Z Cam stars: a particular response to a general phenomenon

8 Pages·0.23 MB·English

by  V. Buat-Menard

A&A manuscript no. ASTRONOMY
(will be inserted by hand later) AND
Your thesaurus codes are: ASTROPHYSICS
06(02.01.2; 02.09.1; 08.02.1; 08.14.2)
Z Cam stars: a particular response to a general phenomenon
Valentin Buat-M´enard1, Jean-Marie Hameury1 and Jean-Pierre Lasota2
1 UMR 7550 du CNRS, Observatoire de Strasbourg, 11 rue de l’Universit´e, F-67000 Strasbourg, France, [email protected]
strasbg.fr
2
Institut d’Astrophysiquede Paris, 98bis Boulevard Arago, 75014 Paris, France, [email protected]
1
0
Received / Accepted
0
2

n
Abstract. We show that the disc instability model can various physical processes such as irradiation of the disc
a
J reproduce all the observed properties of Z Cam stars if and the secondary star, inner disc truncation and mass
the energy equation includes heating of the outer disc transferfluctuations.Alsoheatingofthediscbythemass-
8
1 by the mass-transfer stream impact and by tidal torques transfer stream impact and by tidal torque dissipation
andifthemass-transferratefromthesecondaryvariesby plays an important role in the dwarf-nova outburst cycle

1 about 30% around the value critical for stability. In par- (Buat M´enard et al., hereafter Paper I).
v
ticular the magnitude difference between outburst max- Dwarf novae can be divided into three subclasses: U
9
2 ima and standstills corresponds to observations, all out- Gem-type stars which have the most regularoutburst cy-
3 bursts are of the inside-out type and can be divided into cles; SU UMa-type stars showing both short and very
1 two classes: long (wide) and short (narrow) outbursts, as long outbursts (superoutbursts) and Z Cam stars. The
0 observed. Mass transfer rate fluctuations should occur in last group is characterized by a ‘standstill’ phenomenon:
1
other dwarf novae but one can exclude variations simi- the decline from outburst maximum is interrupted and
0
/ lar to those observedin magnetic systems (AM Her’s and the luminosity of the systems settles to a value ∼ 0.7
h some DQ Her’s) and some nova-like systems (VY Scl’s), mag lower than the peak luminosity. In some cases the
p in which M˙ become very small during low states; these magnitude difference is smaller (see e.g. Fig. 19 in Lin,
-
o would produce mini-outburst which, although detectable, Papaloizou & Faulkner 1985). Such standstills may last
r have never been observed. from ten days to years. After that, the system luminos-
t
s ity declines to the usual quiescent state. In his pioneer-
a
: Key words: accretion, accretion discs – instabilities – ing work, Osaki (1974) interpreted standstills as stable
v
(Stars:) novae, cataclysmic variables – (stars:) binaries : phases of accretion in the framework of the disc instabil-
i
X close ity model he then proposed. In his disc-radius and mass-
r transfer rate diagram, Smak (1983) described these stars
a
asanintermediatecasebetweenstablenova-likestarsand
1. Introduction unstable dwarf novae. Meyer & Meyer-Hofmeister (1983)
proposed that Z Cam stars are dwarf novae with a mass-
Dwarf novae are a subclass of cataclysmic variable stars,
transfer rate that fluctuates about the critical rate. Lin
whichareclosebinarysystemsinwhichmattertransferred
et al. (1985) concluded that moderate fluctuation of the
from a Roche-lobe filling secondary star is accreted by a
mass-transfer rate can produce Z Cam-type light curves.
primary white dwarf (see Warner 1995). In dwarf novae
This is now widely accepted, but until now no model has
accretionproceedsthroughadiscwhichisthesiteofmore
beenabletoreproducetheobservedlightcurvesofZCam
orlessregularoutbursts.Therecurrencetime ofthese2-6
(e.g. King & Cannizzo 1998).
