Mon.Not.R.Astron.Soc.000,1–13(2004) Printed2February2008 (MNLATEXstylefilev2.2) Time-series Paschen-β spectroscopy of SU Aurigae Ryuichi Kurosawa⋆, Tim J. Harries and Neil H. Symington SchoolofPhysics,UniversityofExeter,StockerRoad,ExeterEX44QL 5 Datestobeinserted 0 0 2 ABSTRACT n a We present time-series echelle spectra of the Paβ line of the T Tauri star SU Aur, ob- J servedoverthreeconsecutivenights.Thelineshowsstrongvariability(∼ 10percent)over 0 the velocity range (100kms−1, 420kms−1) in the red broad absorption component, and 1 weaker variability (∼ 2 per cent) over the velocity range (−200kms−1, 0kms−1) in the bluewing.Thevariabilityinthevelocityrange(−200kms−1, 0kms−1)iscorrelatedwith 1 thatin(200kms−1, 400kms−1),andthevariabilityinthesevelocityrangesanti-correlates v withthatin(0kms−1, 100kms−1).Themeanspectrumfromthesecondnightshowsasug- 5 6 gestionofablue-shiftedabsorptioncomponentatabout−150kms−1,similartothatfound 1 intheHαandHβ lines.Wefindthepositionofthesubpeakintheredabsorptioncomponent 1 changessteadily with time, and its motion modulateson half the rotationalperiod.We also 0 findthatthemodulationofthelineequivalentwidthisassociatedwithahalfandathirdofthe 5 rotationalperiod,whichisconsistentwiththesurfaceDopplerimagesofSU Aur.Radiative 0 transfermodelsofarotationallymodulatedPaβ line,producedintheshock-heatedmagneto- h/ sphericaccretionflow,arealsopresented.Modelswithamagneticdipoleoffsetreproducethe p overallcharacteristicsoftheobservedlinevariability,includingthelineequivalentwidthand - themotionofthesubpeakintheredabsorptiontrough. o r Keywords: stars:formation– stars:individual:SU Aur– circumstellarmatter– stars: pre- t s main-sequence a : v i X 1 INTRODUCTION CollierCameron&Campbell 1993; Shuetal. 1994a). This r a picture of the accretion flows is supported by the obser- T Tauri stars (TTS) are young (<∼ 3 × 106yrs, vation that CTTS have relatively strong (∼ 103G) mag- Appenzeller&Mundt 1989) low-mass stars, and are thought netic fields (e.g. Johns-Krull,Valenti,Hatzes,&Kanaan to be the progenitors of solar-type stars. Classical T Tauri stars 1999; Guenther&Emerson 1996; Symingtonetal. 2004b) (CTTS) exhibit strong Hα emission, and typically have spectral and by radiative transfer models which reproduce the types of F–K. Some of the most active CTTS show emission in gross characteristics of the observed profiles for some TTS higher order Balmer lines and metal lines (e.g. CaII, H and K). (e.g. Muzerolle,Calvet,&Hartmann2001). They also exhibit an excess amount of continuum flux in the SU Aurigae is a bright (J ∼ 7, Chakraborty&Ge 2004) ultraviolet(UV)andinfrared(IR). young star with a G2 spectral type (Herbig 1960), and has Line profile studies of CTTS show evidence for both been classified either as a CTTS (e.g. Giampapaetal. 1993; outflows and inflows, as seen in the blue-shifted absorption Bouvieretal.1993)orearly-typeTTS(e.g.Herbstetal.1994).It features in Hα profiles (e.g. Herbig 1962) and the inverse isalsothe prototype ‘SU Aur type’ (Herbig&Bell1988). Based P Cygni (IPC) profiles (e.g. Kenyonetal. 1994; Edwardsetal. onmodellingofthespectralenergydistribution(SED),SUAuris 1994) respectively. Typical mass-loss rates of CTTS are about 10−9M⊙yr−1 to10−7M⊙yr−1 (e.g.Kuhi1964;Edwardsetal. known tohave an accretion disc (∼ 400au) along withan outer envelope (e.g. Akesonetal. 2002). Near-infrared coronagraphic 1987; Hartiganetal. 1995), and mass-accretion rates range from 10−9M⊙yr−1to10−7M⊙yr−1(e.g.Kenyon&Hartmann1987; observations of Nakajima&Golimowski (1995) and Gradyetal. (2001) have shown that the object is associated with a reflection Bertout,Basri,&Bouvier1988;Gullbringetal.1998). nebulaandoutflows.Mostrecently,Chakraborty&Ge(2004)have In the currently favoured model of accretion on to presented high resolution (0.3 arcsec) J-, H- and K-band adap- CTTS, the accretion discs are disrupted by the stellar mag- tiveopticsimagesdisplayingnebulositywithadisc-likestructure netosphere which channel the gas from the disc on to the aroundSUAur. stellar surface (e.g. Uchida&Shibata 1985; Koenigl 1991; SUAurhasbeenasubjectofanumberofvariabilitystudies, mainlyintheoptical,e.g. Giampapaetal.(1993),Johns&Basri ⋆ E-mail:rk@astro.ex.ac.uk (1995),Petrovetal.(1996),Oliveiraetal.(2000)andmostrecently 2 R. Kurosawaetal. Unruhetal.