198lApJS...45..457A The AstrophysicalJournalSupplementSeries,45:457-474,1981March © 1981.TheAmericanAstronomicalSociety.Allrightsreserved.PrintedinU.S.A. white dwarfsforevidenceofmagneticfields.Forcon- Astronomy, Inc.,undercontract withtheNationalScienceFoun- operated bytheAssociationof UniversitiesforResearchin venience, dataonthe13singlemagneticwhitedwarfs dation. reported todatearefistedinTable1;fiveofthesewere first identifiedthroughoursurveyprogram.Reviewsof the magneticwhitedwarfsaregivenbyAngel(1977, During thepasttenyears,wehaveobservedover100 'Visiting Astronomer,KittPeakNational Observatory,whichis © American Astronomical Society •Provided by theNASA Astrophysics DataSystem 48 6 -1 86 have beenmeasuredwithgreateraccuracybyZeemanmeasurementsinabsorptionlines.These observed formagneticfieldsbycontinuumcircularpolarizationmeasurements.Twelvewhitedwarfs have errorsofonlyafewkilogauss.Fieldstrengthsinthestarsshowingnocontinuumpolarization with weakerfieldshavebeenfoundbyanysearchmethod,althoughthemostaccuratemeasurements observations arereportedinfullthispaper. limit toit)offindingsurfacefieldstrengthBovertherange3X10-3X10gauss.Wefindthat magnetic circulardichroismandradiativetransfer.Ourdata,combinedwiththoseofTrimble BP(B), theprobabilityperoctave,isroughlyconstantat~0.005forfieldsinrange3X10-X Greenstein andofEliasGreenstein,areusedtodeterminetheprobabilityP(B)(oranupper are foundtobetypicallylessthan500kilogauss,basedonanapproximatetreatmentofatmospheric All themagneticwhitedwarfsthathaveidentifiableatmosphericconstituents,exceptLP790-29, currently knowngrouptobesignificantlycoolerthanthecompletesampleofclassifiedwhitedwarfs. stars havebeensampledwithhighaccuracytosetveryseverelimitsonBP(B). well-established rotationperiods. contain somehydrogen.Thishydrogenhasprobablynotbeenaccretedfromtheinterstellarmedium, since thefieldsarealmostcertainlystrongenoughtopreventaccretion. significant changeinpositionangle,withanupperlimitofA0<1°yr.Thissuggeststhateither spin axesarecloselyaligned.Improvedephemeridesgivenfortwomagneticwhitedwarfswith these whitedwarfsarerotatingwithperiodsofhundredsyearsormorethattheirmagneticand Subject headings:stars:magnetic—whitedwarfs and magneticwhitedwarfs,suggestingtheremaybean evolutionfromonetotheother. 10 gauss,anddoesnotexceedthisvaluedowntogauss.Belowfieldstrength,enough 6 All knownmagneticwhitedwarfshavesurfacefieldsgreaterthan5X10gauss.No In asurveyprogramcarriedoutoverthepastdecade,morethan100whitedwarfshavebeen While thefirstfewmagneticwhitedwarfsdiscoveredwereusuallycool,wedonotfind The spacedensity-to-lifetimeratioisfoundtobeabout thesameformagneticpeculiarAstars Continued monitoringofallthreemagneticwhitedwarfswithlinearpolarizationhasrevealedno Département dePhysique,UniversitéLavalandObservatoireAstronomiqueduMontMégantic I. INTRODUCTION THE MAGNETICFIELDSOFWHITEDWARFS Department ofAstronomy,UniversityWesternOntario Received 1980June20;acceptedSeptember16 Steward Observatory,UniversityofArizona 1 Ermanno F.Borra, J. D.Landstreet 1 J. R.P.Angel, ABSTRACT AND 457 Table 1.Thenullresultsareofinterestbecause unusual compositionsofmany whitedwarfatmospheres convection, gravitationalsetting, andtherateofinter- fields inwhitedwarfatmospheres whichmightmodify of whitedwarfsnofieldcanbemeasuredeventhough field strengthsfound.Bycontrast,inthelargemajority acteristic ofthemagneticwhitedwarfsisverylarge constraints theysetonthepresenceofmoderatestrength some limitsare1000timessmallerthantypicalfieldsin (Strittmatter andWickramasinghe 1971).Furthermore, stellar accretion.Theseprocesses mayaccountforthe 1978) andLandstreet(1979).Themoststrikingchar- 198lApJS...45..457A - 6 5 VI). TypicalCPandtypicalLParevaluesofcontinuumcircularlinearpolarization(%)observedinbluehght;“noobs” indicates photometry orspectrophotometry,andchemicalcompositionbasedonatomicmolecularspeciesidentifiedinthespectrum.Ris radius much lesscommoninwhitedwarfsthanneutron our resultsshowthatdetectablemagneticfieldsare in unitsof/?/100>derivedfromTandadistancebasedonmeasuredorphotometricparallax.Misthemasssolar from the mass-radius relationshipforcarboncores.Thevariableoisthetotalspacemotion,obtainedbycombiningobservedtransverse motion context oftheoriginandevolutionstellarmagnetism. references giveninthefinalcolumn. and anassumedradialvelocityof27kms*.Z?(BH)istheminimumfieldtopreventaccretionassumingBondi-Hoyletype (see§ stars, afactwhichhastobeconsideredinthewider Angel 1980;(10)Greenetal.(11)Liebert1978;(12) Kemp 19776;(13)Angeletal.19746;(14)Angel,Hintzen,andLandstreet linear andquadraticZeeman effectsinDAstarshave Landstreet 1975;(6)WickramasingheandMartin1979;(7)Angeletal.1974a;(8)Angel,Illing,1972;(9) and that noobservationsareavailable.Bandeffectivelongitudinalmeansurfacefieldsdeterminedfrommodelingasdescribed inthe been madebyAngelandLandstreet (1970a),Preston can beappliedtostarswithstrongatomiclines,is netic fieldsinwhitedwarfs.Themoresensitive,which (1970), TrimbleandGreenstein (1972),andElias using thequadraticeffect. gauss usingthelinearZeeman effect,and~10gauss Greenstein (1974).Thesegive typicalupperlimitsof10 to attemptdetecttheZeemaneffect.Searchesfor 1975; (15)LandstreetandAngel(16) 1974. oe tot 0 es 458 L795-7 Name G35-26 BPM25114 G99-37 PG1015+01 G99-47 Table 1liststhecommonname(s),WDnumberincatalogueofMcCookandSion(1977),effectivetemperatureTbasedonavailable LP790-29 GD90 G240-72 G195-19 GD229 Grw+70°8247 G227-35 References.—(1) Liebertetal:1977;(2)Greenstein1978;(3)AngelandLandstreet(1974);(4)(5)Liebert,Angel, and Two techniquesaregenerallyusedtosearchformag- e * Feige7 © American Astronomical Society •Provided by theNASA Astrophysics DataSystem WD Number 0041-10 0548-00 0553+05 0816+37 0912+53 2010+31 1748+70 1829+54 1900+70 C Composition H, Hev H, He? H H 22000 no ident no ident,v no lines 6200 H 5600 no ident 2 16000 no ident no ident 6000 12000 20000 7000 8600 10000 : 7000 22000 12000 T (K) e ANGEL, BORRA,ANDLANDSTREET Known SingleMagneticWhiteDwarfs 0.8 0.8 0.7 0.6 0.6 1.2 1.8 0.4 0.6 1.0 0.9 1.1 1.2 0.9 0.7 0.9 1.2 0.9 0.9 0.9 1.5 1.1 M R B (BH)(megagauss)TypicalLP o Notes toTable1 55 264 54 0.0003 0.07 480 1.3 49 31 11 87 30 59 44 1.4 33 20 43 16 18 10 49 (km/sec) TABLE 1 zation inwhitedwarfatmospheresisgivenbelow(§II). measurement ofcontinuumcircularpolarization.This effect ofamagneticfieldwasfirstpointedoutbyKemp of itsvalueindetectingverystrongfields,hasbeenthe Essentially thecircularpolarizationdependslinearlyon (1970). Adiscussionoftheexpectedstrengthpolari- where Bisthemeanfieldprojected onthelineofsight, effective field)as the meanlongitudinalfieldoverdiskofstar(the e The mostextensivelyusedsearchtechnique,because Typical CP <0.2 < 0.2 < .2? < .05 <0.3 no obs no obs no obs no obs no obs 0.4 0.4 v <.2 8 0.9 no obs -Iv -1.5 1.5 v 2.5 -1.5 4 -4 -3 3 1.5 v? (%) (megagauss) l4v 6.5 0 5.5 3.5 3.6 18 15 8-10(v?) 50? 