The Universal Nature of Accretion-induced Variability: The RMS-Flux Relation in an Accreting White Dwarf

0.35 MB·English

by  S. Scaringi

Mon.Not.R.Astron.Soc.000,1–7(2011) Printed5January2012 (MNLATEXstylefilev2.2)
The Universal Nature of Accretion-induced Variability:
The RMS-Flux Relation in an Accreting White Dwarf
2 S. Scaringi1⋆, E. Ko¨rding1, P. Uttley2,3, C. Knigge2, P.J. Groot1, M. Still4,5
1 1Department of Astrophysics/IMAPP, Radboud University Nijmegen, P.O. Box 9010, 6500 GL Nijmegen, The Netherlands
0 2Department of Physics and Astronomy, University of Southampton, Highfield, Southampton, SO17 1BJ, UK
2 3Astronomical Institute “AntonPannekoek”, Universityof Amsterdam, Science Park 904, 1098XH, Amsterdam, The Netherlands
n 4NASA Ames Research Center, Moffett Field, CA 94035, USA
a 5Bay Area Environmental Research Institute, Inc., 560 Third St.West, Sonoma, CA 95476, USA
J

3

]
R
S ABSTRACT
.
h We report the discovery of a linear relationship between the root-mean-square (rms)
p variability amplitude and the mean flux in the accreting white dwarf binary system
- MV Lyrae. Our lightcurve, obtained with the Kepler satellite, spans 633 days with
o
quasi-continuous 58.8 second cadence resolution. We show, for the first time, how
r
t thiscataclysmicvariabledisplayslinearrms-fluxrelationssimilartothoseobservedin
s
manyotherblackholebinaries,neutronstarbinariesandActiveGalacticNuclei.The
a
[ phenomenologicalsimilarity between the rms-flux relationobservedhere and in other
X-raybinariessuggestsacommonphysicaloriginforthebroad-bandvariability,inde-
1
pendentofsourcetype,massorsizeofthecompactaccretor.Furthermore,weinferthe
v
viscosity parameter, α, and disk scale height, H/R, using two independent methods.
9
In both cases, both values are found to be uncomfortably high to be accommodated
5
by the disk instability model.
7
0
Key words: accretiondiscs,stars:binaries:close,stars:novae,cataclysmicvariables,
.
1 stars: MV Lyrae, black hole physics, stars: oscillations.
0
2
1
:
v 1 INTRODUCTION Variability is a common characteristic of X-ray binary
i
X systems (XRBs, consisting of NS or BH accretor), cata-
Compactinteractingbinaries(CBs)areclosebinarysystems
clysmic variables (CVs, consisting of a WD accretor) and
r usually consisting of a late-type star transferring material
a ActiveGalacticNuclei(AGN,wheretheaccretorisasuper-
onto a compact object such as a black hole (BH), neutron
massiveblackhole).Specifically,thepowerspectrumofthis
star (NS) or a white dwarf (WD) via Roche-lobe overflow.
variability consists of two components: single or multiple
With an orbital period on the order of hours, the trans-
quasi-periodic oscillations(QPOs), and an aperiodic broad-
ferred material from the donor star forms an accretion disk
bandnoisecomponentspanningseveraldecadesintemporal
surroundingthecompactobjectinordertoconserveangular
frequency. QPOs have been extensively studied in a num-
momentum. The dynamics and physics governing the flow
berofaccretingsources,rangingfromWDbinaries(Warner
of matter accreting onto compact objects is however still
2004;Pretorius et al.2006),tosuper-massiveblackholesat
debated. BH and NS compact binary systems are powerful
the centre of AGN (Gierlin´ski et al. 2008). On the other,
and highly variable sources in X-rays,and it is by studying
handthepropertiesofthebroad-bandnoisecomponenthas
the fluctuations in X-ray luminosities that we have made
been examined in detail only in XRBsand AGN.
