The accretion flow in the discless intermediate polar V2400 Ophiuchi

10 Pages·0.37 MB·English

by  Coel Hellier

Mon.Not.R.Astron.Soc.000,000–000 (0000) Printed1February2008 (MNLATEXstylefilev1.4)
The accretion flow in the discless intermediate polar
V2400 Ophiuchi
Coel Hellier and A.P.Beardmore
Astrophysics Group, School of Chemistry and Physics, KeeleUniversity, Keele, Staffordshire, ST5 5BG
Accepted ???.Received???
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ABSTRACT
2 RXTE observations confirm that the X-ray lightcurve of V2400 Oph is pulsed at the

n beat cycle, as expected in a discless intermediate polar. There are no X-ray modula-
a tions at the orbital or spin cycles, but optical line profiles vary with all three cycles.
J Weconstructamodelforline-profilevariationsinadisclessaccretor,basedontheidea

9 that the accretion stream flips from one magnetic pole to the other, and show that
2 this accounts for the observed behaviour over the spin and beat cycles. The minimal

variabilityovertheorbitalcycleimpliesthat1)V2400Ophisataninclinationofonly
1 ≈10◦, and 2) much of the accretion flow is not in a coherent stream, but is circling
v
the white dwarf, possibly as a ring of denser, diamagnetic blobs. We discuss the light
3
this sheds on disc formation in intermediate polars.
7
4
Key words: accretion, accretion discs – stars: individual: V2400 Oph – novae, cat-
1
aclysmic variables – binaries: close – X-rays: stars.
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p 1 INTRODUCTION cycles;thusV2400Ophshowsthesignatureofpole-flipping
- accretion, as expected in a discless IP.
o Themagneticcataclysmic variablescanbedividedintotwo
r classes. In polars (or AM Her stars) the magnetic field of V2400 Oph is a prime opportunity to study the inter-
t
s the white dwarf is strong enough to lock its rotation to the action of an accretion stream with amagnetic field in asit-
a binary orbit, and accretion proceeds via a stream which is uation where the flow is continually changing as the dipole
:
v deflected by the field onto a magnetic pole. In contrast, in rotates.Thiscontrastswithmostmagneticcataclysmicvari-
i intermediatepolars(IPsorDQHerstars)alower-fieldwhite ableswheretheflowisexpectedtosettle(atleasttemporar-
X
dwarf spins more rapidly than the orbit, and the stream ily)intoaquasi-equilibrium.(Inprincipletheasynchronous
r feedsintoanaccretiondisc,whichthenfeedsfieldlinesfrom polars offer the same opportunity, but it is much harder to
a itsinneredge(seeWarner1995foracomprehensivereview). obtaingoodcoverageoftheir∼50-dbeatcycles.)Inthispa-
perwepresentnewX-rayobservationsofV2400Oph,along
The distinction is blurred, however, by the existence
withopticalspectroscopyaimedattracingtheaccretionflow
of several asynchronous polars, in which the spin periods
differ from the orbit by ∼1 per cent (e.g. Schwope etal. as it connects to thefield lines.
1997). There has also been a long debate on the existence V2400 Oph is the most polarised IP, leading to a mag-
of discless IPs (e.g. Hameury, King & Lasota 1986; King netic field estimate of 9–27 MG (Buckley etal. 1995; V¨ath
& Lasota 1991; Hellier 1991; Wynn & King 1992). In such 1997),thehighestforanyIPandoverlappingwiththerange
systems, the stream would be expected to flip first to the for low-field polars. The high field may explain why a disc
upper pole, then to the lower pole, as the magnetic dipole hasnotformedinthissystem,whereastheydoinIPsat∼1
rotates (e.g. Hellier 1991; Wynn & King 1992). Such pole MG.Buckleyetal.(1995)alsofoundthatthecircularpolar-
flippingwouldoccuratthefrequencywithwhichtherelative isationisalwaysofthesamesign,andsoconcludedthatwe
geometry changes, namely the beat frequency ω–Ω, where onlyeverseeonemagneticpole.Given,also,alackofradial
Ω and ω are theorbital and spin frequencies respectively. velocity motion at the orbital period, they proposed that
Buckleyetal.(1995;1997)reportedthefirstsecureevi- V2400Ophisatalowinclination,andthatweonlyseethe
denceforadisclessIP,withthediscoveryoftheRosat source pole nearest us (the‘upper’ pole). From thefact that there
V2400 Oph (RXJ1712.6–2414). They found that polarised werenodetectablevariationsinlinearpolarisation,Buckley
lightfromthesystemvariesat927s,whichisinterpretedas etal. (1995) suggested that this pole was never viewed side
thespinperiodofthemagneticdipoleandthusofthewhite on,andsoproposed thatboththeinclination ofthebinary,
dwarf. The X-rays, though, are pulsed at 1003 s, which is and the angle between the spin and magnetic axes of the
the beat period between the 3.42-h orbital and 927-s spin white dwarf, δ,are low.
