Документ взят из кэша поисковой машины. Адрес оригинального документа : http://mavr.sao.ru/hq/lizm/conferences/pdf/1996/1996_p105.pdf Дата изменения: Wed Apr 21 21:00:57 2010 Дата индексирования: Sat Jun 26 16:21:34 2010 Кодировка: Поисковые слова: m 8

S t a t i s t i c a l a n a l y s i s o f t h e i n f l u e n c e o f b i n a r i t y o n t h e A p p h e n o m e n o n . P r o g r e s s r e p o r t
J . B u d a j , V . G . E l k i n , I . I . R o m a n y u k , G . A . W a d e , J . Z i z n o v s k y , J . Z v e r k o
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A s t r o n o m i c a l I n s t i t u t e , S l o v a k A c a d e m y o f S c i e n c e s , 0 5 9 6 0 T a t r a n s k a L o m n i c a , T h e S l o v a c R e p u b l i c

S p e c i a l A s t r o p h y s i c a l O b s e r v a t o r y o f t h e R u s s i a n A S , N i z h n i j A r k h y z 3 5 7 1 4 7 , R u s s i a A s t r o n o m y d e p a r t m e n t , U n i v . o f W e s t e r n O n t a r i o , L o n d o n , O n t a r i o , C a n a d a N 6 A 3 K 7

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3 · 1 0 d a y s o c c u r s i n t h e o r b i t a l p e r i o d d i s t r i b u t i o n ( O P D ) o f A p b i n a r i e s a n d t h a t t h i s i n c o n s p i c u o u s f e a t u r e b e c o m e s , a t t h e s a m e t i m e , a b r e a k i n g p o i n t i n a n i n c r e a s i n g b e h a v i o u r o f 5 2 0 0 d e p r e s s i o n a s w e l l a s m a g n e t i c f i l e d s t r e n g t h w i t h o r b i t a l p e r i o d , P o r b . B o t h l a t t e r q u a n t i t i e s a r e u n c o v e r e d t o e x h i b i t e v e n m u c h m o r e p r o n o u n c e d d e c l i n e w i t h t h e e c c e n t r i c i t y o f t h e o r b i t b u t o n l y i f t h e s t a r s o n t h e s h o r t p e r i o d s i d e o f t h e g a p a r e c o n s i d e r e d . T h e o t h e r s t a r s r a t h e r o b e y t h e r e v e r s e d r u l e . I t i s a l s o p o i n t e d t o a c o n t r o v e r s i a l f a c t t h a t a l t h o u g h t h e A p p h e n o m e n o n i s g e t t i n g o n w e l l a t c i r c u l a r o r b i t s , o n t h e o t h e r h a n d , t h e r e a r e a
d n u m b e r o f h i g h e c c e n t r i c o r b i t s s t i l l a t r a t h e r s h o r t p e r i o d s ( o r b > 5 ) .

T h e m a i n l e s s o n t o b e l e a r n e d f r o m t h i s c o n t r i b u t i o n i s t h a t t h e p h y s i c a l c h a r a c t e r i s t i c s o f t h e A p b i n a r i e s i n c l u d i n g t h e i r m a g n e t i s m a r e g o v e r n e d b y t h e s t e l l a r b i n a r i t y .

