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A multiwavelength study of superoutbursts in dwarf novae

van der Woerd, H.J.

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Citation for published version (APA):van der Woerd, H. J. (1987). A multiwavelength study of superoutbursts in dwarf novae.

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Download date: 22 Mar 2020

Chapte rr V I

DISCOVERYY O F SOFT X-RA Y OSCILLATION S I N V W HYDRI

Summary y

I nn thi s pape r w e repor t th e discover y o f short-perio d oscillation s i nn th e sof t X-ra y flux , emitte d b y th e dwar f nov a V W Hydr i durin g outburst .. A modulatio n o f 1 5 % wit h a perio d o f 14.0 6 ± 0.0 2 s wa s detecte dd nea r th e en d o f th e Novembe r 198 3 superoutburst . Th e oscillatio nn wa s observe d fo r tw o hour s an d i s coheren t t o withi n th e limit ss o f observatio n ( Q > 2500) . A les s coheren t oscillatio n wa s detecte dd nea r th e maximu m o f th e Octobe r 198 4 superoutburst . Thi s oscillatio nn show s errati c perio d change s betwee n 14. 4 an d 14. 2 s . Th e pulse dd emissio n ha s probabl y a harde r spectru m tha n th e non-pulse d emission .. Uppe r limit s t o th e amplitud e o f oscillation s durin g othe r observation ss o f V W Hydr i a t outburs t an d quiescenc e indicat e tha t thes e 144 s oscillation s ar e a transien t effect . Th e propertie s an d origi n o f th ee sof t X-ra y oscillation s i n dwar f nova e ar e discussed . Possibl e connection ss betwee n th e low-coheren t sof t X-ra y an d optica l oscillation ss i n non-magneti c cataclysmi c variable s ar e pointe d out .

Keyy words : Cataclysmi c Variable s X-ray s Oscillation s

1.. Introductio n

Cataclysmi cc variable s ar e close-binar y system s i n whic h a low-̂ mas s sta rr transfer s matte r t o a whit e dwar f b y Roche-lob e overflow . Thes e system ss ca n b e divide d i n tw o groups : th e "non-magnetic " cataclysmi c variables ,, i n whic h th e whit e dwar f ha s a negligibl e magneti c moment , andd th e "magnetic " cataclysmi c variable s wher e th e magneti c fiel d o f th ee whit e dwar f i s stron g enoug h t o dominat e th e accretio n flo w nea r th ee whit e dwar f (intermediat e polars ) o r eve n i n th e whol e binar y syste mm (polar s o r A M Her-typ e systems) , se e Kin g e t al . (1985) . I n non-magneti cc system s th e transferre d matte r form s a n accretio n disc , throug hh whic h th e matte r slowl y diffuse s inward s an d accrete s ont o th e whit ee dwarf . Thi s accretio n dis c dominate s th e spectru m a t optica l an d UVV wavelengths . Th e transitio n betwee n th e accretio n dis c an d th e white-dwar ff atmospher e (boundar y layer ) i s th e regio n wher e th e inflowin gg matte r lose s mos t o f it s kineti c energy , befor e i t settle s ont oo th e whit e dwarf . Thi s energ y i s mainl y radiate d i n th e sof t (k TT < 0. 5 keV ) o r har d (k T > 1 keV ) X-ra y ban d (Pringle , 1977 ; Pringl e andd Savonije , 1979 ; Patterso n an d Raymond , 1985a,b) . Dwar f nova e show , i nn contras t t o th e novalik e variable s an d ol d novae , sudde n outburst s att al l wavelengths , whic h ar e cause d b y a n increas e o f th e

109 9

mass-transpor tt rat e throug h th e disc . Al l dwar f nova e ar e likel y t o b e stron gg sof t X-ra y source s durin g outburst , althoug h thi s i s confirme d observationall yy fo r onl y thre e o f the n (Cordov a an d Mason , 1984 ; va n derr Woer d e t al. , 198 6 / Chapte r V ) .

Coheren tt oscillation s hav e bee n observe d i n th e optica l an d sof t X-ra yy ban d i n al l type s o f cataclysmi c variables . A discussio n o f th e observation ss an d model s ha s bee n give n b y Patterso n (1981 ) an d Cordov a andd Maso n (1983) . Tw o classe s o f oscillation s ca n b e distinguished : th e high-coheren tt oscillation s ( Q > 10 1 0 ) , whic h ar e du e to th e rotatio n o f th ee whit e dwarf , an d th e low-coheren t oscillation s ( Q < 10 6 ) , whos e origi nn i s stil l unknown . Th e facto r Q denote s th e numbe r o f cycle s ove r whic hh a n oscillatio n ca n b e describe d b y a constan t wavefor m an d period .. Thi s definitio n include s th e coherenc e i n phase , an d i s a stronge rr limitatio n t o a n oscillatio n tha n a stabl e period , expresse d byy Q p = IdP/dtl -1 .

Thee high-coheren t oscillation s ar e observe d i n magneti c systems , wher ee accretio n ont o th e whit e dwar f occur s onl y nea r on e o r bot h magneti cc poles . Thes e pole s ar e therefor e a majo r sourc e o f radiation , whic hh range s fro m har d X-ray s t o th e infrare d (Lamb , 1983) . Rotatio n o f th ee whit e dwar f result s i n th e observe d oscillation s ( Q > 10 1 0 ) , whe n onee look s eithe r directl y ont o on e o f th e magneti c poles , o r t o ligh t whic hh i s reprocesse d a t th e accretio n dis c o r companio n star . Th e accretio nn colum n generate s flickerin g an d sometime s oscillation s o f lo w coherenc ee (se e Cordov a an d Mason , 1983 ; Larsson , 1985) .

Thee rotatio n perio d o f th e whit e dwar f ha s neve r bee n observe d directl yy i n non-magneti c cataclysmi c variables . Th e optica l an d sof t X-ra yy oscillation s i n thes e system s hav e Q-value s les s tha n 10 6 . Th e optica ll oscillation s sho w a larg e variet y i n thei r behaviour , whic h makess a clea r descriptio n an d classificatio n difficult . Patterso n (1981 )) ha s propose d a divisio n i n tw o classes : "dwarf-nov a oscillations "" an d "quasi-periodi c oscillations" .

Dwarf-nov aa oscillation s see m t o b e a genera l propert y o f dwarf-nov a outbursts ;; se e Patterso n (1981 ) fo r a review . Thes e oscillations , wit h typica ll amplitude s o f 0. 2 % i n th e v-band , hav e a purel y sinusoida l puls ee shap e an d ar e onl y detecte d nea r maximu m light . Th e period s rang e betwee nn 7 an d 4 0 s , an d th e oscillation s ar e coheren t i n phase , wit h typicall yy 10 4 < Q < lO 6. Th e distinguishin g propert y o f dwarf-nov a oscillation ss i s a relatio n betwee n th e oscillatio n perio d an d th e visua ll flux . Quasi-periodi c oscillation s hav e bee n observe d i n ol d novae ,, novalik e variable s an d i n dwar f nova e durin g outburst . Thes e oscillation ss hav e amplitude s o f th e orde r o f 0. 5 % an d mea n period s i n th ee rang e 3 0 to 40 O s ; se e Robinso n an d Nathe r (1979 ) fo r a review . Th e coherenc ee o f thes e oscillation s i s onl y a fe w cycles , bu t i f on e ignore ss th e fas t change s i n phas e an d amplitude , th e period s ca n b e quit ee stabl e (however : Q » < 10 6 ) .

Thee syste m V W Hy i i s (i n th e visual ) durin g outburs t on e o f th e brightes tt dwar f novae , an d i t ha s bee n extensivel y studie d fo r th e occurrenc ee o f optica l oscillations . Oscillation s hav e bee n observe d durin gg 7 outburst s (se e Robinso n an d Warner , 1984) , bu t ar e no t alway s presen tt (Warne r an d Brickhill , 1978) . Th e oscillation s hav e period s betwee nn 2 3 an d 41 3 s , an d sho w larg e variation s i n coherenc e (fro m 2 t o moree tha n 10 0 cycles) .

