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DRAFTVERSIONJANUARY19,2016 PreprinttypesetusingLATEXstyleemulateapjv.05/12/14 THENANOGRAVNINE-YEARDATASET:MONITORINGINTERSTELLARSCATTERINGDELAYS LINALEVIN1,2,MAURAA.MCLAUGHLIN1,GLENNJONES3,JAMESM.CORDES4,DANIELR.STINEBRING5,SHAMICHATTERJEE4, TIMOTHYDOLCH4,6,MICHAELT.LAM4,T.JOSEPHW.LAZIO7,NIPUNIPALLIYAGURU1,ZAVENARZOUMANIAN8, KATHRYNCROWTER9,PAULB.DEMOREST10,JUSTINA.ELLIS7,ROBERTD.FERDMAN11,EMMANUELFONSECA9, MARJORIEE.GONZALEZ9,12,MEGANL.JONES1,DAVIDJ.NICE13,TIMOTHYT.PENNUCCI14,SCOTTM.RANSOM15, INGRIDH.STAIRS9,11,KEVINSTOVALL16,JOSEPHK.SWIGGUM1,WEIWEIZHU9,17 DraftversionJanuary19,2016 ABSTRACT 6 Wereportonanefforttoextractandmonitorinterstellarscintillationparametersinregulartimingobserva- 1 tions collected for the NANOGrav pulsar timing array. Scattering delays are measured by creating dynamic 0 spectra for each pulsar and observing epoch of wide-band observations centered near 1500MHz and carried 2 outattheGreenBankTelescopeandtheAreciboObservatory. The∼800-MHzwidefrequencybandsimply n dramaticchangesinscintillationbandwidthacrossthebandpass,andastretchingroutinehasbeenincludedto a accountforthisscaling. Formostofthe10pulsarsforwhichthescalinghasbeenmeasured,thebandwidths J scalewithfrequencylesssteeplythanexpectedforaKolmogorovmedium. Wefindestimatedscatteringdelay 8 valuesthatvarywithtimebyuptoanorderofmagnitude. Themeanmeasuredscatteringdelaysaresimilarto 1 previouslypublishedvaluesandslightlyhigherthanpredictedbyinterstellarmediummodels. Weinvestigate the possibility of increasing the timing precision by mitigating timing errors introduced by the scattering de- ] lays. Formostofthepulsars,theuncertaintyinthetimeofarrivalofasingletimingpointismuchlargerthan E themaximumvariationofthescatteringdelay,suggestingthatdiffractivescintillationremainsonlyanegligible H partoftheirnoisebudget. h. Subjectheadings:methods: dataanalysis–stars: pulsars–ISM:general–gravitationalwaves p - o 1. INTRODUCTION is dispersion, which occurs when the radio wave propagates r throughacolumnoffreeelectronsintheISMandischarac- t The interstellar medium (ISM) consists partly of ionized s plasma,whichinteractswithpulsarradioemission. Thishas terizedbyafrequency-dependenttimedelay. Thedelaysare a proportional to DM × ν−2, where the dispersion measure, several effects on pulsar signals, and will impact the times [ DM,istheintegratedcolumndensityoffreeelectronsandν of arrival (TOAs) of the pulses at Earth. One such effect 1 istheobservingfrequency. SincethepulsarandtheISMhave v 1DepartmentofPhysicsandAstronomy,WestVirginiaUniversity,P.O. differentrelativevelocities,theDMofapulsarisnotconstant 0 Box6315,Morgantown,WV26505,USA in time. By observing pulsars at two or more separate fre- 9 2JodrellBankCentreforAstrophysics,AlanTuringBuilding,School quencies,theDMvariationscanbetrackedandcorrectedfor 4 ofPhysicsandAstronomy,TheUniversityofManchester,OxfordRoad, inthedata(e.g.,Demorestetal.2013;Keithetal.2013;Lee 4 Manchester,M139PL,UK etal.2014). 3DepartmentofPhysics,ColumbiaUniversity,550W.120thSt.,New 0 Incontrasttodispersion,whichwouldbepresentinacom- York,NY10027,USA 1. 4Department of Astronomy, Cornell University, Ithaca, NY 14853, pletely homogeneous medium, scattering arises when radio USA wavestravelthroughaninhomogeneousmedium. Multi-path 0 5DepartmentofPhysicsandAstronomy,OberlinCollege,Oberlin,OH scattering manifests itself in several ways, including diffrac- 6 44074,USA 1 6DepartmentofPhysics,HillsdaleCollege,33E.CollegeStreet,Hills- tiveintensityscintillationsandpulsebroadening. Diffractive : dale,Michigan49242,USA scintillation effects were first observed in pulsars by Lyne v 7Jet Propulsion Laboratory, California Institute of Technology, 4800 & Rickett (1968), and are the effects in focus in this paper. Xi OakGroveDrive,Pasadena,CA91106,USA The basic model usually used to describe diffractive scintil- 8CenterforResearchandExplorationinSpaceScienceandTechnology lation assumes that the ISM is a thin screen of plasma, lo- r andX-RayAstrophysicsLaboratory,NASAGoddardSpaceFlightCenter, a Code662,Greenbelt,MD20771,USA cated between the pulsar and the observer (Scheuer 1968). 9Department of Physics and Astronomy, University of British Asthesignalpropagatesthroughthescreen,inhomogeneities Columbia,6224AgriculturalRoad,Vancouver,BCV6T1Z1,Canada in the plasma introduce phase perturbations that are corre- 10NationalRadioAstronomyObservatory,P.O.Box0,Socorro,NM, lated over a scintillation bandwidth, which is inversely pro- 87801,USA 11DepartmentofPhysics,McGillUniversity,3600rueUniversite,Mon- portionaltothescatteringtimescale. Theseperturbationsare treal,QCH3A2T8,Canada alsoknownasscatteringdelays. Thescintillationpattern,and 12DepartmentofNuclearMedicine,VancouverCoastalHealthAuthor- hence the scattering timescale, of a pulsar can change dras- ity,Vancouver,BCV5Z1M9,Canada tically over time (Hemberger & Stinebring 2008). Similar 13DepartmentofPhysics,LafayetteCollege,Easton,PA18042,USA to the case of DM variations, the relative velocities of the 14UniversityofVirginia,DepartmentofAstronomy,P.O.Box400325 pulsar and the ISM give rise to the time variable scattering Charlottesville,VA22904-4325,USA 15NationalRadioAstronomyObservatory,520EdgemontRoad,Char- delays. The scaling of the scintillation parameters with fre- lottesville,VA22903,USA quency is often described as that of a Kolmogorov medium, 16DepartmentofPhysicsandAstronomy,UniversityofNewMexico, withthescintillationbandwidth,∆ν ∝ν4.4,andthescintil- NM87131,USA d 17Max-Planck-Institutfu¨rGravitationsphysik,AlbertEinsteinInstitut, lation timescale, ∆td ∝ ν1.2 (Cordes et al. 1985), although AmMu¨lenber1,14476Golm,Germany ithasbeenshownthatsomesourceshavescalingindicesthat 2 L.Levinetal. deviatefromthese(e.g.,Lo¨hmeretal.2004;Bhatetal.2004). servations to investigate the effect of interstellar scintillation These observed deviations may not necessarily be indicative anditscontributiontothetotalnoisebudgetforthisimportant ofanon-Kolmogorovspectrum,butmaybeduetothesizeof setofpulsars. the dominant scattering region transverse to the line of sight (Cordes&Lazio2001). 2. DATA In a Pulsar Timing Array (PTA), millisecond pulsars (MSPs) are observed in an effort to detect nanohertz gravi- This paper makes use of data from regular NANOGrav tationalwaves. TheNorthAmericanNanohertzObservatory timing observations. The data are all included in the latest forGravitationalWaves(NANOGrav)usesthe100-mGreen NANOGrav data release (9-year dataset; Arzoumanian et al. Bank Telescope (GBT) and the 300-m Arecibo Observatory 2015),andhereweuseasub-setspanning∼3.7yearsfordata (AO) to observe ∼40 MSPs every 7−28 days. To succeed fromGBTand∼1.7yearsfordatafromAO.TheexactMJD in detecting gravitational waves, it is necessary to obtain as range of the data used for each pulsar is shown in Table1, high a timing precision as possible, over a long time span. together with observational properties of the pulsar as well The achievable timing precision of MSPs is continually in- as of the ISM along the line-of-sight to the pulsar. We have creasingwithlongerdatasetsandimprovedinstrumentation. focused on observations carried out at a center frequency of This makes it ever more important to understand all non- ∼1500MHzfor20pulsarsatGBTand19pulsarsatAO.Two gravitationalwaveeffects,toimprovethesensitivityofPTAs ofthepulsars(J1713+0747andB1937+21)areobservedwith togravitationalwaves. bothtelescopes. Asdescribedabove,theperturbationscausedbyinterstellar AtGBT,thedataarecollectedwiththeFPGA-basedspec- scintillation,aswellastheperturbationsfromDMvariations, trometerGUPPI(GreenBankUltimatePulsarProcessingIn- limitthetimingprecisionforallpulsars.Somepulsarswillbe strument)usingcoherentdedispersiontechniques. Theobser- moreaffectedthanothers,however,dependingontheproper- vationsarecarriedoutoverafrequencybandof800MHzcen- tiesoftheISMalongtheirlineofsight. MostMSPsinPTAs teredat1500MHz,dividedinto1.5625-MHzwidefrequency havebeenchosenpartlyduetohavingalowDM,andhence channels. Allobservationsare∼30minutesinlengthandare it is expected that scattering will only contribute to a small foldedinrealtimewith15-ssubintegrations. part of the total timing error for these pulsars. However, ac- At AO, we are using data collected and coherently dedis- curately correcting for ISM perturbations needs to be done persedwiththePUPPI(PuertoRicoUltimatePulsarProcess- carefully, soasnottointroduceadditionalerrors. Tocorrect ingInstrument)backend.Heretheobservationsareconducted for DM variations, nearly simultaneous observations with at overa700-MHzbandwidthcenterednear1500MHz,divided least two separate frequency bands at widely spaced center in 1.5625-MHz wide channels. The data are recorded in 1-s frequenciesareused. Becauseofthedifferentfrequencyscal- subintegrations (or 10-s subintegrations for observations be- ing of dispersion and interstellar scattering, by only correct- foreMJD∼56540)for∼30minutesperpulsarandepoch. ing for DM variations systematic errors are introduced into At the start of each observation, a polarization calibration thetimingprocedure(seeAppendixA).Oneimportantcaveat scan is performed by injecting a 25-Hz noise diode for both tothiscorrectionprocedureisthatmeasurementsatdifferent polarizations.Onceduringeachepochandforeachobserving observing frequencies sample different parts of the interstel- frequency,afluxcalibrator(B1442+101)isobserved. Forthe lar medium (Cordes et al. 2015). This significantly affects analysisinthispaper,totalintensityprofileshavebeenused, DMmeasurementsandcouldalsoaffectinterstellarscintilla- by summing the polarizations of the calibrated data (Arzou- tionmeasurementsforsomepulsars. manianetal.2015). Anumberofauthorshaveaddressedtheissuesofmeasur- The GUPPI and PUPPI backends provide substantially ing scintillation parameters and mitigating ISM effects pre- larger observation bandwidths compared to previously used viously. A few examples include Coles et al. (2010) and backends ASP (Astronomical Signal Processor) and GASP Keith et al. (2013), who analyzed DM variations and scin- (GreenBankAstronomicalSignalProcessor),whichbothhad tillation parameters for pulsars in the Parkes Pulsar Timing 64-MHzbandwidthcapacity(e.g.,Demorestetal.2013).The Array (PPTA). Their observations were carried out at three wider bandwidths not only result in higher timing precision differentfrequencies:a64-MHzbandcenteredat685MHz,a due to a higher signal-to-noise value for the pulsar signal 256-MHzbandcenteredat1369MHz,anda1024-MHzband overall,buttheyalsoprovidealargernumberofscintillation centeredat3100MHz(Manchesteretal.2013). Someofthe maximaandminimaovertheobservedband. Thewide-band pulsarsinthePPTAsamplearealsoobservedbyNANOGrav observationscarriedoutwithGUPPIandPUPPIprompteda and a comparison of the results is included in this work. In needtoinvestigatetheeffectofinterstellarscatteringdelays, a different paper, Gupta et al. (1994) studied the scintilla- andareessentialfortheanalysisinthispaper. tion properties of 8 pulsars over a 16 month period with the Lovell telescope at Jodrell Bank, using a 5-MHz band cen- 3. ANALYSIS teredat408MHz. Theyfoundthattheobservedfluctuations inthespectracouldbeexplainedasrefractivemodulationof We have created and analyzed 2-dimensional dynamic the diffractive scintillation parameters. Bhat et