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Astronomy&Astrophysicsmanuscriptno.Gj141 February2,2008 (DOI:willbeinsertedbyhandlater) A Galactic Plane Relative Extinction Map from 2MASS 1 1 1 2 DirkFroebrich ,ThomasP.Ray ,GarethC.Murphy ,andAlexanderScholz 5 0 0 1DublinInstituteforAdvancedStudies,5MerrionSquare,Dublin2,Ireland 2 2UniversityofToronto,Dept.Astronomy&Astrophysics,66St.George’sSt.,Toronto,Canada n a Receivedsooner;acceptedlater J 9 Abstract. We present three 14400 square degree relative extinction maps of the Galactic Plane (|b|<20◦) obtained from 2 2MASSusingaccumulativestarcounts(Wolfdiagrams).Thismethodisindependentofthecolourofthestarsandthevariation ofextinctionwithwavelength.Starswerecounted in3.′5×3.′5boxes,every20′′.1◦×1◦ surrounding fieldswerechosen for 1 reference, hence the maps represent local extinction enhancements and ignore any contribution from the ISM or very large v clouds.DatareductionwasperformedonaBeowulf-typecluster(inapproximately120hours).Suchaclusterisidealforthis 4 5 typeofworkasareasoftheskycanbeindependentlyprocessedinparallel.Westudiedhowextinctiondependsonwavelength 6 inallofthehighextinctionregionsdetectedandwithinselecteddarkclouds.Onaverageapowerlawopacityindex(β)of1.0 1 to1.8intheNIRwasdeduced.Theindexhoweverdifferedsignificantlyfromregiontoregionandevenwithinindividualdark 0 clouds.Thatsaid,generallyitwasfoundtobeconstant,ortoincrease,withwavelengthwithinaparticularregion. 5 0 Keywords.ISM:dust,extinction–Infrared:ISM–Methods:miscellaneous / h p - 1. Introduction Dustnotonlyabsorbslightfrombackgroundstarsbutalso o r reddensit.Bymeasuringextinctioninanumberofwavebands, st Dustisnotonlyoneofthemostimportantcoolantsinmolec- onecandeterminehowitvarieswithwavelength(λ).Normally a ularcloudsbutisalso an excellenttracerof molecularhydro- this variation is assumed to be a power law, i.e. A λ−β λ v: gen. Determiningits distributionis thuscrucial to understand whereβ isthe opacityindex.A constantvalueforβ h∝owever i the early stages of star formation.It givesus information,for isnotnecessarilyguaranteedapriori. X example, on how clouds fragment and ultimately this knowl- One drawback in the past of the star counting method, at r a edgemustbereconciledwiththeinitialmassfunction(Padoan, least for large areas, is that it is computationally very expen- Nordlund,&Jones1997).Moreoverbycombiningdustextinc- sive. This type of data reduction, however, is ideally suited tionmapswithinfraredandsubmillimeterdustemissionmaps, to a parallel computing environment provided, for example, we canderivebasic knowledgeofgrainpropertiesandsearch by a Beowulf-type cluster. Large swathes of the sky can be forevidenceofgrainevolution. processed simultaneously and independently of each other. Extinctiontowardsan individualstarcan ofcoursebyde- Moreover,thepossibilityforexploitingsuch“numbercrunch- terminedbymeasuringitscolourexcessalthoughthismethod ing” facilities coincides with the availability of large ground requiresknowledgeofthestar’sintrinsiccolour(e.g.Heetal. basedIRsurveyssuchas2MASSandDENIS.Forthefirsttime 1995, Racca et al. 2002). The technique is also highly selec- itspossibletomanufactureextinctionmapscoveringlargefrac- tive as it only gives us information along very precise lines tionsofthesky. of sight. An alternative approach, developed many years ago Herewepresentahighspatialresolutionrelativeextinction (Wolf 1923, Bok 1956), and particularly appropriate for dark map of the Galactic Plane, in J, H, and K, derived from the clouds, is to count the number of stars in the cloud’s vicinity 2MASSdatabaseusingthestarcountmethod.Themethodand downtoalimitingmagnitudeandcomparethiswithacontrol