missing Stations Severely Compromised Stations Comments Quality02/03/2019 MK and BR ... east-west resolution severely degraded un-useable02/08/2019 NL BR and HN much data deleted only ∼ Note —Details of the observations generously provide by A. Marscher, 2019. Station acronyms: MK (Mauna Kea), BR(Brewster, Washington), NL (North Liberty, Iowa), HN (Hancock, New Hampshire), LA (Los Alamos, New Mexico),SC (St. Croix) component based methods. This forms a bridge between the simulations in Appendix A and theCLEAN component based method presented here.So, in theory, there is information within the observations that can resolve east-west features largerthan 0.1 mas, provided their signal-to-noise ratio (SNR) is high. The 0.28 mas × ◦ from the east-west direction.The net result is a suggestive image, but Gaussian fits to the multiple components fail to converge toa unique decomposition. The same circumstance exists with efforts to fit the visibilities with simpleGaussian models (see Section 5). The other alternative is to use the CC models. Even though themodels cannot be considered robust in a single epoch, they should be suitable for identifying a trendthat persists over time, especially with regards to very bright features as is the case here. This is theprimary guiding principle of the following analysis.Before describing our models we first note that most observations in 2019 are degraded to varyingdegrees by bad weather, down observing stations and inaccurate antennae pointing. The issues aresummarized in Table 1. Modest degradation of observations in 2019 adversely affect the CC modelsand one of the main tasks of this analysis is to quantify this degradation in terms of an uncertaintyin our results.In order to transition from the images in Figure 2 to the CC models, we investigate intensityprofiles of the CLEAN image along a particular direction (east-west). We define a pixel size as0.005 mas × THE CLEAN COMPONENT MODELSCC models are provided for each observation epoch on the BU website. During the first year ofmonitoring in Figure 2, the western component of the double nucleus (WN, hereafter) is brighter andfortunately is predominantly a tight east-west distribution of the bright CCs that always includes thebrightest CC. We face two primary technical issues that we illustrate in Figure 4 with four examples.The issues are:1. How should the cluster of components be defined for both the eastern component of the nucleus(EN, hereafter) and the WN?2. How do we define the coordinates of the cluster of components and the uncertainty in thislocation?We explore these issue below.3.1.
Defining the Clustering of the CLEAN Components
This is a slightly subjective exercise at times in which we use the visual evidence from Figures 2and 3 and the structure of the components in the previous epoch and the subsequent epoch. Thepeak surface brightness is about 1 . − . ∼ −
35 mJy as significant. This varies depending on the quality ofthe observation. This choice typically scales with the magnitude of the strongest negative contourin the FITS image file (see Table 2). In practice, components less than 40 mJy never contributesignificantly to our flux density related results (component centroids and uncertainties). Figure 4plots all the components larger than 20 mJy in the vicinity of the nucleus in four epochs. The redellipse defines all the components that we associate with the WN and the blue ellipse encapsulates all0
Table 2.
Details of the CLEAN Component Models of the Double Nucleus (1) (2) (3) (4) (5) (6) (7) (8) (9) (10) (11)Date Day F ν, WN F ν, EN Uniformly Weighted Beam I peak Min. Neg. Smallest ∆RA ∆dec Separation(Naturally Weighted Beam)Size/PA Cont. CC(Jy) (Jy) (mas/degrees) (Jy/beam) (mJy/beam) (mJy) (mas) (mas) (mas)08/26/2018 0 1.448 0.479 0.303 x 0.179/+11.0 1.572 -15 20 0 . ± .
013 0 . ± .
021 0 . ± . . ± .
011 0 . ± .
022 0 . ± . . ± . − . ± .
024 0 . ± . . ± . − . ± .
024 0 . ± . . ± . − . ± .
021 0 . ± . . ± . − . ± .
028 0 . ± . . ± .
015 0 . ± .
027 0 . ± . . ± .
014 0 . ± .
029 0 . ± . . ± . − . ± .
023 0 . ± . . ± . − . ± .
022 0 . ± . . ± . − . ± .
023 0 . ± . . ± . − . ± .
022 0 . ± . the components associated with the EN. We crudely estimate that the east-west spread of the CCs inthe WN and EN will be distributed within a length < . < ∼ . ≤ . < .
15 mas, similar to the resolution ofthe longest north-south baselines ( ∼ . − .
14 mas).1The details of our CC models of the WN and EN can be found in Table 2. The first two columns arethe date of the observation and the number of days since the nuclear separation was first detected.This is not the same as the time from the epoch of physical separation due to the finite resolution ofthe array. The next two columns are the flux densities of the WN, EN and the total of these numbers,respectively. The absolute flux calibration accuracy of the BU data is about 5% (Jorstad et al. 2017) .Column 5 provides the properties of the uniformly weighted beam on top and the naturally weightedbeam below in parenthesis. Column (6) is the peak intensity from the CLEAN images (Figure 2)for comparison with the numbers in the previous columns. Columns (7) and (8) are the largestmagnitude negative contour values from the CLEAN image and the CC cutoff used in or models,respectively. Columns (9) - (11) are the uncertainties in the nuclear separation that are computedper the methods of Section 3.2.First, let us consider the epoch of August 26 2018. Since the absolute astrometry is lost in the phaseself-calibration step of the VLBI data reduction, we are only interested in the relative positions ofthe EN and WN and we place the brighter WN at the origin. We include all the CCs within a region ≤ . The Position of the Features
We calculate the position of the features by taking the flux-density weighted mean (centroid) of theCC positions in the feature. In Figure 4, the red triangle inside the red ellipse and the blue triangleinside the blue ellipse are the locations of the centroids of the flux density of the CCs encapsulatedwithin each ellipse. We assign an uncertainty to the centroid location. The origin of the coordinates Normally, the VLBA-BU-BLAZAR fluxes are accurate to within ∼ D i s p l ace m e n t ( m a s ) Elapsed Time (days)
Displacement of Eastern Component from Western Component vs. Time
Ejection A = EN Ejection B
Displacement (mas) = 0.000205 [Time (Days)] + 0.122783 masDisplacement (mas) = 0.000134 [Time (Days)] +0.038142 mas D i s p l ace m e n t ( m a s ) Elapsed Time (days)
East-West Displacement vs. Time
Ejection A = EN Intensity Cross Section
East - West Displacement (mas) = 0.000196 [Time (Days)] + 0.120308 masEast - West Displacement (mas) = 0.000120 [Time (Days)] - 0.041913 mas -0.10-0.050.000.050.10 -25 75 175 275 375 475 575 D i s p l ace m e n t ( m a s ) Elapsed Time (days)
Southern Displacement of Eastern Nucleus vs. Time
Displacement (mas) = 0.000898 [Time (Days)] + 0.010585 mas
Figure 5.
