Are disk in dwarf novae during their superoutbursts really eccentric?

0.17 MB·English

by  J. Smak

Are Disks in Dwarf Novae during their Superoutbursts
Really Eccentric ?
9
0 J.Smak
0
2

n NicolausCopernicus AstronomicalCenter, Polish AcademyofSciences
a
ul. Bartycka18, 00-716 Warsaw,Poland
J
e-mail: [email protected]
9
1

]
R
Abstract
S
.
h
Theevidencepresentedearlier by severalauthorsfor the substantialdisk eccentricityin
p
- dwarfnovaeduringtheirsuperoutburstsisshowntoresulteitherfromerrors,orfromarbitrary,
o
incorrectassumptions.
r
t (1)TheevidenceforZChaandWZSge(Vogt1981),basedonradialvelocitiesmeasured
s
fromabsorptioncomponents,wasanartifact,resultingfrommiscalculatedbeatphases.
a
[ (2)TheevidenceforOY Car (Krzemin´skiandVogt1985)andIYUMa (Pattersonetal.

2000),basedonthe observeddependenceofeclipse parametersonthe beatphase, involved
1
v an implicit assumption that the observed eclipses are pure disk eclipses, which is not true.
9 Inparticular,theobservedvariationsofeclipseparametersarelikelyduetothecontributions
3 fromthehotspotandfromthesuperhumpsource,whichdependstronglyonthebeatphase.
8
(3)TheevidenceforOYCar(Hessmanetal1992)andWZ Sge(Pattersonetal. 2002),
2
resulting from the analysis of hot spot eclipses, was based on the assumption that the spot
.
1 distancesareidenticalwiththeradiusofthedisk,whichisnotalwayscorrect. Inparticular,
0
in the case of eclipses of "peculiar" spots (involvingthe stream overflow), observedat beat
9
phasesawayfromf ∼0.5,theresultingspotdistancesaresmallerthattheradiusofthedisk.
0 b
: NewdeterminationofdiskeccentricityinZCha,usingVogt’sradialvelocitiesmeasured
v
fromemissioncomponents,givese=0.05±0.05.
i
X
r
a Key words: accretion, accretion disks – binaries: cataclysmic variables, stars: dwarf novae,
stars: individual: OYCar,ZCha,WZSge,IYUMa
1 Introduction
The concept of an eccentric, "precessing" 1 disk was a crucial ingredient of the tidal-thermal in-
stability modelofsuperoutbursts proposed byOsaki(1996, 2005andreferences therein). Results
of recent analysis of superoutbursts of Z Cha (Smak 2007, 2008a) definitely show, however, that
superoutbursts are due to a major enhancement in the mass transfer rate. It is worth to recall
1Theterm"precession",usedcommonlybymanyauthors,isobviouslyincorrect. Wewilluseit–forsimplicity–
onlyintheIntroductionbutwillrevertlatertothecorrectterm:the"apsidalmotion".
1
thatanalternativemodelforsuperoutbursts, involvingsuchenhancedmasstransferresultingfrom
variable irradiation of the secondary component, was considered earlier by Osaki himself (Osaki
1985;seealsoMineshige1988). Furtherworkinthisdirection appearsnowhighlydesirable.
Eccentric, "precessing" disk continues to be an essential ingredient of the commonly ac-
ceptedmodelforsuperhumps (seealsoOsaki1996,2005andreferences therein).
Observationalevidenceforeccentric,"precessing"disksindwarfnovaeduringtheirsuper-
outbursts was presented during the last three decades by numerous authors. Under those circum-
stances the question posed in the title of the present paper can be considered rather provocative.
Evenmoreprovocative, however,willbeournegativeanswertothatquestion.
The organization of the present paper will be as follows. In Section 2 we will clarify
problems of terminology. The main part of the paper will then be devoted to a detailed critical
review of the observational evidence for eccentric, "precessing" disks resulting from the analysis
of radial velocities (Section 3), of the observed (disk?) eclipses (Section 4), and of the spot of
eclipses(Section5). Resultswillbediscussed inSection6.