itslimitationsaredescribedindetailinSect.2,thedetermina- “unextincted”regionnearby.Suchso-calledWolfDiagramsare tionofthenoiseisdiscussedinSect.3.Resultsoftheopacity of limited use in the optical, as one can only probe the outer index computations are presented in Sect.4 and our conclu- peripheriesofacloudwheretheextinctionislow.Themethod sionsaregiveninSect.5. workswellhoweverintheinfrared,duetoitsimprovedtrans- mission with respectto the optical,allowingregionswith AV 2. MethodandLimitations valuesashighas30–40tobemeasured. RelativeextinctionmapsweredeterminedusingWolfdiagrams (e.g.Kissetal.2000).Ateachpositionaccumulatedstarcounts Sendoffprintrequeststo:[email protected] were performedin a small box. These countswere compared 2 D.Froebrichetal.:AGalacticPlaneRelativeExtinctionMapfrom2MASS +20 0 −20 +20 b[◦] 0 .............................................. −20 +20 0 −20 180 120 60 0 300 240 180 l[◦] Fig.1. JHK colourcompositeofthe star countmap(top),relativeextinctionmapobtainedfromtheJ-banddata(middle)and threesigmanoiseduetothenon-uniformdistributionofstarsintherelativeextinctionmapsforJ(bottom).Thenoiseisdisplayed inlinearscalefromzero(white)to0.7mag(black)ofopticalextinction.TherectanglemarkstheregionmagnifiedinFig.2. to the average accumulated star count in a (co-centred but 63.5%oftheareawith b <10◦,inJ,H,andK,respectively.It | | larger) comparison field to determine the relative extinction. alsoleadstoameandensityofabout100starsormoreperbox The method is independent of stellar colour and variation of intheJ-bandforalargearea( 28002◦).Suchadensitycon- extinction with wavelength. A number of assumptions, how- verts to aroundone star per 2≈0′′ 20′′. Hence performingstar ever,havetobemade(e.g.Froebrichetal.2005):(1)starsare counts with a spatial frequency×of 20′′ ensures optimal sam- distributeduniformlyandallapparentvoidsareduetoextinc- plingofthe2MASScatalogue.Notethatthisoversamplingof tion(2)onemaydefineaconstantaverageabsolutemagnitude about10isnotunconditionallyrequiredinregionswithfewer forthestarsinabox(3)thecompletenesslimitofthecatalogue stars, but was kept to ensure a uniform pixel size throughout doesnotdependonposition.Inrealitytheseassumptionsmay thewholeextinctionmap. onlybe validundercertain conditions.Forexamplereference Counts in the 3.′5 3.′5 box where compared with a co- toanaverageabsolutemagnitudeisonlymeaningfulifthebox centred larger control×field. For the latter we chose a 1◦ 1◦ × containsenoughstars. Moreoverstars are not distributed uni- area. Thishas the effectthatour mapsrecordlocalextinction formlyontheskybutifthecontrolfieldisnottoofaraway,the enhancements,duetosmallcloudsorglobules,andnotglobal assumption of uniformity is locally valid. Thus, to apply the extinctioneffectsduetotheISMorextendeddarkclouds. methodproperlyone must ensure that the choice of box size, Achieving a high S/N in our maps depends on extending controlfield,etc.,arewithincertainlimits(seebelow). thestarcountstothefaintestpossiblemagnitude(andthusthe Usingthe2MASScataloguealreadyensuresahighlevelof largestpossiblenumberofstars).Carehoweverhastobetaken uniformityandqualityofthephotometry.Toavoidphotometric asthecompletenesslimitofthecataloguevariesstronglywith errorsforfaintobjectsweonlyselectedsourceswithasignalto galacticcoordinates.Weobtainedthislimitforeachpositionby noise(S/N)ratio>5.ThiscorrespondstoqualityflagsA/B/C determiningthe peak in the histogram of stars per magnitude inthe2MASScatalogue,andanerrorinstellarmagnitudeofat binintheassociatedcontrolfield.Ourrelativeextinctionmaps most0.17mag.Suchavalueisslightlyhigherthanourstepsize arethenobtainedexclusivelyusingstars0.3magbrighterthan inbrightness(countswereperformedevery0.1mag).However, thiscompletenesslimit. theextinctionisderivedusinganaverageforallstarsinthebox