198 7MNRAS.227. . .23W 3 Mon. Not.R.astr.Soc.(1987)227,23-73 Absolute magnitudesofcataclysmicvariables Hanover, NewHampshire03755,USAandDepartmentofAstronomy,University Accepted 1987January29.Received26;inoriginalform1986August27 Brian WarnerDepartmentofPhysicsandAstronomy,DartmouthCollege, Cape Town,Rondebosch7700,SouthAfrica effects ofinclination)starsintheprincipalclassescataclysmicvariable found mostlyfrominfraredobservationsoftheirsecondaries,atightrelationship Summary. AbsolutemagnitudesMoftheaccretiondiscs(withallowancefor is foundbetweenM(max)atmaximumofoutburstandorbitalperiod: without knowndistances.Formanyofthesestarsitispossiblealsotoderive Mv(max)=5.64-0.259 P(hr). are derivedfromavarietyoftechniques.Fordwarfnovae,whosedistances Use ofthisequationprovidesM(min)atminimumlightforfurtherdwarfnovae theoretical valueforstable(ratherthanepisodic)masstransferthroughaccretion functions oforbitalperiodPandmeantimeTbetweennormaloutbursts.is Momean), averagedovertheoutburstcycle. discs. Abovethatcriticallevelallobserveddiscsarestable. shorter forthebrightersystems.TheZCamstarshaveMy(mean)closeto disc instabilities,toapredictedrelationshipbetween durationofdwarfnova dwarf novae.Togetherwiththeaboveresultsitleads, throughasimplemodelfor outbursts andPwhichisverifiedbyobservation. is closetotheluminosityofdwarfnovaeduringoutburst. Nova-likevariables have similarluminosities.Togethertheseresultssuggest thepossibilityofan application oftheM(max)-ratedeclinerelationship, averageM=4Awhich v upper limittotherateofmasstransferinanaccretion disc. v between successivenovaoutbursts appearslikely. classical novae,dwarfnovae andnova-likevariablesareshowntoagree v should betargetsfortrigonometrical parallaxes. qualitatively withthesystematics foundhere.Arelativelyshortinterval(~10yr) n v V Analysis ofthisextensivedatasetdisclosesthatM(min)andMomean)are An amplitude-T(Kukarkin-Parenago)relationshipisfoundtoexistforthe Absolute magnitudesofclassicalnovaeatminimum light,derivedfrom The Appendixlistscataclysmic variableswhicharenearerthan300pc, A scenarioisgiveninwhichrecentsuggestionsoncyclical evolutionthrough v n © Royal Astronomical Society • Provided by theNASA Astrophysics Data System 198 7MNRAS.227. . .23W _1 which, apartfromeffectsofinterstellarabsorption,isindependentdistance,quantitative frequency flux,requiresestimatesoftheratesmasstransferwhichcanonlybeobtainedif out ofthesystemasawhole.Althoughmuchcanbelearnedfromoverallfluxdistribution, transfer (i)fromthesecondary,(ii)throughdisc,(iii)ontowhitedwarfprimaryand(iv) modelling oftheX-ray,UV,visibleandIRemissions,emission-linefluxesradio structure andevolution.CrucialparametersinthemodellingofaCVareratesmass Current studiesofcataclysmicvariablestars(CVs)areaimedatimprovingourknowledgetheir distance totheCVisknown. comparing resultsfromthetechniquesthatarecommontoallCVsandthosespecific draw attentiontosystematicdifferencesbetweentechniques;itcanalsorevealsimilaritiesor subclasses. Suchasurveymayhelptoevaluatethereliabilityofparticulartechniqueorit 1 Introduction differences betweenthevariousCVsubclasses. parallaxes frompropermotionsandradialvelocities.AlthoughthefaintnessofCVshas 24 B.Warner deterred effortsofanastrometricnature,itremainsthecasethatanyfutureassistanceindistance accessible totrigonometricparallaxdeterminationsoratleaststatisticalderivationsofgroup proper motionsofclassicalnova(CN)remnantsandKraft&Luyten(1965)foundM=1.S±0 base since1965whenLuyten&Hughes(1965)foundameanabsolutemagnitudeM—4from determinations fromthisdirectionwillcomethelargeastrometricreflectorsmorethan velocity ill-determined.ForafewoftheCVsreliablevelocitiescanbeobtainedfrom from propermotionsandvelocitiesofdwarfnovae(DN).Thenumberradialvelocitymeasure- small-aperture astrometricsatellites.Therehasbeenlittleimprovementinthedata the uncertaintiesofinterpretationemission-lineprofileswhichcanleaveevensystemic ments forCVshasgreatlyincreasedsince1965,butconcomitantlytherebeenarealizationof is verysmall. periods. ThenumberofCVsforwhichthesystemicvelocityisknowntoanaccuracy±5kms absorption-line spectraofthesecondaries,butthesedonotcoverallsubclassesandorbital basic absolutemagnitudesinfavourofthephysicalpropertiesaccretiondiscs.Empirical rates ofmasstransfer.Therehasbeenatendencyinrecentyearstoreducetheemphasisplacedon that themotivationisprincipallyofestimatingphysicallysignificantparameterssuchas period P(e.g.Patterson1984),ortherelationshipbetween MandradiusRoftheaccretiondisc relationships suchasthevariationofmasstransferrateindisc,M,afunctionorbital calibrated fromtheoreticalinterpretations(e.g.lines of constantradiusintheM,B-Vdiagram, through uncertainM(L,T)andTJJB-V)relationships. Theobservationaldiagrammaybe model-dependent fittoatheoreticalmainsequence), nottransformedtoalogL,diagram diagram ispresented(or,perhaps,anM,B-V ,whereM^-Vhasbeenobtainedfroma of thelatterinevitablyareinterpretiveandmodel-dependent). Theprincipleisthesameasthat here toretainasfarpossibletheobservationaldata andempiricalcalibrations(althoughsome adopted instudiesofcolour-magnitudediagrams clusters:thebasicobservationalV,B-V relatively invarianttoimprovements intheory. or linesofconstantMinCV diagrams)buthopefullytheunderlyingobservational dataremain (e.g. Smak1982)usederivedparameterswhicharehighly model-dependent.Itisourphilosophy distribution, Manddistances maybeobtained.However,thedifferencesbetween themodel expansion-parallax method appliesonlytoCNandwillbediscussedlater.From fitsoftheflux V v d d v Ve v d d There isstillmuchtobegainedfromageneralsurveyofabsolutemagnitudesCVs, Many ofthecurrentlyknownCVslieatdistances50F>6.5.(3b) k wanted istheabsolutemagnitudeofaccretiondiscalone-anumberadditionaldataand corrections arerequired.Toapplyequation(3)weneedtheorbitalperiodoragoodapproxima- where wehaveusedalimbdarkeningcoefficient of 0.6.Equation(4)fitswellthemodel from theUBVcoloursatminimum(Echevarria&Jones1984)ormaximum(Vogt1981) tion toit.ForthosesystemswherePhasnotbeendirectlymeasuredanestimatemaybeobtained 2o from therateofdeclinedwarfnovaoutbursts(vanParadijs1983)orothercorrelations between outburstpropertiesofdwarfnovaeandtheirorbitalperiods(Szkody&Mattei1984). calculations ofMayo,Wickramasinghe&Whelan (1980).ItgivesAM(56.l)=0and eclipses, amplitudeofradial velocitiesororbitalmodulationofbrightness.The correction factor long timebases,whereasothersareshortaveragesorevenindividualobservations.Formost given byBruch(1984)mustbeusedwithcircumspectionassomemeasurementsareaveragesover above stateswouldbepreferable.Thecompilationofphotoelectricallymeasuredmagnitudes all immediatelyavailableincatalogues.Forourpurposesmeanvisualmagnitudesforeachofthe AM=—0.361 (averagedoverallinclinations)=AMy(44°). luminosity is(Paczynski&Schwarzenberg-Czerny1980): Variable StarSectionoftheRASNewZealand.Alltoooftenonlymagnitudesavailable dwarf novaemagnitudesarebestobtainedfromthelong-termobservationsofAAVSOor than thesamesystemseen at/=85°. systems; theapparentmagnitude ofasystemviewedat0°inclinationisSVimagnitudes brighter AM(/) isanimportantfactor indeterminingthetrueabsolutemagnitudesof disc-dominated (apparent) visualabsolutemagnitudeofanoptically thickdiscfromitsdirection-average which doesnot,forexample,distinguishbetweenordinaryandsupermaximainSUUMaStars. are thephotographicdeterminationsinGeneralCatalogueofVariableStars(Kholopov1985) In manyofourapplicationsweareaidedbythefactthatP-V~0atmaximumoutburstCVs, so m~matthistime,andtherangeofoutburstm^(min)-m(max)isindependentinterstel- lar absorptionA.ValuesofthathavebeenmeasuredphotoelectricallyaregivenbyBruch v (1984) andDuerbeck(1981). V y pgv v For P^6.5hr,however,Sisnotindependentofspectraltype.FromBailey’s(1981)fig.1and To progressfromadistanceestimatetotheabsolutemagnitudeofCV-particularlyifwhatis K To applyequation(4)anestimate of/isrequired,whichvariouslyobtained from observed Apparent magnitudesatmaximumlight,minimumlightorstandstill(forZCamstars)arenot Allowing forprojectedareaandlimbdarkening,the correctiontobemadeproducethe © Royal Astronomical Society • Provided by theNASA Astrophysics Data System log (l+|cos/)cos/, (4) 198 7MNRAS.227. . .23W 2 13 contribution ofthesecondary,whitedwarfand/orbrightspot.Where which agreeswellwithasimilarequationgivenbyWarner1976)and,forthedisc, formed ofhowimportantitmightbefromuse secondary isnotdirectlymeasurable(e.g.fromitspresenceinthespectrum)anestimatemaybe where MisthemeanabsolutemagnitudeforCVsubclass.Anticipatingresultsfound (Patterson 1984),whichgivestheabsolutemagnitudeofsecondaryfor105=P$4hr(and Mv<2)=22.0-17.46 logP(hr)(5) later, equations(5)and(6)implythatthesecondarywillbeatleastonemagnitudefainterthan log P(hr)scO.95-0.057AM(i)forCNremnants,nova-likevariablesandDNatmaximum the discif M=M+A(0 (6) cannot beusedforpurposesof calibration ashisdiscfluxdistributionsdonotmatchtheobserved valuesofB-V. * Wade’s(1984)modeldiscsshow atightrelationshipbetween5^andcolour,asrequiredbyequations (7)and(8)but log P(hr)^0.68-0.057AM(Í)forDNatminimum. and 3 Absolutemagnitudesfromsurfaceintensities v Before applyingtheabovemethodstoindividualCVsweexplorepossibilityofemploying M=S+15.l— logR/R,(7) gave therelationship[analogoustoequation(1)] surface intensityapproachofWesselink(1969)toCVdiscs.Forstellaratmospheres v where SisthesurfacebrightnessinV-band.FromWesselink’scalibrationdatafor, yv 5=3.65 (P-V)—12.6for-0.1<(P-V)<9(8) Warner (1972)found The discradiusRiscalculatedfromP=0.7(Sulkanen,Brasure&Patterson1981),where reliable data*weadoptthestellaratmospheresresultsexpectingthatsomesystematicerrorsmay In anidealworlditwouldbepossibletorecalibratetherelationshipsexpressedinequations(7) P isthemeanradiusofRochelobeprimary. Thisresultappearstobewidelyapplicable correction istobemadeeachside[AM(i)MandcositheRfactor]itinsensitivei. emerge. and (8)byappealtoCVdiscsofknownradiusoverarange(B-V),butintheabsence V to theCVs;ingeneraltherearenolargechanges R duringoutbursts.Forexample,thedisc below (Cook&Warner1984;Cook1985a,b;O’Donoghue 1986);however,althoughinUGem radii measuredatquiescenceandoutburstinZCha OYCaragreecloselywithequation(10) maximum ofoutburstandalmostcompletelyfillsthe Rochelobeoftheprimary.Ifthisisa common occurrenceamongtheDNwithlongerorbital periodsthenourcombinationofequa- r tions (7)andR=0.7willunderestimatetheirbrightness atmaximumlight. (Smak 1984)thediscradiusatquiescenceagreeswith equation(10),itis~35percentlargerat vq v 1/0 —=0.46 (l+g)“' (9) dL L v 0 d dL a If wewantthebrightnessofdiscalonethenatminimumlightmayneedtosubtract Assuming thatequation(7)appliestoanopticallythickdiscwenoteasasimilarinclination For mathematicalconvenienceweadopttheapproximate expressionforR(Warner1976): © Royal Astronomical Society • Provided by theNASA Astrophysics Data System L Absolute magnitudesofCVs27 CT) co CM CM CM 00 r- [■" S á CO SS

