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Astronomy&Astrophysicsmanuscriptno.amher080131 c ESO2008 (cid:13) February4,2008 High and low states of the system AM Herculis 8 0 0 KinwahWu1,2 andLa´szlo´ L.Kiss2 2 n 1 MullardSpaceScienceLaboratory,UniversityCollegeLondon,HolmburyStMary,SurreyRH56NT,UnitedKingdom a e-mail:[email protected] J 2 SchoolofPhysicsA28,UniversityofSydney,NSW2006,Australia 1 e-mail:[email protected] 3 Received...;accepted... ] h p ABSTRACT - o Context. WeinvestigatethedistributionofopticallyhighandlowstatesofthesystemAMHerculis(AMHer). r t Aims. Wedeterminethestatedutycycles,andtheirrelationshipswiththemasstransferprocessandbinaryorbitalevolutionofthesystem. s a Methods. WemakeuseofthephotographicplatearchiveoftheHarvardCollegeObservatorybetween1890and1953andvisualobservations [ collectedbytheAmericanAssociationofVariableStarObserversbetween1978and2005.Wedeterminethestatisticalprobabilityofthetwo states,theirdistributionandrecurrencebehaviors. 1 Results. WefindthatthefractionalhighstatedutycycleofthesystemAMHeris63%.Thedatashownopreferenceoftimescalesonwhich v highorlowstatesoccur.However,thereappearstobeapatternoflongandshortdutycyclealternation,suggestingthatthestatetransitions 9 1 retain memories. We assess models for the high/low states for polars (AM Her type systems). We propose that the white-dwarf magnetic 0 field plays a key role in regulating the mass transfer rate and hence the high/low brightness states, due to variations in the magnetic-field 0 configurationinthesystem. . 2 0 8 Keywords.accretion,accretiondisk–stars:binaries:close–stars:individuals:AMHerculis(=4U1813+50)–stars:magneticfields–stars: 0 variable–nova,cataclysmicvariables : v i X 1. Introduction withaspinrateroughly10timeshigherthantherateoftheor- r bitalrotation.Forareviewofcataclysmicvariablesandpolars, a Magnetic cataclysmic variables (mCVs) are close interacting see Cropper (1990); Warner (1995); Wu (2000); Beuermann binaries containinga Roche-lobe filling low-mass companion (2002);Wuetal.(2003). star, usually an M dwarf, transferring material to a magnetic Polars are found to show alternating bright and faint white dwarf.Most mCVs have orbitalperiodsaround1.3 5 − optical/X-ray states, commonly referred to as high and low hours, and the magnetic fields of the white dwarfs in mCVs are sufficiently strong (B 106 108 G) that the accretion states, respectively. In the absence of an accretion disk, the ∼ − highandlow statesofpolarsarelikely tobeconsequencesof flowisfield-channellednearthewhitedwarf.mCVsarestrong changesinthemass-transferrateinthesystem.Ithasbeenar- X-rayemitters,andmanymCVswerefirstidentifiedinX-ray guedthatthehigh/lowstatesofpolarsarerelatedtotheatmo- surveys. spheric magnetic activity of the mass-donor star. In the star- The two main subclasses of mCVs are the polars and the spotmodel(Livio&Pringle1994),a lowstate iscausedbya intermediate polars. Polars are also known as AM Herculis temporary cessation of mass transfer, due to a magnetic spot type systems. Unlike other cataclysmic variables and binary on surface of the Roche-lobe filling mass-donor star travers- X-raysources,polarsdo nothaveanaccretiondisk.Allcom- ing the inner Lagrange (L1) point. While we may have some ponentsinthesystemarelockedbyastrongwhite-dwarfmag- understandingof thelong-termvariationsinthemasstransfer neticfieldintosynchronized(oralmostsynchronized)rotation. ofcataclysmicvariables,wearestilluncertainwhatcausesthe Intermediate polars contains white dwarfs with weaker mag- highandlowstatesandthestatetransitionsofpolars. netic fields. An intermediate polar has an accretion disk, but the inner disk is truncated by the white-dwarf magnetic field. The bright polar AM Herculis (AM Her = 4U 1813+50, White dwarfs in intermediate polars are often fast-spinning, withavisualmagnitudeV 13 15.5andanorbitalperiodof ∼ − 185.6 min) has been monitoredin the optical bands for more Sendoffprintrequeststo:K.Wu than100years.Theopticalbrightnessofthesourcehasshown 2 KinwahWuandLa´szlo´ L.Kiss:HighandlowstatesofthesystemAMHerculis largevariations.Anearlystudy(Feigelsonetal.1978)claimed those of Hudec & Meinunger (1977). In 23 cases when the that there was no strong evidenceof a well definedlow state. Harvard and Sonneberg plates were taken on the same day, A later study (Go¨tz 