The separation between WN and EN versus time is demonstrated in two ways. The top left panel is aplot of total displacement versus time. The east-west displacement is plotted in the top right panel. The two methodsyield a similar separation velocity. The solid black line is a least squares fit with uncertainty in the vertical variable(Reed 1989). The dashed lines define the standard error of the fit. The equation for the best fit is printed on the plot.We also provide a crude fit for ejection B in green. The top right panel also plots the east-west separation from theintensity profiles (in red) with no information from January 10, 2019 available from Figure 3. We consider these dataless rigorous and are shown as a consistency check. The peak separation of the intensity cross-sections lies below theuncertainty of the CC model fit for April 2020 (day 590). This is a consequence of a curved trajectory of the EN.As can be seen in Figure 2, the EN starts veering south relative to the declination of the WN in 2020 and is mostpronounced in April. Thus, there is no east-west cross section that captures intensity peaks of both the EN and WN.The April data indicates the breakdown of the simple east-west cross section method for a curved trajectory for theejection. For completeness, we include the southern displacement of the EN with its fit in the bottom panel. Themagnitude of the trend is small compared to the uncertainties and this is reflected in the standard error of the bestfit. Thus, the result should be viewed with caution. The three outliers are January 10, 2019 (that is discussed inAppendix B) and the two low SNR observations in June and July 2019. will be the centroid of the WN and all displacements are measured relative to this. The uncertaintyin the positional locations is ∼
10% of the synthesized beam FWHM for these bright components3(Lister et al. 2009) . In Table 2, the uncertainties in coordinate separation, σ ∆ X and σ ∆ Y ( X is rightascension and Y is declination), are the uncertainties on the individual centroid coordinates addedin quadrature. Similarly, the uncertainty of the total displacement between the EN and WN, σ D ,is calculated as the error propagation of the centroid uncertainties. The random noise contributionto the separation uncertainty can be estimated by σ D (noise) ≈ p σ rms /S peak , where σ rms is thepost-fit rms noise of the image and S peak is the flux density of a putative unresolved component ofsize d (Fomalont 1999; Lee et al. 2008). σ rms < S peak >
479 mJy so all the SNR are > & THE SEPARATION RATE OF THE DOUBLE NUCLEUSThe motivation for defining the locations of the EN and WN and the corresponding uncertainty isto track the time evolution of the separation of the components. This is performed in Figure 5. Thetop left panel is the plot of the displacement versus time. However, we note that the displacementis primarily east-west and the highest resolution is in this direction. We plot east-west (x direction)displacement in the top right panel for direct comparison to the intensity cross-sections in Figure 3.The data were fit by a least squares fit with uncertainty in the vertical variable (Reed 1989). Thesolid line is the fit and the dashed lines represent the standard error to the fit. Based on the fitand standard error, the time averaged nuclear separation speed is 0 . ± .
008 c. The fit to thetotal displacement yields a separation rate of 73 ± µ as per year compared to 70 ± µ as per year forpure east-west displacement. Note that we also plot (in green) the separation of the second ejection,ejection B, in the lower right hand corner of the two panels. We also provide very crude four pointfits to the ejection velocity.It is apparent that the EN-WN separations in the spring and summer of 2019 (days 217 − see also https://science.nrao.edu/facilities/vla/docs/manuals/oss/performance/positional-accuracy ∼ November 6,2017. The two ejections originated at least 7 months apart and represent two distinct nuclear events.Our estimate of the January 1, 2017 ejection is not tightly constrained, but we would be remiss notto mention that there was a major gamma ray flare reaching TeV energies that was detected bythe Large Area Telescope on board the Fermi satellite and MAGIC telescopes that peaked aroundDecember 31, 2016 to January 1, 2017 (Baghmanyan et al. 2017; Ansoldi et al. 2018). THE DOUBLE NUCLEUS IN THE UV-PLANEIt is customary for astronomers to fit the visibility data with a small number of Gaussians in theorder to track component separations. Thus, we explore the possibility of evidence of the doublenucleus in the ( u, v ) plane by making Gaussian fits to the nuclear region. However, there are twoconcerns for this method in the context of the separating nuclear features in Figure 2. Firstly, theradio source 3C 84 is extremely complex compared to a typical blazar nucleus and it is extended.So, one needs to use a CC model to represent it, but that creates a problem regarding how largeof an area around the core should be cleared from CCs before model-fitting. This is always a bitsubjective and can influence the results significantly. The second issue is that the initial stages of theexpansion in Figure 2 are at the limits of the resolution of the VLBA. There is no unique solutionto the fitting method. Each ambiguity and assumption adds a possible error to the fitting process.After some initial attempts to make Gaussian fits to the nuclear region we found two methods thatgive reasonable results. 5.1.
