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Astronomy&Astrophysicsmanuscriptno.0643aa February2,2008 (DOI:willbeinsertedbyhandlater) Spiral shock detection on eclipse maps: ⋆ Simulations and Observations E.T.Harlaftis1,R.Baptista2,L.Morales-Rueda3,T.R.Marsh3,andD.Steeghs4 1 Institute of Space Applications and Remote Sensing, National Observatory of Athens, P. O. Box 20048, Athens 118 10, Greece 4 e-mail:[email protected] 0 2 DepartamentodeF´ısica,UniversidadeFederaldeSantaCatarina,CampusTrindade,88040-900,Floriano´polis,Brazil 0 e-mail:[email protected] 2 3 DepartmentofPhysicsandAstronomy,SouthamptonUniversity,SouthamptonSO171BJ,UK n e-mail:[email protected], [email protected] a 4 HighEnergyAstrophysicsDivision,CenterforAstrophysics,MS-67,60GardenStreet,Cambridge,MA02138,USA J e-mail:[email protected] 9 ReceivedNovember4,2003;acceptedDecember27 1 v 5 Abstract.Weperformsimulationsinordertorevealtheeffectofobservationalandphysicalparametersonthereconstruction 5 ofaspiralstructureinanaccretiondisk,usingeclipsemappingtechniques.Weshowthatamodelspiralstructureissmeared 1 to a “butterfly”-shape structure because of the azimuthal smoothing effect of the technique. We isolate the effects of phase 1 resolution,signal-to-noiseratioandaccuratecenteringoftheeclipseatzerophase.Wefurtherexplorediskemissivityfactors 0 suchasdilutionofthespiralstructurebythedisklightandrelativespiralarmdifference.Weconcludethatthespiralstructure 4 can besatisfactorily recovered inaccretion diskeclipse mapswithphase resolution |∆φ| ≤ 0.01, S/N > 25 and zero phase 0 uncertainty|∆φ| ≤ 0.005,assumingthetwospiralarmshavesimilarbrightnessandcontribute≥ 30%tothetotaldisklight. / h Underthelightoftheperformedsimulations,wepresenteclipsemapsoftheIPPegaccretiondiskreconstructedfromeclipse p lightcurvesofemissionlinesandcontinuumduringtheoutburstofAugust1994,wherespiralshocksweredetectedwiththeaid - ofDopplertomography(Morales-Ruedaetal.2000).Wediscusshowthedetectionofspiralsshockswitheclipsemappingis o improvedwiththeuseofvelocity-resolvedeclipselightcurveswhichdonotincludeanycontaminatinglow-velocityemission. r t s a Keywords.Stars:cataclysmicvariables–Stars:dwarfnovae–Stars:Individual:IPPegasi–accretion,accretiondisks–shock : waves–Methods:dataanalysis–techniques:highangularresolution v i X r 1. Introduction:spiralshocksincataclysmic ontheaccretiondiskinquiescence(Marsh1989)orthe“spiral a variables structure”raisedbytidesfromthecompanionstarontheouter accretiondiskduringoutburst(Steeghs2001;Boffin2001). Cataclysmic variables (CVs) are binaries where an accretion disk is formed around the white dwarf from gas escaping a IP Pegasi is an eclipsing dwarf nova and one of the best companion red dwarf (Warner 1995). Their study is attrac- studied CVs thus providinga paradigmfor the accretion disk tiveforunderstandingbinaryformationandevolutionandthe model. Spiral shocks in its accretion disk have been found physicalprocessesoccuringintheaccretionflow.Forexample, throughoutthe various stages of an outburst (rise, maximum, the semi-regular radiation outbursts from the accretion disks decline;Steeghsetal.1997;Harlaftisetal.1999;andMorales- around white dwarfs in the CV sub-class of the dwarf novae Ruedaetal.2000,respectively),usingtheDopplertomography arethoughttobedrivenbyathermalinstabilitywithinthedisk technique(Marsh&Horne1988).Thephase-resolvedspectra (Hameury2003 and referencestherein).The optical radiation in Harlaftis et al. (1999), which were used to reconstruct the patternontheaccretiondiskisasymmetricandisdominatedei- Doppler maps - two-dimensional velocity