Table 1. Absolute magnitudes of dwarf novae. 28 B.Warner © Royal Astronomical Society • Provided by theNASA Astrophysics Data System 198 7MNRAS.227. . .23W CSJ 4-> W 4J a CO >1 u O o c CO £ 0H +J 4J CO i & V 4M 5 ^ c s >1 M > G J Z H I 3 8 r 1 o P “Q il •| -C en <4H '^Q4) en XJ 7Z bû 1 = w On CM 00 ë x Ë l- 4J rHU3 N ^3 t-H S 00 0 ^ si 5b ^ Ë o w U ffi G >% «-• G C3 S X o X XJ C/5 <4H ^ ^1 'E -S Os -«-j 00 G uo -a ^ 2 ^ m p B G P to Ë ^ > _ G . G ê U N w O irT u á s UH »P X "O CQ ^ •S 1 S Æ 00 » ^ X 2 G 6 1 ^ 0 h! § J3 G <3 O 5 g Ë N o Sn G S) , 2 C/5 Q 1-4 s en 2 7? CM en ^s: > 2 oo < XJ X UH en P^ .X •o XJ •o -o >5 os 00 s •| -S rn^ m s -*H Ä ^5 bd oGg P Ë O q o N o O o G cd g a (U o* cr G 3 VO "C o. G <0 w f| 8 '^•ë' X UH /-v G is"! 2J3 CQ en m ^ ^ o 'S ^ «£3 GrH S ¿a £ S Cn r -X ^4) ^v EC« rH o--H a AS G Ouh O o Ë O O G 2 -g^ G B Q> p-H CT Os G 00 G vo G -- - "Ow Ë G^ G S Ë ^ • S 2 f • O s_^ •ë 'Ë en ■S s OS VO rH 00 4H 2 >> .tî Cü •*-» CO 'w' > ^ O Op a G G Ë bd N G >» G o > < XJ UH cg á ^ X ’S Ë C ? UH 45 ië 2 os -i, 00 § XJ _. en 11 rH OS OS 00 00 S> en ^ 2 § Ë Ë o bû CQ G p 30 Table 1-continued © Royal Astronomical Society • Provided by theNASA Astrophysics Data System BX Pup d from membership of NGC 2482 (Moffat & Vogt 1975). P from Vogt (1981). AH Her d from K of Berriman et ai (1985) and equation (3) ; mv(max) from average of Bruch (1984) and Mattei (1986, private communication) ; / from Horne, Wade & Szkody (1986).

TZ Per d and P fromc Sherrington & Jameson (1983); Av from Hassall (1985); m,^standstill) from Matei (1986, private communication); B. Warner w o On X rH O ^ O 'g ^ 1 -S 7^ 1 ^ «4^ o _ G 0 ^ - 2 1 -o S .2 2 cd < > T3 VO On^ ON r-H<1 O ÖJD o B X) T3 T3 T3 X) ^ Cu «3 ctj G OÛ ^ Ui O. r—H t-i cd § 2 O m oo -J O ON n-i 00 ON ^ G •c 05 2^ á 1 i-H ^ G eu « Ë G ü I 5 Í£ ü X o ’S N Ë o-3 g ä?>n ï, -1 u? ^ O G G ¡S.2 >

Figure 1. Absolute magnitudes of the accretion discs of dwarf novae at maximum of outburst and at minimum light as a function of orbital period. The symbols as defined here for Z Cam, U Gem and SU UMa stars are used in Figs 2-5. Underlined solid circles for Mv (max) indicate that distances were not obtained from the /^-magnitude method. Lines of constant rate of mass transfer through the disc M are indicated. The linear fits to the points are those of equations (13) and (18). both Z Cha and OY Car the secondary completely dominates in the K-band (Bailey 1981; Sherrington et al. 1982) and the discs could be up to two magnitudes brighter (as is the case in SU UMa: Table 1) without preventing detection of the secondary. That we should look closely for selection effects is shown by the following equation, obtained from combining equation (3a) with the equation defining absolute magnitude:

Mv(max)=mV'(max)-Æ'(secondary)+9.65-5.36 log ^(hr). (14) This shows that if M^(max)-K were for any observational reason restricted to a small range, then Ml^max) would inevitably show a trend with P. Evaluation of m^max)—K from the data of Table 1 and of Berriman et al. (1985) shows that it ranges from —0.5 to -6 and, although there is a correlation such that the most negative values of mv(max)-K occur at the shortest orbital periods, there is a spread —2 mag at any given P. It is this spread that is greatly reduced by applying the corrections Av, ¿±Mv(i) and A to give the final My(max). This observational spread shows that it is unlikely that the tight correlation between AfK(max) and P seen in Fig. 1 arises from difficulties of detecting the secondary in the presence of the disc [which would limit values of mw(mm)—K and thereby cause some restriction on values of mv(max)—K]. It should be noted en passant that equation (14) shows that for those CVs without known orbital periods, an accurate guess of P is required before the ^-magnitude method may be used: a 20 per cent uncertainty in P transforms into an uncertainty of ±0.23 mag in My(max).

A completely independent method of estimating Mv{max) is provided by the surface brightness technique. Vogt (1981) found a strong correlation between dereddened UBV colours of DN at outburst and their orbital period:

1 (B-V)o=0.0293 P(hr) — 0 130 1 /2

© Royal Astronomical Society • Provided by the NASA Astrophysics Data System 198 7MNRAS.227. . .23W should representanaverageoveri,probablyweightedtowardslowerinclinationswhich,from AMmax)=0.107 P(hr)-—logP(hr)--logf—)+6.06. equation (4),producebrightersystemsatmaximumlightthanhighlyinclinedsystems. Adopting +/,=().9A7:(Ritter&Burkett1986)wehavethefollowingMi(max): The correlationbetweenM(max)andPforDNcanbeusedtogiveM^(min)anywith 4.2 DWARFNOVAEWITHOUTDISTANCEDETERMINATIONS reasonable accordofthesurfacebrightnessmethodwithindependentlydeterminedM(max) Aiv(max) 5.354.874.564.344.184.073.983.92 P (hr)23456789 uniform distributionoftemperatureoverthediscanddifferentaveragingprocessesa suggests thatthecalibrationeffectsweignoredinderivingequation(11)(e.g.non- Over mostoftherangePtheseareclosetowhatisobtainedfromFig.1orequation(13).The disc andasphere)havelargelycompensatedeachother. independent ofAandThecorrectionA,however, mustbeappliedwhenrequired.If,in M(min)=M(max)—m(max)+m(mm)+A (17) known orbitalperiod.Wemakeuseofthefactthat maximum, andarethereforerepresentativeofslightlyfaintermagnitudes,thereisonaverage mv(max)=9.3. Asisseenfrom Table2,adoptingthisinterpretationofthemagnitudesleads toM^min)and addition, wehavesomeestimateofiandAthena distance canalsobederived. the M(min)derivedfromassumingthatequation(13) appliestoallDNarealsoplottedinFig.1. discussion ofUGemsuggeststhis);thenthroughequation(7)M(standstill)willbefainterthan however, theradiiofDNaccretiondiscsatmaximummaybelargerthanstandstill(ourearlier appears thereforetogivemagnitudeswhicharetoobrightfortheZCstarsinstandstill.Inreality, quiescence; equation(10)isanaverageoverthesestates.Inconsequence,applicationof observational datatodeterminetheRd(P)relationshipseparatelyformaximum,standstilland Mv(max) evenforidentical(B-V).Thebasicproblemisthatwedonotyethavesufficient (ZC) starsatstandstill.Althoughmanyofthe(B-V)maynothavebeenobservedexactly we haveAf,(min)=9.2,whichis a moreacceptableresult.Thisreinterpretationofthelightcurve ofWWCetimplies M^standstill) thataretoofaint relative tootherZCstars.Ifinsteadwereassignthem=13.9level tora^min)then Ritter (1984)andasanSUUMastarbyBateson(1979). givesmv(min)-15.0-15.7,m(standstill)=13.9and *The classificationofWWCetisproblematical.Itlistedasnova-like (ZC?)byPatterson(1984),asDN(ZC) and otherdatafromsourceslistedinthesupplementary notes.WiththeexceptionofWWCet*, state, andthesubclassofnova-like variablesknownasMVLyraestars. that thestarisaDNwithquiescent magnitude13.9,outburststo9.3andoccasional lowstatesof15.0- : (11) isnotabletodistinguishbetweendifferentoutburststatesofCVaccretiondiscs. ±1.0 magdifferencebetweenmaximumandstandstillmagnitudes(Table1).Equation(16) K v 15.7. Assuchitcouldrepresent animportantlinkbetweenthenormalDN,noneofwhichisknown tohavealow K v v v v 0 0 v v v Although frommodeldiscs(¿?-V)mustbeafunctionofi(Mayoetal.1980),equation(15) Equations (11)and(12)give Table 2givesinformationforDNwithorbitalperiods fromPatterson(1984)andRitter According toVogt(1981),equation(15)appliesequallywellDNatmaximumandZCam 0 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System 3 \MJ e Absolute magnitudesofCVs33 3.87 (16) 10 CT) co CM CM CM 00 r- r" S á CO SS 34 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System

Table 2. Absolute magnitudes and distances of additional dwarf novae. •H (0 G e 9 <Ù B. Warner ID W IS] 4) S' U CO >i (0 O IT) CM rH ^ o o to rH CM 00

