galaxies Article Proper Motions of Jets on the Kiloparsec Scale: New Results with HST EileenT.Meyer1,*,WilliamB.Sparks2,MarkosGeorganopoulos1,RoelandvanderMarel2, JayAnderson2,SangmoT.Sohn2,JohnBiretta2,ColinNorman2,MarcoChiaberge2 andEricPerlman3 1 DepartmentofPhysics,UniversityofMaryland,BaltimoreCounty,Baltimore,MD20742,USA; [email protected] 2 SpaceTelescopeScienceInstitute,Baltimore,MD21218,USA;[email protected](W.B.S.);[email protected] 7 (R.v.d.M.);[email protected](J.A.);[email protected](S.T.S);[email protected](J.B.); 1 [email protected](C.N.);[email protected](M.C.) 0 3 FloridaInstituteofTechnology,Melbourne,FL32901,USA;eperlman@fit.edu 2 * Correspondence:[email protected] n a AcademicEditors:JoseL.Gómez,AlanP.MarscherandSvetlanaG.Jorstad J Received:13September2016;Accepted:16January2017;Published:date 0 2 Abstract: TheHubbleSpaceTelescoperecentlycelebrated25yearsofoperation. Someofthefirst imagesofextragalacticopticaljetsweretakenbyHSTinthemid-1990s;withtimebaselinesonthe ] A orderof20yearsandstate-of-the-artastrometrytechniques, wearenowabletoreachaccuracies G inproper-motionmeasurementsontheorderofatenthofamilliarcsecondperyear. Wepresent the results of a recent HST program to measure the kiloparsec-scale proper motions of eleven . h nearbyopticaljetswithHubble,thefirstsampleofitskind. WhenpairedwithVLBIproper-motion p - measurementsontheparsecscale,wearenowabletomapthefullvelocityprofileofthesejetsfrom o near the black hole to the final deceleration as they extend out into and beyond the host galaxy. r t Weseeconvincingevidencethatweak-flavorjets(i.e.,FRIs)haveaslowlyincreasingjetspeedupto s a 100pcfromthecore,wheresuperluminalcomponentsarefirstseen. [ 1 Keywords: propermotions;extragalacticjets;HubbleSpaceTelescope v 6 4 8 5 1. Introduction 0 1. Many aspects of the physics of relativistic jets from super-massive black holes are not well 0 understood, including the particle makeup of the jet, their lifetimes, and the speed profile of the 7 plasmaasitextendsoutofthehostgalaxyandintotheintergalacticmedium. Proper-motionstudies 1 : allowustodirectlyobservetheapparentspeedsofthesejets,resultinginconstraintsontheirLorentz v factors(Γ). Hundredsofobservationsofjetswithverylongbaselineinterferometry(VLBI)intheradio i X havedetectedpropermotionsofjetsonparsecandsub-parsecscales,relativelyneartotheblackhole r engine(e.g.,[1–5]). Becausethesejetsarehighlyrelativistic,apparentsuperluminalmotionscanresult a fromvelocitiesnearthespeedoflightcoupledwithrelativelysmallviewingangles. Westartwith somedefinitions: thedimensionlessobservedapparentvelocity β isrelatedtotherealvelocity app β = v/c(wherecisthespeedoflight)andviewingangleθthroughthewell-knownDopplerformula β = βsinθ/(1−βcosθ). Ameasurementofβ impliesbothalowerlimitontheLorentzfactor app app (Γ ≈ β )andanupperlimitontheviewingangle. Theseconstraintsaredifficulttoderiveusing min app othermeanssuchasspectralfitting,duetotheinherentdegeneracybetweenintrinsicpower,angle, andspeedintroducedbyDopplerboostingoftheobservedflux. Whiletherearelargesamplesofproper-motionmeasurementsforjetsonparsecscales,direct observationsofjetmotionsonmuchlargerscales(kpc–Mpc)withhigh-resolutiontelescopessuch as the Very Large Array (VLA) or Hubble Space Telescope (HST) are rare. However, the much Galaxies2017,5,8;doi:10.3390/galaxies5010008 www.mdpi.com/journal/galaxies Galaxies2017,5,8 2of9 lower-than-VLBI resolution necessarily also limits potential observations of apparent motions to sourcesintheverylocalUniverse,andoftenrequireyearsorevendecadesofrepeatedobservations. For many