maps - of the spi- therbythe“brightspot”causedbytheimpactofthegasstream ralshocks,werealsousedtomakeeclipselightcurvesinvari- ousemissionlines.Thelightcurves(integratedintensityversus phase)werethenanalysedusingtheeclipsemappingtechnique Sendoffprintrequeststo:E.T.Harlaftis ⋆ BasedonobservationsmadewiththeIsaacNewtonandWilliam (Baptista 2001) in order to reconstruct the surface brightness Herschel telescopes operated on the island of La Palma by the distributionoftheaccretiondiskandthusdefinethespatialex- Isaac Newton Group in the Spanish Observatorio del Roque de los tentofthespiralarms(Baptistaetal.2000).Directcomparison MuchachosoftheInstitutodeAstrofisicadeCanarias. of the Doppler (velocity) and eclipse (spatial) maps showed 2 E.T.Harlaftisetal.:Spiralshockdetectiononeclipsemaps:SimulationsandObservations thattheouterdisk-largelyaffectedbythevelocityfieldofthe spiralshocks-inIPPegasiislargelynon-Keplerianandthatthe spiral arms extend between 0.2-0.6R , contributingbetween L1 16-30%ofthetotallineflux. Here, we address the parameters affecting the reconstruc- tionofthespiralstructureusingtheeclipsemappingtechnique. Weundertakesimulationsinordertodemonstratetheeffecton thedetectabilityofspiralarmsinsituationswithanunfavorable combinationoflowS/N,lowtimeresolution,andthedilution of the shock light by the disk. Hence, we define the observa- tionalrequirementsforfutureobservationsofspiralshocksus- ing the eclipse mappingtechnique. Finally, in the light of the simulationsperformedweinterprettheeclipsemapsbuiltfrom lightcurvesofIPPegasiduringoutburst(Morales-Ruedaetal. 2000).Thisisanepochwherethespiralshockshavebeenex- citedintheaccretiondisk,asshownbyDopplertomography. Fig.1. The spiral arm definition using the parameters θ0, the anglebetweenthetangenttothespiralpattern(extrapolatedto the disk centre at R = 0 R ) and the line-of-centres,and 2. Simulations α(= −180◦),theopsepnirailngangleL1ofthespiral,orthechangein angle (θ−θ ) it takes to go from R = 0 to R = R . Doppler tomography of IP Peg has clearly revealed the disk 0 spiral spiral L1 The line-of-centres is the positive direction of the x-axis and spiral structure on a number of occassions and showed its theanglesaremeasuredcounter-clockwise. strength in imaging sub-structures within the accretion disk (Steeghs 2001). However, the disk spiral structure of IP Peg is,apparently,notimagedasclearlyusingtheeclipsemapping havearadialwidthof0.08R andaradialrangebetween0.2– technique(Baptista et al. 2000),eventhoughthe eclipse light L1 0.6R ,asfoundinBaptistaetal.(2000).Thetraceofthespiral curvesarefromthesameoutburstmaximum(November1996). L1 isdefinedby, There, the same phase-resolved spectra show one of the best examples of spiral shocks in an accretion disk using Doppler R (θ)=(θ−θ )/α spiral 0 tomography as the reconstruction technique (Harlaftis et al. 1999).Asaconsequence,wehaveperformedaseriesofsimu- whereθ0 istheanglebetweenthetangenttothespiralpattern (extrapolatedtothediskcentreatR = 0R )andtheline- lationsinordertobetterunderstandthestructuresreconstructed spiral L1 witheclipsemapping.Thereconstructionswereobtainedusing of-centresandincreasescounter-clockwiseinstepsof30◦,us- ingasareferencetheobservedrotationangleat46◦ (Baptista thePRIDAcode(Baptista&Steiner1993),whichcomputesan et al. 2000); θ is the angle between the tangent to the spiral eclipsemapasanarrayof51x51pixels,withasizeof2R and centredonthewhitedwarf.AnyadditionaluneclipsedcoLm1 po- pattern at 0 < Rspiral < RL1 and α (= −180◦) is the opening angleofthespiral,thechangeinangle(θ−θ )fromR =0 