(2004).TheHαline,whichismostcommonlyusedfor trabyusingtheleastsquarefitofthespectrawithacombination variability studies of TTS, is produced over a large circumstellar oftwoGaussianfunctionsandathirdorderpolynomial.Afterthe volume, and shows evidence of outflow (winds) as well as mag- preliminary reduction by the pipeline was finished, a wavelength netosphericinflow.Johns&Basri(1995)studiedthevariabilityof calibration was performed using a combination of OH sky emis- HαandHβ profilesofSUAur,andfoundthatthemodulationof sionlinesandcomparisonarclines.Finallyweappliedheliocentric thewindandtheaccretioncomponentsintheprofilesareapprox- velocity corrections and shifted the spectra into therest-frame of imately180◦ outofphase.Thisledthemtosuggestthatthemag- SUAur, adopting theradial velocity measurement (+16kms−1) neticfieldaxisisslightlytiltedwithrespecttotherotationaxisof ofHerbig&Bell(1988). thestar. Thetopologyofthemagneticfieldisstillindispute.Despite of the overall success of the dipole field geometry used in ex- plainingmanyobservedfeaturesofCTTS,Johns-Krull&Gafford 3 RESULTS (2002) re-examined the validity of this assumption. They found that observations didnot support the relationshipsbetween mass, A general overview of the dataset is presented in Fig. 1. The radius, and rotation period that magnetospheric accretion theory mean spectrum shows a classic inverse P Cygni (IPC) profile, predicts under the assumption of a dipolar field, but found bet- with the blue-wing of the emission component extending to ter agreement when a non-dipole fieldtopology was used. In ad- −200kms−1andtheabsorptioncomponentwithmaximumdepth dition, forSU Aur,Unruhetal. (2004)found alackof thecircu- at+100kms−1 andextendingoutto+200kms−1.Thepeakin- larpolarisationacrosssomestrongphotosphericlines;onceagain tensity of the line, relative to the continuum, is about 1.25. Al- in conflict with the expectations for a large-scale dipole. Further, though comparable in strength, the Paβ profiles of SU Aur pre- Oliveiraetal.(2000)foundthetime-laggedbehaviourinthevari- sentedbyFolha&Emerson(2001)showsignificantemissionred- abilityofsomeopticallines,andproposedthatthiscanbecaused wardsoftheabsorptiondip,andalsohavemaximumabsorptionoc- bythepresenceofanazimuthalcomponentinthemagnetosphere. curringat0kms−1 i.e.theyappeartobeshiftedby∼ 90kms−1 Near-IR profiles, such as Paβ and Brγ are likely to become bluewardcomparedtoourdataset. importantprobesofaccretioninCTTSandtheirlower-masscoun- The mean spectra from each night are shown in Fig. 2. It is terparts,sincetheyappeartosufferfromlesscontaminationbyout- immediatelyapparentthatthebluesideoftheprofileismorestable flowsthanHα(e.g.Folha1998;Folha&Emerson2001,although than the red, with variability of less than 10 per cent (in contin- seeWhelanetal.2004)andarelessaffectedbydustobscuration, uumunits)atthelinepeakandblueward.Thereisasuggestionof enablingthestudyofaccretioninhighlyembedded objects.Here blue-shiftedabsorptionatabout−150kms−1onthesecondnight. we present time-series Paβ spectra of SU Aur, which we use to Interestingly, theblue-shifted absorption feature at −150kms−1 probetheaccretiongeometry. InSection2wegivedetailsonthe isalsoseeninHα(Giampapaetal.1993)andHβ (Johns&Basri observations and the data reduction. The results and analysis are 1995)profiles,andthemodulationperiodoftheabsorptionfeature presentedinSection3.Radiativetransfermodelsarecomputedin isidentified as therotational period of SU Aur (∼ 3 d). The red anattempttoexplaintheoverallobservedvariabilityfeatureinSec- sideof the mean profilesshows strong variability, extending red- tion4.TheconclusionsaregiveninSection5. wardtoover+400kms−1.Onthefinalnightthereisemissionon theredsideoftheabsorptiontrough,andtheprofilemoreclosely resemblesthatpresentedbyFolha&Emerson(2001). The greyscale dynamic spectra (Fig. 1) reveal the gradual 2 OBSERVATIONS changes that occur over a timescale of hours. On the first night thereisafeaturethatacceleratesmonotonicallyredwardacrossthe A total of 503 Paβ (λ = 1.28181µm) spectra with a signal-to- noise ratio (S/N) of ∼ 90 per pixel (in the continuum) were ob- absorptiontrough.Onthesecondnightboththeredandbluesides of theprofilearelower thanthemean. Finally,on thethirdnight tainedover3nights(2002December1–3)attheUnitedKingdom weseethegrowthofanemissionfeatureintheabsorptiondip.The InfraredTelescope(UKIRT)onMaunaKea,Hawaii.Theapproxi- characteristiclevelofthisred-wingvariabilityisabout10percent. matetemporalsamplingratewasonespectrumevery3minutes. The