(cid:13)c 0000RAS
2 C. Hellier and A.P.Beardmore
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Time (secs)
Figure 1.The2–15-keVX-raylightcurveofV2400OphasrecordedbyRXTE.
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0.0 0.5 1.0 1.5 2.0
Frequency (mHz)
Figure 2.The Fouriertransformofthe RXTE observation, partofwhichisshowninFig.1.Theorbital (Ω) and spin(ω) frequencies
aremarked.Thedominantmodulation,withanaliasstructurecausedbythespacecraftorbit,isatthebeatfrequency,ω–Ω.
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Figure 4. An illustration of the discless accretion geometry in
V2400 Oph. In our model (Section 4) the stream attaches to a
20◦swatheoffieldlines(showninbold).Thechangeingeometry
over the beat cycle can be visualised by imagining the feeding
pointmovingroundthering.
0
0.0 0.5 1.0 1.5
Beat-cycle phase
transform of theentireobservation isshownin Fig. 2.Both
Figure 3. The X-ray lightcurve of V2400 Oph folded on the lightcurve and transform are dominated by a pulsation at
1003-sbeatperiod.Atypical errorisshown.
the 1003-s beat period; this has a maximum amplitude of
≈50 per cent [(peak–trough)/peak] and a mean amplitude
2 AN RXTE OBSERVATION of25percent,asshownbythefoldedpulseprofileinFig.3.
There is no sign of variations at the orbital period (<7
We report, first, on an RXTE X-ray observation obtained per cent) or at the spin period (<2 per cent). A prelimi-
overthe interval2000 June 24–25. This resulted in 39 ks of narylookatfiveotherRXTEobservations,ofsimilarlength
data from the PCA instrument, with either 3 or 4 of the and spaced at intervals of a few months, findsthesame be-
5 PCU modules in operation at any time. A section of the haviour:astrongbeat-cyclepulsebutnomodulationatthe
resulting lightcurve is shown in Fig. 1, while the Fourier orbital or spin cycles.
(cid:13)c 0000RAS,MNRAS000,000–000
The intermediate polar V2400 Oph 3
HeI 4388 OII 4416 HeI 4471 HeII 4542 Bowen HeII 4686 HeI 4713 HeI 4921 HeI 5015
s
nt
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4300 4400 4500 4600 4700 4800 4900 5000
Figure 5.ThesummedspectrumofV2400Oph.
The absence of an orbital modulation in the X-ray remains a puzzle, which we defer to Section 8, where we
lightcurveisunexpectedinadiscless IP.Ifthestream flows suggest a possible explanation.
to the magnetosphere, latches onto the nearest field line,
and follows it onto the white dwarf (see Fig. 4), then the
accretion sites will always be on the hemisphere facing the
3 SPECTROSCOPIC OBSERVATIONS
secondary, and thustheirvisibility should vary overtheor-
bit,asinanAMHerstar.Thelackofanorbitalmodulation WeobservedV2400Ophwiththe3.9-mAATandtheRGO
can, though, be explained if we concur with the suggestion spectrographplusaTEK CCD.A1200linesmm−1 grating
that V2400 Oph is at so low an inclination that the upper gave a resolution of 1.4˚A, covering the range Hγ to Hβ.
pole is always in view and thelower pole neverin view. Observingfor5.0h,4.5h&4.5 hronthethreeconsecutive
nights1996May10–12 weobtained900integrationsof50s
Thenextpuzzlearisesfromthefactthatthebeat-cycle each,thuscovering≈4orbitalcyclesand≈50spincycleof
modulationisnottotal.Ifalltheaccretingmaterialpartici- the star. The summed spectrum, containing Hei and Heii
patesinthepoleflipping,then,giventhelowinclination,the
lines in addition tothe Balmer lines, is shown in Fig. 5.