progresstowardsunderstandingthephysicsinvolvedwithin
accretiondisks(Belloni2007;van derKlis2007).Forexam- One feature of the broad-band noise X-ray variabil-
ple, thanks to the Rossi X-Ray Timing Explorer (RXTE), ity which seems to be ubiquitous in XRBs and AGN is
van derKlis et al.(1996)havebeenabletodetectfast(kHz) the so-called rms-flux relation, which is a linear relation-
quasi-periodic oscillations (QPOs) in NS binaries, associat- ship between the absolute root-mean-square (rms) ampli-
ing these with the inner edges of the accretion disk. The tudeofvariabilityandtheflux,suchthatthesourcesbecome
detected kHz QPOs can immediately be used to constrain morevariableastheygetbrighter(Uttley & McHardy2001;
themass and radius of theNS (Miller et al. 1998). Uttley et al. 2005; Gleissner et al. 2004; Heil & Vaughan
2010). The rms-flux relation is remarkably linear and ap-
plies over a broad range of time-scales, so that the rms of
⋆ E-mail:[email protected] high frequency variations correlates with those at low fre-
2 S. Scaringi et al.
quencies (Uttley et al. 2005). Crucially, the rms-flux rela- AGN, is well studied because of the high throughput X-
tion is observed while the power-spectrum shape is itself ray missions with good timing capability (RXTE, XMM-
stationary, implying that the rms-flux relation is a funda- Newton),allowingveryshortcadence(downto ms)obser-
≈
mentalpropertyofthevariabilityprocess,andnotconnected vations, at high sensitivities. In the optical, Gandhi (2009)
with otherprocesses which can changethevariability prop- observed three XRBs with ULTRACAM (Dhillon et al.
erties on longer time-scales. Finally, it can be shown that 2007) and, as expected,also found that thelightcurves dis-
the rms-flux relation predicts a log-normal distribution of play similar rms-flux relations as those observed in the X-
fluxes and implies that the variability process is non-linear rays(although theopticalemission couldpossibly originate
(Uttley et al. 2005). The current most-favoured model to from the jet and not the disk). Accreting white dwarfs are
explain the rms-flux relation, as well as many other fea- faint in X-rays, since their gravitational potential wells are
turesof thevariability in XRBsand AGN,is thepropagat- not as deep as those of XRBs (so they show lower inner
ing fluctuations model (Lyubarskii 1997; Kotov et al. 2001; disc temperatures) and also (unlike AGN and XRBs) they
Ar´evalo & Uttley 2006). In this model, the observed vari- do not seem to possess strong Comptonising coronae. Be-
ability is associated with modulations in the effective vis- cause of this, detailed timing studies in the X-ray region
cosity of the accretion flow at different radii. More specifi- have not been possible for disk-fed white dwarfs, and most
cally, the model assumes that, at each radius, the viscosity timingstudiesofthesesystemsconcentratedonopticallight.
– and hence accretion rate – fluctuates on a local viscous Specifically,aseriesofpapers(Warner2004;Pretorius et al.
time scale around the mean accretion rate, whose value is 2006) already noted analogies between the QPOs observed
set by what is passed inwards (again on the viscous time inCVsandthoseobservedinXRBs.However,detailedanal-
scale) from larger radii. Theoverall variability oftheaccre- ysis of the broad-band noise component in CVs was so far
tionrateintheinnermostdiskregionsisthereforeeffectively not as straight forward as for XRBs. The reason for this
theproduct of all the fluctuationsproduced at all radii. is twofold: first, the broad-band noise component displays,
ForCVs,thepresenceofbroad-bandnoiseinthepower in the optical, low-amplitude, few per cent fractional rms
spectrum has been recognised for many years and is usu- variations requiring sensitive cameras; second, the broad-
ally referred to as “flickering” in the literature. However, band noise component can only be studied with long, con-
the methods employed to study XRB lightcurves have not tinuous, observations. This is because optical broad-band
been applied to CV data. The properties of flickering have noiseisthoughttobegeneratedfurtheroutintheaccretion
been mainly studied through the use of eclipse maps (eg. disk compared to X-rays, and is thus observed on longer
Baptista & Bortoletto(2004)),whichhaveidentifiedtheex- timescales. Furthermore, broad-band noise is a stochastic
istenceoftwodifferentandindependentsourcesofflickering: process, requiring statistical studies of many realisations.
thelowandhigh-frequencyflickeringcomponents.Thelow- This, in turn,demands long continuous observing. In order
frequency component originates from the overflowing gas to truly assess whether accreting white dwarfs display the
stream from the secondary star, and is associated with the rms-flux relation, and thus determine if this phenomenon
mass transfer process. The high-frequency component, on is indeed ubiquitous in all accreting compact objects, irre-
the other hand, originates from the inner accretion disk re- spectiveofaccretortype,asensitive,long,high-cadenceand
gion,andnoevidenceofvariableemissionfromthehotspot, continuous light curve in the optical light is required. This
gas stream, or white dwarf has been observed (contrary to kind of observation has only now become possible, thanks
some previous suggestions, see Bruch 1992, 2000). to theKepler satellite (Koch et al. 2010).