years, there were only two measured proper motions of jets on kpc scales, both taken with the VLA. These were the famous result of β up to 6c measured by [6] for the jet in M87 app (z=0.004,d=22Mpc),andaspeedof≈4cforaknotinthejetin3C120(z=0.033,d=130Mpc)by[7], thoughthiswaslatercontradictedbyadditionalVLAandMerlinobservations[8,9]. In1999,thefirst measurementofpropermotionsintheopticalwasaccomplishedby[10], usingfouryearsofHST FaintObjectCamera(FOC)imagingtoconfirmthefastsuperluminalspeedsintheinnerjetofM87. Inthispaper,wepresentsomerecentproper-motionsresultsforthreenearbyopticaljetsobtained fromarchivalandnewHSTdata,enabledinmajorpartbythelongoperatinglifetimeofHSTandthe resulting20-yearbaselinesfromtheoriginalsnapshotimagesofopticaljetsfirsttakeninthe1990s. 2. Methods All three optical jets were observed with several of the Hubble Space Telescope imaging instruments over a span of 10–20 years. The analysis of the new and archival data was similar forallthreejets. WewillpresentfirstthemethodsforthejetinM87,andthenbrieflyremarkonthe data used for 3C 264 and 3C 273, which was treated very similarly. The data used for all jets and furtherdetailscanbefoundin[11–13]. 2.1. M87 2.1.1. Astrometry ForM87,thereferenceframeisbasedonhundredsofbrightglobularclustersassociatedwith the host galaxy which are effectively stationary to proper motions over the time of this study. ThereferenceframewasbuiltusingtheAdvancedCameraforSurveysWideFieldCamera(ACS/WFC) exposures in the F606W filter, by first detecting the positions of the globular clusters in each flat-fielded, CTE-corrected ACS/WFC image using a PSF-peak-fitting routine, then applying the standard (filter-specific) geometric correction to those positions, and then finding the best linear transformationforeachimagewhichmatchesthepositionsintheindividual(geometrically-corrected) framestoamasterreferenceframe.ThislaststepisdonebyaroutinesimilartoMultiDrizzle,butbetter optimizedforastrometry(see[14,15]). Theprocessoffindingtransformationsforallframesisiterated sothatthemasterreferenceframe(super-sampledtoapixelscaleof0.025(cid:48)(cid:48)/pixel)effectivelygivesthe averagepositionofeachreferencesourceinageometrically-correctedframe. Thefinalreferencesystemconsistsofpositionsandmagnitudesforover1300globularclusters within ∼100(cid:48)(cid:48) of the M87 core position. Among all clusters, the median one-dimensional RMS residualrelativetothemeanpositionwas0.05(reference-frame)pixels(1.25mas),correspondingtoa √ systematicastrometricaccuracy(×1/ 56)of0.17mas;overthe13.25yearbaselinethisisequivalent to0.003c. AstrometricsolutionswerethenfoundforalltheACSHighResolutionCamera(ACS/HRC), ACS/WFC,andWideFieldPlanetaryCamera2(WFPC2)imagesintheF814Wfilter. Typicalnumbers ofglobularclustersusedtomatchtheframeswere∼200–500forACS/WFC,∼15–30forWFPC2images, and∼15–25forACS/HRC;correspondingsystematicerrorswere∼0.006,∼0.03,and∼0.05pixels, or0.003c,0.015c,0.025cover13.25years,respectively. 2.1.2. MeasuringtheKnotPositions Within the M87 jet, we first identified the significant features (peaks) of interest using stacked images. The image stacks include the 2006 ACS/WFC stack, four WFPC2 stacks (epochs 1995–1996, 1998–1999, 2001, and 2007–2008), and three stacks of ACS/HRC exposures (November 2002–December 2003, July 2004–September 2005, November 2005–November 2006). The host galaxy was modeled using the ACS/WFC stacked image with the IRAF/STSDAS tasks ellipseandbmodelandthensubtracted. Atwo-dimensionalcontinuousfunctionalrepresentationof Galaxies2017,5,8 3of9 