Astronomy&Astrophysicsmanuscriptno.perseus˙sun (cid:13)c ESO2008 February5,2008 A KOSMA 7 deg2 13CO 2–1 & 12CO 3–2 survey of the Perseus cloud I. Structure Analysis 6 0 0 K.Sun1,C.Kramer1,V.Ossenkopf1,2,F.Bensch3,J.Stutzki1 andM.Miller1 2 n a 1 KOSMAI.PhysikalischesInstitut,Universita¨tzuKo¨ln,Zu¨lpicherStraße77,50937Ko¨ln,Germany J 2 SRONNationalInstitutforSpaceResearch,P.O.Box800,9700,AVGroningen,theNetherlands 9 3 RadioastronomischesInstitutderUniversita¨tBonn,AufdemHu¨gel71,53121Bonn,Germany 2 Received;accepted 2 v ABSTRACT 0 5 Context.Characterizing the spatial and velocity structure of molecular clouds is a first step towards a better understanding of interstellar 6 turbulenceanditslinktostarformation. 1 0 Aims.Wepresentobservationsandstructureanalysisresultsforalarge-scale(∼7.10deg2)13COJ=2–1and12COJ=3–2surveytowardsthe 6 nearbyPerseusmolecularcloudobservedwiththeKOSMA3mtelescope. 0 Methods.Westudythespatialstructureofline-integratedandvelocitychannelmaps,measuringthe∆-varianceasafunctionofsizescale.We / determinethespectralindexβofthecorrespondingpowerspectrumandstudyitsvariationacrossthecloudandacrossthelines. h Results.WefindthatthespectraofallCOline-integratedmapsofthewholecomplexshowthesameindex,β≈3.1,forscalesbetweenabout p - 0.2 and 3pc, independent of isotopomer and rotational transition. A complementary 2MASS map of optical extinction shows a noticeably o smaller index of 2.6. In contrast to the overall region, the CO maps of individual subregions show a significant variation of β. The 12CO r 3–2dataprovidee.g.aspreadofindicesbetween2.9inL1455and3.5inNGC1333.Ingeneral,activestarformingregionsshowalarger t s power-lawexponent.Wefindthatthe∆-variancespectraofindividualvelocitychannelmapsareverysensitivetoopticaldeptheffectsclearly a indicating self-absorption in the densest regions. When studying the dependence of the channel-map spectra as a function of the velocity : v channelwidth,theexpectedsystematicincreaseofthespectralindexwithchannelwidthisonlydetectedinthebluelinewings.Thiscouldbe i explainedbyafilamentary,pillar-likestructurewhichisleftatlowvelocitieswhiletheoverallmoleculargasissweptupbyasupernovashock X wave. r a Keywords.ISM:clouds–ISM:structure–ISM:Perseus 1. Introduction where physical processes insert energy in the turbulence cas- cade (outflows, supernovae, super-bubbles, galactic rotation) The structure of the interstellar medium (ISM) is random and at scales of turbulence dissipation (Elmegreen&Scalo to a large degree, with a complex spatial density distribu- 2004). Thus, a study of the scaling behavior of the cloud tion and velocity field. This is evident in large-scale sur- structure and the velocity field as traced by the power spec- veys of spectral line tracers, such as CO, made for parts trum of observedspectral line maps can help to constrain the of the Galactic plane (e.g. Heyeretal. 1998; Simonetal. turbulent energy cascade in the ISM. A number of power- 2001) and individualmolecularclouds(e.g.Ballyetal. 1987; spectrumstudieshavebeencarriedoutfortheatomicmedium Ungerechts&Thaddeus 1987). The spatial structure of the usingHobservations(Crovisier&Dickey1983;Green1993; emission has been quantified in terms of its power spectrum Stanimirovic´etal. 1999; Dickeyetal. 2001; Elmegreenetal. (Scalo 1987; Stutzkietal. 1998; Elmegreen 1999). When fit- 2001).Theyfindspectralindicesbetweenabout2.7and3.7for ting the azimuthally averaged power spectrum with a power theline-integratedmaps(Falgaroneetal.2004). law, the slope of the power law β provides information on The ∆-variance is an alternative method to determine the the relative amount of structure at the linear scales resolved indexofthepowerspectrumofisotropicimages(Stutzkietal. in the image. A pure power law is expected for structure 1998). In contrast to the power spectrum, the ∆-variance can on the linear scales of a self-similar turbulent energy cas- be computedin the spatialdomain.It allowsfor a better sep- cade. Deviations from a power law are expected at scales aration of the intrinsic cloud structure from contributions re- Sendoffprintrequeststo:[email protected] sultingfromthe finite signal-to-noisein the data andthetele- 2 Sunetal.:AKOSMA7deg2CO2–1&3–2surveyofthePerseuscloud scopebeam.Inaddition,problemsrelatedtothediscretesam- between0.3–3pc,andPadoanetal.