Gaussian Fitting Method 1
The first method addresses the issue of the complex background emission by a simple excisionmethod that can be uniformly applied to each epoch. We took the CLEAN model and automaticallyremoved CCs from the area three times the uniformly weighted beam size (from Table 2) around thecore. The excised region is then modelled with circular Gaussians. We added new components inthe model if a clear peak was seen in the residual image after fitting. The background subtractionis not perfect so it introduces additional Gaussian components in addition to those associated with5
Table 3.
Gaussian Fits to the Double Nucleus (1) (2) (3) (4) (5) (6) (7) (8) (9)Date Model F ν, WN F ν, EN ∆RA ∆dec Separation Gaussian FWHM WN Gaussian FWHM EN(Jy) (Jy) (mas) (mas) (mas) (mas) (mas)08/26/2018 1 1.137 1.437 0.093 0.046 0.104 0.073 0.15608/26/2018 2 1.146 0.840 0.135 0.001 0.135 0.068 0.10210/15/2018 1 2.525 1.138 0.157 -0.053 0.166 0.104 0.12710/15/2018 2 2.219 1.459 0.146 -0.008 0.146 0.088 0.13412/09/2018 1 3.211 1.435 0.166 -0.027 0.168 0.113 0.05212/09/2018 2 2.819 1.856 0.151 -0.034 0.155 0.085 0.08201/10/2019 1 1.179 4.634 0.139 0.019 0.140 0.085 0.19001/10/2019 2 2.030 2.321 0.127 0.018 0.128 0.076 0.07203/31/2019 1 1.193 1.576 0.169 -0.009 0.169 0.068 0.13203/31/2019 2 1.819 0.932 0.166 0.022 0.167 0.066 0.07105/12/2019 1 2.735 0.593 0.200 -0.007 0.200 0.143 0.01805/12/2019 2 2.601 0.786 0.199 -0.043 0.204 0.119 point source06/18/2019 1 2.794 0.970 0.170 -0.010 0.170 0.091 0.01106/18/2019 2 2.470 0.795 0.151 0.018 0.152 0.074 0.10707/01/2019 1 2.716 1.961 0.162 0.007 0.162 0.019 0.05507/01/2019 2 3.876 2.032 0.151 0.028 0.153 0.071 0.02910/19/2019 1 2.505 1.629 0.183 -0.066 0.195 0.155 0.10010/19/2019 2 1.284 1.454 0.221 -0.026 0.223 0.091 0.09211/03/2019 1 0.688 1.041 0.234 -0.040 0.237 0.063 0.05311/03/2019 2 1.193 1.120 0.222 -0.031 0.224 0.061 0.04201/04/2020 1 1.370 1.109 0.232 -0.066 0.242 0.104 0.05901/04/2020 2 1.222 1.523 0.240 -0.064 0.249 0.075 0.08104/07/2020 1 2.517 0.706 0.264 -0.111 0.286 0.144 point source04/07/2020 2 1.878 1.286 0.262 -0.080 0.274 0.109 0.046 the EN, WN and ejection B. This method typically needs many components to represent the core,which can make the fit unstable. 5.2. Gaussian Fitting Method 2
We took the CLEAN model, but removed only those CCs that roughly correspond to the double(triple) nucleus in a super-resolved image (created with a 0.1 mas circular beam). This CC excisionwas done “by eye”, so there is some subjectivity here. We modelled this region with 2 or 3 circularGaussian components. The method is less subjective than the first as a result of incorporatingadditional information from the super-resolved image. However, the method relies significantly onthe CLEAN model, and it is therefore not independent.5.3.
Comparison of Methods
In Figure 6 we reproduce Figure 5 with the addition of the separation derived from the Gaussianmodels of the nuclear region described above. There are two things to note. First of all, the east-westseparation in 2018 and early 2019 displayed in the bottom panel deviates much more from the cross-sectional method of Figure 3 than the CC approach used in this paper. Secondly, because Model 2is derived using super-resolved images, it agrees better with the CC model data. The Gaussian fitsto the EN and WN are listed in Table 3. The two fits can be compared to each other as well as theCC based method in Table 2. There are some large differences in the flux density of the EN andWN between the two models in columns (3) and (4). This might be a consequence of the differentmethods of removing the background and the relatively large Gaussian FWHM in columns (8) and(9) that are comparable to the separations in column (7). If we perform a linear fit to the separation6 D i s p l ace m e n t ( m a s ) Elapsed Time (days)
Displacement of Eastern Component from Western Component vs. Time
Ejection A = ENEjection BGaussian Model 1AGaussian Model 2AGaussian Model 1BGaussian Model 2B D i s p l ace m e n t ( m a s ) Elapsed Time (days)
East-West Displacement vs. Time
Ejection A = EN Intensity Cross SectionEjection B Gaussian Model 1AGaussian Model 2A Gaussain Model 1BGaussian Model 2B
Figure 6.
The Gaussian components produced by the Difmap fit in the visibility domain are indicated byblue and orange symbols, for Method 1 (described in Section 5.1) and Method 2 (described in Section 5.2).These are overlayed on the plots from Figure 5. Method 1A and 2A points are the distances from theGaussian representing the EN from the Gaussian representing the WN. Similarly, method 1B and 2B pointsare the distances from the Gaussian representing the ejection B from the Gaussian representing the WN. Wedo not present error bars on the Gaussian fit data since it would clutter the graph making it unintelligible. .