nentcanalsobemodelledasaconstantflux.Weadoptthebi- 0 spiral nary geometry of Wood & Crawford (1986) with (i,q)=(81◦, toRspiral = 0.6RL1.Notethattheabovedefinitionisforlinear 0.5),whereiistheinclinationandqisthemassratio(seealso spiralarms(seeBinney&Tremaine1988forlogarithmicspi- ralarms).Fig.1showsgraphicallythespiraldefinitionwithθ section3.1).Forthereconstructionsweadoptedthedefaultof 0 limitedazimuthalsmearing(Rutten,vanParadijs&Tinbergen and α as defined above. Setting a small (large) α results in a tightlywound(open)spiralarm.OurmodelmapinFig.2has 1992),whichisbettersuitedforrecoveringasymmetricstruc- anunderlyingsymmetricdiskcontaining40%ofthetotalflux turesthantheoriginaldefaultoffullazimuthalsmearing(e.g., Baptista2001).Formoredetailsonthetechnique,seeBaptista andaflatbrightnessdistributionwhichdropssharplyatR=0.6 R following a exp[−|(r−r )/dr|3] law. The spirals are also (2001).Using a model map with a symmetric disk and a spi- L1 0 cutoffwiththesameradialdependency,bothattheinnerand ral structure, we test the limits of the technique in resolving the spiral arms. The parameters we change are either defined outerradius. by the observing technique, geometrical constraints or physi- calprocesses: 2.1.Spiralstructureorientation(θ ) 0 – spiralstructureorientation InFig.2,wepresentmodelmapsofspiralarmsatdifferentro- – phaseresolution tationangleswhichweuseasinputimagesforthesimulations, – signal-to-noiseratio sothatwecomparethepredictedeclipselightcurveswiththe – accuratezerophaseofmid-eclipse observedones. The dashed lines in the left hand panels show – spiralstructuredilutionbythesymmetricdiskcomponent the contributionofthetwo spiralarmstothe lightcurves;the – brightnessdifferencebetweenthetwospiralarms dash-dottedlinesshowthecontributionofthesymmetricdisk componenttothelightcurves;andthesolidlinesshowthetotal Forthesimulations,weuseasinputamodelmapconsisting lightcurve.Therotationangleθ ofthespiralarmmainaxisis 0 of two spirals superimposedon a symmetricdisk. The spirals indicatedineachpanel.Themodelsurfacebrightnessdistribu- E.T.Harlaftisetal.:Spiralshockdetectiononeclipsemaps:SimulationsandObservations 3 Fig.2. A model accretion disk with a spiral structure at different rotation angles and the correspondingtotal, disk, and spiral lightcurves.Themodelsurfacebrightnessdistributionsareshowninalogarithmicgrayscale(darkregionsarebrighter).Dotted lines depictthe primaryRoche lobe, the gasstream trajetory,and the disk radius at 0.2 and 0.6 R (extentof observedspiral L1 shocks;Baptistaetal.2000).Acrossmarksthediskcentre.Thestarsrotatecounter-clockwiseandthesecondaryistotheright ofeachmap.Intheleft-handpanels,verticaldottedlinesdepicttheingress/egressphasesofthediskcentre(whitedwarf).The rotationangleofthespiralarmaxisisindicatedineachpanel(seealsotext).Weadoptthemodelwithanangleα = 46◦ which correspondsto the one observed(Baptista et al. 2000;Harlaftis et al. 1999).The modelwith an angle θ = 136◦ producesan 0 eclipseshapewhichresemblesthatobservedbyBaptistaetal.(2002).Thetwospiralarmsofequalbrightnessarelabeled”A” and”B”intwoofthepanels.Thedashedlinesintheleft-handpanelsshowthecontributionofthetwospiralarmstothelight curves;thedot-dashedlinesshowthecontributionofthesymmetricdiskcomponenttothelightcurves;andthesolidlinesshow the total light curve. For visualization purposes, the curve of the symmetric disc componentis vertically shifted to match the out-of-eclipselevelofthetotallightcurve.Notethattheeclipseshapeisindeedaffectedbytherotationofthespiralstructure. tion maps are shown in a logarithmicgrayscale (dark regions