(2003b)comparedtheve- pling of the data can be avoided. Benschetal. (2001) pre- locitystructureofPerseustoMHDsimulations. senteda∆-varianceanalysisforCOmapsofthePolarisFlare A complete census of the stellar content of nearby and six other molecular clouds. The index β is close to 3 for (<∼ 350pc) molecular clouds (Perseus, Serpens, Ophiuchus, most clouds, but it steepens in the Polaris Flare from 2.5 to Camaeleon, and Lupus) is currently obtained by the Spitzer 3.3 for maps with a linear resolution increasing from >∼ 1pc legacyproject“CorestoDisks”(c2d,Evansetal.2003).Large- to <∼ 0.1pc. Ossenkopfetal. (2001) used the ∆-variance to scale12CO,13CO1–0andAvmapsofthenortherncloudswere studynumericalmodelsofself-gravitating,supersonicallytur- recentlyobtainedbytheCOMPLETEteam(Goodman2004). bulent clouds and compared the results to observations.They TheKOSMAsurveyofPerseusinhigherCOtransitionstraces showed that the ∆-variance traces deviations from an inertial thewarmeranddensergasduetotheelevatedcriticaldensities scaling behavior at the scales of driving and dissipation (see and excitation energies (∼ 105 cm−3 and 33.2K for CO 3–2) alsoOssenkopf&MacLow2002). relative to the J = 1–0 transition. Moreover, 12CO is largely ConstraintsonthevelocitystructureoftheISMcanbeob- opticallythick,while13CO,beingafactor∼65lessabundant tainedfromananalysisofindividualchannelmapsofaspectral (Langer&Penzias 1990), is often optically thin, thus tracing line cube, and by comparing the results with those obtained column densities. We plan to extend this work to the other for the line-integrated maps. Stanimirovic´&Lazarian (2001) nearby clouds using the KOSMA and NANTEN21 observa- haveanalyzedHobservationsoftheSmallMagellanicCloud tories. inthisway,notingasystematicvariationofthemeasuredindex The KOSMA observations are described in Sect. 2. The βwiththewidthofthevelocity-channels,thusconfirmingtheo- general properties of the CO data sets are discussed in Sect. reticalpredictionsbyLazarian&Pogosyan (2000).Usingthe 3. Sect. 4 presents the results of the ∆-variance analysis. The BostonUniversity/FiveCollegeRadioAstronomyObservatory discussionoftheresultsandasummaryaregiveninSection5 (BU/FCRAO) Galactic ring survey, Bensch&Simon (2001) and6,respectively. found that the index of the channelmaps is smaller than that oftheline-integratedmaps.Itshowedasignificantvariationas 2. Observations afunctionofthechannelvelocity.Butβdidnotincreasewith increasingvelocitychannelwidth,incontrasttothepredictions We mapped the Perseus region simultaneously in 13CO 2–1 byLazarian&Pogosyan (2000).Apartfromthisfirstattempt, and12CO 3–2usingthe KOSMA3msubmillimetertelescope no systematic structure analysis of velocity-width dependent onGornergrat,Switzerland,equippedwithadual-channelSIS channelmapsofmolecularlineshasbeenperformedyet. receiver (Grafetal. 1998) and acousto optical spectrometers We present a new CO survey of the Perseus molecular (Schiederetal. 1989). Main beam efficienciesandhalf power cloud complex and analyze the cloud structure in the line in- beamwidths (HPBWs) are 68%, 130′′ at 220GHz and 70%, tegrated and the channelmaps. The observationsof the 12CO 82′′ at 345GHz. The HPBWs correspond to linear resolu- 3–2and13CO2–1transitionsweremadewiththe3mtelescope tions of 0.22pc and 0.14pc, where we adopted a distance of the Ko¨lner Observatorium fu¨r Sub-Millimeter Astronomie of 350pc (Borgman&Blaauw 1964; Herbig&Jones 1983; (KOSMA)andcovertheentirePerseusmolecularcloudcom- Bachiller&Cernicharo1986).Alltemperaturesquotedinthis plex(7.1squaredegrees).ThePerseuscloudisoneofthebest paperaregivenonthemainbeamtemperaturescale. examples of a nearby star-forming region. The cloud is re- For the observations, we divided the ∼7.10 deg2 re- lated tothe PerseusOB2 association(Bachiller&Cernicharo gion in 10′ × 10′ fields. Each field was mapped using the 1986; Ungerechts&Thaddeus 1987), which is located in the position-switchedon-the-fly(OTF)mode(Krameretal.1999; area mostly free of CO emissions northeast of the cloud Beutheretal. 