1978ApJ. . .225. . .40B The AstrophysicalJournal,225:40-55,1978October1 © 1978.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. tion havecenteredonmeasuringeitherthevariations generally accepted“best”methodhasnotyetbeen measure thereddeningofextragalacticobjects,a the Hicolumndensity(e.g.,KnappandKerr1974), established. AsshowninPaperI(BursteinandHeiles in galaxycounts(e.g.,ShaneandWirtanen1967)or account fortheirregularitiesinreddeningdistribu- tion indicatorsandthereddening.Thepreviouslarge- of thepatchinessinterstellardust.Waysto that therewerenosimplerelationshipsamongthese galaxy counts,andreddening(Heiles1976)concluded and thenderivingarelationshipbetweentheseextinc- problems. extinction indicatorsandproducedsomeunresolved scale investigationintotheinterdependenceamongHi, 1978), smoothesc\b\modelsdonotworkwellbecause among thesequantitiesand areabletoresolvemany of theproblems.Mostthem originatedbecausethe Despite manyattemptstofindareliablemethod In thispaperwefurtherinvestigate therelationship * LickObservatoryBulletin,No. 807. © American Astronomical Society • Provided by theNASA Astrophysics Data System H I,GALAXYCOUNTS,ANDREDDENING:VARIATIONINTHEGAS-TO-DUSTRATIO, galaxies andpermitsareasonableestimateoftheerrorinlogVasfunctionlatitude. ties, andreddenings,resolvemanyoftheproblemsraisedbyHeiles.Thesewere the galaxy.WepresentacompilationofreddeningsforRRLyraestarsandglobularclusters caused bytwofactors:subtlebiasesinthereddeningdataandavariablegas-to-dustratio which areonthesamesystemandwebelievetoberelativelyfreeofbiases.Theextinction average, lessthan0.03maginE{B—F). to-dust ratiocanvarybyafactorof2fromtheaverage,andwepresenttwomethodsforcorrect- The analysisshowsthatgalaxycounts(orclustercounts)aretoonoisytoallowdirect analyze galaxycounts.Thisnewmethodpartiallyaccountsforthenonrandomclusteringof at thegalacticpoles,asdeterminedbygalaxycounts,isreexaminedusinganewmethodto galactic absorbinglayer.Wepresentaprescriptionforpredictingthesereddenings;inthearea ing forthisvariabilityinpredictingthereddeningofobjectswhicharelocatedoutside determination oftheextinction,orvariationinneargalacticpoles.Fromall of skycoveredbytheShane-Wirtanengalaxycounts,errorinthesepredictionsis,on at leastpartlytheresultofaninstrumentaleffectinradiodata.Wealsoshowthatgas- offsets intherelationsbetweenE{B—V)andHi,galaxycountswhichare over muchofthenorthgalacticpole]andirregularlydistributed.Wefindthattherearezero available data,weconcludethatthereddeningatpolesissmall[<0.02maginE(R—V) Subject headings:galaxies:clustersof—interstellar:matterradiosources:21cmradiation gal THE EXTINCTIONATHIGHGALACTICLATITUDES,ANDANEWMETHOD We reanalyzetheinterrelationshipsamongShane-Wirtanengalaxycounts,Hicolumndensi- I. INTRODUCTION Board ofStudies,AstronomyandAstrophysics,UniversityCalifornia,SantaCruz FOR DETERMININGGALACTICREDDENING* Astronomy Department,UniversityofCalifornia,Berkeley Received 1978March3;acceptedApril5 David Burstein ABSTRACT Carl Heiles AND 40 2 2 the correlationbetweenHiandgalaxycounts previously beenfoundbySeki(1973)inhisstudyof gas-to-dust ratioisvariable,aphenomenonwhichhas medium (JenkinsandSavage1974;Bohlin1975; by UVobserversintheirstudiesoftheinterstellar variable gas-to-dustratioandtopredictthevalueof with Hicolumndensitiesenablesustocorrectforthe E{B —V)withconsiderableaccuracy. type starsfromAbtandGolson(1962).Allofthese 49 globularclusters,84RRLyraestars,andtwoearly- hydrogen columndensities(Ah)inthedirectionsof Savage etal.1977).Comparisonofthegalaxycounts bers givenbyShaneandWirtanen (1967,hereafter 300 pc.Thegalaxycountsarederivedfromthenum- objects have\b\>10°andzdistanceslargerthan SW), correctedasinHeiles’s (1976)work.Theunits on eachobject;Aisunavailable forobjectswith are numberperdeg,averaged over13degcentered 8 <—23°becauseofthesouthern limitoftheSW gal Table 1liststhegalaxycounts(Ag)andneutral al II. THEDATA 1978ApJ. . .225. . .40B NGC 5824. NGC 2808. NGC 2298. NGC 1261. NGC 362.. NGC 104.. NGC 5286. NGC 5139. NGC 6397. NGC 5986. NGC 6584. NGC 6541. NGC 6715. NGC 6652. NGC 6637. NGC 6752. NGC 6809. NGC 6723. NGC 5466., NGC 5272.. NGC 5897. NGC 5694.. NGC 5634., NGC 5053.. NGC 5024., NGC 4590., NGC 4147., NGC 2419. NGC 1904. NGC 288.. NGC 6171. NGC 5904. NGC 6205. NGC 6093. NGC 6229. NGC 6218. NGC 6333. NGC 6287. NGC 6254. NGC 6402. NGC 6356. NGC 6341. NGC 6981. NGC 6934. NGC 6864. NGC 7089. NGC 7078. NGC 7006. NGC 7099. TZ Agr.. XX And. YZ Aqr.. SW And. BR Aqr.. SX Aqr.. DN Aqr. CP Aqr.. TZ Aur.. X Ari.... 341 Aql.. ST Boo.. SV Boo.. TW Boo. SW Boo. UU Boo. SS Cnc.., Reddening DataforGlobularClusters,RRLyraeStars,andAbtGolsonStars:\b\>10° © American Astronomical Society • Provided by theNASA Astrophysics Data System Object 282.2 245.6 270.6 332.6 301.6 305.9 342.1 349.3 338.2 337.0 311.6 309.1 336.5 299.6 252.8 335.6 227.2 II 342.9 331.1 342.2 333.0 352.7 180.4 149.7 128.4 115.7 169.1 176.8 198.9 42.2 42.1 73.6 59.0 / 21.3 68.4 15.7 20.3 52.1 15.1 27.2 63.8 35.2 53.4 65.0 48.9 48.7 75.4 53.2 57.9 45.6 35.7 68.8 62.5 57.4 71.1 56.5 0.0 5.6 1.5 1.7 8.8 0.1 3.4 3.9 6.7 5.5 RR LyraeStars+AbtandGolson -11.2 -16.0 -10.3 -16.4 + 13.3 + 22.1 + 10.6 -11.3 -52.1 -46.3 -44.9 -14.1 -11.4 -12.0 + 15.1 -17.3 -25.6 -23.3 + 78.7 + 78.9 + 36.0 + 77.2 + 25.3 -89.4 + 49.3 + 73.6 + 79.8 -29.3 + 26.3 + 30.3 + 40.3 + 40.9 + 23.0 + 19.4 + 46.8 + 30.4 + 23.1 11 + 34.9 + 10.7 + 11.0 + 14.8 + 10.2 -46.8 -35.8 -27.3 -19.4 -32.7 -18.9 -25.8 -23.6 -33.1 -44.3 -34.0 -31.3 -55.2 -49.8 -22.0 -69.0 -39.8 + 20.9 + 55.2 + 67.8 + 65.5 + 62.9 + 58.0 + 26.3 b Globular Clusters—Southern Globular Clusters—Northern E(B —V)Source TABLE 1 + 0.14 + 0.25 + 0.04 + 0.20 + 0.10 + 0.18 + 0.18 + 0.17 + 0.28 + 0.11 + 0.08 + 0.02 + 0.17 + 0.10 + 0.04 + 0.03 + 0.03 + 0.03 + 0.02 + 0.03 + 0.03 + 0.03 + 0.01 + 0.03 + 0.03 + 0.02 + 0.02 + 0.30 + 0.17 + 0.11 + 0.09 + 0.17 + 0.27 + 0.02 + 0.02 + 0.37 + 0.40 + 0.40 + 0.06 + 0.12 + 0.20 + 0.17 + 0.37 + 0.06 + 0.10 + 0.07 + 0.058 + 0.074 + 0.006 + 0.035 + 0.024 + 0.064 + 0.05 + 0.034 + 0.01 + 0.157 -0.016 + 0.045 + 0.024 + 0.007 + 0.005 + 0.113 + 0.002 0.00 0.00 0.00 11 10 14 15 15, 16 15, 16 15 15 15 15 15 16 15 15 15, 16 15, 16 15 15 15 15, 16 4 4 2,3 5 5 3 5 1 1 1 1 1 1 1,2 1 9 3 7,8 1 1,6 3 5 5 1 1 1 1 1 1 1,12 1 5 5, 13 5 5 1 1 1.5 1 1.4 1,3 1 1 1 1 1 502 432 441 246 461 425 421 499 434 638 680 292 324 581 194 226 114 389 458 331 300 570 394 123 409 745 117 140 153 904 148 475 468 798 192 188 251 747 849 536 220 104 214 332 391 144 258 249 202 230 237 249 327 401 684 331 118 204 162 112 110 Nu 46.2 94 96 24 99 log JVsal 0.700 0.740 1.757 1.663 1.418 0.114 0.204 0.342 0Í9Í9 0.114 0.826 1.447 1.865 1.542 1.760 1.