flow would flip to the far, hidden hemisphere of the white
As a first look at the data we computed the equiva-
dwarfforroughlyhalfthebeatcycle,leadingto100percent
lent widths and the V/R ratios for the lines in each spec-
modulation. If some of the flow does not flip, but manages
trum(V/Rbeingtheratiooftheequivalentwidthsoneither
to feed both poles continually, then this could explain the
sideoftherestwavelength).TheFouriertransformsofthese
non-totalmodulation.Butwhy,then,doesthisnotresultin quantitiesfor Hβ and Heiiλ4686 are shown in Fig. 6.
aspin-cyclepulsation,asseeninalltheIPswhereadiscen-
All four Fourier transforms show significant power at
sures continual feeding of both poles? Oneanswer could be
the beat (ω–Ω) frequency, which is always stronger than
to invoke a field aligned exactly with the spin axis, δ = 0,
the power at the spin frequency (ω). A harmonic of the
but this would also remove the beat pulse, since nothing
beatfrequency,2(ω–Ω),isalsoprominentintheequivalent
wouldchangewithbeatphase.Italsoconflictswiththefact
widths. Other sidebands detected include ω–2Ω in the Hβ
that we see spin-cycle variations of the emission lines (see V/R ratios and 2ω–Ω in theHeiiλ4686 equivalent widths.
Section 7).
There is significant power at the orbital frequency in the
V/Rratios(aone-dayaliasbeingthehighestpeak)butnot
Asecondanswermightbetoinvokelarge,extendedac-
in the equivalentwidths.
cretion footprints, coupledwith alargeδ sothatthesesites
To help us interpret the line profiles of V2400 Oph we
wouldbenearthewhite-dwarfequator.Inaface-onsystem,
havecomputedsimulationsoftheprofilesexpectedinadis-
any accretion sites extending across the equator would al-
cless IP. We first describe this model, and then present a
waysbepartlyinview,and,withbothpolespartiallyvisible,
comparison of simulated and observed profiles.
any pole-flipping modulation would not be total. Arguing
against this, however, is the fact that the visibility of the
poles would then be exquisitely sensitive to orbital phase,
andwedonotseeanyorbitalmodulation intheX-rayflux. 4 MODEL LINE PROFILES
Also, the fact that we see variable circular polarisation but
ThemodelweusetosimulatethelineprofilesofV2400Oph
not variable linear polarisation argues that we do not see
isillustrated inFig. 4.Weassumeadipolefieldcenteredat
thepoles sideways on (Buckley etal. 1995).
thewhite-dwarfcentre—observationsofAMHerstarsoften
A final possibility could invokeafield geometry that is indicatetheneedforamorecomplexfield(e.g.Wickramas-
more complex than a dipole, in which both poles were al- inghe & Ferrario 2000) but we know less about the fields
ways on the near, visible hemisphere. However, this is con- in IPs, so adopt the simplest approach. We assume that at
tradicted by the fact that the circular polarisation always some radius, Rmag, the stream attaches to the nearest field
hasthesamesign,arguingthatweonlyseeonepole(Buck- lineandfollowsthisline,takingthegravitationallydownhill
ley etal. 1995). Thus, the absence of an X-ray spin pulse direction,ontothewhitedwarf.(Strictly,thefieldstrength,
(cid:13)c 0000RAS,MNRAS000,000–000
4 C. Hellier and A.P.Beardmore
Figure 6.TheFouriertransformsoftheequivalentwidthsandV/RratiosoftheHβ andHeiiλ4686lines.
and thus Rmag, would be a function of the dipole orienta- themaindifferencebeingthattheyaimedformodelFourier
tion,buthowthematerialfeedsontothefieldlines,whether transforms whereas we aim to compare line profiles.
itpassesthroughashock,andhowmuchtherateoffeeding Fig. 7shows asamplesetof simulatedlineprofiles. We
dependsondipoleorientation arealluncertain,soagain we adoptedspinandorbital cyclesof927 sand 3.42 h,awhite
adopt thesimplest approach.) dwarf mass of 0.80 M⊙, and a secondary mass of 0.37 M⊙.