I nn sof t X-rays , low-coheren t oscillation s hav e bee n observe d i n

110 0

bot hh s s cy g an d U Ge m durin g th e pea k an d declin e o f outburst . Th e oscillation ss durin g tw o outburst s o f S S Cy g (Cordov a e t al. , 1980,1984 ) hadd «ea n period s o f 8. 8 an d 1 1 s wit h Bea n amplitude s o f 3 0 % an d 1 8 % respectively .. Th e har d X-ra y componen t (2-2 5 keV ) showe d n o pulsation s wit hh amplitude s large r tha n * * 6 %. U Ge m ha s bee n searche d thre e time s fo rr th e presenc e o f oscillation s durin g outburst , bu t onl y onc e a significan tt oscillatio n (mea n amplitud e 1 5 % an d perio d * • 2 7 s ) i n th e sof tt X-ra y flu x wa s detecte d (Cordov a an d Mason , 1984) . Thes e oscillation ss hav e a lo w phas e coherenc e (28 , 2 an d 1 cycle s respectively) ,, whil e th e perio d i s mor e stabl e (Q p * io s ) . Durin g tw o outburst ss o f S S Cygni , observe d wit h th e EXOSAT observatory , low-coheren tt oscillation s wer e detecte d i n th e sof t X-ra y flux , wit h meann period s o f 9. 6 an d 10. l s (Watso n e t al. , 1985) . i t i s clea r tha t period ,, amplitud e an d coherenc e chang e fro m observatio n to observatio n off thes e outbursts . Thei r larg e amplitude s (o f th e orde r o f 1 0 to 5 0 %) andd shor t period s (o f th e orde r o f th e Keple r perio d a t th e white-dwar f surface )) indicat e tha t thes e oscillation s ar e a n importan t aspec t o f th ee sof t X-ra y generatio n process , an d migh t contai n informatio n o n th e accretio nn proces s nea r th e whit e dwarf .

wee hav e mad e EXOSAT observation s o f th e dwar f nov a v w Hydri , whic h i ss a stron g sof t X-ra y sourc e durin g outburs t (va n de r Woer d e t al. , 19866 / Chapte r V ; va n de r Woer d an d Heise , 198 6 / Chapte r VIII) . Severa ll outburst s wer e observe d durin g a long-ter m monito r progra m i n 1983 ,, 198 4 an d 1985 . We discus s i n thi s pape r th e short-ter m variabilit yy o f th e sof t X-ra y emissio n fro m th e syste m V W Hyi.

Afte rr a descriptio n o f th e observation s (Sect . 2) , w e discus s th e method ss an d result s o f searche s fo r coheren t oscillation s i n th e sof t X-ra yy emissio n o f V W Hydr i (Sect . 3) . Th e coheren t oscillation s foun d durin gg tw o superoutburst s ar e considere d i n mor e detai l i n Sect . 4 . Th e origi nn o f th e sof t X-ra y oscillation s i s discusse d i n Sect . 5 , whil e th ee possibl e connectio n betwee n sof t X-ra y oscillation s an d low-coheren tt optica l oscillation s i s discusse d i n Sect . 6 .

2.. Observation s

Thee observation s hav e bee n obtaine d wit h th e Low-Energ y (LE ) telescop ee aboar d th e EXOSAT observator y (d e Kort e e t al. , 1981) . Th e LE-telescop ee imag e o f th e X-ra y sk y (diamete r 2. 2 degrees) , a s observe d throug hh severa l filters , i s projecte d o n a Channe l Multiplie r Arra y (CMA) .. We use d th e 3000 - an d 4000-Lexan , an d Aluminiu m Parylen e (Al-Pa ) filters .. Thes e observation s giv e informatio n o n th e "soft " par t o f th e X-ra yy spectrum , typicall y betwee n 8 an d « 30 0 A . Th e positio n o f a n even tt a t th e CMA i s determine d o n a gri d o f 102 4 x 102 4 pixels . A sourc ee nea r th e centr e o f th e imag e take s 1 2 x 1 2 pixel s (9 5 % o f th e counts) .. Th e coun t rat e fo r th e res t o f th e imag e i s determine d b y th e backgroun dd an d serendipitou s sources .

Thee arriva l tim e o f eac h photo n i s determine d wit h a n accurac y o f 2~13s .. Th e event s o f th e whol e imag e ar e directl y transmitte d t o Earth . Forr hig h coun t rates , however , th e informatio n exceed s th e limit s se t byy telemetry . A s a resul t th e accumulatio n o f event s i s the n temporaril yy interrupted . Thi s cause s gap s i n th e dat a strea m ("dea d time") .. Th e telemetr y limi t i s determine d b y th e tota l informatio n rat e

111 1

sen tt t o Earth , an d therefor e depend s o n th e othe r EXDSAT experiment s (MEE an d GSPC) an d th e mod e o f observation . I t als o depend s o n th e numberr o f event s gathere d ove r th e whol e L E imag e (i.e . mostl y background) .. Al l thes e effect s resul t i n a dea d tim e whic h varie s erraticall yy i n time .

Itoi ss pape r consider s i n detai l a selectio n o f al l EXDSAT observation ss o f v w Hydri . A lo g o f th e 198 3 observation s o f thi s sourc e i ss give n i n va n de r Woer d e t al . (198 6 / Chapte r V ) an d th e 198 4 observation ss ar e describe d i n va n de r Woer d an d Heis e (198 6 / Chapte r VIII) .. Th e lo g o f observation s obtaine d i n 198 5 i s give n i n Chapte r VII .. I n thes e paper s th e spectra l an d tempora l behaviou r o f th e sof t x-ra yy flu x o n th e tim e scal e o f day s (quiescenc e an d outburst ) i s discussed .. I n th e presen t pape r w e concentrat e o n th e tempora l behaviou rr o n th e tim e scal e o f seconds .

AA heliocentri c correctio n wa s applie d t o al l data . N o correctio n i s madee fo r th e Dopple r shif t du e t o th e binar y motio n o f th e whit e dwarf , orr th e movement o f th e satellite . Th e light-trave l tim e i n th e orbi t o f aa whit e dwar f o f 1 M Q i n a close-binar y syste m wit h a n orbita l perio d off 2 hour s an d mas s rati o 6 (whic h i s likel y th e cas e fo r V W Hyi ; Schoembss an d Vogt , 1981 ) i s les s tha n 1 second . Thi s implie s a smoothin gg o f th e ligh t curv e withi n 0. 1 o f th e phase , fo r period s o f th ee orde rr o f 1 0 s an d larger . Th e error , mad e b y neglectin g th e exac t positio nn o f th e satellite , i s a t mos t equa l t o th e light-trave l tim e t o apoge ee { « 0.6 4 s ) .

Fas tt optica l photometr y wa s obtaine d a t L a Silla , Chil i wit h th e ESOO 1 mete r telescope . Th e observations , wit h tim e resolutio n o f 0, 4 o r 0. 55 s , too k plac e aroun d J D 2445661.76 6 (2 3 No v 1983 ) an d J D 2445668.52 66 an d laste d 2.1 6 an d 6.4 8 hour s respectively . Th e observation ss wer e obtaine d wit h a n EMI 625 6 photomultiplie r tube , an d a 16"" diaphragm , withou t filter . Thi s give s informatio n o n th e blu e par t off th e optica l spectru m (300 0 - 500 0 A ) , wit h a n effectiv e wavelengt h att X * 420 0 A .

3.. Searc h fo r fas t oscillation s

Al ll observation s wit h a larg e enoug h numbe r o f counts , i.e . almos t al ll observation s mad e durin g outburst s an d tw o observation s mad e durin g quiescence ,, wer e teste d fo r th e presenc e o f coheren t oscillations . A Fas tt Fourie r Transfor m (FFT ) wa s mad e fro m eac h observation , an d th e powerr spectr a wer e checke d fo r significan t peaks . Th e criteri a fo r uppe rr limits , amplitude s an d significanc e o f peak s i n th e powe r spectru mm hav e bee n take n fro m Leah y e t al . (1983) .