1993), however, showed the presence of themeanSonnebergminusHarvardmagnitudewas0.08 0.27 ± high and low states with good statistical significance. On the mag; since AM Her can show much larger variations over a other hand, analysis of the fraction of polars in high and low time-scale of hours, the small mean difference provides re- states during the XMM-Newton and ROSAT X-ray survey ob- assurance about the homogeneity of the two photographic servations (Ramsay et al. 2004) suggested that polars spend datasets. roughlyhalfoftheirtimeinahighstateandhalfinalowstate. Whilesurveysofensemblesofsystemsmightestablishtheef- fectivedurationofthehigh/lowstatedutycycles,todetermine Thethirdandthemostcontinuousdatasetcomesfromthe thecharacteristicsofthestatetransitionsandthedrivingmech- hundreds of visual observers of the AAVSO. These observa- anismsweneedtoanalyzethelong-termbehaviorofindividual tionswere begunin mid-1977and have beencontinuousever systems. since.Thefirst20yearsofthedatawereanalyzedbyHessman Inthispaperwepresentaquantitativeanalysisofhigh/low et al. (2000) in terms of mass-transfer variations in AM Her. states and their transition for the polar AM Her. We use the The present set is 7.5 years longer, containing almost 18,000 photometricdataofthesystemtakeninthelast115years.We individual observations. Since we are interested in the transi- assessthemodelsforthestatetransitionsandproposeapossi- tionsbetweenhighandlowstates, wecalculated10-daybins. blescenariofortheprocess.Weorganizethepaperasfollows. Thisway,weaveragedoutrapidbrightnessfluctuationsthatoc- In section 2 we presentthe data andanalysis; in section 3 we curonshortertime-scalesandappearasanadditional“noise” commenton the statistics and in section we discuss the mag- inthelightcurve. neticspotmodelandanalternative.Abriefsummaryisgiven insection5. The photographicdata are less useful for determiningthe 2. Datasourcesandanalysis statisticsofthehighandlowstates.Comparedtothevisualob- servations, the photographicones are quite sparse. The mean Our study is based on three different datasets, which al- distance between two consecutive Harvard plates is 35 days lowed the reconstruction of AM Her’s light curve for most (forthemorecontinuouscoveragebetweenJD 2,423,000and of the last 115 years: (i) photographic magnitudes deter- 2,433,000),whiletheSonnebergplatesweretakenonlyslightly mined by the second author on 348 blue plates from the morefrequently(onepointinevery30days).Forcomparison, HarvardCollegeObservatory’splatecollection;(ii)600photo- themeandistancebetweentwoconsecutive10-daybinsis10.9 graphicmagnitudesmeasuredbyHudec& Meinunger(1977) days, which shows that the duty cycle of the visual data was on Sonneberg plates; (iii) 17,704 visual observations col- about90%withthe10-daysampling(andstillover70%with lectedbytheAmericanAssociationofVariableStarObservers 3-daysampling).Nevertheless,thephotographiccurvecanstill (AAVSO).ThecombinedlightcurveisplottedinFig.1,which beusedtochecktherangeofbrightnessfluctuationsinthehigh showsthatthelast 85yearsarecoveredwithalmostnolong ∼ state over a time scale of a century. Figure 1 reveals that the (i.e.extendingmanyyears)gaps. overall brightness distribution did not change significantly in The earliest observations are those of the Harvard patrol the last 113 years. There are hints for gradual change in the program.ThehistoriclightcurvefromtheHarvardplateswas maximumbrightness,similarly to the trend seen in the visual alreadyobtainedbyFeigelsonetal.(1978);however,thosedata data,butthefull 3magpeak-to-peakamplitudewasquitesta- were never published in tabulated form. Moreover, we found ∼ ble.Itisalsoremarkablehowsimilarthephotographicandvi- 378usefulblueplatesinthearchive,whichis40morethanthe sualmagnitudeswere.Fromthemeanvaluesofthemaximum sampleanalyzedbyFeigelsonetal.