Ï79 1.878 1.664 1.568 1.152 1.657 1.346 1.187 1.294 1.767 1.387 1.538 1.656 1.423 1.385 1.501 1.800 1.593 1.493 1.356 1.555 1.649 1.ÓÍ7 1.431 1.639 1.497 1.693 + 0.5 -2.0 -1.0 + 1.7 + 1.0 -3.0 -1.0 -2.0 + 1.0 -1.5 — 2.0 -4.0 + 2.0 + 0.5 -2.0 + 1.5 -1.0 + 1.8 -0.2 -1.0 + 1.5 + 1.0 -0.5 -0.5 + 3.5 + 2.5 -Ï.0 + 1.0 -2.0 -0.5 ’ 0.0 ‘ 0.0 R 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1978ApJ. . .225. . .40B TTCnc Z CVn W CVn RR CVn... SW CVn.... RR Cet SZ CVn V Ind OX Her VZ Her VX Her... TW Her TV Leo EP Her.... EE Her BB Eri AE Dra IU Car S Com RZ Cet RXCet AN Ser CG Peg BF Peg 452 Oph.. 445 Oph.. IO Lyr AQ Lyr TT Lyn V LMi V LMi A Leo RR Leo SZ Gem RR Gem SU Dra ST Com RY Com.... AVSer AT Ser VYSer DZ Peg AV Peg AO Peg AEPeg. .... ST Oph.... SS Leo RX Leo UZ Eri RX Eri RYPsc VV Peg KX Lyr..... AW Ser 866 Oph 531 Oph.. 530 Oph (3) Estimatedfrom,orquotedin, Harris1975.(4)etal.1976.(5)Table2ofBursteinand McDonald (two-color, spectraltypemethod) 1975.(6)Menzies1974.(7)Cannon(8)Alcaino (9)Stetson AE Tue SS Tau CS Ser and Harris1977.(10)Racine Harris1975.(11)Walkeretal.1976.(12)andRacine 1974.(13) Harris 1976.(14)Lee1977.(15)Sturch 1966,1969+McDonaldcalibration.(16)Epsteinand 1973+ TU UMa.... AG Tue UV Vir UU Vir BD +84°02. BD +80°32. BC Vir AT Vir McDonald calibration.(17)Abt andGolson1962. AS Vir Sources.—(1) Table1ofBurstein andMcDonald1975.(2)QuotedinIllingworth 1976. © American Astronomical Society • Provided by theNASA Astrophysics Data System Object 212.1 213.1 124.0 201.8 218.8 154.0 201.3 268.3 208.4 355.3 214.3 269.6 134.9 254.1 263.0 209.4 347.9 342.4 143.5 198.9 102.4 187.4 178.2 176.1 182.5 133.4 11 100.7 303.2 286.5 280.7 302.4 180.1 304.6 303.5 198.8 323.4 123.9 122.0 71.8 76.7 65.2 59.6 51.9 32.8 93.1 38.2 55.9 23.8 77.2 69.9 24.5 22.8 60.6 84.3 68.6 55.4 89.5 77.4 80.2 78.4 32.0 30.3 32.5 28.7 11.3 18.1 l 6.2 7.9 7.2 + 81.1 + 73.3 + 71.0 + 28.4 -59.9 + 79.8 + 57.8 + 73.7 -43.1 + 43.0 + 25.4 + 34.6 -54.5 + 81.3 -23.0 + 85.8 -77.6 +23.4 + 22.1 + 19.5 -34.4 -33.9 + 48.3 -60.4 -20.8 + 39.1 + 24.8 + 85.1 -41.4 -22.6 + 15.5 + 15.4 + 28.5 + 20.0 + 15.2 + 53.7 + 49.1 + 57.1 + 70.5 + 53.1 + 25.4 + 45.2 -62.9 -30.4 -24.1 -33.9 -30.4 + 15.3 + 16.6 + 20.4 + 41.6 + 66.1 -38.5 + 36.8 + 42.4 + 44.1 + 25.7 + 45.4 + 43.4 -54.8 -50.4 n + 60.5 + 71.9 + 62.3 + 57.4 + 52.6 + 67.5 + 18.6 + 22.1 b TABLE 1—Continued E(B -V) -0.006 -0.036 + 0.013 + 0.069 -0.001 + 0.006 -0.023 -0.005 + 0.024 + 0.026 + 0.09 + 0.04 + 0.072 + 0.003 + 0.01 + 0.015 + 0.035 + 0.046 -0.014 + 0.05 + 0.201 + 0.213 + 0.06 + 0.039 + 0.02 + 0.041 + 0.023 + 0.08 + 0.036 + 0.013 + 0.127 + 0.028 + 0.019 + 0.074 + 0.01 + 0.222 + 0.20 + 0.294 + 0.226 + 0.034 + 0.014 + 0.071 -0.014 + 0.049 + 0.035 + 0.055 + 0.026 + 0.003 + 0.017 + 0.056 + 0.004 + 0.008 + 0.12 -0.024 + 0.01 + 0.083 + 0.01 + 0.241 -0.022 -0.007 -0.025 + 0.004 + 0.01 + 0.007 -0.02 + 0.249 + 0.112 0.00 0.00 Source 15 15 15, 16 15, 16 15 15 15, 16 15, 16 16 16 16 15 15 15, 16 15 15 15, 16 16 15 15 16 15, 16 15 16 15 15 15, 16 15 15 15 15 15 15 15 16 15 15 15 15 15 15 15, 16 15 15, 16 15 15 15 15 15 15 15 15, 16 15 16 15 15 15 15 15 15, 16 15 15 15, 16 15, 16 16 15 15 17 17 248 252 272 116 279 217 220 361 121 267 298 456 316 142 161 162 131 296 460 268 276 252 667 527 362 374 175 211 272 261 622 185 514 549 101 195 205 215 313 124 146 618 395 182 179 164 197 719 119 120 151 186 169 176 178 103 164 300 46 98 44 95 72 68 41 96 77 87 71 log Agai 1.509 1.565 1.844 1.756 1.700 1.476 1.804 1.636 1.789 1.580 0.447 0.491 0.919 0.908 0.342 0.751 1.158 1.942 1.619 1.746 1.373 1.591 1.614 1.645 0.519 1.373 1.516 1.312 1.500 1.290 1.675 1.459 1.294 1.072 1.464 1.310 1.465 1.583 1.500 1.717 1.842 1.486 0.875 1.682 1.714 1.301 1.369 1.352 1.507 1.663 1.730 1.544 1.648 1.300 1.494 1.682 1.737 1.621 1.787 1.389 1.471 1.494 1.710 1.575 1.587 -2.0 -1.0 -1.0 + 0.6 + 0.6 -Ï.0 + 0.6 -2.5 -1.0 + 0.5 -1.0 + 1.0 -1.0 + 1.0 + 4.0 + 1.0 + 0.8 —Ï.5 + 1.0 -1.0 -2.0 -2.5 -4.0 -1.0 -1.5 -0.2 -2.0 + 1.0 -4.0 -2.0 -2.0 -4.0 + 0.8 -1.0 + 1.0 + 1.5 -2.0 + 1.0 + 1.0 + 2.0 -1.0 + 1.0 -1.0 + 0.5 + 1.0 -2.0 R 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 0.0 1978ApJ. . .225. . .40B 18-2 2 from theintegratedcolor-spectraltyperelationship, properties oftheclusters.Infewcaseswheresuch tions wereallmadewithoutreferencetotheintegrated here wereobtainedbyplacingtheindependent fore, mostoftheglobularclusterreddeningspresented for 8>—30°andfromHeilesCleary(1978) reddening determinationsfromthequotedreferences data wereunavailable,thereddeningsobtained on acommonsystem.Theseindependentdetermina- McDonald (1975)forclusterswith\b\>10°.Asbe- sion andanupdateofTable1Burstein survey. ThevaluesofNaretakenfromHeiles(1976) clusions ofthispaper.Becauseproblemsinherent by Harris(1976),andtheonespresentedhere;use globular clusterreddeningsofR.Racine,asquoted We notethatthereissomedisagreementbetweenthe as listedinTable2ofBursteinandMcDonald(1975). curate, onaverage,toabout0.03magforhigh-latitude