Befor ee applyin g thes e criteria , w e hav e checke d i f thei r analysi s i ss applicabl e t o ou r dat a set . Leah y e t al . (1983 ) assum e tha t a n observatio nn consist s o f a continuou s stretc h o f data , wher e th e incomin gg event s follo w a Poisso n distribution . Thi s i s no t strictl y th e cas ee fo r th e EXDSAT L E observations : th e dea d tim e o f th e CMA detecto r give ss ris e t o gap s (0. 1 - 0. 5 s ) i n th e dat a stream , wit h a typica l recurrenc ee tim e o f 0. 5 - 1. 0 s . Eac h bin , o f a n observatio n wit h lengt h T,, numbe r o f photon s N an d lif e tim e T L (liv e tim e i s equa l t o T minu s th ee dea d time) , consist s o f tw o parts : i n on e par t th e photon s arriv e followin gg a Poisso n distribution , wit h a mea n coun t rat e o f N/TL , an d 112 2

i nn th e othe r peur t n o event s ar e accumulated . Therefor e th e binnin g wit h smal ll bi n siz e (o f orde r 0. 5 s ) o f observation s wit h a larg e dea d tim e result ss i n a binne d dat a se t whic h deviate s fro m a Poisso n distribution . .

I nn orde r t o tes t whethe r th e dea d tim e result s i n larg e deviation s off th e binne d dat a fro m a Poisso n distribution , a n FF T wa s mad e o f th e backgroun dd o f eac h observatio n (wit h th e sam e bi n size) . I n th e L E X-ra yy imag e severa l boxe s wer e chose n whic h containe d n o source s abov e th ee 20 level . Di e dimensio n o f eac h bo x wa s adjuste d t o giv e a numbe r off backgroun d event s equa l t o th e numbe r o f event s o f th e source . A n FFTT wa s performed , an d th e resultin g distributio n o f th e powe r wa s compare dd wit h th e expecte d x2 distributio n (Leah y e t al. , 1983) . I n thi ss wa y on e ca n easil y tes t th e influenc e o f binnin g an d th e dead-tim e (not ee tha t th e sam e dead-tim e histor y applie s t o th e backgroun d an d sourc ee file ) o n a sourc e wit h a give n mea n coun t rate . Thi s i s fo r ou r purpos ee a quicke r an d mor e convenien t tes t tha n a n extensiv e Mont e Carl oo simulatio n fo r eac h observation .

Wee foun d fo r almos t al l observation s tha t onl y fo r a bi n siz e o f orde rr 1. 5 s o r mor e th e influenc e o f th e dead-tim e become s unimportant . Forr thi s bi n siz e th e binne d dat a se t mimic s a Poisso n distributio n wit hh a mea n coun t rat e o f N/T . We hav e binne d eac h observatio n wit h a bi nn siz e o f orde r 2 s , suc h tha t 2 n (wit h n a n integer ) time s th e bi n siz ee equal s th e observatio n time . I n eac h cas e wa s checke d whethe r th e distributio nn o f th e powe r o f th e FF T follow s a x2 distributio n wit h 2 degree ss o f freedom , an d , i f so , th e significanc e o f peak s i n a powe r spectru mm wa s determine d (Leah y e t al. , 1983) .

Durin gg som e observation s long-ter m change s i n th e sof t X-ra y flux , andd larg e change s i n th e mea n dea d tim e (stron g sola r activity ) occured .. Bot h effect s resul t i n exces s powe r a t th e lowes t frequencie s (period ss o f 1 0 mi n o r more) . Thi s ca n influenc e ou r criteri a fo r th e detectio nn o f fas t coheren t oscillations . We foun d tha t mos t o f thi s powerr a t th e lowes t frequencie s coul d b e remove d b y subtracting , instea dd o f th e mea n leve l (polynomia l o f orde r 0) , a highe r polynomia l (u pp t o orde r 9 ) fro m th e data .

I nn tabl e l th e result s o f th e searc h fo r coheren t oscillation s ar e given .. Fo r eac h observatio n tw o uppe r limit s t o th e amplitud e o f oscillatio nn ar e quoted . Th e firs t limi t applie s t o th e perio d rang e fro mm 4 t o 40 0 s . Th e amplitude s i n thi s colum n ar e give n u p t o a facto r sin (( 77j/N)/(TTj/N) , wit h j th e bi n numbe r o f th e perio d an d N th e tota l numberr o f bins . Thi s functio n correct s fo r th e fac t tha t th e binnin g o f th ee dat a ha s influence , dependin g o n th e period , o n th e determinatio n off th e amplitud e (se e Leah y e t al. , 198 3 fo r details) . Th e secon d limi t applie ss t o th e perio d rang e 1 3 t o 1 5 s , an d i s alread y correcte d fo r th ee abov e give n effect . Thi s perio d rang e wa s define d a posteriori , afte rr th e detectio n o f oscillation s nea r 1 4 s i n tw o observations . Th e uppe rr limit s ar e base d o n tw o confidenc e levels : ther e i s onl y a 1 % probabilit yy tha t thi s amplitud e (an d power ) i s equale d o r exceede d b y chanc ee (fals e alar m probability) , an d whe n a n oscillatio n i s present , th ee give n oscillatio n amplitud e woul d lea d t o detectio n 9 9 % o f th e tim ee (se e Leah y e t al . (1983 ) fo r details) .

Thee EXOSAT observation s cove r 4 superoutburst s an d 3 norma l outburst ss o f V W Hydri . Als o th e precurso r befor e th e superoutburs t o f

113 3

TableTable 1 . Upper Itmlts and detec t ton s of coherent oscillations In the softsoft X-ray flux of VW Hydrl. The second of the first 5 columns which describedescribe the observation denotes the state of the systemt normal- (N) oror super- (S) outburst, quiescence (Q) or precursor (P) to the superoutburstsuperoutburst of October 1984. The upper limits to the amplitude are determineddetermined In the period ranges 4 to 400 s and 13 to 15 s. A detection IsIs Indicated by a +.

Dat e e

198 33 No v

198 44 Ha y Sep p

Oct t

NOV V 198 55 Ap r

Nov v

14 4 15 5 15 5 21 1 21 1 21 1 25 5 30 0

2 2 7 7

23 3 7 7 7 7

23 3 23 3 27 7 27 7 27 7 27 7 30 0 30 0

3 3 16 6 16 6 16 6

6 6 6 6

10 0

stat e e

s s s s s s s s s s s s s s Q Q Q Q N N

N N N N N N P P P P

s s S S

s s s s s s s s s s s s s s s s s s s s s s

Exp.(8 ) )

1464 5 5

443 2 2 84 0 0

159 2 2 712 8 8 273 6 6

1246 8 8 2875 2 2 5597 6 6

936 0 0 2366 4 4 1197 6 6

272 0 0 1434 4 4

189 6 6 1436 8 8

932 0 0 104 8 8

1435 0 0 620 0 0 111 2 2

1601 6 6 397 6 6 276 8 8 149 6 6 604 0 0 667 2 2 874 4 4

Counts/ s s

0.O5 0 0 0.42 1 1 1.51 3 3 0.30 9 9 1.12 8 8 0.12 3 3 0.O3 1 1 0.O2 8 8 0.O3 6 6 0.O6 9 9 0.O8 7 7 0.69 0 0 0.12 7 7 0.88 4 4 0.15 8 8 4.25 9 9 1.24 9 9 0.6O 9 9 3.45 8 8 1.02 9 9 0.29 9 9 0.19 9 9 1.32 4 4 0.31 7 7 0.11 1 1 1.16 3 3 0.29 4 4 0.20 1 1

Pilte r r

3L L

3L L AL L 3L L AL L 4L L AL L 3L L 3L L AL L AL L AL L 3L L AL L 3L L AL L 3L L 4L L AL L AL L 3L L AL L AL L 3L L 4L L AL L 3L L AL L

(4-40 00 8 )

0.30 6 6 0.18 1 1 0.25 1 1 0.43 4 4 0.09 1 1 0.52 2 2 0.47 7 7

0.32 4 4 0.19 2 2 0.37 0 0 0.24 2 2 0.10 5 5 0.42 8 8 0.07 4 4 0.43 7 7 0.0 3 3 0.1 44 + 0.29 8 8 0.04 4 4 0.10 6 6 0.43 5 5 0.16 2 2 0.11 1 1 0.26 2 2 0.58 1 1 0.12 9 9 0.20 6 6 0.21 2 2

(13-1 55 8 )

0.27 2 2 0.16 7 7 0.21 2 2 0.37 2 2 0.1 55 + 0.45 9 9 0.42 7 7 0.28 9 9 0.17 3 3 0.32 3 3 0.21 5 5 0.09 3 3 0.36 8 8 0.06 6 6 0.37 0 0 0.07 44 + 0.1 77 + 0.2 99 + 0.08 55 + 0.09 3 3 0.36 5 5 0.14 6 6 0.09 7 7 0.22 4 4 0.52 3 3 0.11 3 3 0.18 0 0 0.19 0 0

Octobe rr 198 4 wa s observe d nea r maximum . Thi s precurso r mimic s a norma l outburs tt (se e va n de r Woer d an d Heise , 198 6 / Chapte r viii) . Fro m al l th ee quiescenc e observation s onl y tw o hav e a larg e enoug h numbe r o f count ss t o giv e a meaningfu l uppe r limi t t o th e oscillatio n amplitude .