Theinclinationwas10◦,thedipole-offset,δ,was60◦andthe
TheradiusRmag,theangleδ,andtheinclinationofthe radius Rmag was 20 Rwd. The four panels are for emission
at different distances from thewhite dwarf.
binary are all free parameters. We assume, arbitrarily, that
the stream feeds a 20◦ swathe of azimuth. We then calcu- Avelocityvariationattheorbitalcycleisobviousinall
panelsofFig.7.Notethatthisisprimarilytheinfallvelocity
late the free-fall velocities along the field lines and project
of the stream, as in an AM Her star, and is not the orbital
them onto the line of sight to produce line profiles. We as-
velocityofthewhitedwarf,whichismuchsmaller.Thespin
sume that the emitting regions are optically thick, and so
andbeat cyclesare seen as themuch faster variation in the
scalethelineintensitybyprojectedarea.Also,formaximum
simulated profiles.
simplicity, we assume that the field lines are not distorted
by their interaction with the flow, and that the material
starts infalling with near-zero velocity at Rmag, as though
it passes through a shock. We also assume that the infall
5 LINE PROFILES OVER THE ORBITAL
time is short compared to the spin cycle, and thus do not
CYCLE
allowforthefactthatthestreamwillhavemovedonbythe
time thematerial accretes. Lastly, we rotate thedipole and The Fourier transforms (Fig. 6) revealed a variation of the
streamlocation tomimicthespinandorbitalcycles.Wedo line profiles over the orbital cycle, but when the observed
not includeany emission from thestream itself, furtherout profiles are folded on the orbital cycle it is hardly visi-
thanRmag,whichwouldproducealower-velocityS-waveon ble (Fig. 8). To enhance the variation we have subtracted
the orbital cycle. Note that the above model is very simi- the phase-invariant profile (for each velocity we found the
lartothatdevelopedbyFerrario&Wickramasinghe(1999), phase bin with the lowest value and subtracted that from
(cid:13)c 0000RAS,MNRAS000,000–000
The intermediate polar V2400 Oph 5
Figure7.Simulatedlineprofilesinatimesequencecoveringtwo
Figure 8. Line profiles folded on the orbital period. The top
orbitalcycles.Thefourpanelsshowprofilesfordifferentdistances
panel shows the Hβ line; below it are the Hβ and Heiiλ4686
fromthewhitedwarf.Darkercolouringsignifiesstrongeremission
lines after subtraction of the phase-invariant profile. At bottom
inallfigures.
arethesimulatedprofilesfor5–10 Rwd.
(cid:13)c 0000RAS,MNRAS000,000–000
6 C. Hellier and A.P.Beardmore
the data). In the portion of the line remaining, only 5 per
centoftheoriginal,theslightvariationisdiscernable.Since
theorbitalmodulationissosmall,itisclearthatV2400Oph
must be at a very low inclination (as already suggested by
theX-raydata).Butevenso,thelackofvariationisclearly
discrepant with themodel, which is calculated for i=10◦.
By fitting Gaussians to the phase-resolved Hβ profiles
we measure a radial-velocity variation of only 5.8 kms−1,
which agrees with Buckley etal. (1995) who report a limit
of <10 kms−1. If this is the motion of the white dwarf it
implies an inclination of only 3◦ (assuming stellar masses
of 0.7 and 0.3 M⊙). Even this could be too high, since, as
shown by the simulations, we expect the orbital motion to
bedwarfedbyaninfallvelocityofanythinguptothewhite-
dwarfescapevelocity.Theobservationsandsimulationscan
bereconciledonlyif1)thesystemisataninclinationof<1◦
(unlikely, since the a priori probability is only 1.5×10−4),
or 2) much of the emission comes from material that has
circularised about thewhite dwarf and dilutes theemission
fromtheinfallingstream.Thusthevariationsintheemission
lines might be tracing only a part (possibly a small one) of
theflow.
6 LINE PROFILES OVER THE BEAT CYCLE
Fig.9showsthesimulatedprofilesfoldedonthebeatperiod,
againforfourdistancesfromthewhitedwarf.Thechangesin
velocityasthestreamchangesdirectiontoflowtoadifferent
pole are obvious. Note that, at such a low inclination, the
dominantcomponentofthevelocityisthemotionoutofthe
planefollowing thearch ofthefieldlines. Atphasezerothe
stream is flowing to the upper pole, and the emission 10–
20 R out is blueshifted, since it is rising out of the plane
wd
towardsus;theemission 1–10R outisfallingbacktothe
wd
plane and so is redshifted.