relationships, oneeachforhaloandolddisk the period-color-AS(anFe/Hindex)relationshipde- to determinereddening(Burstein1978a),webelieve in usingtheintegratedpropertiesofglobularclusters cluster andtheRRLyraereddeningsshouldbeac- lished (B—F)colorsofSturch(1966,1969)and rived byMcDonald(1977)forRRLyraetypeab of thoseotherreddeningswouldnotchangethecon- 8 <—30°;theunitsare2.23x10cm. stars atminimumlight.Twoseparateperiod-color observations ofMcDonald(1977).Boththeglobular Epstein and(1973),supplementedbythe RR Lyraestars(asdeterminedfromtheirvaluesof 0.25. However,itisunlikelythatthispossibledepen- (Burstein andMcDonald1975;1977). objects and0.05magforlow-latitudeglobularclusters our reddeningstobethemorereliable. together intheOphiuchusregion,andaretherefore relation betweenE{B—V)andlogNforthesix evident, asisshowninourFigurela.In\b the relationbetweenE{B—V)andNisnolonger data areused,however,thelatitudedependencein AS), wereusedtoobtainE(B—V)fromthepub- dence issignificant,sincefourofthepointslieclose there isasuggestionoflatitudedependenceinthe between E(B—V)andlogJV.Whenthepresent dence intherelationbetweenE(B—V)andiV, objects having\b\<20°and0.13E(B—V) u boundary separatingcrossesandstarsinthediagram. not independentbecause7^isaveragedover13deg. nate. TheRRLyraereddenings usedbyHeilescame from Sturch(1966,1969). These datadifferintwo At highgalacticlatitudes, RR Lyraestarspredomi- product ofsubtlebiasesinthe reddeningdataheused. One oftheotherpointshasb=19?4,closeto20° min respects fromthoseusedhere. First,Sturchassumed ebX n gal H gal The globularclusterreddeningsarebothanexten- RR Lyraereddeningshavebeenobtainedbyusing Heiles (1976)foundevidenceforalatitudedepen- The latitudedependencefoundbyHeileswasthe © American Astronomical Society • Provided by theNASA Astrophysics Data System III. RELIABILITYOFTHEE{B-V)DATA: ABSENCE OFTHEHEILES(1976) LATITUDE DEPENDENCE H i,GALAXYCOUNTS,ANDREDDENING 2 12 used U—Basameasureoflineblanketing,which ings areused.Second,thereddeningsofMcDonald having |Z?|>50°,whichis0.03maghigherthanthe the 18RRLyraestarsinoriginalHeilessample tic poles;however,McDonald(1977)concludesfrom correct forline-blanketingeffectsdirectly,byusinga reflected intheaverageofreddeningvaluesfor E(B —V)=0.00atthepoles.Thisdifferenceis his analysisofRRLyraecolorsandHßindicesthat introduces addederrorbecauseU—Bismorepoorly (B —JOo-period-ASrelationship;incontrast,Sturch average forthesamestarswhenMcDonald’sredden- a esc|è|lawwithE(B—V)=0.03magatthegalac- the high-latitudereddeningvaluesusedbyHeileswere were settoE(B—V)=0.00bySturch.Therefore, which wereanomalouslylarge;thenegativevalues determined thanisi?—F.Thelargeerrorsproduced latitude datatowardanomalouslylowreddenings. biased tohigherreddenings. some reddeningswhichwerenegativeandothers clusters havingE(B—V)>0.35hadhighredden- reddenings inourTable1.)Furthermore,thethree (These fourclustershavesubstantiallyhigherpositive a verysmallreddening;thisbiasedtheintermediate- clusters usedbyHeileslyingintherange20°< reddenings forspecificclusters.Threeoftheglobular possibly intrinsicscatterinthisrelationship(Burstein to higherreddenings. latitude reddeningvaluesusedbyHeileswerebiased reddenings forthesethreeclusters(NGC6171,6287, ings inthecompilationusedbyHeiles.However, and McDonald1975),itispossibletoobtainerroneous relationship toderiveE(B—V).Owingthelarge, (1974), whousedanintegratedcolor-spectraltype dominate. Theglobularclusterreddeningsusedby tively freeofthebiasesaffectingpreviouslist. he used.Webelievethatourreddeningdataarerela- are infactconsiderablysmaller.Therefore,thelow- and 6402),asgivenbythesourcesquotedinTable1, Heiles camefromthelistofHarrisandvandenBergh counts belown,theaveragenumberperdegexpected galactic extinctionfromthereductionofgalaxy E(B —V)witheitherNorlogiV. because oftwooppositebiasesinthereddeningdata for zeroabsorption,canbeestimatedfromexisting significant latitudedependenceintherelationshipof tion isn~andwouldamountto147fortheactual data. ThefractionaluncertaintyduetoPoissonvaria- Figures laandlbleadustoconcludethatthereisno count n£:50inthegalacticcaps;at\b\=20°, where onlyabout^asmany galaxieswerecounted, it wouldbe257.Thecorresponding valuesofthe \b\ <50°hadnegativereddenings,andafourth <7(log 7V),wouldbe0.06 and0.10,respectively. error duetothePoisson variationinlogAf, However, thisisconsiderably lessthanthetotal 0 Kgal Q0 0 0 Pgal gal At lowgalacticlatitudes,globularclusterspre- The uncertaintiesthatareencounteredinevaluating In summary,Heilesfoundalatitudedependence IV. THEVALIDITYOFGALAXYCOUNTSAS AN EXTINCTIONINDICATOR 43 1978ApJ. . .225. . .40B 2 Fig—(Hesus EBfora11obectsm ing orcorrectionerrorsin the SWanalysis.Froma 20°. statistical studyofoverlap zones intheSWcounts, rature, Poissonstatisticsareunimportantinincreasing latitudes. Becauseuncorrelatederrorsaddinquad- uncertainty. OverthenorthpolargalacticcapHeiles Seldner etal(1977)found thatthermsfractional a(log Agai),tobe0.15;thus50°;crosses20°<\b\stars 44 ga This excessofaover50° D □ Vx 0D X x XD □o ¡Bbo x X o|M X xX^J S^ a a°0a xxx s »°B g JDSx* D DÜ B x BURSTEIN ANDHEILES a *X^ xx» x * M * r» ,10 .20 .10 .20 Fig. Ib Fig. la E CB-V) E CB-V) tical errora,theyaddin quadrature andtherefore correlated witheachother or withthepurelystatis- equivalent toonly0.06 If resolvedstarstom<19areexcluded,then variations inthezodiacallightwithinpolarcap plane, whichpassesnearthenorthgalacticpole; threshold. Sincetheareaofagalaxyincreaseswith galaxy. Fromstatisticalconsiderations,weexpect image profile,nottheapparentmagnitudeof would contributetothevalueofafoundbyHeiles. intensity andisconcentratedtowardtheecliptic time andposition.Zodiacallightiscomparablein illumination arethelargestcontributorstosky the skyinmagnitudeunits.Airglowandartificial This providesAw(threshold)=xA/x,(sky),whereAm ground level—say,as(background)^,wherex>0.5. vary morerapidlythanthesquarerootofback- the detectablethresholdofagalaxytoincreaseas Checks oftypicalastrographplateslikethoseusedby decreasing surfacebrightness,thethresholdshould by theareaoverwhichgalaxyisbrighterthan below, recognitionofagalaxyasbeingdifferentfrom SW areconsistentwiththisdensity.Therefore,crowd- affect Am(threshold)totheextentthattheyvarywith brightness (RoachandGordon1973)would is thevariationindetectablethresholdcausedby SW counts,unlessthepersonal equationoftheindi- square rootofthebackgroundbrightnessleveldivided a starinvolvesthethresholdsurfacebrightnessin suggested asaffectingtheSWcounts.Asdiscussed No. 1,1978 A/z(sky), thevariationofsurfacebrightness 1950), predictabout12,000starsdegat\b\=10°. 