1

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T h e b a c k b o n e o f t h e r e s e a r c h o f C P s t a r s i s t h e i r m o d e r n c l a s s i f i c a t i o n s c h e m e b y P r e s t o n ( 1 9 7 4 ) . H e c l e a r l y d i s t i n g u i s h e d a n o n - m a g n e t i c s e q u e n c e o f C P 1 a n d C P 3 ( A m a n d H g M n ) s t a r s a s w e l l a s a m a g n e t i c s e q u e n c e o f C P 2 ( A p ) a n d s o m e C P 4 ( H e - w e a k ) s t a r s . T a b l e 1 s u m m a r i z e s t h e w e l l k n o w n b a s i c f a c t s a b o u t t h e m o s t p o p u l a t e d C P 1 a n d C P 2 g r o u p s a l o n g w i t h t h e p h y s i c a l p r o c e s s e s i n v o k e d f o r t h e i r e x p l a n a t i o n . W h i l e , a t p r e s e n t , w e h a v e a t h a n d s o m e e x p l a n a t i o n o f t h e o r i g i n o f a b u n d a n c e a n o m a l i e s o r s l o w r o t a t i o n o f t h e s e s t a r s i t i s n o t t h e c a s e o f t h e i r m a g n e t i c f i e l d s a n d b i n a r i t y b o t h o f w h i c h a r e o f t e n r e f e r r e d a m o n g t h e p r i m o r d i a l c a u s e s o f C P p e c u l i a r i t y . H o w e v e r , n o a c c o u n t fo r C P s t a r s i n t h e i r t o t a l i t y c a n b e f i n a l , w h i c h l e a v e s t h e s e m e n t i o n e d d i s t i n g u i s h i n g c h a r a c t e r i s t i c s c o m p l e t e l y d i s r e g a r d e d . T h e a p p a r e n t l y r e v e r s e d a p p e a r a n c e s o f m a g n e t i c f i e l d s a n d b i n a r i t y i n A m a n d A p s t a r s s u g g e s t c l o s e r e l a t i o n o f t h e s e q u a n t i t i e s , w h i c h , i f c o n f i r m e d , m i g h t p u s h o u r u n d e r s t a n d i n g o f C P p h e n o m e n o n m u c h d e e p e r .

2

I n t r o d u c t i o n

F i r s t i n d i c a t i o n o f B a b c o c k ( 1 9 5 8 ) s t i m u l a t e d A b t a n d S n o w d e n ( 1 9 7 3 ) t o t h e p i o n e e r i n g a n d s t i l l f u n d a m e n t a l w o r k f a v o u r i n g a c o n n e c t i o n b e t w e e n m a g n e t i s m a n d b i n a r i t y . M a g n e t i c A p s t a r s t u r n e d o u t t o r a r e l y o c c u r i n b i n a r i e s w h i l e n o n - m a g n e t i c A m s t a r s a r e d o m i n a n t l y s h o r t - p e r i o d o n e s . L a t e r o n G e r b a l d i e t a l . ( 1 9 8 5 ) e x t e n d i n g t h e s t u d y o f F l o q u e t ( 1 9 8 3 ) c o n f i r m e d t h e l o w e r f r e q u e n c y o f b i n a r i e s a m o n g h o t A p ( 3 7 % ) s t a r s b u t n o t f o r c o o l A p s t a r s ( 4 6 % ) w h e n c o m p a r i n g t o

176


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th e expecte d standar d valu e o f 47 % o n th e mai n sequenc e (Jasche k an d Gomez , 1970) . The y eve n firs t pointe d ou t tha t th e (V -- G ) photometri c inde x reache s th e highes t value s for low eccentricitie s o f th e orbit s i f lon g period s P < 200 ar e excluded . Thi s was , however , buil t onl y o n tw o point s a t low eccentricities . Recently , Nort h (1994 ) obtaine d agai n a muc h lowe r percentag e o f cool A p star s amon g binarie s -- 19 % whic h i s close t o tha t o f Ab t an d Snowde n (1973) . Furthe r studie s o f Seggewiss (1981 , 1993) , Gerbald i e t al . (1985 ) an d Lebede v (1987 ) confirme d th e lac k o f shor t periods , th e lac k o f circula r orbits , lowe r SB2/SB 1 rati o an d Lebede v als o foun d a predominanc e o f orbit s wit h smalle r amplitude s o f radia l velocitie s a s well a s n o correlatio n betwee n inclination s o f rotatio n an d orbita l axe s i n A p binaries . All thi s rouse s ou r suspicion , supportin g agai n com pletel y reverse d binar y characteristic s o f A m an d A p stars , o n a n interpla y o f stella r binarit y an d magnetism .
1 d orb