In Fig. 10 we show the observed profiles of Hβ and
Heiiλ4686 folded on the beat cycle. Again, we have first
subtractedthephase-invariantprofile(leavingonly5and10
percentofthetwolines,respectively),sincethevariationis
barely discernable in the raw fold. Accompanying the data
are the simulated profiles from 5–10 R out, which give a
wd
roughmatch.ThesimilarityoftheHβlinetothesimulation,
withbothshowingchangesfrom redshift toblueshift,sug-
geststhatweareseeingthechangeinvelocityasthestream
flipsfrompoletopole.Intheobservations,however,theflip
islessabruptthaninthemodel,perhapsindicatingthatthe
stream feeds field lines over a larger range of azimuth than
the20◦ adoptedinthemodel.TheHeiiλ4686linedoesnot
matchsowell,andshowslittlevariationinvelocity.Possibly
thislinecomesmostlyfromneartheapexofthearch,where
motion out of theplane is minimal.
Ourmodelpredictsthatthelineintensityismodulated
at twice the beat frequency (as did the model of Ferrario
&Wickramasinghe1999),andthisagreeswiththepresence
of a 2(ω–Ω) modulation in the equivalent widths (Fig. 6).
Theweakermodulationseenintheequivalentwidthsatω–
Ωisnotpredictedbyourmodel,whichhassymmetricupper Figure 9.Thesimulatedlineprofilesfoldedonthebeatperiod.
and lower poles, but would result from any asymmetry be- Thefourpanelscorrespondtodifferentdistances fromthewhite
tween the poles. Another factor is that X-ray illumination dwarf.
ofthestreamwillvarywithbeatphase,andthiswouldalso
modulate theequivalent widths at thebeat period.
(cid:13)c 0000RAS,MNRAS000,000–000
The intermediate polar V2400 Oph 7
Figure10.Theobservedandsimulatedlineprofilesfoldedonthe
beat period. The data are shown after subtraction of the phase-
invariant profile. The relative phasing of data to simulation is
arbitrary.
7 LINE PROFILES OVER THE SPIN CYCLE
Fig.11showsthesimulatedprofilesfoldedonthespincycle.
Thesymmetricshapeistheresultofthetwooppositepoles,
butnotethatat any onetimeonly oneisaccreting. Thusa
‘snaphot’ of the simulation would show an S-wave, snaking
from red to blue over the spin cycle; after a pole-flip the
inverseS-wavewouldbeseen,andsuchS-wavesaccumulate
to produce the symmetric pattern when a long sequence is Figure11.Thesimulatedlineprofilesfoldedonthespinperiod.
folded. Thefourpanelscorrespondtodifferentdistances fromthewhite
Again, the dominant velocity is the motion out of the dwarf.
plane, so that the profiles 10–20 R out (where material
wd
risesoutoftheplane)tendtoshowthereverseoftheprofiles
(cid:13)c 0000RAS,MNRAS000,000–000
8 C. Hellier and A.P.Beardmore
from 1–10 R (wherematerial falls back).Iftherewereno
wd
effect of inclination the profiles would repeat exactly twice
perspincycle,butthetilttoaninclinationof10◦ isenough
to break thesymmetry.
Fig. 12 shows the spin-folded Hβ and Heiiλ4686 pro-
files, again accompanied with the simulated profiles from
5–10 R , which give a good match to the Heiiλ4686 line.
wd
In the simulation the upper pole is at the “3 o’clock” posi-
tion at phase zero and rotates counterclockwise. At phases
0.2–0.3 we are seeing the upper pole furthest from us and
the lower pole towards us. The material at 5–10 R is be-
wd
ginning to fall back to the plane. The 10◦ inclination tilts
this motion towards the plane of the sky,reducing the pro-
jected velocities, and the profile is thus narrowest. Half a
cyclelater (upperpole towards us),theinclination tilts the
infallmotiontowardstheline-of-sight,andtheobservedve-
locities are higher.
The profiles from Hβ are noisier than those from
Heiiλ4686: after subtraction of the phase-invariant profile
only 3 per cent of the original Hβ line remained. However,
the profile can be interpreted as being similar to that of
Heiiλ4686, with the exception that the blue wing seen at
phases 0.4–0.8 is missing.