magnitude outbursts can range from 10 days to several
We applied the disc instability model to a system in
tens of years. The dwarf nova outbursts are attributed whichthemasstransferratefromthesecondarystarM˙ is
2
to a thermal-viscousinstability occurringin the accretion assumedto varyaroundthe criticalrateM˙ ,abovewhich
c
disc. Although the thermal-viscous disc instability model
the disc is stable. In Section 2 we show that the mag-
(DIM) identifies a physical cause for the instability, par-
nitude difference between standstills and outburst peaks
tial hydrogen ionization, the outburst cycles it produces dependsonthedifferencebetweenM˙ andtheactualmass
c
differ in many important respects from the observedones transfer rate reached during standstill M˙ . We also show
h
(seee.g.Smak2000,Lasota2000).Itis nowratherwidely
that it is easier to find a large enough ∆ when the
mag
accepted that the original DIM has to be completed by
model includes the outer disc heating by the stream im-
Send offprint requests to: V. Buat-M´enard pact and the tidal dissipation as discussed in Paper I. In
Correspondence to: [email protected] addition, including these additional heating processes in
2 Buat-M´enard et al.: Z Cam: a particular response of a general phenomenon
theDIMallowstoobtaininside-outoutburstsasobserved < M˙ > is the average mass-transfer rate from the sec-
in some Z Cam stars. We show therefore that in such a ondary. Transitions between the two states are made by
generalizedDIMthe responseofadwarfnovadisc tolow- sinusoidal interpolation during a time interval ∆t . In
trans
amplitudemass-transferratevariationsistheexplanation this paper we use P = 400 days; this is long enough to
m
of the Z Cam phenomenon. accountfor relaxationduring standstills andto allowsev-
Mass-transfer rate variations are also occurring in eral outbursts cycles. The transition time is taken to be
other dwarf novae (e.g. Smak 1999, 2000; Hameury, La- ∆ttrans =20 days.
sota&Warner2000).Thebrighteningofthehotspot,the The brightening of the quiescent level and the out-
region where the mass-transfer stream interacts with the burst amplitude reduction observed in some Z Cam sys-
outerdisc’srim,whichisobservedneartheoutburstmax- tems(Szkody&Mattei1984)mayresultfromaparticular
ima,shouldbe the resultofa mass-transferrateenhance- time-dependenceofthemass-transferratefluctuationsbut
ment. Large variations of the mass transfer rate are di- we are not attempting to model such effects here. The M˙
rectly observedin polars,which aremagnetic cataclysmic variations used in this paper are not supposed to corre-
variableswithno accretiondiscs.The prototype,AM Her spond to any particular physical mechanism. We are in-
showslargeamplitude variationsofthemasstransferrate terested in the disc’s response to mass-transfer rate fluc-
which can be vanishingly small during low states. Similar tuationsandnotinthepossiblecausesofthesevariations.
luminosity drops observed in some DQ Her stars, mag- The latter are far from being known. Irradiation induced
netic non-synchronous binaries and in VY Scl, nova-like cycles of mass-transfer rate variation are excluded in this
systems with orbital periods between 3 and 4 hours, are context as they last much longer than the observed in-
alsoattributedtomass-transferfluctuations.However,be- terval between standstills (Gontikakis & Hameury 1993).
cause of the presence of a disc, it is much more difficult Star spots could be be responsible for M˙ fluctuations
toconverttheseluminosityfluctuationsintomass-transfer that are relevant for Z Cam stars (Livio & Pringle 1994;
rate variations. Contrary to Schreiber et al. (2000), who King & Cannizzo 1998).