(1978).Amongstthese,we andminimumbrightnesseswecouldnotinferanymeasurable coulddetectAMHeron348plates.Photographicmagnitudes zero-pointshift(greaterthan0.1–0.2mag). werethenestimatedwithreferencetoasequenceof10nearby comparisonstarsuniformlycoveringthebrightnessrangefrom B=12.6toB= 16.3.Themagnitudevaluesweretakenfrom The Guide Star Catalog (GSC 2.2, STScI 2001). The bright- Figure2showsthe10-daybinnedvisuallightcurve,which ness estimates of AM Her were made visually through a 9 is dominated by the transitions between high and low states. × viewing eyepiece with an estimated photometric accuracy of Tomeasurethetime-spansofthese,wedefinedaboundarybe- about 0.1–0.2mag.TheearliestplatewastakenonAugust1, tween them at m = 14.0 mag (dashed line in Fig. 2). This vis ± 1890, while the first positive detection was on July 18, 1892; way,wecouldincludetheshort-lived(10–30days)andfainter thelastdetectionwasrecordedbyusonJuly23,1952.Weig- (13.5–14.0mag)maximaamongthehighstates.Wethenmea- nored the few yellow plates because their temporal coverage sured the durations of high and low states as the time-spans was very poor. Also, a few blue plates from 1976–1977were of being brighter or fainter than 14.0 mag. Since the typical omittedfromtheanalysisbecauseforthatperiodtheothertwo fadingorrisingtimesrangedfrom10to30days,thissimplifi- setsprovidedafullcoverage. cationhasonlyslightlyaffectedthemeasuredlengths,ranging It is worth noting that contrary to what Feigelson et al. from10to1400daysand10to700daysforthehighandlow (1978) found, our Harvard magnitudes are in agreementwith states,respectively. KinwahWuandLa´szlo´ L.Kiss:HighandlowstatesofthesystemAMHerculis 3 10 pg - Harvard 11 AM Her 1892 - 2005 pg - Sonneberg visual 12 e d 13 u nit g a 14 m 15 16 17 10000 15000 20000 25000 30000 35000 40000 45000 50000 JD − 2400000 Fig.1. The combinedphotographicandvisuallightcurveof the system AM Her between1892and 2005(negativedetections omitted). AM Her 1977 - 2005 (10-day means) Table 1. Best fit Gaussian (f(x) = C e (x µ)2/2σ2) and 12 1 − − Lorentzian (f(x) = C [1+ ((x µ)/Γ)2] 1) functions to the 13 2 − − mvis 14 histogramofthebinnedvisuallightcurve. 15 function parameters rms 16 43000 43500 44000 44500 45000 45500 46000 46500 12 2Gaussians 0.140 13 µ1 13.29±0.04 mvis 14 σ1 0.36±0.04 15 µ2 14.97±0.05 σ 0.29 0.05 1466500 47000 47500 48000 48500 49000 49500 50000 2 ± 12 3Gaussians 0.122 13 µ1 13.23±0.03 mvis 14 σ1 0.23±0.03 15 µ2 14.97±0.04 1560000 50500 51000 51500 52000 52500 53000 53500 σ2 0.28±0.04 Julian Date (− 2400000) µ3 13.84±0.07 σ 0.17 0.06 3 ± 2Lorentzians 0.116 Fig.2.ThebinnedAAVSOlightcurve.Thedashedlinesshow µ 13.25 0.02 theadoptedboundarybetweenhighandlowstateatmvis =14.0 Γ1 0.26±0.03 mag. 1 ± µ 15.01 0.04 2 ± Γ 0.28 0.07 2 ± 3Lorentzians 0.101 3. Results µ 13.23 0.02 1 ± Γ 0.19 0.03 3.1.Distributionofhighandlowstatesanddurationof 1 ± µ 15.01 0.03 dutycycles 2 ± Γ 0.27 0.05 2 ± µ 13.78 0.04 The normalized histogram of the binned visual light curve 3 ± Γ 0.12 0.07 (Fig. 3) clearly shows the two main states of the star. 3 ± Furthermore,thereisasmallerthirdpeakcenteredat13.7mag, which correspondsto the longer periodsof faintermaxima in thetoppanelofFig.2andtheshort/fainthighstatesinthemid- dle and bottom panels of Fig. 2. The integralunder the curve Of these, the three-component Lorentzian profile yielded the from12.5to14.0magsgivesameasureofthetotaldurationof smallest residual mean scatter. In Table 1 we give the best fit highstates, whichis62%,whenaddingupthe areaunderthe parametersofthefourfunctionsandcorrespondingrmsvalues. stepsofthehistogram. TheLorentzianfitsgive 20%smallerrms,whichreflectsthe ∼ Toimprovethedurationcalculation,wetriedtofindagood observation that the peaks in the histogram are rather sharp. analytic fit to the histogram. The best results were given by Theintegraloftheanalyticfitgives62.8%asthetotalduration two-andthree-componentGaussianandLorentzianfunctions. of the high state, which we adopt as the best estimate of this 4 KinwahWuandLa´szlo´ L.Kiss:HighandlowstatesofthesystemAMHerculis 1.2 visual data high state 3-component Lorentzian 1400 low state 1 1200 normalised frequency 000...468 length of high/low state (d) 1 046800000000 200 0.2 0 0 12.5 13 13.5 14 14.5 15 15.5 16 43000 44000 45000 46000 47000 48000 49000 50000 51000 52000 53000 54000 visual magnitude Julian Date (-2400000) Fig.3.ThehistogramofthebinnedAAVSOlightcurvewitha Fig.5.Timevariationsofthedurationofhigh/lowstates. three-componentLorentzianfit. 