al. (1998) spectra of each 1500-MHz observation for each of the analyzed scintillation parameters for 20 slow pulsars with NANOGravpulsars,followingaproceduresimilartothatde- lowDM(<35pccm−3),usingobservationsata9-MHzfre- scribedinCordes(1986)unlessotherwisestated(e.g. forpart quencybandcenteredat327MHzat10−90epochsspanning ofthedelayuncertaintiesasdescribedineq3below). Ady- ∼100days. Theyreportlargefluctuationsinbothdiffractive namicspectrumdisplayshowtheintensityofthepulsarsignal scintillationtimescaleandbandwidth,withvariationsofafac- varieswithtime,t,andobservingfrequency,ν. Eachpointin torof3−5formostpulsarsintheirsample. thespectrumiscalculatedby Inthispaper,weanalyzethemagnitudeandvariationofin- P (ν,t)−P (ν,t) terstellar scattering delays in regular NANOGrav timing ob- S(ν,t)= on off (1) P (ν) bandpass MonitoringInterstellarScatteringDelays 3 where P is the total power of the observation as a bandpass function of observing frequency, and P and P are the (cid:21)(cid:19) on off pspoewcetirveinly.thTehoeno-na-pnudlsoeffp-aprutlissehpearertdoeffintheedpauslaslelbpirnosfiilnetrhee- (cid:80)(cid:76)(cid:81)(cid:88)(cid:87)(cid:72)(cid:86)(cid:12) (cid:20)(cid:20)(cid:24)(cid:19) summedpulseprofilethathaveanintensity>5%ofthemax- (cid:80)(cid:72)(cid:3)(cid:11) (cid:24) ifieiikhttmnnoianelmtcecnotueohhecwrbmrefeirpaennetnuraioslneadnlapsndtstaeaficoploanrryew.eanszsqnAbinectfueeyiuntlettn,onhwnoetacel6cxfefety4taeiiF.eonmnibrsTntgeeirpso.napr(ml1fAsdeace,.oiraCroowaToelftcFnthwheuah)clie.aliysedranvTeiytgapesehnlnsaidteatdgthahotmhAeenenatridCeeoncsGrrie,Ffsziaoapwgpeuicriiessxeshnecestoaatclhilrlfocasoeuhnc2mtnimhan0ofplesd4ubcuumi8nssacmtcecneaapirtmxtnuivbaeoitlaeemlsn2gtedeif,Drusooeocmpnuaaaevrtnnoouneeiddsrf-r-- (cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:55)(cid:76)(cid:80)(cid:72)(cid:3)(cid:11)(cid:80)(cid:76)(cid:81)(cid:88)(cid:87)(cid:72)(cid:86)(cid:12)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:55)(cid:76) (cid:21)(cid:20)(cid:20)(cid:19)(cid:24)(cid:19)(cid:19)(cid:24)(cid:19)(cid:3)(cid:19)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:20)(cid:3)(cid:3)(cid:3)(cid:21)(cid:3)(cid:3)(cid:19)(cid:3)(cid:3)(cid:19)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:53)(cid:20)(cid:3)(cid:3)(cid:23)(cid:72)(cid:3)(cid:3)(cid:19)(cid:73)(cid:3)(cid:72)(cid:3)(cid:19)(cid:3)(cid:85)(cid:3)(cid:3)(cid:72)(cid:41)(cid:81)(cid:85)(cid:70)(cid:72)(cid:72)(cid:84)(cid:3)(cid:88)(cid:73)(cid:3)(cid:85)(cid:3)(cid:72)(cid:72)(cid:3)(cid:3)(cid:81)(cid:84)(cid:3)(cid:3)(cid:70)(cid:88)(cid:3)(cid:3)(cid:92)(cid:72)(cid:3)(cid:3)(cid:3)(cid:11)(cid:81)(cid:3)(cid:3)(cid:48)(cid:3)(cid:70)(cid:3)(cid:92)(cid:3)(cid:43)(cid:20)(cid:3)(cid:20)(cid:93)(cid:25)(cid:12)(cid:24)(cid:19)(cid:19)(cid:19)(cid:19)(cid:3)(cid:3)(cid:48)(cid:43)(cid:93)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:20)(cid:3)(cid:3)(cid:27)(cid:3)(cid:3)(cid:19)(cid:3)(cid:3)(cid:19)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:27)(cid:19)(cid:19) tered at zero lag, is fitted to the two 1D ACFs to determine thescintillationparameters. Thescintillationtimescale,∆t , FIG.1.— The top panel shows an original dynamic spectrum for d PSRJ1918–0642atMJD56066. Thebottompanelshowsthesamespec- isdefinedasthehalf-widthate−1 ofthesummedfrequency trumafterithasbeenstretchedtoareferencefrequencyof1500MHz,using lagandthescintillationbandwidth,∆νd,isthehalf-widthat ascalingindexofζstretch=4.4. half-maximum of the summed time lag. Most of the obser- vationshavetotalintegrationtimeT < ∆t atourobserving d the four separate bands were then plotted against the center frequencies,andhencewecannotcalculatevaluesfor∆t . d frequencyofthebands,andafunctionoftheformτ = ν−ζ The scatteringdelay, τ , thatarises asa resultof scintilla- d d wasfittedtothedatatocalculatethescalingindex,ζ. Anex- tioncanbecalculatedfrom ampleofascalingindexmeasurementisgiveninFig.2. Not- 2π∆ν τ =C (2) ing that the number of scintles in each sub-band drastically d d 1 changes with observing frequency, which could potentially whereC isaconstantwithvalueranging0.6−1.5(Lambert 1 affect this analysis, we also tried dividing the band up into &Rickett1999)dependingonthegeometryandspectrumof fourpartswiththesamenumberofscintlesperbandinstead theelectrondensityfluctuations. HereweassumeC =1. 1 of a set bandwidth. The result of this exercise agreed well Theuncertaintiesofthescatteringdelaymeasurementscon- withthesetbandwidthmethod,andhencethevaluesreported sist partly of a “finite scintle error” and partly of the uncer- hereareallcalculatedfrom200-MHzsub-bands. taintyoftheleast-squarefitofaGaussiantotheACF,which This method was used to measure scaling indices for 10 areaddedinquadraturetogetthetotaluncertainty. Thefinite of the NANOGrav pulsars. The remaining pulsars all have scintleerroriscalculatedas either too wide scintillation bandwidths to get reliable mea- (cid:15)≈τ N−1/2 surements in a 200-MHz band, or too narrow scintles to get d scint resolved scintillation bandwidths with the 1.5625-MHz fre- ≈τd[(1+ηtT/∆td)(1+ηνB/∆νd)]−1/2 (3) quency channels. However, in an effort to keep the number ofvariablestoaminimum,wechoosetouseascalingindex whereN isthenumberofscintles,T andB aretotalin- scint as predicted in a Kolmogorov medium (ζ = 4.4) in the tegration time and total bandwidth, respectively, and η and stretch t stretchingevenforthesourceswithameasuredζ-value. This η are filling factors in the range 0.1−0.3, here set to 0.2 ν choice is also based on the observation of possible variable (Cordes&Shannon2010). Sincecommonlyforourobserva- scaling indices between epochs (see Sec 5.4), and hence us- tionsT (cid:28) ∆t ,thefirstterminEquation3isapproximately d ingameasuredscalingindexfromoneepochinthestretching equalto1andhence(cid:15)dependsonlyonvaluesrelatedtothe ofanotherepochmaybiasthedynamicspectrumanalysis. In bandwidth. 18 addition,comparisonsshowthattheconsequencesofusinga Apositiveconsequenceofthewidebandwidthobservations fixedζ aresmallerthantheotherstatisticaluncertainties isthelargernumbersofscintlesobservedcomparedtoobser- stretch onthescatteringdelaymeasurements. vations with narrower bandwidths. However, it also implies Hence,eachdynamicspectrumwasstretchedusingascal- large differences in the scintillation bandwidths measured at ing index ζ = 4.4, by rescaling the frequency axis and thelowestpartofthebandcomparedwiththehigherpartof stretch setting the reference frequency, ν , to the center of the theband,whichinturncausesproblemswhencreatingACFs. ref band. Theresultisan800-MHzwidedynamicspectrumwith This is only problematic if the collected data span a large evenly-sizedscintlesthatallrefertothesameobservingfre- range in frequency. Current methods to calculate scintilla- quency. We calculated ACFs of these stretched spectra and tion parameters were developed for narrower bands, and do derived from them the scintillation bandwidths that are used not provide a direct solution to the scaling issue. To resolve intheremainderofthispaper. SeethebottompanelofFig.1 this,wehavedevelopedamethodto“stretch”thespectratoa foranexampleofastretchedspectrum. referencefrequencybasedonhowthescintillationbandwidth scaleswithobservingfrequency. 4. RESULTS To investigate the scaling, we divided the wide bandwidth 4.1. Scalingovertheobservedfrequencyband observationsintofourequallysizedsub-bands.Thescattering delaysinferredfromthemeasuredscintillationbandwidthsof Using the sub-banding method described in Sec.3, we have successfully measured scaling indices for 10 of the 37 18 IfT ≈ ∆td, implyingthatthefirsttermwouldbeequalto1.2, we NANOGrav MSPs. These values are given in Table 2. For wouldbeslightlyunderestimatingNscintandhenceslightlyoverestimating mostofthepulsars,thescalingindexislowerthanthatfora thescatteringdelayuncertainties. Kolmogorov medium (ζ = 4.4). In addition to the variation 4 L.Levinetal. 99666 66644 48481 34448 81884 33131 99888 88888 89899 98889 99998 99999 e 55555 55555 55555 55555 55555 55555 g 66666 66666 66666 66666 66666 66666 n 55555 55555 55555 55555 55555 55555 a ––––– ––––– ––––– ––––– ––––– ––––– Drs)8989727500 5175757575 6523757518 9675776789 8997758975 9675973918 MJ(day559559559552557 563552552552552 552560552552560 559552559563559 559559552559552 559552559561560 dA meσTO(ns)72104638180394 62220733870681 1703319220126 9381445169148 591784196219 2145161566223 d 67 1 91 7 0 3 08 52 ∆τ(ns)6.3–23.20.– –0.53.83.1– 18.2.8–11.11. 20.4.1––12. 45.–7.083.11. 3.688.23.–– s b 0 No 2427284933 1151525150 6432511120 2447251024 3321592549 2367211721 m N 5–1525– 1454– 429–6212 1012––4 26–172432 41116–3 dnt meci Ns 7–1612– 4373– 184–811 45––11 26–56311 64312–63 ) /3 4 4 4 3 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 0 − − − − − − − − − − − − − − − − − − − − − − P.S −2m×10 ×10×10 ×10×10×10×10 ×10×10 ×10×10 ×10×10 ×10 ×10 ×10×10×10 ×10×10×10 ×10 MS Mpc9 62 4846 58 39 27 7 4 633 161 2 V S(k2.–2.2.– 6.1.2.1.– 3.8.–2.1. 2.2.––1. 5.–2.6.2. 1.3.2.–3. A R G 85 6 3 7 ANO ±6.6 3.3±4.3 ±5.6±17.±17. 2.6±14. ±8.6±7.7 ±17.±9.1 ±5.1 2.4 ±14.0.9±5.1 ±9.51.3±5.1 N z) ± ± ± ± ± BLE1ESOF ∆¯νd(MH20.5–9.111.1– 50.366.446.869.6– 9.056.3–21.116.8 17.142.1––12.7 5.2–39.02.314.9 21.62.810.6–2.9 TARTI 6 4 ROPE 2.1 ±5.5±3.9 0.11.31.1 ±4.31.1 2.42.3 4.41.3 ±4.5 ±9.9 1.8±16.3.0 0.8±21.±5.6 P ± ±±± ± ±± ±± ± ± ± G 77 2 7 3 8 31 3 ERIN ¯τd(ns)6.2–14.11.– 3.22.52.84.0– 16.2.6–7.19.4 5.03.8––11. 21.–4.957.9.7 6.144.10.–55. T SCAT 2001 5 00 000 NEτd(ns)2.50.0549166.2 241.20.170.9493 295.8904.121 0.860.02230185.3 4.02301.58.410 1.71302.9610240 1 0 NE20Tref(days)0.280.0292.01.10.45 1.50.150.0550.152.7 1.30.563.20.421.2 0.190.020190.970.72 0.472600.180.960.78 0.364.70.50147.3 00y)8 1 9 2 5 00 7 7 95 1 0 23 22 S14(mJ0.41.10.31.70.2 0.43.21.50.62.2 0.70.73.88.50.6 0.32.81.00.70.4 3.80.61.60.51.4 0.213.2.60.10.8 ) 3 − m 9 5 15 DM(pcc14.34.349.638.818.2 41.59.06.513.652.3 34.518.462.416.033.8 24.03.1152.28.230.6 13.3297.10.438.126.6 18.971.024.3164.104. d o 4 peri(ms)3.054.873.293.068.85 4.645.265.167.993.60 3.153.164.624.575.85 3.754.081.652.724.09 5.362.152.954.987.65 3.881.565.1913.16.13 31008 27903 04473 14663 7462 5 76 Pulsar J0023+092J0030+045J0340+413J0613–020J0645+515 J0931–190J1012+530J1024–071J1455–333J1600–305 J1614–223J1640+222J1643–122J1713+074J1738+033 J1741+135J1744–113J1747–403J1832–083J1853+130 B1855+09J1903+032J1909–374J1910+125J1918–064 J1923+251B1937+21J1944+090J1949+310B1953+29 MonitoringInterstellarScatteringDelays 5 cont.SNANOGMSPCATTERINGPROPERTIESOFRAVSmedNE2001NE2001med∆τστ¯τ∆¯νNNMJDrangePulsarperiodDMSTSMNmobsd1400ddscintTOArefd−3−20/3(ms)(pccm)(mJy)(days)(ns)(ns)(MHz)(kpcm)(ns)(ns)(days)−4±±×10J2010–13235.2222.20.600.576.619.36.46.92.35.121304826.529355275–56584−4±±×10J2017+06032.9023.90.280.533.88.43.421.69.51.485298.79555989–56598−3×10J2043+17112.3820.70.0940.412.01.886.34.23133–6855997–56591−4±±×10J2145–075016.059.05.50.120.532.80.747.813.31.749483.221455275–56584−4±±×10J2214+30003.1222.60.530.483.23.13.423.017.91.2672510.116055989–56598 −4±±×10J2302+44425.1913.80.900.220.8414.12.79.92.43.515102612.263755972–56586−4±±×10J2317+14393.4521.90.800.271.93.01.041.811.81.463192.18156100–56599 NE2001τNotes.Fluxdensityvaluesat1400MHz(S)areaveragevaluesfromthecalibratedtimingobservations.ScatteringdelaysfromtheNE2001model()havebeenscaledtoan1400dNE2001observingfrequencyof1500MHz,andtherefractivetimescales(T)arecalculatedfromthescaledvaluesofthescintillationbandwidthandtimescaleestimatedwithinthemodel.ref¯τ∆¯νTheweightedaverageofthescatteringdelayisgivenasandtheweightedaverageofthemeasuredscintillationbandwidthisgivenas,wheretheerrorisrepresentedbythestandarddddeviationoftheweightedmeaninbothcases.Themaximumvariationofthescatteringdelayiscalculatedasthemaximummeasuredscatteringdelayminustheminimummeasured∆τscatteringdelayandisheregivenas.Thescatteringmeasure(SM)iscalculatedthrougheq9,usingdistancesestimatedfromtheNE2001model.Thenumberofepochsincludedind¯τisgivenasN,whilethetotalnumberofepochsanalysedisgivenasN.ThenumberofscintlesineachoftheNepochsarecalculatedthroughtheexpressionforNgivenmmscintdobsmedmedσinEquation3andthemediannumberofscintlesisgivenasN.ThemedianTOAuncertainty()isgivenastheaveragedresidualerrorforthecombinedband,withvaluesfromscintTOAArzoumanianetal.