1976), correctedby0.5magfortheerrorinScares 10° <|è|20°evenfurther;at\b\=15°thesky T pg T SBi1 pg T Thus skybrightnesseffectswouldhavebeenim- We concludethat,overmost ofthesky,major Crowding ofgalacticstarsatlowlatitudes Variations inthediffuseskybrightnesshavebeen © American Astronomical Society • Provided by theNASA Astrophysics Data System H I,GALAXYCOUNTS,ANDREDDENING 21/ 2 2 2 galaxy clustercounts(e.g.,deYaucouleursandMalik & =4.0,whichisthegenerallyacceptedvalue.In larger thanthevaluesderivedfromphotometric extinction ofabout0.25mag.Thisisconsiderably near thepolesisirregularly distributed betweenvalues references citedinPaperIandBurstein Heiles 1976)aswellanalysesofothergalaxyand layer willbeneeded,however,toestablishanysuch many moreobjectsoutsideofthegalacticabsorbing in §VI,makeNuselessfor resolvingthediscrepancy. studies ofreddeningathighgalacticlatitude(e.g.,the dependence ofyonA. (1976); thusanyvalueadoptedcanbeonlyarepre- independent of^,forthereasonsnotedbyHeiles ever, wenotethatthereisnoreasontoexpectybe is thevalueweshalladoptforourdiscussion.How- lieve thattheavailableevidencefavorsy=1.0,which contrast, y=0.47wouldprovide^7.7.Webe- consistent with^=3.6ify1.0;thisiscloseto log A=(1.645±0.024)-(3.620.2l)E(BF), volves athresholdsurfacebrightnessintheimage of A.Accuratedeterminationthereddenings sentative oneaveragedoversomeappropriaterange kind (e.g.,Neckel1965).Furthermore,theleast- profile, notmerelythedetectionofanimageany offset andvariablegas-to-dust ratio,tobediscussed of 0.00and0.03maginE(B —V).Thezero-point McDonald 1975),whichindicate thatthereddening squares fittothedatapresentedinFigure16yields nition ofagalaxyasbeingdifferentfromstarin- empirical valuey=1.0determinedbycalibrating (Heiles 1976)supportsthecontentionthatrecog- actual countsagainstknownextinctiondifferences counting limitinthesamewaythatitdoesstars.The assumed thatextinctionaffectsgalaxyimagesnearthe i.e., Figurelb. tical partoftheuncertainty;at\b\=20°,<7isre- to aradiusofabout2?5(GrothandPeebles1977). borne outbythecorrelationplotsinpresentpaper, tendency) wouldprobablybeareductionof0.7.Thisestimateis duced from0.10to0.03.Areasonableestimateofthe counts (HeilesandJenkins1976)orthe10'squares in thephotographicrepresentationof1deg Smoothing over13degdoesreducethepurelystatis- scatter ofcorrelationplotswasreducedbyaveraging (Seldner etal.1977).Heiles(1976)foundthatthe counts smoothedover4deg,isevenmorestriking galaxies. Thisunevenness,apparentintheSWmapsof component inthetotalc7=0.15isintrinsic mottling inthesurfacedensityofdistribution u vg pg gal ps P t gal r Previous analysesoftheSWgalaxycounts(SW; The theoreticalvaluey=0.47derivedbySW V. GALAXYCOUNTSANDTHEEXTINCTION AT HIGHGALACTICLATITUDES 45 1978ApJ. . .225. . .40B 2 2 the averagevalueofiV. counts withinagivenlatituderange,obtainingthe We nowresolvethisdiscrepancybyareanalysisofthe the determinationofmeanvaluelog.V,since, galaxy counts,usinganewtechniqueforobtaining for |6|>60°,latitudebinssubtendarelativelysmall these mottlingvariationscanbecomeimportantin 46 clusters (e.g.,thoseintheLocalSupercluster)whose counts themselves(see§IV).Nearthegalacticpoles, in theintrinsic,large-scalemottlingofgalaxy both byextinctioninourGalaxyandvariations ever, thesemeanvaluesoflogNaredetermined mean valueoflogiVasafunctionesc|è|.How- log Vduetothepresenceoflarge,relativelynearby angular sizeonthesky.Inparticular,polarregions are susceptibletovariationsinthemeanvalueof value oflogiVasafunctionbissomewhatanalo- sky. angular distributionisnotaveragedoutoverthe the latterproblem(Burstein1978Z>),weplothisto- 0.09 deg;fortheotherintervals,1pixel=0.18. graphic plate.Borrowingatechniquedevelopedfor gous totheproblemofhowbestdetermine than thenumberofindependentdatapointsineach gram ofthenumber“pictureelements”(pixels) average skybackgroundinafieldofstarsonphoto- gal histogram. Fortheintervalsinescb=0.02,1pixel the SWsurvey;thusnumberofpixelsislarger which aresmallerthanthe1degelementalareasof elements arethoseusedbyHeilesandJenkins(1976), with logVbetweenNand+AN.Thesepicture gal gal gal gal gal N and+AN,versuslogiVgai- (a)Northgalacticpolarregion;(b)southregion. Thecenterofeachescinterval is given,andthevaluesoflogN i(C) andlog7Vi(HW)aredenotedbyverticallines. gal g&ga The problemofhowbesttodeterminean“average” Past galaxycountanalyseshaveaveragedall Fig. 2.