2000) with a sampling of 30′′. Three emission- (Ungerechts&Thaddeus 1987). It includes a region where free off positions were selected from the 13CO 1–0 FCRAO intermediate-massstarsform(NGC1333),ayoungopenclus- map. The pointing was accurate to within 10′′. The accuracy ter (IC348), and a dozen dense cloud cores with low levels of the absolute intensity calibration is better than 15%, de- ofstar-formationactivity(L1448,L1455,B1,B1EAST,B3 terminedwithfrequentobservationsofreferencesources.The andB5).91 protostarsandpre-stellarcoreshave beenidenti- channel spacing ∆v and the correspondingaverage baseline ch fied in a 3 squaredegreesurveyof the dustcontinuumat850 noise rms of the spectra is 0.22kms−1, 0.48K for 13CO 2–1 and 450 µm made with the James Clerk Maxwell Telescope, and 0.29kms−1, 1.02K for 12CO 3–2.The observationswere JCMT(Hatchelletal.2005). takenfromFebruarytoDecember2004. ImagingobservationsofthePerseuscomplexinmolecular cloud tracers exhibit a wealth of substructure, such as cores, 3. DataSets shells,filaments,outflows,jets,andalarge-scalevelocitygra- dient (Padoanetal. 1999). Padoanetal. (1999) compared the 3.1.Integratedintensitymaps structuretracedby13CO1–0observationstosyntheticspectra Themapsofvelocityintegrated13CO2–1and12CO3–2emis- andfindthatthemotionsinthecloudmustbesuper-Alfve´nic, sion (Figs. 1,2) show the Perseus region,viz. the well known withtheexceptionoftheB1core,whereGoodmanetal.(1989) stringofmolecularcloudsrunningover∼ 30pcprojecteddis- and Crutcheretal. (1993) detected a strong magnetic field. tancefromNGC1333andL1455inthewesttoB1,B1East, Padoanetal.(2003a)findthatthestructurefunctionoftheline- integrated13CO1–0mapfollowsapowerlawforlinearscales 1 http://www.ph1.uni-koeln.de/nanten2 Sunetal.:AKOSMA7deg2CO2–1&3–2surveyofthePerseuscloud 3 and B3 in the center, and to IC348 and B ,5 in the east (cf. Bachiller&Cernicharo 1986; Ungerechts&Thaddeus 1987). Generally, there is a good correlation between 12CO 3–2 and 3.5 13CO2–1integratedintensities. tsheeenIsntirnuthcientudnrieevxisdteuseeancltirineogntih,oewnsee.ncFtoiormerptPhaeirsres,etwhueesdsmteaafitpinsewtidcitashlevptheroenpsbetorrutxiceetssuooreff -1O 2-1 (kms)3.0 C tA5c1e3l0nloCv′suOeF×idtsiisgem5eu(st0cara′fepa.lnw.Fc2d2hiog0ivsac.0he1h5rom)s).wr,aoasapultlgao2rhnef.l5gyoo′iocpvanoetnisircdnlaaacl5ybid′oeeovrxefetwsinoi7inctlmhutteitoagitohngrnaesat,ekn(rdGnedsoo1p∼wo3eCdnc7mOt0imva%eno2ll–yeo2.1cf0Tu0tilhhn4aee-r; 13Average equivalent linewidth of 122...505 LLNBBB11113G44EC45A851S3T33 regionsabove3mag. A linear least squaresfit to a plot of Av 1.0 IeCq3u4a8l line width vs. 13CO 2–1 results in a correlation coefficient of 0.76. The 1.5 2.0 2.5 3.0 3.5 4.0 4.5 5.0 regionmappedin13CO hasamassof1.7×104 M⊙ usingthe Average equivalent linewidth of 12CO 3-2 (kms-1) A dataandthe canonicalconversionfactor[H ]/[A ]= 9.36 V 2 V ×1020cm−2mag−1(Bohlinetal.1978). Fig.4.Meanandrmsoftheequivalentlinewidths∆v ofthe eq 12CO 3–2and13CO 2–1spectra forthe observedpositionsof 3.2.Velocitystructure theseven50′×50′subregions(Fig.1).Thedashedlinedelin- eatesequalwidthsin12COand13CO. Mapsof13CO2–1emissionintegratedoversmallvelocityin- tervals(Fig.3)illustratethefilamentarystructureofthePerseus clouds.Thechannelmapsshowthewell-knownvelocitygradi- All Sky Survey) by the COMPLETE team (Goodman 2004; entbetweenthewesternsources,e.g.NGC1333at∼7kms−1, Alvesetal.2005). andtheeasternsources,e.g.IC348at∼9kms−1.Thechannel mapintegratedbetween5 and6kms−1 exhibitstwofilaments 4.1.The∆-varianceanalysis originatingatL1455,onerunsnorthtoNGC1333,thesecond runsnorth-easttoB1.Wewilldiscussthestructuralproperties The∆-varianceanalysiswasintroducedbyStutzkietal.(1998) ofindividualvelocitychannelmapsinthenextsections. asa meanstoquantifytherelativeamountofstructuralvaria- To study the statistics of the velocity field we start with tionataparticularscaleinatwo-dimensionalmaporathree- thedistributionofthelinewidthsacrossthemap.Sincemany dimensionaldataset.The∆-varianceisdefinedasthevariance spectrashowdeviationsfromaGaussianlineshape,weusethe ofanimages(r)convolvedwithanormalizedsphericallysym- equivalentlinewidth ∆veq = R Tdv/Tpeak asa measureofthe metricwavelet⊙ofsizeL linedispersionalongindividuallinesofsight.Figure4shows σ2 =h[s(r)∗⊙ (r)]2i , (1) themeanequivalentlinewidthsandtheirscatterfortheseven ∆ L r sub-regionsshowninFigure1. wheretheasterixdenotesthespatialconvolution(Stutzkietal. The mean 12CO widths vary significantly between 1998). For structures characterizedby a power-law spectrum, 2.2kms−1 in the quiescent dark cloud L1455 and 3.8kms−1 P(|k|)∝|k|−β,the∆-variancefollowsaswellapowerlaw,with in the active star forming region NGC1333, while the rms is theexponentd =β−2intherange0≤β≤6. ∼0.7kms−1.Incontrast,the13COwidthsaresmallerandshow ∆ Unfortunately, the ∆-variance spectrum of any observed