used a code in which the outer boundary radius is kept
fixed,we findusing the correctouter boundarycondition,
2.2. Mass-transfer fluctuations
that such drastic mass-transfer fluctuations do not occur
inmostdwarfnovae.King&Cannizzo(1998)reachedthe Fig. 1 shows the results of our calculations when no ad-
same conclusion as ours using a fixed outer radius and ditional disc heating is included. We assumedthe average
varying the mass-transfer rate by 6 orders of magnitude. mass-transferrates<M˙ >tobe equalto the criticalrate
M˙ = 8 × 1017 g s−1 (see Hameury et al. 1998 for the
c
formula). We took ∆M˙ / < M˙ >= 30%. The modulation
2. Modeling the Z Cam phenomenon
of the mass-transferrate occurs att=200+kP day.As
m
2.1. Model and parameters can be seen, the outburst amplitudes gradually increase
after a standstill, as the disk relaxes towards the new sit-
We use the versionof the disc instability model described uation in which the mass transfer rate is reduced. Since
in Hameury et al. (1998). We assume that α = αcold = nowmassaccumulatesinthedisc,itismoremassivethan
0.04 in quiescence and α = αhot = 0.2 in outburst. As before,whenitwassteady.Itis alsolargerafteraninitial
in Paper I the fixed, inner radius is at rin = 109 cm. contractionphaseduetothepassageofacoolingfront.All
We allow for the inclusion of the streamimpact and tidal outbursts are of the outside-in type, as the mass transfer
dissipation effects (see Paper I for details). We do not rateislarge(seePaperI).Theinstabilitysetsinatapprox-
includetheeffectsofthesecondarystarirradiation,i.e.the imately the same position (∼3×1010 cm, except for the
mass-transfer rate variations are supposed, in this model, lastoutburstwhichistriggeredbyanincreaseofthemass
to be unrelated to the accretion onto the white dwarf. transferratefromthesecondary).Asonlyasmallfraction
We choose Z Cam as the system to model. From the of the disk mass is accreted during outbursts, a relaxed
Ritter and Kolb’s catalogue (1998) we took mass of the regime is reached only after a large number of outbursts,
primary M1 = 1M⊙, the mass of the secondary M2 = close to the end of the dwarf nova phase. The luminos-
0.7M⊙ and the orbital period Porb =6.96 hr. We use the ity increase of successive outbursts, a characteristic fea-
tables from Lubow & Shu (1975) and Paczyn´ski (1977) ture ofthis model,is notobservedinreality.To solvethis
to estimate the circularization radius rcirc = 1.52×1010 problemonecoulduseseveralsremedies.Forexample,one
cm and the mean outer disc radius < rout >= 5.4×1010 could add to the model mass-transfer rate enhancements
cm. The size of the disc is controlled by the tidal torques due to the irradiation of the secondary by the accretion
which depend on the value of the circularization radius flow (Smak 1999;Hameury et al. 2000).We will show be-
(see Hameury et al. 1998 and Paper I for details). low, however, that this is not necessary since taking into
We assume that the mass-transfer rate from the sec- account the heating by the stream impact and/or tidal
ondary varies from a low state M˙ =< M˙ > −∆M˙ to a torquedissipation(PaperI)givesverysatisfactoryresults.
l
high state M˙ =< M˙ > +∆M˙ with a period P , where In any case Fig. 1 shows that ∆ < 0.6 mag, which is
h m mag
Buat-M´enard et al.: Z Cam: a particular response of a general phenomenon 3
the model. Therefore to obtain the observed ∆ ∼ 0.7
mag
9.8 would require M˙ ≃ M˙ . Fine tuning would be required
e h c
ud for the ∼30 Z Cam known, because the critical and the
nit 10.2 peak accretion rate have the same r-dependence.
g
ma Another problem with our parameters is that the re-
V quiredvicinity to the criticalrate implies veryhighmass-
10.6
transfer rates. This produces outside-in outbursts in con-
tradictiontoobservation.Moreover,accordingtothemost
recentworkonCV’sevolutionZCamshouldhaveamass-
g) 4.0 transferratelowerthan∼3.2×1017gs−1(Baraffe&Kolb
240 2000).
1
( It is therefore possible to produce a Z Cam-type light
s
as 2.0 curve by varying the mass-transfer rate around the value
m
criticalfordiscstability,butneithertheparametersofthis
light-curvenortherequiredparametersofthesystemsare
satisfactory.One shouldalsonote that the rangeof possi-
) ble parametersis veryrestricted. While the mass-transfer
−1g s 2.0 rateis8×1017gs−1theaccretionrateatmaximumisonly
180 lessthanafactor2to3larger(1.3−2.5×1018gs−1).This
1 1.0 means that a mass-transfer rate enhancement by a factor
(
.M acc more than ∼2wouldproduce a “Z Cam”light-curvewith
∆ <0asinKing&Cannizzo(1998),whoincreasedthe
mag
mass-transfer rate by a factor 6. The reason for this very
m) narrow range of mass-transfer fluctuations which allow a
100 c 5.0 ZnoCna-lmoc-atylpeffeescttasnddusrtiilnlgisththeaotuctlbousresttobtrhinegdtihsce’ssuorufatecreeddegne-
1
s ( sity very close to the critical value Σmin (see e.g. Smak
diu 1998, Fig. 4), i.e. M˙ close to M˙c. Since at maximum the
ra 3.0 accretionrateinthediscisroughlyconstantM˙ ∼M˙ .