100 c. This is surprising considering that on a point bypoint level the agreement is not that tight.In Figure 7, the Gaussian components for both models given in Table 3 are overlayed on CCdistribution for two adjacent epochs. We define EN and WN as in Figure 4. The image is qualitative,but it gives the reader a feel for the difference between the two model results and the differencebetween the models and the CC based methods. Method 2, which utilizes information from thesuper-resolved images, seems very consistent with the EN and WN identifications in May 2019.Figure 6 and Tables 2 and 3 indicate some significant discrepancies between the results of the CCmethod of Sections 3 and 4 and the Gaussian models during the epoch April 7, 2020. This is mostpronounced for ejection B. In Figure 8, we overlay the Gaussian fits on the CC scatter plot fromFigure 4. There is clearly disagreement between the two fits. Furthermore, Model 1 seems to blendthe EN and ejection B and Model 2 seems to ignore all the CCs at the north end of the EN. Thissuggests that the Gaussian fit methods have difficulty resolving 3 components within a total extentof 0.24 mas. The figure clearly shows the origin of the larger displacements for ejection B in the April2020 epoch of Figure 6 given by the Gaussian models compared to the CC based analysis.The main objective of this study is to track the time evolution of the double separation as closeto its inception as possible in order to estimate the trajectory and separation speed as accuratelyas possible. There is arbitrariness in the Gaussian fitting procedure that is accentuated in the earlyepochs (in 2018) when the component separation was smaller. The intensity cross-sections wereintroduced in Figure 3 to provide a clear diagnostic of the model fitting schemes. Based on Figure 6,both Gaussian decomposition schemes give worse fits to the east-west separation derived from theintensity cross-sections in the early epochs than the CC based methods of Section 3 and 4. We donot advocate extrapolating the Gaussian fitting method to the first three epochs of small componentseparation. Similarly, Figure 8 seems to indicate that the second ejection crowds the narrow 0.24 masfield making it difficult for the Gaussian fits to segregate components uniquely or with high accuracy.For this reason, we consider the CC method of this paper preferable to conventional Gaussian fittingfor exploring the partially resolved compact nuclear region of 3C 84. The Gaussian fitting does providequalitative agreement with CC model fitting. As such, along with the intensity cross-sections, thiscorroborates the results of the CC based analysis. We have also demonstrated that with proper carein the definition of the Gaussian models, one can achieve a similar estimate (within 15%) to thenuclear separation. THE NUCLEAR SEPARATION IN THE CONTEXT OF RADIOASTRONIn order to create more context for these results in 2018-2020, we compare the nuclear structure tothe triple nucleus observed on September 21-22, 2013 by RadioAstron (Kardashvev et al. 2013, 2017).First of all, the RadioAstron observations were accompanied by a 43 GHz observation with an arrayof the VLBA combined with the phased VLA (Giovannini et al. 2018, Savolainen et al., in prep.).We use the clean component model from imaging of these data together with the methods of thispaper to detect evidence of a triple nucleus using the east-west resolution of the VLBA. There wereno September or October observations by the BU monitoring program. The top panel of Figure 9 is anuclear clustering model similar to Figure 4. It shows all the CCs >
20 mJy in a nuclear region thatis a square, 0.4 mas on a side. Without the RadioAstron results, this compact configuration wouldhave been more ambiguous to decompose into three components. Based on the RadioAstron images,8 -0.150-0.100-0.0500.0000.0500.100 -0.200-0.150-0.100-0.0500.0000.0500.1000.1500.2000.2500.300 R e l a v e D e c li n a o n ( m a s ) Real ve Right Ascension (mas)
Gaussian Fits Model 1 March 31, 2019
WN Centroid EN Centroid 360 - 370 mJy 225 mJy 110 - 180 mJy75 - 100 mJy 50 - 75 mJy 35 - 50 mJy 25 - 35 mJy Gaussian Fits mas -0.150-0.100-0.0500.0000.0500.100 -0.200-0.150-0.100-0.0500.0000.0500.1000.1500.2000.2500.300 R e l a v e D e c li n a o n ( m a s ) Real ve Right Ascension (mas)
Gaussian Fits Model 2 March 31, 2019
WN Centroid EN Centroid 360 - 370 mJy 225 mJy 110 - 180 mJy75 - 100 mJy 50 - 75 mJy 35 - 50 mJy 25 - 35 mJy Gaussian Fits mas -0.200-0.150-0.100-0.0500.0000.0500.100 -0.200-0.150-0.100-0.0500.0000.0500.1000.1500.2000.2500.300 R e l a v e D e c li n a o n ( m a s ) Real ve Right Ascension (mas)
Gaussian Fits Model 1 May 12, 2019
WN Centroid EN Centroid 718 mJy 249 mJy 100 - 150 mJy75 - 100 mJy 50 - 75 mJy 35 - 50 mJy 20 - 35 mJy Gaussian Fits
894 mJy 1613 mJy
593 mJy 2735 mJy -0.200-0.150-0.100-0.0500.0000.0500.100 -0.200-0.150-0.100-0.0500.0000.0500.1000.1500.2000.2500.300 R e l a v e D e c li n a o n ( m a s ) Real ve Right Ascension (mas)
Gaussian Fits Model 2 May 12, 2019
WN Centroid EN Centroid 718 mJy 249 mJy 100 - 150 mJy75 - 100 mJy 50 - 75 mJy 35 - 50 mJy 20 - 35 mJy Gaussian Fits
894 mJy 1613 mJy
786 mJy 2602 mJy
Figure 7.