Coheren tt oscillation s wer e detecte d o n tw o occasions . Th e firs t oscillation ,, wit h a perio d o f 14.0 6 ± 0.0 2 s an d mea n amplitud e o f 155 %, i s detecte d durin g th e observatio n wit h th e Al-P a filte r a t 2 1 Novv 1983 , whic h too k plac e toward s th e en d o f th e Novembe r 198 3 superoutburs tt ( V • 9. 4 ± 0.2) , 3 day s befor e th e rapi d declin e toward s quiescenc ee (va n de r Woer d e t al. , 198 6 / Chapte r V ) . Figur e 1 show s th e FFTT fro m thi s observation . Th e oscillatio n i s no t detecte d i n th e quasi-simultaneou ss 3000 - an d 4O00-Lexa n observation . Neithe r i s a

114 4

0.0 6 6

0.0 0 0 1000 12 0 14 0 16 0

FREQUENCYY ( mill i Hert z

Fig.Fig. 1. The fast Fourier transform from the Al-Pa filter observation on 2121 November 1983. The power peaks at a period of 14.06 s, with anan amplitude of 15 per cent.

significan tt oscillatio n (uppe r limit s o f 2 1 % an d 4 2 %) detecte d i n th e perio dd interva l 1 3 t o 1 5 s i n th e othe r Al-P a observatio n durin g thi s superoutburst ;; i n contras t t o earlie r statement s (Heis e e t al. , 1984) . Thee secon d coheren t oscillatio n i s detecte d durin g a n 1 1 hou r observatio nn o f th e Octobe r 198 4 superoutburst , 4 day s afte r th e onse t off thi s superoutburs t (va n de r Woer d an d Heise , 198 6 / Chapte r VIII) . VWW Hy i wa s extremel y brigh t i n th e sof t X-ra y ban d an d i n th e visua l (V == 8. 8 ± 0.2) . Th e oscillatio n perio d drift s betwee n 14. 4 an d 14. 2 s , andd i s detecte d i n al l thre e filters . I n additio n a transien t (• »» 450 0 s ) oscillatio n wit h a mea n perio d o f 6 5 s i s presen t i n th e 3000-Lexa nn observation . Thes e oscillation s ar e considere d i n mor e detai ll i n th e nex t section .

Thee lac k o f detectio n o f oscillation s i n th e 1 3 t o 1 5 s perio d interva ll durin g al l othe r observation s indicate s tha t thes e oscillation ss normall y hav e smalle r amplitude s o r ar e absent . E.g . a 155 % modulatio n o f th e Al-P a flux , lik e observe d a t 2 1 No v 1983 , woul d easil yy hav e bee n detecte d durin g th e norma l outburs t a t 7 Oc t 1984, o r durin gg th e tw o superoutburst s i n 1985 . A n 8 % modulatio n o f th e Al-P a flux ,, lik e observe d a t 2 7 Oc t 1984, woul d hav e bee n detecte d 4 day s earlie rr a t th e precursor . Whethe r th e detectio n o f oscillation s durin g superoutburs tt i s onl y a n observationa l selectio n effect , ca n no t b e decide dd o n th e basi s o f ou r observations .

Thee X-ra y spectru m o f V W Hy i durin g quiescenc e i s muc h harde r tha n durin gg outburs t (va n de r Woer d e t al. , 198 6 / Chapte r V ; va n de r Woer d andd Heise , 198 6 / Chapte r VIII) . N o coheren t oscillation s wit h a n amplitud ee o f mor e tha n 1 7 % ar e detecte d i n th e sof t par t o f thi s spectrum ,, a t a 9 9 % confidenc e level .

Fastt white-ligh t photometr y wa s obtaine d durin g th e outburs t maximumm (V»9.6 ) o f th e Novembe r 198 3 superoutburs t o f V W Hyi . Thi s wa s

115 5

1500 0

> > u u o o L. .

- t ^ ^

-Q Q L. . O O

CC C

w w

O O CL L

1000 0

5 0 0 0

400 50 60 70 FREQUENCYY ( m i l l i H e r t z )

80 0 90 0

Fig.Fig. 2. The FFT of the fast uhtte-ltght photometry on 23 November 1983. TheThe mean count rate was "43000 count/s. An artificial oscillation with amplitudeamplitude of 40 count/s and a period of 12 s uas inserted.

TIME E

Fig.Fig. 3. The light curves of the Al-Pa observation on 21 November 1983 (a),(a), and the 3000-Lexan (b), first Al-Pa (c) and second Al-Pa (d) observationobservation on 27 October 1984. Four bins of a light curve form one section,section, which uas analysed for the presence of oscillations; see text. TheThe length of the bins is 446.5, 583, 67 5 and 67 5 s respectively. A H curvescurves shou modulations uhich exceed the Poisson noise.

116 6

approximatel yy on e da y afte r th e sof t x-ra y observation s wit h a - 1 5 % modulatio nn i n th e Al-P a flux . Mo oscillation , wit h a n amplitud e large r tha nn 0.000 6 mag , wa s detecte d nea r 14.0 6 s (se e Fig . 2) . A secon d observatio nn wa s mad e jus t afte r th e optica l declin e ( V w 13.3) . A n uppe rr limi t o f 0.001 5 mag fo r th e amplitud e o f a 14.0 6 s oscillatio n i s derived . .

4.. Coheren t sof t X-ra y oscillation s

Thee observation s durin g whic h a significan t modulatio n wa s detecte d hav ee bee n spli t i n sections , i n orde r to stud y th e behaviou r o f thes e oscillation ss o n a shorte r tim e scale . Th e siz e o f a sectio n i s a trade-of ff betwee n a minimu m numbe r o f cycle s an d a maximu m signal-to-nois ee rati o o f th e modulatio n i n tha t section . Eac h sectio n off th e dat a wa s chose n t o b e m 200 0 s long . Thi s mean s tha t i t show s th ee averag e characteristic s o f • * 14 0 cycle s o f a 1 4 8 oscillation .

Thee section s hav e bee n studie d b y performin g a n FF T an d b y epoc h folding .. Epoc h foldin g i s mor e sensitiv e t o non-sinusoida l puls e shapes .. Moreove r i t i s les s sensitiv e fo r gap s i n th e data , whic h resul tt fro m th e dead-time . I n eac h cas e w e hav e checke d tha t th e periodi cc variation , foun d i n th e observation , di d no t resul t fro m non-unifor mm samplin g o f th e puls e phase , b y foldin g th e windo w function .. We applie d a fas t foldin g cod e t o th e data , analogou s t o th e Fastt Fourie r Transfor m (Stealin , 1969) . Th e binne d ligh t curv e i s compare dd wit h th e mea n coun t rate , an d th e x2 o f thi s fi t i s calculated .. A highe r x2 indicate s a mor e significan t modulatio n (Leah y ett al. , 1983) .

