The Outburst of the Blazar S40954+658 in March-April 2011
D.A. Morozova, V.M. Larionov, I.S. Troitsky, S.G. Jorstad, A.P. Marscher, J. L. Gómez, D.A. Blinov, N.V. Efimova, V.A. Hagen-Thorn, E.I. Hagen-Thorn, M. Joshi, T.S. Konstantinova, E.N. Kopatskaya, L.V. Larionova, E.G. Larionova, A. Lähteenmäki, J. Tammi, E. Rastorgueva-Foi, I. McHardy, M. Tornikoski, I. Agudo, C. Casadio, S.N. Molina, A. E. Volvach, L. N. Volvach
aa r X i v : . [ a s t r o - ph . H E ] J un Draft version October 26, 2018
Preprint typeset using L A TEX style emulateapj v. 5/2/11
THE OUTBURST OF THE BLAZAR S4 0954+658 IN MARCH-APRIL 2011
D.A. Morozova , V.M. Larionov , I.S. Troitsky , S.G. Jorstad , A.P. Marscher , J. L. G´omez , D.A. Blinov ,N.V. Efimova , V.A. Hagen-Thorn , E.I. Hagen-Thorn , M. Joshi , T.S. Konstantinova , E.N. Kopatskaya ,L.V. Larionova , E.G. Larionova , A. L¨ahteenm¨aki , J. Tammi , E. Rastorgueva-Foi , I. McHardy ,M. Tornikoski , I. Agudo , C. Casadio , S.N. Molina , A. E. Volvach , L. N. Volvach Draft version October 26, 2018
AbstractWe present the results of optical ( R band) photometric and polarimetric monitoring and Very LongBaseline Array (VLBA) imaging of the blazar S4 0954+658, along with Fermi γ -ray data during amulti-waveband outburst in 2011 March-April. After a faint state with a brightness level R ∼ ∼ ∼ ◦ . At the same time, within 1 σ uncertainty a new superluminalknot appeared with an apparent speed of 19 . ± . c . We have very strong evidence for association ofthis knot with the multi-waveband outburst in 2011 March-April. We also analyze the multi-frequencybehavior of S4 0954+658 during a number of minor outbursts from August 2008 to April 2012. We findsome evidence of connections between at least two more superluminal ejecta and near-simultaneousoptical flares. Subject headings: galaxies: active — BL Lacertae objects: individual (S4 0954+658) — galaxies: jets— polarization INTRODUCTION
The blazar S4 0954+658 (z=0.367) is a well studiedBL Lac object at optical wavelengths. Its optical vari-ability was analyzed by Wagner et al. (1993), who foundlarge amplitude variations (of ∼ B − R color variations allowed them to conclude that mid- andlong-term brightness variations of the source are not as-sociated with spectral variability. Gabuzda et al. (2000,and references therein) analyzed the radio morphologyof S4 0954+658 and showed that the jet is bent on bothparsec and kiloparsec jet scales. They also found sub-stantial intranight polarization variability of the radio Astronomical Institute of St. Petersburg State University,Universitetsky Pr. 28, Petrodvorets, 198504, St. Petersburg,Russia; [email protected] Isaac Newton Institute of Chile, St. Petersburg Branch Institute for Astrophysical Research, Boston University, 725Commonwealth Ave., Boston, MA 02215-1401; [email protected] Department of Physics , University of Crete, 71003, Herak-lion, Greece Pulkovo Observatory, Russian Academy of Sciences,Pulkovskoe sh. 65, St. Petersburg, 196140 Russia Aalto University Mets¨ahovi Radio Observatory, Mets¨ahov-intie 114,FIN-02540 Kylm¨al¨a, Finland. Aalto University Dept of Radio Science and Engineering, PL13000, FIN-00076 Aalto, Finland Department of Physics and Astronomy, University ofSouthampton, Southampton, SO17 1BJ, United Kingdom Instituto de Astrof´ısica de Andaluc´ıa, CSIC, Apartado 3004,18080, Granada, Spain Joint Institute for VLBI in Europe, Postbus 2, NL-7990 AADwingeloo, the Netherlands Radio Astronomy Laboratory of the Crimean AstrophysicalObservatory, Katsiveli, Crimea, 98688 Ukraine core at 5 GHz. Kudryavtseva et al. (2010) have foundseveral moving components in the jet at 22 GHz withmean velocity 4 . ± . γ -ray emissionof S4 0954+658 first was detected by EGRET in 1993.S4 0954+658 was also detected by Fermi LAT accord-ing to the Fermi first and second catalogs of γ -ray brightsources (Abdo et al. 2010; Nolan et al. 2012). In this pa-per we present a detailed study of the optical outburst ofS4 0954+658 in 2011 March-April (Larionov et al. 2011a)along with an analysis of the γ -ray variability and be-havior of the innermost radio jet at 43 GHz. Prelimi-nary results of our observations have been described byLarionov et al. (2011b). OBSERVATIONS AND DATA REDUCTION