2 Terminology and Definitions
Three periodicities are observed during superoutbursts: the orbital period P , the superhump
orb
periodP ,andthecorresponding beatperiodP
sh b
1 1 1
= − . (1)
P P P
b orb sh
Accordingly, three sets of phases are to be considered: the orbital phase f (or simply
orb
f ),thesuperhumpphasef ,andthebeatphase
sh
f = f − f = f (SH) = −f (ecl). (2)
b orb sh orb sh
ItiscommonlyassumedthatthebeatperiodP represents theapsidalmotionofaneccen-
b
tric disk (or an outer eccentric ring), usually referred to – incorrectly – as "precession". Conse-
quently, the beat period is called the "precession" period while the beat phase – the "precession"
phase.
The orientation of an eccentric disk/ring can be defined by the position angle q of the
◦
periastron withrespecttothelineofsight. Thisposition angleisdirectlyrelatedtothebeatphase
f . In general, they could differ by a constant phase shift. In practice, however, using various
b
kinds ofobservational evidence, nearly allauthors (e.g. Vogt1981, Hessmanetal. 1992) assume
or conclude that the beat phase f =0 corresponds to the situation when the periastron is facing
b
theobserver, i.e. that
q ◦ ≡ f b . (3)
2
3 Evidence from Radial Velocities
3.1 RadialVelocitiesfrom anEccentric Ring
Using textbook formulae for the two body problem we find that the radial velocity of a point on
anelliptical ringisgivenby
Vr = Vr(orb) + Vd sini [sin(q ◦+q ) + e sinq ◦)] , (4)
whereV (orb)isdescribingtheorbitalmotion,q isthepositionangleofthepointconsideredwith
r
respect tothe periastron, q – theposition angle ofthe periastron withrespect to the line ofsight
◦
(bothcounted counterclockwise), and
GM 1/2
1
V = , (5)
d (cid:20)A (1−e2)(cid:21)
d
is an equivalent of the standard expression for the rotational velocity of the disk/ring. Here A is
d
themajorsemi-axis oftheringande–itseccentricity.
Fortheradialvelocity ofanelementoftheringseeninprojection onthewhitedwarfand
thecentralpartsofthedisk(tobediscussed inSections3.2and3.3)weobtain
Vr = Vr(orb) + Vd sinie sinq ◦ . (6)
For the maximum and minimum radial velocity, corresponding to the red and blue peaks
oftheemissionline(tobeusedinSection3.4)weget
Vr = Vr(orb) + Vd sini(±1 + e sinq ◦). (7)
3.2 ZCha – absorptionlines
Thefirstevidence foraneccentric diskinadwarfnovaduring thesuperoutburst camefromspec-
troscopic observations ofZChamadebyVogt(1981) duringits1978March/Aprilsuperoutburst.
Vogt measured radial velocities from the central absorption components of the double emission
lines and found (see his Fig.7) that those measured on 1978 March 28/29 were very high (his
g =+267±13 km/s)whilethose measured on1978March 27/28 (i.e. ontheprevious night) –
28
verylow(g =−197±37km/s).
27
Tointepret those results Vogtproposed the following model (see Fig.9ofhis paper): The
centralabsorptioncomponentsareproducedintheoutereccentricring,specifically–intheregion
which is seen in projection on the central parts of the disk. The difference between g and g
27 28
3
resultsfromtheapsidalmotionofthering: thevalueofthebeatperiodP ≈2.1dimpliesthatthe
b
orientation oftheeccentricdiskontwoconsecutive nightsdiffersbyabout180◦.
This interpretation, however, can be easily shown to be incorrect. To do so we calculate
the beat phases corresponding to the times of Vogt’s spectroscopic observations. For the night
of March 27/28 we obtain f = 0.39, while for the night of March 28/29 we get f = 0.83−
b b
0.90. FromEq.6itimmediatelyfollowsthatradialvelocitiesmeasuredonMarch27/28shouldbe
systematically positive, while those on March 28/29 – systematically negative. This, however, is
just opposite to the observed effect. In other words, the orientations of the ring during those two
nightswere–roughly –opposite tothetwoorientations showninVogt’sFig.9.