I n connectio n wit h thi s Buda j (1994 , 1996a,b ) showe d alread y tha t th e physica l characteristic s o f A m binarie s gaine d a ne w dimensio n -- th e dependenc e o n th e orbita l perio d o f th e binary . Thei r orbita l period s wer e splitte d b y a 180 - 800 unpopulate d ga p int o tw o area s (se e als o Abt , 1965) . Th e ga p seeme d t o b e als o a brea k i n th e smoot h decreasin g behaviou r o f inde x toward s large r orbita l period s (i.e . increasin g o f metallicity ) for P < 180 becaus e suc h a behaviou r did no t continu e o n th e othe r sid e o f th e gap . I n his subsequen t analysi s o f A p binarie s (Budaj , 1995 ) h e point s t o th e presenc e o f a n analogou s perio d gap , t o a possibl e analogou s dependenc e o f (V - G ) inde x an d magneti c fiel d strengt h o n th e orbita l perio d (like i n Am's ) a s well a s t o th e fac t tha t bot h quantitie s wer e seemin g t o decreas e wit h eccentricity . Thi s analysi s wa s base d o n Seggewiss (1993 ) dat a wh o consider s jus t th e A p binarie s liste d i n th e Eight h Catalogu e o f Orbita l Element s o f S B System s (Batte n e t al. , 1989 ) i.e . o n th e bes t availabl e critica l sourc e o f orbita l parameters . Nevertheless , a mor e complet e lis t o f A p binarie s ca n b e derive d fro m th e catalogu e o f A p star s b y Renso n e t al . (1991) .
d d orb 1

I n th e following w e ai m a t rerevisio n o f th e abov e analysi s usin g th e latte r sourc e o f dat a whic h i s intende d t o b e a startin g poin t o f a mor e detaile d stud y (in progress ) o f th e interpla y betwee n stella r magnetis m an d binarity . A mor e comple x researc h shoul d no t disregar d a n investigatio n o f possible : - anomalie s i n orbita l parameters , mas s rati o an d ages , - dependenc e o f A p peculiarit y o n orbita l parameters , - a s well a s tha t o f rotationa l characteristic s includin g differentia l rotation , - influenc e o f circularization , synchronizatio n a s well a s pseudo-synchronizatio n mechanis m o n th e A p phenomeno n an d s o o n ... Thus , a lo t o f wor k i s ahea d an d w e will tr y t o address , a t least , partiall y t o som e o f thes e point s below .


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3

Sampl e star s

Mos t o f th e dat a analyze d her e ar e extracte d from th e databas e o f Renso n e t al . (1991 ) apar t from th e mea n effective magneti c field. Thi s wa s take n from Glagolevski j e t al . (1986) . Th e following rule s wer e obeye d t o avoi d an y ambiguit y whe n compilin g th e sampl e o f stars : w e carefull y selecte d all th e binar y component s o f Si, Sr , C r o r E u peculiarit y withi n B5-F 5 spectra l typ e alon g wit h a few binarie s o f mixe d peculiarit y (Si , Sr , C r o r E u accompanie d b y e.g . He-w , H g o r Mn ) i f th e latte r exhibite d als o eithe r light-spectra l variation s o r detecte d magneti c field. Fo r suspecte d tripl e system s w e left ou t th e orbita l period s o f thir d bodies . All thes e wer e the n complemente d b y th e recen t dat a fro m Nort h (1994 ) an d Wad e e t al . (1996) . Du e t o th e scarcit y o f dat a i t probabl y does no t mak e a sens e t o distinguis h betwee n cool an d ho t CP2's , a t present , bu t althoug h th e resultin g sampl e i s a littl e inhomogeneou s th e grea t majorit y o f object s ar e withi n B9-A 1 spectra l types . Th e tota l numbe r o f A p binarie s include d i s thu s 50 .