XRBs and AGN, which do show the rms-flux relation,
share many properties with CVs. Both XRBs and CVs are
observed to exhibit large-amplitude outbursts, which are HereweanalysetheKepler lightcurveoftheaccreting
theoreticallyexplainedasarisingduetothermal/viscousin- whitedwarfsystemMVLyrae(oneofabout14CVsknown
stabilities in the accretion disks surrounding the compact to exist within the Kepler field-of-view), and show that it
objects (Shakura& Sunyaev 1973). Furthermore, similarly does indeed exhibit an rms-flux relation similar to that ob-
to XRBs, CVs also display outflowing jets in conjunction served in Cyg X-1 by Gleissner et al. (2004). MV Lyrae is
with specific changes in the spectral energy distribution aVYSclnova-likesystem,spendingmost ofits timein the
(K¨ording et al.2008).Therefore,itisnaturaltosuspectthat highstate(V 12 13) andoccasionally (everyfewyears)
≈ −
CVsshould alsoshowbehaviourassociated with afluctuat- undergoingshort-duration (weeks/months) dropsin bright-
ing accretion flow, including the rms-flux relation which is ness (V 16 18, Hoard et al. 2004). It is not clear why
≈ −
seeninaccretingBHandNS.However,althoughCVsshare MV Lyrae, and all VY Scl type stars, undergo this kind
manysimilaritieswithXRBsandAGN,theyalsodiffersub- of behaviour, but it is known that these systems have ex-
stantiallyinotherrespects.Specifically,theradiusofaWD tremelylowmasstransferratesattheirminimumbrightness
is over an order of magnitude larger than that of a NS or (6 10−10M Linnell et al. 2005; Hoard et al. 2004). The
the event horizon of a BH. Because of this, accreting white infe×rreddista⊙ncetoMVLyraeis 530pc,withasecondary
≈
dwarfsarenotsubjecttotheeffectsofstronggravity.Addi- star cooler than 3500K (Hoard et al. 2004).Theorbital pe-
tionally,accretingWDshavenotbeenobservedtodisplaya riod of this CV is 3.19 hours, with a binary mass ratio of
comptonisedcomponentasinXRBsandAGN,andfurther- 0.43 (Skillman et al. 1995). We observed MV Lyrae during
more they do not posses the extreme magnetic fields which itsfinalascent,inalow-to-highluminositytransition,where
are found in some NS. Therefore it remains an important itsopticallightmostlyoriginatesfromitsnearlyface-onac-
open question as to whether accreting WDs should show cretion disk (Skillman et al. 1995). In the next section we
thesame rms-fluxbehaviouras seen in XRBs and AGN. will describe the data acquisition and analysis, whilst our
Thebroad-bandnoisecomponent,presentinXRBsand results and discussion are presented in Section 3.
Accretion induced variability in CVs 3
2 DATA ANALYSIS 5000
The MV Lyrae light curve was obtained with the Kepler
satellite andprovidedtousbytheScienceOperationsCen- 4500
tre1 inreducedandcalibratedformafterbeingrunthrough
the standard data reduction pipeline (Jenkins et al. 2010).
The response function for the photometry covers the wave- 4000
lengthrange4000 9000˚A.Here,weonlyconsidertheSingle
AtopaerntaulryesePhthoteomPre−et-rsyea(rScAhPD)alitgahtCcounrdvietiaonndindgo(nPoDtCat)telmigphtt −−1e s)3500
curve, as the latter is optimised for planet transit searches. σ (
Asa consequence of thischoice, data artifacts which would 3000
havebeenremovedbythePDC,remain inourKepler SAP
light curve. These artifacts are the result of rapid attitude
tweaks to correct pointing drift, caused by the loss of fine 2500
pointingaccuracy.Thispointingaccuracy loss is duetothe
spacecraft thrusters firing regularly every 3 days to desat-
2000
urate the reaction wheels and can affect Kepler data for
7 7.5 8 8.5 9 9.5 10 10.5
several minutes. Furthermore, data gaps occasionally occur Flux (104 e− s−1)
due to Kepler entering anomalous safe modes. During such
events no data is recorded and following data is often cor- Figure 2. Rms-flux relation obtained from a 10 day segment
(indicatedbytheyellowshadeinFig.1)inMVLyrae.