Tocomplete ourdiscussion letusreturn totheproblem oftheorigin ofcentralabsorption
components. Vogt assumed – arbitrarily – that they are formed in the outer eccentric ring. In
reality, however, the double emission lines, including their central absorption components, are
produced in the atmosphere of the entire disk. Furthermore, in the particular case of Z Cha, an
additional,variablecontributionduetotheabsorptionintheoverflowingpartsofthestream(Smak
2007)islikelytobepresent. Suchapossibilityissuggestedbythefactthat,accordingtoVogt,the
absorption components are strongest near the orbital phase f =0.9, i.e. when the overflowing
orb
streamisdirectly projected againstthecentralpartsofthedisk.
3.3 WZSge– absorptionlines
Tostrengthen hisinterpretation ofZChaVogtpresentedadditionalevidencebasedonabsorption-
lineg -velocities ofWZSgemeasured byseveral authors during its1978 superoutburst. HisFig.8
didindeedshowsinusoidalvariationsoftheg -velocitieswiththebeatphase. However,tocalculate
f Vogt adopted an incorrect value of the beat period: P =6.176d. Thecorrected version of his
b b
g vs.f diagram, with f calculated with P = 7.16d (Patterson et al. 1981), shows only large
b b b
scatterwithnoobviousdependence ofg -velocities onf .
b
3.4 ZCha – emissionlines
Theeccentricity ofthediskcanbedetermined,usingEq.7,fromVogt’sradialvelocitiesmeasured
from thepeaks ofthedouble emission lines. Forthis purpose weuseradial velocities E+ and E−
listed inhisTable6(excluding onlyfour uncertain values ofE+ withf between 0.10 and0.40
orb
which were near-blends with the absoprtion component). First, we correct them for the orbital
motion
Vr(orb) = g − K1 sin(f − f ◦), (8)
usingtwo,ratherdifferentsetsofparametersdeterminedfromobservationsatquiescence,namely:
(1)K1=87km/s,f ◦=−0.020,g =0km/s(Vogt1981),and(2)K1=192km/s,f ◦=0.098,g =2
km/s(Marschetal. 1987).
Results, obtained withthose twosetsofparameters, are: (1)V sini=650±21km/s,e=
d
4
0.05±0.05,r =0.54±0.04,and(2)V sini=649±21km/s,e=0.02±0.05,r =0.53±0.03.
d d d
As can be seen the eccentricity, if any, is close to zero. Worth noting is that in both cases the
resulting disk radius turns out, as expected, to be close to the mean radius of the Roche lobe
r =0.52.
Roche
4 Evidence from the Observed (Disk?) Eclipses
4.1 General comments
Theevidence discussed below for OY Car(Section 4.2) and IY UMa(Section 4.3) was based on
thedependenceofvariouseclipseparametersonthebeatphase,interpretedintermsoftheapsidal
motionofaneccentricdisk. Suchaninterpretation, however,assumesimplicitlythattheobserved
eclipsesarepurediskeclipses. Thisisobviously nottrue.
Wenow have evidence, based on the detailed analysis of eclipses in ZCha (Smak2007),
showing that, depending on the beat phase, they represent a combination of eclipses of several
differentsources: (1)thedisk,(2)the"standard"spot(aroundf ∼0.5),or(3)the"peculiar"spot,
b
involving stream overflow (around f ∼0.25 and 0.75), and (4) the superhump source (around
b
f ∼ 0.0). Their relative contributions depend strongly on the beat phase. Consequently, the
b
resulting dependence ofthe observed eclipse parameters onf isquite complicated. Under those
b
circumstances the only practical solution is to decompose the observed light curves into their
separate components (as it was done in the case of Z Cha; Smak 2007). It can be hoped that the
existing light curves of OY Car and IY UMa will eventually be analyzed in such a way. For the
time being wecan only mention that the shapes of the pure disk eclipse light curves obtained for
ZCha(Smak2007)donotshowanydependence onthebeatphase.
4.2 OYCar
Krzemin´ski and Vogt (1985) collected light curves of OY Car during its January 1980 superout-
burst anddetermined several parameters describing theshape oftheobserved eclipses: (1)devia-
tionsoftheeclipse amplitude D AfromtheamplitudeAvs. epochE relation, (2)deviations ofthe
eclipsewidthD W fromthewidthW vs. epochE relation,(3)theeclipseasymmetryD T,measured
athalf-depth, and(4)thevalues of(O−C). Theyfound thatallthose parameters show –roughly
–sinusoidal variationswiththebeatphase(seetheirFigs.7-11)andinterpreted themasbeingdue
to the apsidal motion of an eccentric disk. In what follows we will show that this interpretation
wasincorrect.