Cooled GratingSpectrometer No. 4 (CGS4), a 1–5 µm multi-purpose 2-D grating spectrometer with a 256 × 256 InSb array, with the echelle grating and long camera (300mm), was 3.1 Temporalvariancespectra used. This provides a velocity resolution (at 1.28181µm) of ∼ 16kms−1 using∼ 1pixslitwidthwithouttheNyquiststepping. Inordertoquantifythelevelandsignificanceofthevariabilityseen Thewavelengthrangeoftheechellespectraisabout3600kms−1 inthePaβprofiles,thetemporalvariancespectrum(TVS)analysis methodproposedbyFullerton,Gies,&Bolton(1996)wasapplied providing enough continuum on either side of the line for accu- to the time series spectra from each night separately, and also to raterectification.Unfortunatelythereareinsufficientphotospheric allthreenightscombined. Thismethod statisticallycompares the featurestoperformaveilingcorrection(butseeSection4.2). Tel- deviationsinlinefeatureswiththoseoftheadjacentcontinuum.In luricstandardstarswereobservedthroughouteachnight(every2–3 other words, thelevel of deviation at agivenwavelength iscom- hours)tocorrectforinstrumentresponseandatmospherictransmis- putedwithaweightfunctionwhichisinverselyproportionaltothe sion. signal-to-noise(S/N)levelofthecontinuum. Byusingthedefini- ThedataobtainedwithCGS4werereducedusingastandard tionofFullertonetal.(1996),thej-thvelocitybinoftheTVS,in procedure(c.f.Puxleyetal.1992):1.biassubtraction,2.flat-field, thelimitofhighphoton-count,canbewrittenas: and3.optimalextraction(Horne1986).Allspectrawerereduced inthesamemanner,usingtheORAC-DRpipelineprogram.Intrin- N sicabsorptioncomponents inthestandardstars,usedinstep3to (TVS) = 1 S −S¯ 2 wi (1) correctforthetelluriclines,weresubtractedfromtheoriginalspec- j N−1 Xi=1(cid:0) ij j(cid:1) Sij Time-series Paschen-β spectroscopyofSU Aurigae 3 1.3 1.2 x u Fl malized 1.1 or N 1 0.9 0.8 -400 -200 0 200 400 Velocity (km s-1) Figure2.Meanspectrafromeachnight:Thefirstnight(solid),thesecond night(dashed),andthethirdnight(dotted). Whilemostofthevariability occurs in the red side (50 kms−1, 500 kms−1) of the line, small yet noticeablechangesinfluxlevelcanbeseenin(−200kms−1,0kms−1). Thefluxlevelat∼250kms−1isbelowthecontinuumonthefirstandthe secondnight,butitisinemission(abovethecontinuum)onthethirdnight. Ahintofablue-shiftedabsorptioncomponentat∼150kms−1isseenon thesecondnight. deviations; hence, it provides a more accurate impression of the deviationfromthevariabilitywithrespecttothecontinuum. Using equation 1, the temporal deviation spectrum of the times-seriesspectrafromeachnightwascomputed,andtheresults were placed in the top panels of Fig. 3. In the same figure, the spectradividedbythemeanspectrumof eachnight (thequotient Figure1.Thetime-seriesspectraofPaβ.Themeanspectrum(normalised) spectra) and themean spectrum areshown asa function of time. ofthe503spectraobtainedduringthethreenight(2002December1–3)is Similarly, (TVS)1/2 computed from all three nights is placed in shownatthebottom.Inthemiddlepanels,thequotientspectra(dividedby thetopofFig.1. themeanspectrum)asafunctionoftime(HJD−2452600)areplotted The(TVS)1/2 valuewhichcorresponds tooneper centsta- asgreyscaleimageswiththecolourscaledfrom1.1(white)to0.9(black). tisticalsignificance(theχ2-probability)isalsoshowninthesame Thetemporaldeviationspectrum(TVS)1/2fromthe503spectraisshown figure as a reference point. In the absence of real variability, the onthetoppanel(c.f.Section3.1).Inallplots,thehorizontal axesarein observed (TVS)1/2 values should be below this level for 99 per velocityspaceinthestellarrestframe.Thegreyscaleimagesclearlyshow cent of time. From the (TVS)1/2 plot in Fig. 1, we confirm variabilityonbothredandbluesidesofthespectra,butlittlevariabilityis that the line displays strong variability within the velocity range seennearthelinecentre.Thedashedlineinthetoppanelshowsthesta- tisticalsignificanceatthe1percentlevel,anditindicatesthatthevelocity (100kms−1, 420kms−1) in the red wing, and weaker variabil- range(−200kms−1,420kms−1)hassignificantvariability. itywithinthevelocityrange(−200kms−1, 0kms−1)intheblue wing.The(TVS)1/2 plotsinFig.3showthatthevelocityranges inwhichthevariabilityismostactivechangefromnighttonight. whereS isthesignalofthej-thvelocitybinbelongingtothei-th Using the mass (M∗ = 2.25M⊙) and the radius (R∗ = ij spectrumofatime-series,andNisthenumberofobservedspectra. 