4

Orbita l period s an d eccentricitie s

Let u s star t wit h th e orbita l perio d distributio n (OPD ) o f A p binaries . I t i s displaye d i n Fig . 1 an d represent s th e numbe r o f period s falling withi n 0.5 wid e interval s (in log P ) plotte d versu s thei r centers . A ga p a t 3 · 10 day s i s no t muc h pronounce d bu t i s stil l th e mos t apparen t featur e o f thi s distributio n whic h support s ou r earlie r findings . Ther e i s jus t on e star , th e well-know n A p binar y H D 9996 , withi n 160-630 interval . Whil e th e mentione d perio d ga p i s a commo n featur e o f A p an d A m binarie s th e distribution s o f eccentricitie s see m rathe r different . Th e eccentricitie s o f magneti c star s (Fig . 2 ) d o no t see m t o b e effectively circularize d an d hig h eccentri c orbit s ar e presen t a t th e orbita l period s a s shor t a s 5 day s comparin g t o abou t 9 day s i n Am' s (Budaj , unpublished ) o r t o norma l binarie s (se e e.g . Gerbald i e t al. , 1985) . Thu s th e lac k o f circula r orbit s i s no t probabl y onl y du e t o missin g shor t perio d binarie s bu t rathe r ther e i s no t enoug h tim e for th e circulatio n mechanism , o r A p binarie s themselve s ar e selecte d b y th e natur e t o hav e suc h eccentricitie s for some reason .
orb 2 d

5

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1

-- G ) versu s orbita l perio d an d eccentricit y
1

photometri c index , measurin g On e ca n stud y anothe r importan t characteristi c o f A p stars , (V -G) th e 5200 depression . Th e large r i s th e abov e inde x th e mor e pronounce d i s thi s A p anomaly . W e


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star t wit h plottin g thi s quantit y versu s orbita l perio d a s seen i n Fig . 3 . On e migh t feel a tendenc y o f increasin g A p peculiarit y wit h P spreadin g fro m shor t period s u p t o th e perio d ga p whil e i t look s reverse d o n it s opposit e side . Unfortunately , thi s behaviou r i s no t ver y convincin g bu t resembl e ver y inde x i n A m binarie s (Budaj , 1996b ) whic h emphasize s significanc e o f thi s feature . muc h tha t o f T o spea k i n mor e objectiv e terms , w e hav e calculate d Pearson' s linea r (r ) a s well a s Spearman' s ran k orde r (r ) correlatio n coefficients togethe r wit h thei r two-side d significance s o r p-value s (p , p , see Pres s e t al. , 1986 for furthe r details) . Th e latte r simpl y represent s th e probabilit y o f appearanc e o f a bette r correlatio n coefficient tha n tha t foun d her e unde r th e assumptio n tha t th e quantitie s ( V - G ) an d logP d o no t correlat e a t all (th e so-calle d nul l hypothesis) . Generall y -- bu t i t depend s o n you r choic e o r degre e o f pessimis m -- a p-valu e less tha n abou t 0.05 i s accepte d a s a seriou s suppor t for th e presenc e o f th e correlation . W e see from Tabl e 2 , colum n 2 , tha t neithe r th e correlatio n coefficients o n th e left sid e o f th e perio d ga p ar e larg e no r thei r significance s ca n favou r a correlation . However , thi s i s no t a full stor y an d no t a reaso n for givin g up . A possibl e correlatio n migh t b e easil y smoothe d b y som e othe r mechanis m and , i n connectio n wit h this , please , not e a remarkabl e fac t tha t hig h eccentri c orbit s ( e > 0.2 ) clearl y occup y th e botto m o f Fig . 3 for Porb < 160 emphasizing , a t th e sam e time , possibl e P dependence . O n th e lon g perio d side o f th e gap , however , th e opposit e seem s true .
orb l $ l s 1 orb d orb

Thi s motivate s a searc h for eccentricit y dependence . Correspondin g situatio n i s illustrate d i n