theimagecutoutswasthencreatedusingtheCosineTransformfunction(FourierDCT)inMathematica, whichallowedustofindprominentpeaks,aswellascontoursofconstantfluxlevelaroundthosepeaks. Ingeneral,thenumberofinterestingpeakswaschosenbyhand,andthecontourlinelevelswereat50% ofthefluxofthepeak,aftera“background”levelwassubtracted. Thepositionsdefiningthecontour werereverse-transformedfrommasterframecoordinatesintoeachdistorted,galaxy-subtractedimage sothatanintensity-weightedcentroidpositionfromthepixelswithinthecontourcouldbecalculated. Thesefinalpositionswerethentransformedbackintothecommonreferenceframe,sothateachpeak ofinterestwasmeasuredineveryexposure,resultinginover400positionmeasurementsspreadover the13yearbaseline. Tomeasuretheapparentmotionofthejetcomponentsovertime,wedefinethex-directionasthe linefromthecorethroughthecenterofknotI(PAof290◦),withy-directionperpendicular. Datawere binnedinto26timebins(shownontherightinFigure2),andalinearmodelwasfitusingstandard weightedleastsquares. Theweightsweretakentobetheinverseofthevarianceforeachtimebin, asmeasuredfrom10nearbyglobularclusterreferencesources. 2.2. 3C264 WeobtaineddeepV-bandimagingof3C264withtheACSinMayof2014inordertocompare nearly20yearsofimagestakenbyHSTforevidenceofpropermotionsoftheseknots. Inaverysimilar approachaswithM87,welocalizedover100globularclustersinthehostgalaxyasareferencesystem onwhichtoregisterpreviousimagestakenwithWFPC2in1994,1996,and2002. Thesystematicerror intheregistrationoftheWFPC2imagesisgenerallyontheorderof5milliarcseconds(mas)orless. Tomeasuretheirapparentspeeds,thepositionofeachknotwasmeasuredwithacentroiding technique. InthecaseofknotsBandC,wealsomodelledthejetasaconstant-densityconicaljetwith superimposedresolvedknots,inordertobettermeasuretheirfluxesandpositions,particularlyinthe finalepochwhentheyappeartooverlap.Weplottedthepositionofeachknotalongthedirectionofthe jetaxisversustime,andfittedthedatawithaleast-squareslinearmodel. Aslopesignificantlylarger thanzeroindicatessignificantpropermotions,andweusedtheconversionfactor1.442cyear/masto convertangularspeeds(µ )tounitsofc. app 2.3. 3C273 WeobtainedfourorbitsofACS/WFCimaginginF606WinMayof2014. Thesewerestackedinto ameanreferenceimage(withcosmic-rayrejection)onasuper-sampledscalewith0.025(cid:48)(cid:48) pixels. The registrationoftheeightindividualexposuresutilizedafull6-parameterlineartransformationbased onthedistortion-correctedpositionsof15–20point-likesources. Themedianone-dimensionalrms residualrelativetothemeanpositionwas0.07reference-framepixels,or1.75mas,correspondingtoa √ systematicerrorontheregistration(×1/ 16)of0.44mas,orabouttwohundredthsofapixel. 2.3.1. BackgroundSourceRegistration UnlikewithM87and3C264,theglobularclustersof3C273arenotdetectableintheolderWFPC2 imagingandthuscannotbeusedasareferenceframe. Instead,weidentified15backgroundgalaxies basedonthecriteriathattheycanbeseenbyeyeabovethenoiseintheindividualWFPC2exposures. ThesereferencegalaxiesarehighlightedinFigure1. Notethatgalaxies4,5,and6havebeenpreviously identifiedasunrelatedtothejetbytheirlackofradioemission,andthebrightpointsourcenearthejet isactuallyaforegroundstar(andthusunsuitableforregisteringimagesduetolikelypropermotions). Galaxies2017,5,8 4of9 Figure1.Theimmediateenvironmentof3C273asseenintheACS/WFCreferenceimagefrom2014. Thebackgroundgalaxiesusedforimageregistrationareboxed.Thelargeroutlineisapproximately theimagefootprintoftheearlier1995WFPC2imaging. (NotethattheimageisinthenativeCCD orientation,andNorthisapproximatelytotheright.) To match the archival images to a common reference frame, our general strategy was to use the shape and