1.4 as a functionof time, where the durationsare assigned to the photographic visual mid-timesof each state. There seems to be a well-defined re- 1.2 currence in both states, in the sense that alternating long and shortstatesoccurovertime.Ifthispatternisnotduetostatisti- 1 malised frequency 00..68 3cpar.2elvc.ioCoiunoscmisdtpaetanecrsiesa,onthndetwhsyeitshttrearmnesshiutaiolstnsresf.traoinmedXc-erratayinsumrevmeyosryofthe nor 0.4 In the ROSAT X-ray survey of 28 polars, 16 were in the low state,andintheXMM-NewtonX-raysurveyofthe37systems, 0.2 21 were in the low state. Bayesian analyses give a probabil- 0 ity of0.585forthe polarsin thelow state,with the90%con- 12 12.5 13 13.5 14 14.5 15 15.5 16 magnitude fident intervals being (0.342, 0.863), for the ROSAT sample, andaprobabilityof0.442,withthe90%confidentintervalbe- Fig.4.Acomparisonofthehistogramsofthephotographicand ing (0.258, 0.734), for the XMM-Newton sample (Ramsay et visualdata.Notethelackoffaintphotographicobservations. al. 2004). Moreover, there were no significant differences in theglobaldistributionsoforbitalperiodsamongthehigh-state andthelow-statesystemsineithertheROSATorXMM-Newton parameterwithlessthan1%uncertainty(but,ofcourse,subject samples.Thehigh-stateandthelow-statesystemswerenotsta- tosystematicbiasarisingfromthedefinitonofthehighstate). tisticallybiasedtowardlongorshortorbitalperiods,andthere Wealsocalculatedthehistogramofthephotographiclight wasnoevidenceofperiodclumpingofhigh-andlow-statesys- curve.Forthis,wecombinedtheHarvardandSonnebergmag- tems.Thedistributionsofthehigh-stateandthelow-statesys- nitudes,as thereis no systematic differencebetweenthem. In temswereconsistentwithrandomorders,whenrankedaccord- Fig.4wecompareittothehistogramofthevisuallightcurve. ingtotheirorbitalperiods.Thefindingsthathalfofthesources Notethatthemagnitudebinsinthehistogramsareslightlydif- areinthehighstateandtheotherhalfinthelowstate,andthat ferent, in order to avoid oversampling of the sparser photo- thehighandlowstatesofthesystemsareunrelatedtothesys- graphiccurve.Thecloseagreementofthebrighterpeaksindi- tem orbital periods suggest a 50/50 high-low state duty cycle catesthestabilityofthefullmagnituderangeofthehighstate forindividualsystems. overthelastcentury.Thesecondarypeakat 13.7magisnot Our analysis of the AAVSO optical photometric data ∼ resolved, but the broader shoulder of the main peak suggests showed that the system AM Her has spent about 60% of its thepresenceofthatdistinctfeatureinthe earlydata.Thelow time in thehighstate. Ifpolarsgenerallyhavethe same highstate, on the other hand, is heavily affected by the magnitude low state duty cycle as the system AM Her, we wouldexpect limits of the patrol plates. Nevertheless, the extension of the that 3/5 of the systems will be in their high state in a snap- fainterpeakisverysimilarinbothhistograms,sothatitisvery shotsurvey.TheinferenceoftheX-raysurveyobservationsof likelythatthestatisticsofthelowstatealsostayedverysimilar Ramsayetal.(2004)thatthehigh/low-statefractionaldutycy- throughoutthe20thcentury. cle ofan individualpolarisabout50%isthereforeconsistent We find a remarkablebehaviorin the durationof the high withtheobservedhigh-lowstatedutycyclesofthesystemAM andlowstates.InFig.5weplotthetime-spansofthetwostates Herinthelast100years. KinwahWuandLa´szlo´ L.Kiss:HighandlowstatesofthesystemAMHerculis 5 4. Modelsforhigh/lowstates wouldleadtovariations/fluctuationsinthevisualmagnitudeV. ItfollowsfromEq.(3)that 4.1.Variationsinopticalbrightnessandmasstransfer γ 2 δρ 2 2δc 2 The total bolometric luminosity of a polar is the sum of its (δV)2 = 0 + s + γlog e 2(2ξδξ)2 .(4) hLahxrd+XL-srxay+,sLoufvt+X-Lroapyt,.UTVheahnadrdopXti-craalylsuamreinforseiet-iefrse,ei.ee.mLisbsoilo=n (cid:18)ln10(cid:19)  ρ0 ! cs !  (cid:0) 10 (cid:1) The two-Gaussian and two-Lorentzian fits to the optical from the shock-heated accretion gas at the bottom region of brightness variations of the AAVSO data of the system AM theaccretioncolumn.ThesoftX-raysprobablyoriginatefrom Herbothyieldameanbrightnessµ 13.3,andastandardde- the thermalized atmosphere of the accretion pole bombarded 1 ≈ viationσ 0.3(seesection2)forthehighstate.Thisgivesa by dense accretion blobs. The UV radiation is generally in- 1 ≈ characteristichigh-statebrightnessvariationδV σ 0.3.In terpretedas reprocessedemission of the X-rays, and its lumi- 1 ∼ ≈ ordertoexplainthespreadintheopticalbrightnessduringthe nosity is roughly proportionalto the X-ray luminosity. In the highstate,fluctuationsofeither(δρ /ρ ) 0.4,(δc /c ) 0.2 highstate, the opticalemission is dominatedby the cyclotron 0 0 s s ∼ ∼ or δξ 0.2 (for ξ 1) are required (Eq. 4). The