180

B U D A J ,

E L K IN ,

R O M A N Y U K ,

W A D E ,

Z IZ N O V S K Y ,

ZV ERKO

F i g . 4 a n d d o e s n o t l o o k v e r y p r o m i s i n g a g a i n . F o r t u n a t e l y , w e k n o w n o w t h a t t h e s t a r s o c c u p y i n g d i f f e r e n t s i t e s o f t h e p e r i o d g a p s h o u l d b e d i s t i n g u i s h e d f r o m o n e a n o t h e r . P e r f o r m i n g t h e t a s k w e s e e t h a t t h e s i t u a t i o n h a s c h a n g e d i m m e d i a t e l y . W h i l e t h e s t a r s , c o m i n g f r o m t h e le f t h a n d s i d e o f t h e p e r i o d g a p , e x h i b i t a p p a r e n t a n d s i g n i f i c a n t a n t i c o r r e l a t i o n w i t h e c c e n t r i c i t y , t h e s t a r s f r o m t h e o t h e r h a n d s i d e o f t h e g a p s e e m t o b e h a v e j u s t o p p o s i t e . F o r c o r r e s p o n d i n g s t a t i s t i c s c h e c k e c o l u m n s 4 - 5 o f T a b l e 2 . T h i s a l l o w s u s t o c a l i b r a t e t h e d e p e n d e n c e o f ( V 1 - G ) o n e c c e n t r i c i t y a n d c o n s e q u e n t l y t o r e m o v e i t w h e n s t u d y i n g o t h e r e f f e c t s . A s a p r e l i m i n a r y a p p r o x i m a t i o n f r o m t h e s k e t c h e d b o u n d a r y l i n e s i n F i g . 4 w e a c c e p t e d : ( 1 ) a n d c a l c u l a t e d v a l u e s w h i c h a r e r e f e r r e d t o z e r o e c c e n t r i c i t y . ( 2 )

W e t a k e a b e n e f i t f r o m t h i s a n d j u m p i n f e e t b a c k t o F i g . 3 w h e r e w e s t u d i e d t h e P o r b d e p e n d e n c e . O n c e ( V 1 - G ) i s r e p l a c e d b y ( V 1 - G ) e = 0 o n t h e le ft s i d e o f t h e p e r i o d g a p o n e c a n r e a l i z e i m m e d i a t e l y ( F i g . 5 ) t h a t a s i g n i f i c a n t c o r r e l a t i o n w i t h o r b i s e m e r g i n g ( s e e c o l u m n 3 , T a b l e 2 ) .

6

M a g n e t i c f i e l d v e r s u s o r b i t a l p e r i o d a n d e c c e n t r i c i t y

T h e s i t u a t i o n i s n o w r i p e f o r r e i n v e s t i g a t i o n o f t h e i n t e r p l a y b e t w e e n m a g n e t i c fie ld a n d b i n a r i t y . E f f e c t s s i m i l a r t o t h o s e u n c o v e r e d a b o v e m i g h t b e e x p e c t e d h e r e b e c a u s e t h e r e i s a s o r t o f c o r r e -


S T A T I S T I C A L A N A L Y S I S O F T H E I N F L U E N C E O F B I N A R I T Y O N T H E A P . . .

1 8 1

l a t i o n b e t w e e n

5 2 0 0 d e p r e s s i o n a n d m a g n e t i c f i e l d s t r e n g t h ( H a u c k , 1 9 7 5 ; N o r t h , 1 9 8 0 ; C r a m e r

a n d M a e d e r , 1 9 8 0 ; H a u c k a n d N o r t h , 1 9 8 2 ; L e b e d e v , 1 9 8 8 ; R o m a n y u k 1 9 8 6 ; G l a g o l e v s k i j , 1 9 9 4 ) . U n f o r t u n a t e l y , t h e m a g n e t i c o b s e r v a t i o n s a r e s t i l l r a t h e r r a r e a m o n g A p b i n a r i e s a l t h o u g h m o s t o f t h e m a r e r a t h e r b r i g h t s t a r s . I n t h e f o l l o w i n g w e a c c e p t t h e m e a n e f f e c t i v e m a g n e t i c f i e l d , < B e > , ( s e e G l a g o l e v s k i j e t a l . , 1 9 8 6 ) a s a m a g n e t i s m p a r a m e t e r . R e a l l y , t h e b e h a v i o u r o f < B e > v e r s u s P o r b ( F i g . 6 ) s e e m s a n a l o g o u s t o t h a t o f F i g . 3 i n c l u d i n g t h e b e h a v i o u r o f h i g h e c c e n t r i c o r b i t s ( e > 0 . 2 ) w h i c h i m p l y l o w e r ( h i g h e r ) f i e l d o n t h e le f t ( r i g h t ) s i d e o f t h e p e r i o d g a p . H o w e v e r , a l s o h e r e , t h i s P o r b d e p e n d e n c e i s n o t s i g n i f i c a n t w h e n s p e a k i n g s t r i c t l y i n t e r m s o f s t a t i s t i c s ( s e e c o l u m n 2 , T a b l e 3 ) a n d w e p r o c e e d t o i n s p e c t t h e e c c e n t r i c i t y d e p e n d e n c e i n F i g . 7 . G u i d e d b y t h e ( V 1 - G ) s c e n a r i o w e d i s t i n g u i s h e d s t a r s o n d i f f e r e n t s i d e s o f t h e p e r i o d g a p a n d t h e o r i g i n a l l y u n p r o m i s i n g p i c t u r e t u r n e d c l e a r r i g h t a w a y . T h e s i g n i f i c a n t d e c l i n e o f < B e > w i t h e c c e n t r i c i t y f o r
Porb