Theexerciseof countingstars can be describedas an em- andisthusdeterminedwithgreaterprecision. barrassingly parallel problem, as results from one part of the Aswe haveemphasised,accumulatedstarcountsareonly skydonotdependonanyother.Theentire2MASScatalogue meaningful, providing boxes contain a sufficient number of covering b <20◦ fromtheGalacticPlanewasprocessedwith stars.InparticulartheS/Ninthefinalrelativeextinctionmaps asamplin|g|frequency(effectivepixelsize)of20′′ usingour32- strongly depends on the number of stars in the area being node Beowulf-type cluster of 2.67GHz P4 HyperThreat pro- countedandhenceonthebox-sizeofthereseau(seeAppendix cessors. The three 144002◦ relative extinction maps (in J, H CinFroebrichetal.2005foradetaileddiscussion).Takinginto andK)tookabout40hourseachtocalculate. accountthedensityofstarsinthe2MASScatalogueinall3fil- InFig.1wepresentathreecolourcomposite(J,HandK) ters,weselectedabox-sizeof3.′5 3.′5toperformthecounts. fullsize star countmap(toppanel)andthe relativeextinction × Thisensuresapproximately25starsperbox(S/N=5,assuming map (middle panel) obtained from the 2MASS J-band data. aPoissondistribution)atthecompletenesslimitfor99.5,73.5, The small rectangle in the figure marks the region blown-up D.Froebrichetal.:AGalacticPlaneRelativeExtinctionMapfrom2MASS 3 -6 * S152 BHR79 BHR82 -7 14 BHR80 DCld 15 b[◦] -8 13 ? 12 11 109 8 7 ? * * 6 -9 5 * 4 -10 ................................................................................................................................N.4.......3...G.....7......C.2............3...................................21..................................................................................... ........................................................................................................................................................................................................................................................................................... 303 302 301 300 303 302 301 300 303 302 301 300 l[◦] Fig.2. Relative extinction map obtained from J-band 2MASS data of the Musca Dark Cloud. Contoursin the left panel start atAV=1magandareinstepsof1mag.Wemarkedpreviouslyknownandnewregionswithpeakextinctionvalueslargerthan AV=2mag.“Fake”globulesduetobrightstarsarelabelledwith*,andnumbersrepresentregionsfromVilas-Boasetal.(1994) (MU16couldnotbedetected).Themiddlepanelshowstherelativeextinctionmapingrey-scaleandtherightpanelthe100µm IRASimageofthisregion.Inthemarkedrectangle,aroundNGC4372,extinctionvaluesarelessreliableduetoadditionalnoise (seealsoSect.2). in Fig.2. Thelatter figure,of the Musca Dark Cloud,demon- 3. NoiseDetermination strates the full resolution obtained in our relative extinction Wedeterminedthenoiseinourimagestocompareourmethod maps (in contours in the left and grey-scale in the middle with the NICER techniqueof Lombardi& Alves (2001). Our panel).Knowndarkcloudsarelabelled,aswellas“fake”glob- relativeextinctionmapsshownoiseduetothenon-uniformdis- ules(seebelow).ThepaneltotherightofFig.2showsforcom- parison the IRAS 100µm image and nicely demonstrates the tributionofstars, σ1,andthebox-sizewithinwhichwecount correspondencebetweendustinemissionandabsorption. stars(so-calleddithernoise),σ2. Thelatter manifestsitself as structures of around the size of the box used for star-counts. We thussmoothedthe originalmapswitha filter ofwidththe Comparingaccumulatedstarcountsina3.′5 3.