—HistogramsfortheSW galaxycountsnearthegalacticpoles,plottedasnumber of pixelswithlogN,ibetween ea © American Astronomical Society • Provided by theNASA Astrophysics Data System BURSTEIN ANDHEILES them, thenallofthehistogramswouldbesimilarin there issubstantialvariationofextinctionwithinthe interval. Iflarge-scaleclustering,inexcessofthe half-width ofapproximately0.15in\ogN(§IV) mottling andhadlittlevariationinextinctionwithin histogram havingananomalouslyhighvalueof histogram. these effectswillproduceabroadorill-defined toward lowvaluesoflog.V.Anycombination latitude interval,thenthehistogramwillbedistorted and withthepositionofpeakdistribution appearance. Theywouldappearsymmetric,witha long tails. logA insteadofahistogramhavingabnormally covered byahistogram,itwillproducesymmetric distort thehistograminthatdirection.Conversely,if number ofpixelswithhighvalueslogNwill average, ispresentwithinalatitudebin,thelarger determined bytheaverageextinctioninthatlatitude regions, inintervalsof0.02cscè,fromesc\b\= galactic pole(NGP)andthesouth(SGP) can varyinhalf-widthfromAlog=0.12to have anextrabumpatlargevaluesoflogN(e.g., flat maxima,othershavesharpwhileone esc b=1.00-1.02;eseb1.08-1.10);(c)histograms are primarilyGaussianinshape;(b)somehistograms Most oftheNGPandsomeSGPhistograms several propertiesofthesedataareapparent:(a) Alog A=0.20;(d)somehistogramshavebroad, g&l 1.00 toesc\b\—1.16.Thehistogramsarenoisy,but gal gal Sfil gal gaiï gal If alllatitudeintervalswereequallyaffectedby Note that,ifaclusteroccupiesthewholearea Figures 2aand2bplotthehistogramsfornorth Vol. 225 No. 1, 1978 Hi, GALAXY COUNTS, AND REDDENING 47 TABLE 2 Values of log Ng&l, from Histogram Method, as a Function of esc b No. of esc Interval Pixels log NgaX (C) log A^al (HW) + 1.00 to + 1.02. 4498 1.65 ± 0.05 1.48 ± 0.05 + 1.02 to + 1.04. 4356 1.70 ± 0.06 1.52 ± 0.06 + 1.04 to + 1.06. 4260 1.72 ± 0.05 1.54 ± 0.05 +1.06 to + 1.08. 4048 1.70 ± 0.05 1.53 ± 0.05 + 1.08 to + 1.10. 3996 1.67 ± 0.05 1.50 ± 0.05 + 1.10 to + 1.12. 3869 1.67 ± 0.05 1.50 ± 0.05 + 1.12 to + 1.14. 3706 1.69 ± 0.05 1.50 ± 0.05 + 1.14 to + 1.16. 3403 1.69 ± 0.04 1.54 ± 0.04 + 1.13 to + 1.20. 13200 1.68 ± 0.05 + 1.21 to + 1.31. 13219 1.62 ± 0.05 + 1.32 to + 1.47. 13200 1.58 ± 0.05 + 1.48 to + 1.69. 12568 1.56 ± 0.05 + 1.70 to + 2.03. 11067 1.48 ± 0.06 + 2.04 to + 2.56. 10386 1.36 ± 0.08 + 2.57 to + 3.56. 9691 1.22 ± 0.08 + 3.57 to + 5.75. 8488 0.74 ±0.16 -1.00 to -1.02. 1305 1.78 ± 0.06 1.60 ± 0.06 -1.02 to -1.04. 1836 1.75 ± 0.06 1.55 ± 0.06 -1.04 to -1.06. 1919 1.71 ± 0.05 1.57 ± 0.05 -1.06 to -1.08. 1889 1.69 ± 0.06 1.50 ± 0.06 -1.08 to -1.10. 1911 1.69 ± 0.05 1.47 ± 0.05 —1.10 to -1.12. 1877 1.70 ± 0.04 1.52 ± 0.04 -1.12 to -1.14. 1828 1.70 ± 0.05 1.54 ± 0.05 — 1.14 to -1.16. 1680 1.68 ± 0.04 1.49 ± 0.04 -1.13 to -1.20. 6865 1.68 ± 0.05 -1.21 to -1.31. 7046 1.60 ± 0.05 -1.32 to -1.47. 7477 1.62 ± 0.08 -1.48 to -1.69. 7402 1.55 ± 0.08 Fig. 3.—The average value of log Ne&i, as determined from -1.70 to -2.03. 7569 1.47 ± 0.08 the histogram method, versus esc |6|, from Table 2. (a) NGP -2.04 to -2.56. 7574 1.32 ± 0.12 region: Filled circles are log Vgai(C), and open circles are -2.57 to -3.56. 7791 1.18 ± 0.12 log Vgai(HW); a slope corresponding to a esc law coefficient -3.57 to -5.57. 7570 0.62 ±0.16 of 0.25 mag is given, (b) SGP region: Symbols are the same as in Fig. 3a. The galaxy count data, as evidenced by Figs. 3a and 3b, are too noisy to allow one to discriminate between esc law coefficients of 0.00 and 0.25. (c) Log Vgai(C) versus appears to have two separate maxima (esc è = esc \b\ for the SW counts: Filled circles have 6 > 10°; open 1.04-1.06). All of these effects can be understood in circles have 6 < —10°. terms of galaxy clustering and of variation in the extinction within latitude bins. of the histogram method of determining logiVgal, We wish to minimize the effects of excess, large- Table 2 lists, and Figure 3c plots, log iVgal(C) versus scale clustering, in order to derive relatively unbiased esc \b\ for the rest of the SW data, in esc intervals as values of log iVgal with which to investigate the varia- noted in Table 2. Comparison of this figure with the tion of extinction with latitude. Gaussians could be analogous figure in Heiles (1976) shows little difference fitted to these histograms, but it is not clear that these between the two figures for esc |6| < 1.5. histograms should necessarily be intrinsically Gaussian For the NGP, log Agal exhibits little systematic in shape. Instead, two other methods were used: (1) variation with esc \b\; indeed, a least-squares fit to Choose the point midway between the half-power the data gives a positive (i.e., logiVgal decreasing points of the central maximum of the histogram toward the pole) coefficient of esc |¿>| of 0.03 ± 0.16. [= log Agal(C)] ; (2) choose the value of log iVgal at However, the SGP measurements indicate that log Afgal the half-power point toward smaller values of increases substantially toward the south galactic pole. log Agal [= log iVgal(HW)]. [In practice, the value of Inspection of the SW maps shows that much of the log iVgal(C) and that determined by a Gaussian fit area very near the SGP is influenced by four large are essentially the same.] Both estimates of log iVgal clusters, which cause the value of log NsbX to increase are listed in Table 2 for this latitude range, along with for esc b > —1.03. Three additional points argue that the total number of pixels in each latitude interval. the increase in log ATgal near the SGP is due to statis- These estimates are plotted versus esc |Z>| in Figures tical fluctuations in galaxy clustering: (1) At esc \b\ = 2>a and 3è. 1.00-1.02, the value of log A^gal at the SGP is 0.13 A further advantage of the histogram method is higher than at the NGP, so that either the SGP has that it provides an independent, realistic estimate of 0.03 mag less reddening than the NGP or logAgal the error in log Ngal(average); we estimate the error can vary widely (e.g., by 0.13, in agreement with the to vary from 0.04 to 0.06 in log JVgal for csc\b\ = estimates of § IV) ; (2) the slope of the esc law at the 1.00-1.16. These error estimates are given in Table 2 SGP predicts E(B — V) = 0.15 esc \b\, a rather large and plotted in Figure 3. As a check on the reliability amount of reddening at the SGP and contradictory