(2015). 6 L.Levinetal. 11200 MHz, (cid:54)(cid:105)d=5.2 MHz 1 1400 MHz, (cid:54)(cid:105)d=6.6 MHz TABLE2 MEASUREDSCATTERINGDELAYSCALINGINDICES. 0.8 0.8 0.6 0.6 Pulsar ζ MJD Nsubband scint CF 0.4 0.4 J0613–0200 2.8(2) 55275 11 A 0.2 0.2 1.2(8) 56130 8 0 0 J1614–2230 2.6(9) 55269 6 -0.2 -0.2 6.3(4) 55304 9 -100 -50 0 50 100 -100 -50 0 50 100 2.5(4) 55892 13 11600 MHz, (cid:54)(cid:105)d=16.9 MHz 1 1800 MHz, (cid:54)(cid:105)d=16.5 MHz 2(2) 56288 13 J1713+0747 1.1(5) 55949 5 0.8 0.8 4.1(2) 56299 4 0.6 0.6 F 0.4 0.4 3.7(5) 56391 3 C A 0.2 0.2 B1855+09 3.8(3) 56294 10 0 0 J1910+1256 2.3(6) 56319 29 -0.2 -0.2 J1918–0642 2.4(6) 55463 5 -100 -50 0 50 100 -100 -50 0 50 100 3(1) 56066 5 Frequency [MHz] Frequency [MHz] B1937+21 1.3(3) 56131 11 2.7(5) 56403 13 100 3(1) 56451 10 s] (cid:99) = 3.2 +_ 1.0 y [n 3(1) 56492 24 ela 1.8(1) 56548 8 g D 10 4.9(8) 56593 26 n atteri J1944+0907 3(2) 56018 7 Sc J2010–1323 3.9(4) 56095 10 1 1000 1200 1400 1600 1800 2000 4.4(1) 56250 10 Observing frequency [MHz] 1.9(4) 56352 9 1(1) 56472 9 FIG.2.— PSRJ1918–0642 scattering delay scalings over the frequency band for an observation from MJD 56066. The four top panels show the 3.1(5) 56523 23 autocorrelationfunctionofeach200-MHzsubbandasasolidlineandthe J2145–0750 3.1(2) 56195 6 Gaussianfitasadashedline. Thebest-fitvalueforeachscintillationband- width,∆νd,isconvertedintoascatteringdelayandplottedinthebottom panel,togetherwiththebestfitofthescalingindex,ζ,asadashedline. Notes. Scattering delay scaling over frequency band, where τd ∝ ν−ζ. The indices are measured at the given observing epoch, and the numbers in parenthesis are the errors on the last given digit. between different pulsars, the scaling index for a particular Nsubbandrepresentstheaveragenumberofscintlesineachsubband, pulsarmaynotnecessarilybeconstantintimeandideallyalso scint calculatedthroughtheexpressiongiveninequation3. this variation should be monitored. However, it has proven difficult to measure scaling indices at most epochs because scintlesarenotvisibleinallofthesub-bands,orbecausera- (cid:20)(cid:24) dbiaondf.reOqunelyncayfienwteroffertehnecpeuilssasresvhearevleymauffleticptilnegscpaalrintsgoifndthexe (cid:80)(cid:76)(cid:81)(cid:88)(cid:87)(cid:72)(cid:86)(cid:12) (cid:20)(cid:19) measurements(forfurtherdiscussion,seeSection5.4). (cid:80)(cid:72)(cid:3)(cid:11) (cid:24) (cid:55)(cid:76) aitmnerreoIiTndngategeiblvrldesfeotenelr1laal.fyasrretaFsehnoce4dear.ltw2etrc.eeceorftiSmirrgncoahpgacntattseditrvdeeiisernlaoainvtyntighes,mre(daveτ¯egIasdSlleca)uMayfeoloesvvrs(eaCfarrogloiraliavrlNdtlteiheAonoesnbNb&spyOerreGLtvdhiarienaczgvtiNeopdeEup22slo0s0cc0aa0h2rt1ss-) (cid:55)(cid:76)(cid:80)(cid:72)(cid:3)(cid:11)(cid:80)(cid:76)(cid:81)(cid:88)(cid:87)(cid:72)(cid:86)(cid:12)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3) (cid:20)(cid:19)(cid:27)(cid:23)(cid:21)(cid:3)(cid:19)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:53)(cid:72)(cid:73)(cid:72)(cid:85)(cid:72)(cid:81)(cid:70)(cid:72)(cid:3)(cid:73)(cid:85)(cid:72)(cid:84)(cid:88)(cid:72)(cid:81)(cid:70)(cid:92)(cid:3)(cid:20)(cid:24)(cid:19)(cid:19)(cid:3)(cid:48)(cid:43)(cid:93)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:26)(cid:19)(cid:19) athree mlisatxedimfuomr avllartihaetiopnulmsaeras.suIrnedad(∆diτtion=, tτhe table−iτnclude)s, (cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3) (cid:19)(cid:3)(cid:19)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:53)(cid:72)(cid:73)(cid:72)(cid:85)(cid:72)(cid:81)(cid:70)(cid:72)(cid:3)(cid:73)(cid:85)(cid:72)(cid:84)(cid:88)(cid:72)(cid:81)(cid:70)(cid:92)(cid:3)(cid:20)(cid:24)(cid:19)(cid:19)(cid:3)(cid:48)(cid:43)(cid:93)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:26)(cid:19)(cid:19) d d;max d;min togetherwiththemedianTOAuncertaintyresultingfromtim- FIG.3.— Examplesofdynamicspectrawithnarrowandwidescintilla- ing.Comparingthesevaluescangiveinsightintothefeasibil- tionbandwidths.BothobservationsarecollectedwiththePUPPIbackendat ityofcorrectingthetimingresidualsforscatteringdelaysfor Arecibo,andhavebeenstretchedtoareferencefrequencyof1500MHz.The toppanelshowsanobservationofPSRJ1910+1256atMJD56519,andthe aparticularpulsar(seeSec. 5.5formoredetails). bottompanelisanobservationofJ2317+1439atMJD56100. Two typical observations are shown in Fig.3, with the top dynamic spectrum displaying narrow scintles for PSRJ1910+1256 with ∆νd ≈ 3MHz and the bottom dy- atleasttenτd measurementsareplottedalongwiththeirDM namic spectrum showing wide scintles for PSRJ2317+1439 variations. with∆ν ≈ 34MHz. Examplesofscatteringdelayvariabil- d itycanbefoundinFig.4,whereallNANOGravpulsarswith 5. DISCUSSION MonitoringInterstellarScatteringDelays 7 3450 J0340+4130 (r = 0.57; mb = 0.29) 3305 J0613−0200 (r = −0.48; mb = 0.29) 3305 J1614−2230 (r = 0.14; mb = 0.29) 30 25 25 [ns](cid:111)d 11220505 [ns](cid:111)d 112050 [ns](cid:111)d 112050 5 5 5 −3−3DM [10 pc cm] − 00−. .15015 0 −−− 000000... ...6420246 0 −3−3DM [10 pc cm] −− 0000.. ..84048 0 (cid:54) 56000 56100 56200 56300 56400 56500 55400 55600 55800 56000 56200 56400 56600 (cid:54) 55400 55600 55800 56000 56200 56400 56600 MJD MJD MJD 20 J1713+0747 (r = 0.068; mb = 0.32) 20 J1738+0333 (r = 0.11; mb = 0.58) 2350 J1741+1351 (r = 0.27; mb = 0.67) [ns](cid:111)d 1105 [ns](cid:111)d 1105 [ns](cid:111)d 112050 5 5 5 −3−3 DM [10 pc cm](cid:54) −− 0000.. ..21012 0 55400 55600 55800 56000 56200 56400 56600 −3−3 DM [10 pc cm](cid:54) − 00−. . 15015 506000 56100 56200 56300 56400 56500 −3−3 DM [10 pc cm](cid:54) −− 0000.. ..42024 0 56100 56200 56300 56400 56500 56600 MJD MJD MJD 1102 J1744−1134 (r = 0.31; mb = 0.14) 6700 B1855+09 (r = −0.31; mb = 0.43) 1250 J1909−3744 (r = −0.13; mb = 0.08) 8 50 [ns](cid:111)d 46 [ns](cid:111)d 3400 [ns](cid:111)d 10 20 5 2 10 −3−3 DM [10 pc cm](cid:54) −− 0000.. ..42024 0 55600 55800 56000 56200 56400 56600 −3−3 DM [10 pc cm](cid:54) −−− 000000... ...6420246 0 56000 56100 56200 56300 56400 56500 56600 −3−3 DM [10 pc cm](cid:54) −− 0000.. ..42024 0 55600 55800 56000 56200 56400 MJD MJD MJD 112400 J1910+1256 (r = −0.44; mb = 0.35) 25 J1918−0642 (r = 0.14; mb = 0.34) 112400 B1937+21 (r = 0.029; mb = 0.40) 100 20 100 [ns](cid:111)d 468000 [ns](cid:111)d 1105 [ns](cid:111)d 468000 20 5 20 −3−3DM [10 pc cm]−− 21012 0 −3−3DM [10 pc cm] − 00−. .15015 0 −3−3DM [10 pc cm] − 00−. .15015 0 (cid:54) (cid:54) (cid:54) 56000 56100 56200 56300 56400 56500 56600 55400 55600 55800 56000 56200 56400 56000 56100 56200 56300 56400 56500 56600 MJD MJD MJD 3305 J1944+0907 (r = −0.21; mb = 0.47) 4500 J2010−1323 (r = 0.37; mb = 0.42) 2350 J2302+4442 (r = 0.11; mb = 0.24) 25 20 [ns](cid:111)d 112050 [ns](cid:111)d 2300 [ns](cid:111)d 1105 5 10 5 −3−3DM [10 pc cm] − 00−. .15015 0 −3−3DM [10 pc cm] − 00−. .15015 0 −3−3DM [10 pc cm] − 00−. .15015 0 (cid:54) (cid:54) (cid:54) 56000 56100 56200 56300 56400 56500 56600 55400 55600 55800 56000 56200 56400 56100 56150 56200 56250 56300 56350 56400 56450 56500 MJD MJD MJD FIG.4.—Scatteringdelayvariations(toppanels)andDMvariations(bottompanels)forpulsarswithatleasttenscatteringdelaymeasurements.AllDMvalues measuredwithinthesametimespanforeachpulsarareincluded,evenforepochswherenoscatteringdelaymeasurementwaspossible. TheDMvaluesare measuredindatafromatleasttwoseparatefrequencybandsinthe9-yeardataset. Foreachpulsar,thecorrelationcoefficient,r,betweenthetwovariationsis givenintheparenthesesinthetoppanel. Inaddition,thenoise-correctedmodulationindexofthescintillationbandwidthisgivenasmbforeachpulsar(see Equations4and5). 8 L.Levinetal. TABLE3 PREVIOUSLYPUBLISHEDSCINTILLATIONPARAMETERS. Thiswork NE2001 Previouslypublishedvalues Pulsar τ¯ τNE2001 τ ν Ref. d d d;1500MHz (ns) (ns) (ns) (MHz) J0030+0451 – 0.055 0.12 435 Nicastroetal.(2001) J0613–0200 11.7±3.9 16 61.2 1369 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 97.0∗ 1500∗ Keithetal.(2013) J1024–0719 2.8±1.3 0.17 0.34 685 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 0.59∗ 1500∗ Keithetal.(2013) J1455–3330 4.0±1.1 0.94 0.51 436 Johnstonetal.(1998) J1600–3053 – 93 1768∗ 1500∗ Keithetal.(2013) (cid:113) (cid:113) (cid:113) 1072 3100 Colesetal.(2010) J1640+2224 2.6±1.1 5.8 3.3 430 Bogdanovetal.(2002) J1643–1224 – 90 7234∗ 1500∗ Keithetal.(2013) (cid:113) (cid:113) (cid:113) 2918 3100 Colesetal.(2010) J1713+0747 7.1±2.4 4.1 1.1 430 Bogdanovetal.(2002) (cid:113) (cid:113) (cid:113) 0.48 436 Johnstonetal.(1998) (cid:113) (cid:113) (cid:113) 1.1 685 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 6.6 1500∗ Keithetal.(2013) J1744–1144 3.8±1.3 0.020 0.52 436 Johnstonetal.(1998) (cid:113) (cid:113) (cid:113) 1.87 660 Johnstonetal.(1998) (cid:113) (cid:113) (cid:113) 0.40 685 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 2.7∗ 1500∗ Keithetal.(2013) B1855+09 21.3±9.9 4.0 6.5 430 Deweyetal.(1988) (cid:113) (cid:113) (cid:113) 1.1 685 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 13.0 1369 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 28.9∗ 1500∗ Keithetal.(2013) J1903+0327 – 2.3×105 9.3×104 1400 Championetal.(2008) J1909–3744 4.9±1.8 1.5 0.68 685 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 4.3∗ 1500∗ Keithetal.(2013) B1937+21 44.3±21.4 130 127 320 Cordesetal.(1990) (cid:113) (cid:113) (cid:113) 155 430 Cordesetal.(1990) (cid:113) (cid:113) (cid:113) 48.4 1369 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 127 1400 Cordesetal.(1990) (cid:113) (cid:113) (cid:113) 132∗ 1500∗ Keithetal.(2013) J2145-0750 2.8±0.7 0.53 0.47 436 Johnstonetal.(1998) (cid:113) (cid:113) (cid:113) 0.45 685 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 0.82∗ 1500∗ Keithetal.(2013) J2317+1439 3.0±1.0 1.9 1.4 436 Johnstonetal.(1998) Notes. Thepublishedvaluesarereportedatthegivenobservingfrequency(ν)andhere convertedtoscatteringdelays(τ )at1500MHzusingascalingindexofζ =4.4. d;1500MHz Forreference,scatteringdelayvaluesfromthisworkisincludedasτ¯ andscaledvalues d fromtheNE2001aregivenasτNE2001. d ∗Onlyanalreadyscaledvalueisreportedintheoriginalpublication. MonitoringInterstellarScatteringDelays 9 Previous work on scintillation properties of pulsars has 1000 been carried out at various radio frequencies. To compare the scattering delays in this paper with previously published values, we need to scale all values to a common observing s] n 100 frequency. Thisintroduceslargeuncertainties,sincethecom- ay [ parison will be largely dependent on the chosen scaling law del g and,asshowninthispaper,themeasuredscalingindicesare n eri 10 not only different for different pulsars and hence observing att c directions,butmayalsovarywithtime(asdiscussedinmore e s detailinSec5.4).Nevertheless,acomparisonwithpreviously ag er 1 publishedvaluesislistedinTable3,byscalingthepublished v A scattering delays to their value at an observing frequency of 1500MHz,usingascalingindexζ =4.4. Insomecases, thepreviouslypublishedvaluesshowlarge 0.1 0.01 0.1 1 10 100 1000 discrepancieswiththevaluesinthiswork. Colesetal.