Fourie rr analysi s o f th e observation s o n 2 1 No v 198 3 reveale d th e presenc ee o f a coheren t oscillatio n wit h a perio d o f 14.0 6 ± 0.0 2 s i n th ee extremel y sof t X-ra y flu x (Al-P a filter) , se e Fig . l . Ther e i s n o indicatio nn fo r th e presenc e o f a highe r harmoni c wit h amplitud e highe r tha nn 7 %. Th e observatio n o f 712 8 s wa s spli t i n 7 section s o f 178 6 s each ,, wit h a n overla p o f 5 0 % betwee n th e sections . Th e intensit y o f th ee sof t X-ra y flu x varie s erraticall y wit h a modulatio n o f "1 0 %. Th e ligh tt curv e an d a n indicatio n o f th e section s i s show n i n Fig . 3a . Th e FFTss o f th e firs t 4 section s sho w a variabl e amplitud e o f th e oscillatio nn (1 6 ± 1 t o 2 1 ± 1 % ) , whic h i s no t correlate d wit h th e X-ra yy flux . Durin g th e nex t tw o sections , betwee n 360 0 an d 630 0 s afte r th ee star t o f th e observation , n o oscillatio n i s observe d wit h amplitud e greate rr tha n 11. 8 %, a t a 9 9 % leve l o f confidence . Th e intensit y lie s 66 % belo w th e mea n level . Th e las t 178 6 s sectio n agai n show s th e 14.0 66 s oscillatio n wit h a n amplitud e o f 1 6 ± 1 %.

Thi ss chang e i n amplitud e o f th e oscillatio n i s depicte d i n Fig . 4 . Section ss o f exactl y 14 2 cycle s o f 14.0 6 s (1996. 5 s) , wit h a 5 0 % overlap ,, ar e folde d betwee n 13. 5 an d 15. 0 s . Verticall y th e x2 i s plotte dd a s functio n o f th e period . Th e origi n o f eac h sectio n i s shifte dd upwards . Th e perio d i s constan t withi n 0.0 2 s ove r a n interva l off w 700 0 s (Fig . 4) , whic h indicate s a lowe r limi t o f Q p - 3 10 5. Figur ee 5 show s th e ligh t curve s fo r thes e section s o f th e observation , folde dd wit h th e fundamenta l perio d o f 14.0 6 s . Curv e 1 i s a fol d o f th e whol ee observation . Th e curve s 2 t o 7 ar e fold s o f th e abov e mentione d section ss o f 14 2 cycles , wit h a 50 % overlap . Th e puls e profile s ar e

117 7

14. 22 14. 4 14. 6

PERIODD I see l

Fig.Fig. 4. Th e chl-sauare as function of the fold period for each section ofof 142 cycles of 14.OB s of the Al-Pa observation on 21 November 1983. TheThe sections overlap by 50 % , and the time proceeds with every section byy 89 3 s. Bach section is shifted upwards by x2 = 3.0 compared to the previousprevious one. This shift t s indicated by the bold lines at the ordinate. ordinate.

Fig.Fig. 5. A diagram of the change of the pulse profile In the Al-Pa filterfilter observation on 21 November 1983. Profile 1 Is a fold of — 7000 secondsseconds of data uith a period of 14.06 s. The profiles 2 to 7 are folds ulthulth this same period, of — 2000-second sections of these data ulth a SOSO % overlap. 118 8

ii i i i ; i i i i i i 1 1 1 1 1 1 1 r

Fig.Fig. 6. The cht-square as function of the fold period for 7 sections of 23322332 s from the 3000-texan observations on 27 October 1984. The sectionssections overlap by 50 %, and the time proceeds uith every section by 11661166 s. Each section is shifted upward s by X2 = 3.0, uhich is indicatedindicated by the bold lines at the ordinate.

stabl ee i n phase , wit h a maximu m phas e jitte r o f « • 0.2 . Th e variatio n i nn amplitude , an d th e apparen t disappearanc e o f th e oscillatio n betwee n 30000 s an d 600 0 s afte r th e beginnin g o f th e observatio n (curve s 5 an d 6)) ar e visible . Th e oscillatio n observe d i n th e las t sectio n o f 14 2 cycle ss i s exactl y i n phas e wit h th e oscillatio n i n th e res t o f th e observation .. We conclud e that , althoug h th e oscillatio n i s no t prominen tt fo r par t o f th e observation , th e phas e seem s t o b e coheren t fo rr th e whol e observatio n ( Q > 2500) .

Coheren tt oscillation s wer e als o presen t durin g th e observation s o n 277 Oc t 1984 . Thes e oscillation s wer e detecte d i n al l thre e filters . Th e stronges tt modulatio n occur s i n th e 4000-Lexa n an d 3000-Lexa n filters . Thee modulatio n i n th e Al-P a i s onl y hal f o f tha t durin g th e Al-P a observatio nn a t 2 1 No v 1983 . Th e uppe r limit s t o th e oscillatio n amplitud ee i n th e 3000 - an d 4000-Lexa n observation s a t 2 1 No v 198 3 ar e to oo hig h t o verif y whethe r th e pulse d fractio n i n th e thre e filter s wa s differen tt o n th e tw o occasions . Th e fac t tha t th e oscillatio n amplitud e i ss ver y differen t fo r th e severa l filter s suggest s tha t th e colou r temperatur ee o f th e oscillatin g par t o f th e spectru m differ s fro m th e meann colou r temperature . On e mus t b e carefu l wit h thi s conclusion , however ,, becaus e th e oscillatio n amplitud e i s know n t o var y i n tim e (se ee above) , an d thes e observation s wer e no t take n simultaneously . Th e rati oo o f amplitude s i n th e severa l filter s (tabl e 1 ) indicate s a highe r temperatur ee fo r th e oscillatin g component . A mor e quantitativ e

119 9

conclusio nn i s no t possible , becaus e th e spectra l characteristic s o f th e unmodulate dd sof t X-ra y flux , observe d wit h KXOSAT, ar e no t wel l understoo dd (va n de r Woer d an d Heise , 198 6 / Chapte r VIII) .

Thee 30O0-Lexa n observatio n wa s divide d int o 7 section s o f 233 2 s each ,, wit h a 5 0 % overla p betwee n th e sections . Th e ligh t curv e i s shownn i n Pig . 3b . Figur e 6 show s th e resul t o f epoc h foldin g o f thes e section ss a t period s betwee n 13. 5 an d 15. 0 s . Th e firs t thre e section s sho ww a maximu m x 2 a t 14.3 4 ± 0.0 3 s . Betwee n th e 3r d an d 4t h sectio n th ee mea n perio d jump s fro m 14.3 4 t o 14.2 6 s , whic h give s a forma l Qpp « • 1. 5 10 4 . I n section s 4 t o 7 th e oscillation s hav e a "best " perio d off 14.2 6 ± 0.0 3 s . Bot h th e 14.3 4 an d 14.2 6 s oscillatio n ar e presen t i nn th e foldin g o f th e whol e 3000-Lexa n observation . Th e change s i n amplitud ee ar e small .

Figur ee 7 show s th e FF T o f th e firs t thre e sections . Th e mos t prominen tt featur e i s th e oscillatio n wit h a perio d o f 14.3 4 s an d amplitud ee o f 20. 0 %. Th e firs t harmoni c i s als o detecte d an d ha s a n amplitud ee o f 12. 1 %. Anothe r significan t oscillatio n i s detecte d nea r 655 s , wit h a n amplitud e o f 1 4 %. Th e firs t harmoni c o f th e 14.3 4 s modulatio nn wa s detecte d i n hal f th e numbe r o f sections , wit h th e abov e give nn amplitude . Th e long-perio d oscillatio n i s onl y detecte d i n th e firs tt thre e sections . Th e perio d graduall y change s fro m ~ 6 3 t o 6 8 s , whil ee th e amplitud e change s fro m 14 t o 2 1 %.

Thee amplitud e o f th e • » 14. 3 s oscillatio n i s larges t i n th e shor t observatio nn wit h th e 4000-Lexa n filter . Th e bes t fit , foun d b y epoc h folding ,, i s 14.2 7 ± 0.0 5 s , an d th e amplitud e i s equa l t o 29. 1 %.