The foreground Gaussian components from Table 3 are indicated by the dashed black circleswith the inscribed black crosses. Both Model 1 (described in Section 5.1) and Model 2 (described in Section5.2) are plotted, but separately for clarity. The diameter of the circle represent the FWHM of the Gaussiancomponent. These are superimposed on the CC component models as defined in Figure 4. The flux densitiesare in black near or inside each Gaussian component. The eastern component of Gaussian Model 2, in May,is a point source and it is represented by a black cross. we cluster the CC components into three regions of concentration, RA East (blue), RA Central (red)and RA West (green). The nuclear region is very clean, there are relatively few CCs compared tothe other epochs considered and the background CC field is sparse near the triple nucleus in theinnermost 0.2 mas. This fortuitous circumstance facilitates the identification of the components ofthe triple nucleus. The distance from RA East to RA Central is ≈ .
08 mas and RA Central to RAWest is ≈ .
09 mas.We overlay the locations of the RA East, RA Central and RA West as blue, red and green triangles,respectively from the top panel on the RadioAstron image. The locations appear to be close to whatis expected from the 22 GHz image. The flux densities of the RA East, RA Central and RA Westare 456 mJy, 2106 mJy and 845 mJy, respectively in the 43 GHz CC decomposition of the top panelof Figure 9. Gaussian fits to the nuclear region of the RadioAstron data yield flux densities of theRA East, RA Central and RA West of 564 mJy, 775 mJy and 389 mJy, respectively at 22 GHz. RA9 -0.200-0.1000.0000.100 -0.150-0.0500.0500.1500.2500.350 R e l a v e D e c li n a o n ( m a s ) Rela ve Right Ascension (mas)
Gaussian Fits Model 1 April 7, 2020
402 mJy 250 -300 mJy 200-250 mJy 150-200 mJy 100- 150 mJy75mJy -100 mJy 60-75 mJy 20-60 mJy Gaussian Fit -0.200-0.1000.0000.100 -0.150-0.0500.0500.1500.2500.350 R e l a v e D e c li n a o n ( m a s ) Rela ve Right Ascension (mas)
Gaussian Fits Model 2 April 7, 2020
402 mJy 250 -300 mJy 200-250 mJy 150-200 mJy 100- 150 mJy75mJy -100 mJy 60-75 mJy 20-60 mJy Gaussian Fit
Figure 8.
The figure compares the Gaussian models with the CC derived components during the epochApril 7, 2020. The figure is formatted the same as Figures 4 and 7. The three bright components in closeproximity to each other seems to provide a challenge for the Gaussian models as evidenced by the significantdifferences between the models from methods 1 and 2. The eastern component of Gaussian Model 1 is apoint source and it is represented by a black cross. We have not included the 0.1 mas rulers in this figure inorder to avoid distracting clutter.
Central and RA West have a highly inverted (rising) spectrum between 22 GHz and 43 GHz eitherfrom synchrotron self-absorption or from free-free absorption (Walker et al. 2000).We try to assess the degree to which the nuclear region has changed in terms of morphology and sizein 2018-2020 compared to 2013. The cross-identification of components is rather uncertain due to 5years between the observations. We cannot make any robust cross-identifications of the componentsfrom epoch to epoch due to the known variability of the morphology and the effects of blending withlow resolution. We simply give two plausible cross-identifications in the bottom panel of Figure 9 andFigure 10 to help elucidate the large qualitative changes that might be occurring over time. First,we identify the brightest component of VLBA with the brightest component of RadioAstron. Withthis chosen scenario, we tentatively identify RA Central as the same physical feature as the WN inFigure 4. We also overlay the locations of the EN in August 26, 2018 and May 12, 2019 on theRadioAstron image in the bottom panel of Figure 9. In this cross-identification scenario, the nuclearstructure has widened by ∼ µ as and the whole pattern is shifted to the east.The first cross-identification scenario is straightforward, but just one of many possible choices.Thus, in Figure 10 we show a different plausible cross-identification based on the high SNR January4, 2020 observation of the nuclear triple. The color coding of the triangles corresponds to the colorcoding in the CC model in the bottom right hand panel of Figure 4. Note that the triangles havea different identification than in Figure 7. In this scenario the nuclear structure has widened by ∼ µ as and the point of origin of the ejections is the red triangle at the far west edge of the jet.The triple axis is tilted relative to September 22, 2013. In summary, both the interpretation inFigure 9 and Figure 10, indicate a highly dynamic nuclear region that evolved to a wide state in2019. The physical identification of the components is not obvious, but our time evolution studyclearly identified luminous plasma ejected towards the east. CONCLUSION0 -0.2-0.15-0.1-0.0500.050.10.150.2 -0.2-0.15-0.1-0.0500.050.10.150.2 R e l a v e D e c li n a o n ( m a s ) Rela ve Right Ascension (mas)
CLEAN Components September 22, 2013
Central Centroid East Centroid West Centroid 863 mJy513 mJy 350-400 mJy 200 - 300 mJy 100-150 mJy35 -50 mJy 20 -35 mJy
RA CentralRA East RA West R e l a ti v e D ec li n a ti on ( m a s ) Figure 9.
The top panel shows the location of the nuclear CCs >
20 mJy on September 22, 2013 based on a43 GHz VLBA plus phased VLA observation that was quasi-simultaneous with the 22 GHz RadioAstron ob-servation in the bottom panel. We cluster the CCs as three physical components RA East (blue), RA Central(red) and RA West (green). Their positions are overlaid on the RadioAstron image from Giovannini et al.(2018). We cross-identify the brightest component, RA Central, with the bright component in 2018/2019,the WN. Based on this identification, we also show the positions of the EN in August 26, 2018 and May 12,2019 relative to the RadioAstron image in the bottom panel. The contour levels are (-10, -7.50, -3, 7.500,10, 30, 50, 100, 150, 200, 300, 500)mJy. Relative Right Ascension (mas) R e l a ti v e D ec li n a ti on ( m a s ) Figure 10.