low-state emissionfromtheshock-heatedgasnearthewhite-dwarfsur- ∼ ∼ mean brightness is about 15.0 and the standard deviation is face. In the low state, where cyclotron emission from the ac- about 0.05. The difference between the optical brightness of cretion gas is negligible,the optical luminosity is mainly due thehighandlowstatesisδµ = µ µ 1.7.Duringthelow to the emission of the low-mass mass-donor star. From the 2 1 − ≈ statetheopticalluminosityiscontributedmainlybytheemis- BeppoSAX,ROSATandEXOSATobservations,Hessmanetal. (2000)demonstratedascalingrelation L Lγ forthesys- sionfromthemass-donorstarandtheheatedwhitedwarf(see opt ∝ bol Bonnet-Bidaudet al. 2000).Thereforewe can use the bright- tem AM Her in a bright(high)state, where mass transfer oc- nessvariationtoconstrainthevariationsofρ ,c orξ. curred.Theindexparameterγ 2forV magnitude<15. 0 s ≈ The accretion luminosity of an accreting white dwarf is Lacc = GMwdM˙/Rwd, whereG is the gravitationalconstant, 4.2.Star-spotmodelandmagnetic-lockingmodel − M and R are the mass and radius of the white dwarf, re- wd wd spectively,andM˙ isthemasstransferrate.Forpolarsinahigh Themagnetic-spotmodel(Livio&Pringle1994)attributesthe state, L is much higher than the intrinsic luminosity of the occurrenceofthelowstatetothecessationorreductionofthe acc two stars. Thus, we have L L . Polars are Roche-lobe mass-transferratewhenamagnetic-starspotonthesurfaceof bol acc fillingsystems,withthemasstra≈nsferrategivenby the mass-donor secondarystar traverses the inner Lagrangian point. If the area covered by the star spot is not a large frac- M˙ AL1csρ0exp (∆r/H)2 (1) tion (say less than 50%) of the total stellar surface area, the ≈− − h i highstate isa ‘default’state, wherethe masstransferis unin- (Lubow & Shu 1975; Papaloizou & Bath 1975; Meyer & terupted.Unlessthereisanunderlyingmechanismtosynchro- Meyer-Hofmeister 1983), where c is the gas sound speed at s nizethemovementofmagneticspotsonthestellarsurface,the the L1 point, ρ is the characteristic atmospheric density of 0 migrationofthestarspottotheinnerLagrangianpointisran- the companion star, H is the atmospheric scale height of the dom, and the occurrence of low state and the duration of the companionstar,and∆r isthedifferencebetweentheeffective low state can be modelled by Poisson processes. Moreover, Roche-lobevolumeradiusandtheradiusofthecompanionstar. one would also expect that brightness (mass-transfer) varia- The effective area of the nozzle of the gas stream at the first tions during the high state are Poisson/Gaussian-type fluctu- Lagrangian(L1)point,A ,isgivenby L1 ations,providedthatthedistributionofthehot-spotsizeisnot 2πc a3 narrowandresemblingaδ-function. A = s , (2) L1 GM (1+q)k(q) Analysis by Hessman et al. (2000) had highlighted some wd difficultiesofthegenericstar-spotmodel.Inaddition,thestar- where a is the orbital separation,q is the ratio of the mass of spotmodelhasdifficultiesinexplainingwhythiskindofhigh- the secondary star to the white dwarf, and k(q) is a function low state phenomenonoccursin all polarsbutdoesnot occur with value 7 (see Hessman et al. 2000; Meyer & Meyer- inothercataclysmicvariables(magneticornon-magnetic)and ≈ Hofmeister1983). low-mass X-ray binaries in general, when all these systems ThevisualmagnitudeVofanastrophysicalobjectisrelated havelate-typelow-masssecondarystarssimilartothoseinpo- to the optical luminosity: V = log L + λ, where λ is a − 10 opt lars. constant determined by the distance, and the bolometric and From the long-term brightness variations of the system photometriccorrections.Itfollowsthatforapolarwehave AM Her, we havequantifiedthreepropertiesof its highstate. V =−γ log10ρ0+2log10cs− log10e ξ2 +λ′, (3) hFiigrshtlys,tatthee.rTehiseavaslpureeaodfothfebrsipgrhetandesiss(rδoVbu≈st 0–.3it) disuriinnsgentshie- h (cid:0) (cid:1) i where ξ = ∆r/H. When the system parameters λ, M , a tive to whether Gaussian fits or Lorentzian fits are used; it wd and q are specified, the quantity λ is a ‘constant’. The vi- is also insensitive to whether a two-componentfit or a three- ′ sual magnitude V, however, is an observable quantity (which component fit is used. Secondly, Lorentzian fits to the V- is a random variable) determined by the indirectly observ- magnitude variations give better statistics than Gaussian fits, ablesρ ,c ,and∆r/H (whicharealsorandomvariables).Any in the two-component model as well as the three-component 0 s variations/fluctuationsin these indirectly observablevariables model. Thirdly, there is an additional weaker high state (at 6 KinwahWuandLa´szlo´ L.Kiss:HighandlowstatesofthesystemAMHerculis V 13.8,forLorenztianfits)inadditiontotheusualhighand The surface temperature of the mass-donor M star of the ≈ low states (at V 13.2 and 15.1 respectively, for Lorentzian systemAMHerisabout3250K(Baileyetal.1991).Intheab- ≈ fits). Moreover, the occurrence and duration of high and low senceofexternalforces,thephotosphericpressureisestimated states are not well described as Poission processes, and the tobe 103 104ergcm 3(seee.g.Edwards&Pringle1987). − ∼ − alternation of the two states appears to show certain memo- Theenergydensityofthestellarfieldofthemass-donorstaris ries(seeFig.5).Giventhesepropertiesandtheuniquenessof 106ergcm 3.AttheinnerLagrangianpoint,theenergyden- − ∼ the high/lowstate in polars, we arguethat the high/lowstates sityofthewhite-dwarfmagneticfieldis,however,greaterthan of polars are unlikely to be simply caused by random migra- 109 ergcm 3.TheatmosphericscaleheightH isthereforede- − tion of magnetic star spots of the secondary star to the inner terminedbyanexternalforce,duetothewhite-dwarfmagnetic Lagrangianpoint. field. Inalow-massclosebinarysystem,themagneticfieldofthe If the brightnessvariationsin the high state of the system compactstargenerallyhasnegligibledirecteffectsonthesys- AM Her are caused by mass transfer variations, it would re- temorbitaldynamics.However,inapolar,themagneticfieldof quire10–20%variationseitherinthesoundspeedcs attheL1 thecompactprimarystarissostrongthatitaffectstheaccretion point, the atmosphere base density ρ0, or the quantity ∆r/H flowandtheorbitaldynamicsofthesystem.Thismakespolars (seesection4.1).Althoughonecannotdogmaticallyrejectthe veryuniqueamongalllow-massclosebinarysystems.Wepro- possibility of large amplitude variations in the surface tem- posethatthehigh/lowstatesandtheirtransitionsarecausedby perature and base density of the mass-donorstar, providinga variationsinthemagneticinteractionbetweenthewhitedwarf sensible explanation for the cause of such atmospheric varia- and the mass-donor secondary star. In other words, the mag- tions is not easy. The more likely causes would be the varia- netic field of the white dwarf can alter the mass transfer rate. tions in ∆r/H. The quantity ∆r is the difference between the IncertaincontextsthesituationresemblesthatintheRSCVn stellarradiusandtheRoche-lobevolumeradius.Itvarieswith systems,wherethemagneto-activitiesofacomponentstarare the secular evolutionary timescale of the binary orbit, which greatlyinfluencedby the magneticfield ofits companionstar is much longer than the timescales of the brightness fluctu- (seee.g.Uchida&Sakurai1985).Thisis incontrastwiththe ations of the system. Variations in the local magnetic field star-spot model, where the magnetic field of the mass-donor strength or geometrical configuration may result in a change playsthecentralrole. intheatmosphericscale heightH ofthemass-donorstar. The In the canonicalmodel of polars (Chanmugam& Wagner local magnetic field at the L1 point is jointly determined by 1977),the magnetic stress exerted by the white-dwarf field is thewhite-dwarfmagneticmomentanditsorientation,thestel- strongenoughto disruptthe formationofanaccretiondiskin lar atmosphericmagnetic field, and the dynamicsof the mass the white-dwarfRoche lobe.Moreover,allcomponentsin the transfer flow. The linear width of the nozzle at the L1 point binaryaremagneticallylockedintosynchronousrotationwith is √AL1 109 cm (Eq. 2), and the local sound speed is ≈ ∼ onesingleperiod(Wu&Wickramasinghe1993,see alsoJoss 106 cm s−1 (inferred from the atmospheric temperature of ∼ etal.1979;Hameuryetal.1987;Campbell1990). 3250K). Itfollowsthattheshortesttimescale allowedforthe Theorbitalseparationofapolarisgivenby brightness variations is 103 s, which is the sound crossing ∼ time. This is the minimum timescale on which the geometry M (1+q) P 2 1/3 of mass transfer flow is readjusted in response to changes in a = 4.8 109 wd o cm, (5) themagnetic-fieldconfigurationatthevicinityoftheL1point. × " M !