7.1 Varying the model parameters
In the previous sections we have compared observed line
profiles with models calculated for emission 5–10 R from
wd
the white dwarf. We should emphasise that we do not re-
gard the models as fits, since the model contains too many
assumptions and adjustable parameters to lead to a unique
solution. Instead,we describe heretheresult of varyingthe
parameters. Sincethesimulation calculates infall velocities,
changing Rmag or the white-dwarf mass simply scales the
velocities without altering the shape of the model profiles.
Similarly, adding an injection velocity at Rmag would in-
crease the velocities at all points. Increasing the 20◦ range
ofazimuthoverwhichaccretionoccurswouldsmearoutthe
profiles, but retain the overall shape.
However, the shape of the spin-resolved profiles is af-
fected by the dipole offset, combined with the inclination.
At zero inclination, of course, our view would not change
with spin phase and there would be no spin-cycle modu-
lation. This rules out the extreme inclinations of <3◦ dis-
Figure12.Theobservedandsimulatedlineprofilesfoldedonthe
cussed in Section 5—only byadoptingan inclination ofat
spin period. The data are shown after subtraction of the phase-
least 10◦ do we reproduce the observed spin-resolved pro-
invariant profile. The relative phasing of data to simulation is
files, in which the narrow profile at phase ≈0.2 changes to arbitrary.
abroader,splitprofileatphase≈0.7.Evenwithaninclina-
tion of 10◦, theprofile is only reproduced with δ>30◦: any
lowerandthechangeinviewing angleoverthespincycleis
flips from one magnetic pole to the other over the beat cy-
insufficienttoreproducetheobservedprofiles.Ofcourse,we
cle—thehallmark ofdiscless accretion in anasynchronous
can also reproduce the spin-resolved profiles using a higher
magneticcataclysmicvariable.Wehavefoundthatasimple
inclination, but that only increases the problem of the lack
modelofthisbehaviour,inwhichastreamfallstothemag-
of orbital modulation.
netosphere and then feeds thenearest field line, reproduces
theobserved line-profile changes overthespin and beat cy-
cles.However,itshouldbenotedthattheline-profilevaria-
tionsinvolveonly≈5percentofthelineemission,andthat
8 DISCUSSION
thebulk of the emission shows no detectable variation.
WehaveshownthattheemissionlinesinV2400Ophvaryon As a result of this, thevariations overtheorbital cycle
both the spin and the beat cycles, and that the variations arehardertointerpret.Weadoptaninclinationof10◦,since
are compatible with a model in which the accretion flow this is the minimum necessary to reproduce the line-profile
(cid:13)c 0000RAS,MNRAS000,000–000
The intermediate polar V2400 Oph 9
variationsoverthespincycle(Section7).However,ifallthe 8.1 Relation to other systems
emissioncamefromacollimated,infallingstream,thisincli-
We have detected variations of the line profiles over the
nation would lead to an orbital modulation of hundreds of
kms−1,whereas theobservedvalueisonly5.8kms−1 (Sec- spinfrequencyinV2400Oph,whereashithertothespinfre-
quencyin thisstar has been seen only in circular polarime-
tion5).Thisimpliesthatthebulkoftheemittingmaterialis
try. This is reassuring, for the following reason. Most IPs
not in the infalling stream, but is instead symmetric about
show little or no polarised light, and in such systems an X-
thewhite dwarf.
raypulseistypicallyinterpretedasthespinperiod.Butifit
ThisinterpretationissupportedbyX-raydata,inwhich
wasactually thebeat period,howcould weknow?Thefact
the beat-cycle modulation is only 25 per cent deep. Given
thatbothspinandbeatfrequenciesshowupinthelinepro-
thatthesystemisatsolowaninclinationthatweonlyever
filesofadisclessaccretorlikeV2400Ophmeansthatwecan
seetheupperpole,thissuggeststhatonlyaminorityofthe
distinguishbetweenthespinandbeatfrequenciesevenwith-
accretingmaterialflipsfrompoletopole,andthatthereisa
outpolarimetry.Thismeansthatwecanunambiguouslyde-
continualflowtobothpolesirrespectiveofbeat-cyclephase.
terminespinfrequenciesintheclassasawhole,sincenearly
What is the nature of this flow? One possibility might
all well-studied IPs show both spin and beat cycles in the
be a conventional accretion disc. This could feed field lines
emission lines [e.g. Hellier (1997a) and references therein,
from its inner edge, forming ‘accretion curtains’ of mate-
an exception being TV Col, where neither cycle is convinc-
rial in the usual manner for an IP. However, why, then, do
inglydetectedintheoptical(Hellier1993a;Augusteijnetal.