Thee Al-P a observation s wer e take n a t th e beginnin g an d en d o f th e EXDSATT pointin g t o V W Hydr i a t 2 7 Oc t 1984 . Betwee n th e firs t an d secon dd Al-P a observatio n th e coun t rat e droppe d b y 1 9 %. Th e ligh t curve ss o f th e firs t an d secon d Al-P a observatio n ar e show n i n Figs . 3c ,, d . Bot h observation s wer e spli t int o section s o f 270 0 s wit h a 5 0 % overlap .. Thes e section s wer e epoch-folde d wit h period s betwee n 13. 5 an d 15. 00 s . Th e resul t i s show n i n Figs . 8a,b . I t i s clea r tha t stron g variation ss ar e presen t i n th e amplitud e o f th e oscillation . Durin g th e firs tt Al-P a observatio n th e oscillatio n initiall y ha s a perio d o f 14.3 44 ± 0.0 3 s , the n disappears , an d finall y come s bac k wit h a perio d off 14.2 8 t o 14.2 6 s wit h a n amplitud e o f almos t 1 0 %. Durin g th e secon d Al-P aa observatio n th e oscillatio n ha s a n amplitud e betwee n 6 an d 9 %. Thee perio d seem s t o increas e slowl y fro m 14.2 1 t o 14.2 5 s wit h Opp * 1. 7 10 5 .

5.. Origi n o f th e sof t X-ra y oscillation s

Thee propertie s o f th e sof t X-ra y oscillation s i n V W Hy i sho w som e similarit yy t o thos e observe d i n S S Cy g an d U Gem. Cordov a e t al . (1980 ) discus ss i n grea t detai l th e low-coheren t oscillation s i n th e sof t X-ra y flu xx o f S S Cygni , observe d durin g a n outburs t i n Jun e 1978 . Durin g thi s observatio nn stron g change s occu r i n th e pulse d fraction , phas e an d mea n perio dd o f th e oscillation . Th e amplitud e ha s a mea n valu e o f 3 0 %, bu t change ss i n amplitud e u p t o lo o % ar e observed . Th e perio d drift s betwee nn 8.8 9 an d 8.7 6 s . Th e long-ter m perio d chang e ca n b e descibe d b y aa slowl y decreasin g perio d (dP/d t - -8. 9 ± 2. 6 1 0 - 6 ) . However , tw o constan tt period s (8.8 8 an d 8.7 6 s ) als o fi t th e data . Th e dat a sho w

120 0

0.. 00 00 20 40 60 80 100 120 140 160 180 200

FREQUENCYY ( milli Hertz )

Fig.Fig. 7. The FFT of the first 4663 s of the 3000-Lexan observation on 27 OctoberOctober 1984. Beside the dominant oscillation at 14.34 s and its first harmonic,harmonic, a modulation in the range 63 to 68 s t s present.

PERIODD I sec ]

Fig.Fig. 8. The cht-square as function of the fold period for 9 and 7 2700 ss sections from the first (loner panel) and second (upper panel) Al-Pa observationobservation on 27 October 1984. The sections overlap by 50 %, and the timetime proceeds with every section by 1350 s. Each section is shifted upwardsupwards by x2 ~ 2.0, which is indicated by the bold lines at the ordinate. ordinate.

121 1

perio dd excursion s o n a shor t tun e scale . I n Fig . e o f Cordov a e t al . (1980) ,, change s o f th e mea n perio d wit h 0.2 s withi n 100 0 s ca n b e see n {Qpp - 5 10 3 ) . Occasionall y multipl e period s see m t o b e present . Th e dat aa ca n b e describe d b y a n oscillatio n wit h a rando m wal k i n phas e du e t oo whit e nois e i n th e perio d o f th e oscillation . Th e phas e wander s b y 900 degree s i n °*2 8 cycles . Th e perio d ca n b e describe d b y a rando m variable ,, whic h ca n tak e value s fro m a limite d perio d distributio n ( PP = 8.7 7 ± 0.4 4 s ) .

Subsequen tt observation s o f rapi d variabilit y o f th e sof t X-ra y flu x durin gg outburst s o f SS Cy g an d U Ge m (Cordov a e t al. , 1984 ) sho w th e samee features . Th e coherenc e is , however , muc h lowe r durin g thes e observations .. Th e secon d observatio n o f SS Cy g show s a modulatio n o f 188 % wit h a coherenc e i n phas e o f 2 cycles . Th e perio d distributio n ha s aa mea n an d standar d deviatio n o f 10. 7 ± 1. 8 s . I n U Ge m th e modulatio n ca nn b e describe d b y a rando m wal k i n phas e wit h a typica l 9 0 degree s chang ee withi n 1 cycle . Th e perio d lie s i n th e rang e 2 7 t 6 s . We not e however ,, tha t durin g th e firs t 5 orbit s (th e HEAO- l observatio n consist ss o f 7 subsequen t orbits ) th e perio d remain s constan t a t «« 2 5 s , whil e th e las t 2 orbit s sho w a mea n perio d o f 2 9 s (se e Fig . 4 i nn th e abov e quote d paper) .

Thee descriptio n o f thes e oscillation s b y a rando m wal k i n phas e doess no t poin t directl y t o a specifi c model . I t i s fo r exampl e no t clea rr whethe r th e principl e featur e i s th e phas e nois e o r th e rando m chang ee i n period . Cordov a e t al . (1984 ) discus s fou r mathematica l models ;; the y fin d tha t bot h a stabl e oscillato r wit h phas e noise , an d a dampedd harmoni c oscillato r wit h rando m excitation s ca n describ e th e observations .. A stabl e oscillato r wit h onl y amplitud e nois e i s rule d out .. Superpositio n o f modes , excite d i n th e surfac e laye r o f a a rapidl y rotatin gg whit e dwar f (propose d b y Papaloizo u an d Pringle , 1978) , doe s nott fi t th e observation s eithe r (se e als o Patterson , 1981) .

AA mode l fo r th e X-ra y oscillation s whic h use s th e rotatio n o f th e oute rr layer s o f th e whit e dwar f a s basi c cloc k i s simpl e an d attractive .. Durin g a dwarf-nov a outburst , materia l wit h a hig h specifi c angula rr momentu m i s accrete d a t a hig h rat e nea r a n equatoria l bel t o f th ee whit e dwarf . Thes e layer s wil l dispos e o f thei r angula r momentu m t o th ee res t o f th e star . Thi s redistributio n o f angula r momentu m wil l probabl yy occu r bot h radiall y an d i n th e directio n o f th e poles . I t i s therefor ee expecte d tha t th e rotatio n rat e o f th e oute r layer s o f th e whit ee dwar f depend s o n th e pola r angle , wit h th e highes t rotatio n rat e att th e equator . Thi s differentia l rotatio n wil l influenc e th e structur e off th e boundar y layer , an d thereb y migh t influenc e th e sof t X-ra y generatio nn process . O f cours e th e boundar y laye r itsel f i s a regio n wit hh stron g differentia l rotation . Th e oute r layer s spi n u p unti l th e los ss o f angula r momentu m t o th e sta r i s balance d b y th e accretio n o f angula rr momentum. A correlatio n betwee n th e accretio n rat e an d rotatio n rat ee o f th e oute r layer s woul d thu s no t b e surprisin g (Papaloizo u an d Pringle ,, 1978) . When thi s equilibriu m ha s no t ye t bee n reached , th e spi nn rat e depend s o n th e tota l amoun t o f angula r momentu m dumpe d ont o th ee sta rr durin g th e outburs t sofar .

Thee observe d period s i n S S Cy g ar e al l o f th e sam e order . Recen t EXOSATT observation s o f S S Cy g (Watso n e t al. , 1985 ) confir m tha t a perio dd aroun d 1 0 s i s typica l fo r S S Cyg . When th e rotatio n perio d o f th ee boundar y laye r slowl y changes , th e differenc e i n observe d period s

122 2

cann simpl y b e du e t o th e observatio n a t differen t epoch s o f thi s slowl y changin gg oscillator . I n cas e th e observe d mea n perio d chang e o f dP/d tt • » - l 10~ 5 i s vali d durin g a larg e par t o f th e outburst , i t onl y take ss tw o day s t o chang e th e perio d fro m e.g . 10. 7 to 8. 8 s . Thi s nigh t als oo explai n th e differenc e betwee n th e M 14. 3 s oscillatio n i n V W Hyi ,, observe d jus t afte r th e star t o f th e superoutburst , an d th e 14.0 6 ss oscillatio n observe d nea r th e en d o f a superoutburst . Whethe r th e connectio nn betwee n hig h coherence , hig h amplitude , an d shor t perio d (observe dd i n bot h S S Cy g an d V W Hyi ) i s a genera l phenomeno n i s no t certain ,, w e mentio n th e analog y wit h th e optica l dwarf-nov a oscillation ss i n SS Cyg , whic h sho w tha t th e coherenc e get s wors e fo r large rr period s (Hildebrand t e t al. r 1981) .

