Table Of ContentAstronomy&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 high-
state, 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 lock-
ing 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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