(2010) NE2001 model scattering delay [ns] and Keith et al. (2013) both list scintillation parameters for millisecondpulsarsintheParkesPulsarTimingArray, some FIG.5.—ComparisonofaveragescatteringdelaytotheestimatedNE2001 model values. The NE2001 values have been scaled to an observing fre- ofwhicharealsoincludedintheNANOGravarray. Theval- quencyof1500MHz,usingascalingindexζ = 4.4. Thetwohorizontal uesinKeithetal. havealreadybeenscaledtoacommonob- dottedlinesmarkmaximumandminimumscatteringdelaysthatcanbemea- serving frequency of 1500MHz, while Coles et al. list the suredfromthedata.Theselimitsarecalculatedfromthefrequencyresolution actual frequency of each observation. Some of the values andthetotalbandwidthofthedatarespectively,usingthedefinitionofthe scintillationbandwidthasthehalf-widthathalf-maximumoftheGaussianfit from Coles et al. were measured at an observing frequency totheACF.Thediagonallinerepresentsequalityofmodelandmeasurement. ν =1369MHz,andthesevaluesagreebetterwithourmea- obs surements than the rest of the pulsars in Coles et al., which its of the data, and hence it is not surprising that no scatter- suggeststhatthechoiceofscalingindexmaybeanissue.An- ing delays have been measured for these pulsars. One ex- otherexplanationforthediscrepancyisthevariationofscat- ception is PSRJ0645+5158, which has τ = 6.2ns teringdelayovertime(seeFig.4),whichisalsoobservedby d;NE2001 at1500MHz. Manualinspectionofthedynamicspectraob- Colesetal. Similarly, Bhatetal.(1998)observedvariations tainedforthispulsarshowsthatinthefewobservationswith ofthescintillationbandwidthofafactorof3−5whenanalyz- scintlesstrongenoughtobedetected,radiointerferencecon- ing scintillation parameters of slow low-DM pulsars. In the tamination caused errors in the ACF calculation. By eye, datapresentedhere,weobservedelayswithavariationofup we estimate a scintillation bandwidth of ν ≈ 100MHz, toanorderofmagnitude. d In the cases where the published values are τ (cid:46)1ns, the which corresponds to τd ≈ 1.5ns. The other exception is d PSRJ1832–0836,withτ =18nsat1500MHz. This valuesmeasuredinthisworkarealwayslarger. Thisislikely d;NE2001 pulsarisarecentadditiontotheNANOGravarray, andonly due to the limited bandwidth of the data, which allows only 10observationsat1500MHzareincludedinthe9-yeardata theobservationswithhigherscatteringdelayvaluesinthedis- release. Even by manually inspecting the dynamic spectra tribution to be resolved. Many of the values published be- forPSRJ1832−0836,noscintlesaredetected,whichislikely fore 2001 are very similar to the corresponding value from duetothelowfluxdensityofthesignal. theNE2001model. Thisisexpected,sinceinthecreationof Forthepulsarswithτ (cid:28) 1ns, themeasuredscat- theelectrondensitymodel,asmanyscatteringdelaymeasure- d;NE2001 teringdelayismuchlargerthanthemodeldelay. Itispossi- mentsaspossiblewereincluded(Cordes&Lazio2002)and ble that there is an underlying structure of wide scintles that hencetheseearlymeasurementswerelikelyusedasinputto are too wide to detect in this dataset, and what is measured themodel. herearesmallmodulationsontopofthelargerstructure. An- 5.1. ComparisonwiththeNE2001model otherpossibilityisthattheNE2001modellargelyunderesti- mates the amount of scattering in the direction of these pul- Themostcomprehensiveandfrequentlyusedmodelofthe sars,whichareallathighGalacticlatitudeswherethemodel freeelectronsintheGalaxyistheNE2001model(Cordes& isknowntohavelargeuncertainties(e.g.Gaensleretal.2008; Lazio 2002). In addition to predicting distances to pulsars Chatterjee et al. 2009). For the cases where the τ - fromtheirDMvalues,thismodelalsoestimatesthescintilla- d;NE2001 valuesarecloseto1ns,wemayonlybedetectingthehighest tionpropertiesfromapositionandaDMvalue.Thescattering values in the distribution of delays. Since the bandwidth of delayspredictedfortheNANOGravpulsarsbythemodelare the observations is limited, the true mean τ -values may be listedinTable1. d lowerthanwhatwecanmeasure. Asimilarargumentcanbe These values have also been plotted against the average applied to the τ -values close to the maximum delay measured scattering delays in Fig 5. The horizontal dotted d;NE2001 limit, where the limited frequency resolution would permit linesshowtheminimumandmaximummeasurabledelaysin detection of only the lower parts of the delay distributions. the data, while the diagonal line shows equality of the mea- In addition, the delays in particular observations may be un- surement to the model. In general, the measured values are derestimatedforpulsarsclosetothemaximumlimit, sincea slightlyhigherthanthepredictions.Itisknownthatthemodel strong scintle with true ∆ν smaller than the channel band- predictionshavelargeassociateduncertainties,inparticularat d widthwouldstillbemeasuredasbeingonechannelwide. higherGalacticlatitudes,wherethenumbersofsourceswith knowndistancesandDMarelow. 5.2. Interstellarmediumvariations Forsomeofthepulsars,nomeasurementwaspossible,e.g., due to too narrow or too wide scintles. All but two of these The measured values of τ are plotted in Fig.4 as a func- d non-detectionsarepredictedtolieclosetothedetectionlim- tionofobservingdayforallpulsarswithatleast10measured 10 L.Levinetal. scattering delay values. To analyze the delay variability we indexforthescintillationbandwidthisgivenby havecalculatedamodulationindexforthescintillationband- widthforeachpulsar,definedastheRMSfluctuationsof∆νd mb;Kolmogorov ≈0.202(Cn2)−1/5νo3b/s5D−2/5 (10) dividedbyitsaveragevalue(Bhatetal.1999)andgivenby where ν is the observing frequency in GHz, D is the dis- obs m = 1 (cid:32) 1 N(cid:88)obs(∆ν −(cid:104)∆ν (cid:105))2(cid:33)1/2 tuannictseotof t1h0e−p4umls−a2r0i/n3k(pBchaatndetCan2l.i1s9t9h9e)s.caFtoterrainKgostlrmenoggtohroivn b;measured (cid:104)∆νd(cid:105) Nobs−1 d,i d spectrum, i=1 (4) C2 =0.002∆ν−5/6D−11/6ν11/3m−20/3 (11) where (cid:104)∆νd(cid:105) is the average scintillation bandwidth, Nobs is n d obs the number of measurements, and ∆νd,i is the scintillation where∆νdisgiveninMHz,Disgiveninkpcandtheobserv- bandwidth at the ith epoch. The measurement error on ∆ν ing frequency, ν , is given in GHz (Rickett 1977; Cordes obs will induce an apparent increase in the modulation indices, 1986). Calculatingthetheoreticalmodulationindicesforthe that needs to be corrected for. Following Bhat et al. (1999), pulsars in Fig.4, using pulsar distances from parallax mea- wecalculatecorrectedmodulationindicesas surements where available19 and otherwise as given by the m2 =m2 −m2 (5) NE2001model(Cordes&Lazio2002),resultsinvaluesrang- b;corrected b;measured b;noise ing 0.15 ≤ m ≤ 0.20. If the density spectrum is not Kol- b wheretheerrorinducedmodulationindex,mb;noise,iscalcu- mogorovinshape, butratherhasβ > 11/3, thefluctuations lated as the typical uncertainty in ∆νd. The corrected val- areexpectedtobeindependentoftheobservingwavelength, ues of mb are given in the upper panel for each pulsar in butgivelargermodulationthanaKolmogorovspectrum. For Fig.4. Fortwoofthepulsars(J1744–1124andJ1909–3744), β = 4.0thetheoreticalm ≈ 0.35andforβ = 4.3thetheo- b mb;noise ≈ mb;measured. Both of these pulsars have only a reticalmb ≈0.57(Romanietal.1986;Bhatetal.1999). small numbers of scintles in each observation, which con- Comparing the corrected modulation indices with the the- tributes to the large uncertainty in the scattering delay mea- oretical ones, all of the measured m -values are larger than b surements,asseeninFig.4,andhenceareexcludedfromfur- those predicted for a Kolmogorov medium. This does how- ther modulation index analyses. For the remaining pulsars, ever not necessarily mean that the density spectrum is not mb;noise (cid:28) mb;measured, so the corrected modulation is ap- Kolmogorov. Instead, if the ISM in these directions is not proximatelyequaltothemeasuredmodulation. well described by a thin screen, but rather as an extended These modulations of the scintillation bandwidths, and Kolmogorovmedium,thatwouldexplainthelargerobserved hence the scattering delays, could originate from refractive modulation. scintillation effects. The theoreticalmodel of the observable Wecanalsoapproachthisdiscussionfromtheotherdirec- modulationeffectsduetorefractivescintillationarehighlyde- tion, by looking at the measured scattering delay frequency pendent on the form of the density spectrum, which can be scaling. ManyofthemeasuredscalingindicesinTable2are writtenas smaller than that expected for a Kolmogorov medium, even Pδne(κ)=Cn2κ−β (6) withintheerrors,andsimilartrendshavebeenshowninpre- vious work by other authors. In an effort to measure pulse for values of the spatial wavenumber, κ, between inner and scattering broadening of slow pulsars, Bhat et al. (2004) ob- outercutoffsinspatialscalesizesofthedensityirregularities served a number of pulsars at a minimum of two different in the ISM (Armstrong et al. 1995). Here C2 represents the n frequencies with the Arecibo telescope. Indeed, for most of scatteringstrengthandβ isthedensityspectralindex,which their sources, they measured a scaling index ζ < 4.4. By foraKolmogorovspectrumisequalto11/3. Forβ < 4, the usingtheirresultstogetherwithpreviouslypublishedvalues, correspondingscalingovertheobservedfrequencybandis Bhat et al. inferred an empirical frequency scaling index of 2β 3.9±0.2. Following the discussion above, the smaller ob- ζ = (7) served scaling indices agree well with the larger modulation β−2 observedinourdata. and hence for a Komogorov medium, ζ = 4.4 (Cordes & Shannon2010). Thescatteringmeasureisdefinedas 5.3. DispersionMeasurevariations TheonlyISMeffectusuallycorrectedforinhigh-precision (cid:90) D SM= C2ds (8) pulsar timing is the DM and its variations. Since dispersion n and scintillation both arise from the same interstellar struc- 0 tures in each observation, itis temptingto assumea correla- whichcanbesimplifiedto tionbetweenthevariationsofthetwodelays. Wehavecom- (cid:16)τ (cid:17)5/6 pared the scattering delay and DM variations by calculating SM=292 d ν11/3 (9) D GHz correlationcoefficientsforallpulsarsinFig.4. TheDMval- uesaremeasuredusingtheDMXmethodinthepulsartiming with units kpc m−20/3 if the scattering delay, τd, is given in software TEMPO20. In this procedure, the DM(t) function is seconds and the distance, D, is given in kpc (Cordes et al. treated as piecewise constant, and an independent DM value 1991). isfittedforoversuccessive14-daywindows, inasimultane- Romanietal.(1986)presentedatheoryfortherefractiveef- ous fit with all other timing model parameters. This is sim- fectsinafewspecialcasesusingpower-lawformsofdensity ilar to the procedure used in Arzoumanian et al. (2015), ex- spectra with different spectral indices. In the case of a Kol- mogorovspectrumandconsideringscatteringinathinscreen 19 With values as given in the ATNF pulsar catalogue: halfwaybetweentheobserverandthepulsar,themodulation http://www.atnf.csiro.au/research/pulsar/psrcat/ 20http://tempo.sourceforge.net