3.6R⊙)ofSUAurfromCohen&Kuhi(1979),wefinditsescape S¯ istheweightedmeanspectrumdefinedas velocitytobeVesc = (2GM∗/R∗)1/2 = 490kms−1.Thisvalue j isan upper-limit for the velocity of the material as it impacts on N thestellarsurface,andindeedweseethattheextentoftheredab- 1 S¯j = N wiSij . (2) sorptioninthelineprofileis∼420kms−1,andthatthemaximum Xi=1 velocityofsignificantvariabilityis∼420kms−1. Theweightingfactorw forthei-thspectrumisdefinedas i 1/σ2 3.2 Motionofasubpeakintheabsorptiontrough ic w = (3) i 1 (cid:0)N (1(cid:1)/σ2 ) In the red absorption trough of the mean spectra (see the bottom N k=1 kc panelsofFig.3),wefindthepresenceofasubpeakatV =∼250, P whereσ andσ arethenoiseinthecontinuumforthei-thand ∼ 180 and ∼ 260kms−1 for the first, second and third nights. ic kc k-thspectra. Wealsofindthepositionofthesubpeak(indicatedbyarrowsinthe As mentioned by Fullertonetal. (1996), a more convenient samefigure)changesduringonenight.Itappearsthatamaincause quantitytobeplottedisthesquarerootofTVS(temporal devia- ofthevariabilityseeninthered-wing(asseeninthegreyscaleim- tionspectrum)because(TVS)1/2 scaleslinearlywiththespectral agesinthesamefigures)isduetothemotionofthissubpeak, 4 R. Kurosawaetal. Figure3.Thesummaryofobservationsfromeachnight(thefirstnighttothethirdnightfromlefttorightrespectively).Foreachnight,thenormalisedmean spectrum(bottom),thequotientspectra(dividedbythemeanspectrum)(middle)withcolourscaledfrom1.08(white)to0.92(black)asafunctionoftime (HJD−2452600),andthetemporaldeviationspectrumTVS−1/2(top)inunitsof1/100ofthecontinuumflux(%Fc)areshown.Thedashedlineinthetop plotindicatesthestatisticalsignificancefor1percentlevel.Inthebottomplots,thepositionsofthesubpeakintheredabsorptiontroughsareindicatedwith arrows,andtheyseemtobemovingfromnighttonight(seeSection3.2). The positions of the subpeak were estimated for each spec- The two lines (nmax = 2 and nmax = 3) are very similar trum,byapplyingaquadraticfittothedatapointsaroundthesub- toeach other aswecanseefromthefigureandthevaluesof the peak. The results are shown in Fig. 4 as a function of time. The Fouriercoefficients.Thecontributionsofthethirdharmonicterms amplitudeofthechangeinthesubpeakpositionisrelativelylarge (a3 and b3) are very small compared to the first and the second on the second night compared to those of the first and the third harmonic terms.Totest whether thethirdharmonic termsshould nights. To demonstrate the motion of the subpeak occurred dur- be included in the fitting functions, we have performed an F-test ing the second night, we plot the time-averaged (∆t = 70 min) (c.f.Bevington 1969). From the table, the numbers of degree of spectrainFig.5.Thefigureshowsaweaksubpeak movingfrom freedomareν2 =497andν3 =495fornmax =2andnmax =3 V ∼170kms−1to∼220kms−1duringthecourseofthenight. respectively.Usingthereducedchi-squarevaluesinthetable,we The subpeak positions were fittedwitha function (f) inthe find Fχ = χ2(nmax =2)−χ2(nmax =3) /χ2ν2 = 2 and formoftheFourierseries, F = χ2 /χ2(cid:8) = 1. Since F > F, the thir(cid:9)d harmonic terms ν2 ν3 χ nmax shouldbeincludedinthefittingalthoughtheircontributionisrela- a0 2πn 2πn f(t)= + a cos t +b sin t (4) tivelysmall. 2 Xn=1 n n (cid:16) P (cid:17) n (cid:16) P (cid:17)o From this analysis we found that the motion of the subpeak in the red absorption trough is possibly associated not only with wheretandP arethetimeofobservationandtherotationalperiod of SU Aur respectively, and nmax = 3. The reasons for choos- P, but also with P/2. This is consistent with the the tilted-axis magnetosphericaccretionmodelmentionedearlier. ingtheformofthefittingfunctionaboveareasfollows:1.asim- InspiteoftheexcellentfitsofthedatawithFourierseries,we plestpossibleformisdesirable,and2.thefirstharmonictermsin theFourierseriesmight bepresentifthevariationisrelatedwith shouldnotignoreapossibilitythattheratherlargeamplitudeofthe changeinthesubpeakpositionseenonthesecondnightwascaused the stellar rotation, 3. the second harmonic terms in the Fourier byasingleepisodicevent (e.g. byatemporal andlocal enhance- series might be present if the variation is caused by the tilted- axis magnetospheric accretion model (e.g. see Shuetal. 1994a; mentoftheaccretionflow).Assumingconservationofenergy,the Johns&Basri1995),and4.thethirdharmonictermsintheFourier free-falltime(tff)ofanobjectfromtheco-rotationradius(r=Rc) series might be present because the surface Doppler images of ofthestartothestellarsurface(r=R∗)canbewrittenas SUAurbyPetrovetal.