25 >100? B B e s P =132min. P =99min. P =1.33days 6, 7 5, 6 Comments 8, 9 3, 4 References Broad depressioninspectrum P =2.84days? 1 9, 16 Unidentified stronglines 6, 12 10 Unidentified weaklines 9, 13 11 4, 15 14 Vol. 45 198lApJS...45..457A 6 8 parameters, andydependsonthecomposition proximately. Itmayalsobedeterminedempiricallyfor polarization (>;10gauss)wouldprobablyhavecaused we generallyavoidedthecommonhydrogenandhelium found thaty~5X10gaussfor\«0.5fim,withina observation. Thevalueofymaybecalculatedap- primarily onstarswithfeaturelessspectra,molecular Wilhams (1973,1974)andBrown,Rich, There arealsodataforeightwhitedwarfsobservedby were observedprimarilytocheckthatthepolarimeter distortion ofthespectragreatenoughtobenoticeable with strongspectrallinesobservedfortheZeemanef- linear polarization,whichispresentinaboutone-third (1974). Coyne(1974)hassurveyed15whitedwarfsfor factor of2orsodependentoncompositionandtemper- stars withfieldsmeasuredfromtheZeemaneffect.Itis temperature oftheatmosphereandwavelength was operatingcorrectly,or because otherobservershad pecuhar orunidentifiedspectra.BrightDADBstars dwarfs, arequiteinsensitivetomagneticfields),and during spectralclassification.Wehaveconcentrated spectra becausefieldsstrongenoughtogivedetectable population ofwhitedwarfs.Thetemperature,composi- and Landstreet1970Z?;Angel1971). accuracy for29whitedwarfs,havebeenpublished(Angel ature. spectra (theSwanbandsofcarbon,foundinsomewhite magnetic whitedwarfs. we discussthespacedensityandpossibleoriginof material fromtheinterstellarmedium.Finally,in§VII III givesnewfieldupperlimitsforseveralwhitedwarfs II givestheobservationsofcontinuouscircularpolariza- observed byusforevidenceofmagneticfields.Section of themagneticwhitedwarfs. Shulov andBelokon(1972),30byRich claimed positivedetection ofcircularpolarization. effect ofwhitedwarfmagneticfieldsonaccretion tively thedistributionofmagneticfieldsover fect. In§IVthismaterialisusedtodeterminequantita- No. 3,1981 Greenstein (1965û,6,1967), Greenstein(1969,1970, Candidates werechosenfrom thelistsofEggenand amined in§V,whileVIweconsiderthepossible tion, androtationofmagneticwhitedwarfsareex- tion andadiscussionofhowBcanbederived.Section V andIarethecirculartotalintensityStokes Strittmatter (1974).(Weare gratefultotheseauthorsfor 1974a, 1975),Wegner(1973, 1974),andHintzen e Two previoussurveysbyus,givingdatato~0.1% In theselectionofwhitedwarftypesforobservation, In thispaper,wepresentthefullhstofwhitedwarfs © American Astronomical Society •Provided by theNASA Astrophysics DataSystem II. FIELDSMEASUREDBYCONTINUOUSCIRCULAR a) Observations POLARIZATION MAGNETIC FIELDSOFWHITEDWARFS m white dwarfsmaybeexpectedtomagnetic. observing programbecauseofthesuggestionby light isanalyzedbyaPockelscelloperatedasreversi- Angel andLandstreet(1970a).Thecircularlypolarized nuclei selectedforradiiestimatedtobe<0.01Rfr° communicating manyoftheirnewclassificationsin pliers wereused,butin1972theyreplacedby ble A/4waveplate,typicallyat~100Hzsquare of McDonaldObservatory,the2.1and1.2mtele- Fontaine, Thomas,andVanHorn(1973)thatthese advance ofpublication).Threeobjectsareoldplanetary modulation, whichisfollowedbyaWollastonprism.In scope oftheLasCampanasObservatory,overperiod scopes ofKittPeakNationalObservatory,the2.3m the listgivenbyAbell(1966).Weincludedthesein with III-Vtubeswithoutfilter,givingsensitivityfrom pliers. Manyofthesurveymeasurementsweremade although theyhavekeptthebasicformdescribedby surement haveevolvedovertheyearsofthiswork, the UniversityofWesternOntario,and1.0mtele- telescope ofStewardObservatory,the1.2m Nova 1200computerperformsthisfunctionandgives is detecteddigitally.ForthedataobtainedatSteward light ofwavelengthAisincident,thenthedegree higher withnarrowerbandwidths.Thisisnotthecase. might seemthatthesensitivitycouldhavebeenmade RCA galliumarsenideC3103Atubes(III-Vtubes). the earlyworkBendixS-20channeltronphotomulti- polarization anderrorfromcountingstatistics.This have increasedtheefficiencyonlyslightlywhileconsid- polarization at3500Áis78%and800083%.The intensities forthetwosettingsofPockelscell.If retardation atAand//_arethemeasured incorporating severalscalars. Ingeneral,eachstarwas Observatory andsomefromMcDonaldObservatory,a (/+—/_)(/++/_) isequaltosinä,where8the modulation ofthelight(theapparentpolarization)as One caneasilyshowthatifpurecircularlypolarized 3100 to8600À.BecausethePockelscellischromatic,it Some datawerealsotakenwithbi-alkaliphotomulti- data systemwasbuiltandprogramedmainlyby an updateddisplayasintegrationproceedsofthe number ofphotonscountedperunittime. erably degradingtheoverallaccuracybyreducing entire continuumforatypicalwhitedwarfis~90%. Pockels cellissetforA/4at5000À,theapparent the cellisswitchedinpolarity,definedby(V/I)^— observed longenoughfor the measuredpolarization observations wereobtained usingahard-wiredsystem Drs. H.S.StockmanandP. G.Martin.Theremaining Decreasing theobservedbandwidthsubstantiallywould average efficiencyweightedbycountingrateoverthe efficiency) tohaveastandard errorof0.1%orless. (taking intoaccountcorrection forskybackgroundand 1970-1977. ThePockelscellpolarimetersusedformea- o + Data wereobtainedusingthe2.1and2.7mtelescopes The modulationproducedifpolarizedlightisincident 459 198lApJS...45..457A 5 69 7 _ - Usted inTable1.Forcompleteness,2includesour white dwarfsofthetypewhichshowCspectralfeatures earHer nullresultsreferredtoabove.Altogether110 dwarfs observedbyusaregiveninTable2,exceptfor (DS stars;seenotestoTable2concerningtheDS observed. Nearlyalltheremainderareratherfaint.Five None isconfirmed.AdiscussionofOx+25°6725has notation) havebeenobserved.ThreeDAstarsarein- DC. SeventypercentofallwhitedwarfsclassifiedDCat stars areUstedinTable2,abouthalfofwhichtype those starsfoundtobedefinitelymagnetic,whichare been givenbyLandstreet,Angel,andIlling(1975). (0205+25) whichwasreportedbyShulovandBelokon are L870-2(0135-05)andNGC2477116(0749-38) cluded becauseofreportedcircularpolarization.These the timewhenthissurveywasfinished(1977)were (1972) tohavevariablecircularpolarizationsof1-2%. for whichRichandWilUams(1973)gaverespectively Table 3. a~0.02%, ~5timessmaUerthanournormalstandard with longintegrationtimestoobtainanaccuracyof netic fields(~10gauss)maybecommon,weobserved polarization propagationeigenmodes)inducedinthe convenience, theseresultsaregivenseparatelyin error. IneachcaseanuUresultwasobserved.For seven ofthebrightestDCstarsandthreebrightDS produced intheemissionfromatomsamagneticfield (10-10 gauss)magneticfields.Thecirculardichroism dichroism (i.e.,opacitieswhicharedifferentfor ing fromanopticallythinemitterisgivenby bound-free transitionsofHandHebyLamb of <5X10gausshasbeendiscussedforfree-free reversing layersofthestarsbypresencelarge the whitedwarfsUstedinTable1arisesasaresultof sometimes linear)polarizationobservedintheUghtof Landstreet andAngel(1975),forfree-freetransi- observing frequency,and0is theanglebetweenfield where v=eB/Anrncisthe Larmorfrequency,visthe In general,thefractionalcircularpolarizationV/Iaris- transitions ofHandHebyKemp(1970,1911a),for 2 direction andthelineofsight. Thecoefficientais4.0 tions ofHbyLiebert,Angel,andLandstreet(1975). Sutherland (1974),forfree-freetransitionsofHeby for free-freeandbound-free transitionsofHandHe, and 