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DRAFTVERSIONJANUARY19,2016 PreprinttypesetusingLATEXstyleemulateapjv.05/12/14 THENANOGRAVNINE-YEARDATASET:MONITORINGINTERSTELLARSCATTERINGDELAYS LINALEVIN1,2,MAURAA.MCLAUGHLIN1,GLENNJONES3,JAMESM.CORDES4,DANIELR.STINEBRING5,SHAMICHATTERJEE4, TIMOTHYDOLCH4,6,MICHAELT.LAM4,T.JOSEPHW.LAZIO7,NIPUNIPALLIYAGURU1,ZAVENARZOUMANIAN8, KATHRYNCROWTER9,PAULB.DEMOREST10,JUSTINA.ELLIS7,ROBERTD.FERDMAN11,EMMANUELFONSECA9, MARJORIEE.GONZALEZ9,12,MEGANL.JONES1,DAVIDJ.NICE13,TIMOTHYT.PENNUCCI14,SCOTTM.RANSOM15, INGRIDH.STAIRS9,11,KEVINSTOVALL16,JOSEPHK.SWIGGUM1,WEIWEIZHU9,17 DraftversionJanuary19,2016 ABSTRACT 6 Wereportonanefforttoextractandmonitorinterstellarscintillationparametersinregulartimingobserva- 1 tions collected for the NANOGrav pulsar timing array. Scattering delays are measured by creating dynamic 0 spectra for each pulsar and observing epoch of wide-band observations centered near 1500MHz and carried 2 outattheGreenBankTelescopeandtheAreciboObservatory. The∼800-MHzwidefrequencybandsimply n dramaticchangesinscintillationbandwidthacrossthebandpass,andastretchingroutinehasbeenincludedto a accountforthisscaling. Formostofthe10pulsarsforwhichthescalinghasbeenmeasured,thebandwidths J scalewithfrequencylesssteeplythanexpectedforaKolmogorovmedium. Wefindestimatedscatteringdelay 8 valuesthatvarywithtimebyuptoanorderofmagnitude. Themeanmeasuredscatteringdelaysaresimilarto 1 previouslypublishedvaluesandslightlyhigherthanpredictedbyinterstellarmediummodels. Weinvestigate the possibility of increasing the timing precision by mitigating timing errors introduced by the scattering de- ] lays. Formostofthepulsars,theuncertaintyinthetimeofarrivalofasingletimingpointismuchlargerthan E themaximumvariationofthescatteringdelay,suggestingthatdiffractivescintillationremainsonlyanegligible H partoftheirnoisebudget. h. Subjectheadings:methods: dataanalysis–stars: pulsars–ISM:general–gravitationalwaves p - o 1. INTRODUCTION is dispersion, which occurs when the radio wave propagates r throughacolumnoffreeelectronsintheISMandischarac- t The interstellar medium (ISM) consists partly of ionized s plasma,whichinteractswithpulsarradioemission. Thishas terizedbyafrequency-dependenttimedelay. Thedelaysare a proportional to DM × ν−2, where the dispersion measure, several effects on pulsar signals, and will impact the times [ DM,istheintegratedcolumndensityoffreeelectronsandν of arrival (TOAs) of the pulses at Earth. One such effect 1 istheobservingfrequency. SincethepulsarandtheISMhave v 1DepartmentofPhysicsandAstronomy,WestVirginiaUniversity,P.O. differentrelativevelocities,theDMofapulsarisnotconstant 0 Box6315,Morgantown,WV26505,USA in time. By observing pulsars at two or more separate fre- 9 2JodrellBankCentreforAstrophysics,AlanTuringBuilding,School quencies,theDMvariationscanbetrackedandcorrectedfor 4 ofPhysicsandAstronomy,TheUniversityofManchester,OxfordRoad, inthedata(e.g.,Demorestetal.2013;Keithetal.2013;Lee 4 Manchester,M139PL,UK etal.2014). 3DepartmentofPhysics,ColumbiaUniversity,550W.120thSt.,New 0 Incontrasttodispersion,whichwouldbepresentinacom- York,NY10027,USA 1. 4Department of Astronomy, Cornell University, Ithaca, NY 14853, pletely homogeneous medium, scattering arises when radio USA wavestravelthroughaninhomogeneousmedium. Multi-path 0 5DepartmentofPhysicsandAstronomy,OberlinCollege,Oberlin,OH scattering manifests itself in several ways, including diffrac- 6 44074,USA 1 6DepartmentofPhysics,HillsdaleCollege,33E.CollegeStreet,Hills- tiveintensityscintillationsandpulsebroadening. Diffractive : dale,Michigan49242,USA scintillation effects were first observed in pulsars by Lyne v 7Jet Propulsion Laboratory, California Institute of Technology, 4800 & Rickett (1968), and are the effects in focus in this paper. Xi OakGroveDrive,Pasadena,CA91106,USA The basic model usually used to describe diffractive scintil- 8CenterforResearchandExplorationinSpaceScienceandTechnology lation assumes that the ISM is a thin screen of plasma, lo- r andX-RayAstrophysicsLaboratory,NASAGoddardSpaceFlightCenter, a Code662,Greenbelt,MD20771,USA cated between the pulsar and the observer (Scheuer 1968). 9Department of Physics and Astronomy, University of British Asthesignalpropagatesthroughthescreen,inhomogeneities Columbia,6224AgriculturalRoad,Vancouver,BCV6T1Z1,Canada in the plasma introduce phase perturbations that are corre- 10NationalRadioAstronomyObservatory,P.O.Box0,Socorro,NM, lated over a scintillation bandwidth, which is inversely pro- 87801,USA 11DepartmentofPhysics,McGillUniversity,3600rueUniversite,Mon- portionaltothescatteringtimescale. Theseperturbationsare treal,QCH3A2T8,Canada alsoknownasscatteringdelays. Thescintillationpattern,and 12DepartmentofNuclearMedicine,VancouverCoastalHealthAuthor- hence the scattering timescale, of a pulsar can change dras- ity,Vancouver,BCV5Z1M9,Canada tically over time (Hemberger & Stinebring 2008). Similar 13DepartmentofPhysics,LafayetteCollege,Easton,PA18042,USA to the case of DM variations, the relative velocities of the 14UniversityofVirginia,DepartmentofAstronomy,P.O.Box400325 pulsar and the ISM give rise to the time variable scattering Charlottesville,VA22904-4325,USA 15NationalRadioAstronomyObservatory,520EdgemontRoad,Char- delays. The scaling of the scintillation parameters with fre- lottesville,VA22903,USA quency is often described as that of a Kolmogorov medium, 16DepartmentofPhysicsandAstronomy,UniversityofNewMexico, withthescintillationbandwidth,∆ν ∝ν4.4,andthescintil- NM87131,USA d 17Max-Planck-Institutfu¨rGravitationsphysik,AlbertEinsteinInstitut, lation timescale, ∆td ∝ ν1.2 (Cordes et al. 1985), although AmMu¨lenber1,14476Golm,Germany ithasbeenshownthatsomesourceshavescalingindicesthat 2 L.Levinetal. deviatefromthese(e.g.,Lo¨hmeretal.2004;Bhatetal.2004). servations to investigate the effect of interstellar scintillation These observed deviations may not necessarily be indicative anditscontributiontothetotalnoisebudgetforthisimportant ofanon-Kolmogorovspectrum,butmaybeduetothesizeof setofpulsars. the dominant scattering region transverse to the line of sight (Cordes&Lazio2001). 2. DATA In a Pulsar Timing Array (PTA), millisecond pulsars (MSPs) are observed in an effort to detect nanohertz gravi- This paper makes use of data from regular NANOGrav tationalwaves. TheNorthAmericanNanohertzObservatory timing observations. The data are all included in the latest forGravitationalWaves(NANOGrav)usesthe100-mGreen NANOGrav data release (9-year dataset; Arzoumanian et al. Bank Telescope (GBT) and the 300-m Arecibo Observatory 2015),andhereweuseasub-setspanning∼3.7yearsfordata (AO) to observe ∼40 MSPs every 7−28 days. To succeed fromGBTand∼1.7yearsfordatafromAO.TheexactMJD in detecting gravitational waves, it is necessary to obtain as range of the data used for each pulsar is shown in Table1, high a timing precision as possible, over a long time span. together with observational properties of the pulsar as well The achievable timing precision of MSPs is continually in- as of the ISM along the line-of-sight to the pulsar. We have creasingwithlongerdatasetsandimprovedinstrumentation. focused on observations carried out at a center frequency of This makes it ever more important to understand all non- ∼1500MHzfor20pulsarsatGBTand19pulsarsatAO.Two gravitationalwaveeffects,toimprovethesensitivityofPTAs ofthepulsars(J1713+0747andB1937+21)areobservedwith togravitationalwaves. bothtelescopes. Asdescribedabove,theperturbationscausedbyinterstellar AtGBT,thedataarecollectedwiththeFPGA-basedspec- scintillation,aswellastheperturbationsfromDMvariations, trometerGUPPI(GreenBankUltimatePulsarProcessingIn- limitthetimingprecisionforallpulsars.Somepulsarswillbe strument)usingcoherentdedispersiontechniques. Theobser- moreaffectedthanothers,however,dependingontheproper- vationsarecarriedoutoverafrequencybandof800MHzcen- tiesoftheISMalongtheirlineofsight. MostMSPsinPTAs teredat1500MHz,dividedinto1.5625-MHzwidefrequency havebeenchosenpartlyduetohavingalowDM,andhence channels. Allobservationsare∼30minutesinlengthandare it is expected that scattering will only contribute to a small foldedinrealtimewith15-ssubintegrations. part of the total timing error for these pulsars. However, ac- At AO, we are using data collected and coherently dedis- curately correcting for ISM perturbations needs to be done persedwiththePUPPI(PuertoRicoUltimatePulsarProcess- carefully, soasnottointroduceadditionalerrors. Tocorrect ingInstrument)backend.Heretheobservationsareconducted for DM variations, nearly simultaneous observations with at overa700-MHzbandwidthcenterednear1500MHz,divided least two separate frequency bands at widely spaced center in 1.5625-MHz wide channels. The data are recorded in 1-s frequenciesareused. Becauseofthedifferentfrequencyscal- subintegrations (or 10-s subintegrations for observations be- ing of dispersion and interstellar scattering, by only correct- foreMJD∼56540)for∼30minutesperpulsarandepoch. ing for DM variations systematic errors are introduced into At the start of each observation, a polarization calibration thetimingprocedure(seeAppendixA).Oneimportantcaveat scan is performed by injecting a 25-Hz noise diode for both tothiscorrectionprocedureisthatmeasurementsatdifferent polarizations.Onceduringeachepochandforeachobserving observing frequencies sample different parts of the interstel- frequency,afluxcalibrator(B1442+101)isobserved. Forthe lar medium (Cordes et al. 2015). This significantly affects analysisinthispaper,totalintensityprofileshavebeenused, DMmeasurementsandcouldalsoaffectinterstellarscintilla- by summing the polarizations of the calibrated data (Arzou- tionmeasurementsforsomepulsars. manianetal.2015). Anumberofauthorshaveaddressedtheissuesofmeasur- The GUPPI and PUPPI backends provide substantially ing scintillation parameters and mitigating ISM effects pre- larger observation bandwidths compared to previously used viously. A few examples include Coles et al. (2010) and backends ASP (Astronomical Signal Processor) and GASP Keith et al. (2013), who analyzed DM variations and scin- (GreenBankAstronomicalSignalProcessor),whichbothhad tillation parameters for pulsars in the Parkes Pulsar Timing 64-MHzbandwidthcapacity(e.g.,Demorestetal.2013).The Array (PPTA). Their observations were carried out at three wider bandwidths not only result in higher timing precision differentfrequencies:a64-MHzbandcenteredat685MHz,a due to a higher signal-to-noise value for the pulsar signal 256-MHzbandcenteredat1369MHz,anda1024-MHzband overall,buttheyalsoprovidealargernumberofscintillation centeredat3100MHz(Manchesteretal.2013). Someofthe maximaandminimaovertheobservedband. Thewide-band pulsarsinthePPTAsamplearealsoobservedbyNANOGrav observationscarriedoutwithGUPPIandPUPPIprompteda and a comparison of the results is included in this work. In needtoinvestigatetheeffectofinterstellarscatteringdelays, a different paper, Gupta et al. (1994) studied the scintilla- andareessentialfortheanalysisinthispaper. tion properties of 8 pulsars over a 16 month period with the Lovell telescope at Jodrell Bank, using a 5-MHz band cen- 3. ANALYSIS teredat408MHz. Theyfoundthattheobservedfluctuations inthespectracouldbeexplainedasrefractivemodulationof We have created and analyzed 2-dimensional dynamic the diffractive scintillation parameters. Bhat et al. (1998) spectra of each 