(1996),Mennessier(1997)andUnruhetal. (2004)weaklysuggestthepresenceofcoolspotsonthesurfaceat tff =− 1 R∗ Rc −1 −1/2dr (5) threedifferentlongitudeswhichareapproximatelyequallyspaced. Vesc(Rc)ZRc (cid:16) r (cid:17) withTnhmeaxfit=wit1hannmdanxm=ax3=is2shfoowrncoinmFpiagr.is4ona.loInngawllicthastehse, tfihtes whereVesc(Rc) = (2GM∗/Rc)1/2,andR∗ andM∗arethestel- lar radius and mass respectively. By evaluating the integral, one fixedperiodof2.7d(Unruhetal.2004)wasadopted.SeeTable1 obtains forthesummaryofthefittingparameters.Thefigureclearlyshows thhaantdt,htehefitfiwtsiwthitnhmnamxa=x =12faailnsdtonmreapxre=se3ntatrheesdigantaifi.cOannttlhyeboetthteerr. tff = VescR(cRc)nπ2 +q1/2(1−q)1/2−arcsin(cid:0)q1/2(cid:1)o (6) Time-series Paschen-β spectroscopyofSU Aurigae 5 0.5 300 -1m s)250 0.4 k ns ( o ositi 0.3 P k 200 a Sub-Pe ed Flux 0.2 z ali 150 m or N 0.1 9.5 10 10.5 11 11.5 12 12.5 HJD - 2452600 (days) 0 Figure4.Thepositionsofthesubpeak(circles)intheredwingofthePaβ profilefromthethreenightsareplottedasafunctionoftime.Thedatawere fittedwiththeFourierseries(equation4)withthetermsuptonmax = 1 (dash-dotline),nmax = 2(dashedline)andnmax = 3(solidline).The -0.1 corresponding fittingcoefficients aresummarisedinTable1.Itisclearly shownthatthelinewithnmax =1doesnotfitthedataverywell,butthe 50 100 150 200 250 300 350 lineswithnmax =2andnmax =3fitthedataequallywell.Thecontri- butionfromthethirdharmonictermsintheFourierseriesisverysmall.The Velocity (km/s) motionofthesubpeakintheredabsorptiontroughisassociatednotonly withtherotationalperiodofSUAur(P),butalsowithhalfoftheperiod Figure5.Thetime-seriesspectraofthePaβfromthesecondnight(solid) (P/2).Atypicalsizeoftheuncertaintyinthepeakpositionsisindicatedon andthequadraticfitsforthesubpeakpositions(dashed).Eachspectrumis thelower-leftcorner. theaverageof27consecutivespectra(∆t=70min)inchronologicalorder fromthetoptobottom.Eachspectrumisverticallydisplacedby-0.1from whereq = R∗/Rc.Usingthemass(M∗ = 2.25M⊙)andthera- trheed-pwrienvgioaupspesparescttroumbefmorovcilnargitfyr.oTmhVep∼osi1ti7o0nkomfas−w1eatok∼sub2p2e0akkmins−th1e dius(R∗ = 3.6R⊙)ofSUAurfromCohen&Kuhi(1979)along duringthecourseofthesecondnight.Thepositionsofthesubpeakwere with the co-rotation radius (Rc = 3R∗) in equation 6, we find estimatedusingtheoriginalspectra(beforebeingaveragedover27spectra), tff = 10.5h.Thistime-scaleiscomparabletotheobservingtime byapplyingaquadraticfittothedatapointsaroundthesubpeak(Fig.4). spanofagivennight,sotheassociationofthesubpeakmotionon Thearrowsindicatethemeasuredpositionsofthesubpeak. thesecond night withasingleepisodicevent cannot beruledout by timescale arguments alone. However, the systematic trends in theaccelerationofthefeatureonthefirstandthirdnightsstrongly The map is useful to visually identify velocity bin regions suggeststhatthefeatureisproducedbyrotationalmodulation.To thatcorrelateoranti-correlatewitheachother(e.g.Johns&Basri excludethepossibility,theobjectmustbeobservedforafewrota- 1995; Oliveiraetal. 2000). The figure shows the profile vari- tionalperiods. ability in the velocity range (−200kms−1,0kms−1) weakly correlates with that for (200kms−1,400kms−1). On the other hand, they seem to weakly anti-correlate with the variability in 3.3 Auto-correlationmap (0kms−1,100kms−1).Thepatternseeninthemapisverysimi- lartothatseenintheHβauto-correlationfunctionofOliveiraetal. Theauto-correlationmapforthePaβspectra(withall503spectra) (2000).Theyalsofoundthreesimilarwavelengthrangesinwhich was calculated toexamine ifvariability at a given velocity bin is thefluxlevelscorrelateandanti-correlatewithoneanother. correlatedwiththoseatadifferentpartofspectra.Theresultwas The auto-correlation maps with time lags of P/2, P/3 and placed in Fig.6 asa greyscale image. Thecorrelation coefficient P/4 where P is the rotational period were also computed (with value (C ) of the i-th row and the j-th column in the map was ij P =2.7dfromUnruhetal.2004).Becauseofthepoortimecov- computedbyusing: erages(3nightsatasinglelocation)ofthedata,wewereunableto N S −S¯ S −S¯ drawanysignificantconclusionfromthosemaps,andtheyarenot Cij = Pm=1(cid:0)Nmi S i(cid:1)−(cid:0)S¯mj2 j(cid:1) (7) shownhere. m=1 mi i P (cid:0) (cid:1) whereS isthesignalofthen-thvelocitybininthem-thspec- mn 3.4 Lineequivalentwidth trumof thetime-series,andN isthetotalnumber of spectra.S¯ n isthemeansignalofthen-thvelocitybininthetime-series.The