Assumed. +Not plotted in Figure 1: see text. 198 7MNRAS.227. . .23W The leastsquareslinearfittothe33starswithM(mm)listedinTables1and2is 4.3 Mv(min)fordwarfnovae M(min)=9.72—0.337 P(hr) and thermsscatteraboutthisrelationshipis±0.70mag. driven bylossofangularmomentumviagravitationalradiation,whereasabovethegapmagnetic that belowtheperiodgap(2.22.8hrandfoundthefollowing From theM(min)listedinTables1and2wefindthataverage(min)=8.4±1.0,whichis In Fig.1itcanbeseenthatM(min)fortheZCstarsissystematicallybrighterthanUGem v v © Royal Astronomical Society • Provided by theNASA Astrophysics Data System ±0.25 ±0.056 ±0.54 ±0.095 unpublished). Absolute magnitudesofCVs (18) 35 198 7MNRAS.227. . .23W 1 18 the disc. calibrate theabsolutemagnitudesinTable1asafunctionofM,ratemasstransferthrough M-(M, Mi,Ri,R).(19) Bell &Pringle1974): which wecaninvertinordertofindM=(,P),i.e.asafunctionofpositionthe computations ofdiscshavebeenperformed,andusingequation(10)we Adopting anMi-Rirelationshipforwhitedwarfs,choosingM^IM©,whichmostpublished M—Mv{M, P)(20) calculation (Wade1984).Forourpurposeswehavehadtoextrapolatethesecomputations 36 B.Warner larger valuesofM.Inaddition,asthegridsmodelsdonotcoversufficientboth those whichprovideM(M,R)directly(Tylenda1981)orwithasmallamountofadditional observational diagram,Fig.1. and P,wehaveassumedM(MR)=M()+F(R),whereF(R)isdeterminedfromthe models madeforaspecifiedMandassumedtoapplyother,notgreatlydiffering,valuesof. function F(R)fromWade’s(Kurucz)modelstoderiveM{M,Randhence(MP).InFig. variation ofMwithRwhich,fromWade’smostluminousmodels,isMy—const—logand d observed M(max)quitewellforP<7hr.Theslopeofthetheoreticallineisaresult vd hence mostoftheincreaseinMfromP=9toP=l/2hrisaccountedforbythiseffectalone.It dv very well. vd for thisgrouprelativetolongerperiodsanditispossiblethatM=constwilldescribeMy(max) systematically smallerprimarymasses(e.g.Ritter&Burkett1986)thenthiswouldincreaseM should benoted,however,thatwehaveusedMi=M©throughout.IftheshortestperiodDN 1 thelineM(P)obtainedfor=.5xl0gs“24-M©yrisseentorepresent which hasapreviouslyunsuspectedupperlimit. d vd the intervalsbetweenoutbursts,maybetransferredthroughdiscduringoutburstatarate Hoshi (1979)]orinthesecondarystar[inmodulatedmasstransfermodelofBath(1969)] dv M withP.However,conversionofequation(18)gives d for whichshowsthatabovetheperiodgap mass transferratesaverageabout10times log M(min)—14.9+0.15P(hr) (21) dv thus eliminatingtheextrapolationsandinterpolations foundnecessaryhere. those below. vd 4.5 STABILITYOFACCRETIONDISCS v v therefore atquiescenceM ^—M- Themodeldoes,however,showthatthemass lossratefrom In thediscinstabilitymodelofdwarfnovae,material isstoredinthediscbetweenoutbursts; which resultsfromincluding M(outburst)averagedovertime.Patterson(1984) hasgiven the secondarycanbeobtained from-M~M(quiesc)x2,whereQisthecorrection factor ray(min)], obtainedfrom averaging theirlightcurvesoveranumberofoutbursts. Asdefined d v Vd d Q-values foranumberof systems [notethathisQsarenotalwayscalculated withrespectto d d 2 d 2d The absolutevisualmagnitudeMofamodeldiscisfunctionmanyvariables(e.g.Lynden- Computations ofdiscshavebeenmadeforavarietypurposes.Theonlyonesusablehereare We haveusedanextrapolationoftheM(M)relationshipgivenbyTylendaandobtained v This suggeststhatmassstoredinthedisc[ininstabilitymodelofOsaki(1974)and At minimumlightthelargespreadofMy(min)precludesanexactdescriptionvariation vd The conversionfromMtowouldbemademore secureiffurthermodelswereavailable, © Royal Astronomical Society • Provided by theNASA Astrophysics Data System vd 198 7MNRAS.227. . .23W 3 4A = here, theß-valuesaretobeappliedi.e.withcontributionsAofsecondary measured relativetotheobservedofsystem,thenß=ß(system)xICH. and brightspotremoved.Wherethelatteraresignificantcontributors,ß-values the ordinaryoutbursts(i.e.withoutinclusionofsupermaxima),wemodifyPatterson’sß-values for periodswhennormaloutburstsareoccurringisclosetothefluxatstandstill.Forthesestarswe according totheprescriptiongiveninSection4.6. adopt ß(standstill)=1,or-M2^d(standstill). purely observationalquantities,notdependentonmodels.Althoughdirectlyobservablein The latterareplottedinFig.2. momean) areincluded,whereavailable,inTables1and2,togetherwiththededucedM(mean). other thanZCamstars,thetime-averagedmagnitudemv(mean)=m(min)—2.5logß[=m (standstill) forZCstars]isanobservationalquantityopentotheoreticalevaluation.Estimatesof Tables 1and2. Fig. 1.Thissteepeningarisesfromthetendencyforsystemswithlongerorbitalperiodsto trend towardshigherluminosityatlongerorbitalperiodsthatissteeperthanforin have largeß-values,ascanbeseenfrominspectionofthevaluesray(min)-ra(mean)in critical Mforagivensizeofdisc,abovewhichstableratherthanintermittentmasstransfer P>3 hr.Ithaslongbeenhypothesized(seeWarner1976)thatZCamstarsatstandstillareDN stuck temporarilyinanoutburstcondition.InthediscinstabilitymodelofDNoutburststhereisa occurs (e.g.Smak1982).TheconclusionisthatwhereastheUGsubsetofDNhave\M\too small tosatisfythecondition,inZCstarssituation-M~^d(crit)obtains,whichenables them occasionallytoremainjustinthestablestate.Supportingevidenceforthisisgivenby v Kv Figure 2.Absolutemagnitudes of dwarfnovaeatmeanlightasafunctionorbitalperiod.The pointsarelabelled with therecurrencetimesTof thedwarfnovaenormaloutbursts(seeSection4.6).Thecurve isthetheoretical K relationship forstablemasstransfer inanaccretiondisc. d 2 2 n For theSUUMastars,wherewewillrequireMomean)forlightcurvesaveragedonlyover For ZCamstarsthereisevidence(Zuckerman1954;Warner1976)thatthetime-averagedflux In thecontextofourpresentinvestigationitmaybenotedthatß-valuesareinprinciple Unlike thesmallscatterinM(max),(mean)Fig.2showalargerangeatanyP,with The ZCstarsinFig.2formwhatcouldbeconstruedasanupperenvelopetotheMomean)for v © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Absolute magnitudesofCVs37 198 7MNRAS.227. . .23W ,2 1680 both becauseofthedecreaseinM(min)andincreaseQ\combinedeffectcouldtake but itiswhatwouldbeexpectediftherewereagradualratherthanrelativelyfastincreasein in otherZCstars(Mattei1986,privatecommunication),itdoesnothappenbeforeallstandstills, the quiescentstateprecedingstandstillsofRXAndandZCam.Althoughthishasnowbeenseen worthwhile examiningthesituationfurther. close toM(crit)intheZCstarsbutnotUGs.Withourmoreextensivedatasetitis star acrosstheMy(crit)boundaryrequiredforstablemasstransferthroughdisc. Szkody &Mattéi(1984)whofindanincreaseinfrequencyofoutburstsandarisebrightness \M\. Fortheshorttimebeforestandstillsinwhichtheseeffectsareseen,M^(mean)willbrighten steady-state accretiondisc(Lynden-Bell&Pringle1974): where ristheradialdistanceindisc.IfTtemperatureofdiscabovewhichstable transfer takesplacethenwerequireT(r)>Teverywhere,whichrequiresonlythatT(R)>T. 38 B.Warner As R>Ri,equation(22)becomes v for stability. Aid>-r n,-7-(23) d Burkert 1986) 2 log 7=3.81—67xl0~logR/R(24) Other theoriesofdiscinstabilityleadtoverysimilarvaluesM(crit)(Shafter,Wheeler& M(crit)=1.60x 10—P(hr)gs'.(25) Cannizo 1986). zúx in theobservationaldiagramFig.2.Ascanbeseen,theoreticallinepassesclosetoregion from Mto,withthehypothesisthatZCstarshave —M~(crit). Equation (25),transformedthroughequation(20),givesthefunctionM(TP)whichisdrawn cútdcúl of theZCstarsandiscompatible,withinuncertainties ofthetheoryandtransformation wide rangeofMand,requiresfurtherattention tocheckonthepossibilitythatscatter The largespreadinM(min)orMomean)atagivenorbital period(Figs1and2),whichimpliesa 4.6 CORRELATIONSWITHOUTBURSTTIME-SCALES d originates inobservationalerror.Fortunatelythere isapropertyoftheDN,meantime the observationalparameters thatwehaveusedthusfar. between theiroutbursts,whichisanobservationalquantity unrelatedto,orinfluencedby,anyof critdQ probably throughheating of thesecondary(Vogt1982;Osaki1985).Thevisual fluxradiated during asupermaximum the rateofmasstransferfromsecondaryisgreatly increased, d d dv 2d vCTiu T betweennormaloutbursts andTbetweensuperoutbursts.Evidenceisaccumulating that d2 v n s Smak (1982)hasshownfromacomparisonoftwoZCandthreeUGstarsthat-Misindeed Following Smak(1982)weusetherelationshipdescribingtemperaturedistributionina For TentweadopttheexpressiongivenbyMeyer&Meyer-Hofmeister(1983)(seealsoRitter 2 Together withequations(10)and(22),equation(24)gives Among theSUUMastars (Warner 1985a)twooutbursttime-scalesareknown: the meantime © Royal Astronomical Society • Provided by theNASA Astrophysics Data System 3 8¿r ^R d 3 GMi 010 /MA- \M/ 0 198 7MNRAS.227. . .23W during asupermaximumisthereforenotcharacteristieoftheaveragebehavioursystem; bright spotandtheadditionaldurationofmaximumresultsfromperiodincreasedmass greater luminositynearthebeginningofasupermaximumarisesprobablyfromanenhanced transfer. Inouranalysisofthesystematicsordinaryoutburstswethereforerequireß-values which omittheeffectsofsupermaxima(otherthancountingasupermaximumasanordinary maximum becausetheformerappearstobetriggeredbylatter).Ifdurationsoftwo ima canbeconvertedintoaQ'whichdoesnotbytheformula types ofmaximaareATandrespectively,thenaQwhichincludesaveragingoversupermax- From theestimatesofwidthsoutburstsinSUUMastars(Szkody&Mattei1984;vanParadijs can provideM(min)fromTables1and2.TheapparentmagnitudesatsuperoutburstfortheSU UMa starsareobtainedmostlyfromRitter’s(1984)compilation.ThevaluesofTandcome 1983.) wefindAT/AT—5forallstars. Sn v ns sn For theordinaryUGem(UG)DNandZCstarsalloutburstsareconsiderednormal. In Table3wecollecttogetherinformationontheoutburstpropertiesofthoseDNforwhich © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Table 3.(a)OutburstpropertiesofSUUMastars. VW Hyi AY Lyr WX Hyi HT Cas EK TrA RZ Sge OY Car1.51 V436 Cen1.50 TU Men YZ Cnc TY PsA TY Psc CU Vel T Leo SW UMa SU UMa Z Cha Star IR Gem Deduced fromapplication ofequation(13). AT Tj n P(h) nVy,(super)A 2.82 2.10 1.79 1.78 1.77 1.75 1.70 1.94 1.83 1.85 1.85 1.79 1.64 1.53 1.36 1.41 s -1 11.2 11.6 10.5 12.0 11.7 11.0 11.2 11.4 11.9 10.8 12.3 12.0 Q- 11.4 11.3 8.5 5.0 4.0 3.2 3.3 4.3 5: 4.6: 4.4 4.3: 3.8 4.5 4.4 4.8 5.8 4.7 4.4 3.9 4.7 4.1 5.7 5.7: A r 2.6 4.1 2.5 2.9 3.8 3.9 3.8 3.8 4.1 3.9 4.1 Absolute magnitudesofCVs39 T(d) Mmin)ean) snv 200 205 266 487 318 335 333 386 287 500 157 134 174 140 179 459 420 <164 231 165 21 39 24 26 39 27 33 77 12 19 14 93 <11.1: 11.0 8.8 7.7* 7.9 8.1 8.8 9.6: 9.0* 9.8: 9.1 9.0: 9.1 9.1 9.0 9.3 9.4 9.3 7.4: 8.7 8.7 7.1 8.5 8.5 7.9 8.5 6.5 6.7 9.4 9.0 9.0 (26) 198 7MNRAS.227. . .23W Mean amplitudeofsuperoutburstsA=m(mm)—m(super)+A partly fromRitter(1984),supplementedwithimprovedestimatesSzkody&Mattei Mean amplitudeofnormaloutburstsA=m(mm)—m(max)-\-A significantly atmaximumlight,theseare Bateson (1979)andMattei(1986,privatecommunication). correlated withorbitalperiod-Fig.4(a).Asimilarresultisfoundfortherelationshipbetween However, thedeparturefromlinearrelationshipdefinedbySUUMastarsishighly gives theimpressionthatSUUMastarsfollowadifferentrelationshipthanotherDN. factor governingtherecurrencetimeT. Momean) andT:Figs3(b)4(b).ClearlyneitherM^min)norM^(mean)aloneisthesole 40 B.Warner demonstrated thatthespreadinM(min)Fig.1andMomean)2islargely sv nv n n v The correlationbetweenM(min)andT,seeninFig.3(a),showsconsiderablescatter The amplitudesofoutburstareforthedisc.Assecondaryandbrightspotdonotcontribute Before pursuingthisfurther,wenotethattheuseofindependentparameterThas vn n © Royal Astronomical Society • Provided by theNASA Astrophysics Data System X Leo U Gem CN Ori CZ Ori Star CW Mon BD Pav RU Peg KT Per RX And TW Vir EM Cyg AH Her HL CMa UZ Ser SS Aur SS Cyg TZ Per SY Cnc Z Cam Table 3.(b)Outburstpropertiesofdwarfnovae. Deduced fromapplication ofequation(13) Type UG UG UG UG UG UG UG ZC UG UG UG UG ZC ZC ZC ZC ZC ZC ZC (4.0) (7.1) (6.6) (6.5) P(h) 3.94 3.91 4.17 4.23 4.30 4.38 4.38 7.79 7.00 6.63 5.20 5.08 9.1: 6.96 6.19 ~n 3.4 3.5 2.3 3.5 5.3 3.4 3.2: 3.7 3.7 4.2 4.0 2.7 3.4 4.2 3.3 4.4 3.1 4.0 1.8 T(d) 101 n 26 22 26 22 23 43 17 21 27 40 32 43 65 17 18 15 13 M(min) v 8.0 8.1* 8.7 8.1 6.9 7.4 7.2: 7.7 8.4 8.9 9.6 7.7 7.6 7.3 7.7 6.9: 8.3 6.4: 6.2* M(mean) v 5.5 8.1 7.9 6.8 7.4 5.5 6.6: 4.2: 5.0: 4.9: 5.3 4.7* 5.6 6.3 6.6 6.5 Absolute magnitudes of CVs 41