max c
Esin, Lasota & Hynes (2000) assumed that M˙ = M˙
100 300 500 700 900 max c
and deduced that an enhancement of mass transfer rate
time (days)
above M˙ will always produce a standstill brighter than
c
theoutburstmaximum.Thisisnottruebecauseinreality
Fig.1. Results of the standard DIM for the parame-
the peak accretion rate is larger than M˙ by a factor of
ters of Z Cam, assuming a modulated mass-transfer rate c
8.0×1017±30%g s−1. The upper panelshows the visual about 2. Therefore King & Cannizzo (1998) guessed cor-
rectly that they had increased the mass-transfer rate by
magnitude (solid line). The dashed line represents the V
an amount too large to get a Z Cam-type standstill. One
magnitude (10.5) of a disc which accretes at exactly the
criticalvalue:M˙ =8.0×1017gs−1.Thesecondpanelfrom should note, however, that some low-mass X-ray binary
c
transient systems show plateau brighter than a preceding
above shows variations of the disc’s mass. The third one
localmaximumwhichcouldbeduemass-transferenhance-
represents the mass accretion rate onto the white dwarf
ments by factors larger than 2 (see e.g. Esin et al. 2000).
(solidline),aswellasthe masstransferratefromthe sec-
ondary (dashed line). The bottom panel shows the varia-
tions of the outer disc radius. The dots show point where 2.3. Effects of heating by stream impact and tidal torque
the instabilityistriggeredattheonsetofanoutburst.All dissipation
outbursts are of the outside-in type.
We found in the preceding section that in order to pro-
duce credible Z Cam light-curves one should lower the
too low since the observedmagnitude difference often ex- criticalmass-transferrate.One needs therefore a physical
ceeds0.7mag.Togetabetterresultwouldrequiretheuse mechanism which would produce such an effect without
ofsomefinetuning.Forobviousreasons,the standstilllu- lowering the peak luminosity. Heating of the disc by the
minosity cannot be lower than that corresponding to M˙ , impact of the mass-transfer stream from the secondary
c
i.e. for our parameters the brightest standstill magnitude and/or by tidal torque dissipation (Paper I) could do the
can only be mV = 10.5. The outburst peak luminosity job: it has a stabilizing effect, therefore allowing the disc
depends mainly onthe disc radius,which only weaklyde- to be dimmer during standstills, but does not affect the
pendsonthemass-transferrate.Thereforethe magnitude outbursts properties near the dwarf-nova maximum be-
at maximum, in our case mV =9.8 is just an invariant of cause (i) as mentioned earlier they depend only weakly
4 Buat-M´enard et al.: Z Cam: a particular response of a general phenomenon
upon the average mass transfer rate, and (ii) the addi- thestandardDIM(Smak2000).Ourlongeroutburstscor-
tional heating is small compared to the energy released respond to the ‘plateau’ outbursts of Oppenheimer et al.
during outbursts. Moreover, heating of the outer disc re- (1998).
duces both the value of the critical mass-transferrate M˙
c
and the value M˙ for which the outburst type changes; In this particular model all outbursts inside-out type.