First of all, as noted by Krzemin´ski and Vogt themselves, variations predicted by their
eccentricdiskmodel(seetheirFig.12)forD W andD T donotagreewiththeirobservedvariations.
Specifically,theirmodelpredictsdoublesinusoidalvariationsforD W,whileinthecaseofD T the
modelpredicted variations areshifted inf by±0.25.
b
To interpret the observed variations of D A Krzemin´ski and Vogt assumed that the outer
partsofthedisk,ontheothersideofthewhitedwarf,remainuneclipsed. Usingsystemparameters
5
of OY Car (Wood et al. 1989) we find, however, that this assumption would require the disk
radius to be larger than r =0.78, which is already larger than the upper limit to the disk radius
r =0.72, obtained from the condition that it must be smaller than the distance from L to the
max 1
whitedwarf. Thisimpliesthatthefarsideofdiskisfullyeclipsed. Thegeometryofeclipsesofthe
hypotheticaleccentricdiskinOYCarisshownschematicallyinFig.1. Itcanimmediatelybeseen
that, regardless of the surface brightness distribution, the eclipse amplitude should show double
sinusoidal variations withf ,whichisinconsistent withobservations.
b
Figure1: Geometry ofeclipses ofahypothetical eccentric disk inOYCaratf =0and atbeat
orb
phasesf =0.0,0.25,0.5,and0.75.
b
Theobserved variations ofD Awithf can, infact, bequalitatively explained bythe vari-
b
able contribution from the hot spot. In particular, around f ∼0.5, when the "standard" hot spot
b
ispresent, itseclipsesmakethefulleclipseamplitudelarger.
4.3 IYUMa
Patterson et al. (2000) presented results of their extensive photometry of IY UMa covering the
declining part of its 2000 January superoutburst. From the analysis of the observed light curves
they found that all eclipse parameters depend strongly on the beat phase. In particular, around
f ∼ 0.5 the eclipse amplitude is largest and all characteristic phases are systematically more
b
positive (see their Figs.7 and 9). Patterson et al. interpreted those effects as being to due the
apsidalmotionofastrongly eccentric(e=0.29)disk.
There are several arguments against such an interpretation. First of all, wecan recall our
general comments from Section 4.1. Secondly, we may note that the observed dependence of
eclipse parameters on f (similar to the case of OY Car; Section 4.2) is most likely due to the
b
variable contribution from the hot spot which – on account of the orbital inclination (i=86.8)
being much higher than in the case of OY Car (i = 83.3) – is expected to be relatively larger.
Aroundf ∼0.5,whenthe"standard"hotspotispresent,thecontributionfromitseclipsesmakes
b
the observed eclipses deeper and shifted toward later phases. In partcular, the large values of f
4
observedaroundf ∼0.5(Fig.9inPattersonetal. 2000)correspond probablytotheegressofthe
b
"standard" hotspot.
6
5 Evidence from Spot Eclipses
5.1 Historicalcomments
Thepresenceofthehotspotinadwarfnovaduringitssuperoutburstwasdetectedforthefirsttime
by Schoembs (1986). His light curves of OY Car obtained during the final decline from its 1980
November/December superoutburst showedclearlythecharacteristic eclipses ofthehotspot. Six
years later Hessman et al. (1992) published results of their photometry of OY Car, made also
duringthefinaldecline fromanother ofitssuperoutbursts, theirlightcurvesshowingalsocharac-
teristicspoteclipses. Unfortunately,thesignificanceofthesediscoverieswasnotfullyappreciated
at that time, the presence of those eclipses being interpreted in terms of the reappearance of the
quiescent hotspot.
ThehotspoteclipsesduringsuperoutburstmaximumwerefirstdetectedbyPattersonetal.
(2002) in WZ Sge during its 2001 superoutburst. Regretfully, this interpretation was challenged
byOsakiandMeyer(2003)whoargued thatthoseeclipses werenotduetothehotspotbutrather
dueto"thesuperhump lightsourceitself".