Thelineequivalentwidths(EWs)ofPaβprofiles(showninFig.1) mapissymmetricaboutthediagonal(i = j pixels).Therangeof are computed by averaging/rebinning over 10 profiles obtained thecorrelationvalues variesfrom−1to1whichcorrespond toa consecutively (approximately over 30 minutes), in order to de- stronganti-correlationandastrongcorrelationrespectively. crease the size of variance due to the relatively low average S/N 6 R. Kurosawaetal. Table1.Thesummaryofthefittingparametersinequation4forthepositionsofthesubpeakshowninFig.4.Nandχ2are ν thenumberofdatapointsandthereducedchi-squarerespectively. nmax N χ2ν a0 a1 b1 a2 b2 a3 b3 1 503 3.5 224. −35.7 −13.2 ... ... ... ... 2 503 2.8 288. −46.2 36.6 −36.7 29.9 ... ... 3 503 2.8 234. −42.3 33.9 −39.4 28.2 −9.14 −1.06 but not on the third night. With much larger time steps (∼ 1d), Johns&Basri(1995)foundasimilaranti-correlationbehaviourof theHαEWsmeasuredusingthevelocitybinsV ∼−150kms−1 andthosemeasuredusingV ∼100kms−1.Thisisconsistentwith theauto-correlationmap(Fig.6)shownearlier. ThedatapointswerefittedwiththeFourierseries(equation4) for nmax = 2 and nmax = 3 cases separately. As done for the fittingofthethesubpeakpositionsinSection3.2,theperiodwas constrainedtobe2.7d(Unruhetal.2004)inthefittingprocedure. TheresultsarealsoshowninFig.7,andthecorrespondingFourier coefficientsaresummarisedinTable2alongwiththereducedchi- square(χ2)values. ν Forallcases(total,redandblueEWs),thelineswithnmax = 3arebetterrepresentationsofthedatapoints,aswecanseefrom the figure and the χ2 values in the table. To test the validity of ν the statement above, we performed an F-test. For the total EWs fits, the numbers of degrees of freedom are ν2 = 42 and ν3 = 40 for nmax = 2 and nmax = 3 (Table 2) respectively. Using the values of the reduced chi-square values in the table, we find Fχ = χ2(nmax =2)−χ2(nmax =3) /χ2ν2 = 37 and F = χ2 /χ2(cid:8)=8.1;hence,F >F.Fromth(cid:9)istest,wefoundthatthe ν2 ν3 χ inclusionofthethirdharmonictermsarearealimprovementinthe fittingandtheyshouldbeincluded.Similarconclusionswerefound Figure6.Auto-correlationmapofthePaβspectra(3nights)withnotime fortheblueandtheredEWvariabilitycurves. delay.Thestrongerthecorrelation,thebrighterthepixelsinthemap.Sim- Interestingly,thecontributionofthethirdharmonictermsare ilarly, thethestronger theanti-correlation, thedarker thepixels are.The asimportantasthefirstandthesecondharmonictermsasonecan fluxchangesseenbetween(−200kms−1,0kms−1)and(200kms−1, 400kms−1)arecorrelated witheachother.Ontheotherhand,theflux seefromthevaluesof theFourier coefficientsinTable2.Thisis consistentwiththeideathatvariationiscausedbythecombination changesseenbetweenthosewavelengthrangesweaklyanti-correlatewith thefluxchangesseenin(0kms−1,100kms−1). ofthetilted-axismagnetospheric accretionmodel (forthesecond harmonicterms)andthepresenceofthecoolspotsofthesurfaceat threedifferentlongitudeswhichareapproximatelyequallyspaced (∼ 90) intheoriginal profiles.Threedifferent ranges of velocity fromthesurfaceDopplerimages(forthethirdharmonicterms),as brieflymentionedinSection3.2. binswereusedforcomputingtheEWs.ThetotalEWswerecom- putedusingthevelocityrange−500kms−1 ∼ 85◦). At lower modelofMuzerolleetal.(2001).Thetemperaturestructurealong inclinations(i<∼70◦),thefluxlevelofthebluesideoftheprofileisvery themagneticfieldwasadoptedfromMuzerolleetal.(2001) with sensitivetochangeininclination. Ontheotherhand,athigherinclination themaximumtemperature(Tmax)of8000K(seetheirfig.2).The angles (i >∼ 70◦),theyareinsensitive tothechange intheinclination angle. stellar continuum of the core star is described by a model atmo- sphereofKurucz(1979)withTeff =5750Kandlogg=4(cgs). Asimplegeometricallythinandopticallythickaccretiondisc isplacedjustoutsideoftheouteredgeofthemagnetosphere. All Time-series Paschen-β spectroscopyofSU Aurigae 9 shapeand relativeintensityof theobservations (Fig.1),although Table3.Modelparameters themodellineprofilesarerathermoretriangular.Littledifference Model θm #ofgaps M˙ is seen in the shape of the mean spectra from three models. The (◦) 10−7M⊙yr−1 amnodde∼ls−ov1e0r0esktimmast−e1t)hecolemvpelasreodftthoetbhleueo-bwseinrvga(tbioentw. Teehne∼dis−cr2e0p0- (cid:0) (cid:1) A 10 0 1.15 ancycouldbecausedbye.g.thewronginclinationangle,thewrong B 0 3 1.25 geometryofthemagneticfieldlineusedinthemodel,andthefact C 10 3 1.15 thatthemodeldoesnotincludetherotationalvelocitycomponentin