2.85forfree-freetransitions ofHe”.Itis~2.0for -0.23±0.06% and+0.4±0.1%,Ox+25°6725 460 L x The polarizationmeasurementsforallthewhite To explorethepossibiUtythatrelativelyweakmag- It isgeneraUybeUevedthatthecircular(and © American Astronomical Society •Provided by theNASA Astrophysics DataSystem b) RelationshipbetweenPolarizationandField I Strength =a —cos#, } v ANGEL, BORRA,ANDLANDSTREET (2) relations. Hisresultmaybeexpressedas found byShipman(1971)fromtheEddington-Barbier coefficients forleftandrightcircularpolarizationare free-free transitionsofH“around5000Á,andvaries comes fromdifferentaveragedepthsinthephotosphere, different, soradiationinleftandrightpolarization from ~2.1at3600Áto1.69000À. analytical expressionforthepolarizationofstellar and thenetradiationiscircularlypolarized.Asimple flux fromastarwithuniformmagneticfieldwas is givenapproximatelybytheEddingtonapproximation, In mostappUcationsofthisexpression,ithasbeen assumed thattheatmospherictemperaturestratification known magneticwhitedwarfs ispossible.Thus,these Wickramasinghe andMartin(1978,1979).Theircalcula- lished onlyforafewdiscrete models(6000K,12000 with whatareprobablyreasonablyreahsticmagnetic (3) and(4)havebeencarriedoutbyMartin model atmospheresthanthoseembodiedinequations gent fluxandpolarizationformagneticwhitedwarf calculations cannotbeused practically asabasisforour calibration neededhere.However,thedetailedcalcula- pole distributions.Thecalculationsincludethesphtting and Wickramasinghe(1978,1979û,Z>,c) 20000 K;logg—8,H-richcomposition) forwhichatmo- predicted intheblue,evenaband2000Àwide,by so that — =«,-^0080- spheres areavailableand for whichcomparisonwith tions ofMartinandWickramasinghehavebeenpub- Wickramasinghe 1979c). produce anevenmorestrikingeffect(Martinand field distributions,namelycenteredanddecentereddi- full setofequationstransferforpolarizedradiation, tions arebasedonaccuratenumericalsolutionsofthe to constructthedesiredpolarization-fieldstrength edges. Inclusionoflinescanchangethepolarization and dichroismofspectrallinesaswellabsorption ~25%; inclusionoftheBalmerabsorptionedgemay vi”) »L2 Ñ This dichroismalsooccursinabsorption.Absorption Recently muchmorereaUsticcalculationsofemer- Such calculationswouldbeasuitablebasisonwhich T dT v \—ex$( —hv/kT)Tdr v hv/kT 1dT T v —2/3 (3) 198lApJS...45..457A =L11 Ox+25°6725 W1516 VMa2 G134-22 =L9 =LFT 122 =G21-27 F24 Ross548 LTT 375 =LTT 17144 G218-8 G217-37 G4-34 HL Tau76 W219=L15 G174-14 G5-28 =G83-10 GH7-21 L182-61 HZ 14 L879-14 G175-34B IB1320 40 EriB LTT 17943 He3=L23 GD72 G102-39 G191-B2B G39-27 G87-29 GD 78 G108-42 G105-30 American Astronomical Society •Provided bythe NASAAstrophysics DataSystem WD Number 0142+23 0205+25 0135-05 0213+42 0133-11 0115+15 0038-22 0046+05 0038+55 0009+50 0232+03 0239+10 0315+15 0245+54 0606+28 0551+12 0435-08 0433+27 0341+18 0706+37 0654+02 0644+37 0618+06 0615-59 0501+52 0438+10 0426+58 0416+27 0413-07 0347+09 0648+36 0423+12 Broad-Band CircularPolarizationSurveyofWhiteDwarfs DA 10 DC DA 7.0 DG 5.5 DA DC 11 DC Sp T^/1000Composition DC DC DC DA dM3 DM DB DA DA DSH DS DS DC DC DA DC DA DA DS DC DC DC DA DC 20 60 10 13 20: 62 22 13 29 17 10: 17 5.5 7.0 5: 6: 5.5 6: 6.1 6.2 7.7 5.5 7.9 5.7 5.7 7.1 5: (K) He He H? H H? H? H H? He He He H H? H He H? H H? H H He H? H H? TABLE 2 (2440000+) 1719.7 2003.75 2037.65 2120.5 2121.5 2305.95 1719.65 1152.83 1954.79 1954.76 1954.87 2719.92 2719.87 1774.64 2718.92 2004.79 1275.67 1919.78 1719.62 1954.81 2719.95 1180.83 1328.72 1320.95 1032.77 1328.61 1328.59 1328.63 1954.91 1275.65 1032.82 1329.80 1717.8 1320.94 973.58 771.95 925.60 972.65 973.65 923.62 972.69 977.68 JD bialk Band III-V -.08±.13 III-V/OR2 -.0231.075 III-V III-V/C500 -.051.07 III-V III-V III-V/C500 -.161.12 III-V/4-96 -.0461.041 III-V +.0421.023 III-V III-V III-V/CÜSCX+ .0551.101 III-V -.1201.041 III-V III-V III-V III-V III-V III-V III-V +.141.09 III-V/OR2 III-V III-V III-V III-V III-V III-V III-V III-V III-V/4-96 III-V/HA30 +.01±.10 S20 S20 -.16±.10 S20 S20 S20 S20 S20 S20 S20 S20 +.199*.079 +.020*.016 +.023±.037 +.017±.021 +.038±.057 +.020±.016 +.0321.024 +.022±.022 -.0211.026 +.050±.038 -.006±.013 -.0031.019 -.0261.022 -,029±.057 + .12—.13 +.04±.05 + .10±.08 -.03-.11 +.161.10 -.07±.06 +.031.09 +.141.15 +.01±.10 -.12-,09 -.03-.11 -.01-.07 -.08-.11 -.06±.10 -.131.11 -.051.09 +.121.10 -.08*.13 -.111.10 V±0 (%) +1710*680 +11201720 6000A), atmosphere fittingtonarrowbandcolors.Temperaturesfromthiscalibrationarenotveryaccuratelydetermined,butsufficefor Greenstein (1976).Forcaseswherethisisnotpossible,acalibrationofJohnsonUBVcolorsvs.effectivetemperaturewas from Grenfell(1974),Liebert(1979),Wegner(1972),andWehrse(1979).Wehaveobtainedsomefurthereffective rely mainlyhereonBues(1973,1974,1979),Shipman(1972,1977,andWehrse(1975),withafewindividualstarstaken were usedtoreduceinfrarednightskyonfaintstars.Coppersulfate crystals(A<5800À)andComing4-96(3800-5600were color class0,and10000Kfor—1.UncertainvaluesofTaremarkedwithcolons. temperatures byapplyingthemodelcalculationsofShipman(1977)toextensivemultichannelspectrophotometry used todefineblue-greenobservingbands. Coming 2-63(A>6000À)and2-64(A>6600À).Infraredabsorbing HoyafiltersHA30(A<7000À)andC500(A<6200A) 2 are calculatedfromcountingstatistics.Thesepolarizationstransformed tofieldstrengthsusingvaluesofytakenfromFig.1 for theassumedTandcompositiongiveneachstar. e 0 p e G188-27 =GL895.2 =PHL459 =BPM97895 G28-27 G18-34 GD 248 0)246 LTT9491 L1512-34B G171-27 Notes onindividualstars.—(1)Thesestarshavebeenanalyzed forlinearZeemaneffect(seeTable4).(2)L870—2.Rich “WD Number”isthenumberofstarinMcCookandSion(1977)wheremuchfurtherusefulobservationalmaterialon Effective temperatureslistedinthe“7^/1000”columnareobtainedfromavarietyofsources.Inmanycases In the“Compos”columnwelistassumedcompositionwhichcorrespondstospectraltypeinmostcases.ForDC’s Circular polarizationvalueslistedinthe“K±a”columnarecorrected fornightskybackgroundandefficiency,errors © American Astronomical Society •Provided by theNASA Astrophysics DataSystem WD NumberSpT/1000CompositionJD e 2147+28 DC 2309+10 DA 2254+07 DS 2207+14 DAM 2323+15 DC 2317-17 DC 2341+32 DA 2352+40 70: 11 10 13 6: 8.4 6: (K) (2440000+) H H? H He H? TABLE 2—Continued Notes toTable2 2032.67 2305.84 2306.86 2718.67 2305.89 2034.69 1272.68 1152.85 1954.71 1180.81 1274.70 1273.75 1272.69 Band bialk -.0411.051 bialk +.091.08 III-V +.043±.058 III-V -.026±040 III-V/4-96 -.041.05 III-V .001.04 III-V -.064±.051 III-V/C500 +.16±.10 III-V -.025±.054 III-V/2-64 -.0381.055 III-V/C500 +.021.04 S20 +.01±.ll S20 +.141.11 Via (%) +6701420 +5701450 +2001270 +370±330 -3101250 -190±300 +1501300 -190±400 -1701210 -1601230 -1601210 (Kilogauss) B ±a_ e B 01210 198lApJS...45..457A because thecalculatedpolarizationspectra(Martinand we mustconsiderhownearlyequation(3)agreeswith we areforcedtorelyontheanalyticalapproximationof calibration ofpolarizationversusfieldstrength.Instead, Wickramasinghe 1978;andMartin compared tothepredictionsofequations(3)and(4) more exactcalculations. equation (3)forthiscalibration.Sinceisthecase, compressed