(cid:18)3hr(cid:19) # ⊙ Note that as the mass transfer rate has an exponentialdepen- where P istheorbitalperiod.TheRoche-lobevolumeradius dence on (∆r/H)2 (Eq. 1), a reduction of H by a factor of 3 o ofthewhitedwarfisgivenby wouldbebeenoughtoquenchthemasstransfer. Althoughthecomponentstarsinpolarsareexpectedtobe RL = a 0.500+0.227log10q −1 (6) magnetically locked into synchronous rotation, perfect locking isan idealisationratherthana reality.Severalpolarshave (cid:0) (cid:1) (Plavec & Kratochvil 1964). The surface polar field of the been found to show asynchronous white-dwarf spin and or- white dwarf in system AM Her is about 20 MG (Schmidt et bital rotation (e.g. BY Cam, Silber et al. 1992; Honeycutt & al. 1981; Bonnet-Bidaud et al. 2000). The mass-donor of the Katfla 2005). Spin-orbit synchronism is preserved only if the system AM Her is a M4.5 M5star (Lathametal. 1981).For torquegeneratedbythe accretionflow is counter-balancedby − awhite-dwarfof 0.75M ,R 2.9 109 cm.Ifthewhite- the magnetictorque.Thereare observationsthatthe locations L dwarf magnetic fi≈eld is di⊙polar,∼the fi×eld strength would be of the accretion spots in certain polars changed in different about140kGattheinnerLagrangianpoint.Theobservedmean epochs. An interpretation is that spin-orbital asynchronism is surfacemagneticfieldstrengthsoflate-typeMstarsare 5kG continuallyperturbed,asthe accretionflow andhence the ac- ∼ (Johns-Krull&Valenti1996),andtheoreticalmodelspredicted cretion torque are not steady (Bailey et al. 1993; Wu et al. field strengths around 10 kG (see Buzasi 1997). These val- 1994). uesaresignificantlysmallerthanthefieldexertedbythemag- The high-low state and the transition fit very well in this neticwhitedwarf.Thewhite-dwarfmagneticfieldplaysamore scenario.Ifthemagneticfieldconfigurationissufficientlyper- dominantroleindeterminingthemagnetosphericactivityinthe turbed, the mass transfer will be suppressed, and the new inner Lagrangian point, where mass transfer from the donor equilibriumconfigurationis established forthe zero accretion starinitiates. torque situation. This also provided a consistent explanation KinwahWuandLa´szlo´ L.Kiss:HighandlowstatesofthesystemAMHerculis 7 foranintermediatestate(Fig.3),whichis,incontrast,noteas- Insummary,whilethestar-spotmodelhashighlightedthe ily explained in the frame-work of the conventionalstar-spot importanceofmagnetismintheroleforthehighandlowstates model. Moreover, our analysis of the brightness distribution andthestatetransitionofpolars,analyseshaveshownthatthe showed Lorentzians rather than Gaussians, especially for the modelhasfallenshortofsatisfactorilyexplainingthe100-year highandtheintermediatestates, suggestingthatthespreadof dataofopticalbrightnessvariationsofthesystemAMHer(see thebrightnessmightnotbeduetopurelyrandomfluctuations Hessman et al. 2000). Here, we propose an alternative mag- butcontrolledbycertainunderlyingresonantprocesses.Apos- neticmodel.Thekeyregulatorofthemasstransferistheglobal sible explanation for such resonant is that the locking occurs magneticfieldofthewhitedwarf,insteadofthelocalmagnetic attheminimumenergyfieldconfigurationinthepresenceofa fieldvariationsatthesurfaceofthemass-donorstar.Thestates multipolarwhite-dwarfmagneticfield(Wickramasinghe&Wu correspondtovariousequilibriumlockingconfigurationsinthe 1991;Wu & Wickramasinghe1993),and any small perturba- presence or absence of the accretion torque. The Lorentzian tionswill lead to oscillationsof the relativeorientationof the distributionofbrightnessvariationcanbeattributedbydamp- magneticfieldandhencethemasstransferratesandthebright- ened oscillations around the equilibrium configuration. This nessofthesystem.Whentheoscillationsaredampened,itnat- scenario is the same frame-work of synchronism of polars as urally givesrise to Lorentziantype profilesfor the brightness a unique class of interacting binaries. It also reconciles with distribution. theobservationsthatprominenthigh/lowstatesoccurinallpo- lars,inwhichthewhite-dwarfmagneticfieldisstrongenough Therearetwonecessaryconditionsfortheoperationofthe toaffectthedynamicsofthewholesystem,butnotininterme- high-low state-transition mechanism described above. Firstly, diate polars or non-magnetic cataclysmic variables, in which thesystemmustbemagneticallylockedorquasi-magnetically thewhite-dwarfmagneticfieldistooweaktoinfluenceaccre- locked.Secondly,themagneticfield ofthe compactstar