onlyaweaktrendaround∼2kms−1. datasetdoesnotonlyreflectthespectralindexβoftheastro- Several positions in L1455, but also in e.g. IC348, show physical structure, but it is also affected by radiometric noise small line widths of ∼1kms−1, only a factor of ∼8–11 larger andthefinitetelescopebeam(Benschetal.2001).Botheffects than the CO thermalline width, which is ≈ 0.16 kms−1 for a changethespectrumatsmallscales.Whenweignorethesmall kinetictemperatureof10Kaswasfoundforthebulkofthegas contributionfrombeamblurring,we canwrite the ∆-variance inPerseusbyBachiller&Cernicharo(1986). as 4. Structureanalysis σ2∆(L)≈a1Lβ−2+a2Ldnoise, (2) Inthissection,westatisticallyquantifythespatialstructureob- (Eq. (10) from Benschetal. 2001). For white noise, β = noise served in the maps, both for the overall structure and for the 0, so that d = −2. In the KOSMA data we noticed that noise structure of individual regions within the Perseus molecular the noise doesnotfollow a pure white noise behaviour,but it cloud. We measure the spectral index of the power spectrum is “colored”due to artifactsfrominstrumentaldrifts, baseline usingthe∆-varianceanalysis,awaveletconvolutiontechnique. ripples,OTFstripesetc.Thishastobetakenintoaccountwhen We analyzeournewCOdataandcomparetheresultswithan derivingthecloudspectralindexβfromthe∆-variancespectra. equivalentanalysisof theFCRAO 12CO 1–0,13CO 1–0maps Thuswe measuredthe spectralindex of the colored noise andthe A Perseusmap obtainedfrom2MASS(Two Micron d byanalyzingmapscreatedfromvelocitychannelswhich V noise 4 Sunetal.:AKOSMA7deg2CO2–1&3–2surveyofthePerseuscloud Fig.1. The Perseus molecular cloud complex. KOSMA maps of integrated intensities of 13CO 2–1 (colors) and 12CO 3– 2 (contours) at 150′′ resolution. The integration interval is 0–16kms−1. Colors run from 1Kkms−1 (∼ 1σ) to 32Kkms−1. Contoursrangefrom6.6Kkms−1 (∼3σ) to83Kkms−1 instepsof9Kkms−1.The(0,0)positioncorrespondstoRA=03:26:00, DEC=+31:10:00(B1950).Sevensub-regionsaremarkedbydottedsquareboxesof50′×50′. donotseeanylineemissionbutwhichcoverthesamevelocity (Table1).Thegoodagreementofthespectralindicesobtained widthastheactualmolecularlinemaps.Theresultisshownin fromthedifferentCOdataisremarkable.Theycoveronlythe Fig.5.Wefindanearlyconstantindexd ≈−1.5foralloff- narrow range between 3.03±0.14 and 3.15±0.04. In contrast, noise linechannelsatscalesbetweenabout1and6′.Atlargerlags, the extinction data result in a significantly lower index. This thenoisedeviatesfromtheβ=0.5behaviour,butthisdoesnot indicatesamorefilamentarystructureinA .Whenweactually V affect the structure analysisas the absolute noise contribution comparetheA mapwith13CO2–1datasmoothedtothesame V isnegligiblethere. resolution, it is also noticeable by eye that the A map looks V FortheFCRAOdataandtheCOMPLETEA mapwehave moreclumpyorfilamentarythanthe13COmap.Thisindicates V noemission-freechannelsavailablesothatwecannotperform that 13CO does nottrace all details of the cloudstructure,but anequivalentnoisefitthere.The∆-varianceatsmalllagsshows rather measures the more extended, and thus more smoothly however no indications for a deviation from the pure white distributedgas. noise behaviour, so that we stick to d = −2 for the fit of noise thesedata. All ∆-variance spectra show a turnover at about 3pc. To test whether this peak measures the real width of the Perseus 4.2.Integratedintensitymaps cloudor whetheritis producedbythe elongatedshape ofthe COmaps,wehaverepeatedthe∆-varianceanalysisfortheA Figure 6 compares the ∆-variance spectra of the different in- V data of the entire region shown in Figure 2. In this case we tegrated intensity maps for the entire region mapped with find almost the same spectrum below 3 pc, but instead of a KOSMA (see Fig. 1)2. When corrected for the observational turnoveronlyaslightdecreaseoftheslopeatlargerlags.Thus noise, the ∆-variance spectra of all maps follow power laws wehavetoconcludethatthe∆-variancespectraoftheCOmaps between the linear resolution of the surveys and about 3pc atscalesbeyond3pcaredominatedbyedgeeffects,duetothe 2 NotethattheareacoveredbytheFCRAOisslightlysmallerthan shapeofthemaps,sothatthesescalesshouldbeexcludedfrom thatobservedwithKOSMA. theanalysis.InFigure6wecompareonlyspectraforthesame Sunetal.:AKOSMA7deg2CO2–1&3–2surveyofthePerseuscloud 5 Fig.2. Overlay of 13CO 2–1 integrated intensities (contours) with a map of optical extinctions in colors (Goodman 