tocontainusefulinformationaboutthe (4) giveresultswhichdifferfrommorerealisticcompu- continuum polarization. expect. tations byonly~20-30%(MartinandWickramasinghe by WickramasingheandMartin(1979)is~2.5times 1979) areonlypresentedgraphically,onascaletoo Wickramasinghe andMartinislessthanhalfassteep relationship forthemodelatmosphereadoptedby given meanlongitudinal(effective)field.Thisdiffer- 1979c). Thisiscertainlyasmuchaccuracyonewould predicted byequation(4). If thelogarithmictempera- ence isalmostentirelyduetothefactthatT(t) smaller thanthatfromequations(3)and(4)fora (because ofconvectioninoptically thinregions)asthat ture gradientinequation(3) isevaluatedforthemodel atmosphere usedbyWickramasinghe andMartinrather than fromequation(4),then equation(3)predictsthe v 1 proper motiontoderivetangentialmotion,assumingaradialvelocityof41kms“forallstarsasdiscussedintext.ValuesÑand R used arefromShipman(1979). At 7;=20000K,thepubhshedresultscannotbe For 7;=12000K,itappearsthatequations(3)and For 7^=6000K,however,thepolarizationpredicted Name W1516 =LTT 17144 G218-8 G175-34B =LFT 122 L879-14 G107-70 017-21 =L66 L845-70 L145-41 =G126-27 L1363-3 G125-3 © American Astronomical Society •Provided by theNASA Astrophysics DataSystem Noth.—Data inthefirstsixcolumnsaretakendirectlyfromTable2.Spacevelocityt?isestimatedbyusingobservedparallaxand tot WD NumberSp 0426+58 0347+09 0115+15 DC 0038+55 DC 0435-08 0727+48 1142-64 2140-20 1708-14 1917+38 Bright DCandDSWhiteDwarfsMeasuredwithHighAccuracy DC DSH DS DC DC DS DC DC MAGNETIC FIELDSOFWHITEDWARFS T /1000 e 13 11 (K) 7.7 +.017±.021 5.5: +.020Í.016 7.1 -,005±.013 9.5 +.0141.016 4.8 -.007±.022 6.8 +.021.03 8.5: -.0241.022 8.6 -.0251.017 -.026±.022 -,003±.019 V±CT (%) TABLE 3 (kilogauss) -1501120 +1601120 +1001160 proximation tocalculatetheT~\dT/dT)terminequa- B ±0 wavelengths, sothatthecharacteristicsharpdropof peratures (T>15000K)becauset„/t»1atoptical proximation willgreatlyaffectthecalculatedtempera- convection makesthetemperaturegradientsubstantially equation. Thisapproximationisexpectedtoproduce in realisticmodelsbutisabsenttheEddingtonap- also expectedtoleadlargeerrorsforhightem- same polarizationastheaccuratecalculationwithin smaller thanthatpredictedfromaradiativemodel.Itis severe errorsatlowtemperatures(7^<6000K)where tion (3)maybethelargestsourceoferrorinusingthat +60170 temperature atsmallmeanopticaldepthfwhichoccurs -20140 -10190 ~20%. ItthusappearsthatusingtheEddingtonap- +60160 ture gradientfortherelevantr. -601180 variety ofcompositionsandeffectivetemperatures,we because thisexpressioncanreadilybeappliedtoa ment withmoreprecisecalculationswhenthevalueof -90160 -90180 Wehrse (1975,1976),Wickramasinghe (1972),and polarization calibration.Wehavedeterminedvaluesof use equation(3)asthebasisofourfieldstrengthversus Wickramasinghe, Bessel,and Cottrell(1977).Although using publishedmodelatmospheresfromBues(1973), v present purposebecause no T(t)relationshipsare numerous otherwhitedwarf atmospheremodelsare e discussed intheliterature,they couldnotbeusedforthe T~\dT/dr) isdeterminedfromrealisticmodels,and T~\dT/dT) wheret=2/3,foratornear5000Á, v v vj/ e Because thesimpletheoryofequation(3)isinagree- (km/sec) (M) tot 64 54 73 75 0.73 80 0.37 43 59 0.68 0.84 0.64 0.44 0.83 _2 (10R )(kilogauss) 0.93 1.11 0.95 1.15 1.05 1.49 1.40 R B(BH) 14000 o 1500 2100 250 420 130 14 465 466 ANGEL, BORRA, AND LANDSTREET Vol. 45 presented. A fairly complete calibration oiT~\dT/dTv) tion (4). Equations (3) and (4) together predict, for versus Te is possible for H-rich models; the gradient example, that y will vary in He-rich atmospheres from rises rapidly from 0.085 at 5000 K to a value of 0.25 at less than 2X106 gauss per percent for 7^=4000 K to 6 12000 K, and then settles to a value between 0.19 and more than 26 X 10 gauss per percent at Te = 18000 K, a 0.17 which changes little up to 25000 K. For helium variation by a factor of ~ 13. models, the situation is much less satisfactory, with only As a further test of the results shown in Figure 1, we one available gradient (at 7^ =7000 K) below 15000 K. plot values of y determined from model calculations by All available gradients are between 0.13 and 0.19, how- Shipman (1971) and Wickramasinghe and Martin (1979). ever, and we have simply interpolated cautiously. Below Shipman’s results have been corrected from the value of 7000 K we expect that convection also produces a sharp a, =8 assumed by him to the values used here, to make drop in the gradient, which we somewhat arbitrarily his results comparable to ours. It will be seen that the take to be the same as for H-rich atmospheres. agreement with our simple calculation is quite good. The resulting run of y in units of 106 gauss per We may remark that for comparison the value of y is percent polarization at 5000 A for H- and He-rich 1.07 X 106 gauss per percent for optically thin radiation models is shown in Figure 1 as a function of Te. The (eq. [2]) due to brehmsstrahlung, for which a, =4.0 large values of y below 7000 K reflect the reduced independent of temperature. It will be seen that the temperature gradients produced by convection. The dip result of radiative transfer is to decrease considerably in the y curve for H-rich atmospheres near 10000 K the polarization produced by the star compared to the comes from the change in as the main opacity source optically thin value, especially at high temperature. _ changes from free-free transitions of H (a1^2.0) to The curves of Figure 1 have been used to assign field bound-free transitions of H(a! =4.0). Similarly, the wig- strengths to the polarization measurements given in gle in the curve for He-rich atmospheres around 17000 Table 2. Effective temperatures were estimated based K is produced by change in «j as the opacity switches on whatever photometry is available for each star, from He- to neutral He. The exact variation of y at with preference given to the narrow band colors of these switchover points is rather uncertain, and we have Graham (1972) and Greenstein (1976). The temperature simply linked curve segments smoothly. calibrations of Strittmatter and Wickramasinghe (1971), It is notable that over the full range of 5000-25000 Shipman (1972, 1977, 1979), and Wehrse (1975) were K, y varies by only a factor of ~ 2 in either direction used for the hydrogen-rich stars, while the temperature from a value of y=5 megagauss per percent polariza- scales of Bues (1973, 1974) and Shipman (1972, 1977, tion, so that the uncertainty introduced into the polari- 1979) were used for the helium-rich stars. zation-field strength calibration by inaccuracy in theory Once the effective temperature and composition of probably will not have a large impact on the conclusions the atmosphere were chosen, y was read directly from below. Figure 1. We assumed that DA and DMA stars (except This situation is in marked contrast to the predictions LDS 678B= 1917 —07) are hydrogen-rich and that all resulting from using values of T~(dT/drv) from equa- other white dwarf types hotter than 8000 K are helium- rich (see notes to Table 2 concerning the notation DMA). The coolest DC white dwarfs may be either H- or He-rich (Shipman 1977). We have assumed that such stars, with temperatures below —8000 K, have H-rich atmospheres, as this results in larger values of y and less stringent field upper limits than assuming that such stars have He atmospheres. No field strengths were calculated for stars above 25000 K because no temperature gradients are available for hotter models. Field strengths were also not calcu- lated for stars found not to be degenerate.