related with electronic warming. Furtherdetails of artifacts
withinKepler light curvescan befoundintheKepler Data
ReleaseNotes32.Here,wemakenoattempttocorrectthese
reasonably well, although occasionally large χ2 values are
artifacts, butsimply remove them from thelight curve.
recovered,implyingthereexistssomeintrinsicscatter.This
Fig.1 shows the short cadence (58.8 seconds;
scattercanbecausedbyanynon-stationarityinthevariabil-
Gilliland et al. 2010), barycentre corrected, light curve
ityprocesseswhichcausesvariationsintherms-fluxrelation
for MV Lyrae obtained during the first four quarters of
on the 10 day time-scale of the segments. Furthermore, the
Kepler operations. The lightcurve spans an interval of 633
presenceofanyfrequency-varyingQPOcouldbreakthelin-
days. The visible data gaps present in the light curve are
earrms-fluxrelationbyvaryingthepowerspectrumoverthe
due to the artifacts described above as well as the monthly
frequency-rangeused tomeasure therms.In Fig.3 we show
data down-links. At first glance the light curve reveals an
the noise-subtracted power spectral density (PSD) of the
obvioussteady increase in flux(over1magnitude) and also
fourcoloured,independent,sectionsshowninthelightcurve
an increase in theflux variability (rms) during therise.
of Fig.1. The timescales used to measure the rms are those
To characterise the relationship between the rms vari-
at frequencies higher than 10 minutes, marked the dashed
ability and the mean flux, we followed a similar proce-
black line in Fig.3. For each segment, these rms values will
dure as used by Gleissner et al. (2004) on Cyg X-1. Whilst
respondtofluxvariationsonlongertime-scales,downtothe
Gleissner et al.(2004) usedthemean PSD leveltomeasure
10 day length of the segment.
rms,wedirectlymeasureitfromthespreadinthelightcurve
The PSDs shown in Fig.3 show possible candidate
datapoints.First,theMVLyraelightcurvewassplitinto10
QPOs at low frequencies and breaks just above 10−3Hz.
day segments. For each segment we computed 10 minute
Fromthemodelling performed byAr´evalo & Uttley(2006),
flux averages and corresponding rms. All 10 day segments
thesebreakscanbeassociatedwiththeviscoustimescaleat
analysed displayed linear rms-flux relations after binning
theinner-mostedgesoftheaccretion disk.Abovethebreak
the 10 minute averages by flux. One example is shown in
frequency,noannulicontributesignificantvariabilitypower,
Fig.2. We carried out the same exercise employing smaller
andthePSDbendsdownwards.Giventhatthefourdifferent
andlarger datasegments,and longer andshorteraveraging
quadrantsappeartodisplayshiftsinthebreakfrequency,it
timescales. In each case, we still recovered linear rms-flux
is possible that mass accretion rate variations are displac-
relations. This is already strong evidence that the optical
ing the inner edges of the accretion disk. Furthermore, at
variabilityobservedintheaccretingWDisanalogoustothe
frequencies below the break, there appears to be candidate
X-ray variability seen in XRBsand AGN.
QPOs.Thesefeaturesatlowfrequencies,andthePSDbreak
InordertoquantifythelinearrelationshipinFig.2,we
shifts, will be analysed and discussed in a paper in prepa-
modelleditwithafunctionoftheform(Uttley& McHardy
ration: here we are only concerned with the high-frequency
2001),
component observed in MV Lyrae.
σ=k(F C) (1) AnotherinterestingfeatureobservedinMVLyraecon-
−
where σ is the rms value, F is the flux in e−s−1, whilst cerns the evolution of the rms-flux relation with both flux
andtime.InFig.4weshowthebest-fitlinesfortherms-flux
k and C are the fit parameters. This linear model fits the
relations in all of our 10-day segments. In order to give a
general shape of the majority of our flux-sorted segments
feelforthetemporalevolutionoftherms-fluxrelation,each
colour represents a different section in the lightcurve, with
1 Thedataispropritary.ThefirstfivequartersofKepler obser- thecoloursinFig.1associatedtothoseinFig.4.Specifically,
vationswillbecomepubliconJanuary72012 there appears to be a hysteresis-like behaviour in the evo-
2 http://archive.stsci.edu/kepler/documents.html lution of the rms-flux relation within the broad-band noise
4 S. Scaringi et al.
Figure1.MVLyraelightcurveobtainedbytheKepler satellite.Thesourcewasobservedinshortcadencemode(58.8secondcadence)
for 633 consecutive days. The light curve segment within the yellow shaded region was used to produce the rms vs. flux plot in Fig.2.