The observations reported here were collected as a partof a long-term multi-wavelength study of a sample of γ -ray bright blazars. An overview of this program is givenby Marscher (2012). Optical Observations
We carry out optical
BV RI observations at the 70-cm AZT-8 reflector of the Crimean Astrophysical Ob-servatory, and 40-cm LX-200 telescope in St. Peters-burg, Russia. The telescopes are equipped with identi-cal photometers-polarimeters based on ST-7 CCDs. Weperform observations in photometric and polarimetricmodes at the 1.8-m Perkins telescope of Lowell Obser-vatory (Flagstaff, AZ) using the PRISM camera and atthe 2.2 m telescope of Calar Alto Observatory (Almer´ıa, Morozova et al.Spain) within the MAPCAT program . Photometricmeasurements in R band are supplemented by observa-tions at the 2-m Liverpool Telescope at La Palma, Ca-nary Islands, Spain. Polarimetric observations at theAZT-8, Perkins, and Calar Alto telescopes are carriedout in Cousins R band, while at the LX-200 telescopethey are performed in white light, with effective wave-length close to R band.The Galactic latitude of S4 0954+658 is 43 ◦ and A V =0 . m
38, so that the interstellar polarization (ISP) in thisdirection is less than 1%. To correct for the ISP, themean relative Stokes parameters of nearby stars weresubtracted from the relative Stokes parameters of theobject. This accounts for the instrumental polarizationas well, under the assumption that the radiation of thestars is unpolarized. The errors in the degree of polariza-tion, P , are less than 1% (in most cases less than 0.5%),while the electric vector position angle (EVPA), χ , is de-termined with an uncertainty of 1–2 ◦ . The photometricerrors do not exceed 0 . m
02. Photometry and polarimetryof the source during the flare are presented in Table 1.
Gamma-ray Observations
We derive γ -ray flux densities at 0.1-200 GeV by ana-lyzing data from the Fermi Large Area Telescope (LAT),provided by the Fermi Science Space Center using thestandard software (Atwood et al. 2009). We have con-structed γ -ray light curves with a binning size of 7 days,with a detection criterion that the maximum-likelihoodtest statistic (TS) should exceed 10.0. Although the γ -ray flux fell below the detection limit during most of theperiod of our observations ( ≤ × − ph · cm − s − ),there are a number of positive γ -ray detections that areinteresting to compare with behavior of the source atother wavelengths. Single-Dish Radio Observations
We use 37 GHz observations obtained with 13.7 m tele-scope at Mets¨ahovi Radio Observatory of Aalto Univer-sity, Finland. The flux density calibration is based onobservations of DR 21, with 3C 84 and 3C 274 usedas secondary calibrators. A detailed description of thedata reduction and analysis is given in Ter¨asranta et al.(1998). These data are supplemented by observationscarried out at the 22-meter RT-22 radio telescope of theCrimean Astrophysical Observatory at 36.8 GHz. In thiscase the sources 2037+421, 1228+126, and 2105+420 areused for the flux density calibration. A detailed descrip-tion of the data reduction and analysis can be found inNesterov et al. (2000).