1500-MHz observation for each of the analyzed scintillation parameters for 20 slow pulsars with NANOGravpulsars,followingaproceduresimilartothatde- lowDM(<35pccm−3),usingobservationsata9-MHzfre- scribedinCordes(1986)unlessotherwisestated(e.g. forpart quencybandcenteredat327MHzat10−90epochsspanning ofthedelayuncertaintiesasdescribedineq3below). Ady- ∼100days. Theyreportlargefluctuationsinbothdiffractive namicspectrumdisplayshowtheintensityofthepulsarsignal scintillationtimescaleandbandwidth,withvariationsofafac- varieswithtime,t,andobservingfrequency,ν. Eachpointin torof3−5formostpulsarsintheirsample. thespectrumiscalculatedby Inthispaper,weanalyzethemagnitudeandvariationofin- P (ν,t)−P (ν,t) terstellar scattering delays in regular NANOGrav timing ob- S(ν,t)= on off (1) P (ν) bandpass MonitoringInterstellarScatteringDelays 3 where P is the total power of the observation as a bandpass function of observing frequency, and P and P are the (cid:21)(cid:19) on off pspoewcetirveinly.thTehoeno-na-pnudlsoeffp-aprutlissehpearertdoeffintheedpauslaslelbpirnosfiilnetrhee- (cid:80)(cid:76)(cid:81)(cid:88)(cid:87)(cid:72)(cid:86)(cid:12) (cid:20)(cid:20)(cid:24)(cid:19) summedpulseprofilethathaveanintensity>5%ofthemax- (cid:80)(cid:72)(cid:3)(cid:11) (cid:24) ifieiikhttmnnoianelmtcecnotueohhecwrbmrefeirpaennetnuraioslneadnlapsndtstaeaficoploanrryew.eanszsqnAbinectfueeyiuntlettn,onhwnoetacel6cxfefety4taeiiF.eonmnibrsTntgeeirpso.napr(ml1fAsdeace,.oiraCroowaToelftcFnthwheuah)clie.aliysedranvTeiytgapesehnlnsaidteatdgthahotmhAeenenatridCeeoncsGrrie,Ffsziaoapwgpeuicriiessxeshnecestoaatclhilrlfocasoeuhnc2mtnimhan0ofplesd4ubcuumi8nssacmtcecneaapirtmxtnuivbaeoitlaeemlsn2gtedeif,Drusooeocmpnuaaaevrtnnoouneeiddsrf-r-- (cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:55)(cid:76)(cid:80)(cid:72)(cid:3)(cid:11)(cid:80)(cid:76)(cid:81)(cid:88)(cid:87)(cid:72)(cid:86)(cid:12)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:55)(cid:76) (cid:21)(cid:20)(cid:20)(cid:19)(cid:24)(cid:19)(cid:19)(cid:24)(cid:19)(cid:3)(cid:19)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:20)(cid:3)(cid:3)(cid:3)(cid:21)(cid:3)(cid:3)(cid:19)(cid:3)(cid:3)(cid:19)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:53)(cid:20)(cid:3)(cid:3)(cid:23)(cid:72)(cid:3)(cid:3)(cid:19)(cid:73)(cid:3)(cid:72)(cid:3)(cid:19)(cid:3)(cid:85)(cid:3)(cid:3)(cid:72)(cid:41)(cid:81)(cid:85)(cid:70)(cid:72)(cid:72)(cid:84)(cid:3)(cid:88)(cid:73)(cid:3)(cid:85)(cid:3)(cid:72)(cid:72)(cid:3)(cid:3)(cid:81)(cid:84)(cid:3)(cid:3)(cid:70)(cid:88)(cid:3)(cid:3)(cid:92)(cid:72)(cid:3)(cid:3)(cid:3)(cid:11)(cid:81)(cid:3)(cid:3)(cid:48)(cid:3)(cid:70)(cid:3)(cid:92)(cid:3)(cid:43)(cid:20)(cid:3)(cid:20)(cid:93)(cid:25)(cid:12)(cid:24)(cid:19)(cid:19)(cid:19)(cid:19)(cid:3)(cid:3)(cid:48)(cid:43)(cid:93)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:20)(cid:3)(cid:3)(cid:27)(cid:3)(cid:3)(cid:19)(cid:3)(cid:3)(cid:19)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:27)(cid:19)(cid:19) tered at zero lag, is fitted to the two 1D ACFs to determine thescintillationparameters. Thescintillationtimescale,∆t , FIG.1.— The top panel shows an original dynamic spectrum for d PSRJ1918–0642atMJD56066. Thebottompanelshowsthesamespec- isdefinedasthehalf-widthate−1 ofthesummedfrequency trumafterithasbeenstretchedtoareferencefrequencyof1500MHz,using lagandthescintillationbandwidth,∆νd,isthehalf-widthat ascalingindexofζstretch=4.4. half-maximum of the summed time lag. Most of the obser- vationshavetotalintegrationtimeT < ∆t atourobserving d the four separate bands were then plotted against the center frequencies,andhencewecannotcalculatevaluesfor∆t . d frequencyofthebands,andafunctionoftheformτ = ν−ζ The scatteringdelay, τ , thatarises asa resultof scintilla- d d wasfittedtothedatatocalculatethescalingindex,ζ. Anex- tioncanbecalculatedfrom ampleofascalingindexmeasurementisgiveninFig.2. Not- 2π∆ν τ =C (2) ing that the number of scintles in each sub-band drastically d d 1 changes with observing frequency, which could potentially whereC isaconstantwithvalueranging0.6−1.5(Lambert 1 affect this analysis, we also tried dividing the band up into &Rickett1999)dependingonthegeometryandspectrumof fourpartswiththesamenumberofscintlesperbandinstead theelectrondensityfluctuations. HereweassumeC =1. 1 of a set bandwidth. The result of this exercise agreed well Theuncertaintiesofthescatteringdelaymeasurementscon- withthesetbandwidthmethod,andhencethevaluesreported sist partly of a “finite scintle error” and partly of the uncer- hereareallcalculatedfrom200-MHzsub-bands. taintyoftheleast-squarefitofaGaussiantotheACF,which This method was used to measure scaling indices for 10 areaddedinquadraturetogetthetotaluncertainty. Thefinite of the NANOGrav pulsars. The remaining pulsars all have scintleerroriscalculatedas either too wide scintillation bandwidths to get reliable mea- (cid:15)≈τ N−1/2 surements in a 200-MHz band, or too narrow scintles to get d scint resolved scintillation bandwidths with the 1.5625-MHz fre- ≈τd[(1+ηtT/∆td)(1+ηνB/∆νd)]−1/2 (3) quency channels. However, in an effort to keep the number ofvariablestoaminimum,wechoosetouseascalingindex whereN isthenumberofscintles,T andB aretotalin- scint as predicted in a Kolmogorov medium (ζ = 4.4) in the tegration time and total bandwidth, respectively, and η and stretch t stretchingevenforthesourceswithameasuredζ-value. This η are filling factors in the range 0.1−0.3, here set to 0.2 ν choice is also based on the observation of possible variable (Cordes&Shannon2010). Sincecommonlyforourobserva- scaling indices between epochs (see Sec 5.4), and hence us- tionsT (cid:28) ∆t ,thefirstterminEquation3isapproximately d ingameasuredscalingindexfromoneepochinthestretching equalto1andhence(cid:15)dependsonlyonvaluesrelatedtothe ofanotherepochmaybiasthedynamicspectrumanalysis. In bandwidth. 18 addition,comparisonsshowthattheconsequencesofusinga Apositiveconsequenceofthewidebandwidthobservations fixedζ aresmallerthantheotherstatisticaluncertainties isthelargernumbersofscintlesobservedcomparedtoobser- stretch onthescatteringdelaymeasurements. vations with narrower bandwidths. However, it also implies Hence,eachdynamicspectrumwasstretchedusingascal- large differences in the scintillation bandwidths measured at ing index ζ = 4.4, by rescaling the frequency axis and thelowestpartofthebandcomparedwiththehigherpartof stretch setting the reference frequency, ν , to the center of the theband,whichinturncausesproblemswhencreatingACFs. ref band. Theresultisan800-MHzwidedynamicspectrumwith This is only problematic if the collected data span a large evenly-sizedscintlesthatallrefertothesameobservingfre- range in frequency. Current methods to calculate scintilla- quency. We calculated ACFs of these stretched spectra and tion parameters were developed for narrower bands, and do derived from them the scintillation bandwidths that are used not provide a direct solution to the scaling issue. To resolve intheremainderofthispaper. SeethebottompanelofFig.1 this,wehavedevelopedamethodto“stretch”thespectratoa foranexampleofastretchedspectrum. referencefrequencybasedonhowthescintillationbandwidth scaleswithobservingfrequency. 4. RESULTS To investigate the scaling, we divided the wide bandwidth 4.1. Scalingovertheobservedfrequencyband observationsintofourequallysizedsub-bands.Thescattering delaysinferredfromthemeasuredscintillationbandwidthsof Using the sub-banding method described in Sec.3, we have successfully measured scaling indices for 10 of the 37 18 IfT ≈ ∆td, implyingthatthefirsttermwouldbeequalto1.2, we NANOGrav MSPs. These values are given in Table 2. For wouldbeslightlyunderestimatingNscintandhenceslightlyoverestimating mostofthepulsars,thescalingindexislowerthanthatfora thescatteringdelayuncertainties. Kolmogorov medium (ζ = 4.4). In addition to the variation 4 L.Levinetal. 99666 66644 48481 34448 81884 33131 99888 88888 89899 98889 99998 99999 e 55555 55555 55555 55555 55555 55555 g 66666 66666 66666 66666 66666 66666 n 55555 55555 55555 55555 55555 55555 a ––––– ––––– ––––– ––––– ––––– ––––– Drs)8989727500 5175757575 6523757518 9675776789 8997758975 9675973918 MJ(day559559559552557 563552552552552 552560552552560 559552559563559 559559552559552 559552559561560 dA meσTO(ns)72104638180394 62220733870681 1703319220126 9381445169148 591784196219 2145161566223 d 67 1 91 7 0 3 08 52 ∆τ(ns)6.3–23.20.– –0.53.83.1– 18.2.8–11.11. 20.4.1––12. 45.–7.083.11. 3.688.23.–– s b 0 No 2427284933 1151525150 6432511120 2447251024 3321592549 2367211721 m N 5–1525– 1454– 429–6212 1012––4 26–172432 41116–3 dnt meci Ns 7–1612– 4373– 184–811 45––11 26–56311 64312–63 ) /3 4 4 4 3 4 4 4 4 3 4 4 4 4 4 4 4 4 4 4 4 4 4 0 − − − − − − − − − − − − − − − − − − − − − − P.S −2m×10 ×10×10 ×10×10×10×10 ×10×10 ×10×10 ×10×10 ×10 ×10 ×10×10×10 ×10×10×10 ×10 MS Mpc9 62 4846 58 39 27 7 4 633 161 2 V S(k2.–2.2.– 6.1.2.1.– 3.8.–2.1. 2.2.––1. 5.–2.6.2. 1.3.2.–3. A R G 85 6 3 7 ANO ±6.6 3.3±4.3 ±5.6±17.±17. 2.6±14. ±8.6±7.7 ±17.±9.1 ±5.1 2.4 ±14.0.9±5.1 ±9.51.3±5.1 N z) ± ± ± ± ± BLE1ESOF ∆¯νd(MH20.5–9.111.1– 50.366.446.869.6– 9.056.3–21.116.8 17.142.1––12.7 5.2–39.02.314.9 21.62.810.6–2.9 TARTI 6 4 ROPE 2.1 ±5.5±3.9 0.11.31.1 ±4.31.1 2.42.3 4.41.3 ±4.5 ±9.9 1.8±16.3.0 0.8±21.±5.6 P ± ±±± ± ±± ±± ± ± ± G 77 2 7 3 8 31 3 ERIN ¯τd(ns)6.2–14.11.– 3.22.52.84.0– 16.2.6–7.19.4 5.03.8––11. 21.–4.957.9.7 6.144.10.–55. T SCAT 2001 5 00 000 NEτd(ns)2.50.0549166.2 241.20.170.9493 295.8904.121 0.860.02230185.3 4.02301.58.410 1.71302.9610240 1 0 NE20Tref(days)0.280.0292.01.10.45 1.50.150.0550.152.7 1.30.563.20.421.2 0.190.020190.970.72 0.472600.180.960.78 0.364.70.50147.3 00y)8 1 9 2 5 00 7 7 95 1 0 23 22 S14(mJ0.41.10.31.70.2 0.43.21.50.62.2 0.70.73.88.50.6 0.32.81.00.70.4 3.80.61.60.51.4 0.213.2.60.10.8 ) 3 − m 9 5 15 DM(pcc14.34.349.638.818.2 41.59.06.513.652.3 34.518.462.416.033.8 24.03.1152.28.230.6 13.3297.10.438.126.6 18.971.024.3164.104. d o 4 peri(ms)3.054.873.293.068.85 4.645.265.167.993.60 3.153.164.624.575.85 3.754.081.652.724.09 5.362.152.954.987.65 3.881.565.1913.16.13 31008 27903 04473 14663 7462 5 76 Pulsar J0023+092J0030+045J0340+413J0613–020J0645+515 J0931–190J1012+530J1024–071J1455–333J1600–305 J1614–223J1640+222J1643–122J1713+074J1738+033 J1741+135J1744–113J1747–403J1832–083J1853+130 B1855+09J1903+032J1909–374J1910+125J1918–064 J1923+251B1937+21J1944+090J1949+310B1953+29 MonitoringInterstellarScatteringDelays 5 cont.SNANOGMSPCATTERINGPROPERTIESOFRAVSmedNE2001NE2001med∆τστ¯τ∆¯νNNMJDrangePulsarperiodDMSTSMNmobsd1400ddscintTOArefd−3−20/3(ms)(pccm)(mJy)(days)(ns)(ns)(MHz)(kpcm)(ns)(ns)(days)−4±±×10J2010–13235.2222.20.600.576.619.36.46.92.35.121304826.529355275–56584−4±±×10J2017+06032.9023.90.280.533.88.43.421.69.51.485298.79555989–56598−3×10J2043+17112.3820.70.0940.412.01.886.34.23133–6855997–56591−4±±×10J2145–075016.059.05.50.120.532.80.747.813.31.749483.221455275–56584−4±±×10J2214+30003.1222.60.530.483.23.13.423.017.91.2672510.116055989–56598 −4±±×10J2302+44425.1913.80.900.220.8414.12.79.92.43.515102612.263755972–56586−4±±×10J2317+14393.4521.90.800.271.93.01.041.811.81.463192.18156100–56599 NE2001τNotes.Fluxdensityvaluesat1400MHz(S)areaveragevaluesfromthecalibratedtimingobservations.ScatteringdelaysfromtheNE2001model()havebeenscaledtoan1400dNE2001observingfrequencyof1500MHz,andtherefractivetimescales(T)arecalculatedfromthescaledvaluesofthescintillationbandwidthandtimescaleestimatedwithinthemodel.ref¯τ∆¯νTheweightedaverageofthescatteringdelayisgivenasandtheweightedaverageofthemeasuredscintillationbandwidthisgivenas,wheretheerrorisrepresentedbythestandarddddeviationoftheweightedmeaninbothcases.Themaximumvariationofthescatteringdelayiscalculatedasthemaximummeasuredscatteringdelayminustheminimummeasured∆τscatteringdelayandisheregivenas.Thescatteringmeasure(SM)iscalculatedthrougheq9,usingdistancesestimatedfromtheNE2001model.Thenumberofepochsincludedind¯τisgivenasN,whilethetotalnumberofepochsanalysedisgivenasN.ThenumberofscintlesineachoftheNepochsarecalculatedthroughtheexpressionforNgivenmmscintdobsmedmedσinEquation3andthemediannumberofscintlesisgivenasN.ThemedianTOAuncertainty()isgivenastheaveragedresidualerrorforthecombinedband,withvaluesfromscintTOAArzoumanianetal.