theaccretionstreams.Ifalower(e.g.60◦)inclinationangleisused, theprofilewillbecomelesstriangular.Althoughalowerinclination the photons which encounter the discare absorbed. Withthisas- modelwillgiveusabetterfittotheobservedmeanprofile,thevari- sumptionofthedisc,aphotonemittedfromthebottomhalfofthe abilityintheredabsorptiontroughwillbemuchsmallerthanthat magnetosphere can beocculted by thedisc, but aphoton emitted oftheobservation,andthevariabilityinthebluesidewillbemuch fromthetophalfcannotbeoccultedbythedisc.Thisisreasonable larger than that of the observation. The mean spectra from Mod- forcomputingPaβprofilesexceptforcaseswithveryhighinclina- elsAandCshowthesubpeakintheredabsorptiontroughsimilar tionangles.Ifamorerealisticdisc(e.g.aflareddisc)wasusedin totheoneinseenintheobservation;howeverthepositionsofthe themodel,wewouldexpectthereductionofthephotosphericcon- subpeakinbothmodelsare∼100kms−1smallerthanthatofthe tinuum(e.g.Chiang&Goldreich1999)aswellasthelineemission observedspectra. duetoobscurationbytheouterpartofthedisc.Predictingtheexact InModelA,themagneticaxisisperpendiculartotheobserver effectsonthelineprofileshapescausedbythistypeofobscuration when phase = 0. Around this phase, the subpeak in the red ab- requiresmodellingofaself-consistentaccretiondisc,whichisbe- sorptiontroughbecomemostprominent(seenasbrighterpixelsin yondthescopeofthispaper. thegreyscaleimage).Thesubpeakarisesfromasimplegeometri- Sincewedonothavetheestimateoftheamountoftheveiling caleffect:athighinclinationtheobserver’sline-of-sight(LOS)to- around Paβ line, the flux contribution from the disc itself is not wardsthehotspotspassesthroughbothlowvelocitymaterialnear consideredinourcalculations.Arecentmeasurementoftheveiling thedisc,andhighvelocitymaterialnearthestellarsurface,leading at2.2µmforSUAuris0.6±0.3(Muzerolleetal.2003),butthe to two absorption components on the red side of the line profile. valueshouldbesignificantlysmallerat1.3µm(Paβ).Iftheveiling Therelativepositionandstrengthofthesecomponentschangesas correctionwastakenintoaccount,thelinestrengthofthemodels themagnetospherebecomesmoreface-on.Thelevelofthesubpeak presentedinthispaperwouldbeweaker.Themass-accretionrates shouldbecomelowerasthephasechangesfrom0to0.5because (M˙) for the models were chosen so that the mean observed line ofthisgeometrical/projectedvelocityeffect.Thegreyscaleimage strengthisapproximatelyreproduced. of Model A shows this effect. Overall line variabilityseen in the The inclination is set to i = 80◦ which is higher than the redabsorptiontroughiswellreproducedbyModelsAandC.Since previouslyassumedvalues(e.g.Muzerolleetal.2003;Unruhetal. thisvariabilityisprimarilyageometricallyeffect,itisquiteinsensi- 2004).Fig.9showsthePaβlineprofilescomputedatdifferentin- tivetotheadoptedtemperaturestructure,andwefindqualitatively clinationanglesusingthesamemagnetosphericaccretionstructure similar behaviour for models with 6000K < Tmax < 10000K asinModelA,butwithnodipoleoffseti.e.θm = 0.Atlowerin- (althoughnaturallythemodelsdifferindetail). clinations(i<∼70◦),thefluxlevelofthebluesideoftheprofile ThegreyscaleimageofModelBshowtheperiodicvariation isverysensitivetochangesininclination.Thiswillcausetoomuch (with1/3ofaphase)ofthefluxlevelsintheredabsorption.The variabilityinthebluewingifθm = 10◦ (asinModelA);henceit fluxlevelintheredabsorptionincreasesasalongitudinalgapap- willbeinconsistentwiththeobservation(c.f.Figs.1and3).Onthe proachesthelineofsightoftheobserversincelinephotonssuffer otherhand,athigherinclinationangles(i>∼70◦),theyareinsen- less absorption. Finally, the greyscale of Model C shows a com- sitivetothechangeintheinclinationangle.Interestingly,wefound plicated variation pattern, but it is easy to see that the pattern is thatthehigherinclinationangle(i>∼85◦ inFig.9)isneededto essentiallyacombinationofthevariabilitypatternsfromModelsA havethesubpeak intheredabsorptiontroughinemission(above andB. continuum)asseeninthemeanspectraofPaβfromthethirdnight The temporal deviation spectra of Models A and C re- oftheobservation(Fig.3). produce approximately the same range of the line variability In Models B and C, the locations of the gaps are at the az- (−400kms−1, 500kms−1)asseenintheobservations(Fig.1). imuthangles105◦,225◦and345◦(measuredfrom+x-axisbefore Model B does not fit the (TVS)−1/2 of the absorption at all. In tilting)attimet = 0orequivalentlyphase = 0.Forthemodels the(TVS)−1/2 