VLBA Observations
The BL Lac object S4 0954+658 is monitored monthlyby the BU group with the VLBA at 43 GHz within asample of bright γ -ray blazars . The VLBA data arecalibrated and imaged in the same manner as discussedin Jorstad et al. (2005). We have constructed total andpolarized images at 33 epochs from 2010 August to 2012April. Each image in Stokes I, Q, and U parameters wasfit by a model consisting of a number of components with circular Gaussian brightness distributions. Identificationof components in the jet across epochs is based on anal-ysis of their flux, position angle, distance from the core,size, degree of polarization, and EVPA. During this pe-riod we have identified 12 components, A1, K1, K2, K3,K4, K5, K6, K7, K8, K9, K10, K11, in addition to thecore, A0. The core is a stationary feature located at thesouthern end of the portion of the jet that is visible at 43GHz. We have computed kinematic parameters of knots(the proper motion, velocity, acceleration) by fitting the(x, y) positions of a component over epochs by differ-ent polynomials of order from 1 to 3, in the same man-ner as described in Jorstad et al. (2005). The methodproduces uncertanties of polynomial coefficients with anassumption that the true value lies with probability W within the confidence region around the estimated value( W =0.95 is applied). The ejection time of a componentis the extrapolated time of coincidence of the position ofa moving knot with the core in the VLBA images, and T eject is the average of T xeject and T yeject weighted by theiruncertainties, which are calculated using uncertainties ofthe polynomial coefficients.Table 3 lists for the core and each superluminal knotthe flux, fractional polarization level, p , and EVPA, χ .Table 4 lists for each superluminal knot the apparentspeed, β app , acceleration, if detected ( ˙ µ || and ˙ µ ⊥ , alongand perpendicular to the jet, respectively), mean positionangle with respect to the core, < Θ > , and extrapolatedtime of zero separation from the core, T eject . RESULTS AND DISCUSSION
Optical Polarization Analysis
Figure 1 displays the entire set of optical photomet-ric and polarimetric data collected by our team during2008-2011. The blazar shows prominent activity duringthe period covered by our observations, with the R bandamplitude of variations exceeding 2 m and a record levelof P exceeding 40%. Even on such an active backgroundthe outburst, which started in early 2011, is quite promi-nent. An enlargement of the event is shown in Figure 2.Unlike all of the previous years, starting from the endof February 2011 a smooth rotation of χ (Fig. 2, bottompanel) with an amplitude of ∼ ◦ is prominent. Wesee a steady rotation of χ ∼ . ◦ per day during March2011. The rotation stops at RJD 55643 (2011 March 22),near the peak of the R -band outburst. After that, onlyminor changes of EVPA are observed, despite continuedstrong variability of the flux density and fractional po-larization. After RJD ∼ ∼ ◦ ).During two nights, on March 9 and April 24, we ob-served violent intranight variability, ∼ . m ∼ . m Q vs I ) and ( U vs I ) Stokes polarization parameters(see Fig. 3) and found that the entire data set can be splitinto sections with its own behavior in ( I, Q, U ) parame-he Outburst of the Blazar S4 0954+658 in March-April 2011 3
TABLE 1Photometry and polarimetry of S4 0954+658 during 2011 April-Mayoutburst
RJD
R σR p σp EV P A σEV P A
Telescope(days) (mag) (mag) (%) (%) ( ◦ ) ( ◦ )55577.4520 17.105 0.014 15.57 0.44 172.5 0.1 CAHA55588.5160 17.182 0.016 15.48 1.12 163.1 2.1 AZT-8+ST755601.4340 16.924 0.010 12.55 0.70 162.2 1.6 AZT-8+ST755603.9170 16.985 0.007 13.54 0.57 148.3 1.2 Perkins55604.3090 16.896 0.054 13.82 3.60 180.1 7.5 LX-20055604.8940 16.987 0.012 11.84 1.31 146.8 3.2 Perkins55605.8860 16.869 0.010 12.05 0.02 148.8 0.0 Perkins55607.3730 16.980 0.026 17.48 2.05 171.8 3.4 AZT-8+ST755608.2500 16.901 0.069 9.01 3.86 218.1 12.3 LX-20055609.3790 16.904 0.107 22.39 6.46 133.0 8.3 LX-200 Note . — RJD=JD-2400000.0; Table 1is published in its entirety in the elec-tronic edition of the Journal. A portion is shown here for guidance regarding itsform and content.