light distribution of the galaxy to assist in matching their locations in each image. Instead of identifying a single location associated with each galaxy in the deep reference image, weinsteadsamplethegalaxyinagridpattern,resultinginalistofpositionsalongwiththefluxat eachpoint,samplingacrosseachgalaxy. Aninitialastrometrictransformationsolutionwasfoundby supplying≈10pairsofmatchedlocationsfoundbyhandbetweenthegeometrically-correctedraw imageandtheACSreferenceimageandcalculatingthesixtransformationparameters(withoutmatch evaluation/rejection). Theinitialtransformationsolutiondescribedaboveisusedasastartingpoint to transform the x,y locations for each galaxy grid in the reference frame into x ,y location in gc gc the geometrically corrected image. The intensity can then be sampled at each location in the raw image,tobecompareddirectlytothescaledcountsvaluepredictedbythescaledreferencepixelvalue. Thisinformationisusedtocalculatetheoptimalpositionshiftwhichisusedtoupdatethelocationof thegalaxyinthereferenceframe. For each individual exposure, we then compile an updated list of position matches between thereferenceframeandtheGCimagefromthemeanx,yvalueofthegalaxysamplinggridineach. Ingeneral,weusedasubsetofthebackgroundgalaxieswhichwereidentifiablebyeyeandnotoverly affectedbycosmicrayhits. Theprocessoffindingtheinitialx ,y values,followedbyfindingthe gc gc optimal δx,δy improvement on the mean position, was iterated until the positions of the galaxies stoppedimproving. 2.3.2. MeasuringKnotPositionsin3C273 Asaconsistencycheck,wealsomeasuredtheshiftofeachknotusingasecondmethodwhichwe refertoasthe“cross-correlation”method. Overagridwithsub-pixelspacingof0.2super-sampled pixels(5mas),weshiftedthe1995and2003imagesofeachindividualknotrelativetothe2014image (samecutoutarea)overa6 × 6pixelarea, evaluatingthesumofthesquareddifferencesbetween interpolatedfluxovertheknotareaforeachx/yshiftcombination. Theresultingsum-of-squared differences image in all cases clearly shows a smooth “depression” feature which is reasonably well-fitbyatwo-dimensionalGaussianunderthetransformationg =1− f/max(f),where f isthe originalsumofsquareddifferences. Takingtheminimum f locationasmeasuredbythepeakofthe two-dimensionalGaussianfit,wemeasuretheoptimalshiftforeachknot. To measure the approximate error on the positions measured, we repeated both of the above methodsforsimulatedimagesofthejetateachepoch. Thesimulatedimageswerecreatedbytaking the deep 2014 ACS image and adding a Gaussian noise component appropriately scaled from the countsintheoriginalWFPC2exposures. Sincethe2014imageitselfhassomenoise,andalsoaslightly Galaxies2017,5,8 5of9 differentPSFfromtheWFPC2images,thismethodlikelyslightlyoverestimatestheerrors. Wetakethe erroroneachknotmeasurementtobethestandarddeviationofthemeasurementsinthesimulated images(10ineachepoch). Finally,weplottedthepositionofeachfeaturerelativetothe2014position,versustime,tolook forevidenceofpropermotions. Wehavetransformedfromthecoordinateframeofthealignedimages (Northup)toonebasedonthejet,wherepositivexisintheoutflowdirectionalongthejet(takenas positionangle(PA)42◦ southofeast)andpositiveyisorthogonalandtothenorthofthejet. Forboth methods,theestimatederroronthemeasurementhasbeenconvolvedwiththesystematicerrorof theregistration,whichis0.18,0.22,and0.02referencepixels(4.5,2.8,and0.5mas)forthe1995,2003, and2014epochs,respectively. 