AB
In Z Cam and AH Her, outbursts are presumed to be of
this makes outside-in outbursts possible for reasonably
typeBwhereasinRXAndtheyarepresumedtobeoftype
low values of the mass transfer rate (paper I). The rel-
ative difference (M˙ −M˙ )/M˙ is also slightly reduced. A (see table 3.6 in Warner (1995)). As mentioned above,
c AB c
with the inclusion of heating by stream impact and tidal
Itisthuspossibletohavealsoinside-outoutburstsduring
torques, (M˙ −M˙ )/M˙ is reduced so that it is possible
the unstable phase of Z Cam systems even for moderate c AB c
to obtain type B outbursts even with a moderate mass
fluctuations of the mass-transfer rate. This could explain
transfer rate fluctuation. Depending on the characteris-
why type B outbursts are observed in some Z Cam sys-
tics of these fluctuations, one could obtain either type A
tems,while otherwouldratherhavetype A ones(Warner
outbursts, or type B ones, or a mixture of both. In addi-
1995).
tion, the last outburst of the unstable phase should be of
In a recent paper, Stehle & King (2000) argued that type A if M˙ > M˙ before it starts. If the mass transfer
AB
heating of the disc by the stream impact is responsible rate varies smoothly, one would therefore expect to ob-
for the standstill luminosity being less than the outburst servetype A outbursts just before a standstill; this would
peak luminosity, providedthat the amplitude of the mass not be the case if M˙ varied rapidly (for example if the
transfer fluctuations is large enough : they require that secondary irradiation during outbursts affects M˙ ).
themasstransferislowenoughduringtheunstablephase
for heating by the stream impact to be negligible, and As M˙c is close to M˙AB ( M˙c ∼ 1.2M˙AB for Z Cam
largeduring standstill.However,asclearlyshowedby our and SS Cyg), one should expect U Gem systems in which
model calculations such constraints are not necessary. In outside-inoutburstsoccur,tohavestandstilsfromtimeto
addition,Stehle&Kingmodelwouldrequireveryfinetun- time. Warner (1995) noted that the suggestion that “all
ing: the mass transfer fluctuations would have to be large U Gem stars are unrecognizedZ Cam stars” is somewhat
enoughforheatingbythestreamimpacttobe,depending exagerated, but a number of U Gem stars with short re-
on the mass-transfer fluctuation phase, either negligible currence times have been reclassified as Z Cam stars. It
or quite important, and yet the mass transfer rate during would therefore not be surprising if SS Cyg were to ex-
standstills could not be larger than approximately (1.5 – hibit a standstill, even though none has been observed in
2)M˙ ,inorderto preventthe standstillphasefrombeing the past 100 years. This only requires a slight increase of
c
toobright.Obviouslyonewouldexpectto findsystemsin the mean mass transfer rate.
which both conditions are not satisfied and such systems
In general, despite the simplicity of its assumptions,
would have excessively bright standstills.
our model represents very well the outburst properties of
Includingonlytheheatingofthediscbythestreamim- ZCamstars.Therecurrencetime is32daysbetweennar-
pact (see Buat-M´enardet al. 2000) gives 0.55 < ∆mag < rowoutburstsand40daysbetweenplateauoutbursts,the
1.00 mag for a fluctuation of 30 % around < M˙ >= duration of the two narrow outburst 8 and 9 days, of the
3.0 × 1017g s−1. The values of both the mass transfer two‘plateau’outbursts16and20days.Theseresultscom-
rate and the magnitude difference are thus in a better parereasonablywellwiththeobservedvalues:theaverage
agreement with the observed properties of Z Cam stars. cycle length of common and plateau outbursts is 23 and
Adding to this effect the tidal dissipation term in the en- 31 days respectively, and their average duration 10 and
ergy balance equation, gives 0.6 < ∆mag < 0.8 mag for 17 days. However, the duration of the last outburst be-
a fluctuation of 30 % around < M˙ >= 2.0×1017g s−1 fore standstill is too long compared to observations: we
(Fig. 2), which is very satisfactory. The cause of this suc- predictthatitshouldbe significantlylongerthanthe pre-
cess is a faster relaxation of the disc after the drop in the vious ones, whereas this is not the case for the observed
mass-transferrate,whenbotheffectsareincluded.Thisis outbursts.As a matter offact, the transitionbetween the
duetotwoeffects.First,alargermassfractionisaccreted outburstphaseandstandstilldependssignificantlyonhow
during an outburst: ∆M/M ∼ 0.25. Second, the differ- M˙ increasesbeforestandstill.Fig.3showsdifferenttransi-
ence between the disc mass during standstill and during tionstostandstill,forthesameparametersasinFig.2,ex-
the outburst phase is now smaller: additional heating re- ceptthatmasstransfernowincreasesduringtheoutburst.