Theblue,red,greenandmagentaregionshavebeenusedtoproducethePSDsandrms-fluxrelationsinFig.3,Fig.4andFig.5.Thelast
233days,markedbythemagentaregion,hasbeenusedtoproducethefluxdistributioninFig.6.
fluxinFig.1,afterabout 250daysof observations,therms-
flux relations seem to change behaviour once again during
theirfluxdescent(redlines),seeminglyloopingbacktotheir
d) originaltrackafterhavingreachedamaximumrmsvariabil-
e
alis10−3 ity of about 6%. This behaviour has not been observed in
m any other accreting compact binary or AGN, and it is not
or
n clear at the time of writing what the physics behind this
ms phenomenonis.InFig.5weshowthegradientandintercept
y (r forthebest-fitlines inFig.4,colourcoded in thesameway.
c
en SimilarlytotheresultsobtainedontheBHbinaryCygX-1
u
eq byGleissner et al.(2004),thegradientandinterceptinMV
× Fr Lyraeseemtobecorrelatedaswell.Thissuggeststhatsome
er fundamentalandanalogousprocessisgivingrisetotherms-
w
Po fluxbehaviourinbothXRBsandCVs.Interestingisalsothe
factthatinthegradientvs.interceptplanethereseemtobe
two distinct “tracks”: the rms-flux relations obtained from
10−4 the blue and red lightcurve segments seem to have a sys-
10−4 10−3 10−2 tematic offset in the gradient when compared to the green
Frequency (Hz)
andmagentasegments.Althoughwecannotproperlyquan-
Figure 3. Power spectral distribution obtained from the MV tify this behaviour at the moment with the available data,
Lyrae lighcurve shown in Fig.1. The colour coding is analogous the evolution in Fig.4 also seems to suggest that the rms-
tothat inFig.1,sothat eachindependent PSD wasobtained by fluxbehavioursystematically changesduringthelightcurve
the corresponding light curve segment. The Poisson noise level, evolution.
rangingbetween2−3×10−5,hasbeensubtracted.Inthispaper Finally, we also examined the flux distribution within
we analyse frequencies higher than those marked by the black
the MV Lyrae lightcurve. Specifically, the observed fluxes
dashedline.
in XRBs and AGN which do show the rms-flux relation
are log-normally distributed. In order to perform this test,
of MV Lyrae. After about 150 days, the rms-flux relations we produced a histogram of fluxes from the last 233 days
seemtochangebehaviouranddetachfromtheoriginaltrend (marked by the magenta region in Fig.1) of the MV Lyrae
(markedwith bluelinesin Fig.4)and movetohigherfluxes lightcurve. We then fitted the histogram with both a sym-
maintainingsimilarrmsvariability.Inproximityofthepeak metric Gaussian and a three-parameter log-normal model.
Accretion induced variability in CVs 5
0.8 7
6.5
0.7
6
0.6
5.5
0.5 %)
4−−1σ (10 e s)00..34 actional rms (4.545
Fr
3.5
0.2
3
0.1
2.5
0 2
0 2 4 6 8 10 12 14 16 2 4 6 8 10 12 14 16
Flux (104 e− s−1) Flux (104 e− s−1)
Figure 4. Right: The best-fit lines for the rms-flux relations in all of our 10-day segments, where one is shown in Fig. 2. In order to
followthe temporal evolution of the rms-fluxrelations, colours arematched to those inFig.1. Theblack data points arethe mean flux
andmeanrmsvaluesofthecomputedrms-fluxrelationfits.Left:Samefigure,wherethey-axisdisplayspercentage fractionalrms.
0.14
0.12
103
0.1
nt0.08
e
di N
a
Gr0.06 102
0.04
0.02
0 101
0 0.1 0.2 0.3 0.4 0.5 0.6 0.7 7 8 9 10 11 12 13 14
Intercept / Mean Flux Flux (104 e− s−1)
Figure5.Best-fitparameters(gradientandinterceptfromEq.1 Figure6.Binnedfrequencydistributionofthemeansourceflux
normalised by the mean flux of each 10-day segment) from the for the magenta section of the MV Lyrae light curve in Fig.1
rms-fluxrelations shown in Fig.4. The colour coding is matched (blackdatapoints).Alog-normaldistributionfitisshowninred
tothoseinFig.1. andaGaussianfitinblue.Alog-normalfitstatisticallydescribes
thedatabetter thanaGaussian.