Fig. 1.—
From top to bottom: γ -ray light curve (open trianglesare the upper limits); optical (R band) light curve; fractional po-larization vs. time; position angle of polarization vs time; lightcurve of the VLBI core at 43 GHz (open circles), and light curvefrom the whole source at 37 GHz (filled diamonds) and 35 GHz(open diamonds). The vertical bars show the times of ejection ofsuperluminal knots within 1- σ uncertainty. ter space. We mark these sections with different colorsin Figure 3 and apply the same colors to the data plottedin Figure 2.The regression lines in Figure 3 represent components,each with constant parameters of polarization, P comp and χ comp , while its total and polarized fluxes vary. There Fig. 2.—
Optical flux density (corrected for Galactic extinction),fractional polarization, and position angle of polarization in R bandvs. time in 2011 January-May; magnified symbols refer to thenights with violent intranight variability, colors designate sectionsof the data with different Stokes parameter behavior (see Table2). Red vertical bars in the upper panel mark positive Fermi LATdetections, a bar’s height is proportional to the γ -ray flux. Fig. 3.—
Absolute Stokes parameters variation during 2011January-April; left:
Stokes Q vs. I, right:
Stokes U vs. I. Dif-ferent colors refer to different stages of the evolution in (
I, Q, U )parameter space (see Table 2). are 8 different components with respect to the Stokes pa- Morozova et al.
TABLE 2Optical Polarization Parameters of theVariable Sources name RJD p % σ p % χ ◦ σχ ◦ a 55572-55629 12.66 1.91 -26.8 4.2b 55630 19.24 5.18 23.3 7.4c 55631-55637 27.79 1.22 -24.5 1.2d 55638-55639 15.26 9.00 -24.7 17.0e 55641-55647 30.00 2.83 31.3 2.6f 55651-55657 17.35 11.22 42.3 17.8g 55660-55701 18.08 1.24 31.2 1.9h 55676 33.05 2.14 17.0 1.8 TABLE 3Polarization properties of knots on VLBA images
MJD Knot Flux (Jy) p % χ ◦ Date55724.5 K8 0.10 27.4 146.2 12 JUN 201155763.5 . . . 0.12 19.0 135.0 21 JUL 201155796.5 . . . 0.15 18.7 116.8 23 AUG 201155820.5 . . . 0.08 23.2 117.3 16 SEP 201155850.5 . . . 0.08 23.8 122.6 16 OCT 201155897.5 . . . 0.11 15.4 144.8 02 DEC 2011
Note . —
MJD = JD − .
5; Table 3 is publishedin its entirety (with parameters for all of the components)in the electronic edition of the Journal. A portion is shownhere for guidance regarding its form and content. rameters behavior. Since these components are variablein flux, we will refer to them as variable sources. Wenotice that the regression lines tend to converge on thelocus of points corresponding to the pre-outburst valuesof the Stokes parameters. This implies that one of thecomponents, probably responsible for the flux and polar-ization of S4 0954+658 before the outburst, has constantStokes parameters. We estimate the constant source’sparameters as R=17.8 (corresponding to flux density of0.308 mJy after correction for interstellar extinction),p=15% and χ = − ◦ . We assume that the componentshould contribute the same amount of the total and po-larized flux during the outburst as well. Hence, we sub-tract its contribution from the Stokes parameters of S40954+685 to get the radiation parameters of the variablesources. These are listed in Table 2.We use the technique developed by Hagen-Thorn (see,e.g., Hagen-Thorn et al. 2008, and references therein) toanalyze the color variability of S4 0954+65. If the vari-ability is caused only by the flux variation but the relativespectral energy distribution (SED) remains unchanged,then in n -dimensional flux space { F , ..., F n } ( n is thenumber of spectral bands used in multicolor observa-tions) the observational points must lie on straight lines.The slopes of these lines are the flux ratios for differentpairs of bands as determined by the SED. With somelimitations, the opposite is also true: a linear relationbetween observed fluxes at two different wavelengths dur-ing some period of flux variability implies that the slope(flux ratio) does not change. Such a relation for severalbands would indicate that the relative SED of the vari-able source remains steady and can be derived from theslopes of the lines.We use magnitude-to-flux calibration constants for op- tical BV RI bands from Mead et al. (1990). Galac-tic absorption in the direction of S4 0954+65is calculated according to Cardelli’s extinction law(Cardelli, Clayton,& Mathis 1989) and A V = 0 . m F i = A i + B i · F R , where i corresponds to B, V, and Ibands. Values of B i , the slopes of the regressions, vs. thefrequency of the corresponding band represent a relativeSED of the variable source. As can be seen in Fig. 5, ona logarithmic scale the SED is fit very well by a linearslope α = − . ± .
15 that suggests that the variablesource emits synchrotron radiation with F ν ∝ ν α . FR , mJy F i , m Jy FB vs FRFV vs FR FI vs FR
Fig. 4.—
Dependences of the flux in B, V, and I bands on theflux in R band (the fluxes are corrected for the Galactic extinction).The lines represent linear regression fits to the dependences.