2004; Alvesetal.2005).Contoursrangefrom2.7Kkms−1(3σ)to32Kkms−1by3Kkms−1.ColorsrangefromA =1magto11mag. v Resolutionsare2.5′for13COand5′forA .Apolygonmarkstheboundaryofthe13COmap. V region,i.e.the∆-variancespectraofthe A dataoftheregion Table 1. Results of the ∆-variance analysis of the integrated CO V alsomappedwithKOSMA. mapsandtheA datafortheregionmappedwithKOSMA(Fig.1). V Transition Telescope resol. FitRange β As it is notguaranteedthatthe structureof the overallre- [′] [′] gionisrepresentativeforindividualcomponents,wehavealso A 2MASS 5 5.0-28 2.55±0.02 appliedthe∆-varianceanalysistotheKOSMAdataofthein- V 13CO1–0 FCRAO 0.77 0.8-28 3.09±0.09 dividual clouds contained in the seven 50′ × 50′ subregions 12CO1–0 FCRAO 0.77 0.8-28 3.08±0.04 shown in Fig. 1. The results of the power-law fits to the ∆- 13CO2–1 KOSMA 2.17 2.2-28 3.03±0.14 variancespectraarelistedinTable2.Theydiffersignificantly 12CO3–2 KOSMA 1.37 1.4-28 3.15±0.04 betweentheindividualregions.Theactivestar-formingregion NGC1333 shows the highest spectral indices in both transi- Table2. Resultsofthe∆-varianceanalysisoftheKOSMAdatafor tions. The low end of the spectral index range is formed by seven50′×50′sub-regionsofthecloud(Figure1).Thespectralindices the dark cloud L1455 together with the environment of the βwerefittedinthesizerange2.2-14′forthe13CO2–1andinthesize young cluster IC348. The ∆-variance spectra of the two ex- range1.4-14′forthe12CO3–2data. treme examples NGC1333 and L1455 are shown in Fig. 6b. Startingfromthesamenoisevaluesatsmallscalesthespectra Region β(13CO2−1) β(12CO3−2) of the two regions show an increasing difference in the rela- L1448 2.96±0.42 3.41±0.16 tiveamountofstructureatlargescalesreflectedbythestrongly L1455 2.86±0.09 2.85±0.30 deviatingspectralindices. Altogether,we find highindices as NGC1333 3.76±0.48 3.52±0.11 characteristicsof large condensationsfor the regionswith ac- B1 3.14±0.29 3.00±0.20 B1EAST 3.16±0.09 3.39±0.09 tivestarformationandlowerindicesquantifyingmorefilamen- B3 3.36±0.09 3.14±0.06 tarystructurefordarkclouds,butIC348asanexceptiontothis IC348 2.71±0.42 3.06±0.24 rule,showingalsoaveryfilamentarystructure. 6 Sunetal.:AKOSMA7deg2CO2–1&3–2surveyofthePerseuscloud Fig.3. 13CO2–1velocitychannelmapsofthePerseusregion.Thevelocityrangerunsfrom3kms−1to11kms−1withaninterval of1kms−1whichisindicatedonthetopofeachplot.Theintensitiesareplottedfrom0.7Kkms−1(∼1σ)to15Kkms−1. 4.3.Velocitychannelmaps Lazarian&Pogosyan (2000),thechangeofthespectralindex of channelmaps as a functionof the channelwidth was used When performing the ∆-variance analysis not only for maps tosimultaneouslydeterminethescalingbehaviorofthedensity of integrated intensities, but for individual channel maps we andthevelocityfieldsfromasingledatacubeoflinedata.Here obtain additional information on the velocity structure of the weconductsuchastudyfortheKOSMACOdata. cloud. In the velocity channel analysis (VCA), introduced by Sunetal.:AKOSMA7deg2CO2–1&3–2surveyofthePerseuscloud 7 Lag L (pc) 10 -1.5 3b45 2b20 LL 11445555 1123CCOO 32--21 100 0.06 FbCRAO 3b45 2b20 0.62bM1ASS 2.87 6.10 a 12 NGC 1333 CO 3-2 13 NGC 1333 CO 2-1 L) 2 ( 1 L) 10 e -1.5 2 ( nc e a c ari an a-v vari 1 elt 0.1 a- D elt D 12 CO 3-2 13 CO 2-1 12 CO 1-0 0.1 13CO 1-0 0.01 Av 0.01 0.1 Lag (deg) 0.01 0.1 1 Lag L (deg) 3b45 2b20 12CO3-2 13CO2-1 0.06 Lag L (pc) 0.61 -1.5 Vch ; Vcen Vch ; Vcen 100 NGC 1333 12CO 3-2 3b45 2b20 b 0.29 ; -1.60 0.22 ; -1.65 13 1 0.29 ; -1.89 0.22 ; -1.87 NGC 131323 CO 2-1 1.47 ; -5.15 0.68 ; -5.10 L 1455 13CO 3-2 L) 1.47 ; -5.52 0.68 ; -6.46 L 1455 CO 2-1 2 ( e 0.1 2 (L) c elta-varian 0.01 -1.5 variance 10 D a- elt 1E-3 D 1 0.01 0.1 Lag L (deg) 0.01 0.1 Fig.5.∆-varianceanalysisoftheoff-linechannelmaps.Inthe Lag L (deg) upper plot a velocity span correspondingto the integratedin- Fig.6. ∆-variancespectraofintegratedintensities.a)Spectra tensitymapsisused.Thetworegionsrepresentingoppositeex- obtained from the CO maps and the AV data of the region tremesinthestructuralbehaviour,NGC1333andL1455,show mapped with the KOSMA telescope. b) Spectra of integrated aboutthesamespectralindexofthecolorednoiseinbothtran- intensity maps of two 50′× 50′sub-regions: NGC1333 and sitions for small lags. In the lower plot, the influence of dif- L1455.Power-lawfitstothedatacorrectedfornoiseandbeam- ferentvelocityspans, as used in the velocitychannelanalysis blurringareindicatedassolidlines. (Sect.4.3),isstudiedforL1455.Thecolorednoiseindexd noise is nearly constant independentof species, transition, velocity range∆v ,andcentervelocityv . closetotheaveragelinepeak.Thismayimplicatethatextended ch cen smoothstructureprovidesthemajorcontributiontotheoverall emission,whilethevelocitytailofthisstructureisformedby We start with the analysis of individual channel maps as small-scalefeatures.However,theindicesshowanasymmetric theyareprovidedbythechannelspacing∆v ofthebackends behaviorwithrespecttotheblueandtheredwing.Theindices ch (cf.