we see no X-ray spin pulse? Given that the inclination and
1994)].
dipoleoffsetaresufficienttoproduceobviousspin-cyclevari-
Secure identification of the spin and beat frequencies
ations in the emission lines, we would expect the aspect of
strengthenstheclassificationofIPsusingtheideathatdisc-
theaccretionsitestovarywithspinphase,andthusabsorp-
fedaccretorsshowX-raypulses(predominantly)atthespin
tionandscatteringofX-raysintheaccretion curtainwould
cycle while discless accretors show X-ray pulses (predomi-
produce a spin pulse (this is best documented in AO Psc;
nantly) at the beat cycle. Based on this, we would assign
Hellier, Cropper & Mason 1991; Hellier etal. 1996; see also
V2400 Oph as the sole secure member of the discless cate-
themodelofKim&Beuermann1995).Anotherissueishow
gory,andadozenotherstothedisc-fedcategory(e.g.Hellier
thestreamcoexistswiththedisc,since,havingdifferentve-
1991; 1998). An unclear case is TX Col, in which the spin
locities, they couldn’t both occupy the orbital plane. One
pulsedominatesatsomeepochsandthebeatpulseatothers
plausible answer is that the stream could overflow the disc
(Norton etal. 1997; Wheatley 1999).
(see Armitage & Livio 1998 for theoretical simulations of
this).ThisideahasbeeninvokedtoexplaintheIPsshowing V2400 Oph has a 3.42-h orbit and is the highest-field
bothspinandbeatpulsesintheX-raylightcurves(e.g.Hel- IPat9–27MG.Itislikelythatthissystemisontheedgeof
lier 1991). However, again, a spin-cycle pulsation is nearly discformationsincewecanaccountforourobservationsonly
always seen, and, taking the example of FO Aqr, the beat- if there is a substantial ring-like structure of blobs circling
cycle modulation is always weaker or even absent (Norton thewhite dwarf. If the field were a little lower, or the orbit
etal. 1992; Hellier 1993b; Beardmore etal. 1998). slightly wider (so that the angular momentum of the blobs
In view of the difficulties in invoking a disc, we turn caused them to orbit further out), the ring of blobs might
insteadtotheideaofmagneticallythreadedaccretionflows, turn into an accretion disc. Note that PQ Gem, the only
developed by King (1993) and Wynn & King (1995). This IP with a comparable field estimate (9–21 MG; V¨ath etal.
model treats the flow as diamagnetic blobs, which are di- 1996; Potteretal. 1997) has awider orbit of 5.19 h(Hellier
vertedfrom aballistic trajectory bythemagneticdragpro- 1997a). It appears to accrete though a disc, judging by the
ducedbytheircrossingfieldlines.Theresultingtrajectories dominanceoftheX-rayspinpulse(Mason etal.1992). It is
depend on blob size and density. Simulations by King & thuslikely that, with these two systems, we are delineating
Wynn (1999) suggest that it is possible for less-dense mat- theconditions for disc formation in an IP.
tertobeeasilythreadedandcontrolledbyfieldlines(which The theoretical requirements for disc formation have
would then act as in our simulations), while denser blobs longbeendebated(e.g.Hameuryetal.1986;Lamb&Melia
crossfieldlinesandcirculatearoundthewhitedwarf.These 1988). The issue centers on the three distances Rmin (the
blobswouldloseknowledgeoforbitalphase,andeventually radius of closest approach to the white dwarf of a ballistic
bedestroyedbymagnetohydrodynamicinstabilities,feeding streamfromtheLagrangianpoint),thelargercircularisation
their material ontothe white dwarf’s poles. radius, Rcirc (where orbiting material hasthesame angular
Back to the same question, why doesn’t this result in momentumthatithadattheLagrangianpoint),andRinner
anX-rayspinpulse?Wespeculatethatthisprocessismuch (theradiusatwhichthediscismagneticallydisrupted).[We
less orderly than in a disc-fed accretor. A disc might sup- distinguishRinnerfromtheRmag usedabovesincetheradius
plyasteadyflowoverarelativelysmalldisc–magnetosphere isdifferentfor spherical, stream, anddiscflows; seeWarner
transition region, and so feed accretion sites that are small (1995) for a fuller discussion and formulae for these radii.]