curvesconfirmtheresultsofprevioussimulations(Baptistaet arebrighter).There,thedottedlinesdepicttheprimaryRoche al. 2000), namely, that the orientation and radial position of lobe,thegasstreamtrajectory,andthediskradiiat0.2and0.6 the arms are well recovered in the eclipse maps. The panels R . A cross marks the disk centre. The stars rotate counter- present spiral models for increasing steps of 30◦ starting at L1 clockwiseandthesecondaryistotherightofeachpanel.The 16◦.Theeclipseshapeofthespiralmodelwithrotationangle two spiralarms,of equalbrightness,are labeled”A” and ”B” 46◦ resembles best the observed eclipse maps presented here intwoofthepanels.Thechangeintheshapeoftheeclipseis and in Baptista et al. (2000).Thisis clearerin the nextfigure notable as the spiral arms rotate from 16◦ to 166◦. The wider whichpresentsthesimulationresultswiththephaseresolution eclipseingressshiftstoa wideregressofthespiralarms.The oftheobserveddata.Theeclipseshapeofthespiralmodelwith spiral arm light curvesshow best the change in eclipse shape θ = 136◦ resemblesthe eclipselightcurvesofBaptista etal. 0 withrotationangle.Reconstructionsobtainedfromtheselight (2002). 4 E.T.Harlaftisetal.:Spiralshockdetectiononeclipsemaps:SimulationsandObservations Fig.3.Theeffectofthephaseresolutionofthelightcurveontheimagereconstructions.Theleft-handpanelsshowdatalight- curvesfromthesecondpanelofFig.2forthreephaseresolutions:∆φ=0.005,0.01and0.015cycles.Thecorrespondingasym- metricpartsoftheeclipsemapsforS/N=50and25arepresentedinlogarithmicgrayscale. 2.2.Phaseresolution(∆φ)andS/Nratio tiesineachbin.Thefitisthensubtractedfromeachpixeland theresultingmapiswrittenastheasymmetriccomponent.We Fig.3showstheeffectofreducingthephaseresolutionofthe practicallyremovethebaselineoftheradialprofile,leavingall light curve on the map reconstructions.These and all follow- azimuthal structure in the asymmetric map. We further set to ingsimulationswereperformedwiththeadoptedspiralmodel zeroallnegativeintensitiesintheasymmetricmap. (θ = 46◦). The left hand panels show data light curves of 0 S/N=50 for three phase resolutions: ∆φ= 0.005, 0.010 and The quality of the reconstruction is sensitive to the phase 0.015cycles.Gaussiannoisehasbeenaddedinthelightcurves. resolution of the data. The light curve with the highest phase Notethatthephaseresolutionof∆φ = 0.010issimilartothat resolutionandbestS/N showsthatthe spiralstructureiscon- of the average light curves extracted from the blue spectra of siderablyblurredto a “butterfly”pattern,as a consequenceof theAugust1994outburst(seesection3).Theright-handpanels the azimuthalsmearingeffectofthe eclipsemappingmethod. showtheasymmetricpartoftheresultingeclipsemapsinlog- Poor phase resolution (∆φ=0.015) results in spiral arms with arithmicgreyscaleforS/N=50and25,respectively.Theasym- poorerdefinition,sincethegradientchangeintheeclipselight metriccomponentofeacheclipsemapiscomputedasfollows. curve shape – which testifies the presence of the spirals – is The radial intensity profile is separated into 9 radial bins of poorlysampled.Thenoisemaskstheingress/egressofthespi- equal width. We then sort the intensities in each bin, and fit ralarms(gradientchangesintheeclipselightcurveshape)and a smooth spline function to the lower quartile of the intensi- the eclipse mapping method producesa V-shaped fairly sym- E.T.Harlaftisetal.:Spiralshockdetectiononeclipsemaps:SimulationsandObservations 5 pushthelighttowardsasinglesegmentoftheouterdisk,infact wherethebluespiralarmliesat.Thisexerciseemphasizesthe importanceofknowingthevalueofφ withgoodaccuracy. 