Radio VLBI Versus Optical and Gamma-ray Data
Figure 1 presents the multi-frequency light curves ofS4 0954+658 and optical polarization parameter curvesalong with an indication of times of ejection of the su-perluminal knots. Figure 6 shows the γ -ray light curveoverlaid by the optical light curve (top panel); the degreeof optical polarization and polarization of VLBI core at43 GHz (middle panel); the position angle of optical po-larization and the position angle of VLBI core at 43 GHz(bottom panel). Similar plots that show light curves andpolarization parameters’ curves of other VLBI knots areavailable on-line in the electronic edition. Figure 7 showsthe evolution of the distance of knots from the core,while Figure 8 displays the VLBA image of the sourceat 43 GHz with trajectories of the knots superposed.We carefully study the optical polarization behavior ofS4 0954+658 near the ejection times of the components.For the majority of knots (8 of 11) we have found a con-nection between the time of the ejection of a componenthe Outburst of the Blazar S4 0954+658 in March-April 2011 5 log n, Hz l og ( F i / F R ) -0.4-0.3-0.2-0.10.00.10.2 Fig. 5.—
Relative spectral energy distribution of the variablesource in S4 0954+64 obtained by using the linear regressionsshown in Fig.4. The solid line represents a linear fit of the SED. and activity at the optical and radio wavelengths (37GHz). A visual inspection of Figure 6 reveals that dur-ing most of the observational period the optical EVPAwas χ ∼ − ◦ , close to the mean radio EVPA of the radiocore ( − ◦ ) and mean jet direction ( − ◦ ).A number of flares are apparent in the optical lightcurve during the period of observations 54800-56000(Fig.1 ). Of particular interest are the flares 2, 3, 3a,5, 5a, during which γ -ray detections occurred. To com-pare epochs of optical flares with the epochs of ejectionsof superluminal knots, we separate the sample of opti-cal flares into 2 groups. Group A includes positive de-tections, for which | ( T opt max − T eject ) | ≤ σ , where σ isthe 1 σ uncertainty in T eject and Group B, for which | ( T opt max − T eject ) | ≤ σ . Table 5 lists the epochs of op-tical flares (Fig. 1), epochs of γ -ray detections, presenceof optical χ rotation during each flare, speed of optical χ rotation if rotation is found, epoch of knot ejection ifdetected, and type of the flare according to classificationintroduced above. Component K1:
Knot K1 is very bright, but we do nothave enough data at optical wavelengths for a detailedanalysis. Nevertheless, the 37 GHz light curve shows astrong flare that precedes the ejection time of knot K1within 1 σ uncertainty of T eject . Component K2:
The ejection of knot K2 was simulta-neous with an optical flare and an increase of the opticalpolarization up to 24% within 1 σ uncertainty of T eject .Although there are a number of short rotations of theoptical EVPA within 3 σ uncertainty of T eject of K2, wehave too few measurements ( ≤ < Θ > = − ◦ )is quite different from the mean jet direction ( ∼ − ◦ ).Before the ejection of K2 we see a modest flare in thecore (RJD=54885), which coincides with the optical flare ∼ ◦ that differs significantly from both the mean opti-cal EVPA and mean EVPA of the core ( ∼ − ◦ ). Thereis a sharp jump in the optical EVPA at RJD ∼ χ varying from 78 ◦ to 45 ◦ . The latter agrees withthe EVPA of K2 ( χ = 45 ◦ ) at RJD=54981, when theknot is first resolved from the core at the VLBA images. This suggests a connection between the optical and radioevents. Component K3:
The appearance of knot K3 was ac-companied by a ∼ ◦ rotation of the optical EVPA(RJD 55063—55068, ∼ σ un-certainty of T eject . In addition, a broad flare in R bandwith maximum at RJD 55024 was contemporaneous withthe ejection of K3 within 3 σ uncertainty of T eject , as wellas with two detections in γ -rays. Component K4:
The ejection of K4 was accompanied(within 1 σ of T eject ) by a ∼ ◦ rotation of the opticalEVPA ( ∼ . ± .