and localised. For example they cover only <0.002 of the It is easy to form a disc with Rinner<Rmin, since the
white-dwarf surface in XY Ari (Hellier 1997b). This would stream could freely orbit outside the magnetosphere, cir-
leadtosteady,welldefinedaccretioncurtains,abletoabsorb cularise at Rcirc, and form the disc. It is not possible to
orscattertheX-rayfluxandsomodulateitoverthespincy- form a disc with Rinner>Rcirc since the stream has insuf-
cle.Inthediamagnetic-blobmodel,theaccretionsitescould ficient angular momentum to orbit at these radii. The in-
bewidelystrewnandtransient;theymaynotformcoherent termediate case, Rcirc>Rinner>Rmin, is less clear, but is
accretion curtains and so the spin-cycle modulation could the case applying to most IPs. For example, if we assume
bereduced tobelow thedetection threshold. that PQ Gem has a red-dwarf mass of 0.5 M⊙ (appropri-
(cid:13)c 0000RAS,MNRAS000,000–000
10 C. Hellier and A.P.Beardmore
ate for its 5.19-h orbital period), a white-dwarf mass of 0.7 Lamb D.Q., Melia F., 1988, in Coyne G.V., ed, Polarized ra-
M⊙, and that its magnetosphere corotates with the Kep- diation of circumstellar origin, Univ. Arizona Press, Tucson,
lerian orbit at Rinner, then, given the 833-s spin period, p.45
we have Rinner≈1.1×1010cm, which is larger than Rmin MasonK.O.etal.,1992,MNRAS,258,749
(≈0.6×1010cm) and close toRcirc (≈1.1×1010cm). Norton A.J., Watson M.G., King A.R., Lehto H.J., McHardy
I.M.,1992,MNRAS,254,705
V2400Ophcouldbeshowingusthemechanismfordisc
Norton A.J., Hellier C., Beardmore A.P., Wheatley P.J., Os-
formationunderthesecircumstances.Inthisdisclesssystem
borneJ.P.,TaylorP.,1997,MNRAS,289,362
aringofdiamagneticblobsorbitsinsidethemagnetosphere.
PotterS.B.,CropperM.,MasonK.O.,HoughJ.H.,BaileyJ.A.,
In doing so, theblobs cross field lines and lose angular mo- 1997,MNRAS,285,82
mentum to the field, and so eventually accrete. However, Schwope A.D., Buckley D.A.H., O’Donoghue D., Hasinger G.,
if the field were weaker, as in most IPs, the drag on the TruemperJ.,Voges W.,1997,A&A,326,195
diamagnetic blobs would be lower, and their inward spiral Va¨thH.,ChanmughamG.,FrankJ.,1996, ApJ,457,407
wouldbeslower.Theblobsmightaccumulate,screeningthe Va¨thH.,1997,A&A,317,476
field from each other, and so accumulate further in a run- WarnerB.,1995,CataclysmicVariableStars,CambridgeUniver-
sityPress,Cambridge
away process leading to theformation of a disc.
Wheatley P.J., 1999, in Hellier C., Mukai K., eds, Annapolis
Workshop on Magnetic Cataclysmic Variables, ASP Conf.
Ser.,Vol157,Astron.Soc.Pac.,SanFrancisco,p.47
9 CONCLUSIONS WickramasingheD.T.,FerrarioL.,2000,PASP,112,873
WynnG.A.,KingA.R.,1992,MNRAS,255,83
• V2400 Oph is at a low inclination, estimated as 10◦. We WynnG.A.,KingA.R.,1995,MNRAS,275,9
only ever see theuppermagnetic pole.
•Thereisnoaccretiondiscinthissystem.Thestream-
fed accretion flips from pole to pole on the beat cycle, and
this can be seen directly in the line profiles. However, only
≈25 per cent of the accreting material participates in this
motion.
• The rest of the material appears to be circling the
whitedwarf,perhapsintheformofdiamagneticblobs.Such
blobs may havebeen a precursor to disc formation in other
intermediate polars.
•Thespin-cyclevariationsoftheemission linesareac-
counted for bya simple model of stream-fed accretion. The
bestmatchbetweenmodelanddataisfoundforditances5–
10 R from the white dwarf. The offset between the mag-
wd
neticandspinaxesofthewhitedwarfmustbeatleast 30◦.
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