′5boxwith box-size and subtracted the resulting image from the original thesurrounding1◦ 1◦ fieldisidealforfinding×smallregions toobtainthenoiseduetothenon-uniformdistributionofstars. × These noise images were then gaussian filtered (5′ FWHM), of enhanced extinction. All fields containing high extinction inordertoobtainthesameresolutionasinLombardi&Alves regions,whicharemoreextendedthanasignificantportionof onesquaredegree,however,willnothavethecorrectextinction (2001), and the 3σ noise level was determined. The noise is values.InparticularthisincludesthelargeOrion,Taurus,and transformed into AV using the conversion factors 4.04, 6.47, 9.75forJ,H,andK,respectively,giveninMathis(1990).The Ophiuchus clouds. Here a larger comparison field is needed, butseethediscussioninSect.4. bottompanelinFig.1showsingrayscaletheresultantσ1noise inourJ-bandmap,averagedover1◦ 1◦. × This noise ranges from 0.2-1.0mag (J), 0.4-1.8mag (H), Veryrichstar clusters(mainlyglobularclusters) areprob- and 0.6-3.8mag (K) in equivalentopticalextinction.The val- lematic in the sense that star counts are anomalously high at uesfortheJ-banddataareslightlyhigherthanobtainedbythe their centre compared to their peripheries. This gives rise to NICER technique (compared with the maps of Lombardi & regions of apparent negative extinction at the cluster centre Alves(2001)intheOrionregionataboutl=210◦, b= 18◦). − andapparentpositiveextinctionfurtherout.Fig.2,showingthe All three noise maps show the same principle structure globular cluster NGC4372, illustrates this effect. Fortunately with the lowest noise levels obtained north and south of theseregionsareusuallynotveryclosetoareasofrealhigher the Galactic Plane within 60◦ longitude from the Galactic ± extinction.Anothereffectisthatextremelybrightstarsprevent Centre. Regions directly in the Galactic Plane and within the detectionofsourcesclosebyandhencealsomimichighextinc- large dark clouds (Ophiuchus, Orion, Taurus) are affected by tionregions(alsoseeFig.2forafewexamples).Finallythere higher noise, due to extended extinction and hence a smaller arephysicalandeffectivegapsinthe2MASScataloguewhich numberofstars. also resultin higherapparentextinction.Fortunatelythese re- The additionalnoise, due to dithering,is only slightly de- gionscoveronly0.006%ofthewholesky. pendentonthechosenbox-size.Alargernumberofstarsinthe 4 D.Froebrichetal.:AGalacticPlaneRelativeExtinctionMapfrom2MASS boxreducesσ2.Byvaryingthebox-sizethevalueforthisnoise Table 1. Peak position and width of the distribution of the canbeestimated.Forourbox-sizeweobtaintypicalvaluesof opacityindexβ forselected darkclouds,determinedbetween about0.7,1.0,1.3magopticalextinctionforthe J,H, K-band J and H (βJH) and between H and K (βHK). In some regions dither-noise,respectively.SeetheAppendixofFroebrichetal. βHK couldnotbedeterminedproperly,duetolowS/N. (2005)foradetaileddescriptionofthiseffectinthecontextof aparticularregion(IC1396).Theactualdetectionlimitinour Region βJH βHK Region βJH βHK relativeextinctionmapcanbedeterminedbyσdet=pσ12+σ22 CrA 1.4±0.3 1.4±0.4 LupusIII 1.5±0.3 1.9±0.4 foreachpositionandfilterindividually. Ophiuchus 1.5±0.3 1.7±0.4 LupusIV 1.5±0.3 1.9±0.3 LupusI 1.5±0.3 1.7±0.5 Monocerus 1.4±0.5 1.0±0.4 LupusII 1.3±0.2 - Cepheus 1.4±0.4 1.2±0.4 4. NIR OpacityIndex Musca 1.7±0.3 - S140 1.0±0.3 1.5±0.4 Circinus 1.7±0.4 2.0±0.4 Serpens 1.7±0.4 2.0±0.3 Usingourthreelargescalemapswecandeterminehowextinc- tion varies in the NIR. The power law index β of the wave- 5. Conclusions lengthdependenceoftheextinctioncanbedeterminedusing: We have shown that accumulated star counts in the NIR can βλ1λ2 =log(Aλ1/Aλ2)/log(λ2/λ1) (1) beusedtoobtainlargescalerelativeextinctionmaps.Parallel techniquesallowedusto process14400squaredegreesofthe where Aλ1 is the extinction at a wavelength λ1. We chose sky within 40 hours computing time on a 32-node Beowulf- the wavelength for the 2MASS filters1 of 1.235, 1.662, and typeclusterof2.67GHzP4HyperThreatprocessors.Theaccu- 