(2015). 6 L.Levinetal. 11200 MHz, (cid:54)(cid:105)d=5.2 MHz 1 1400 MHz, (cid:54)(cid:105)d=6.6 MHz TABLE2 MEASUREDSCATTERINGDELAYSCALINGINDICES. 0.8 0.8 0.6 0.6 Pulsar ζ MJD Nsubband scint CF 0.4 0.4 J0613–0200 2.8(2) 55275 11 A 0.2 0.2 1.2(8) 56130 8 0 0 J1614–2230 2.6(9) 55269 6 -0.2 -0.2 6.3(4) 55304 9 -100 -50 0 50 100 -100 -50 0 50 100 2.5(4) 55892 13 11600 MHz, (cid:54)(cid:105)d=16.9 MHz 1 1800 MHz, (cid:54)(cid:105)d=16.5 MHz 2(2) 56288 13 J1713+0747 1.1(5) 55949 5 0.8 0.8 4.1(2) 56299 4 0.6 0.6 F 0.4 0.4 3.7(5) 56391 3 C A 0.2 0.2 B1855+09 3.8(3) 56294 10 0 0 J1910+1256 2.3(6) 56319 29 -0.2 -0.2 J1918–0642 2.4(6) 55463 5 -100 -50 0 50 100 -100 -50 0 50 100 3(1) 56066 5 Frequency [MHz] Frequency [MHz] B1937+21 1.3(3) 56131 11 2.7(5) 56403 13 100 3(1) 56451 10 s] (cid:99) = 3.2 +_ 1.0 y [n 3(1) 56492 24 ela 1.8(1) 56548 8 g D 10 4.9(8) 56593 26 n atteri J1944+0907 3(2) 56018 7 Sc J2010–1323 3.9(4) 56095 10 1 1000 1200 1400 1600 1800 2000 4.4(1) 56250 10 Observing frequency [MHz] 1.9(4) 56352 9 1(1) 56472 9 FIG.2.— PSRJ1918–0642 scattering delay scalings over the frequency band for an observation from MJD 56066. The four top panels show the 3.1(5) 56523 23 autocorrelationfunctionofeach200-MHzsubbandasasolidlineandthe J2145–0750 3.1(2) 56195 6 Gaussianfitasadashedline. Thebest-fitvalueforeachscintillationband- width,∆νd,isconvertedintoascatteringdelayandplottedinthebottom panel,togetherwiththebestfitofthescalingindex,ζ,asadashedline. Notes. Scattering delay scaling over frequency band, where τd ∝ ν−ζ. The indices are measured at the given observing epoch, and the numbers in parenthesis are the errors on the last given digit. between different pulsars, the scaling index for a particular Nsubbandrepresentstheaveragenumberofscintlesineachsubband, pulsarmaynotnecessarilybeconstantintimeandideallyalso scint calculatedthroughtheexpressiongiveninequation3. this variation should be monitored. However, it has proven difficult to measure scaling indices at most epochs because scintlesarenotvisibleinallofthesub-bands,orbecausera- (cid:20)(cid:24) dbiaondf.reOqunelyncayfienwteroffertehnecpeuilssasresvhearevleymauffleticptilnegscpaalrintsgoifndthexe (cid:80)(cid:76)(cid:81)(cid:88)(cid:87)(cid:72)(cid:86)(cid:12) (cid:20)(cid:19) measurements(forfurtherdiscussion,seeSection5.4). (cid:80)(cid:72)(cid:3)(cid:11) (cid:24) (cid:55)(cid:76) aitmnerreoIiTndngategeiblvrldesfeotenelr1laal.fyasrretaFsehnoce4dear.ltw2etrc.eeceorftiSmirrgncoahpgacntattseditrvdeeiisernlaoainvtyntighes,mre(daveτ¯egIasdSlleca)uMayfeoloesvvrs(eaCfarrogloiraliavrlNdtlteiheAonoesnbNb&spyOerreGLtvdhiarienaczgvtiNeopdeEup22slo0s0cc0aa0h2rt1ss-) (cid:55)(cid:76)(cid:80)(cid:72)(cid:3)(cid:11)(cid:80)(cid:76)(cid:81)(cid:88)(cid:87)(cid:72)(cid:86)(cid:12)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3) (cid:20)(cid:19)(cid:27)(cid:23)(cid:21)(cid:3)(cid:19)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:53)(cid:72)(cid:73)(cid:72)(cid:85)(cid:72)(cid:81)(cid:70)(cid:72)(cid:3)(cid:73)(cid:85)(cid:72)(cid:84)(cid:88)(cid:72)(cid:81)(cid:70)(cid:92)(cid:3)(cid:20)(cid:24)(cid:19)(cid:19)(cid:3)(cid:48)(cid:43)(cid:93)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:26)(cid:19)(cid:19) athree mlisatxedimfuomr avllartihaetiopnulmsaeras.suIrnedad(∆diτtion=, tτhe table−iτnclude)s, (cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3) (cid:19)(cid:3)(cid:19)(cid:3)(cid:3) (cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:53)(cid:72)(cid:73)(cid:72)(cid:85)(cid:72)(cid:81)(cid:70)(cid:72)(cid:3)(cid:73)(cid:85)(cid:72)(cid:84)(cid:88)(cid:72)(cid:81)(cid:70)(cid:92)(cid:3)(cid:20)(cid:24)(cid:19)(cid:19)(cid:3)(cid:48)(cid:43)(cid:93)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:3)(cid:26)(cid:19)(cid:19) d d;max d;min togetherwiththemedianTOAuncertaintyresultingfromtim- FIG.3.— Examplesofdynamicspectrawithnarrowandwidescintilla- ing.Comparingthesevaluescangiveinsightintothefeasibil- tionbandwidths.BothobservationsarecollectedwiththePUPPIbackendat ityofcorrectingthetimingresidualsforscatteringdelaysfor Arecibo,andhavebeenstretchedtoareferencefrequencyof1500MHz.The toppanelshowsanobservationofPSRJ1910+1256atMJD56519,andthe aparticularpulsar(seeSec. 5.5formoredetails). bottompanelisanobservationofJ2317+1439atMJD56100. Two typical observations are shown in Fig.3, with the top dynamic spectrum displaying narrow scintles for PSRJ1910+1256 with ∆νd ≈ 3MHz and the bottom dy- atleasttenτd measurementsareplottedalongwiththeirDM namic spectrum showing wide scintles for PSRJ2317+1439 variations. with∆ν ≈ 34MHz. Examplesofscatteringdelayvariabil- d itycanbefoundinFig.4,whereallNANOGravpulsarswith 5. DISCUSSION MonitoringInterstellarScatteringDelays 7 3450 J0340+4130 (r = 0.57; mb = 0.29) 3305 J0613−0200 (r = −0.48; mb = 0.29) 3305 J1614−2230 (r = 0.14; mb = 0.29) 30 25 25 [ns](cid:111)d 11220505 [ns](cid:111)d 112050 [ns](cid:111)d 112050 5 5 5 −3−3DM [10 pc cm] − 00−. .15015 0 −−− 000000... ...6420246 0 −3−3DM [10 pc cm] −− 0000.. ..84048 0 (cid:54) 56000 56100 56200 56300 56400 56500 55400 55600 55800 56000 56200 56400 56600 (cid:54) 55400 55600 55800 56000 56200 56400 56600 MJD MJD MJD 20 J1713+0747 (r = 0.068; mb = 0.32) 20 J1738+0333 (r = 0.11; mb = 0.58) 2350 J1741+1351 (r = 0.27; mb = 0.67) [ns](cid:111)d 1105 [ns](cid:111)d 1105 [ns](cid:111)d 112050 5 5 5 −3−3 DM [10 pc cm](cid:54) −− 0000.. ..21012 0 55400 55600 55800 56000 56200 56400 56600 −3−3 DM [10 pc cm](cid:54) − 00−. . 15015 506000 56100 56200 56300 56400 56500 −3−3 DM [10 pc cm](cid:54) −− 0000.. ..42024 0 56100 56200 56300 56400 56500 56600 MJD MJD MJD 1102 J1744−1134 (r = 0.31; mb = 0.14) 6700 B1855+09 (r = −0.31; mb = 0.43) 1250 J1909−3744 (r = −0.13; mb = 0.08) 8 50 [ns](cid:111)d 46 [ns](cid:111)d 3400 [ns](cid:111)d 10 20 5 2 10 −3−3 DM [10 pc cm](cid:54) −− 0000.. ..42024 0 55600 55800 56000 56200 56400 56600 −3−3 DM [10 pc cm](cid:54) −−− 000000... ...6420246 0 56000 56100 56200 56300 56400 56500 56600 −3−3 DM [10 pc cm](cid:54) −− 0000.. ..42024 0 55600 55800 56000 56200 56400 MJD MJD MJD 112400 J1910+1256 (r = −0.44; mb = 0.35) 25 J1918−0642 (r = 0.14; mb = 0.34) 112400 B1937+21 (r = 0.029; mb = 0.40) 100 20 100 [ns](cid:111)d 468000 [ns](cid:111)d 1105 [ns](cid:111)d 468000 20 5 20 −3−3DM [10 pc cm]−− 21012 0 −3−3DM [10 pc cm] − 00−. .15015 0 −3−3DM [10 pc cm] − 00−. .15015 0 (cid:54) (cid:54) (cid:54) 56000 56100 56200 56300 56400 56500 56600 55400 55600 55800 56000 56200 56400 56000 56100 56200 56300 56400 56500 56600 MJD MJD MJD 3305 J1944+0907 (r = −0.21; mb = 0.47) 4500 J2010−1323 (r = 0.37; mb = 0.42) 2350 J2302+4442 (r = 0.11; mb = 0.24) 25 20 [ns](cid:111)d 112050 [ns](cid:111)d 2300 [ns](cid:111)d 1105 5 10 5 −3−3DM [10 pc cm] − 00−. .15015 0 −3−3DM [10 pc cm] − 00−. .15015 0 −3−3DM [10 pc cm] − 00−. .15015 0 (cid:54) (cid:54) (cid:54) 56000 56100 56200 56300 56400 56500 56600 55400 55600 55800 56000 56200 56400 56100 56150 56200 56250 56300 56350 56400 56450 56500 MJD MJD MJD FIG.4.—Scatteringdelayvariations(toppanels)andDMvariations(bottompanels)forpulsarswithatleasttenscatteringdelaymeasurements.AllDMvalues measuredwithinthesametimespanforeachpulsarareincluded,evenforepochswherenoscatteringdelaymeasurementwaspossible. TheDMvaluesare measuredindatafromatleasttwoseparatefrequencybandsinthe9-yeardataset. Foreachpulsar,thecorrelationcoefficient,r,betweenthetwovariationsis givenintheparenthesesinthetoppanel. Inaddition,thenoise-correctedmodulationindexofthescintillationbandwidthisgivenasmbforeachpulsar(see Equations4and5). 8 L.Levinetal. TABLE3 PREVIOUSLYPUBLISHEDSCINTILLATIONPARAMETERS. Thiswork NE2001 Previouslypublishedvalues Pulsar τ¯ τNE2001 τ ν Ref. d d d;1500MHz (ns) (ns) (ns) (MHz) J0030+0451 – 0.055 0.12 435 Nicastroetal.(2001) J0613–0200 11.7±3.9 16 61.2 1369 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 97.0∗ 1500∗ Keithetal.(2013) J1024–0719 2.8±1.3 0.17 0.34 685 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 0.59∗ 1500∗ Keithetal.(2013) J1455–3330 4.0±1.1 0.94 0.51 436 Johnstonetal.(1998) J1600–3053 – 93 1768∗ 1500∗ Keithetal.(2013) (cid:113) (cid:113) (cid:113) 1072 3100 Colesetal.(2010) J1640+2224 2.6±1.1 5.8 3.3 430 Bogdanovetal.(2002) J1643–1224 – 90 7234∗ 1500∗ Keithetal.(2013) (cid:113) (cid:113) (cid:113) 2918 3100 Colesetal.(2010) J1713+0747 7.1±2.4 4.1 1.1 430 Bogdanovetal.(2002) (cid:113) (cid:113) (cid:113) 0.48 436 Johnstonetal.(1998) (cid:113) (cid:113) (cid:113) 1.1 685 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 6.6 1500∗ Keithetal.(2013) J1744–1144 3.8±1.3 0.020 0.52 436 Johnstonetal.(1998) (cid:113) (cid:113) (cid:113) 1.87 660 Johnstonetal.(1998) (cid:113) (cid:113) (cid:113) 0.40 685 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 2.7∗ 1500∗ Keithetal.(2013) B1855+09 21.3±9.9 4.0 6.5 430 Deweyetal.(1988) (cid:113) (cid:113) (cid:113) 1.1 685 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 13.0 1369 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 28.9∗ 1500∗ Keithetal.(2013) J1903+0327 – 2.3×105 9.3×104 1400 Championetal.(2008) J1909–3744 4.9±1.8 1.5 0.68 685 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 4.3∗ 1500∗ Keithetal.(2013) B1937+21 44.3±21.4 130 127 320 Cordesetal.(1990) (cid:113) (cid:113) (cid:113) 155 430 Cordesetal.(1990) (cid:113) (cid:113) (cid:113) 48.4 1369 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 127 1400 Cordesetal.(1990) (cid:113) (cid:113) (cid:113) 132∗ 1500∗ Keithetal.(2013) J2145-0750 2.8±0.7 0.53 0.47 436 Johnstonetal.(1998) (cid:113) (cid:113) (cid:113) 0.45 685 Colesetal.(2010) (cid:113) (cid:113) (cid:113) 0.82∗ 1500∗ Keithetal.(2013) J2317+1439 3.0±1.0 1.9 1.4 436 Johnstonetal.(1998) Notes. Thepublishedvaluesarereportedatthegivenobservingfrequency(ν)andhere convertedtoscatteringdelays(τ )at1500MHzusingascalingindexofζ =4.4. d;1500MHz Forreference,scatteringdelayvaluesfromthisworkisincludedasτ¯ andscaledvalues d fromtheNE2001aregivenasτNE2001. d ∗Onlyanalreadyscaledvalueisreportedintheoriginalpublication. MonitoringInterstellarScatteringDelays 9 Previous work on scintillation properties of pulsars has 1000 been carried out at various radio frequencies. To compare the scattering delays in this paper with previously published values, we need to scale all values to a common observing s] n 100 frequency. Thisintroduceslargeuncertainties,sincethecom- ay [ parison will be largely dependent on the chosen scaling law del g and,asshowninthispaper,themeasuredscalingindicesare n eri 10 not only different for different pulsars and hence observing att c directions,butmayalsovarywithtime(asdiscussedinmore e s detailinSec5.4).Nevertheless,acomparisonwithpreviously ag er 1 publishedvaluesislistedinTable3,byscalingthepublished v A scattering delays to their value at an observing frequency of 1500MHz,usingascalingindexζ =4.4. Insomecases, thepreviouslypublishedvaluesshowlarge 0.1 0.01 0.1 1 10 100 1000 discrepancieswiththevaluesinthiswork. Colesetal.