3 DISCUSSION
Thenumberoffluxmeasurementsperbin(N)wasrequired
to be at least 50 for the fits, with bin error assigned as We showed how the accreting WD MV Lyrae obeys a lin-
√N.Weperformedthisexerciseonthelast 233daysofthe ear rms-flux relation like many other BH/NS compact in-
lightcurve,astheseappeartobemostthestationaryinmean teracting binaries and AGN. This is the first time such a
flux: a requirement for the log-normal behaviour to be ex- correlation was found in an accreting object other than a
pected (see Uttley et al. 2005; Gandhi 2009). Statistically, BH/NSX-raybinaryorAGN.Furthermore,weshowedhow
the Gaussian fit resulted in the goodness-of-fit parameter therms-fluxrelationevolveswithtime,displaying,whatap-
χ2/d.o.f of 18802/269, whilst the log-normal fit resulted in pears to be, a hysteresis-like behaviour. The physics of this
334/269.MVLyraeclearlyexhibitsalog-normalfluxdistri- phenomenon is not yet understood, and it is the first time
bution.Theexcessresidualofourfitcanbeexplainedbythe it has been observed in an accreting compact object. Addi-
weaknon-stationarityofthelightcurve,asalsoexplainedin tionally, we confirmed our findingsby ascertaining that the
Uttley et al. (2005) and Gandhi (2009). fluxdistributionofMVLyraefollowsalog-normaldistribu-
6 S. Scaringi et al.
tion, as seen in other accreting compact objects displaying
thelinear rms-fluxrelation.
The leading interpretation of the rms-flux relation is
thatofafluctuatingaccretiondisk(Lyubarskii1997),where
variations in the accretion rate occur at all radii and then
propagate inwards on the viscous timescale within the ac-
cretion disk. These fluctuations couple together in a multi-
plicativeway astheypropagate downtothecentre,so that
lowfrequencyfluctuationsproducedatlargeradiimodulate
the higher frequency fluctuations produced further in. The
multiplicativenatureoftheprocesswillyieldfluxvariations
whichfollowalog-normaldistribution,liketheoneinFig.6.
Churazov et al.(2001)havepointedoutthat,inastan-
dard thin disk, viscous damping will smooth accretion rate
fluctuations on the viscous timescale. This means that, for
theLyubarskii(1997) modeltowork, thefluctuationsmust
happen in a geometrically thick accretion disk flow (such
as an advection dominated flow or thick disk). We can use
the PSD break just above 10−3Hz ( 13 minutes, shown in
≈
Fig.3), or the relative rms variations, to constrain the vis- Figure7.ViscoustimescaleasafunctionofH/Rfromthestan-
cosity parameter, α, and thedisk scale height, H/R. dard α-disk solution (Franketal. 2002, Eq. 5.68). Each colour
The PSD break in Fig.3 can be associated to the vis- corresponds toadifferentαwithblack, blue,green andredcor-
cous timescale at the inner edges of the accretion disk respondingto 0.001, 0.01, 0.1and 1respectively. Thehorizontal
(Ar´evalo & Uttley2006).Ifthiswerethecase,wewouldre- linemarksthePSDbreakat≈13minutes.
quireageometrically thickdiskofaboutH/R 0.1(where
≈
H/R is the ratio of the vertical scale height to radius in
the disk), and a viscosity parameter α 1. This is shown One other important implication of our discovery re-
≈
in Fig.7, where we computed the viscous timescales result- gardstheinterpretationofflickeringnoiseinCVsingeneral.