Figure 3. Correlations of recurrence time-scale Tn for dwarf novae with (a) absolute magnitude at minimum light and (b) absolute magnitude at mean light. The linear fits are to the SU UMa stars only.

intrinsic and does not originate in observational error. For the SU UMa stars (which have a small range of P) in Fig. 3(a) the rms scatter about the linear fit is ±0.39 mag. As there are some residual uncertainties in the values of Tn (partly an interpretive problem as the DN do not outburst regularly, so Tn can depend on the completeness or length of observational coverage), this result suggests that the error in determination of MK(min) in Tables 1 and 2 is probably not greater than —0.3 mag.

There are therefore two parameters that influence MK(min). One of these is the orbital period P; the other is as yet undetermined but it is the controlling factor in the recurrence cycle (it can be seen from inspection of Table 3(a) and (b) that P does not influence Tn).

The slightly poorer correlation between Momean) and P [Fig. 3(b)] than between MK(min) and P [Fig. 3(a)] could arise in part through the additional uncertainties of the Q-values.

P(hrs)

Figure 4. Correlation between orbital period and the deviations AMK in (a) Fig. 3(a), and (b) Fig. 3(b).

© Royal Astronomical Society • Provided by the NASA Astrophysics Data System 198 7MNRAS.227. . .23W The rmsscatterofthe33DNwithM(min)inTables1and2is±0.49magwhencompared Mv(min)=7.11-1-1.64 logT(day)—0.264P(hr)._ equation (28).AgainpartofthisscattermustbeattributedtouncertaintiesinT.Equation(28)is line ofM(T)inFig.2bytheapproximaterelationship a generalizationofequation(18). 42 B.Warner M(r)-6.5-0.26 P(hr), then, fromequation(28), independent oforbitalperiod.Thatis,thetimebetweennormaloutburstsisafunctiononly Mv^min)-Mv(r)=0.6+1.64 logr(42) factor bywhichtheluminosity(ormasstransferrate)ofquiescentdiscfallsshort minimum neededtoproduceasteadystatedisc.Thisisnewobservationalresultwhichrequires v explaining bymodelsofthedwarfnovaoutburst. n n vctit Kcrit critn following section.TheexistenceofacorrelationbetweenMomean),TandPisclearlyseenin Fig. 2,wherewehavelabelledthepointsinMomean)-Pdiagramwiththeircorresponding those withlargeT,inspectionofM(mm)-My(mean)inTables1and2willshowthatnosuch described inSection4.5,whichcouldreducetheMomean)ofsystemswithsmallTrelativeto strong correlationexists:awithPis,however,present.Thebetween My(mean), TandPismerelyamodificationofthecorrelationthatexistsbetweenMv(min), The datacontainedinTables1and2constitutethemosthomogeneousobservationswithwhich and P.ThelatterisseeninFigs3(a)4(a). A=M/(min)-M(max)=1.08+1.67 logT(day)-0.005 P(hr)^ 4.7 THEKUKARKIN-PARENAGORELATIONSHIPFORDWARFNOVAE T. IncaseitbethoughtthatthecorrelationhasbeenintroducedthroughQcorrections, n to examinethecorrelationbetweenamplitudeandoutbursttime-scale,i.e.Kukarkin- Parenago (KP)relationship(Kukarkin&1934).Inparticular,theamplitudesof latest determinedTareavailable.TheseshouldprovideabettertestfortheexistenceofKP outburst, freedfromdistortionbycontributionsthesecondariesandbrightspots, relationship thandoestheuseofheterogeneous datacontainedintheGCVS(e.g.van nv n A=1.85 (±0.44)+1.40(±0.23) logT(day)fromtheGCVScompilation. The essenceofthiscorrelationiscoursealreadycontained inFigs1and4equations(13) the conclusionobtainedfromlesshomogeneousdata (vanParadijs1985)andconvincingly Paradijs 1985). which isstatisticallyindependent oforbitalperiod.Forcomparison,vanParadijs (1985)found n demonstrates therelationshipwhichhaspreviouslybeen questioned(Payne-Gaposchkin1977). and (28).FromFig.5(a)wefind niK n has intheKPdiagram.Itis trivial,oncethetightrelationshipbetweenM(max) andPhasbeen n n n v From thecorrelationsseeninFigs3(a)and4(a)wederiverelationship Another wayofviewingthecorrelationforistonotethat,aswemayrepresent A similaranalysiscanbemadeforM(mean),butwepostponediscussionofthistothe v © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Fig. 5(a)showstheA-TrelationshipforourDNdata. Acorrelationexists,whichconfirms One problemthatisevident inFig.5(a)istheeffectthatspreadMy(min) seeninFig.1 n ±0.44 ±0.24±0.037 ±0.46 ±0.24 ±0.044 198 7MNRAS.227. . .23W uncovered, torecognizethatstarswithexceptionallybrightM(m\n)willlielowintheKP A'= Momean)-Mv/(max)(30) diagram. Thatis,thespreadabout-PrelationshipinFig.1ispropagatedinto with thesameproblemsasM(min)-Prelationship. KP diagram[butthereisnodependenceonPbecauseofthenearlyparalleltrendsMy(max) and M(min)withP].Itisclear,therefore,thattheKPrelationship,asusuallydefined,inflicted we canplotamodifiedKPdiagramfromthedatainTable3(a)and(b),asshownFig.5(b).This Figure 5.Correlations(Kukarkin-Parenagorelationships)ofrecurrencetime-scaleTwith(a)amplitudedwarf Figs 3(b),4(b)and5(b)thiscouldbethoughttoarisefromthedifferentwayinwhichQ-values Fig. 5(a)havebecomemorecompatiblewiththegeneraltrend. shows agoodcorrelationbetweenA'andlogTinwhichsomeofthemorediscrepantpoints nova outburstmeasuredfromminimumluminosityand(b)amplitudemeanluminosity. This iswhytheyoccupysuchdisplacedpositionsin Fig.3(b)andmayalsoaccountfortheir Afv(mean), whereasforotherstarsweusedaveragesoverthevisuallightcurves.However,in were derivedinSection4.5-fortheZCstarsweusedM(standstill)asameansofobtaining place ofMv'(min)alsoleadstostrongcorrelations.Defining Momean) thatareabletoenterintothestandstillconditionandhencebeclassifiedasZCstars. context ofourunderstandingtheZCphenomena,itisonlyDNwithpeculiarlybright A;=-0.05+2.06 logT(day)-0.20P(hr). 3(a), 4(a)and5(a)showsthatitisnottheß-values that areatfault. occupying theupperpartofscatterinFig.4(b).The similarsystematicdisplacementsinFigs v v v n 4.8 INTERPRETATIONOFTHE KPRELATIONSHIP n stated intheIntroductionof workingwithobservablequantities.Adwarfnova, ofcourse,isnot accounts formuchofthescatterinFig.5(b). In contrastwiththeresultforA',equation(29),this containsasignificantterminP,which F In ourcontinueduseofthe variousMswehavemaintainedasfarpossible thephilosophy n v We turntoanalternativeapproach.FromFigs3(b)and4(b)weseethattheuseofMomean)in In Figs3,4and5theZCstarstendtobesystematicallydisplacedfromaveragetrend.For From Figs4(b)and5(b)wefindthefollowingrelationship: ( © Royal Astronomical Society • Provided by theNASA Astrophysics Data System ±0A6 ±0.29±0.04 Absolute magnitudesofCVs43 198 7MNRAS.227. . .23W 010±012 : 021 instance inthatwerequireonlyMforthevariousMyofanindividualdwarfnova,i.e.atnearly overly influencedbyahuman’sviewofitsluminosity:itradiates,eruptsandevolvesaccordingto R appropriatetoDN,wefind constant R.Fromthelimitedrangeofdiscmodels(Tylenda1981;Wade1984),for outbursts wemustagaintransformMytoMthroughequation(20).Weareassistedinthepresent the valuesofA/,MiandM.Therefore,inordertogaininsightintomechanismsDN 44 B.Warner My—-1.85 logM+constant(ÆandMiconstant).(32) log M(min)=-0.58-0.90T(day)+log(max) log M(mean)=0.03-l.llT(day)+0.11P(hr)+logM(max). and fromequations(30),(31)(32)wehave 4.4, gives M(min) Tn,which,fromequation(33)andtheapproximation(max)~constantSection d Neither theexponentofMinequation(32)northatT(33)iswellenough d d d d2 conclusion wasreachedbyvanParadijs(1985),basedonthenormalKPrelationshipandVogt’s determined toexcludethepossibilitythatinfactAM(min)=constant.Justsuchatentative d AM(min) ocT(day).(35) work ofthediscinstabilityandmodulatedmasstransfermodels,however,thisresultdoesnot white dwarfprimary,withconsequentsmall-scalethermonuclearrunaways.Withintheframe- support tothehypothesisthatDNresultfromaccumulationofhydrogen-richmaterialon dn (1981) resultthatMy(max)=constant. have anyobviousrelevance. nd outbursts is log AT„(day)=logT(day)+log M(max). Thedurationofanormaloutburstistherefore During anoutburstaDNmustpassthisaccumulatedmass throughthedisc,anditdoessoatarate d AM=[M(mean)-M(min)] T. (36) AT (day) log AT(day)=0.03—0.11 log T(day)+log[1-0.21(day)]+0.11P(hr). and useequations(29) (31)todeduce dn We writethisas n n d dn n n n From equations(29)and(32)wehave We considertwopossibleinterpretationsofDNoutbursts,basedonequations(33)and(34). (i) TheaverageamountofmassAM(min)passingthroughthediscbetweenoutburstsis Ten yearsago(e.g.Warner1976)thepossibilitythatAM(min)=constantwouldhavegiven (ii) Intermsofthediscinstabilitymodel,averagemassAMaccumulatedinbetween © Royal Astronomical Society • Provided by theNASA Astrophysics Data System [M(mean) -M(min)] ±0.25 ±0.16±0.02^ d ±0.19 ±0.12 ±0.25 ±0.16 ±0.02 M(max) d M(mean) M(max) d T * n• Flog M(max) M(min) d d (37) (38) Absolute magnitudes of CVs 45

Figure 6. Correlation between outburst duration ¿sTn and orbital period.

The log [ ] factor in equation (38) can be approximated in the range 10

Again the coefficient in equation (32) is not well enough known to exclude the possibility that equation (39) is in fact independent of Tn. However, this equation makes the prediction (based on the model for DN outbursts that we are exploring) that the duration of DN outbursts should be a function of P.