3. ResultsandDiscussion 3.1. M87 ThemostnotablefindingsforM87werethefindingsofbothdecelerationandtransversemotions for the first time. In Figure 2, we show the knot complex D, which consists of three sub-knots. KnotDisthemostconsistentlybrightfeatureaftertheknotA/B/Ccomplex,andsignificantproper motions were measured in previous studies. As suggested by the contours overlaid on Figure 2, D-Middleisoneofthefastestcomponentswithaspeedof4.27±0.30calongthejet,whilethebrighter D-West shows evidence of deceleration radially, slowing to a near stop by the final epoch in 2008, while maintaining one of the largest transverse speeds of −0.59 ± 0.05c (right panel of Figure 2). PreviousresultsonknotD-Easthavebeenconflicting: B95foundthatitmovedinwardalongthejetat 0.23±0.12c(possiblyconsistentwithbeingstationary),whileB99foundalargeoutwardapparent velocity of 3.12 ± 0.29c; our result of 0.28 ± 0.05 is more in line with B95. It is possible that there isastationaryfeatureatD-East,throughwhichcomponentsemerge(analogoustowhatisseenin HST-1). Inthatcase,thehigher-resolutionFOCwasperhapstrackinganemergingbrightcomponent, whileoverlongerperiodstheglobalfeatureatD-Eastisstationary. Intheouterjet(fromknotA), wefindapparentvelocitiesthatarestillsuperluminalandvelocityvectorsthatappeartolineupintoa helical/side-to-sidepattern. Figure2. SomeresultsfromtheM87study. Atupperleft,acloseviewofknotDcomplexoverfour epochsfrom1995to2008. Asshown,theEasterncomponent(farleft)extendsbutdoesnotchange thecorelocation,whilethetwosub-knotstotherightshowbothradialmotionanddeceleration.On theright,thepositionversustimeoftheWesternmostcomponentofknotD.Inthelowerpanel,we showthesuperimposedvelocityvectorsoneachcomponentintheM87jet.Lengthcorrespondstothe magnitudeofthetotalspeed. Galaxies2017,5,8 6of9 On the left in Figure 3, we show the complete radial and transverse velocity field of M87 as a function of distance along the jet, including previous work covering similar scales and radio interferometryresults. Figure3.ApparentspeedversusdistanceforM87(left)and3C273(right).ForM87,themostrecent HSTresultsareindarkblue. Notethefastriseinspeedsonscaleslessthan100parsecs,reachinga peakatHST-1beforegraduallyfallingoff.Inthecaseof3C264,ourresultssuggestagreatsimilarityto thevelocitystructureseeninM87.Lowerpanelshowsthesignificanttransversevelocitiesdetectedin ourstudy. Ontheright,wecomparetheVLBIscalemotionsfor3C273(left-half)fromtheMOJAVE programtotheHSTpropermotions(right-half)onkpcscales(notethebreakinthedisplayedrangeat thegreyverticalbar). 3.2. 3C264 Afteraligningallimagestoacommonreferenceframe,thefastpropermotionofknotBisclearly visible,asshowninFigure4. WefoundthatknotsAandDhaveaβ consistentwithzero,whilethe app innerknotsBandChaveβ =7.0±0.8cand1.8±0.5c,respectively(Figure2). Thevalueforknot app BexceedsthefastestspeedsmeasuredinthejetinM87,theonlyothersourceforwhichspeedson kpcscaleshavebeenmeasured[10,11]. ThedifferenceinspeedsbetweenknotsBandCputsthem onacollisioncourse,aninteractionwhichhasalreadybeguninthefinalepochfrom2014,wherethe knotsbegintooverlap(Figure2). Thisappearstobethefirstdirectobservationofcollidingknotsinan extragalacticjet. Our data show that in the final 2014 epoch, both knots B and C brighten at the same time by approximately 40% over the mean flux level of the previous three epochs (Figure 4, right). This suggeststhatfreshparticleaccelerationhasrecentlytakenplace,whichweattributetotheongoing collisionbetweenthesecomponents. Underequipartition,thecoolinglengthfortheoptical-emitting electronsforknotsBandCislongerthanthedistancetheytravelledinourobservations,consistent withthelackofanydecayinfluxlevelsfortheseknotsoverthefirstthreeepochs. Thisisnotthe caseforstationaryknotA,whichcanbeseentodecaywithatimescaleof∼70years. KnotAappears