2.159µmforJ,H,andK,respectively.Sincewehavethreefil- mulatedstarcountsareperformedindependentofstellarcolour terstherearethreepossiblecombinationstodetermineβ (JH, andonlylocalextinctionenhancementsaredetermined,Hence JK,HK),twoofwhichareindependent. the wavelength dependence of the dust extinction within the Carehastobetakeninderivingβ,sinceitisverysensitive dark clouds can be investigated. A study of selected clouds tosmallerrorsinextinctionespeciallyatlowextinctionvalues. showsthattheopacityindexβrangesfrom1–2.Inmostcasesa Henceonlyregionswhicharethreesigmaabovethelocalnoise constantorincreasingopacityindexwithwavelengthisfound. levelwereconsidered.Afurthermorecomplexsourceoferror The large scatter of β, even within a particular cloud, leads isthesize andpositionofourcontrolfield.Duetoextinction, totheconclusionthata uniformopacityindexshouldbeused afractionf ofthecontrolfieldmightjustshowafractioneof with great care for extinction corrections within dark clouds. stars, compared to unextincted regions. This leads to a mean ThisisincontrasttothegeneralISMwheremixingofthedust, extinctionAC inthecontrolfieldandhenceasmallerapparent plusaveragingoverlonglinesofsight,ensuresa singleindex measured extinction Aλ=Areal AC. It can be shown easily suffices. − thatundertheassumptionsf (1 e) 1andAC Areal,the derivedβ valueisnotinfluenc·ed−,eve≪nifthemeas≪uredextinc- Acknowledgements. We are grateful to the DIAS Cluster Manager, tion values are wrong by AC. The size of AC is smaller than D. Golden, for scheduling the almost 50,000 jobs needed to gener- the noise in our maps as long as √N f (1 e) 1, were N ate our maps and for his assistance when a crucial hard disk failed. · · − ≤ D.Froebrich and G.C.Murphy received support from the Cosmo- isthenumberofstarsinoursmallbox.Accordingtoourbox- Grid project, funded by the Program for Research in Third Level sizeandthestardensity,thisholdsformostregionsaslongas Institutions under the National Development Plan and with assis- f issmallerthan0.3.Consideringthiswealsoexcludedallre- tance fromthe European Regional Development Fund. The work of gionswhere more than 30% of the controlfield is influenced A.ScholzwaspartiallyfundedbyDeutscheForschungsgemeinschaft byextinctionlargerthanthethreesigmanoisefromtheopacity (DFG) grants Ei409/11-1 and 11-2. This publication makes use of indexdetermination. dataproductsfromtheTwoMicronAllSkySurvey,whichisajoint The distribution of βJH, determined over the whole area projectoftheUniversityofMassachusettsandtheInfraredProcessing of our map is rather broad and peaks between 1.0 and 1.8. and Analysis Center/California Institute of Technology, funded by theNationalAeronauticsandSpaceAdministrationandtheNational The same wide distribution is found for βHK, but at slightly ScienceFoundation. largerβ values(shiftedby+0.1).Thereasonforthisparticu- larlybroaddistributioncanbefoundwhenwelookatgroupsof darkcloudsin detail.We findtheycanbecategorisedaccord- References ingtowhethertheopacityindex1)isroughlyconstant,2)in- Bertin,E.&Arnouts,S.1996,A&AS,117,393 creases,or3)decreaseswithwavelengthintheNIR.Notethat Bok,B.J.1956,AJ,61,309 evenwithinindividualsmallcloudsβcanvarysignificantly.In Froebrich,D.&Scholz,A.2003,A&A,407,207 Table1welistpeakpositionsandwidthofthedistributionofβ Froebrich,D.,Scholz,A.,Eislo¨ffel,J.&Murphy, G.C.2005, A&A, foraselectionofdarkclouds.MostregionsbelongtoCategory inpress,astro-ph/0411706 1or2,althoughasmallnumber(e.gCepheus)canbeclassified He, L., Whittet, D.C.B., Kilkenny, D. & Spencer Jones, J.H. 1995, asCategory3.Notethatβvariessignificantlyandrangesfrom ApJS,101335 1.0(e.g.S140)to2.0(e.g.Circinus). 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