From the outburst characteristics of DN listed by Szkody & Mattei (1984) we select the time spent within 0.5 mag of maximum as characterizing our ATn. Their values, supplemented with widths of ‘narrow’ outbursts (which appear to correspond most closely with the parameter measured by Szkody & Mattei) from the compilation of van Paradijs (1983), give the correlation with P shown in Fig. 6. The linear least squares fit to the points is log Arn=0.00+0.087 P (hr). 6 V ' (40) ±0.08 ±0.016

A plot of AT; versus Tn for the above stars, supplemented with additional points for the few known stars with Tn>200 day, shows that for A T;>4 day there is no correlation between A Tn and

Tn. Although for ATn<4 day we find Tn only in the range 10

£v (relative to the mean) radiated during an outburst, instead of the amplitude A': log

£v=logAT;+0.4 A' which, from equations (31) and (40), gives log £v—0.82 log AT; (day)+0.007 P (hr) (41) ±0.11 ±0.016 or EvttTn independent of P within observational uncertainty.

4.9 THE SUPEROUTBURSTS

From Table 3(a) we derive the result* (see also Vogt 1981), displayed in Fig. 7, that there is a tight *HT Cas is omitted from consideration as its supermaximum recurrence time is very uncertain (Wenzel 1985) and it appears to have been for many years in a state where supermaxima did not occur at all (Mattei 1986, private communication).

© Royal Astronomical Society • Provided by the NASA Astrophysics Data System 46 B. Warner

Log Ts

Figure 7. Relationship between supermaximum recurrence time-scale Ts and normal outburst time-scale Tn.

linear correlation between log Ts and log Tn, given by log Ts=0.40 log rn+1.73. ±0.06 ±0.09

This shows that rs=rn when log Ts=2.88±0.18, i.e. atTs=Tn=750±300 day, which is compatible with the observed property that for 7^400 day there is no distinction between normal and superoutbursts [Table 3(a) , supplemented with the known properties of such SU UMa stars as WZ Sge and VY Aqr].

The plot of As versus log Ts shows considerable scatter (not illustrated here), probably due partly to uncertainties in As because in some stars only a rough estimate is available of m^(super) rather than the better quality, time averaged ray(max) available for normal outbursts. If the An and Tn of stars longward of the orbital period gap are included in the same diagram, the SU UMa stars form a separate group, which does not support the suggestion of van Paradijs (1983) that the superoutbursts of SU UMa stars and the normal outbursts of the UG and ZC stars are of the same kind.

5 Classical novae

5.1 ABSOLUTE MAGNITUDES OF CLASSICAL NOVAE

The absolute magnitudes of CN during eruption, and particularly at maximum brightness, have long been a subject of special interest in connection with their uses as extragalactic distance indicators. Early studies, using distances derived from interstellar lines, galactic rotation, tri- gonometric parallaxes and the expansion-parallax method, demonstrated (see reviews by Payne- Gaposchkin & Gaposchkin 1938; Payne-Gaposchkin 1957; McLaughlin 1960) that novae reach at

least Mv=—1 at maximum brightness. From these data, McLaughlin (1942) noticed that slow novae were on average approximately two magnitudes fainter at maximum than fast novae. A few

years later he discovered the Mv(max) - rate of decline relationship (McLaughlin 1945) which has

since been a valuable source of estimates of Mv(max).

Until recently the correlation between Mv(max) and tn (the time in days taken to fall n magnitudes from maximum brightness) has shown a scatter of ±1 mag about the mean relation-

© Royal Astronomical Society • Provided by the NASA Astrophysics Data System 198 7MNRAS.227. . .23W evaluation oftheabsolutemagnitudesatminimumlight. i^10 day,t\.Withthisconversion,welistinTable4alltheCNforwhichdataare sufficiently complete,orforwhichfurtherobservationshaveagoodexpectation,toleaduseful comparison betweentandiforthosestarsincommonthetwolistsshowsthat novae priorto1956,andDuerbeck(1981),wholistsforbotholdrecentnovae.A can provideM(max)forallCNwhoseratesofdeclineareknown. Mv16.5p -7.3: 7.Ip>15p -7.8 7.0B19.3B1.65 -6.1 4.IB14.9B1.25 -6.7 6.2p17.5p -8.1 7.5p20.0:p -7.5 10.3v20.5p -7.3 6.7B17.6,1.6 -7.7 5.5:p17.3:p -8.1 7.6:p18p -9.4 -1.4v11.60.5 -7.7 7.418.Ip2.6 -7.9 6.1:p17.8:p -7.9 5.Op17.5:p -5.4 7.Op16.5p2.04 -7.6 10.5:p>20 -8.1 6.4p19.Op -4.3: 8.6p17.8p -8.3: 7.5p>13.5p 8.0:p 17:p 11 :p15.5p 5.0: 14.3? 6.Op 18.Op Absolute magnitudesofCVs47 A v >10.0 >6 >7.9 12.3 12.0 10.8 11.3 12.5: 10.2 10.9 11.8: 10.4: 13.0 10.7 11.7: >9.5 12.5: 12.6 9.0: a 4.7 9.3? CN 9.5 4.5: 9.2 M '(min)Refs -0.4' >0.5 <4.3 >1.9 4.5 4.7 4.6 4.4: 2.7 3.6 4.1: 2.3 3.6 3.0 3.8: 4.6: 4.1 4.5 4.9 18 10,11 9 198 7MNRAS.227. . .23W 48 V841 Oph184856 V2024 Oph196715 V972 Oph195750? V849 Oph191988 V840 Oph1917 V2104 Oph197615: KT Mon Table 4-continued V400 Per197422 RR Pic192580 BT Mon V1668 Cyg1978 V1500 Cyg1975 V1330 Cyg1970 V476 Cyg1920 V465 Cyg1948200: GK Per19016 GR Ori1916 GI Mon HR Lyr Q Cyg1876 CP Pup19425 RZ Leo DK Lac V533 Her1963 V446 Her1960 V360 Her1892 DN Gem DM Gem HR Del DI Lac DQ Her V450 Cyg1942110 V693 CrA19816 Star Datet2 IM Nor IL Nor CP Lac Royal Astronomical Society •Provided bythe NASA Astrophysics Data System B. Warner 1920 >30 1893 1942 1918 1939 140 1919 45 1918 1950 1910 1936 1934 1912 1903 1967 152 20: 20 54 20 13 26 12 19 11 11 12 17 67 2 5 5 6 >-7.1 M(max) -10.0 v -7.6: -6.0 -9.0 -6.1 -7.5 -7.9: -7.9 -8.3: -6.5 -6.5 -7.6 -8.0 -8.8 -5.5 -8.8 -5.2: -6.7 -7.6 -7.6 -9.0 -7.3 -5.4 -8.2 -8.1 -8.1 -9.0 -6.3 -7.7 -8.2 -5.8 -8.8 m (max) 11.5p 10.5p 8. Op 7.2:p 4 :v 8 .Op 0.2v 8.8v 4.8v 3.3v 3. Ov 2.0B 2 .Ov 0.2v 6.5 :p 5.2 :p 2 •lp 3. Op 3.6B 7.5B 7.3 :p 1.2v 9.5 :v 9.0B 4.0 :p 2.8p 4.8v 7. Op 9.8p 5.0 :p 4.3B 1.3v 6. Ov 6.5B 6.3p 6.5v >20 >18 >16.5p >17.5 >20 >20 :p >16.3p >16p >19v m(min) 20: 13.3v 17. Op 19.5p 13. Ov 15.5p 16.2 15. Ov 12.3V 15. Ip 16.5V 12.lv 14.9 16.3B 18. IB 17.5 :p 16.5 15.8p 15.6p 14.7v 15.8B 15.8B 17.5p 15.5p 14.5B 14.4p 15.8p 0.7 0.72 0.8 0.04 1.25 0.85 0.56 0.45 0.63 0.25 0,16 0.27 1.10 1.25 1.4 0.45 1.4 1.5 1.7 1.2 1.3 Av >11.2 >10.3 >11 : >11.5 >12.5 >8.5 >8.5 >8.5 12.8 10.5: >9.7 11.1 11.5 14.8 14.3 10.6 14.2 10.2 11.8 13.5 11.4 13.4 12.2 11.9 14 .: 10.5 10.2 13.0 11.7 "CN 5.7 9.3: 8.8 9.5 9.9 7.0 9.3 M'(min) Refs v >3.3: >0.2 >4.3 >0.6 >4 >5.0 >3.7 -1.8* 5.0 4.0 4.0 2.8: 2.9:* 5.8 3.7 2.5 2.6 2.9: 2.6 3.7 5.4 5.0: 4.5 3.5 3.4 5.9: 4.3 1.8: 4.1 4.0 7.1 4.5 6.3 5, 6 8 18 1,1: 9 198 7MNRAS.227. . .23W V4065 Sgr1980 V1015 Sgr1905 V4021 Sgr1977 V1012 Sgr1914 V3964 Sgr1975 V3890 Sgr1962 V3889 Sgr1975 V999 Sgr1910 V927 Sgr1944 V3888 Sgr1974 V3645 Sgr1969 V2572 Sgr1969 V1944 Sgr1960 V909 Sgr1941 V1583 Sgr1928 V1275 Sgr1954 V1175 Sgr1952 V787 Sgr1937 V1059 Sgr1898 V1016 Sgr1899 V732 Sgr1936 Table 4-continued V726 Sgr1936 V630 Sgr1936 V441 Sgr1930 V363 Sgr1927 KY Sgr HS Sgr Star Date GR Sgr FM Sgr FL Sgr AT Sgr HS Sge WY Sge HZ Pup HS Pup DY Pup © Royal Astronomical Society • Provided by theNASA Astrophysics Data System 1926 1901 1924 1926 1924 1900 1977 1783 1902 1963 1963 220 3.8 t My(max) 120: -5.7: 120? 2 118 -5.7 50 17 20 20 15 23 15: 10 12 32 45 75: 40 15 -7.9 16 -7.8 18: -7.7: 35 33 10: -8.3: 6: 4 -8.8 -6.6 -7.8 -7.6 -5.0 -7.6 -7.9: -8.3 -7.9 -8.1 -9.3 -7.4 -7.1 -6.7 -9.2 -6.2 -6.8 -7.0 -7.0 9.0 m(max) 11.6?p 11.4?p 8.6p 8.8p 8. Op 6.5 :p 8.4p 7.0 :p 6.5 :p 8.0 :p 8. Op 2.0 :v 7. Op 8.9p 6.3p 7.8p 7. Op 7.3 :p 6.9 :p 6.8p 9.4p 6.5p 9.0 :p 4 .Ov 8.0 :p 7 •9:p 7 •2:p 8.6p 8.3p 8.7 :p 7.2p 7 •7p 8 .Op 6. Ov 7. Op >12p >13p >17p >16.5 >13 >12 >16.5p >16.Op >16.5p >16.Op >16.5p >16p >16.5p >13p >16.5p >2 Op 20 :p 17.2p 18p 14.8p 13p 16.5p 16.5p 14.9p m(min) 14.4V 16. Op 16.5p 16.6p 16.5p 19.5v 18.5p 16. Op Absolute magnitudesofCVs 1.0 1.6 Av >12 >9 11.6: >7.6 10.0: >9.2 >9.2 >-0.1 14.5 6.2 >7.1 >-0.3 >9.5 >2.4 >7.5 >0.8 a >8.1: >1.3: 10.4 1.2* >9.3 >5 >7.8: >0.1: 13.5 10.8 8.5 8.5 3.5 6 8.0: -0.1:* cn 8.0 1.8: 4.9 -0.8:* 5.2? * 7.9 0.0* 9.0 My'(min) Refs >0.0 >5 2.6 0.9* 3.8 3.3 * 49 198 7MNRAS.227. . .23W 50 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Star Datet2 V4077 Sgr198220: DZ Ser1960 T Sco186011 V696 Sco1944 KP Sco192821 FH Ser197040 MU Ser19835 V723 Sco195211: V720 Sco19509 V721 Sco1950120 LW Ser197825 EU Set194914 Re.fexsng.üs. XX Tau192724 V368 Set197016 FS Set195214 Nelles (1984);5.Caldwell(1982);6.Brosch (1981); 7.McLaughlin RR Tel1949670 V373 Set197543 FV Set1960 Table 4-continued X Ser1903400: Rosino (1974);10.Chiasson(1977);11.Vrba, Schmidt&Burke CN Vel1905400 CT Ser1948100: & Willerding(1979);3.Duerbeck(1983);4.Duerbeck, Geffert& 1. DiPaolantonio,Patriarla&Tempesti(1981); 2.Duerbeck,Lemke Borra &Anderson(1970); 17.Tempesti(1972);18.Cecchini& LU Vul196819 NQ Vul197643 Gratton (1942). LV Vul196821 PW Vul1984 (1939); 8.Kruszewski,Semeniuk&Duerbeck(1983); 9.Ciatti& (1977); 12.Deurbeck,Rindermann &Seiter(1980);13.vandenBergh (1976); 14.vanGenderen (1979);15.Burkhead&Seeds(1970);16. B. Warner M(max) m(max) v -8.2 6.7p -7.6: 8.0p -7.5 9.4p -6.8 4.4v -7.3 8.0p -8.4 7.8p -8.2: 9.8p -5.7 9.5p -9.0 7.7p -7.9 7.6p -7.9 10.1p -7.4 6.0p -3.9 6.9p -7.8 6.9p -5.9: 5.0:p -4.4: 8.9p -6.8 7.3p -4.4 10.2p -7.6 9.2p -7.5 4.5v -6.8 6.5p 7.5p 8.0 :p 7.0p 6.4v >2 0p >16.5p >16.5p >18.0p >18.0p >2 0p >16p >16.5p >21p' m(min) Ay 16.9 22p 16.lv 21p 17.0p 16.6p 16.5p 19.3p 18.3p 18.5p 16.5p 16.9p 17.6p 17 :v 2.3 2.6 1.6 1.0 2.5 1.7 1.4 >12: >4.4: >10.2 >12.3 >11 : >11.8 >7.1 >9 >8.5 11.7 12.2 14 >6.3 10.5 12.4 11.2 12.4 11.1 10.6: 8.9: 9.4 6.5 9.4 9.7 >-0.4 >1.8 >2.8 >4.3 -0.3* >1.9 >4.2 4.9 15,16 4.0: 1.5 3.1 4.6 5.8 5.0: 4.4 4.9 17 4.3 >5: 13,14 9 198 7MNRAS.227. . .23W range toM^(max).AtmaximumlightofaCNwehave m(max)=M(max)—5+5 logd+A where, asaresultoftheapproximatesphericityexpandingnovashell,correction m(mm)=M(mm)-5+5 logd+A+A-AM(i) AMv(i) isnotrequired.Atminimumlight My(min)=Mv/(max)+Range+A -AMv(i).(45) and hence As showninSection2,A=0exceptforthelongestperiodsystems(nosignificantcontributionto Mv(min)=M(max)+m(min)-m(max) knowingthatitwillbeindependentoftheoftenheavy for thosesystemswhereiisknown.However,statisticalpurposeswecanuse v interstellar extinctionthataffectsCN. A ismadebythebrightspotsinCN).WecanthereforededuceMy(min)forindividualCNonly unavoidable mixtureofmand,therewillalsobesystematicdifferences(butprobablynot Fortunately, theunreddenedcoloursofCNatmaximumandminimumlightarenotgreatly great importancehere)betweenifoundfromvisualandphotographiclightcurves. v is insensitivetothechoiceofmorg,providedsamesystemusedforbothm(max)and m(min). Thedirectapplicationoftheexpansion-parallaxmethod,oranytechniquesother different fromzero,soanymethodwhichderivesM^(min)byanextinction-independent We havefoundonlyfourCNforwhichdistancesareavailablebothfromtheÄ'-magnitudesof 5.2 COMPARISONOFDIFFERENTMETHODS secondaries andfromareliableindependentmethod.ThesearelistedinTable5. than theM(msix)-trelationship,requiresameasurementofwewillthereforeconcentrate here onapplicationofequation(44). methods. Inparticular,thesamplecontainsCNrangingfromveryfasttoslowyetproduces v the sameorderingamongM^(min)byÆT-magnitudemethodandalternatives.The 3 maginM^(min),isencouraging. absence ofanyverylargedifferences,despitetherangeafactor25intandspread vpg 5.3 ACCRETIONDISCINCLINATIONS known, isgiveninSection5.4. n fortunate thattheeclipsingsystemsaffordbestopportunity offindingiforthehighinclination Direct determinationsoforbitalinclinationsareavailable forafeweclipsingCN.Althoughitis vP A aremostlyfromDuerbeck(1981). vn Notes toTable4: m(max) aremostlyfromEvans & Bode(1987)andincludeextrapolatedvalues. m(min) arefromtheGCVS,with improvementswherepossible. t arefromWarner(1986b)and Duerbeck(1981)-seeSection5.1. 2 *See Section5.6andTable8. v 2 In contrastwiththesituationofDN,inCNwecannotdeduceM{m\n)simplybyadding v There isconsiderableinhomogeneityinthedatagivenTable4:notonlytherean The comparison,althoughverylimited,givessimilarvaluesofM^(min)bythevarious A comparisonwithMy(min)derivedfromthesurface brightnessmethod,whichrequiresitobe © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Absolute magnitudesofCVs51 52 B. Warner Table 5. Comparison of absolute magnitudes. star p h + ++ ( ) mv*(max) mv(min) Av t2 Mv**(max) d(pc) Mv'(min) Mv'(min)