analogoustoknotHST-1intheM87jet;thelatteristhoughttobeastationaryreconfinementshock wherethejetpressuredropsbelowthatoftheexternalenvironment[16]. Theeventthatenergized knotAmayhavebeenthepassageoffast-movingknotBcirca1971+8 , comparabletotheknotA −17 decaytime. Galaxies2017,5,8 7of9 RadiodatatakeninOctober1983withtheVLAsuggestthatknotsBandCweremovingfaster inthepastandmayhavedecelerated. InthecaseofknotB,aquadraticfittotheHST+VLAdata suggeststhatinlate1983,theknothadaspeedof10.2c,slowingby0.16c/yeartoreach5.6catthe beginningof2014. WhileaquadraticfitisverypoorforthecombineddataonknotC,alinearfit betweenthe1983and1994epochssimilarlysuggestsaspeedof9.8c. Itappearsthatamuchmore distinctdeceleration“event”occurredforknotC. Intheinternalshockmodel,theefficiency(η)oftheconversionoftheliberatedkineticenergy (E )intoradiationisgenerallyunknown,withvaluesassumedintheliteratureinordertomatch kin thesourceluminosity. Forthecollisionin3C264,wecanestimatetheenergyavailableforconversion fromourobservationstobeatleast10−3,subjecttouncertaintiesinthetotalcoolingtime,andthe futureevolutionoftheobservedflux. 3.3. 3C273 Inthecaseof3C273, allknotshavespeedsconsistentwithzerowithtypical1σ errorsonthe order of 0.1−0.2 mas/year or 1.5c, and with 99% upper limit values ranging from 1−5c. Nearby backgroundgalaxies,usedasacontrolcheck,showthattheselimitsareconsistentwithstationary objectsinthesamefield(seeFigure3,right). Theseresultssuggestthattheknotsinthekpc-scalejet,iftheyaremovingpacketsofplasma, must be relatively slow, in agreement with previous studies based on jet-to-counterjet ratios in radio-loudpopulations[17,18].Assumingthatthejeteitherremainsatthesamespeedordeceleratesas youmovedownstream,the2σupperlimitspeedderivedfromallknotscombinedof1csuggeststhat theentireopticaljetisatmostmildlyrelativistic,withamaximumLorentzfactorofΓ <2.9. However, wecannotruleoutthepossibilitythattheknotsarestandingshockfeaturesintheflow,wherethebulk plasmamovesthroughthefeatureswithahigherΓ. Thebestlimitsonthebulkplasmaspeedthus remainthelimitsderivedfromthenon-detectionoftheIC/CMBcomponentingamma-raysby[19], whereδ <7.8isimpliedassumingequipartitionmagneticfields. Figure4. Resultsfor3C264. Previousradioobservationshaverevealedthattheinitiallynarrowly collimatedjetbendsby∼10◦atthelocationmarkedbytheyellowcross[20],whichappearstoalign wellwiththecentralaxisofthejetinourimaging,andwhichservesasourreferencepointforall measured positions. On the left, the fast motion of knot B and subsequent collision knot C and brighteningcanbeclearlyseenoverthe20yearstudy.Ontheright,weshowtheincreasingfluxofthe twocollidingknots. Galaxies2017,5,8 8of9 Finally,weshowthattheobservedupperlimitsonthepropermotionoftheknotsconfirmsthatthe anear-equipartitionIC/CMBmodelfortheX-raysofthekpc-scaleknotsisruledout.Theequipartition IC/CMBmodelrequiresthattheknotsareballisticpacketsofmovingplasmamovingatthebulkspeed Γ ≈15−20whichwouldimplypropermotionsontheorderof10cor1.12mas/yearwhichcouldhave beendetectedinourstudy;ourupperlimitseasilyrulethisoutatahighlevelofsignificance(>5σ). Moving away from equipartition conditions, an IC/CMB model consistent with our observations requiresajetpowerontheorderoffivetoseveralhundredtimestheEddingtonlimit,andisthus energeticallydisfavored. In comparison to other recent HST observations of lower-power optical jets M87 and 3C264, wherehighlysuperluminalspeeds(6−7c)havebeenobservedintheopticalkpc-scalejet,ourfirst proper-motionstudyofapowerfulquasarjetrevealsnosignificantpropermotions. 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