III. FIELDS MEASURED BY THE LINEAR ZEEMAN EFFECT Fig. 1.—Effective magnetic field coefficient y (eq. [1]) in units of megagauss per percent continuum circular polarization at 5000 New magnetic observations have been made of seven À, as a function of effective temperature for H- and He-rich white dwarfs by the photoelectric measurement of cir- atmospheres. The smooth curves give the result of using eq. (3) cular polarization in the wings of strong absorption together with values of T~\dT/dTv) from model atmospheres as lines. Most of the data were made at Hy using 30 A discussed in the text. Individual values of y from more elaborate interference filters with the technique described by Angel calculations are plotted, with circles for H-rich models and a square for the single He-rich model (S=Shipman 1971, using and Landstreet (1970 a). The remainder were obtained corrected values of ¿q; WM=Wickramasinghe and Martin 1979). with a single channel scanner at Ha, À5876 of He in

© American Astronomical Society • Provided by the NASA Astrophysics Data System 198lApJS...45..457A + -1 National Observatoryandatthe2.12.7mtele- Angel, McGraw,andStockman(1973).Theobserva- polarimeter instrumentwaspreviouslyusedtosearch scopes ofMcDonaldObservatory. for magneticfieldsinX-raybinariesandisdescribedby tions weremadeatthe2.1mtelescopeofKittPeak GD 358,andtheCaKlineinvMa2.Thescanner- Stockman (1973)weobtain No. 3,1981 lines measuredexcepttheKlinewhere1.17. z-values (Babcock1958)areessentiallyunityforallthe where Bisthemeanlongitudinalfieldoverstar,\ measurement. 7(\)istheobservedlineprofileasmea- normalized intensitygradient(Á)atthepointof the observedwavelengthinÁ,and(dl/d\)/lis sured withthescannerorbytilt-scanningline the interferencefilterusedtoisolatelinewings.The e Following thediscussionbyAngel,McGraw,and © American Astronomical Society •Provided by theNASA Astrophysics DataSystem polarization measurements.(2)For He3andL1512—34Bthemeangradientwascomputedfrom measuredinterferencefilter profile anddigiconscanofHyin thestar.(3)Themeangradientwasestimatedfromlineprofiledata givenbyGreenstein(1960) one nightin1969Augustand/or September. and computedprofilesforHe3 L1512—34B.(4)Themeasurementreportedisameanofobservations obtainedonmorethan W1346 W485A F22 VMa2 Name L1512-34B L711-10 He 3 F108 40 EriB L770-3 Grw+73°8031 GD358 Notes.—(1) ForvMa2,40Eri B atHa,andW1346Hathemeangradientwasmeasuredwith thescanneratsettingof 3 K//=4.67X10-'^^//(X), (5) WD Number 0227+05 0644+37 0413-07 0046+05 2341+32 2093-20 2313-02 2126+73 2032+24 1327-08 1615-15 1645+32 DA DM DA Sp DA DA DA DA DA DA DA White DwarfsObservedforLinearZeemanEffect MAGNETIC FIELDSOFWHITEDWARFS (2440000+) 2002. 1953.64 1956. 1955.67 446.92 629.99 897.95 764.69 953.94 893.86 892.74 897.83 480.80 480.72 772.85 766.93 764.83 772.74 JD He 5876 He 5876 Line Ca K hy hy hy HY HY Hy hy hy hy Ha Hy hy Hy hy hy hy hy hy HY hy TABLE 4 ] because thewhitedwarfshavenolinearpolarization, values obtainedonbothblueandredlinewingswith lated circularpolarizationisobtainedbycombining Angel andLandstreet(1970a)areincluded.Thetabu- have beenrepeatedlymeasured,W1346and40EriB, kilogauss, althoughforthetwobrightestDAstarswhich ence, thepreviouslypublisheddataforwhitedwarfsby resulting inslightlydifferentfieldvalues. Table 4newindividualgradientshavebeencomputed, gradient (0.0088À~)wasusedtoobtainfieldvalues.In ents areobservedwiththescanner,orcomputedfrom computed fromcountingstatistics.Thetabulatedgradi- systematic errorsareverysmall.Thequoted opposite sign.Equaltimeisspentinbothwingssothat the tablenotes.Inpreviouslypublisheddataamean the knowninterferencefilterprofile,andindicatedby any instrumentalsystematiceffectswillcancel.Infact, surement of40EriBmadeatHagives—1.0zb1.7 the errorsare~10kilogauss.Themostaccuratemea- (A) AX 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 30 15 15 15 O The newresultsarelistedinTable4.Forconveni- The accuracyofthefieldmeasurementsistypically50 9 7 +.0391.027 +.0411.097 +.0041.-62 -.0241.085 -.1401.090 -.0421.078 -.0761.081 +.151.04 +.571.50 +.241.19 +.171.19 +.57±.86 +.341.24 -.061.08 +.421.84 +.601.70 -.131.26 -.171.16 -.801.37 -.361.21 -.111.18 -.5911.04 -.201.26 (%) (.01) (.01) .0072 .0050 .0050 .0078 .0078 .0094 .0050 .0072 .0050 .0072 .022 .0068 .020 .0072 .0078 .0078 .0143 .0072 .0068 .0088 .0066 (kilogauss) +1401160 -180184 -1.011.7 + 614 +221 6 +28132 -11112 +95184 +34151 +77155 -53131 -13122 -26134 -22145 -22114 -39136 B ±C +1110 +6141 +6115 -4113 +817 -9113 e 2.4 3,4 3,4 3,4 3.4 2 1 2 3 3 3 3 3 3 3 3 3 3 3 1 467 198lApJS...45..457A 6 12 2 6 kilogauss. Allthemeasurementsobtainedbythismethod emerges fromthesedataisthatwhenfieldsarepresent are null. but becausethesemolecularfeatureshavemuchweaker only exampleofanormallookingspectruminmag- they arestrongenoughtoseriouslydistortatomicspec- Zeeman effectthannormalatomiclines.Thereareno netic whitedwarfisthatG99—37,whichshowsbandsof tral featuresorevenobliteratethemcompletely.The C andCH.Thisisnotaresultofthefieldbeingweak, linear ZeemanmeasurementsofTable4,where10DA displaced a-componentsorlinesslightlyby examples ofmoremoderatefieldswhichproduceslightly white dwarfshaveB<50kilogauss,whiletwo 4. Takingthedatatogetherwecansaythatfraction (1974), withsimilaraccuracy.Twoofthese(L870—2= B <10kilogauss.LinearZeemanmeasurementshave were knowntohavehydrogenspectra,andfiveshow quantitative basis.First,weexaminetheknownwhite in Table2,andafurther10DAstarswithnullresults EG 11,andGrw+82°3818=147)arenotinTable dwarfs withhydrogenatmospheres.Atthetimethis the quadraticZeemaneffect.Letusputthisresultona also beenmadeof5DAstarsbyEliasandGreenstein white dwarfs,itisquitelikelythathydrogen survey wascompletedin1977,about350whitedwarfs large andtheerrorinmeasurementofBisorder (2 a)is<10%,andthatprobablyhalfhaveBlessthan of DAwhitedwarfswithBinexcess100kilogauss Balmer lineZeemansubcomponentsindicatingsurface by TrimbleandGreenstein(1972)basedontheabsence examined andnotalreadyincludedinTable4is dwarfs arenotveryuseful,sincethenumberofstars field EmitsfromcontinuumpolarizationforDAwhite are givenbyRichandWilliams(1973,1974).However, lines areundetectable.Thus,theobservedfractionof polarized DCbecausetheZeeman-broadenedBalmer fields intherange4-25megagauss(Table1).Since dwarfs withstrongerfieldsexistbutareclassifiedas these fivearethemostweaklypolarizedofmagnetic Zeeman effectatYLß10 gaussis±11Â,andthe of thequadraticZeemaneffect inwhitedwarfclassifica- the sensitivityofcontinuummeasurementsisgiven 500 kilogauss.Amuchmorecompletesurveyatabout real fractioncouldbeperhapstwicethisifsomeofthe square fieldwas0.21X10 gauss.Asurfacefieldof tion spectra.Inasample of 141DAstarsthemean magnetic DCstarshavehydrogenatmospheres. strongly magnetichydrogenwhitedwarfsis~1%;the 468 2 e 10 kilogauss. e e e e 10 gausswouldthengive a 4.5effect.