§2).Forallchannelmapsweperformthe∆-varianceanal- dropsteeplytoanoise-dominatedvalueattheredwing,while ysis and fit power laws to the measured structure for all lags the blue wing shows only a very shallow decay. Even at the between the telescope beam size and the maximum scale re- noiselimit,noticeablestructureisdetectedinthechannelmaps solvedbythe∆-variance(about1/4ofthemapsize).Asare- there. sult we get the power-law index as a function of the channel For the full velocity channel analysis, the index spec- velocity,acurvewhichwecallindexspectrum.Asanexample trumhastobecomputedfordifferentvelocitychannelwidths weshowtheindexspectrumobtainedforthe13CO2–1datain (Lazarian&Pogosyan 2000).Thuswehavebinnedthedatato theL1455regionin Fig.7. Thespectrumis alwaystruncated averagesof three, five, and seven velocity channels and com- at velocitieswhere the averageline temperatureis lower than putedtheindexspectraforthesebinnedchannelmaps.InFig.8 thenoiserms. weshowtheresultsforthreeexamples:IC348,NGC1333and Theoverallstructureoftheindexspectrumissimilartothe L1455.Forthesakeofclaritytheerrorbarsoftheindexspec- lineprofile.Thelargestspectralindicesarefoundatvelocities trawereomittedintheseplots. 8 Sunetal.:AKOSMA7deg2CO2–1&3–2surveyofthePerseuscloud 45..50 IC 348 12CO 3-2 VVVccchhh === 001...284987 kkkmmmsss---111 45..50 1.5 IC 348 13CO 2-1 VVVccchhh === 001...261283 kkkmmmsss---111 3.5 Vch = 2.01 kms-1 Vch = 1.58 kms-1 4.0 Integrated intensities 4.0 Integrated intensities 3.5 3.5 1.0 3.0 T (K)mb223...050 223...050 index T (K)mb0.5 2.5 index 1.5 1.5 0.0 2.0 1.0 1.0 0.5 0.5 -0.5 1.5 0.0 0.0 2 4 6 8 -1 10 12 14 2 4 6 8 -1 10 12 14 velocity (kms ) velocity (kms ) 33..72 NGC 1333 12CO 3-2 VVVVcccchhhh ==== 0012....28409871 kkkkmmmmssss----1111 44..05 11..23 NGC 1333 13CO 2-1 34..50 Integrated intensities 2.7 3.5 1.0 3.0 T (K)mb121...227 223...050 index T (K)mb000...578 122...505 index Vch = 0.22 kms-1 0.7 1.5 0.3 Vch = 0.68 kms-1 1.0 Vch = 1.13 kms-1 0.2 1.0 0.2 Vch = 1.58 kms-1 0.5 Integrated intensities -0.3 0.5 0.0 0.0 0 2 4 6 8 10 12 14 0 2 4 6 8 10 12 14 -1 -1 velocity (kms ) velocity (kms ) 2.5 L1455 12CO 3-2 VVcchh == 00..2898 kkmmss--11 4.0 0.9 L 1455 13CO 2-1 3.2 2.0 VVcchh == 12..4071 kkmmss--11 3.5 0.8 2.8 Integrated intensities 0.7 2.4 T (K)mb 11..05 23..50 index T (K)mb000...356 VVcchh == 00..2628 kkmmss--11 112...260 index 0.5 2.0 0.2 VVcchh == 11..1538 kkmmss--11 0.8 0.1 Integrated intensities 0.4 0.0 1.5 0.0 0.0 0 2 4 6 8 10 0 2 4 6 8 10 -1 -1 velocity (kms ) velocity (kms ) Fig.8.Comparisonofthe indexspectra obtainedfordifferentvelocitychannelwidthswiththe averageline profile.Theupper plotsshowtheresultsforIC348,thecentralplotNGC1333andthelowerplotL1455.Fortheleftcolumnweusedthe12CO3–2 data,the rightcolumnrepresentsthe13CO 2–1data.Thedifferentsymbolsindicatetheresultsfromdifferentvelocitychannel widths.Thedashedlinesrepresentstheindexoftheintegratedintensitymaps. TheoverallstructureoftheindexspectraissimilartoFig.7 filamentary appearance of the central channel maps reflected for all sources, transitions and channel widths. In most cases by this dip in the indexspectra. It is interesting to notice that we find the asymmetry of a shallower blue wing relative to the VCA is moresensitiveto self-absorptionthanthe average the red wing. When looking at narrow velocity channels, we spectrum. findadipinthecentreoftheindexspectrumforthe12CO 3– When increasing the channel width by binning, the self- 2dataofNGC1333andL1455.Aslightindicationofsucha absorptiondipissmoothedout,sothattheresultingindexspec- dip is also present in the 12CO 3–2 data if IC348 and in the trapeakagainclosetothepeakvelocityofthelinetemperature. 