Thee relativ e change s i n perio d durin g on e observatio n ar e small . Whenn on e translate s thes e change s t o a chang e i n Kepler-orbit , th e chang ee betwee n 14.3 4 an d 14.2 6 s i n V W Hy i result s fro m a relativ e chang ee i n radiu s o f dr/ r = 3. 7 10 - 3 . Fo r a typica l white-dwar f radiu s off 5 10 8 cm , thi s implie s a chang e o f M 1 9 km . I t i s importan t t o realiz ee tha t th e typica l dimensio n o f th e boundar y laye r i s 10~ 2

white-dwar ff radii , o r * * 5 0 k m (Pringle , 1977) . Thes e change s ar e therefor ee o f th e sam e orde r a s th e dimension s o f th e x-ra y generatin g region .. Thi s implie s tha t th e variation s i n th e sof t X-ra y flu x ca n b e duee t o effect s lik e changin g optica l dept h o r smal l transien t magneti c fields .. I t i s therefor e no t necessar y to conside r th e sof t X—ra y oscillation ss a s a fundamenta l propert y o f th e sof t x-ra y productio n proces ss (Cordov a e t al. , 1980) .

Anyy model , whic h use s th e rotatio n o f th e oute r layer s an d boundar y layer ,, mus t satisf y th e followin g conditions , se t b y th e observations . Cordov aa e t al . (1980 ) sho w tha t th e time-dependen t excitatio n o f closely-spaced ,, an d discret e period s ca n produc e th e observe d change s i nn phase , amplitud e an d period : th e hig h amplitud e o f th e sof t X-ra y oscillatio nn require s tha t ther e ar e onl y on e o r tw o brigh t spot s nea r th ee boundar y layer . Thi s brigh t spo t rotate s wit h on e specifi c perio d att a time , an d i s no t connecte d wit h a continuou s distributio n o f periods .. Th e perio d chang e shoul d occu r o n th e tim e scal e o f a rotatio n period ,, an d thi s discontinuou s chang e mus t occu r betwee n discret e periods .. We hav e alread y discusse d tha t ther e see m t o exis t jump s i n th ee perio d o f th e sof t X-ra y oscillation s o f S S Cyg , U Ge m an d V W Hyi.

AA particula r mode l whic h ha s th e intrinsi c possibilit y o f generatin gg transien t ho t spot s i n a boundar y laye r ha s bee n propose d b y Kin gg (1985) . I n thi s mode l th e low-coheren t sof t X-ra y oscillation s ar e generate dd b y magneti c instabilitie s i n th e boundar y layer . When th e energ yy transpor t proces s mainl y occur s b y electro n therma l conduction , weakk magneti c field s ca n becom e important , becaus e the y ca n determin e a preferentia ll directio n fo r th e energ y transport . Thes e transien t magneti cc field s ar e generate d b y a dynam o proces s i n th e differentiall y rotatin gg boundar y layer . Th e foo t point s o f thes e magneti c loop s wil l bee heated , an d hav e a harde r spectrum , lik e inferre d fro m th e oscillation ss i n V W Hyi. Thi s mode l predict s tha t oscillation s wit h a highe rr amplitud e wil l b e les s coherent . Thi s i s opposit e t o th e observations .. Also , th e coherenc e o f th e sof t X-ra y oscillation s o f v w Hyii a t 2 1 No v 198 3 i s no t attainabl e wit h thi s model . However , a wea k rudimenta ll magneti c fiel d o f th e whit e dwarf , firs t propose d b y Paczynsk ii (1978) , migh t solv e thi s problem .

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©.. Connectio n wit h lo w coheren t optica l oscillation s

Thee optica l flu x i s mainl y generate d i n th e oute r part s o f th e accretio nn dis c an d a t th e brigh t spot , wher e th e mass-transfe r strea m interact ss wit h th e accretio n disc . Althoug h i t ca n no t b e exclude d a prior ii tha t low-coheren t oscillation s ar e generate d a t th e brigh t spot , i tt seem s unlikel y tha t thi s occur s onl y durin g outburst . Coheren t oscillation ss hav e neve r bee n observe d durin g quiescenc e i n system s wit h aa significan t brigh t spo t (Patterson , 1981) . Durin g outburs t th e temperatur ee i n th e accretio n dis c i s high , an d ca n reac h T • » 6000 0 K i nn th e inne r parts . Th e temperatur e slowl y decrease s fo r large r radi i (se ee Pringle , 1981) . Hos t o f th e visua l flu x therefor e come s fro m larg e radi ii wit h lon g Keple r period s (o f th e orde r o f th e orbita l period) . Thee period s o f th e low-coheren t visua l oscillation s ar e shorte r tha n 4133 s . Thi s indicate s tha t thes e oscillation s ca n no t com e fro m th e samee par t o f th e dis c whic h dominantl y radiate s i n th e optical . Thi s i s confirme dd b y observation s o f quasi-periodi c oscillation s i n th e syste m UU Gem, Thes e oscillation s d o no t disappea r durin g th e eclips e o f th e oute rr part s o f th e dis c an d th e brigh t spot . Indirec t evidenc e come s fro mm th e dwarf-nov a oscillations , whic h reac h thei r minimu m perio d slightl yy ( l t o 2 days ) afte r maximu m optica l ligh t (Patterson , 1981) . WhenWhen th e period-luminosit y relatio n reflect s a couplin g o f th e oscillatio nn perio d wit h th e loca l mass-transpor t rat e (se e Bath , 1973 ; Papaloizo uu an d Pringle , 1978) , i t i s possibl e tha t thi s dela y reflect s th ee diffusio n tim e o f matte r fro m th e oute r part s (majo r contributo r optica ll light ) to th e inne r part s (generatio n o f oscillations ) o f th e disc .. Thi s dela y o f on e da y i s ampl y confirme d b y simultaneou s multi-wavelengt hh observation s (va n de r Woer d e t al. , 198 6 / Chapte r V ) . I ff w e assum e tha t th e sof t X-ra y oscillatio n perio d i n V W Hy i o f »1 4 s equal ss th e minimu m rotatio n perio d o f th e whit e dwar f (thi s implie s a masss o f • * 0. 7 M Q fo r a carbo n whit e dwarf ; Hamada an d Salpeter , 1961) , the nn th e period s o f th e visua l oscillation s correspon d t o Keple r period ss betwee n 1. 4 an d 9. 5 white-dwar f radii .

Wee conclud e tha t low-coheren t optica l oscillation s ar e generate d nearr th e inne r ho t par t o f th e accretio n disc , fro m whic h th e visua l bandd onl y show s th e tai l o f th e ho t spectrum . On e woul d thu s expec t tha tt highe r amplitude s mus t b e observabl e wit h spac e Telescop e i n th e uv . .

Wee discus s thre e scenario s fo r th e possibl e connectio n betwee n th e sof tt X-ra y an d optica l oscillations : l . Th e oscillatin g visua l flu x i s th ee tai l o f th e spectra l distributio n o f th e oscillatin g x-ra y flux . 2.. Th e inne r accretio n dis c i s periodicall y heate d b y th e oscillatin g sof tt x-ra y flux , whic h result s i n th e observe d optica l oscillations . 3.. A constan t stron g X-ra y flu x irradiate s th e surfac e o f th e inne r accretio nn dis c an d illuminate s irregularitie s i n th e disc .