0 2.4.Spiralstructuredilutionbythesymmetricdisk component Fig. 5 presents the test results of the spiral structure light di- lution caused by a symmetric disk component. The left-hand panelsshowmodellightcurves(withphaseresolutionof∆φ= 0.01andS/N=50)fordiskmodels(θ = 46◦)inwhichthespi- ralstructurecontributes40,30,20and10percentofthetotal flux. Theright-handpanelsshow the asymmetriccomponents - after subtractingthe symmetric map from the total intensity map-ofthecorrespondingeclipsemapsforS/N=50and25,respectively.Atsmallfractionalcontributions(10%),thespiral structureissignificantlydilutedbythesuperimposedsymmet- ricdisklightandthe“butterfly”-likepattern(bottompanels)is smearedtoa“crescent”-likepatternattheouterdiskfacingthe L point.Providedthatthespiralstructurecontributesasignif- 1 icantfractiontothetotallight(f /f > 0.2),thetwo-arm spiral total structureisthenreasonablyrecoveredasa“butterfly”pattern. Estimatingthecontributionofthespiralsfromtheratioof thefluxintheasymmetricmapcomponentandthatofthetotal eclipse map may lead to systematically underestimated frac- tional contribution.The reason fot this is that part of the flux from the spiral arms goes into the symmetric component be- causeoftheazimuthalsmearingeffectoftheeclipsemapping method.Theerrorincreasesforlightcurvesoflowerphaseres- olution:the fractionalcontributionof the spiral armsis better recoveredwhentheeclipselightcurveshapeisbettersampled. Usingoursimulations,wedeterminethattheinferredfractional Fig.4.Theeffectsofaccuratephasingofthemid-eclipse(phase contributionof the spirals (40%)maybe underestimatedby a offset ∆φ ) on the reconstructions. The value of ∆φ is indi- 0 0 factorof 1.6-2.4forlightcurves(S/N=25)with phaseresolu- cated in each panel; the asymmetric component of the corre- tionof∆φ=0.010−0.015orbitalcycles(asobserved),respec- sponding eclipse maps are shown in the right panels in the tively.LightcurveswithS/N=50and∆φ = 0.005canrecover same logarithmic greyscale. The notation is similar to that of thefractionalcontibutionofthespiralstructurewithin12%.At theotherfigures. smallfractionalcontributions(<10%),thespiralstructurewill start to be overestimated(30-40%) by the technique.The er- metricmodellightcurveofconstantingress/egressslopewhich rorinthefractionalcontributionofthespiralsalsodependson will drive the solution to a more symmetric configuration by theS/Nofthelightcurvebutismuchsmallerthanthatcaused smearingthespiralarms.Thus,thespiralscannotberesolved bylowphaseresolution.Thus,sinceweestimatedafractional onthemapifthelightcurveshavelowS/N(orareaffectedby contributionof0.15–0.3inBaptistaetal.(2000),thetruecon- significantdiskflickering). tributionofthespiralarmsinthoseeclipsemapsmaybeinthe range0.3–0.6.Hence,themodelswith f /f ∼ 0.3−0.4 spiral total shouldbeagoodapproximationoftherealcase.Inconclusion, 2.3.Accuratezerophaseofmid-eclipse(∆φ0) wecanonlyplacealowerlimittothefractionalcontributionof thespiralarmstothetotallightusingeclipsemaps. InFig.4weapplyadditionalphaseoffsetstotheeclipselight curvesinordertoexploretheeffectonthespiralarmsoftheun- certaintyontheexactzerophase(0.006cyclesforIPPeg;see 2.5.Brightnessdifferencebetweenthetwospiralarms section3).Smallerrorsinthemid-eclipse,∆φ ≃0.005cycles, 0 leadtodistortionsintheeclipsemapbychangingtheazimuthal Finally,weundertakeatestwithaspiralstructurewhosearms position and extension of the spiral arms. Positive (negative) are of unequal brightness. This is driven by the fact that ob- phase offsets displace both arms to the trailing (leading) side servedDopplermapsshowanintensitydifferencebetweenthe oftheprimaryRochelobeandalsoreducesthestrengthofthe