(Thelinear The featureofmagneticfieldsinwhitedwarfsthat The mostaccuratenullmeasurementscomefromthe There are10DAstarswithnullcircularpolarization © American Astronomical Society •Provided by theNASA Astrophysics DataSystem IV. DISTRIBUTIONOFFIELDSTRENGTHS ANGEL, BORRA,ANDLANDSTREET 67 5 8 8 6 bility thatoneormoreofthesestarshasB>\.5 limit is~50kilogauss.Thus,wecansetanupper where welistforthedifferentsamplesandmeasuring range 1.5X10-5X10gauss.Forthesampleofseven deduce thattheprobabilityislessthan1.5%aDC megagauss islessthan1%,sofromthesampleof70we 70 presumablytruelow-hydrogenDCstars.Theproba- stars inTable2are<500kilogauss,forasampleof 50 megagauss,thetypicalnullmeasurementsforDC limit toit)thatawhitedwarfofthesampledtypewill dwarf hasameanlongitudinalfieldstrengthinthe have strongpolarization(G195—19,G227—35,G240— less (DC)spectra.Of54surveyed,threewerefoundto have asurfacefieldinthatrange.Wheremeasurements number inthesample,ofmagneticexamples field strengthBintherange10-5X10gauss. of ~15%totheprobabilitythataDCwhitedwarfhas DC’s thatweremoreaccuratelymeasuredtheupper weaker polarization(G99—47)waslaterfoundtoshow mostly onthosewhitedwarfsclassifiedtohavefeature- We havealsoarbitrarilyset anupperlimitof3X10 members oftheDCgroup,whosehydrogen-freeatmo- Thus, thesestarsshouldnotproperlybeclassedas order of10gauss(Angel1977).OneotherDCwith Zeeman effectisimmediatelyapparentinaclassifica- known DAstarsthatnonehavesurfacefieldsinthe A). Thus,wecansaythatforasampleofhalfall gave Bratherthansurfacefield,wetakethelimiton found, ifany,andhencetheprobability(oranupper techniques therangeoffieldstrengthscovered, we cansaythatofthetotalnumberspectroscopically field DCstarmighthavebeenintheabsenceofafield. Ha. Wecannotbesurewhatthespectraltypeofahigh 72), andthesearebehevedtohavesurfacefieldsofthe magnetism withthislowerlimittobethefullnumberof relative quadraticshiftbetweenHßandX3889[H8]is4 magnetic whitedwarfswithunidentifiedspectralfea- dwarfs ingeneral.Thisalsoappliestothestrongly spheres givefeaturelessspectra,butasmagneticwhite classified DAwhitedwarfs. range 1-3X10gauss.Above~gaussthe In evaluatingBP(B)wehave madetheapproximation the quantityBP(B),whereP(B) dBistheprobabilityof surface fieldtobethreetimesthatonB.Wealsogive larger. megagauss). BecauseofincompletesamplingDC a samplememberhavingfield intherange(B,B+dB). classified whitedwarfs(~500),about1%havebeen tion spectrum,sowecantakethesamplesurveyedfor that P(B)isconstantwithin thefieldrangeinquestion. stars, therealfractionisalmostcertainlysomewhat found tohavestrongfields(intherangeabove50 tures, PG1015+01,Grw+70°8247,andGD229.Thus, e e e e Considering theincidenceoffieldstrengthslessthan All oftheaboveresultsaresummarizedinTable5, Our broad-bandpolarimetricsurveyhasconcentrated Vol. 45 198lApJS...45..457A 7 7 57 78 45 67 56 56 6 -3 6 8 No. 3,1981 magnetic starsthaterrorscouldeasilybeafactoroftwo. We havenotincludederrorlimitsonP(B)orBP(B),butit Surface Field Range (gauss) 2x10-5x10 1x10-2x10 4x10-5x10 5x10-3x10 x10-3x10 probability P(B)offindingawhite dwarftohavemagneticfield 3x10-10 3x10-4x10 limits ofBP(B)aredisplayedinFigure2.Itwillbeseen 3x10-3x10 10-3x10 5, asafunctionofsurfacemagnetic fieldstrengthB. gauss forthehighfieldmagneticwhitedwarfs,inorder limit becauseofincompletesampling.Wenotein§VII probability offindingafieldinthisrangeisthus roughly constantandequalto~5X10.Thetotal that overthetwodecadesoffieldstrength3X10-3X to giveadefinitevalueforP(B).Thevaluesandupper local spacedensityofmagneticandnonmagneticwhite below thatadifferentlineofargument,basedonthe star hasasurfacefieldstrengthbetweenBand2B)is l3x\o*P(B) dB=0.027.Thisshouldbetakenasalower 10 gaussthatBP(B)(equaltotheprobability Fig. 2.—Observedvaluesand upper limitstothefractional © American Astronomical Society •Provided by theNASA Astrophysics DataSystem polarization polarization spectra andpolariz- search forZeeman analysis ofspectra classification spectra search forZeeman classification spectra classification spectra effect effect ation Detection Method MAGNETIC FIELDSOFWHITEDWARFS Probability ofFindingMagneticWhiteDwarfs DC starsinTable37 DC starsinTable255 Table 4;Eliasand12 Trimble andGreen-141 all classified500 classified DAstars350 40 EriBandW13462 classified DAstars350 classified DAstars350 white dwarfs Greenstein stein DAstars Sample NOTES TOTABLE5. TABLE 5 should beunderstoodthatbecausetheyarederivedfromveryfew Number in 4 6 Sample proximately byBP(B)<2X\0/B. dwarfs, suggeststhattheincidenceofmagnetisminthis range issomewhatlarger,perhaps5%.Below3X10 gauss wehaveonlyupperlimitsforBP(B),givenap- lute magnitudeandsurfacetemperatureareinfactwell interest toaskifthemagneticgroupreallyissignifi- is muchlargerthanthatoftheconvectivemotion.Now generally coolerthantypicalnonmagneticwhitedwarfs. unlikely becausetheenergydensityofmagneticfield ously coveredfieldstothesurface,althoughthisseems Greenstein (19746)hassuggestedthatdeepconvection distribution ofabsolutemagnituderatherthantempera- cantly coolerthantheaverage.Weshallexamine setting inasthewhitedwarfcoolsmightbringprevi- have ameanabsolutemagnitude of12.3withastandard some oftherecentlydiscoveredonesarehot,itis that thesampleofmagneticwhitedwarfsislargerand diameters. Twohundredninety fivewhitedwarfsfrom correlated becauseofthesmallrangeinwhitedwarf analysis ofSionandLiebert(1977;hereafterSL).Abso- ture becauseitisconvenienttocomparethestatistical deviation ofindividualstars of1.5.Ifgroups10stars the sampleofSLhavephotoelectric colors,andthese are chosenatrandomfrom thisdistributionandthe The firstfewmagneticwhitedwarfsdiscoveredwere V. PROPERTIESOFTHEMAGNETICWHITEDWARFS a) TemperatureandAtmosphericComposition to beMagnetic Number Found 0 1 ih l^ Field inRange Probability of <0.7% 0/1% <2% <15% <50% 0.29% <8% 0.43% 0.43% <0.05 <0.007 <.01 0/. 007 B P(B) <.10 <.3 0.003 0.005 0.006 469 198lApJS...45..457A 8 lute magnitudesforthemainsamplewhich,although 0.47. HereweassumeaGaussiandistributionofabso- particular groupofthe10magneticwhitedwarfsdis- mean absolutemagnitudeofeachgroupcomputed,then not quitecorrect,iscloseenoughforourpurposes.The produce ratherasmallerpolarizationinhotstarthan ness canbereasonablyaccountedforbyverysmall magnitude of13.1,adeviation0.8fromthefull covered uptotheendof1977hasameanabsolute the standarddeviationofgroupmeansis1.5//K)= in acoolone,aneffectwhichmayleadpreferentiallyto note fromFigure1thatagivenfieldisexpectedto number statisticsandpossiblyselectioneffectsinthe hydrogen andhelium,G99—37withCCH). hydrogen (L795—7=Feige7andprobablyG35—26with sample ofwhitedwarfssearchedformagnetism.We significant. Weconcludethattheoriginalapparentcool- sample mean.Thisdeviationisonly1.7a,notvery Thus, sixofthesevenmagneticwhitedwarfswith netic DAtypeswereidentifiedintheearlystudies,but magnetic whitedwarfsdiscoveredisnotreal.Nomag- composition suggestedbythespectraoffirstfew mixed compositionsofL795—7,G35—26,andG99—37 definitely identifiedspectralfeaturesshowhydrogen, the discoveryoffieldsincoolstars. of magneticfieldsonaccretionfromtheinterstellar magnetic fieldmayberesponsible.