13CO 2–1 data of NGC1333. This is due to optical depth ef- Inallsituationswheretheselfabsorptionisnegligible,thein- fects. When we check individualspectra in those regions, we dicesforthelinecorechannelsarealmostindependentfromthe see self-absorption in several positions. This leads to a more channelwidth.Theindicesforthelineintegratedintensitiesal- Sunetal.:AKOSMA7deg2CO2–1&3–2surveyofthePerseuscloud 9 4.5 3.2 L 1455 13CO 2-1 AVvechr a=g 0e. 2s2p ekcmtrsu-1m 3.2 a 4.0 2.8 2.8 3.5 2.4 2.4 ex d 2.0 2.0 w in3.0 T (K)mb11..26 11..26 index power-la22..05 n 0.8 0.8 Mea1.5 IC 348 12CO 3-2 13 IC 348 CO 2-1 0.4 0.4 12 1.0 L 1455 13CO 3-2 L 1455 CO 2-1 0.0 0.0 NGC 1333 12CO 3-2 13 0.5 NGC 1333 CO 2-1 0 2 4 6 8 10 -1 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 velocity (kms ) Fig.7.Comparisonoftheindexspectrumofthe13CO2–1data Velocity channel width (kms-1) inL1455withtheaveragelineprofile.Theindexspectrumis created by power-law fits to the ∆-variance spectrum of indi- 4.0 vidual channel maps (∆v = 0.22kms−1). The vertical error b ch bars represent the uncertainty of the fit. The horizontal error 3.5 barsindicatethevelocitychannelwidth. x de3.0 n w i a er-l2.5 waysfallslightlybelowthepeakindices,astheyrepresentan w o P averagewhichistypicallydominatedbythelinecores. 12 IC 348 CO 3-2 2.0 IC 348 13CO 2-1 In the red line wings, most indices remain approximately 12 L 1455 CO 3-2 13 constant when increasing the velocity width, except for the L 1455 CO12 2-1 NGC 1333 CO 3-2 largestbinwidthwherethecontributionfromthecoreleadsto 1.5 NGC 1333 13CO 2-1 anobservableincrease.Inthebluewing,wefindamonotonic 0.2 0.4 0.6 0.8 1.0 1.2 1.4 1.6 1.8 2.0 2.2 growthofthespectralindiceswiththechannelwidthforboth -1 Velocity channel width (kms ) tracersinallthreeregions.Theadditionalpeakat2kms−1vis- Fig.9.Averagespectralindicesofthechannelmapsasafunc- ibleinthe12CO3–2dataofNGC1333stemsfromaseparate tionofthechannelwidth.a)showstheaverageoverthefullline darkcloudwhichisalsocontainedintheNGC1333map. width.b)representsonlytheindicesinthebluelingwings.The Figure 9 summarizesthe relation between the spectral in- linewingcomponentsarecenteredat5kms−1 forNGC1333, dices and the velocity channel width. In Fig. 9a we plot the at 4kms−1 for L1455, and at 7kms−1 for IC348. The error averagespectralindexovertheline asafunctionofthechan- bars contain the fit errorand the standard deviationof the in- nel width for the six data sets presented in Fig.8. Figure 9b dices within the considered velocity range. To avoid overlap- containstheanalysiswhenrestrictedtoa 2kms−1 windowin pingerrorbarsintheplot,wehaveshiftedthepointsforIC348 the blue line wings. The error bars contain the standard devi- andNGC1333by±0.02kms−1relativetotheiractualposition. ation of the index variation across the line and the fit errors. Theyarenecessarilylargebecauseofthesystematic variation ofindicesoverthevelocityrange.Incontrasttosimilaranaly- 5. Discussion sisbyDickeyetal.(2001);Stanimirovic´&Lazarian(2001)we 5.1.Integratedintensitymaps findnosignificantsystematicvariationofthemeanlineindex as a function of channel width (Figure 9a). In contrast to the Besides the ∆-variance,other toolshave been used to charac- average of the index spectrum we find a continuous increase terize interstellar cloud structure. The second-order structure of the spectral index with the channel width when restricting function for an observable s(r) is S = h|s(r)− s(r+ δr)|2i 2 r the analysis to the blue wing (Figure 9b). The average index which is treated as a function of the absolute value of the in- steepens from about 2.8 to about 3.1 in the 12CO 3–2 maps crement|δr| (Elmegreen&Scalo 2004). Padoanetal. (2003a) andfromabout2.4toabout2.8inthe13CO2–1maps.Asdis- computedthestructurefunctionoftheintegratedintensitymap cussedabovewefindnosystematictrendintheredwings.This of 13CO 1–0 in Perseus. A power-law fit to S ∝ δrζ over a 2 indicatesthattheaveragespectralindextakenoverthefullline range of 0.3 to 3pc provided an index ζ of 0.83. The index profile provides no measure for the velocity structure in our ofthestructurefunctionisrelatedto thepowerspectralindex COmapswhilethepeculiarbehaviourinthebluewingsneeds by ζ = β−2 for 2 < β < 4 (Stutzkietal. 1998) resulting in furtherinvestigation. β=2.83.ThisresultofPadoanetal.(2003a)agreeswithinthe 10 Sunetal.:AKOSMA7deg2CO2–1&3–2surveyofthePerseuscloud errorbarswiththeindicesfoundbythe∆-varianceanalysisof the Perseusmapsof integratedCO intensitiesoveralmostthe samelinearrange(seeTable1). However,the∆-variancespectraofindividualregionsshow significantvariationsofthespectralindexasdiscussedabove. For13CO2–1,thesespantherangebetweenβ=2.86inL1455 and3.76inNGC1333(Table2).Theanalysisofdifferentsub- setsinmolecularcloudcomplexesthusprovidesadditionaland complementaryinformationonthestructureofthecloudcom- plex. 5.2.Velocitychannelmaps Thevelocitychannelanalysis(VCA),wasusedpreviouslyby Dickeyetal.