DQ Her 4.65 1.3 14.7 0.16 67 -6.3 327±84 7.1 7.0±0.5

HR Del 5.14 3.3 12.1 0.56 152 -5.4 285 3.4 4.2

V841 Oph (7.0) 2: 13.3 1.25 56 -6.5 255 4.8: 5.0

GK Per 47.9 0.2 13.0 0.7 2 -8.8 337 4.0 4.7

* From Evans & Bode (1986). **From equation 44. + From My' (min) = M^max) + n^imin) - m^max) ++From My'(min) = m^min) +5-5 log d - ^

Notes: DQ Her m^min) from Patterson (1979a); (for ail stars in Table 5) from Duerbeck (1981); d from Young & Schneider (1981) - from red spectrum of secondary and assumption that it is a normal main-sequence star, which it is according to Patterson (1984). HR Del d from K of Berriman et al. (1985) and equation (3). V841 Oph d from £ of Berriman ei a/. (1985) and equation (3). GK Per Sherrington & Jameson (1983) gave d=126 pc from JHK photometry and the spectral type K2IV of the secondary. From their V-K colour (assumed to be entirely from the secondary) corrected for redden- ing, we find SK=3.11. The other quantity needed in equation (1), namely R2/Rq, is found from Patterson’s (1984) equation (11) and Af2=0.2 MQ. The long period of GK Per excludes use of equation (3). Use of the Sherrington & Jameson distance would give M^min)=3.0. Note that in Tables 4 and 5 no correction for the contribution of the secondary has been made.

systems where AMv(i) [equation (4)] is most sensitive to /, for our present needs we would like to

keep errors in AMv(i) to ^0.2 mag, which requires i to be known to ^10° at intermediate inclinations and ~20° for small inclinations. There are very few CN of intermediate inclination that can meet these strictures. Eclipses are observed in T Aur (Walker 1963; Bianchini 1980), BT Mon (Robinson, Nather & Kepler 1982), RR Pic (Haefner & Metz 1982; Warner 1986a) and WY Sge (Shara & Moffat 1983; Shara et al. 1984), all of which furnish reliable orbital inclinations. The case of DQ Her illustrates a rarely occurring but important point: interpretation of the eclipse profile leads to 680^/^85° (Warner 1976; Young & Schneider 1981) but modelling of the phase variation during eclipse of the 71-s oscillations (Petterson 1980; O’Donoghue 1985) requires /=89°. As the accretion disc subtends an unknown half-angle Ai at the primary, these latter studies actually measure /+À/ which would be used in place of i in equation (4). However, the intensity distribution of the reprocessed beam from the white dwarf probably does not appear at all like the limb-darkened distribution of the underlying disc, so the i=89° from the phase shift arises from a different weighting over the surface of the disc and is not necessarily the precise value to be used in equation (4). There is no doubt, however, that in DQ Her /+À/ is close to 90° where the correction AMy(0 sensitive to / and uncertain. The systems of very low inclination can usually be recognized by their narrow emission-line widths (e.g. V841 Oph and DI Lac: Kraft 1964) or small Ki. The later is not an unimpeachable -1 diagnostic: in the eclipsing GN WY Sge, Kx is only —50 km s (Shara etal 1984). In Table 6 and its supplementary notes, CN with inclinations previously measured or estimated by the above methods are listed. From these data it emerges that, with the caveat that the number

© Royal Astronomical Society • Provided by the NASA Astrophysics Data System 198 7MNRAS.227. . .23W presumably arisesbecausetheemissionlinesareproducedinavolumethatisopticallythinand emission lines,particularlywithHorwhichshowsawiderangeintheCN:Fig.8.Thisrelationship of objectsissmall,thereagoodcorrelationbetweeninclinationandtheequivalentwidth for whichtheorbitalperiodisknownorhasbeenestimatedfromacolour-periodrelationship estimates ofitoseveralmoresystems;thesealsoarelistedinTable6.OnlythoseCNincluded not totallyobscuredbythediscathighinclinations.Itprovidesuswithameansofextendingour The CNlistedinTable6aretheonlyonesthatwecanplaceM(min)-Pdiagram.As 5.4 CLASSICALNOVAEWITHKNOWNORBITALINCLINATIONS previously pointedout(Warner1985b),studiesofCNatminimumhavebeenneglectedrelative (Vogt 1981). to thoseoftheDNandasaresultfeworbitalperiodsareknown.Fig.9confirmsconclusion, based onasimilardataset,thatM(min)forCNshowquitesmallspreadaboutanaverage certainly amountsto±0.5mag],thequiescentCNdiscsandDNatmaximafollowsame equation (44)andtheadditionalproblemsofdeterminingra^max),m(min)AM(/), observational uncertainty[whichfortheCN,includingerrorsintandcoefficientsof DN atmaximumofoutburstnowsuggestsanalternativeinterpretation,namelythatwithin Mv(min)=4.3. However,theinclusioninFig.9ofmeanrelationshipfoundSection4.1for DI Lacissuggestive.AtP=2day,GKPer(Table5)withi~75°(Warner1986b)andhalfofthe uncertainty inPformanysystems,todetectadefinitetrendwithP,butthebrightermagnitudeof rotational period],thebaselineinPistoosmall,givenrelativelylargeerrorsand modulations at95mininCPPup(Warner1985c)haveyettobeprovedanorbitalratherthana relationship. BecauseoftheabsenceCNwithP~ljhr[thespectroscopicandphotometric rather thanmagneticbraking. evolved secondarywhichmaybetransferringmassataratedeterminedbynuclearevolution v the CN.OnlyforDILacisthereseriousdiscord,whichcouldberemovedif/~50°ratherthan Fig. 9. or 86°insteadofthe89°listedinTable6,thenDQHerisnolongerdiscrepant.Twoequally acceptable valuesofM(min)areavailableforHRDelfromTables5and6;bothindicatedin V-flux contributedbythesecondary,hasM(min)~3.6,butsuchalong-periodsysteman 30° assumedhere. v vV 2 v y Fig. 9illustratesthesensitivityofM(min)toadoptedvalueiforDQHer:ifweuse/=87° As canbeseeninTable6,thesurfacebrightnessmethodgivessurprisinglygoodM(min)for v v © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Figure 8.DependenceofHörequivalent widthonorbitalinclinationforclassicalnovaremnants. Absolute magnitudesofCVs 53 54