two spiral arms (Harlaftis et al. 1999; Steeghs 2001). Fig. 6 blue(red)arm,thusseverelydistortingthedisklightdistribu- presents the effect of brightness difference between the two tion.Aphaseoffsetof-0.010tothelightcurvesissufficientto spiral arms on the map reconstructions.We build model light 6 E.T.Harlaftisetal.:Spiralshockdetectiononeclipsemaps:SimulationsandObservations Fig.5.Theeffectsofdilutionofthespiralstructurelightbyasymmetricdiskcomponentontheimagereconstructions.Theleft handpanelsshowmodellightcurves(∆φ =0.01,S/N=50)fordiskmodels(θ = 46◦)inwhichthespiralscontribute40,30,20 0 and10percentofthetotalflux.Thecentreandrighthandpanelsshowtheasymmetricpartsofthecorrespondingeclipsemaps forS/N=50and25,respectively.Whentheemissionfromthespiralarmssufferslargedilution(e.g.,fractionalcontributionof10 percent)themethodlosesitsabilitytorecoverthespiralarmsandreturnsonlyanasymmetricstructurewitha“crescent”shape attheouterdiskandtowardstheL point. 1 E.T.Harlaftisetal.:Spiralshockdetectiononeclipsemaps:SimulationsandObservations 7 Fig.6.Theeffectofbrightnessdifferencebetweenthetwospiralarmsontheimagereconstructions.Theleft-handpanelsshow lightcurves(S/N=50)formodelsinwhichtheredandbluearmshaveequalbrightness(top),andmodelsinwhichtheredarmis fainterthanthebluearminthebrightnessratio1:1.5(middle)and1:2(bottom).Therighthandpanelsshowthecorresponding eclipsemapsinloggrayscaleforthreedifferentS/N.LowS/Ndata(S/N<30)mayleadtoalossofthefainterspiralarm.Model armsofequalbrightnessesarepreservedinthereconstructionmap,regardlessoftheS/N. curves (∆φ = 0.01, S/N=50) from spiral structure/disk mod- and data reduction procedure. In summary, 164 blue spectra els,asdescribedinFig.2inwhichtheredandbluearmshave wereobtainedataspectralresolutionof100kms−1 atHβand equalbrightness(1:1,top-leftpanel),orthe red armis fainter a time resolution of 220 seconds covering the emission lines -asobserved-withabrightnessratiotothebluearmat1:1.5 Hβ,Hγ,HeII4686Å(4040–4983 Å). Here,weextendtheir (middle-leftpanel) and finally at 1:2 (bottom-leftpanel). The analysisinordertoincludetheeclipsemapsforcomparisonto otherpanelsinthefigureshowthecorrespondingeclipsemaps the Dopplermaps. We combinedthe foureclipse lightcurves in logarithmic grayscale for three different S/N ratios (50, 30 (E= 25158, 25159, 25164 and 25165) from the two consec- and20).Itisnotablethatbotharmsappearinthemapasa“but- utive nights the observations took place (30/31 August 1994) terfly”patternwhentheyhaveequalbrightnessesregardlessof to produce average eclipse light curves with phase resolution the S/N ratio. However,the brightnessdifferencebetweenthe of 0.010cycles.Inparticular,we extractedlightcurvesofthe spiral arms at low S/N ratio data (< 30) leads to loss of the bluecontinuumandoftheemissionlinesHγ,HeII4686Å, the fainterspiralarmintheimagereconstruction. BowenblendandtheHeI4472Å(Fig.5inMorales-Ruedaet al. 2000) in order to reconstruct the images of the accretion disk. 3. Spiralshockobservations We processed the light curvesbefore applyingthe eclipse 3.1.EclipsemapsoftheAugust1994outburst mappingprocedureso thatthecontinuumlevelbeforeandaf- Morales-Rueda et al. (2000) present Doppler tomography ter eclipse is the same; otherwise, artifacts are raised. These showing persistent spiral shocks in the accretion disk of IP low-amplitudeorbital variations were removed from the light PegduringtheAugust1994outburst.Thereaderisreferredto curvesbyfittingasplinefunctiontothephasesoutsideeclipse, Morales-Ruedaetal.