We consider an alternative (to Figure 9) cross-identification of components between our 43GHz VLBA monitoring of the multiple nucleus and the RadioAstron image. This interpretation is basedon the CC model for January 4, 2020 in the bottom right hand panel of Figure 4. There is a triple nucleusin that epoch as well. The color coding of the centroid locations are the same as in Figure 4. One verysignificant difference is that in January 2020 the cental component is the weakest and in September 2013 itis the brightest. The multiple nucleus is wider in 2020. The contour levels are (-10, -7.50, -3, 7.500, 10, 30,50, 100, 150, 200, 300, 500)mJy.
In this paper, we consider three methods for resolving the nuclear structure in 43 GHz VLBAobservations of 3C 84, intensity cross-section, Gaussian fitting in the ( u, v ) plane and CC models.The time averaged separation speed from August 2018 to April 2020 is estimated as 0 . ± .
008 c.A second ejected component was identified in October 2019 to April 2020 with a similar speed.The multiple nucleus has been detected before with RadioAstron and 86 GHz global VLBI, but thedynamical evolution has never been seen previously. This separation speed estimate accomplishesthe primary goal of this paper.The most relevant comparison are the component measurements at the base (inner ∼ . − . . ∼ .
25 c at ∼ ∼ µ as downstream (Giovannini et al. 2018; Kim et al. 2019).One thing that we can say is that the double separation is ∼ . ≈ . / sin θ lt-yrs, where θ is the line of sight (LOS) angleto the component motion. This equates to ∼ (1900 / sin θ ) M where M ∼ M ⊙ ∼ . × cm isthe black hole mass in geometrized units (Nagai et al. 2019; Punsly et al. 2018; Scharwachter et al.2013). Thus, this slow apparent separation speed persists very far from the source. The LOS anglehas been estimated at 11 ◦ − ◦ based on jet/counter-jet asymmetry (Walker et al. 1994; Asada et al.2006; Lister et al. 2009; Fujita and Nagai 2017). However, these viewing angle estimates are for thenorth-south jet. The direction of the east-west core motion may differ significantly from this. Itis perhaps more relevant that historical data indicates that 3C 84 sometimes appears moderatelyblazar-like based on broad band variability and optical polarization as high as 6% (Veron 1978;Angel and Stockman 1980; Chuvaev 1985; Nesterov et al. 1995). In current nomenclature, it is aslightly “off angle blazar” at times (Punsly et al. 2018). For the sake of comparison, estimates forblazars are typically θ ≈ ◦ − ◦ (Hovatta et al. 2009; Jorstad et al. 2017). However, the blazar-likeproperties have been far more benign for the last 35 years (Punsly et al. 2018). As an example, in thelast 12 years the optical polarization has been consistently between 1%-3% with the very rare jumpsto 4% . So we cannot rule out θ ∼ ◦ , but this behavior does not favor an extreme blazar-like line ofsight. Based on the published ranges of θ , the physical distance between the EN and WN is ∼ . − . ∼ M − ∼ ∼ . > > > .
15 masseparation of the nuclear double could be a feasible method of tracking the time evolution of theejections accurately. The observations could be triggered by a separation determined by the meth-ods of this paper from the BU data. Perhaps 86 GHz observations with global VLBI (including theAtacama Large Millimeter Array) spread out over 6 months that are triggered simultaneous with theVLBA observations might shed light on what kind of dynamics are occurring. These are challeng-ing observations, but this might be one of our best laboratories for studying the base of a powerfulextragalactic jet. . The VeryLong Baseline Array (VLBA) is an instrument of the National Radio Astronomy Observatory. TheNational Radio Astronomy Observatory is a facility of the National Science Foundation operatedby Associated Universities, Inc. TS was supported by the Academy of Finland projects 274477 and315721. HN is supported by JSPS KAKENHI grant No. JP18K03709.REFERENCES Angel, J. and Stockman, H. 1980, ARA&A 18, 321Ansoldi1, S, Antonelli, L. Arcaro¡ C. et al. 2018,A&A 617, 91Asada K., Kameno S., Shen Z.-Q., Horiuchi S.,Gabuzda D. C., Inoue M., 2006, PASJ, 58, 261Baghmanyan, V., Gasparyan, S., and Sahakyan,N. 2017, ApJ 848 111Blandford, R. and K¨onigl, A. 1979, ApJ 232 34Chael, A., Narayan, R., Johnson, M. D. 2019,MNRAS 486, 2873Chuvaev, K. 1985, PAZh 111, 803Dhawan, V., Kellermann, K. I., Romney, J. D.1998, ApJL, 498, 111Fomalont, E. 1999, in Synthesis Imaging in RadioAstronomy II, ASP Conference Series, eds.Taylor, G., Carilli, C., Perley, R. 180, 301Fujita, Y. and Nagai, H. 2017, MNRAS, 465,L94–L98Giovannini, G., Savolainen, T., Orienti, M. et al.2018, Nature Astronomy 2, 472Hada, K., Giroletti, M., Kino, M., et al. 2014,ApJ, 788, 165Hardcastle, M., Evans, D. and Croston, J. 2009,MNRAS, 396,1929Hodgson, J., Rani, B., Lee, S.-S. et al. 2018,MNRAS 475 368Hovatta, T., Valtaoja, E., Tornikoski, M.,L¨ahteenm¨aki, A. 2009, A&A 498, 723Jorstad, S., Marscher, A., Morozova, D., et al.2017, ApJ, 846, 98Kardashev, N. S., Khartov, V. V., Abramov, V.V. et al. 2013, Astronomy Reports 57, 153Kardashev, N. S., Alakoz, A. V., Adrianov, A. S.et al. 2017, Solar System Research 51, 535Kim, J.-Y., Krichbaum, T., Lu, R.-S., Ros, E. etal. 2018 A&A 616 188Kim, J.-Y., Krichbaum, T. P., Marscher, A. P., etal. 2019, A&A, 622, 196 Lee, S.-S., Lobanov, A., Krichbaum, T. P. et al.2008, ApJ, 136, 59Lightman, A., Press, W., Price, R. and Teukolsky,S. 1975,