© Royal Astronomical Society • Provided by theNASA Astrophysics Data System Table 6. Orbital inclinations and absolute magnitudes of classical novae. + 4 $ sr •H •H C ~ .G »—ico +J G oo vo r-oo^ oo a o >i m oo CM «H 0" invo oo co «sr ^oo & Xi o o «H CM o CM i I vo m in cm CM oo vo .. co 1 1 ■K + •H -H ■^r rH En ''3 «H U 4-> -P g P o 0 CT (0 G G 0 o Q M •H p -H •H rji ^ IN i—I 0) £) T3 _ ‘W TJ Ä O 0 H p •G 00 s ■P cd g U 0 ^ G w (0 G > g a Ä M CQ o ° s lO M C0 § * M TJ PQ 4-> cd G ü (ü Q) M O P G o 198 7MNRAS.227. . .23W from veryfasttoslownovae(Payne-Gaposchkin1957).Thereisnocorrelationbetweent investigate possiblecontaminationofTable4byerrorsandunrecognizedinterlopers.Forthis purpose weturnbrieflytoexaminetherecurrentnovae. and Mv/(min),norbetweentP. The observationaldatabaseforrecurrentnovae(RN)isnotveryextensive.Definiteorbital 5.5 ABSOLUTEMAGNITUDESOFRECURRENTNOVAE periods areknownonlyforTCrB(P=228day)andRSOph(P=230day:Garcia1986).The V476 Cyg Notes toTable6: Notes toTable7.Withintheuncertaintiesofmethods,agreementisexcellent,which calculated fromtherateofdecline[equation(44)]andindependentmethodslistedin secondaries inV1017SgrandUScoareGgiants,whichwouldgiveP~day. V603 Aql 2 WYSge V1500 Cyg Q Cyg 2 HR Lyr RR Pic V841 Oph DN Gem T Aur DQ Her FH Ser V533 Her DI Lac BT Mon HR Del The My(min)plottedinFig.9includenovaewithtrangingfrom2to152day(Table6),i.e. Next wewanttoconsiderwhatmaybelearnedfromtheinTable4,butfirstmust Table 7bringstogetherinformationfromwhichacomparisonmaybemadebetweenM(max) 2 K © Royal Astronomical Society • Provided by theNASA Astrophysics Data System P fromVogt(1981);VP(Ha)anuncertainmeasurementShara(1986,privatecommunication). observed bySharaetal.(1987)givesm~18.5.Thereisevidence,therefore,thatV476Cyg,having The pre-novahadmv(min)>21,butthepost-novahassettleddowntom(min)=16.3.Forreferences was foundfromtheshellstructurebyMustel&Boyarchuk(1970)and15°Warner(1976)vsini been constantformanydecades,maynowbefadingrapidly. £-V=0.15, soitisirrelevantwhethertheearliermeasurementsweremor.Thefluxdistribution Gaposchkin (1957)itislistedas16.2andconstant(onaverage).Bruch(1984)lists17.1gives Our choiceofm„(min)(Table4)requiresanexplanation:inthethirdeditionGCVSandPayne- Wehinger 1977)soW(Ha)isnotusedhere. i fromeclipses;W(Ha)estimatedpublishedspectra(Shara&Moffat1983). i isfromthepresenceofshalloweclipses,probablyabrightspotonrimaccretiondisc and discussionseeWarner(1985b,c).iisfromSanyal&Willson(1980). and oftheaccretiondisc. Pfrom Vogt(1981);W(Ha)fromShara(1986,privatecommunication). tisveryuncertainforthisstar P fromVogt(1981);W(Ha)Shara(1986,privatecommunication). (Haefner &Metz1982;Warner1986a).SpectrashowRRPictobehydrogen-poor(Wyckoff W(Ha) isanaverageofWilliams(1983)andShara(1986,privatecommunication).Aninclination16° P fromVogt(1981);W(Hör)Williams(1983):Shara (1986, privatecommunication)gives (see lightcurveCecchini&Gratton1942)but/=80dayisbetter definedandsuggests40-50day. of Shara(1986,privatecommunication)andWilliams(1983). P fromVogt(1981);inarrownessofemissionlinesandabsence ofdetectable.W(Hör)isaverage i fromPetterson(1980)andO’Donoghue(1985)-butseediscussion intext.W(Ha)fromWilliams i fromwidthofeclipse[thevaluei=57°givenbyBianchini(1980) andrepeatedbyRitter(1984)isonlya v i fromSoderblom(1976),Hutchings(1979)andSolf(1983).Ha is contaminatedwithshellemissionand lower limit].W(Ha)istheaverageofWilliams(1983)andShara (1986,privatecommunication). (1983). W(Ha)<4Ä. v vpg i fromnarrownessofemissionlines (Kraft1964)butexistenceofmeasurable^(Ritter1984).W(Höt) is i fromeclipsewidthanddepth (Robinson, Nather&Kepler1982);W(Ha)fromWilliams(1983). P fromVogt(1981);iHutchings (1972). i fromabsenceofeclipses(Robinson &Nather1983)butlargewidthofemissionlines(Williams 1983). therefore rejectedhere. the averageofWilliams(1983) and Shara(1986,privatecommunication). 2 3 Absolute magnitudesofCVs 55 198 7MNRAS.227. . .23W 56 Figure 9.Absolutemagnitudesoftheaccretiondiscsclassicalnovaeasafunctionorbitalperiod.Theeffect connected withaverticalline. changes intheassumedinclinationofDQHerculisisshown.TwoindependentestimatesMforHRDelare proposed (Webbink1976)thattheTCrBeruptionisanaccretionratherthanathermonuclear establishes empiricallythattheMy(max)-rrelationshipforCNappliestoRN.Asithasbeen event, thisisnotatrivialresult. the sameasthoseofCN.ThespectrumTPyxatquiescenceisdominatedbynarrow secondaries. Aspointedoutpreviously(Warner1976)thetrueamplitudesofRNmaywellbe equation (4)thisgivesMy(min)~3.0forTPyx,whichisinaccordwithTable6ifPyxhasP~1 emission lines(Warner1976)suggestinganaccretiondiscofsmallinclination.FromTable7and T CrBDistancefromDuerbeck(1981),basedonexpansion-parallax method,andSherrington&Jameson day. T PyxDistancefromDuerbeck(1981)andBruch, &Seitter(1981).AfromBruch(1984). The rathersmallselectionofCNthatwehaveinvestigatedinTable6givesthestrongimpression V1017 SgrKraft(1964)gives G5IIIp forthesecondary,whichdominatesvisiblespectrum. Thisagrees,after 5.6 PROBLEMSTARSINTABLE4 v RS OphDistancefromDavies(1986)basedoninterstellar lines,HIabsorption-lineprofilesandabsolute Notes toTable7: that M(min)^3.0andhence^2.0.Thereare,however,afewstarsinTable4which U Scomv(min)andAfrom Hanes(1985),whofindsaspectraltypeofGO(±5)andindeterminate luminosity show unusuallysmallrangeswithresultingMv(min)<2.These‘problem’starsarelistedinTable 8. 2 other thanarealfadingoftheCNitselfbeyondnormalMy(min),thatincreaserange v v v The valuesofinTable7areessentially(exceptforTPyx)theluminosities There areseveraleffectsthatmaycausetherangeAtobetoosmall(butprobablynone, CN © Royal Astronomical Society • Provided by theNASA Astrophysics Data System magnitude ofthesecondary.AfromBruch(1984)andCassatella etal.(1985). for thesecondary.Tobeinaccord withM^min)ofTable7theluminosityclasswouldbeII-III (Allen Bruch (1984). dereddening, withV-K=3.07found byFeast&Glass(1974).M=0JforG5III(Allen1973).A from (1983) from^-magnitudeofthesecondary. 1973). UScowouldthenhavean orbitalperiod~fewdays. v v v B. Warner Table 7. Recurrent novae. © Royal Astronomical Society • Provided by theNASA Astrophysics Data System «H g o u ■M 3 (d U 0) ft (0 +J o •H —' 00CM + * !>egrH 2 ooi- >1 OCM H CO sf 1 . I -H 3, VOCO Z U G > I ^ CM 00 VO O r-t oo vo cn oo oo 00 I I eg oo in in oo oo cr> O cm w O' CM Absolute magnitudesofCVs57 U cr> rH 0 -H O fn T3 ft 8[evenatm(max)~6manyapparently aremissed:Warner1987c]sothe only oneofwhich(USco)issofarrecognized.Thecompleteness ofdiscoverynovaoutburstsis recognition ofRNisdifficult:fromTable7weseethat nonewRNhasbeenfoundsince1946. DN ofSUUMatype(Richter 1983).Thislatterisanotherpossiblecontributing classtoTable8, but probablyonlyforthose novaeforwhichspectrawerenotobtainedatmaximum light(theDN One, however,hasbeenlost:VYAqr,onceclassified asaRN,isnowrealizedtobelong-period because theyarediscrepant comparedwiththoseinTable6,butbecauseweexpect theretobea r are distinctiveinnotshowing anexpandingshellduringeruption). y (i) Unobservedorpoorlyobservedmaxima,leadingtoM^max)toofaint.Payne-Gaposchkin (iii) Unrecognizedrecurrentnovae.Payne-Gaposchkin(1977)considersthistobeadistinct (ii) Incorrectidentificationofthenovaremnantwithabrighterstar.McLaughlin(1960) From Section5.5andTable7weseethat(iii)couldbeanimportantcontaminantof4. We concludethatitisnotunreasonable toviewthestarsinTable8withsuspicion -notmerely © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Table 8.Classicalnovae:problemstars. AR Cir1914208 KT Mon194220 FM Sgr192615 Star DatetM^max)m(ax)m^min)RangeNotes GR Sgr1924120? HS Sgr1901120: V630 Sgr19364 V1016 Sgr189912 V1944 Sgr1960 V2572 Sgr196920 2. Payne-Gaposchkin(1977)sayspossibleRN. 2v 3. Payne-Gaposchkin(1977)saysnv^imaxjisveryuncertain. 1. McLaughlin(1939)suspectswrongidentificationofremnant FS Set195214 4. Thetruemaximumprobablywasunobserved. -7.6 -5.1 -7.9 -9.2 -8.1 -7.6 -7.9 10.3 11.4? 11.6? 10.1 8.6 9.8 4.0 7.0 6.9: 6.3 15.0 15.5 16.5 16.6 16.5 14.4 14.9 13 14.8 16.6 10.4 4.7 5.7 7.9 5.2? 4.9? 8.0 8.5 6 6.5 -0.4 -1.8 -0.1 -0.3 0.0 1.2 0.9 198 7MNRAS.227. . .23W number ofobjectsintheabovecategories(i)to(iii)andthesewillatleastcontributeTable8. faint). Forthetimebeingweexcludethemfromfurtheranalysis. Spectra ofalltheobjectsinTable8arerequiredtochecktheirnature(noneisparticularly Table 9givesthemeanapparentrange,Äc^=mijmn)-m{m2iX)andM'(mm)asafunctionof 5.7 DISTRIBUTIONSOFMv(MIN)ANDRANGE speed class,basedonthedatainTable4.Uncertainhavebeengivenhalfweight.Therms ^=Ä5—AM(0, sothe^4¿inTable9shouldbeincreasedby0.4magtoobtainbetter very slownovae,whichhavei>250dayandareconsequentlydependentonanextrapolationof Within thespreadinvalues,allofM(min)areequal[withpossibleexceptionvery effects oftheAM(/)correctionanddoesnotrepresentactualspreadinAnorM(min). dispersion onallofthemeanvaluesis~±1.0mag,butthiscourseresultspartlyfrom well-known correlationbetweenapparentrangeandspeedclass(Payne-Gaposchkin1957). have M^(min)=4.0,whichgivesM(min)=Mv(min)-AM(i)==4A,inreasonableagreementwith equation (44)whichmaynotbevalid].ExcludingtheWSnovae,otherstakenalltogether will significantlydistortthederivedvalues^4¿.Thetruerange,Ä:,foralargesampleis Because ofthesmallnumbersCNinvolvedwedonotsampleuniformlyoverinclination,which but herewecannotimprovethestatisticalanalysisbytakingallCNtogether.Table9shows the weightedmeanM(min)=4.1±0.4obtainedfromTable6. indicated. shown. Forthestarswithknowninclination(Table6) theeffectofcorrectionAM(i)isalso inclination oftheaccretiondisc[onassumption that alldiscshaveM(min)=4.4]arealso estimates ofthetruemeanranges. v included intheanalysis.However,ifM(min)—constant thentheonlyeffectistobias CN ofsmallrange-manythosewithlarge fadebeyonddetectabilityandcannotbe Nvn 2 v VCv observational sampleawayfromtheraresystemswith verylargeinclinations.Theredoesnot inclination thathasfaded beyond reachandhencehasbeenexcludedfromTable 6. have 11.6250 151-250 26-80 11-25 81-150 t(d) 0-10 2 26 12 n 8 4 3 3 Absolute magnitudesofCVs m M' 3.7 4.4 4.4 v 4.1 5.2: 28 12 n 9 3 4 3 } A' 13.2 11.3 10.9 9.6 9.4: CN 59 60 B. Warner

Figure 10. Amplitude-rate of decline relationship for classical novae. The amplitudes A'CN are uncorrected for inclination of the accretion disc. The effects of different inclinations, corresponding to AMv(/)= -1,0,1 and 2, are shown by the sloping lines. For stars with known inclinations (Table 6: abbreviated names are given here) the effects of making the corrections AMy(i) are shown by arrows: the result is a great reduction in dispersion for those stars.

addition influenced by disc inclination. There is therefore no longer a mystery (Payne-

Gaposchkin 1977) as to why the range of the t2=67 day nova DQ Her should exceed those of the Very Fast novae V603 Aql and GK Per.