(2000)forthedetailsoftheobservations dividing the light curve by the fitted spline, and scaling the 8 E.T.Harlaftisetal.:Spiralshockdetectiononeclipsemaps:SimulationsandObservations Table1.SummaryofSimulations and (i,q)=(86.5◦, 0.31) (Beekman et al. 2000),where i is the inclination and q is the mass ratio. These tests do not show anydifferencecausedbyaslightchangeintheadoptedorbital parameters. Thus, we adopt in the following the geometry of (f /f ) (f /f ) S/N ∆φ spiral total model spiral total recon Wood&Crawford(1986). 0.40 0.17 25 0.015 Fig.3 0.40 0.25 25 0.010 “ 0.40 0.28 25 0.005 “ AllmapsinFig.7showanasymmetricdisk.Inordertore- 0.40 0.18 50 0.015 “ solvetheasymmetricpartofthediskwesubtractthesymmet- 0.40 0.25 50 0.010 “ ricpartofthediskandplottheresidualontherightpanelsof 0.40 0.35 50 0.005 “ thefigure.Thecontinuumeclipseisskewedtowardstheegress 0.40 0.25 25 0.010 Fig.5 andmapsintoanasymmetricdiskwhichisbrightertowardsthe 0.30 0.32 25 0.010 “ 0.20 0.13 25 0.010 “ gasstreamandRL1.TheBowenblendandHeIIhigh-ionization linesshowarelativelynarrow,asymmetriceclipseshapewhich 0.10 0.14 25 0.010 “ mapsintoasymmetricbrightnessdistributionsconsistentwith 0.40 0.25 50 0.010 “ spiral structure and similar to those in Baptista et al. (2000, 0.30 0.27 50 0.010 “ 0.20 0.19 50 0.010 “ see theirFig.2).However,theBalmerandHeIline mapsare 0.10 0.13 50 0.010 “ markedlydifferent.ThestrongasymmetricBalmeremissionis locatedclosetoandevenoutsidethetidalradius,withthemax- (fspiral/ftotal)model:isthefractionalcontributioninthemodeleclipse imumemissionatanangleof−30◦withrespecttotheline-of- map, centres.ThecentreoftheHeIeclipseoccursbeforethatofthe (fspiral/ftotal)recon: is the fraction measured by dividing the aver- Balmer lines, which shifts the asymmetric emission towards agefluxintheasymmetricmapbytheaveragefluxintherecon- a direction opposite to the gas stream (blue-shifted velocities structedeclipsemap of the disk), and beyond the tidal radius. We apparently see onlyoneofthearmsinHeIandthereisalmostnoevidenceof the spirals in the Balmer lines – probablybecause theiremis- result to the spline function at phase zero. This procedurere- sionissignificantlydilutedbyotherlightsourcesintheselines movesorbital modulations,such as the brightspot, with only (see following section on velocity-resolvedlight-curves).The minor effects on the eclipse shape itself (e.g., Baptista et al. “crescent”-shape of the brightness distribution of the Balmer 2000).Theotherfactorthataffectstheeclipsemappingproce- lines is reminiscent of the distributions obtained for simula- dure(seesimulationatFig.4)isanaccurateephemerisforthe tionswherethespiralscontributeonly10percentofthelight eclipseminimum.Here,weusethelinearephemerisbyWolfet at the corresponding wavelength (see Fig. 5). In comparison, al.(1993)aftercorrectingthephasezeroformid-eclipserather Morales-Ruedaetal.(2000)usetheout-of-eclipsespectrafrom than the white dwarf egress (the white dwarf eclipse width is thesameorbitalcyclestoeasilyresolvethespiralshocksusing ∆φ=0.086cycles;Wood&Crawford1986) Dopplertomography. T (HJD)=2445615.4156+0.15820616E mid whereT istheinferiorconjunctionofthereddwarf.IPPeg mid showscyclicalorbitalperiodchangesofamplitude0.002days 3.2.EclipsemapsfromJuly1998outburst (or0.013orbitalcycles;Beekmanetal.2002).Furthemore,the scatterofeclipsetimingsforagivenepochisalsoabout0.001 days(0.006cycles).Clearly,evenasinusoidalephemeriscan- WealsousedWHTservicetimetoobtainphase-resolvedspec- notpredicteclipsetimingswithprecisionbetterthan0.01-0.02 trophotometry with the ISIS spectrograph of an eclipse of IP cycles for IP Peg (Wolf et al. 1993). Therefore, the best