Problem Book in Relativity andGravitation (Princeton University Press,Princeton)Lind, K., Blandford, R. 1985, ApJ 295, 358Lister, M. L. 2001, ApJ, 562, 208Lister, M. L., Cohen, M., Homan, D. et al. 2009,AJ 138, 1874Marscher, A. P. 1985, in Supernovae as DistanceIndicators, Lecture Notes in Physics, 224, 132Mart´ı-Vidal, I,; Perez-Torres, M. A., Lobanov, A.P. 2012 A & A 541 A135.Mo´scibrodzka, M., Falcke, H., Shiokawa, H. 2016A & A 586 38Nagai, H., Suzuki, K., Asada, K., Kino, M.,Kameno, S. et al. 2010, PASJ 62, L11Nagai, H., Haga, T., Giovannini, G., et al. 2014,ApJ 785, 53Nagai, H., Onishi, K., Kawakatu, N., et al. 2019,ApJ 883, 193Narayan R., Yi I., 1994, ApJL, 428, 13Nesterov, N., Lyuty, V., Valtaoja, E. 1995, A&A296, 638Pedlar, A., Ghatuare, S., Davies, R. et al., 1990,MNRAS 246, 477Punsly, B., Marziani, P., Bennert, V., Nagai, H.,Gurwekk, M., 2018, ApJ 869, 143Punsly, B. 2019, ApJL 879, 11Reed, B. 1989, Am. J. Phys. 57 642Rees, M. J. 1966, Nature 211, 468Scharwachter, J., McGregor, P. J., Dopita, M. A.,Beck, T. L. 2013 MNRAS 429, 2315Suzuki, K., Nagai, H., Kino, M., et al. 2012, ApJ746, 140Ter¨asranta, H., Achren, J., Hanski, M. et al. 2004,A&A 427, 769 Trippe, S., Krips, M., Pietu, V., et al. 2011, A&A533, 97Veron, P. 1978, Nature 272, 430Walker R. C., Romney J. D., Benson J. M., 1994,ApJ 430, L45 Walker R. C., Dhawan V., Romney J. D.,Kellermann K. I., Vermeulen R. C., 2000, ApJ530, 233Wright, E. L. 2006, PASP, 118, 1711Yuan F., Narayan R., 2014, ARA&A 52, 529 A. THE RESOLUTION LIMITS OF THE VLBA OBSERVATIONSThe ability to resolve structures in interferometric data depends on several factors, e.g., the lengthof the longest baselines, gaps in the ( u, v ) coverage, signal-to-noise ratio of the data, and the com-plexity of the source structure itself. Giving an accurate number for any given experiment requiressimulations of that exact experimental setup and the source. Therefore, one usually resorts to simplerules of thumb like the fringe spacing, the uniformly weighted beam size or the criterion we haveadopted for the current paper. Since all the observations we consider have similarly high SNR andsimilar complexity of the source structure, it is reasonable to assume that any variation in the reso-lution limit from epoch to epoch is mainly due to the longest baselines available. Since we use onlyepochs that have either MK-SC baseline or MK-HN baseline present, the variation in the maximumbaseline length in E-W direction is only ∼ . − .
10 mas is on average correct for the VLBA in the high SNR case. Weexplore this by means of simulations in the visibility domain.Using aips task uvmod we simulated visibility data with exactly the same ( u, v ) coverage and noiseproperties as in the August 2018 observation, the epoch of minimum detectable separation with ourCC based method presented in this paper. As an input model, we used the August 2018 CC model.From this CC model, we excised an area of 3 uniform beam sizes (FWHM) around the core. To theresulting model, we added two 1 Jy point sources separated from the origin symmetrically in relativeRA by ± .
02 mas. The independent variable in this experiment is the separation in relative RA, thehorizontal axis in Figure 11, measured in mas. We created eight simulated data sets increasing theseparation between the point sources from 0.04 mas to 0.18 mas in steps of 0.02 mas. Then we usedthe modelfit task in Difmap to fit the visibility data with a model consisting of two point sourcesin the core region. After making the fit, we plotted the two dependent variables of the experiment,the flux ratio and the fitted separation of the components in Figure 11, the vertical axis in the topand second panels, respectively. At separations of 0.04 mas and 0.06 mas, the fitted data do notaccurately represent the real separation nor the real brightness ratios. At 0.08 mas, this abruptlychanges to precise fits to both quantities. It clearly shows that two equally bright point sources canbe resolved, if their separation is 0.08 mas or larger.We also made a second set of simulations with the same input model. However, instead of pointsources we used two 1 Jy Gaussian distributions with a FWHM of 0.1 mas each. Recall from Section3.1, there were 20 estimates of the FWHM of the components that range from 0.023 mas to 0.112 maswith a mean of 0.076 mas. The fitting in Difmap was made with point sources as in the previousexperiment. The results are presented in the third and the bottom panels of Figure 11. It seemsthat separations of 0 . − .