Situationwasdefinitelyclarifiedonlyveryrecentlybytheresultsofouranalysisofeclipse
lightcurvesofZChaandOYCar(Smak2007,2008b) observedduringmaximaoftheirsuperout-
bursts. They were decomposed into their disk and spot components, the resulting hot spot light
curvesshowingnotonlythecharacteristicshapeoftheeclipsebutalsothecharacteristicmaximum
aroundtheorbitalphasef ∼0.8−0.9.
5.2 HowReliableareDiskRadiiderived from Spot Eclipses?
According to thecommonly accepted "standard" model, the hot spot is produced bythe collision
of the stream with the outer parts of the disk. In such a case, the distance r of the spot from the
white dwarf, to be referred to as "spot distance", determined from spot eclipses, is identical with
the radius of the disk r . It is worth to emphasize that in the case of an eccentric disk this r
d d
is the local radius of the disk at a specific position angle corresponding to the point of collision.
Furthermore, whensuchaneccentric diskrotatesduetotheapsidal motion, thedependence ofr
d
ontheposition angleproducesitsperiodic variations withthebeatphase.
In the analysis of eclipses of the "standard" hot spot we use the phases of mid-ingress f
i
andmid-egressf whicharerelatedtothemassratioq(definingtheshapeofthestreamtrajectory),
e
theorbitalinclination, thespotdistancer,anditsellongationparameterD s(cf. Smak1996,2007).
Whenthemassratioandinclinationareknown,thetwophasesf andf canthenbeusedtoobtain
i e
twoindpendent determinations ofthespotdistance:
r(f ) = f(f ,D s) and r (f ) = f(f ,D s). (9)
i i i e e e
Itisobvious thatinthecaseofa"standard" hotspottheymustbeidentical
7
r(f ) = r (f ). (10)
i i e e
The observed luminosity of the hot spot depends on the "impact parameter" D V2 (i.e. on
thesquare oftherelative velocity ofcollision between thestream andthedisk). Thevalueofthis
impact parameter increases with decreasing radial distance r. Therefore in the case of variable
diskradiustheluminosityℓ ofthe"standard" spotshould varyas
s
dℓ
s
< 0. (11)
dr
The last two relations provide two crucial tests for the applicability of the concept of a
"standard" hotspotand–inparticular –forassuming thattheradial distance ofthespot (r orr )
i e
isidentical withtheradiusofthediskr .
d
Figure2: ResultsoftheanalysisofspoteclipsesinZChaduringitssuperoutbursts. Bottom: Spot
distances r(f )determined from ingress are compared withspot distances r(f )determined from
i e
egress. Top: DurationsofegressDf areplotted againstspotdistances r(f ).
e e
Recent analysis of hot spot eclipses in Z Cha during its superoutbursts (Smak 2007) pro-
vides good illustration of different situations to be encountered in this area. The "standard" hot
spoteclipsesareobservedonlyatbeatphases0.40<f <0.60. Inparticular, thespotdistancesr
b i
andr determinedfromthosephasesarepracticallyidentical. Ontheotherhand,thespoteclipses
e
observed at intermediate beat phases (around f ∼0.35 and around f ∼0.75) are rather pecu-
b b
liar. First of all, the resulting spot distances are generally smaller, with r being systematically
i
larger than r . This could be seen already from Fig.6 of Smak (2007) and is shown here in the
e
8
lower part of Fig.2. Secondly, the luminosities of the spot observed at intermediate beat phases
aresystematically lower(Smak2007,Fig.5).
Those peculiarities were interpreted (Smak 2007) as being due to a substantial stream
overflow. SupportingthisinterpretationisacorrelationbetweenthedurationofegressDf andthe
e
spotdistance r ,mentioned already inSection 5.3ofthatpaper, and shownhereintheupper part
e
ofFig.2.
Thelesson learned from ZChacan besummarized in theform ofthe following warning:
Thespotdistances r >r , obtained from the analysis ofpeculiar spot eclipses, observed atinter-
i e
mediate beat phases, do not provide any reliable information about the radius of the disk. This
warningbecomesevenstronger whentheobserved spotluminosities implydℓ /dr>0.
s
5.3 OYCar
As already mentioned above, Schoembs (1986) and Hessman et al. (1992) presented extensive
photometriccoverageoftheadvancedstagesofthe1980November/Decemberand1987February
superoutburstsofOYCar. Duringthefinaldeclinetheirlightcurvesshowedcharacteristiceclipses
ofthehotspot. Hessmanetal. (1992)analyzedthoselightcurvesinordertodeterminethelocation
of the hot spot. Specifically, using the phases of mid-ingress, they obtained spot distances r and
i
foundthattheyshowstrongdependence onthebeatphasef ,interpreted bythemasbeingdueto
b
the "precession" of a strongly eccentric (e=0.38) disk. This interpretation, however, can easily
bechallenged.