ofModelsAandC,ratherlargediscrepanciesare withthetiltedmagneticaxis(ModelsAandC),theinclinationof seenintheamountofthevariabilityaroundthelinecentre(slightly themagneticaxiswithrespecttotheobserverchangesfrom90◦to ontheblueside). Whilethepeak ofthevariabilityintheredab- 70◦,thento90◦astherotationalphasechangesfrom0to0.5,then sorptionoccursat∼ 150kms−1 forModelAandC,itoccursat to1.0.ThemodelparametersaresummarisedinTable3. ∼275kms−1intheobservation. Apossiblewaytoshiftthepeakofthe(TVS)−1/2inthered wing(equivalentlythepositionofthesubpeakinthemeanspectra) 4.3 Modelspectra toahigher velocitybinistohavealargermagnetospheric radius WehavecomputedthePaβspectraat50differentrotationalphases, (Rm),inwhichtheaccretiongashashigherinfallingvelocity.Al- andplacedtheresultsinFig.10.Thefigureshowsthemeanspec- though thismeans themagnetic accretion streamshavetoextend traofawholephase,thedeviationsfromthemeanspectra(quotient beyond the co-rotation radius of the star, this would be still con- spectra)asafunctionofphaseinthegreyscaleimage,andthetem- sistentwiththemagneto-hydrodynamicmodelofRomanovaetal. poraldeviationspectra(TVS)−1/2fromthemodels. (2002)whofoundatorque-lessaccretionispossiblewhenRm ≈ Themeanspectraofthemodelsbroadlyreproducetheoverall 1.5RcwhereRcistheco-rotationradiusofastar. 10 R. Kurosawaetal. Figure10.ThesummaryofthePaβspectracomputedforModelA(left),ModelB(centre)andModelC(right).Foreachmodel,spectrawerecomputedat 50differentrotationalphases.Inthebottompanels,themeanspectraofallrotationalphasesareshown.Inthemiddlepanels,thequotientspectra(divided bythemeanspectrum)areshownasgreyscaleimageswithincreasingrotationalphasesinverticaldirection.Thegreyscaleimageisscaledfrom1.1(white) to0.9(black).Thetemporaldeviationspectra(TVS)−1/2areshowninthetoppanels.Whencomputingthetemporaldeviationspectra,thesignal-to-noise ratioof90(incontinuum)wasusedtomatchthatoftheobservation(Section2).SeeTable3forthemodelparametersadopted. 4.4 Modelauto-correlationmaps Theauto-correlationmapsofPaβline(withnotimelag)werecom- putedusingthespectraofModelsA,BandC,andtheresultswere placed in Fig. 11 along with the auto-correlation map shown in Fig.6foracomparison. In the map for Model A, the changes in the flux levels in the velocity range (−200kms−1, 0kms−1) and (0kms−1, 400kms−1) are strongly correlated with themselves while they areanti-correlated witheach other. In other words, as thefluxlevelin(−200kms−1,0kms−1)increasesthefluxlevel in(0kms−1,400kms−1)decreases,andviceversa. The blocks of correlation and anti-correlation (seen as black and white squares in the map of Model A) are less pronounced for Model B. The third quadrant block (−300kms−1, 0kms−1)×(−300kms−1, 0kms−1) of Model B is more complicated than that of Model A because the accretionstreamslocatedonthefar(back)sideofthestar(asseen bytheobserver)willbeseenthroughthegapasitapproachesthe near (front) side of the star. The map for Model C is essentially thesameasthatofModelAsincetheoverallvariabilitycausedby thepresenceofthegapsisrelativelysmallcomparedtothatbythe Figure 11. Auto-correlation maps of Paβ from the observation (upper– precessionofthemagneticaxis. left) and from the radiative transfer models: Models A (upper–right), B (lower–left) andC(lower–right). Thevelocity bins ofthecontinuum are The main differences between the auto-correlation map of excluded from the model auto-correlation maps, and their values are set the observation and the models are: 1. the absence of the anti- correlation between the velocity ranges (0kms−1, 100kms−1) troan0ge(sse(e0nkamsgsr−ay1,o1u0t0erkfmrams−es1)).Nanoda(n2t0i-0cokrmrelast−io1n,4b0e0twkemens−th1e)vieslosceietyn and(200kms−1,400kms−1)inthemodelsand2.ForModelsA inthemodelsunliketheobservation.Thepositionofthetwodarkstripes and C, the two dark stripes (anti-correlation bands) crossing per- (anti-correlationbands)crossingperpendiculartoeachotherisontheblue pendicular to each other are about two times wider than that of side(−125kms−1and−125kms−1)forModelsAandC,butitison theobservation,andtheyappearastwolargedarkblocksandtwo theredside(100kms−1and100kms−1),intheobservation. smallerblocks.Thetotalphasecoverageoftheobservationisap- proximately1/3ofthewholephase;therefore,thismayalsocon- tributetothedifferenceseeninthemapsfromtheobservationand themodels.

Time-series Paschen-beta spectroscopy of SU Aurigae

Similar Time-series Paschen-beta spectroscopy of SU Aurigae