ingfrom thestandardα-disksolution ofFrank et al.(2002) IthasbeenrecognisedformanydecadesthatalmostallCVs
(Eq. 5.68) as a function of H/R for an accretion disk ex- display at least some optical flickering. Many suggestions
tending all the way down to the WD surface at 7 108cm. haveemergedinordertoexplaintheoriginofthisflickering,
×
Both these values are considered to be high for a standard by associating it to the accretion hot spot or the boundary
disk solution, and are pushing into uncomfortable limits of layerclose to theWD surface (Bruch 1992, 2000). More re-
theShakura& Sunyaev(1973) parameter space. cently, Baptista & Bortoletto (2004) showed that CV flick-
Following the procedure adopted by ering is caused by the existence of two different and inde-
Baptista & Bortoletto (2004) on V2051 Oph, we also pendentsources. Thelow-frequency flickeringcomponent is
used the rms variability amplitude to obtain α and H/R. caused by the overflowing gas stream from the secondary
From the inferred 3% rms variability (see Fig.4) we obtain, star,whilstthehigh-frequencycomponentbytheinner-most
similarly to V2051 Oph, α 0.16. This estimate assumes regionsoftheaccretiondisk.Ourresultisinagreementwith
an H/R value of about 10−2≈, and is based on the effects of the interpretation that the high-frequency flickering is cre-
magneto-hydrodynamic (MHD) turbulence in an accretion atedwithintheaccretiondisk.Thefactthatweobservethe
disk, as modelled by Geertsema & Achterberg (1992). linearrms-fluxrelation within MV Lyrae(acanonical flick-
However, when the variability reaches 6% in MV Lyrae, eringCV)givesusconfidencethatthefluctuatingaccretion
α 0.62, again pushing into uncomfortable limits of the disk model is also at play within other CV systems. Fur-
≈
Shakura& Sunyaev (1973) parameter space. To make α thermore, the observed fractional rms amplitude of 3%,
≈
consistent with the expected viscosity of hot disks (Lasota generallyobservedinMVLyrae(seeFig.4),isalsosimilarto
2001), the disk scale height, H/R, would have to increase that found in V2051 Oph byBaptista & Bortoletto (2004).
to 0.1. This would then be in line with a geometrically Although it is clear from the Lyubarskii (1997) model
thick, hot, disk. If this were the case, the rms variability thatthevariability istheresult ofmodulations from an en-
amplitude would be an indicator of the disk scale height sembleofcoupledperturbations,thephysicalmechanismof
(assuming α to remain constant at it’s hot value of 0.1 variableemissionisnotyetknown.Somesuggestedthatsyn-
≈
– 0.2). More importantly, all the above estimates for the chrotronemission at thebaseoftheoutflowingjet couldbe
diskscale height andαaresuggesting thatthepropagating a possibility (King et al. 2004). However MV Lyrae is not
fluctuation models may have difficulty in explaining the known to display a jet (or synchrotron emission), and it is
variability if the disc behaves like a “standard” thin notlikelythatacomptonisedcomponentisdrivingtherms-
disc. One way to overcome these inconsistencies would flux relation out to the large radii observed in the optical.
be to invoke an overflowing gas stream, as mentioned by More likely instead is that instabilities within theaccretion
Baptista & Bortoletto (2004). This flow could exist above disk are responsible for drivingthecontinuum variability.
the standard thin accretion disk, extending all the way This interpretation is also supported by the recent re-
close to the WD surface, and possibly provide the thick sults of Uttley et al. 2011. They showed that for XRBs
disk required to explain the fast viscous timescale inferred the blackbody component in X-rays, associated with the
from the PSD breaks. disk, substantially leads the power law component associ-
Accretion induced variability in CVs 7
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ACKNOWLEDGEMENTS
Uttley P., McHardy I. M., 2001, MNRAS,323, L26
This paper includes data collected by the Kepler mis- UttleyP.,McHardyI.M.,VaughanS.,2005,MNRAS,359,
sion. Funding for the Kepler mission is provided by 345
the NASA Science Mission directorate. This research has Uttley P., Wilkinson T., Cassatella P., et al., 2011, MN-
made use of NASA’s Astrophysics Data System Biblio- RAS,414, L60
graphic Services. S.S. acknowledges funding from NWO van der Klis M., 2007, in Society of Photo-Optical Instru-
project 600.065.140.08N306 to P.J. Groot. P.U. acknowl- mentation Engineers (SPIE) Conference Series Vol. 6603
edges funding from an STFC Advanced Fellowship and of Society of Photo-Optical Instrumentation Engineers
from the European Community’s Seventh Framework Pro- (SPIE)ConferenceSeries,Millisecondphenomenainmass
gramme (FP7/2007-2013) under grant agreement number accreting neutron stars
ITN 215212 “Black Hole Universe”. M.S. acknowledges vanderKlisM.,SwankJ.H.,ZhangW.,etal.,1996,ApJL,
fundingfrom theNASAgrant NNX11AB86G. 469, L1
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