1.. I n S S Cy g th e period s o f dwarf-nov a oscillation s an d sof t X-ra y oscillation ss ar e observe d i n th e sam e smal l perio d range . I t i s energeticall yy possibl e tha t i n thi s sourc e th e oscillatin g visua l flu x i ss th e black-bod y tai l o f th e pulsatin g ho t componen t (Cordov a e t al. , 1980) .. However , th e phas e coherenc e o f th e sof t x-ra y oscillation s i s muchh lowe r tha n th e phas e coherenc e o f dwarf-nov a oscillations . Als o th ee smalles t quasi-periodi c optica l oscillatio n perio d observe d i n U Gemm lie s a facto r 3 abov e th e 2 7 s perio d o f th e sof t X-ra y

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oscillation .. Whic h i s i n contradictio n wit h thi s model . Onee da y afte r th e detectio n o f th e 1 4 s sof t X-ra y oscillation s i n

VWW Hyi , fas t white-ligh t photometr y showe d n o evidenc e fo r optica l oscillation ss wit h a perio d o f * » 1 4 s . Thi s nul l resul t coul d b e du e t o aa stron g reductio n o f th e 1 4 s oscillatio n withi n on e day . However , V W Hyii ha s bee n extensivel y studied , an d neve r a 1 4 s optica l oscillatio n hass bee n reporte d (Robinso n an d Warner , 1984 ; Warne r an d Brickhill , 1978) .. I n al l thre e sources , wher e th e characteristic s o f bot h th e sof t X-ra yy an d optica l oscillation s ar e known , th e observation s argu e agains tt th e mode l o f generatio n o f bot h oscillation s b y th e sam e ho t plasma . .

2.. Sof t X-ra y flu x i s partl y reprocesse d a t th e inne r sid e o f th e disc .. Reprocessin g o f sof t x-ra y flu x to visua l flu x ha s bee n propose d t oo explai n th e high-coheren t optica l oscillation s i n th e system s D Q Her ,, V53 3 He r an d A E Aq r (se e Warner , 1983) . I n favo r o f thi s illuminatio nn mode l ar e th e observation s o f th e phas e shift s a t eclips e i nn th e system s U X Uln a an d H T Ca s (Patterson , 1981) . Th e lon g duratio n off th e shif t indicate s tha t a larg e par t o f th e accretio n dis c participate ss i n th e short-perio d oscillation . Th e eclips e behaviou r o f dwarf-nov aa oscillation s i n OY Ca r (Schoembs , 1986) , suggest s tha t ther e i ss a reprocessin g effec t operatin g nea r th e positio n o f th e brigh t spot .. Th e reprocessin g mode l i s likel y vali d i n th e abov e describe d cases ,, bu t no t i n th e cas e o f S S Cy g o r U Gem. Th e difference s i n phas e coherenc ee an d oscillatio n perio d betwee n th e sof t X-ra y an d optica l oscillation ss (se e mode l 1 ) remai n a problem .

3.. Th e thir d possibilit y i s th e occurrenc e o f irregularitie s i n th e accretio nn disc , whic h ar e irradiate d b y a stron g X-ra y flux . I n thi s cas ee th e X-ra y an d optica l oscillation s do no t hav e t o originat e fro m th ee sam e physica l proces s an d ca n hav e differen t period s an d coherence . Theyy onl y shar e th e sam e caus e o f instability : th e increase d matte r transpor tt an d accretion . Als o th e increas e o f X-ra y luminosit y b y tw o order ss o f magnitud e durin g outburs t make s observatio n o f th e rapi d oscillation ss durin g tha t phas e mor e favorable . Th e x-ra y emissio n o f V W Hyii durin g outburs t i s extremel y soft . Th e X-ra y emissio n i s easil y absorbe dd an d heat s onl y a thi n uppe r laye r o f th e accretio n disc .

Thee optica l oscillation s i n V W Hy i sho w tw o remarkabl e features : th ee amplitude s ar e i n genera l muc h large r tha n i n othe r system s ( l % t o 66 %) an d sometime s tw o oscillation s ar e simultaneousl y presen t an d interact ss th e modulatio n o f th e short-perio d oscillatio n (23. 6 o r 3 0 s ) becomess stronge r durin g th e maximu m o f th e long-perio d modulatio n (25 3 andd 41 3 s respectively) , se e Robinso n an d Warne r (1984) . Thi s phenomenonn coul d b e th e resul t o f a slowl y varyin g sof t x-ra y flux , whic hh illuminate s a short-perio d oscillatio n i n th e disc .

Thes ee dis c instabilitie s hav e bee n observe d i n th e novalik e variabl ee T T Ar i (Jense n e t al. , 1983) . Th e har d x-ra y flux , probabl y originatin gg i n a ho t coron a abov e an d belo w th e inne r accretio n disc , showedd transien t (" » 1 hour ) oscillation s wit h period s o f 32 , 1 2 an d 99 s . Quasi-simultaneou s optica l observation s showe d quasi-periodi c oscillation ss wit h period s o f 3 2 an d 1 2 s . Correlatio n o f simultaneousl y obtaine dd optica l an d x-ra y dat a reveale d a dela y o f 6 0 (±20 ) s o f th e X-ra yy flickerin g wit h respec t t o th e optica l flickering . Thi s migh t indicat ee tha t quasi-periodi c oscillation s occu r i n th e dis c withou t a trigge rr b y X-ra y emission .

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Thee origi n o f thes e dis c oscillation s i s no t known , on e clas s o f model ss propose s th e existenc e o f dis c oscillation s (Va n Hor n e t al. , 1979 ;; Blumentha l e t al. # 1984 ; Papaloizo u an d Stanley , 1986) . Anothe r snodee 1 propose s th e existenc e o f blob s i n th e disc , whic h rotat e wit h th ee Keple r perio d (Bath , 1973) . Th e mai n proble m wit h thi s mode l i s th e effec tt o f differentia l rotation , whic h set s a n uppe r limi t o f a fe w thousan dd second s t o th e lif e tim e o f an y structur e a tt th e inne r sid e o f th ee dis c (Bat h e t al. , 1974) . Th e quasi-periodi c oscillation s hav e coheren tt puls e train s wit h a shorte r duratio n tha n thi s tim e scale . Th e dwarf-nov aa oscillations , however , maintai n coherenc e ove r a muc h longe r tim ee scale .

7.. Conclusion s

wee hav e discovere d twic e th e presenc e o f rapi d oscillation s i n th e stron gg sof t X-ra y flu x o f V W Hy i durin g superoutburst . A modulatio n o f 155 % wit h a perio d o f 14.0 6 ± o.0 2 s wa s detecte d nea r th e en d o f th e Novemberr 198 3 superoutburst . Th e oscillatio n i s coheren t t o withi n th e limit ss o f observatio n ( Q > 250O) . A secon d coheren t oscillatio n wa s detecte dd a t maximu m o f th e Octobe r 198 5 superoutburst . Thi s oscillatio n showss change s i n amplitud e an d sudde n jump s o f th e perio d withi n th e interva ll 14. 4 t o 14. 2 s . A compariso n o f th e oscillatio n amplitude s i n th ee severa l filter s suggest s tha t th e pulse d emissio n ha s a harde r spectru mm tha n th e non-pulse d emission .

I tt i s propose d tha t th e origi n o f thes e transien t sof t X-ra y oscillation ss lie s i n th e differentiall y rotatin g oute r layer s o f th e whit ee dwar f and/o r boundar y layer.Th e rotatio n perio d o f thes e layer s i ss determine d b y th e angula r momentu m an d mas s accretio n ont o th e whit e dwar ff durin g outburst . Th e coherenc e o f th e oscillation s i s determine d byy processe s withi n th e boundar y layer . However , a firs t mode l wit h larg ee shea r i n th e boundar y laye r an d magneti c loop s (King , 1985) , doe s nott compar e ver y favorabl y wit h observations . A compariso n betwee n th e low-coheren tt sof t X-ra y an d optica l oscillation s i n th e non-magneti c cataclysmi cc variable ss sho w n o definit e clue s t o th e origi n o f eithe r o f them .. However , th e stron g irradiatio n o f th e accretio n dis c b y sof t X-ray ss migh t favo r th e detectio n an d existenc e o f oscillation s a t th e inne rr par t o f th e disc .

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