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1978ApJ. . .225. . .40B 48 galaxy countdataaretoonoisytodeterminetheslope log Ngoiwithesc6,inthisrestrictedlatituderange to clusteringperturbations. thereby leavingtheSGPhistogramsmoresusceptible to point1;(3)thenumberofpixelsinSGP near thepoles,arenotsignificant.EvenforSGP, averages areitoJthenumberinNGPand that alinearesclawisvaliduptothepoles.The 0.15 inE(B—F).Thesedatashowexplicitlythatthe the errorsinlogNaretoolargetoenableus there iseitherreddeningorextinctionatthepoles, distinguish betweenesclawcoefficientsof0.00and spread overaconsiderablysmallerrangeinlongitude, cluster data,asanalyzedbyHolmberg(1974).With of aesclawnearthegalacticpoles. galaxy countsalonecannotbeusedtoarguethat § IV)isa=0.06.FromthemapgivenbyHolmberg in logiVdust,perfield,duetoPoissonstatistics(cf. b >60°fortheindividualfields(analogousto (1974), onecanplotthehistogramoflogATfor This histogramhasanapproximatehalf-widthof <7 =0.15inlogAT.AswiththeSWcounts, allow onetodiscriminatebetweennochangein €(Av4) inTable2ofHolmberg1974]istoolargeto counts. Forescô=1.00tob1.10,theaverage of ZwickyareasaffectedbymottlingtheSW o »or,whichshowsthatthegalaxyclustercounts similar plotmadebyHeiles1976fortheSWcounts). galactic poles. for theNGPasdeterminedfromZwickygalaxycluster because thesedataconflictedwithhisreddeningvalue possible zero-pointerrorinthephotometricdata, constraint onthedistributionofreddeningat analysis ofgalaxycountscanplaceonlyaratherweak in thedistributionandamplitudeofreddeningat log Adustasafunctionofesc|ô|andchangecorre- dispersion inthegalaxyclustercounts[thevalueof tion ofsuchazero-pointerrorisunwarranted. counts. Inlightoftheabovediscussion,assump- galactic poleshastocomefromthephotometric tions quotedtherein)andtheMcClureCrawford studies ofstars,globularclusters,orgalaxies.The sponding toaesclawslopeofA=0.25b. 1927 clustersin48fields(forb>63°),thevariation g&1 Furthermore, boththeHilditch,Hill,andBarnes to befreeofzero-pointreddeningerrors;andboth calibrated withasufficientnumberofnearbystandards (1977) AandFstarreddeningsontheStrömgren those fromtheanalysisof galaxycounts,arecon- photometric systemscandetectdifferencesin (1971) KgiantreddeningsontheDDOsystemare system (aswellastheotherAandFstarinvestiga- reddening attheNGP.All availabledata,including metallicity andluminosity. clust distribution attheNGPis perhapsbestgivenby Hilditch etal;theremaybe somewhatmoreredden- sistent withthisconclusion. Thepatchyreddening rclust TP pg We concludethatthepossiblesystematictrendsof The samestatementistruefortheZwickygalaxy Thus wehaveshownthattheweightofevidence Holmberg (1974)introducedadiscussionof We thereforeconcludethatthereislittleorno © American Astronomical Society • Provided by theNASA Astrophysics Data System BURSTEIN ANDHEILES implied bytheAhmapsofHeiles1975). ing, againirregularlydistributed,attheSGP(as § IV),therelationbetweengalaxycountsandhydrogen for 30intervalsofgalacticlongitude,each12°wide column densitycanbeusefulinilluminatingsome relationship. it isusefulinprobingthevariabilityofthis aspects ofthegas-to-dustrelationship.Inparticular, and extinctionhassomeresidualuncertainty(see to-dust ratiowithlongitudebyfitting,intheleast- (eqs. [l]-[3]werederivedfromdataonthewhole venience. Wehavealsofittedequationswiththe in addition,forpurposesofcomputationalcon- sistency withtheresultsofHeiles(1976),weincluded sky, notjustfromthedatainTable1).Forcon- squares sense,equationsoftheform have obtainedsolutionsincludingthelargerlatitude log Ai>0;andweexcludedpointswith\b\64° the ratio(logA-A)INalsovariesamong the slopeBhasverylargevariations,evenchanging term 0.203esc|6|,againfollowingHeiles(1976),and left-hand sideofequation(1)containingtheadditive only pointshaving\b\>20°,A200,and ratio isvariable.WitharepresentativevalueofA, conclusion fromthesefiguresisthatthegas-to-dust point Ahasmodestvariationwithlongitude.However, larger thanusual.Thesefiguresshowthatthezero in Aandlog,isrestrictedsothattheerrorsare the galaxycounts;thusrangeinesc\b\,andalso latitudes, owingtothesoutherndeclinationlimitsof not changeourconclusions. range 10°<\b\64°.Thesemodificationsmake points inFigure4bisverysmall.However,thetrue conclusion. Thestatisticalerrorassociatedwiththe in Figures4aand4b.Inexaminingthesefigures,one minor quantitativedifferencesintheresultsbutdo from thepresentdata. errors arelikelytobesystematicinsteadofrandom sign inthemostextremecircumstances.Thenatural 360° atpositivelatitudesiscoveredonlythehigher should rememberthatthelongitudeinterval250°- and, althoughprobablysmall,cannotbeestimated independent ofA;forexample,iflogA= have for allofthelongituderegions (FejesandWesselius Figure 4bcouldoccuriflogAvariedwithlatitude Since, atleasttoacrudeapproximation, wetypically 12° xbinsbylargeamounts,whichsupportsthis C +Desc|6|£A,asfoundbyHeiles(1976). ga galK H hgal Hgal gal h We havesearchedforpossiblevariationinthegas- Even thoughtherelationbetweengalaxycounts A andBareplottedversustheintervalsoflongitude One otherpossiblewaytoobtaintheresultsin a) TheVariableGas-to-DustRelation, VI. THEGAS-TO-DUSTRELATION as DerivedfromAand galH logA =,4+2?AH(1) gal A =F+Gesc|è| (2) H Vol. 225 No. 1, 1978 Hi, GALAXY COUNTS, AND REDDENING 49

Fig. 4.—(a) A in eq. (1) versus longitude. Least-squares fits were made for data in 12° wide bins of longitude, as explained in the text. Squares joined by the solid line have 20° < b < 64°; crosses joined by the dashed line have — 64° < b < 20°. (¿) B in eq. (1) versus longitude. The meanings of the symbols are the same as for Fig. 4a. Abscissa, longitude x 10; ordinate, B x 10“3. (c) G in eq. (2) versus longitude. The meanings of the symbols are the same as for Fig. 4a. Abscissa, longitude x 10; ordinate, G x 10. (d) I in eq. (3) versus longitude. The meanings of the symbols are the same as for Fig. 4a.