14 Jy), and threedetections at γ -ray energies. Also, the historical maxi-mum level of optical fractional polarization (RJD=55217,P=41%) was achieved within 2 σ uncertainty of T eject . Component K5:
The ejection of K5 was contempora-neous with an optical flare at RJD 55319 ( S R = 1 . P = 12%). At the time when K5 was emergingfrom the core we did not find significant smooth rotationof the EVPA, but we detected an increase of the opticalfractional polarization in the form of a plateau with amean value of ∼ Components K6 and K7:
Knots K6 and K7 are weakand were detected only at 3 epochs. However, they areseen clearly in the polarization maps (see set of Fig. 9).We have not found contemporaneous violent activities inoptical and γ -ray bands, which can be associated withthese components similar to those of K2-K5. Component K8:
The most interesting is knot K8,whose appearance coincides within 1 σ uncertainty withthe major flare in the R-band light curve, a flare at γ -ray energies, a strong flare in VLBI core and at 37 GHz.The emergence of knot K8 from the core was also ac-companied by a significant rotation of the optical EVPA( ∼ ◦ , ∼ Component K9:
Violent intranight variability, ob-served during the night of 2011 April 24 (brightening by ∼ σ uncertainty of T eject .During this flare the flux in R band increased up to 2 . Component K10:
Knot K10 was ejected after a flarein the R band light curve at RJD=55789 (within 2 σ uncertainty of T eject ), which was contemporaneous alsowith a flare at 37 GHz (RJD =55786, S = 1 .
66 Jy) anda flare in VLBI core, while a moderate degree of bothoptical ( ∼ ∼ Component K11:
The knot K11 passed through thecore within 2 σ uncertainty of T eject before a flare in theR band light curve at RJD=55900. We have not foundcontemporaneous violent activities in optical and γ -raybands,The feature A1 is detected at many epochs during ourVLBI observations at a stable position of 0 . ± .
01 maswith respect to the core (see Fig. 7). Jorstad et al. (2001)found that “stationary hot spots”are a common charac-teristic of compact jets, with the majority of such fea-tures located within a range of projected distances of 1-3pc from the core. These authors proposed three cate- Morozova et al.
Fig. 6.—
Top panel: optical (R band) light curve (filled circles) overlaid by γ -ray light curve (triangles), and VLBI core light curve at43 GHz (open circles). Middle panel: optical fractional polarization vs. time curve (filled circles) overlaid by P of the VLBI core vs. timecurve (open circles). Bottom panel: position angle of optical polarization vs. time curve overlaid by EVPA of the VLBI core vs. time curve(open circles). Plots for other components (Figs. 6.1-6.7) are available in the electronic edition of The Astronomical Journal . TABLE 4Kinematic parameters of the VLBI knots
Knot N µ β app T eject ˙ µ ⊥ ˙ µ || < Θ > K1 10 0 . ± .
01 13 . ± .
30 54650 . ± − . ± . − . ± . − . ± . . ± .
01 8 . ± .
02 54883 . ±
15 - - − . ± . . ± .
02 6 . ± .
42 55091 . ± − . ± . − . ± . − . ± . . ± .
06 13 . ± .
42 55184 . ± . − . ± . . ± .
05 15 . ± .
12 55349 . ± . − . ± . . ± .
01 12 . ± .
17 55450 . ±
15 - - − . ± . . ± .
06 19 . ± .
31 55564 . ± . − . ± . . ± .
01 18 . ± .
28 55639 . ± − . ± . − . ± . − . ± . . ± .
06 17 . ± .
39 55704 . ±
15 - - − . ± . . ± .
07 26 . ± .
58 55827 . ± . − . ± . . ± .
04 20 . ± .
91 55871 . ±
15 - - − . ± . gories of models for stationary components in supersonicjets: a) standing recollimation shocks caused by imbal-ances between the pressure internal and external to thejet; b) sites of maximum Doppler beaming where a bentjet points most closely to the line of sight; and c) station-ary oblique shocks, where the jet bends abruptly. Weconsider that knot A a ,since it is quasi-stationary with an observed “lifetime”atleast several months. Statistical analysis of coincidences between opticalflares and ejections of VLBI knots
We carried out numerical simulations in order to de-termine the probability of random coincidences betweenepochs of optical flares and ejection of superluminalknots in the same manner as described in Jorstad et al.(2001). We fixed the number and epochs of optical flaresaccording to Table 5 and generated 1,000,000 samples ofrandom epochs of ejections of VLBI superluminal compo-nents. Each sample consists of 10 random ejections (wedo not include knot K1, which was ejected before the be-he Outburst of the Blazar S4 0954+658 in March-April 2011 7
TABLE 5The summary of optical flares
N Optical flare γ -ray Optical χ Speed of optical χ Knot ejection Type Connection flare - knotRJD “rotation”( ◦ ) “rotation”( ◦ /day)1 54891.807 - - - K2 A ?2 55020.307 Y 27 4.5 K3 B YES3 55182.447 Y 180 15.7 K4 A YES3a 55217.384 Y - - K4 B ?4 55319.363 - - - K5 B ?5 55637.580 Y 333 13.3 K8 A YES5a 55669.434 Y - - K9 B ?6 55789.258 - - - K10 B ?7 55900.574 - - - K11 B ? D i s t a n ce fr o m t h e c o r e ( m a s ) MJDS4 0954+658
A1K1K2K3K4K5K6K7K8K9K10K11
Fig. 7.—
Separations of knots from the core as a function of time.