(Thepossibleeffects 90, BPM25114,G99—47)andthreeothersshowsome three arenowknownthathavehydrogenspectra(GD medium willbediscussedinthenextsection). are quiterareinwhitedwarfs,soitdoesseemthatthe atmospheres, andinfactallmightbehehum-rich.The although someofthesestarscertainlyhavehehum-rich with nosignificantopacityinabsorptionUnes(e.g., have hydrogen-freeandmetal-deficientatmospheres neous group.ThenonmagneticDCstarsarethoughtto magnetic andnonmagneticDCtypesarenotahomoge- be detectedwhentheyaresplitintomanystrongly to reiteratethepointmadein§IVabovethat be severlybroadenedinaninhomogeneousfield. cative ofstrong(>10gauss)fieldsandcouldhaveany DC starsallshowstrongandpeculiarpolarizationindi- 2 known torotate.Theperiodsare1.6hrforPG1015+01, field-dependent Zeemansubcomponentsandwouldthus atmospheric composition.Absorptionlineswouldnot Strittmatter andWickramasinghe1971).Themagnetic BPM 25114(Wegner1977). Theothermapieticwhite 470 ANGEL,BORRA,ANDLANDSTREETVol45 dwarfs haveshownremarkably stablepolarization. 3 hrforL795-7,1?3G195-19, andperhaps2?8for occasionally checkedfor long-term changesinthe It alsoappearsthatthehydrogen-freeatmospheric In concludingthisdiscussionofcomposition,wewish Only fourofthemagneticwhitedwarfsinTable1are In thecourseofourpolarimetric surveywehave © American Astronomical Society •Provided by theNASA Astrophysics DataSystem b) Rotation d d polarization ofthemagneticwhitedwarfs.Thesemea- position anglehasnotchangedsignificantly(Aö<3°) which, iftheyareobliquerotatorswithasubstantial brake whichcouldreasonablybringthestartoanearly have rotationperiodsof>100yr.Short<5 over 21/2yrforGD229,and51/2Grw stars withstronglinearpolarizationshowsthatthe surements aregiveninTable6.Inspectionofthethree stars, shouldberapidrotators.However,steadyrather have topostulatethattherotatingandnonrotating than explosivemasslossatthetimeofformationis,in tional collapsesuggeststhatwhitedwarfs,likeneutron white dwarfsingeneral.Thepossibilityexiststhatthe minutes forGD229andG240—72arenotexcludedby complete standstill(e.g.,Pacini1970).Wewouldthen the presenceofaverystrongmagneticfield,anefficient Grw +70°8247andthelackofsuchrapidrotationin our databutdonotseemlikelybycomparisonwith angle betweenthemagneticandrotationaxis,appearto ditions ofmassloss.Alternatively,theobservedrotators magnetic whitedwarfsareformedunderdifferentcon- not havedetectedrotationatanyperiod. rotation andmagnetic(orpolarization)axesmaybe during subsequentevolution,althoughwehavenoevi- could perhapshavebeenspunupbymasstransfer aligned withinafewdegrees,inwhichcasewewould proved ephemerides.TheephemerisforG195—19ob- polarization ofG195—19andL795—7,whichyieldim- dence forclosebinarycompanionstothesestars. phase nicelyonthisperiod;thereisnoevidenceforany variations withamplitude0.24%aboutameanof 4-96 filter.Thedatawerebestfittedbysinusoidal period change.Ourpresentephemerisisthus period tol?33107±0.00003.Allavailabledata circular polarizationinablue-greenbanddefinedby tained byAngel,Illing,andLandstreet(1972)isfor +70° 8247andG240—72.Wethushavethreestars wave. ThenewperiodisP=131.6036+0.0034minutes was computedbyaleast-squaresfitofthedatatosine observations (Liebertetal.1977),andanewephemeris obtained inthesameunfilteredbandusedforprevious of positivezerocrossingasseenatthesunbecomes onto whitedwarfsislargeenough thatthereisaprob- — 0.23%.Thenewdataallowauniquerefinementofthe =0.0913914±0.0000024, sotheephemerisfordate JD(neg. extremumin4-96)^2440979.071+1.33107E. Conservation ofangularmomentumduringgravita- In Table6wealsogivenewobservationsofcircular New dataonthecircularpolarizationofL795—7were The predictedrateofaccretion ofinterstellarmaterial HJD(positive zerocrossing) VI. MAGNETISMANDACCRETION =2442749.9916 +0.0913914 E. 198lApJS...45..457A No. 3,1981 hereafter SW),Shipman(1972), Sion(1973),D’Antona lem explainingtheexistenceofwhitedwarfswithspec- tra thatindicateverylowhydrogencontent,especially cussed byStrittmatterand Wickramasinghe(1971; Greenstein (1969)forthe DB stars,andfurtherdis- for 7;>10000K.Thisproblemwaspointedoutby and MazzitelH(1975),Koester (1976).SWsuggested that DBstarsarein whicheither{a)accreted © American Astronomical Society •Provided by theNASA Astrophysics DataSystem by Martin,reportedLandstreetandAngel(1974);othermeasurements byKempetal.(1974)at dependence. (2)DataforcomparisonfromAngeletal.(19746); (3)Dataforcomparisonfrom about thesametimegivelinearpolarization. Angel andLandstreet(19706);averageofthreeobservations;(4) Dataforcomparisonsobtained for nightskybutnotoverallefficiencysincewehave no informationonwavelength L795-7 GD90 Grw+70°8247 G240-72 G227-35 GD229 G195-19 Notes.—(1) Tobeconsistentwithpreviousdata,measurementsof L795—7havebeencorrected New Broad-BandPolarizationMeasurementsofKnownMagneticWhiteDwarfs 3051.8653 2923.85 2005.004 2004.826 2393.0 2923.87 2922.92 2039 2923.91 4012.802 3997.824 2037.59 2036.58 4236.922 4237.945 4012.671 2784.9 4237.876 4236.783 3051.9213 3116.924 -2440000 774. JD .8677 .8922 .8899 .8852 .8817 .8793 .8770 .8747 .8723 .9096 .8992 .8945 .8875 .8700 .9166 .9143 .9120 .9073 .9050 .9015 .8968 .9190 MAGNETIC FIELDSOFWHITEDWARFS III-V +B370CUSO4 III-V +4-96 III-V +4-96 III-V +4-96 III-V +4-96 III-V +4-96 III-V to7200A III-V +HA30L42 III-V +056 3000-5000Â III-V +4-96 Filter Band III-V TABLE 6 hydrogen isbeingdilutedbyconvectivemixingwith envelope He,or(6)theaccretionisbeingpreventedby not abletodiluteaccreted hydrogentothepointof Koester (1976)haveshown that convectionisprobably a magneticfield.D’AntonaandMazzitelli(1975) spectroscopic invisibilityfor starsofT>10000Kunless tude lessthanthatinferred fromtheformulaofBondi the accretionoccursatarate severalordersofmagni- e Circular Linear or -.3061.060 -.0701.062 -.2741.070 -.1101.062 -.5271.075 -.3271.052 -.1391.066 -.281.09 -.341.09 -.281.09 -.231.09 -.301.09 -.071.09 -.241.09 -.131.09 -. 191.09 -.011.05 f.011.03 Polarization 0.881.24 @5218 . 10±09 2.701.20 @79.512.4° .21± .09 .02±.09 2.901.10 @78.411° 3.241.15 @19.211.4° 2.91.12 @20.312° 1.291.16 @47.513.5 1.181.17 fi(BH) =3X10Ar/J)(M/Rfgauss,(6) 0 B>S(E)9X10A^/u)M/R)gauss. (7) 0 ANGEL, BORRA,ANDLANDSTREET 3 4 35 -3 68 -3 43 is appropriate,equation(7)givesvaluesofBthe magnitude. Itisthusnotatallclearwhetherwecanrule netic whitedwarfsdousuallyseemadequatetoprevent order of100gauss,farbelowtheobservedlimits. Hoyle accretionradius.IftheEddingtonradius out magneticinhibitionofaccretionassumingaBondi- in whitedwarfs. each magneticstarisgiveninTable1,andweseethat equation (7)holds.Thecomputedvalueof2?(BH)for very effectiveinleadingtohydrogen-freeatmospheres 2?