(2001)tostudyHmapsoftworegionsinthe4th Galactic quadrant.Oneof theregionsisrichin warmH gas, theotherisrichincoolHgas.Forthewarmgas,Dickeyetal. Fig.10.SketchadoptedfromFig.3ofSancisi(1974)illustrat- (2001) find a systematic increase of the mean index with ve- ing the spatial arrangement and motion of the Perseus cloud locity channel width. The cold gas at lower latitudes behaves complex. The gas is swept up by a shock expansion with differentlyandshowsratherconstantindicesof2.7–3.1. 12 kms−1. Due to the overall curvature, the line-of-sight ve- ThelatterresultsresembletheoutcomeoftheVCAofthe locityis9kms−1 forIC348,butonly7kms−1 forNGC1333. 12COand13COchannelmapsinPerseuspresentedabove.We Thediameterofthecloudis∼20pc.Pillar-likestructuresare findsimilarindicesforthevelocityintegratedmapsofthefull left at lower velocities as remainders of high-density regions region(cf.Table1) and the CO data showno significantvari- whichwerenotacceleratedtothesamevelocity. ationoftheindexwithvelocitychannelwidthwhenaveraged over all velocity bins (Figure 9a). The indices stay relatively constant.Since the bulkof the moleculargastracedby CO is spectrumofvelocityslicesasafunctionofthevelocitychannel evencolderthancoldHgas,theseresultssuggestasequence widthisdeterminedbythepowerspectralindicesofthedensity of a reduced dependence of the spectral index of the chan- structureβ andthe velocitystructurem. Theyobtain different nel maps on the bin widths from the warm to the cold ISM. regimesfor shallow (β < 3) and steep (β > 3) density power Theconstancyofthe averagespectralindexcouldalso beex- spectra: plainedbyopticaldeptheffects.Lazarian&Pogosyan (2004) haveshownthatabsorptioncanleadtoaneffectiveslicebroad- k−β+m2−3, thinslices, ening,whichleadsinextremecasestosliceindicesthatbecome P(k)∝k−β, thickslices, (β<3) independentfromtheactualchannelwidth. k−β, verythickslices; Studying the spectral index of individual velocity bins of the CO data across the line profile (Fig.8), we find that the k−9−2m, thinslices, power-lawindicesincreasewiththevelocitychannelwidthin P(k)∝k−3+2m, thickslices, (β>3) twhienbgl.uNeowcionrgre(sFpiogn.9dbin)gwahnialleysstiasywinagscraotnhdeurcctoednsftoarntthienHthedraetda k−β, verythickslices. byDickeyetal.(2001).Onepossibilitytoexplaintheasymme- Thin slices have a velocity width less than the local veloc- trybetweentheblueandredwingsmightbeashockexpansion ity dispersion at the studied scale; thick slices have a width of the CO gasin Perseus. Sancisi (1974) foundan expanding largerthanthevelocitydispersionandverythickslicesessen- shellofneutralhydrogenwhichwascreatedbyasupernovain tiallycorrespondtotheintegratedmaps(Lazarian&Pogosyan thePerOB2associationafew106yearsago.Atthelocationof 2000).We canassumethatasinglechannelofourdatacorre- the molecular cloud complex, the expansion is directed away sponds to thin slices as they are much narrower than any ob- from the Sun. Most of the associated molecular gas has been servedline width.We use β fromthe integratedmapsandthe sweptupbytheshock,butpillar-likefilamentshavebeenleft indexmeasuredinthesinglechannelstoderivem.Fromthein- at the backside of the shock. They are visible in the channel dicesobtainedbyaveragingoverthefulllineprofile(Fig.9a), maps(Fig.3)andproducethevelocitydependenceseeninthe weobtainmvaluesof3.9±1.6,3.9±1.9and3.8±1.7for12CO VCA of the blue line wings, i.e. the increase of indices with 3–2 in IC348, NGC1333 and L1455, respectively; while m size of the velocitybin becauseof a gradualincreaseof large is 3.9±2.0, 3.5±2.5 and 4.1±1.8 for 13CO 2–1 in the same scalecontributionsacrossthelinewing.Weillustratethissce- three regions. In the blue wings (Fig. 9b), we obtain m val- narioinFig.10. uesof3.2±1.6,3.4±1.4and3.6±1.5for12CO3–2;whilemis Thequantitativeresultsfromthevelocitychannelanalysis 4.3±1.9,4.3±1.7and4.1±1.5for13CO2–1inthethreeregions. can be interpreted in terms of the power spectrum of the ve- Thesevalueshavelargeerrorbars,sothattheyarenotdirectly locitystructure.Lazarian&Pogosyan (2000)showedthatthe suitedtodiscriminatebetweendifferentturbulencemodels.At