1973), with G a function of longitude, we have gas-to-dust ratio, embodied in the coefficient B, is log7Vgal = (C — DFIG) + (E + DIG)Nr, i.e., with clearly present as well. the coefficient of NK in equation (1) a function of A different way to show the variability in the gas- longitude even with no variation in the gas-to-dust to-dust ratio is to examine the longitude dependence ratio. In Figure 4c we plot the variation of G with of the factor I in the equation longitude; if this is the source of the variation in B, we should always have B large with G small. There logeai = H + Icsc \b\ (3) are some trends in this direction, which probably indicates that a separate esc |6| dependence of and, in particular, the correlation between G and /. logeai does exist; however, the variability in the The variation of I with longitude is presented in

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1978ApJ. . .225. . .40B 2 2 2 50 have —64°|). Ketil5H Vol. 225 (5) No. 1, 1978 Hi, GALAXY COUNTS, AND REDDENING 51 TABLE 3 Least-Squares Fits a) Least-squares fit to eq. (4):* 3 4 E(B — V) = -0.0372 + 0.357 x 10- AH - 0.346 x 10- RYH ±0.0058 ±0.020 ±0.062 Weighted mean error = 0.032 mag Mean error of globular clusters = 0.026 Mean error of RR Lyrae stars = 0.035 b) Least-squares fit to eq. (6): 3 6 2 3 E(B - V)= -0.0171 + 0.399 x 10- YH + 0.140 x 10- ATH - 0.126 x 10- Yh log Ygal ±0.0092 ± 0.090 ±0.097 ±0.034 Weighted mean error = 0.0326 Mean error of globular clusters = 0.0322 Mean error of RR Lyrae stars = 0.0328 * NGC 6287, 6333, 6356, and 6402, with |Z>| < 15°, have been excluded from the fit.

NH(log Ngal) term for esc |è| large. Since this esc |è| difficult to estimate the intrinsic accuracy of our fit. term exists only because of the original formulation The mean error of an individual prediction using in Heiles (1976), a more correct formulation, to equation (4) or equation (6) would appear to be less account for variation in the gas-to-dust ratio, would than 0.03 mag in E{B — V). be to have equation (5) without the esc term, viz., Galaxy clustering, which produces random errors in 2 the value of R, still affects the values of E{B — V) E(B - F) = ^ + y2NH + y3NH derived from equations (4) and (6). However, the galaxy counts are used only to make a (usually) + ^H(log^gal). (6) relatively small change in the slope of the gas-to-dust The first formulation (eq. [4]) was presented because relation. As discussed briefly in Paper I, clustering should not often produce errors in B larger than of the availability of maps for both NH and R. A comparison of the two methods for the data in Table 1 about 1 ; for NH = 500, corresponding to E(B — V) = shows that both give the same result for values of 0.14 mag, this corresponds to an error of only 0.02 \b\ > 15° and/or E(B - V) < 0.3. Below \b\ = 15°, in E(B — V). A comparable error is expected for equation (4) is probably less accurate than what would equation (6). Of course, the absolute size of the error be obtained by using equation (6). The results of the is smaller for points with smaller NH. fits of equations (4) and (6) are shown in Figures 6a Setting either x3 in equation (4) or and y3 in and 66, and the values of the coefficients and other equation (6) equal to zero is equivalent to assuming data concerning the quality of these fits are presented a constant gas-to-dust ratio. The difference in the zero-point coefficients xx and arises because, for in Table 3. 2 Some care was taken in determining the best fits for |6| > 60°, 'the y3Nn term is negligible compared to both equations. First, for equation (4) we excluded the y^nOog Agal) term in equation (6), and the four globular clusters which had |6| < 15°, for the AH(log Ngal) term is approximately constant and reason given above. To account for any possible dif- equal to —0.02. This, taken together with yl5 is ference in the random errors of the two main classes roughly equal to the value of x± in equation (4). In order to use equation (6) to determine E(B — V), of objects (globular clusters and RR Lyrae stars), 2 the value of log Ngal, smoothed to 13 deg , is needed. each class was weighted differently in each fit, by 2 A map of log Agal, smoothed to 4 deg , is given by weights inversely proportional to the squares of the 2 mean errors from the fit of the objects in each class SW ; further smoothing to 13 deg can be accomplished (see Table 3). Several iterations of each fit were per- by the use of this map. formed in order to be sure that the weighting and the By assuming a constant gas-to-dust ratio, one residuals were indeed correct. obtains The average of the mean errors of the globular E(B - F) = z, + z2Nh. (7) clusters to the fits to equations (4) and (6) is 0.028 mag in E(B — V) ; for the RR Lyrae stars this is 0.034 mag. A least-squares fit to equation (7) for all of the data The globular cluster mean error is comparable to the presented in Figure \a yields coefficients Zi = 3 expected measurement errors for the cluster redden- -0.055 ± 0.006 and z2 = (0.443 ± 0.018) x 10" , ings. Examination of Figure 6 shows that the scatter with a mean error of 0.040 mag, considerably larger increases with reddening, which is a priori expected than the mean errors for the fits to equations (4) and for the measurement errors in globular cluster redden- (6). The mean errors and derived values of Zi and z2 ings (Burstein and McDonald 1975). Apparently, the are not changed by the removal of the southern data measurement errors contribute much to the mean from the fit. The mean error, by including only those errors from our fits. Under these circumstances, it is points used in the fit to equations (4) and (6) and by

© American Astronomical Society • Provided by the NASA Astrophysics Data System 1978ApJ. . .225. . .40B 52 found in§Via. covered bytheSWcounts.For theseobjects,applica- using thesameweightingscheme,is0.037mag— by R.Thebetterfitforequations (4)and(6)repre- again muchlargerthanforequations(4)and(6),when sents confirmationofthe variable gas-to-dustratio small valuesofNsothattheyarenotaffectedmuch one considersthefactthatmostofpointshave RR Lyraestarsincludedineachfit,respectively(seetext).Squares representglobularclusters;starsstars. H Fig. 6.—E(B—V)fromTable1versusE(BV),predicted from (a)eq.(4)and(b)(6),fortheglobularclusters Objects havingS<—23° lie outsideofthearea © American Astronomical Society • Provided by theNASA Astrophysics Data System en UJ . 30r -.10 0.10.20.30.40.50 -.05 -.05 0.05.10.15.20.25.30 » m-mxw* * RRLyraestars □ Globularclusters i- a» * m-**»•*-*- b a□»» BURSTEIN ANDHEILES E CNHYD,R) E CNHYD,GAL1 Fig. 6a Fig. 6b the objectsinTable1isrecommended. tion ofequation(7)withthevaluesderivedfromall resentative ofdatataken withtypicalparabolic The valueofXxgivenin Table 3isprobablyrep- ment usedformakingthe 21cmlineobservations. the valueofinequation (4) andzinequation(7) and Cleary(1978).Notethat,asdiscussedin§Vila, depends onthedetailedcharacteristics oftheequip- x H idatafor8<—30°canbeobtainedfromHeiles . 20.25.3 2 0 3 0 1 0 1 0 0 2 0 4 0 3 0 1 0 1 0 0 Vol. 225 1978ApJ. . .225. . .40B 202 telescopes andprobablyappliestoHeiles Cleary’s southernsurvey. No. 1,1978 increase withtheHicolumndensity.However,some, by aninstrumentaleffect,theresponseofradio and possiblyall,ofthiszerooffsetcanbeexplained as discussedin§Vlè)impliesthatanonzeroamount equation (4)(andthesimilarvaluefoundineq.