duces the difference Σ −Σ in the outer regions of Ascanbeseen,shorteroutburstsareeasilyobtained.This
max min
the disc (Paper I), where most of its mass sits. In addi- mightbeusedasanindicationthatM˙ increasesafewdays
tion, for mass-transfer rates < M˙ >∼ 2.0 × 1017g s−1 after the beginning of anoutburst,maybe as the resultof
thetwoexternalheatingmechanismsproducenarrowand illumination; one must however keep in mind that this is
wide outbursts (see Buat-M´enardet al. 2000 for details). a relatively minor detail compared to many uncertainties
Suchoutburstsareobservedbutcannotbereproducedby of the physics of the model (viscosity prescription, etc.).
Buat-M´enard et al.: Z Cam: a particular response of a general phenomenon 5
10.4
e
d
u
nit 10.8
g
a
m
V
11.2
g) 1.5
240
1
(
s 1.0
s
a
m
Fig.3.Lastoutburstbeforestandstill.Thesolidlineisan
0.8
−1) enlargement of Fig. 2, for which mass transfer increases
g s 0.6 early in the outburst; the dot-dashed curve is obtained
180 0.4 when mass transfer starts increasing linearly 5 days after
1 theoutburstpeak,andreachedthestandstillvalue3days
(
.M acc0.2 later; the dashed curved corresponds to a case where the
increase in M˙ also begins 5 days after the outburst max-
imum, but with a timescale of 30 days. The latter curve
m) 5.0 requires some tuning.
c
100
1 3.0
s ( from the secondary. Also in other systems, the magnetic
u
di non-synchronousDQHerstarsandnova-likeVYSclstars,
a 1.0
r the large brightness variations observed are attributed to
mass-transfer fluctuations (see Garnavich & Szkody 1988
100 300 500 700 900
and references therein).
time (days)
However,the reasonsfor these fluctuations are not re-
Fig.2. Light curve obtained for Z Cam parameters with ally known; irradiation of the donor star and star spots
theDIMincludingstreamimpactandtidaltorqueseffects. have been invoked as possible causes for the variations,
M˙ = 2.0×1017±30%g s−1. The dashed line shows the but no reliable model has been yet proposed. Moreover,
2
standstill magnitude (11.2) for the critical mass transfer the amplitude of these fluctuations remains, in the gen-
rate M˙ =2.4×1017g s−1 eral case, very uncertain. Smak (1995) studied the lumi-
c
nosity of the hot spot in Z Cha and U Gem and showed
that during outburst the mass transfer rate can increase
Z Cam-type light curves can therefore be very well by a factor of about 2 ; there was however no indication
reproducedbythe discresponseto asimple mass-transfer of very significant long term variations. We have shown
rate fluctuations if additional heating is included. that for Z Cam system a mass-transfer rate variation of
less than 50 % (i.e. a factor less than 2) is required to
3. M˙2 variation in other dwarf novae explain their light curves. On the other hand, Schreiber
et al. (2000) suggested that mass transfer rate variations
Variations of the mass transfer rate from the secondary similar to those observed in AM Her could be present in
are not restricted to the Z Cam subclass of dwarf novae. dwarf novae systems. In such a case, the mass transfer
Thevarietyofoutbursttypesobservedinmostdwarf-nova rate M˙ could vary by one order of magnitude and be-
light curves implies the existence of a free parameter for come vanishingly small during low states. This behaviour
anygivensystem,andthemasstransferratefromthesec- wasobservedinsynchronousmagneticsystems,andcould
ondary is a good candidate; as discussed in Paper I the be quite general; one must however point out again that
main different outburst types (outside-in, inside-out, nar- there has been no reportof disappearanceof the hot spot
row and wide outbursts) are triggered for different mass in dwarf novae, even if this might be due to insufficient
transfer rates. Finally, the large luminosity variations of statistics. Two dwarf novae were observed in a low state
AM Her systems, CVs with no accretion discs, must di- during quiescence: HT Cas and BZ UMa. BZ UMa was
rectly result from fluctuations of the mass transfer rate found to be at 17.8 mag instead of the usual ∼ 16 mag
6 Buat-M´enard et al.: Z Cam: a particular response of a general phenomenon
1017 observationsofeightwellsampledSUUMa starsshowno
evidence for large quiescent variations. The evidence for
1016 large mass-transfer fluctuations in dwarf novae is there-
)
−1 fore rather sparse. In any case, if the observed variations
s
g are due to mass-transfervariations,they are smaller than
.M (21015 nova-like (or AM Her) variations: 1 to 1.8 mag against 2
to 6 mag. This is consistent with the conclusion that in
1014 dwarf novae such huge variations can be excluded by the
DIM, as we will show below.