(2010) NE2001 model scattering delay [ns] and Keith et al. (2013) both list scintillation parameters for millisecondpulsarsintheParkesPulsarTimingArray, some FIG.5.—ComparisonofaveragescatteringdelaytotheestimatedNE2001 model values. The NE2001 values have been scaled to an observing fre- ofwhicharealsoincludedintheNANOGravarray. Theval- quencyof1500MHz,usingascalingindexζ = 4.4. Thetwohorizontal uesinKeithetal. havealreadybeenscaledtoacommonob- dottedlinesmarkmaximumandminimumscatteringdelaysthatcanbemea- serving frequency of 1500MHz, while Coles et al. list the suredfromthedata.Theselimitsarecalculatedfromthefrequencyresolution actual frequency of each observation. Some of the values andthetotalbandwidthofthedatarespectively,usingthedefinitionofthe scintillationbandwidthasthehalf-widthathalf-maximumoftheGaussianfit from Coles et al. were measured at an observing frequency totheACF.Thediagonallinerepresentsequalityofmodelandmeasurement. ν =1369MHz,andthesevaluesagreebetterwithourmea- obs surements than the rest of the pulsars in Coles et al., which its of the data, and hence it is not surprising that no scatter- suggeststhatthechoiceofscalingindexmaybeanissue.An- ing delays have been measured for these pulsars. One ex- otherexplanationforthediscrepancyisthevariationofscat- ception is PSRJ0645+5158, which has τ = 6.2ns teringdelayovertime(seeFig.4),whichisalsoobservedby d;NE2001 at1500MHz. Manualinspectionofthedynamicspectraob- Colesetal. Similarly, Bhatetal.(1998)observedvariations tainedforthispulsarshowsthatinthefewobservationswith ofthescintillationbandwidthofafactorof3−5whenanalyz- scintlesstrongenoughtobedetected,radiointerferencecon- ing scintillation parameters of slow low-DM pulsars. In the tamination caused errors in the ACF calculation. By eye, datapresentedhere,weobservedelayswithavariationofup we estimate a scintillation bandwidth of ν ≈ 100MHz, toanorderofmagnitude. d In the cases where the published values are τ (cid:46)1ns, the which corresponds to τd ≈ 1.5ns. The other exception is d PSRJ1832–0836,withτ =18nsat1500MHz. This valuesmeasuredinthisworkarealwayslarger. Thisislikely d;NE2001 pulsarisarecentadditiontotheNANOGravarray, andonly due to the limited bandwidth of the data, which allows only 10observationsat1500MHzareincludedinthe9-yeardata theobservationswithhigherscatteringdelayvaluesinthedis- release. Even by manually inspecting the dynamic spectra tribution to be resolved. Many of the values published be- forPSRJ1832−0836,noscintlesaredetected,whichislikely fore 2001 are very similar to the corresponding value from duetothelowfluxdensityofthesignal. theNE2001model. Thisisexpected,sinceinthecreationof Forthepulsarswithτ (cid:28) 1ns, themeasuredscat- theelectrondensitymodel,asmanyscatteringdelaymeasure- d;NE2001 teringdelayismuchlargerthanthemodeldelay. Itispossi- mentsaspossiblewereincluded(Cordes&Lazio2002)and ble that there is an underlying structure of wide scintles that hencetheseearlymeasurementswerelikelyusedasinputto are too wide to detect in this dataset, and what is measured themodel. herearesmallmodulationsontopofthelargerstructure. An- 5.1. ComparisonwiththeNE2001model otherpossibilityisthattheNE2001modellargelyunderesti- mates the amount of scattering in the direction of these pul- Themostcomprehensiveandfrequentlyusedmodelofthe sars,whichareallathighGalacticlatitudeswherethemodel freeelectronsintheGalaxyistheNE2001model(Cordes& isknowntohavelargeuncertainties(e.g.Gaensleretal.2008; Lazio 2002). In addition to predicting distances to pulsars Chatterjee et al. 2009). For the cases where the τ - fromtheirDMvalues,thismodelalsoestimatesthescintilla- d;NE2001 valuesarecloseto1ns,wemayonlybedetectingthehighest tionpropertiesfromapositionandaDMvalue.Thescattering values in the distribution of delays. Since the bandwidth of delayspredictedfortheNANOGravpulsarsbythemodelare the observations is limited, the true mean τ -values may be listedinTable1. d lowerthanwhatwecanmeasure. Asimilarargumentcanbe These values have also been plotted against the average applied to the τ -values close to the maximum delay measured scattering delays in Fig 5. The horizontal dotted d;NE2001 limit, where the limited frequency resolution would permit linesshowtheminimumandmaximummeasurabledelaysin detection of only the lower parts of the delay distributions. the data, while the diagonal line shows equality of the mea- In addition, the delays in particular observations may be un- surement to the model. In general, the measured values are derestimatedforpulsarsclosetothemaximumlimit, sincea slightlyhigherthanthepredictions.Itisknownthatthemodel strong scintle with true ∆ν smaller than the channel band- predictionshavelargeassociateduncertainties,inparticularat d widthwouldstillbemeasuredasbeingonechannelwide. higherGalacticlatitudes,wherethenumbersofsourceswith knowndistancesandDMarelow. 5.2. Interstellarmediumvariations Forsomeofthepulsars,nomeasurementwaspossible,e.g., due to too narrow or too wide scintles. All but two of these The measured values of τ are plotted in Fig.4 as a func- d non-detectionsarepredictedtolieclosetothedetectionlim- tionofobservingdayforallpulsarswithatleast10measured 10 L.Levinetal. scattering delay values. To analyze the delay variability we indexforthescintillationbandwidthisgivenby havecalculatedamodulationindexforthescintillationband- widthforeachpulsar,definedastheRMSfluctuationsof∆νd mb;Kolmogorov ≈0.202(Cn2)−1/5νo3b/s5D−2/5 (10) dividedbyitsaveragevalue(Bhatetal.1999)andgivenby where ν is the observing frequency in GHz, D is the dis- obs m = 1 (cid:32) 1 N(cid:88)obs(∆ν −(cid:104)∆ν (cid:105))2(cid:33)1/2 tuannictseotof t1h0e−p4umls−a2r0i/n3k(pBchaatndetCan2l.i1s9t9h9e)s.caFtoterrainKgostlrmenoggtohroivn b;measured (cid:104)∆νd(cid:105) Nobs−1 d,i d spectrum, i=1 (4) C2 =0.002∆ν−5/6D−11/6ν11/3m−20/3 (11) where (cid:104)∆νd(cid:105) is the average scintillation bandwidth, Nobs is n d obs the number of measurements, and ∆νd,i is the scintillation where∆νdisgiveninMHz,Disgiveninkpcandtheobserv- bandwidth at the ith epoch. The measurement error on ∆ν ing frequency, ν , is given in GHz (Rickett 1977; Cordes obs will induce an apparent increase in the modulation indices, 1986). Calculatingthetheoreticalmodulationindicesforthe that needs to be corrected for. Following Bhat et al. (1999), pulsars in Fig.4, using pulsar distances from parallax mea- wecalculatecorrectedmodulationindicesas surements where available19 and otherwise as given by the m2 =m2 −m2 (5) NE2001model(Cordes&Lazio2002),resultsinvaluesrang- b;corrected b;measured b;noise ing 0.15 ≤ m ≤ 0.20. If the density spectrum is not Kol- b wheretheerrorinducedmodulationindex,mb;noise,iscalcu- mogorovinshape, butratherhasβ > 11/3, thefluctuations lated as the typical uncertainty in ∆νd. The corrected val- areexpectedtobeindependentoftheobservingwavelength, ues of mb are given in the upper panel for each pulsar in butgivelargermodulationthanaKolmogorovspectrum. For Fig.4. Fortwoofthepulsars(J1744–1124andJ1909–3744), β = 4.0thetheoreticalm ≈ 0.35andforβ = 4.3thetheo- b mb;noise ≈ mb;measured. Both of these pulsars have only a reticalmb ≈0.57(Romanietal.1986;Bhatetal.1999). small numbers of scintles in each observation, which con- Comparing the corrected modulation indices with the the- tributes to the large uncertainty in the scattering delay mea- oretical ones, all of the measured m -values are larger than b surements,asseeninFig.4,andhenceareexcludedfromfur- those predicted for a Kolmogorov medium. This does how- ther modulation index analyses. For the remaining pulsars, ever not necessarily mean that the density spectrum is not mb;noise (cid:28) mb;measured, so the corrected modulation is ap- Kolmogorov. Instead, if the ISM in these directions is not proximatelyequaltothemeasuredmodulation. well described by a thin screen, but rather as an extended These modulations of the scintillation bandwidths, and Kolmogorovmedium,thatwouldexplainthelargerobserved hence the scattering delays, could originate from refractive modulation. scintillation effects. The theoreticalmodel of the observable Wecanalsoapproachthisdiscussionfromtheotherdirec- modulationeffectsduetorefractivescintillationarehighlyde- tion, by looking at the measured scattering delay frequency pendent on the form of the density spectrum, which can be scaling. ManyofthemeasuredscalingindicesinTable2are writtenas smaller than that expected for a Kolmogorov medium, even Pδne(κ)=Cn2κ−β (6) withintheerrors,andsimilartrendshavebeenshowninpre- vious work by other authors. In an effort to measure pulse for values of the spatial wavenumber, κ, between inner and scattering broadening of slow pulsars, Bhat et al. (2004) ob- outercutoffsinspatialscalesizesofthedensityirregularities served a number of pulsars at a minimum of two different in the ISM (Armstrong et al. 1995). Here C2 represents the n frequencies with the Arecibo telescope. Indeed, for most of scatteringstrengthandβ isthedensityspectralindex,which their sources, they measured a scaling index ζ < 4.4. By foraKolmogorovspectrumisequalto11/3. Forβ < 4, the usingtheirresultstogetherwithpreviouslypublishedvalues, correspondingscalingovertheobservedfrequencybandis Bhat et al. inferred an empirical frequency scaling index of 2β 3.9±0.2. Following the discussion above, the smaller ob- ζ = (7) served scaling indices agree well with the larger modulation β−2 observedinourdata. and hence for a Komogorov medium, ζ = 4.4 (Cordes & Shannon2010). Thescatteringmeasureisdefinedas 5.3. DispersionMeasurevariations TheonlyISMeffectusuallycorrectedforinhigh-precision (cid:90) D SM= C2ds (8) pulsar timing is the DM and its variations. Since dispersion n and scintillation both arise from the same interstellar struc- 0 tures in each observation, itis temptingto assumea correla- whichcanbesimplifiedto tionbetweenthevariationsofthetwodelays. Wehavecom- (cid:16)τ (cid:17)5/6 pared the scattering delay and DM variations by calculating SM=292 d ν11/3 (9) D GHz correlationcoefficientsforallpulsarsinFig.4. TheDMval- uesaremeasuredusingtheDMXmethodinthepulsartiming with units kpc m−20/3 if the scattering delay, τd, is given in software TEMPO20. In this procedure, the DM(t) function is seconds and the distance, D, is given in kpc (Cordes et al. treated as piecewise constant, and an independent DM value 1991). isfittedforoversuccessive14-daywindows, inasimultane- Romanietal.(1986)presentedatheoryfortherefractiveef- ous fit with all other timing model parameters. This is sim- fectsinafewspecialcasesusingpower-lawformsofdensity ilar to the procedure used in Arzoumanian et al. (2015), ex- spectra with different spectral indices. In the case of a Kol- mogorovspectrumandconsideringscatteringinathinscreen 19 With values as given in the ATNF pulsar catalogue: halfwaybetweentheobserverandthepulsar,themodulation http://www.atnf.csiro.au/research/pulsar/psrcat/ 20http://tempo.sourceforge.net

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