[6], telescope tostrayradiation. of Himustexistbeforetheextinctionbeginsto telescope ispointed.Radiotelescopesareparticularly comparable toawavelength,whichmakesdiffraction detector fromdirectionsotherthanthatwherethe stray lightwhichisscatteredordiffractedontothe directions aswell,andparticularlyseriousisthe structural membersofthetelescopehavedimensions subject tothisproblem,fortworeasons.First,the reflector antennaoftheBellTelephoneLaboratories have suchproblems;agoodexampleisthehorn We notethattelescopescanbebuiltwhichdonot effects particularlysevere.Second,itisimpossibleto radiation wasespeciallydeleterious(seereviewby been usedforsome21cmlineworkwhichstray at CrawfordHill,Holmdel,NewJersey,whichhas reflected fromthesurfaceoftelescope(Ruze build afeedwhichrespondsonlytotheradiation reflectors inradioastronomytypicallyhave10%-20% Heiles andWrixon1976),wasusedforthefirst detection ofthe3Kcosmicbackgroundradiation “spillover” regionjustoutsidetherimofreflector. was firstrealizedbytheDutchobservers(Raimond (Penzias andWilson1965).Feedsusedwithparabolic elli etal(1978)andbyKalberla(Mebold1977). (Rusch 1976).Theimportanceofthisstrayradiation of theirresponsecomingfromthisstrayradiation than thecontributionsfromstrayradiationestimated 1976). Thefeedrespondstoradiationfromother the materialpresentedbyGiovanellietal(1978). sponding tothevalueofxinequation(4)is—Xi/av= vestigated becauseadifferentfeedsystemhasbeen by Kalberla(Mebold1977)andthoseweinferfrom Unfortunately, therelevantcharacteristicsoffeed substituted. surveys arenotwellknownandcannotnowbein- system whichwasusedfortheHatCreek21cmline 1966) andhasrecentlybeenreemphasizedbyGiovan- stray radiationthanotherparaboloidalradiotele- 100 (or2.3x10cm“);thisis2-4timeslarger zero offsettothiscauseuntil furtherevidencewere scopes, wecannotruleoutthispossibility.Acon- radiation relativetosimilar telescopes islargeenough, available. Therequiredexcess sensitivitytostray servative approachwould perhaps assignallofthe Hat Creeksystemtohavebeenmoresensitive however, tocastdoubtonsuch anexplanation.Ifthe x VII. RAMIFICATIONSFORTHEINTERSTELLARMEDIUM The significantlynonzerovalueoffoundin Telescopes atallwavelengthsareresponsiveto For example,theerrorinvalueofiVcorre- Although wehavenoapriorireasontoexpectthe H © American Astronomical Society • Provided by theNASA Astrophysics Data System a) TheZeroOffset H I,GALAXYCOUNTS,ANDREDDENING has littleresponsetostrayradiationareneeded New 21cmlinemeasurementswithatelescopethat latitude gaswithoutanyappreciableassociateddust. effect werereal,itwouldimplytheexistenceofhigh- variation probablyarisesfromaseparatedependence settle thequestion. in thegas-to-dustratio.However,someofthis in thegas-to-dustratioissmallerthanthatexhibited they haveadeficiencyofHi.Suchregionsincludethe R <0havedE(B—V)ldNlargerthanusual;i.e., coordinates (Fig.9inHeiles1976),regionswith the gas-to-dustratio.FrommapofRingalactic the residualRisareasonablygoodmeasurementof in thesefigures/ of logiVgonesc\b\(see§Via).Thusthevariation negative valuesofRisthepresenceH,which dusty regionsinOphiuchus,Perseus,andOrion—the in thisareaisnotparticularlyhigh,rangingfrom ple, anareaboundedby/#20°to40°,bx—10° not detectedinthe21cmline. Gould Beltregions.Themostlikelycauseofthese Although therearenostarsforwhichHcolumn E(B —V),derivedfromequation(4),equals0.17mag. ring onlyforb>15°).Inthecenterofthisarea N =200to700(withthehighervaluesoccur- are regionshavingnonzerovaluesofRinwhichno is littleornoreddeninginareaswhereV=100. 25% ofthehydrogenisinmolecularform.TheHa relations ofSavageetal(1977)implythatlessthan densities havebeenmeasuredinthisregion,thecor- H oriiisknown,expected,toexist.Forexam- intensity (Reynolds,Roesler,andScherb1974;Sivan variable gas-to-dustratio;butthesenegativevalues negative canbethoughtofasbeingaresultthe in theformofHn. are, ofcourse,dictatedbyourconclusionthatthere latitude. Thelargerratioatlowlongitudesforboth tion (1),iscorrelatedwithlongitudeirrespectiveof dust ratio,asmeasuredbytheparameterBinequa- should besetequalto0.00. positive andnegativelatitudes,forexample,seemsto Since E{B—V)<0.00isunphysical,allsuchcases imply thatthevariabilityofthisratioisnotsimplya H al further, preferablybycorrelatingthe21cmmeasure- 2 ments withE(B—V)datadeterminedforspecific Gould Beltphenomenon.Thisshouldbestudied 1974) istooweaktoaccountforthe“missing”gas total gasincludesHi,n, andH,isvariable.The 2 hu — 30°has6Sun (e.g.,Henryetal.1976). Harris, W.E.1975,Ap.J.Suppl., 29,397. Epstein, I.,anddeA.E.1973,A.J.,78,83. 1973) objects,andfromtheminimaldensityofinter- Groth, E.J.,andPeebles,P.J. E. 1977,Ap.J.,217,385. 54 Giovanelli, R.,Haynes,M.P.,York, D.G.,andShull,J.M. Pejes, I.,andWesselius,P.R.1973, Astr.Ap.,24,1. pg = 4.0. gal The Hicolumndensityalonecannotaccurately The “histogram”methodofanalyzinggalaxy When comparedwithgalaxycountsandHi Athlone Press). Cruz. 142, 387. Galaxy countsshouldbeareliableindicatorof 1978, Ap.J.,219,60. © American Astronomical Society • Provided by theNASA Astrophysics Data System VIII. SUMMARY BURSTEIN ANDHEILES REFERENCES 2 2 and byuptoafactorof2fromtheaverage.This together. Theybothareusedtoderivethegas-to-dust from galaxycountsaloneortheHidataalone. The zerooffsethascausedextinctionspreviously ratio, whichapparentlyvariesslowlywithposition It canbepredictedaccuratelybyuseofthesedata Harris, W.E.,andRacine,R.1974,J.R.A.S.Canada,68, the betterpredictorofreddening,sinceitdoesnot than 0.3mag(e.g.,when>800),equation(6)is use equation(4)todetermineE(B—V).For\b\= recommended thatonedetermineR(=gas-to-dust- derived fromHidatatobetoolargeinregionsof — .1976,Ap.J.,204,379. tion andforassistanceincompilingtheRRLyrae mapped onlyinSW4degsmoothedaverages.To contain aesc|6|term.However,logNiscurrently ratio correction)fromthemapofHeiles(1976, E(B —K)<0.3mag.Thus,intheseregimes,itis (6) giveequivalentresultsfor\b\>15°and/or ing fromeitherequation(4)or(6).Equationsand ratio isthenusedwithHidatatoderivetheredden- Harris, W.E.,Racine,R.,anddeRoux,J.1976,Ap.Suppl., final formofthispaper,especially§IV,butalsoacted E(B —V)forallareasoftheskycoveredbySW is predictedtolessthan0.00,setE(B—V)=0.00. small Hicolumndensity. Harris, W.E.,andvandenBergh,S.1974,A.J.,79,31. as thecatalystformanyofourideas. Whitford, whonotonlymateriallycontributedtothe reddening data.Finally,wesincerelythankDr.A.E. providing hisobservationalresultsbeforepublica- galaxy countsavailable,useofequation(7)isneces- counts. Forthesouthernpartofsky,withno Fig. 9),obtainNfromthemapofHeiles(1975),and Heiles, C.,andCleary,M.N.1978,inpreparation. Heiles, C.1975,Astr.Ap.Suppl.,20,37. discussions. WealsothankDr.L.H.McDonaldfor ratio. E(B —V)owingtovariationsinthegas-to-dust centage errorscanbemadeinthepredictionof Both methodsappeartobeaccurate0.03magin SW map.Foreitherequation(4)or(6),ifE(B—V) obtain 13degaverages,onemustfurthersmooththe Heiles, C.,andJenkins,E.B.1976,Astr.Ap.,46,333. U. Mebold,C.D.Shane,andS.M.Faberforhelpful sary, withtheknowledgethatrelativelylargeper- Jenkins, E.B.,andSavage,B.D. 1974,Ap.J.,187,243. 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