Fig. 8.—
The 43 GHz image of the source with trajectories ofknots superposed. ginning of the optical and gamma-ray monitoring). Weset the uncertainties of generated epochs of zero separa-tions equal to the uncertainties of observed superlumi-nal ejections. A coincidence was registered in the samemanner (groups A and B) as discussed above. In our ob-servations we found 3 coincidences of group A and 6 ofgroup B (see Table 5). Figure 10 shows the results of the numerical simulations, which demonstrate that the prob-ability to have 3 or more coincidences within 1 sigma is more than 80%. The probability to have 9 or morecoincidences within 3 σ (including 3 coincidences within1 σ ) is ∼ ∼ σ uncertainty of ∼
57 days for one compo-nent, which corresponds to a half of the observationalinterval for 10 components.Although there is the quite high probability that theoptical flares and ejections of VLBI knots are not con-nected, it is essential to note that we use more than onecriterion to associate optical flares with the appearance ofsuperluminal knots. These include the relation betweenoptical and radio polarization measurements, connectionwith detections of S4 0954+658 in γ -rays. We considerwith confidence that components K8 and perhaps K4 andK3 are associated with optical flares (5, 3, and 2, respec-tively) due to similarity in the optical/radio polarizationbehavior during the flares and structure of the γ -ray out-bursts, which can be related to the structure of the innerjet.We can not exclude that the γ -ray flares RJD ∼ ∼ γ -ray flare and optical intra-night variability, similar to the case observed in thequasar 3C 454.3 (Jorstad et al. 2013). According to theproper motion, K8 should reach A1 in 30 ±
15 days, whichis similar to the time lapse between the first and second γ -ray flares, ∼
42 days. So the knot K9 may in fact bea new component generated after the interaction of K8and A1. A similar case is observed for component K4and γ -ray flare RJD ∼ ±
21 days,while the time lapse between flares is ∼
30 days. CONCLUSIONS
The BL Lac object S4 0954+658 has displayed veryprominent optical activity starting from 2011 mid-February. Our photometric and polarimetric observa-tions densely cover this period. In addition, we have animpressive set of VLBA images at 43 GHz that allows Morozova et al.
Fig. 9.—
Total (yellow contours) and polarized (color scale) intensity images at 43 GHz; yellow line segments over the color scale showthe direction of the electric vector.