ap- Peg during its July 1998 outburst decline, four days after the proachin order to properlyphase the lightcurvesis to center peakoftheoutburst(18July1998).The23bluespectra(and31 the white dwarf eclipse using contemporaryquiescenteclipse redspectra)coveredtherange4407.6–4847.7Å (and6310.7– timings. The August 1994 data (eclipse cycle E ≃ 25160) 6717.6 Å) at a spectral resolution of 0.2 Å per pixel (and is luckily bracketed by two HST sets of observations of IP 0.8 Å, respectively) and with an exposure of 120 seconds. Peg in quiescence (Baptista et al. 1994). From these timings, Thespectracoveredtheeclipsebetween0.85to1.2cyclesata we infer that the white dwarf mid-eclipse at that epoch oc- phaseresolutionof0.011cyclesfortheredspectraand0.014 curred 0.008 orbital cycles before the prediction of the linear cycles for the blue spectra. The reconstructed eclipse maps ephemerisofWolfetal(1993).Hence,weadded+0.008cycles show similar distributionsto the August1994 maps, but with tothephasesofthelightcurvestomakephasezerocoincident inferior quality which is most likely due to the poorer phase with the inferior conjunction of the red dwarf. The minimum resolution and the later outburst stage (closer to quiescence oftheeclipseinthelinesisdisplacedtowardsearlierphasesin which should result in a fainter spiral structure).In summary, comparisonto the continuumlightcurves.Eclipsemapswere the eclipse maps are consistent with the reconstructionsfrom then made with three different geometries: (i,q)=(81◦, 0.5) the August1994data (previoussection) andthe August1996 (Wood & Crawford 1986), (i,q)=(79.4◦, 0.58) (Marsh 1988) data(Baptistaetal.2000). E.T.Harlaftisetal.:Spiralshockdetectiononeclipsemaps:SimulationsandObservations 9 Fig.7. The light curves, fits, eclipse maps and asymmetric parts of the maps of the blue continuumand of the emission lines HeII 4686Å, Bowenblend,HeI4472Åand Hγ (August1994outburst;Morales-Ruedaetal.2000).Themiddleofingress andegressofthediskcentrearemarkedwithverticaldottedlinesinthelightcurvesandthefitstothedataarealsoplotted.Note thattheeclipseminimumvariesinphasebetweentheBalmerandheliumemissionlinesaswellaswithrespecttothecontinuum minimum.TheRochelobeofthewhitedwarfisplottedtogetherwiththediskradiusat0.6R .Thedonorstarliestotheright L1 of the disk map and the ballistic trajectory of the gas is also marked. The reconstructionleads to asymmetric eclipse maps in 10 E.T.Harlaftisetal.:Spiralshockdetectiononeclipsemaps:SimulationsandObservations Fig.8. Velocity-resolved(core/wings) eclipse light curves can reveal with clarity the spiral structure. The core of the Hγ line profiles(±250km s−1) duringeclipse resultin a reconstructedemission distributiontowardsthe L . Thewings ofthe Hγ line 1 profiles(±700−1300kms−1)duringeclipseresultinareconstructedemissiondistributionconsistentwithaspiral-armstructure. The earlier mid-eclipse caused by the low-velocity emission component results in the distorted, “crescent”-like eclipse map. Lines,lobesandcirclesasinFig.7.Theright-handpanelspresentS/Nratiomaps,madeusingMonte-Carlosimulations(pixels withS/N≤ 5arepaintedwhite . 3.3.Velocity-resolvedeclipsemaps:Revealingthe ponents to the total line fluxes, for example from the donor spiralshocks starduringoutburst(Harlaftis1999).Duringoutburst,another contaminatinglinesourcetothediskemissionisalow-velocity We investigate here velocity-resolvedeclipse maps since it is emissioncomponent(Harlaftisetal.1999;Steeghsetal.1996). a well established fact that there are non-disk emission com- Since the spiral arms and the secondary star contribute to the