To begin with, we must note that the variations of the spot luminosity ℓ and the spot
s
distance r with f , shown in their Fig.8 are strikingly similar to the case of Z Cha (cf. Section
i b
5.2; see also Figs.5 and 6 in Smak 2007). This immediately suggests that – like in the case of Z
Cha–the"standard" hotspotwaspresentinOYCaronlyaroundf ∼0.5andthatspotdistances
b
r obtained from intermediate beat phases should not be treated as a reliable measure of the disk
i
radiusr .
d
To clarify the situation definitely we analyze the available light curves of seven spot
eclipses(eclipses7-1,7-3,9-1,9-2,10-1,and10-2fromFig.3bofSchoembs1986,andtheeclipse
from Fig.1-bottom of Hessman et al. 1992). For each of them we determine the phases of mid-
ingress f and mid-egress f and the duriation of egress Df . Then, using geometrical system
i e e
parameters(Woodetal. 1989)andadoptingtwodifferentvaluesofthespotellongationparameter
D s=0.02 and 0.04, weobtain the spot distances r and r . Results, presented in Fig.3, show that
i e
the situation is indeed nearly identical with that in the case of Z Cha (see Fig.2). In addition, we
have dℓ /dr >0 (Fig.8 in Hessman et al. 1992). Taking all this into account we must conclude
s i
that at intermediate beat phases away from f ∼0.5 we are dealing with a "peculiar" rather than
b
"standard" spot and that – consequently – the spot distances r obtained at those phases do not
i
provideanyreliable information aboutthediskradiusr .
d
9
Figure 3: Results of the analysis of spot eclipses in OY Car during its superoutbursts. Bottom:
Spot distances r(f ) determined from ingress are compared with spot distances r(f ) determined
i e
from egress. Top: Durations of egress Df are plotted against spot distances r(f ). Opensquares
e e
represent results obtained with spot ellongation parameter D s=0.02, while filled squares – with
D s=0.04.
5.4 WZSge
Pattersonetal. (2002) published results ofaworldwide photometric campaign covering the2001
superoutburst of WZ Sge. One of their most important results was the detection – for the first
time–ofhot spot eclipses during the mainpartofsuperoutburst maximum. Theyanalyzed those
eclipses in a standard way finding that all hot spot parameters varied significantly with the "pre-
cession" (i.e. beat) phase. This was interpreted by them as being due to the apsidal motion of a
stronglyeccentric (e≥0.3)disk. Thisinterpretation, however,caneasilybechallenged.
In our analysis we use the values of (O−C) and eclipse widths (Fig.21-left of Patterson
et al. 2002) to recover the phases of mid-ingress (f ) and mid-egress (f ). Then, using system
i e
parameters from Steeghs et al. (2007) we determine the spot distances r(f ) and r(f ). Situation
i e
issomewhatcomplicatedherebythefactthatthezero-pointoftheorbitalphases,definedbymid-
eclipse of the spot, does not correspond to the true zero-phase. The values of the corresponding
phase shift, obtained by different authors from the analysis of spot eclipses (e.g. Smak 1993)
or from radial velocity curves (e.g. Spruit and Rutten 1998, Steeghs et al. 2001), range from
Df =−0.036toDf =−0.046. Inouranalysisweadopt: Df =−0.039and −0.042. Forthespot
ellongation parameterwealsoadopttwovalues: D s=0.02and0.04.
Fig.4 shows an example of the resulting spot distances r(f ) and r(f ) plotted versus the
i e
beat phase and Fig.5 presents a comparison of those two parameters obtained using four combi-
nationsofD sandDf . Ascanbeseen,thesituationisverysimilartothecaseofZCha(Fig.2)and
OYCar(Fig.3). Inparticular, the condition r(f )=r(f )isfulfilled only bythe largest values of
i e
10