(BH). Ifinterstellaraccretionisindeedinhibitedin accretion ifequation(6)isvalid,andcertainlyare gen isabsent.Thissuggeststhatmagneticfieldsarenot one ofthemagneticwhitedwarfswithwell-identified from circularpolarizationaregenerallylargerthan the fieldsmeasuredbyZeemaneffectorderived ranked bydistancedandordinal numbernisplotted ric G-Rcolorversusabsolute magnituderelationship spectra seemstohaveanatmospherefromwhichhydro- the timeofformation.Itisthusnoteworthythatonly spheric compositionshouldshoworiginalmaterialfrom the magneticwhitedwarfs,thenobservedatmo- found byGreenstein(1976). IfthestarsofTable1are calculated withreasonableaccuracy fromthephotomet- for five,anddistancesmostoftherestmaybe stars inTable1.Trigonometricparallaxesareavailable netic whitedwarfsisobtainedfromthedistancesof against d,thenearestfive starsfollowapproximately will be~10iffluxisconservedwhenanApstar possess substantial(10-10gauss)magneticfields.Ne- was estimatedtobe>0.027.Thus,weexpectthespace pc, ingoodagreementwithLuyten’s(1975)estimate of evolvedmagneticApstars. of thispossibilityistocomparethespacedensity collapses toawhitedwarfdiameter.Evenallowingfor glecting theeffectsofmassloss,fieldamplification (including helium-weakandhelium-strongstars),which dwarfs originatebytheevolutionofApandBpstars dwarf havingafieldintherange3X10-X10gauss of 0.006pc.In§IVtheprobabilityanywhite magnetic whitedwarfswiththeexpectedspacedensity surprising ifsuchstarsendedwithfieldscomparableto giant andcollapsingstagesofevolution,itwouldnotbe are theonlyclassofmain-sequencestarsknownto 0 density ofmagneticdwarfsis>1.5X10~pc. than M=15.5isestimatedbySLtobeatleast0.005 those foundinthemagneticwhitedwarfs.Adirecttest substantial lossoffluxbecausemassduringthe 0 0 v In contrast,themagneticfieldsinknownmag- A moredirectestimateofthespacedensitymag- We considerthepossibilitythatmagneticwhite The spacedensityofalltypeswhitedwarfsbrighter VII. SPACEDENSITYANDORIGINOFMAGNETIC WHITE DWARFS Vol. 45 198lApJS...45..457A 8 4 -3 4 -43 _43 9 9 3 5-3 2 _5-3 9 We thereforeestimatethespacedensityfromthissam- largely unexploredregionsouthof—20°,thespace ple offivestars,whichweassumetobearoughly n ocbutbeyondGrw+70°8247at12.2pcitisclear hand, somemagneticstarsmay haveevolvedtoneutron indicated bytherangeof values above.Ontheone rate ofthesestarshasbeenconstantduringthepast M is~1.2X10yr(Tayler1970).Iftheproduction probably atleast2.5X10~forwhichtheprobabilityof pc, thentheprobabilityoffindingfivewithin15pc, dwarfs within13pc.Allowingafactorof1.5forthestill complete sampleofnorthern(0>—20°)magneticwhite course, thisresultissomewhat moreuncertainthan evolved fromamagneticmain-sequence phaseduring luminosity hasbeencalculatedforwhitedwarfswith known magneticwhitedwarfsusingthebolometriccor- within 15pcisatleast50%complete,theupperlimitof obtained fromPoissonstatistics,is0.02.Wededucethat density ofknownmagneticwhitedwarfswithin15pc that substantialincompletenessofthesampleispresent. rection derivedbyWeidemann(1967),itisfoundthat finding fiveormoreis>10%.Assumingthatthesample average spacedensitywereactuallyaslow1.5X10 the sunisapproximately5.3it:2.3X10pc.If that timeshouldbeintherange of4-8X10pc~.Of 5X10 yrthetotalspacedensityofstarswhichhave The typicalhydrogenUnespectralclass(Osawa1965)is less thanthistime(Fontaine,Thomas,andVanHorn white dwarfmagneticfieldsarealsonotsignificantly carbon coresofvariousmassesbySweeney(1976)andis present limitofreliabledetection.ProbablyallApstars Ap starsandaBalmerlineZeemananalyzersurvey published photographicmagneticobservationsofsome within ~120pcoftheSun.Thederivedspacedensity found tobe~5X10yr,soitisreasonablesuppose all arebrighterthanM=15.0.Thecoolingtimetothis the spacedensityis1X10“. the averagespacedensityisverylikelysomewhathigher, range 1-2X10“pc. have magneticfieldsof>10gauss.Thepresentspace netic fieldssignificantlyinexcessof400gauss,aboutthe recently conductedbyBorraandLandstreet(1980)it B9, whichprobablycorrespondsfairlywelltotheactual density ofmagneticApstarsisthereforealsointhe falloff ofdensityawayfromthegalacticplane.From for Apstarsisthen~1-2X10pc,allowinga size andbrightnessofApstars.AB9VstarhasM^ the past5X10yr.Thecharacteristicdecaytimesof No. 3,1981 appears thatmorethanhalfoftheApstarshavemag- that theknownmagneticwhitedwarfswereformedin 0 1973). K=6.0 andnorthoí8=—20°(Landstreetetal.1975). +0.5 (Allen1973),sothattheApstarswithF>:6.0lie B v The main-sequencelifetimeofaB9VstarMæ3.6 If bolometricmagnitudesaredeterminedforthe For theApstars,about55areknownbrighterthan © American Astronomical Society •Provided by theNASA Astrophysics DataSystem MAGNETIC FIELDSOFWHITEDWARFS 9 2 2 6 6 white dwarfsmayformfromtheApstarsconflictswith progenitors. which resultfromtherapidrotationofthesestars,while rendered undetectablebythermalcirculationcurrents magnetic fields(Mestel1976;MestelandMoss1977). most uppermain-sequencestarsmaycontainsubstantial have lowspacevelocitiesandthusmayhighmass ble. Somesupportforthisevolutionschemecomesfrom hypothesis thattheoneevolvedintootherisplausi- in the(slowlyrotating)Apstarsfieldsareableto nants ofmagneticmainsequencestars,sothatthe yr ago. past, perhapsbyasmuchafactorof2or3at5X10 white dwarfsisincreasedbyafactorofatleast10,and emerge fromthesurface.Ifweassume(asopposite stars areforcedbelowthestellarsurfaceandthus On thisview,thefieldsofnormaluppermain-sequence a viewthathasbeenevolvinginrecentyears,allor extreme totheviewthatonlyApmain-sequencestars the observationbySLthatmagneticwhitedwarfs about thesameasexpectedspacedensityofrem- the observedspacedensityofmagneticwhitedwarfsis stars insteadofwhitedwarfs,whileontheotherhand, help ofM.Gresham. not thecase,andthatindeedagoodfractionofwhite we shouldexpecttofindthatmanyormostwhite F5 Vhaveburiedmagneticfieldsof~10gauss,then the formationrateofstarsmayhavebeenhigherin by turningovertousnightsontheMcDonald2.1m Warner gavegreathelpintheearlystagesofthiswork nal magneticfieldsnearlyaslarge10gauss,or(2) dwarfs probablyhavemagneticfieldswellbelow10 dwarfs havemagneticfieldsof>10gauss.Thatthisis are magnetic)thatallmain-sequencestarsearlierthan Engineering ResearchCouncil ofCanada. Research Corporation,and by theNationalScienceand grants GP31356XandAST 75-17845A01,bythe us withamasterlistofwhitedwarfscompiledthe Dr. J.Liebertforhelpfuldiscussionsandsupplying cataclysmic variablephotometry.Wearegratefultothe evolving tothewhitedwarfstateforagoodfractionof fraction ofuppermain-sequencestarsdonothaveinter- gauss (cf.Table5)suggestsinturnthateither(1)agood the deathrateofpotentialprogenitorsformagnetic Observatories forallocationsoftelescopetimeandto directors ofHale,McDonald,andKittPeakNational Illing, P.G.Martin,J.T.McGraw,Schmidt, this paper.WeareparticularlygratefultoDrs.R.M.E. telescope thatwerenotuptohisexactingstandardsfor Schmid-Burgk, H.S.Stockman,andR.Wehrse.Prof.B. the cases. that mostofthemagneticfluxislostinprocess It shouldbenotedthatthehypothesismagnetic Thus, withintheuncertaintiesoftwocalculations, This workhasbeensupported bytheNSFunder Many peoplehaveassistedusintheworkreported 473 198lApJS...45..457A 474 ANGEL,BORRA,ANDLANDSTREET .1978,Ann.Rev.Astr.Ap.,16,487. 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