Fig. 10.—
Probability of chance coincidences between opticalflares and epochs of zero separation within 1 σ (dark shading) and3 σ (light shading) uncertainties. us to compare optical activity with the behavior of theparsec-scale jet. We conclude that:1. During the entire interval of our observations thesource exhibited violent variability in optical bandsand a high level of activity in the jet at 43 GHz.We follow the ejection of new components with arate ∼ γ -ray emission at a flux level exceeding5 × − phot cm − s − . Only one detection at γ -rays was not associated with an optical flare.3. The overall behavior of the source during the mostprominent optical outburst in 2011 March-Aprilcan be explained as a superposition of radiationof a long lived component with constant Stokes pa-rameters and a new, strongly variable one whoseEVPA rotates at a rate of ∼
13 degrees/day from the onset of the outburst until the moment of max-imum flux and then levels at ∼ ◦ . Corrected for k · ◦ ambiguity, this is equivalent to − ◦ , whichis quite different from the pre-outburst direction( − ◦ ). This fast and monotonic rotation might beexplained as the spiral motion of the variable sourcein a helical magnetic field (a new superluminalknot) (Marscher et al. 2008, 2010; Larionov et al.2013). The VLBA images at 43 GHz show the ejec-tion of a new, highly relativistic knot, K8, coincidedwithin 1 σ uncertainty of T eject with the major peakin the R-band light curve, a flare at γ -ray energies,and a flare in VLBI-core and at 37 GHz.4. According to our optical data the polarization pa-rameters of the variable source ( p = 27% χ = − ◦ ,“c”in Table 2) are close to the polarization param-eters of K8 ( p = 27%, χ = − ◦ see Table 3) at theepoch (12 June 2011) when it was first separatedfrom the core at the 43 GHz images (set of Figs. 6).The knot preserved a high level of fractional polar-ization at later epochs.5. According to our analysis, 8 of 11 superluminalcomponents (K2, K3, K4, K5, K8, K9, K10, K11)emerged during strong optical flares (within 1 to3 σ uncertainty of T eject ). However, the MonteCarlo simulation indicates that there is no evi-dence from the timing of the optical flares andVLBI ejecta alone to support the claim that the twoare related. We have very strong evidence to con-nect one superluminal component (K8) to a near-simultaneous optical flare, and some evidence ofconnections between at least 2 more (K4 and K3)superluminal ejecta and near-simultaneous opticalflares.6. The γ -ray outbursts, which can be associated withknots K4 and K8 based on T eject (Fig.1), reveal adouble structure that might be explained by theinteraction of a moving knot with the two station-ary features in the inner jet, the core A0 (the firstpeak) and knot A1 (the second peak), which arepresumably standing recollimation shocks.7. High-amplitude intranight variations were detectedin both optical light and fractional polarization.he Outburst of the Blazar S4 0954+658 in March-April 2011 9This may reflect fine structure of the magnetic field,as would be expected, e.g. if the jet plasma is tur-bulent (Marscher 2014).8. We have found 3 cases of smooth optical EVPArotation that are associated with component ejec-tions (see Table 5) at high confidence supportedby our well-sampled optical and VLBA data. Theslowest rate of the optical EVPA rotation occursduring the appearance of knot K3, whose appar-ent speed was a factor of 2 slower than the averagespeed of superliminal knots in the jet. However, wecannot say that this is a common pattern withoutmore data.9. During the interval of our observations, the highestflux level of the VLBI core at 43 GHz was contem-poraneous with the major optical outburst. Highlevel of fractional polarization ( ∼13%) was seen inthe core during the optical flare and dropped to 2%after the outburst. A lower level of fractional polar-ization at 43 GHz with respect to the optical degreeof polarization may be due to a larger volume of theregion radiating at 43 GHz and turbulent magneticfield. In addition, the polarization position angleof the core and almost all of the components wasclose to the mean jet direction, as was the opti-cal EVPA in quiescent states (see set of Figs. 6).This implies that the magnetic field in the regionsof optical and radio emission has similar structure.Moreover, a simultaneous increase of the degree ofoptical polarization and that of the core leads tothe conclusion that the two regions are co-spatial. We thank anonymous referee for his/her useful com-ments and suggestions. This work was partly supportedby Russian RFBR grants 12-02-00452, 12-02-31193,13-02-00077, St.Petersburg University research grants6.0.163.2010, 6.38.71.2012 and by NASA Fermi GuestInvestigator grants NNX08AV65G, NNX11AQ03G, andNNX12AO90G. The VLBI data were obtained withinthe program VLBA-BU-BLAZAR. The VLBA is an in-strument of the National Radio Astronomy Observatory.The National Radio Astronomy Observatory is a facil-ity of the National Science Foundation operated undercooperative agreement by Associated Universities, Inc.The PRISM camera at Lowell Observatory was devel-oped by K. Janes et al. at BU and Lowell Observa-tory, with funding from the National Science Founda-tion, BU, and Lowell Observatory. The Liverpool Tele-scope is operated on the island of La Palma by LiverpoolJohn Moores University in the Spanish Observatorio delRoque de los Muchachos of the Instituto de Astrofisicade Canarias, with financial support from the UK Sci-ence and Technology Facilities Council. This paper ispartly based on observations carried out at the German-Spanish Calar Alto Observatory, which is jointly oper-ated by the MPIA and the IAA-CSIC. Acquisition of theMAPCAT data is supported by MINECO (Spain) grantand AYA2010-14844, and by CEIC (Andaluc´ıa) grantP09-FQM-4784. The Mets¨ahovi team acknowledges thesupport from the Academy of Finland to their observ-ing projects (