10
e Schreiber et al. (2000) claim that although the ces-
d
nitu 12 sation of mass transfer has immediate consequences on
ag 14 the light curves, these are limited to shortening the out-
m
burst duration and increasing the recurrence time. This
V 16
is apparently in contradiction with the findings of King
& Cannizzo (1998)that the cessation of mass transfer re-
sults in a 2 mag decrease of the outburst amplitude; it
) musthoweverbenotedthatthemass-transferrateduring
g 3.0
230 lowstatewasreducedby6ordersofmagnitudeinKing&
1 Cannizzo’smodels,butonlybyoneorderofmagnitudein
(
ss 2.5 Schreiberet al.A majordrawbackofboth setsofcalcula-
a
m tions, however,is the use of a fixed outer disc radius as a
boundary condition; this severely affects the light curves,
4.0
and is responsible for the occurrence of mini-outbursts at
m) 3.0 a constant M˙ (Hameury et al 1998).
c
1010 2.0 appTlioedsetheewrehfoarteaoruertdhiescreinasltpabreilditicytimonosdeolfttohaefiDcItMitiowues
(
s dwarf nova in which the mass-transfer rate variations are
u
di 1.0 similartothoseofAMHer(seeFig.4).Weincludestream
a
r
impact and tidal dissipation for a dwarf nova with M =
0.0 1
2000 3000 4000 0.6M⊙, M2 = 0.26M⊙, Porb = 3.08 hr and rout = 2.7×
time (days) 1010 cm.Themass-transferratevariesfrom0.01upto4×
1016g s−1; the variations are similar to those in Schreiber
Fig.4.DIMresultsforafictitiousdwarfnovawiththepa- et al. (2000).
rameters and the mass-transferrate variation(top panel) Three different types of modulations can be distin-
of AM Her. The top panel gives the mass transfer rate guished in the mass transfer curve: during the initial
fromthe secondary,the secondpanelthe disc visualmag- phase, M˙ varies by a factor ∼ 10; then in some phases
nitude,thethirdpanelitsmass,andthebottompanelthe themasstransferalmostcompletelyceases,beingreduced
outerdiscradius(thicksolidline),andthe positionofthe by a factor 100,during either a shortor a long time; dur-
external heating or cooling front (thin solid line). ing the last 700 days, only small variations are present.
When the mass transfer rate remains larger than a few
1015 g s−1, the calculated light curve shows little vari-
(Ka luz˙ny 1986). BZ UMa, however, could be a DQ Her ations; the outburst peak magnitudes do not change by
star (Kato 1999). In the 5 year of RoboScope observa- more than 0.2 mag and of the recurrence time remains
tions, during which HT Cas was in quiescence, long term the same, to within a few day. When the mass transfer
(days to hundreds of days) ∼1.8 mag variations were ob- rate increases, so does the outburst peak magnitude with
served. The quiescent luminosity varied from about 15.9 a delay of about ten days. By contrast, during the low
to17.7mag(Robertson&Honeycutt(1996)).Duringone state only mini-outbursts, fainter by 2 mag than the nor-
of the low states Wood et al. (1995) observed eclipsed X- mal ones, are present. The recurrence time increases by
ray emission which shows that accretion onto the white up to a factor 2.