6 Absolute magnitudes of nova-like variables

The nova-like (NL) variables show the spectroscopic and short time-scale photometric behaviour of CVs but have not been observed to erupt (Warner 1976); a few of them (the MV Lyr stars) spend part of their lives in a low state of luminosity. This class of CV is generally considered to include pre-novae, unrecognized post-novae and ZC stars permanently (or at least for long stretches of time in the case of the MV Lyr stars) in standstill. The NL class more generally includes a mixture of other idiosyncratic objects; as more observations of these have been made, common properties have been recognized which have resulted in the definition of further groups such as the polars and intermediate polars. There are still a few stars such as AE Aqr that appear unique. Among the NL there is a subgroup which has broad absorption lines in the visible spectrum as well as emission lines; these are referred to as UX UMa stars (Warner 1976). Except for AE Aqr we refer to the remainder as RW Tri Stars. The observational data (Table 10) for the NLs are less extensive and less homogeneous than for the DN and CN. In the absence of outbursts we do not have the special methods of determining distances offered by the latter classes. Only the X-band technique or other uses of the second-

© Royal Astronomical Society • Provided by the NASA Astrophysics Data System 198 7MNRAS.227. . .23W some havelowstatesofmasstransfer.Inbothcircumstancesthesecondariesaremorereadily aries’ fluxesprovidedistances.FortunatelynotonlyareseveraloftheNLseclipsingsystems, observable. the regionwhereDNoutburstsshouldoccur.However,thesetwonon-eclipsingstarshavenot [whose uniquecharacteristicsarediscussedbyChincarini&Walker(1981)andPatterson and IXVel,fallbelowtheluminosityofZCstarsatstandstillarethereforeapparentlyin (1979b)] theNLsarelocatedingeneralregionofCNatquiescence.Twostars,CMDel met. WemustconcludethattheirsecondarieshavenotreallybeendetectedintheX-bandand been observedinlowstatesandatnormallightthecriteriagivenendofSection2arenot limits. ItmaybenotedthatthebrightNLsV3885SgrandRWSex(Table10),whicharesimilar possible misinterpretationofFig.11wehaveplottedtheMCMDelandIXVelasupper consequence thattheirluminositiesgiveninTable10areactuallylowerlimits.Inordertoavoid in mostrespectstoCMDelandIXVel,havebeenobservedtheX-bandwithoutcertain to theirM. detection oftheirsecondariesandthuscouldalsohavebeenincludedinFig.11withupperlimits try. TheMforMVLyrandIXVelfoundfromtheirestimatesofdistancediffermarkedly interpretation ofredspectraduringthelowstate,ratherthanmorepreciseX-bandphotome- there isreasonableaccordbetweenthemethods. those foundfromthesurfacebrightnessmethod(M£inTable10).Forotherstars10 pre- orpost-novae.Withthepresentdatatheredoesnotappeartobeanysystematicdifferencein between thosesystemsthatareZCstarsinextendedstandstillandmoreprobably luminosity betweentheUXUMaandRWTristars. v Figure 11.Absolutemagnitudes ofaccretiondiscsthenova-likevariablesasafunction orbitalperiod.The 7 Miscellaneousotherstars general locationsofthedwarfnovae atmaximumlight(Fig.1)andoftheZCamstarsstandstill (Fig.2)areshown. The magneticCVs(AMHerstarsorpolars),notpossessingaccretiondiscs,cannotbeplottedin Stars arelabelledwithabbreviated names(seeTable10). them amongtheDNatminimumlight(fig.7ofPatterson1984).Ofintermediatepolars v our M,Pdiagramsevenwhentheirdistancesareknown.Estimatesofhowever,place v v2 Absolute magnitudesfromTable10areplottedinFig.11.WiththeexceptionofAEAqr Another starwhichfallssuspiciouslylowinFig.11isMVLyrforthedistancebasedon With morereliabledistancesfortheNLvariablesitshouldbepossibletodistinguishinFig.11 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System Absolute magnitudesofCVs61 CT) co CM CM CM 00 r- r" S á CO SS 62 © Royal Astronomical Society • Provided by theNASA Astrophysics Data System

Table 10. Absolute magnitudes of nova-like variables. B. Warner p -H n S Ä o -p ^ M-l U tl o co CO 6 0) 00 G O Q> ^ ^ e (Ö 0) o CO o U tö O I P P OQ CO 170 pcfromtrigonometricparallax;Wargauetal.(1982)give¿¿—150E(B-V).i ¿¿from K(obtainedinlowstate)ofBerrimanetal.(1985)andequation(3).Vasilevskis(1975)give Schectman (1981),Robinsonetal.(1981).AfromChiapetti(1982). Limit ondfromabsenceofsecondaryspectrum(Young,Schneider&Schectman1981b);isame d andifromSherringtonetal.(1984). CM DelwasclassifiedasaDNbutisnowconsideredtobenova-like (Shafter1985). P fromShafter(1985);dKofBerrimanetal.andequation (3);¿fromofShafter(1985). source. P fromHutchings&Cowley(1984). d fromKofBerrimanetal.(1985)andequation(3).iPetterson (1980). from membershipoftheSiriussupercluster. (CPD-481577). dfromBerrimanetal.(1985)andequation(3). Eggen&Nienda(1984)give£¿=33pc eclipse. Weusethisratherthan £¿=600 pc,obtainedfromBerrimanetal.(1985)andequation(3), from d fromKofBerrimanetal.andequation(3);iKaitchuck, Honeycutt&Schlegel(1983);Afrom (CD-42° 14462). Oke &Wade(1982). d fromYamasaki,Okasaki&Kitamura (1983);ifromSchlegel,Kaitchuck&Honeycutt(1984). £¿ fromGilliland&Phillips(1982). Szkody &Crosa.ifromHorne, Lanning&Corner(1982);AfromSzkodyCrosa(1981). observations madeoutofeclipse. ThelargerdistanceisalsomorecompatiblewiththeAfound by d fromBerrimanetal.(1985)and equation(3);¿andAfromChincarini&Walker(1981). (Lanning 10).Szkody&Crosa(1981)give£¿—900pcfromtheflux distributionofthesecondaryduring (BD—7° 3007). v K Absolute magnitudesofCVs63 198 7MNRAS.227. . .23W 3 64 B.Warner which caseZ)<800pc. PG1012-029 isunlikelytohaveM<3.8,whetheraNLoranunrecognizedCNremnant,in 8 Masstransferincataclysmicvariables which astrongincreaseofMwithPisapparent:approximately M3cP.Thefactthatonetheory relevant totheestimationofM:namely,My(mean)forSUandUGstarsMédise) In Fig.12webringtogetheralloftheabsolutemagnitudesderivedinearliersectionsthatare M usingthemethodsofSection4.4producesadiagram equivalenttofig.7ofPatterson(1984)in ZC, NLandCNclasses.WehaveincludedthestarsfromTable11.ConversionofMinFig.12to periods. Thisisillustrated inFig.12bythelineforabsolutemagnitudeof thesecondary, interpret Patterson’sfig.7asmerelyastepfunctionin M,withhigherMlongwardoftheperiod gives asimilardependenceofMonPhasbeencited initsfavour(Patterson1984;Prialnik& of magneticbraking(Rappaport,Verbunt&Joss1983 ;Verbunt&Zwaan1981Patterson1984) M(2). Thishasbeenobtained fromequation(5)ofSection2andfigs3 4ofPatterson Fig. 12thefainteraccretion discs,ifsuchexist,willnotbeobservable(exceptin eruptionandof gap andconsiderableobservationalorcosmicdispersion atallperiods(Shatteretal.1986).With Shara 1986);othershaveconsidereddifferentbraking laws(Verbunt1984)orhavepreferredto possibilities. our moredetailedinvestigationweareinabetter positiontoexaminetheseandother (1984); itisinmoderatelygood agreementwiththevaluesofAadoptedinearlier Sections.From v 2 v v We drawattentionfirstto the obviousimpossibilityofdetectinglowMsystems at longorbital © Royal Astronomical Society • Provided by theNASA Astrophysics Data System V426 Oph6.0:10011.8600.10.26.6(0)6.5 FO Aqr4.0327513.528-0.7806.37.1 BV Cen14.613.0620.241.03.80.74.3 PG1012-029 3.24120015.0791.520.24.402.9 Notes toTable11 GK Per47.913.075:1.1:0.74.71.0:4.6 Star P(h)d(pc)i°AM^i)Hy.'A Table 11.Absolutemagnitudesofmiscellaneousstars. PG1012-029 dandifromPenningetal(1984). V426 OphdfromKofBerriman,Szkody&Capps(1985)and FO Aqr(H2215-086)dfromKofBerriman,Szkody&Capps GK PerSeenotestoTable5.ifromCrampton,Cowley&Fisher BV CenHy.'fromvisualbinarycompanion(Menzies,O'Donoghue (1986). equation (3).ifromofSzkody(1986). and Gilliland(1982b). & Warner1986);iandAfromVogtBreysacher(1980) (1985) andequation(3).ifromPenning(1985). 198 7MNRAS.227. . .23W 91 81 will bestoringmassintheir discs.Otherpossibilitiesarediscussedlater. transfer inCVaccretiondiscs. Ifso,thensomeoftheCNandNLsystemsmayhave -M>Mand Section 4.1forDNduringoutburst. Thiscouldbefurtherevidenceforanupper limit onthemass hence higherdeducedrates ofmasstransfer,thanthetheorymagneticbraking allows. radiation canaccountfortheluminosityoffainter systems butthepredictedM(e.g.Patterson general trendoiMabovetheperiodgaporupper bound.Belowtheperiodgap,gravitational in Fig.12.ThisandtheothertheoreticalA/{P)lawsmentioned abovefailtoreproduceeitherthe Below theperiodgapupperboundisM~6.5,or M~5xlQrMyr. 1984) failsbyafactorof10toaccountforthebrightest systems. are relativelyrare,Fig.12iscompatiblewiththehypothesis thatthereisawiderangeofMatall P abovetheperiodgap.Theupperboundtorange isatM~3.5,orM-SxlOyr. correlations betweenMandPfoundforDNdonotarisefromsuchaselectioneffect. plotted inFig.12,thereshouldbenoseriouslossofdetectableCVsforP<10hrandhencethe low inclination)forP>10hr.Recallingthataface-ondiscisonemagnitudebrighterthantheM 2A v v e radiation. gap. ThearrowmarkedGRshowsthevisualluminosityexpectedformasstransferpoweredbygravitational v period. ArelationshipbetweenMandPfromthetheoryofmagneticbrakingisindicatedforstarsaboveperiod v0 v v Figure 12.Generalpictureoftheabsolutemagnitudesaccretiondiscsatmeanlight,superimposingresults M~5xl0 M©yrisshown.TheabsolutemagnitudeM2ofthesecondaryshownasafunctionorbital shown inFigs2,9and11withadditionalstarsfromTable11.Anapproximatelineofratemasstransfer v v The upperboundonluminosity fortheCNandNLsystemsisclosetorelationship foundin In summary:forobservedCVswith1.5