must tionflowatthedistanceofthemass-donorstar,ortoalterthe overwhelmthemagneticfieldofthemass-donorstarattheL1 orbitaldynamicsofthesystem. point. These conditions are satisfied in polars but not in the weakerfieldmCVsandotherbinarysystems.Here,weelabo- 5. Conclusion ratethisbrieflyinthecaseofintermediatepolars.Consideran intermediatepolarwiththesameorbitalparametersandstellar We investigate the high/low states of the system AM Her us- masses as the system AM Her, but a white-dwarf surface po- ing three sources of archival optical data: the photographic larfieldstrengthof 1MG(seeWickramasingheetal.1991). plates of the Harvard College Observatorybetween 1890 and ∼ This field is not strong enough to disrupt the entire accretion 1953,the visualobservationsbythe AmericanAssociationof disk and to enforce spin-orbit synchronism (see Chanmugam VariableStarObserversbetween1978and2005,andthepub- &Wagner1977).Withoutscreening,thewhite-dwarfmagnetic lishedphotographicdatafromSonnebergplates.Wedetermine field is about7 kG atthe L1 pointfora dipolarfield configu- the statistical probabilityof the highandlow states, theirdis- ration,anditisweakerifhigher-ordermulti-polefieldcompo- tributionandrecurrencebehaviors.Thedistributionofthehigh nentsarepresent.Anaccretiondiskisabodyoffastdifferen- states is well fitted by a Lorentzian. There appears to be an tiallyrotatingconductingfluid.Itspresencecausesfieldscreen- intermediate state. The fractional high state duty cycle of the ing.Theactualstrengthofthewhite-dwarfmagneticfieldatthe systemAMHeris63%,whichisconsistentwiththeinference L1pointissignificantlylowerthan7kG,andthecorresponding that the duty cycle of the high state of polars is roughly50% energydensityissignificantlysmallerthan106 ergcm 3. The based on the ROSAT and XMM-Newton survey observations. − magnetic field of the mass-donor M dwarf, however, reaches The data show no preference of timescales on which high or 5 10kG,givinganenergydensityof 106 ergcm 3.The lowstatesoccur.Thereappearsapatternoflongandshortduty − ∼ − ∼ stellarfieldisthereforestrongenoughtosuppressthemagnetic cyclealternation,suggestingthatthestatetransitionsretaincer- harassmentattheL1pointbythewhitedwarf.Thisallowsthe tainmemories.Weproposethatthehigh/lowstatesarecaused M star to self-adjust to establish an atmospheric scale height byvariationsinthemagneticfieldconfigurationofthesystem, thatfacilitatesthemasstransferprocess.Notethatpolarscould andthatthemagneticfieldofthewhitedwarfplaysthekeyrole have evolved from long-period intermediate polars, but long- inregulatingthemassflowattheinnerLagrangianpoint.This periodpolarswouldnotevolvetobecomeshorter-periodinter- scenariomayovercomecertaindifficultiesunexplainedbythe mediate polars (Chanmugam & Ray 1984; King et al. 1985; star-spotmodel,wherethecessationofmasstransferiscaused Wickramasingheet al. 1991). Observationshave shown a de- by magnetic star spots of the mass-donor star traversing the ficiency of intermediate polarswith P < 2 hr in comparison Lagrangianpoint. o with polars. Dipolar magnetic field scales with r 3 and high − Acknowledgements. KW’svisittotheUniversityofSydneywassup- order multi-pole fields have stronger r dependences(where r ported by the NSW State Expatriate Researcher Award. LLK has is the radial distance from the white dwarf). Thus, the white- been supported by a University of Sydney Postdoctoral Research dwarf magneticfield at the L1 pointscales with P α roughly, −o Fellowship.WesincerelythankvariablestarobserversoftheAAVSO whereα 2.Theinfluenceofthewhite-dwarfmagneticfield ≥ whose dedicated observations over three decades made this study onthemass-donorMstarisgenerallyinsignificantforinterme- possible. LLK thanks the kind hospitality of Dr. Arne Henden, the diatepolars.Therefore,intermediatepolarsarenotexpectedto Director of the AAVSO and all the staff members at the AAVSO show high/lowstates and state transitions like those observed Headquarters (Cambridge, MA) during his visit in early 2006. We inpolars. are also grateful toDr. Charles Alcock, the Director of the Harvard 8 KinwahWuandLa´szlo´ L.Kiss:HighandlowstatesofthesystemAMHerculis CollegeObservatory,foraccesstothePhotographicPlateCollection, andtoAlisonDoane,theCuratoroftheCollection,forhelpfulassis- tance. 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