dwarf was still going on. Although HT Cas is an eclips- ThisisquitesimilartothefindingsofKing&Cannizzo
ing system it is notorious for not showing the presence (1998) – but our mass transfer rate is 4 orders of magni-
of a hot spot, so there is no direct evidence that the low tude larger than theirs, and contradicts Schreiber et al.
states are due to a mass-transfer fluctuation of a corre- whoconsiderthe samevariationsofM˙ aswedo.Therea-
sponding size. The dwarf nova WW Ceti shows 1 mag sonforsuchadiscrepancyisthedifferenceintheboundary
variationsduringquiescence,whichcouldbedue tomass- conditions. During an outburst, the disc expands, so that
transfer fluctuations (Ringwald et al. 1996). RoboScope tidal torques can carry the large amount of angular mo-
Buat-M´enard et al.: Z Cam: a particular response of a general phenomenon 7
mentum of matter accreted onto the white dwarf. Under moreover, significant drops of the mass transfer rate
theeffectofboththetidaltorquesandthemasstransfered should result in corresponding drops of the hot spot
from the secondary, the disc contracts during quiescence. luminosity, which have not been observed either. In fact,
When the mass transfer ceases, this contraction does no in the few cases where mass-transfer rate variations in
longeroccur,and the disc remains extended, and the sur- dwarf-nova systems seem to be observed these variations
facedensityislow.Theoutburstsarestilloftheinside-out are order of magnitudes lower.
type, but the heating front can no longer propagate into Similarly,ifthemasstransferrateofnova-likesystems
the outer regions where the disc surface density has been weretoundergovariationssimilartothoseobservedinAM
reduced below Σ under the effect of the previous disc Her systems,most if not all nova-likestars should exhibit
min
expansion (see Fig. 4). The outburst amplitude is then a dwarf-nova behaviour, which obviously is not the case.
very reduced. Itisinterestingtonotethatweknowabout30ZCamsys-
As noted by King & Cannizzo (1998),the light curves tems,amongseveralhundredCVs;thecatalogueofRitter
of dwarf novae do not show such drastic variations of and Kolb (1998) lists 16 Z Cam stars with known orbital
the outburst peak luminosity. Contrary to Schreiber et periods, among a total of approximately 140 systems in
al. (2000), our results exclude drastic variations of mass thesameorbitalperiodrange,meaningthatintheZCam
transfer rate such as those observed in AM Her. period range, there is one chance out of 9 for a system to
cross the stability limit, indicating that the mass-transfer
rate varies by a few tens of percent.
4. Conclusion
The origin of these variations is not yet understood.
Since the work of Meyer & Meyer-Hofmeister (1983) it It is known (Smak 1995, 1996) that during dwarf-nova
has been believed that the Z Cam behaviour is due to outbursts, there is a significant enhancement of the mass
masstransferrateenhancementsthatleadtophasesofthe transfer rate; but this could not account for erratic varia-
outburst cycle during which the accretion disc is steady tionsobservedsometimesinquiescence.Stellarspotsarea
(standstills).However,actualmodelsproducedlight-curve goodcandidateforexplainingthese.Whateverthemecha-
whosepropertiesdidnotreallycorrespondtoobservations nism,itshouldbeinfluencedbythenatureoftheprimary
(Lin et al. 1985;King & Cannizzo 1998). In particular, it and/or the evolutionary status of the secondary since we
was not easy to reproduce the correct magnitude differ- have shown that the pronounced low states of the type
ence (∆ ≃ 0.7 mag) between the standstills and the observedin magnetic systems and in VY Scl cannot exist
mag
outburst peaks and impossible to obtain inside-out out- in most of dwarf novae.
burst with only moderate mass-transfer variations (Smak
Acknowledgements. The authors wish to thank the referee,
1996). We show that one can account for the observed
Prof. Y. Osaki, for his very interesting comments and inspir-
∆ if the amplitude of the mass transfer variations are
mag ingquestionsabouttheoutbursttypesofZCamsystems.This
not too large (typically factors 2 or less), as suggested by
work was supported in part by a grant from Programme Na-
Lin et al. (1985). An even better agreement is obtained tional dePhysiqueStellaire of the CNRS.
when one takes into account the energy released by the
mass-transfer stream impact onto the disc and by tidal
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