12 mas ( ∼
10% accuracy in the separation) or larger are needed in thiscase to accurately estimate the relative positions. We note that the smallest measurable distancewith our CC method in Table 2 is 0 . ± .
013 mas in August 2018. Not coincidentally, the valueobtained by the simulation. We also note that the analysis of the simulations used an inexact modelof the flux distributions. This analysis seems consistent with the model-fitting in the ( u, v ) plane inFigure 6. When compared to the CC model method, the model fits seem less accurate with highermodel dependence for separations less than ∼ .
13 mas.6
Figure 11.
The results of our simulations in the ( u, v ) plane. The horizontal axes are the separationbetween our two injected nuclear components. The vertical axes are the model-fitted values of the flux ratio(for which the ground truth is one by construction) and the separation of the two fitted components. Thetop two panels are for the point source experiment described in the text. Accurate model fitting occurs fora separation of > .
08 mas. The bottom two frames are for Gaussian sources with a FWHM of 0.1 mas. Inthis case a slightly larger separation is required for accurate model-fitting in the ( u, v ) plane.B.
THE CC MODEL FROM JANUARY 10, 2019The January 10, 2019 intensity profile looks different than the adjacent epochs in Figure 3. It hasone peak instead of two. Thus, this epoch needs to be studied in detail. From Section 2, we repeatthe fundamental philosophy of implementing CC models “Even though the models may not be robustin a single epoch, they should be suitable for identifying a trend that persists over time, especiallywith regards to very bright features as is the case here.” We use this as our guide for assessing whathas occurred during this epoch.7 -0.2-0.15-0.1-0.0500.050.1 -0.2-0.15-0.1-0.0500.050.10.150.2 R e l a v e D e c li n a o n ( m a s ) Rela ve Right Ascension (mas)
CLEAN Components January 10 2019 -0.2-0.15-0.1-0.0500.050.1 -0.2-0.15-0.1-0.0500.050.10.150.2 R e l a v e D e c li n a o n ( m a s ) Rela ve Right Ascension (mas)
CLEAN Components January 10 2019
Figure 12.
The distribution of CCs from the January 10, 2019 data reduction on the BU website. Thefigure format is the same as Figure 4. Two models are presented for the CC clustering. The top one is theone used in the main text and Figure 5 and is referred to as Model 1 for the clustering of the CCs. Model2 is the bottom frame.
Figure 12 is an analog of Figure 4 that displays the distribution of CCs. The figure considers twoplausible decompositions into a WN and EN. The single peak structure of the intensity profile isexplained by the figure, the EN lies to the south of the WN by . . u, v ) coverage. Thus, the two features are combined into one feature that isstretched out in the east-west direction in this interpretation. Similarly, the southward veer of theEN would be a result of imperfect ( u, v ) coverage and calibration. The disturbing aspect for ourmethod is that instead of the east-west separation of the CCs comprising the WN being ∼ . u, v ) data with CLEAN +self-cal since the end result of the image reconstruction depends on the “route” that is taken duringthe imaging process for imperfect data (i.e., sampling is poor and/or data has significant gain errors).The resultant images are sensitive to the initial phase self-cal steps and we were able to redistribute9 D i s p l ace m e n t ( m a s ) Elapsed Time (days)
Displacement of Eastern Component from Western Component vs. Time
Ejection A = EN Ejection B
Displacement (mas) = 0.000212 [Time (Days)] + 0.118755 masDisplacement (mas) = 0.000134 [Time (Days)] +0.038142 mas D i s p l ace m e n t ( m a s ) Elapsed Time (days)
East-West Displacement vs. Time
Ejection A = EN Intensity Cross Section Ejection B
East - West Displacement (mas) = 0.000209 [Time (Days)] + 0.113256 masEast - West Displacement (mas) = 0.000120 [Time (Days)] - 0.041913 mas
Figure 13.
Figure 5 is recreated, but instead of using Model 1 from the top panel of Figure 12, we useModel 2 from the bottom panel of Figure 12 to estimate the double nucleus separation speed. the CCs in the image plane. However, none of the images had an intensity cross section that was“in-family” with the cross section expected from Figure 3 (i.e., 2 well defined, distinct peaks). Fur-thermore, none of the images resolved the ambiguity between a two component decomposition of thenucleus or a three component decomposition of the nucleus. Similar to Figure 12, the EN-WN sepa-ration was always in the range 0.13 mas to 0.17 mas, regardless of the self calibration or the particularchoice of the identifications of the CCs with the EN and the WN. It is therefore concluded that the“out of family” properties of the January 2019 observation are inherent to the ( u, v ) data and arenot an artifact of image reconstruction. The re-imaging investigation does not address whether this0is a physical property of the source at the time of observation or an idiosyncracy of this particularpatchy sampling in the ( u, v ) plane.We hypothesize, without proof, the plausibility of ( u, v ) coverage issues with the observation. 3C84is a very complex source with many components. The ( u, v ) data sampling is not ideal for such acomplex source, as it is being observed with 31-32 other sources over a 24 hour period. The ( u, v )coverage is not the same in all epochs. Occasionally, the ( u, v ) coverage might not be sampled wellenough to reconstruct the complex structure adequately or uniquely. We cannot prove if the imageis accurate or adversely affected by patchy ( u, v ) coverage. Our basic premise is that we cannotvouch for the integrity of the CC models in an individual epoch, but we can detect temporal trendsin the bright components. To this point, the results of our analysis do not depend on choosingModel 1 over Model 2. The estimated separation velocity with the choice of Model 1 in Figure 5 was0 . ± .
08 c. By comparison, using Model 2 (as was done in Figure 13), results in almost exactlythe same separation velocity 0 . ± ..