d d < 1 6 0 h a s e m e r g e d a c c o m p a n i e d w i t h j u s t t h e o p p o s i t e t e n d e n c y f o r o rb > 1 6 0 ( s e e c o l u m n s

4 , 5 o f T a b l e 3 ) . I f o n e e s t i m a t e s f r o m t h e l a s t p i c t u r e ( d a s h e d l i n e )

( 3 ) a n d a l l o w s f o r i t w h e n s t u d y i n g P o r b d e p e n d e n c e , t h e n t h e l a t t e r b e c o m e s m u c h m o r e p r o n o u n c e d ( F i g . 8 ) a n d s i g n i f i c a n t ( c o l u m n 3 o f T a b l e 3 ) .


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ZVERKO


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Brie f discussio n
orb

On e ca n sugges t a ver y natura l empirica l explanatio n whic h coul d qualitativel y catc h bot h P a s well a s eccentricit y dependence s o n bot h side s o f th e perio d gap . Namel y all thi s migh t b e a manifestatio n o f on e dependenc e o n periastru m distanc e whic h woul d proclai m a growin g peculiarit y (wit h th e distance ) u p t o th e perio d ga p an d a sinkin g on e behin d it . Unfortunately , i t i s no t s o promisin g quantitativel y a s th e scatte r i n (V -- G ) seem s larg e enoug h t o b e straightene d b y thi s effect. Furthe r account s o n th e ver y pronounce d behaviou r o f peculiarity , o n e.g . eccentricity , migh t pu t som e constraint s als o o n furthe r processe s propose d i n A p stars . I f ther e reall y ar e suc h stric t eccen tricit y dependence s a s see n i n Figs . 4 an d 7 , thi s woul d impl y tha t e.g . evolutionar y (Glagolevskij , 1996) o r rotatio n velocit y effects (Landstree t e t al. , 1975 ; Borr a an d Landstreet , 1980 ; Hauc k an d North , 1982 ) ar e no t stron g enoug h t o smoot h i t an d tha t binarit y effects ar e a t leas t a s importan t a s th e previou s ones . Th e controversia l fac t tha t (1 ) althoug h th e A p phenomeno n i s mor e pronounce d a t low eccentricitie s bu t suc h orbit s ar e lackin g a s well a s tha t (2 ) ther e i s a n apparen t deficiency o f shor t period s an d tha t (3 ) rotationa l an d orbita l axe s ar e no t paralle l an d tha t (4 ) SB2/SB 1 rati o i s prett y low indicat e tha t an Ap star may endure just limited "working hours" of tidal effects of certain intensity or is not allowed to develop under such conditions. Th e mentione d condition s in a binar y ca n well b e characterize d b y th e orbita l parameters , mas s rati o an d ag e o f binar y systems . I t migh t b e the n a n attractiv e ide a tha t eve n typica l "non-binary " star s (in parenthesi s a s i t i s alway s relativ e wha t i s a non-binary) , suc h a s A p stars , coul d b e understoo d a s i n th e framewor k o f binarie s whe n w e ascrib e t o the m som e special-limitin g binarit y parameters . Finally , w e woul d like t o stres s tha t ver y simila r an d analogou s feature s t o thos e mentione d abov e ar e foun d i n A m binarie s a s well. Thu s bot h sample s exhibi t th e sam e sign , probably , o f th e sam e no t well-know n puzzlin g processe s actin g o n larg e distance s betwee n th e companions . Perhap s Tassou l & Tassou l (1992 ) retardation-synchronizatio n mechanis m o r empirica l tida l mixin g + stabilizatio n hypothesi s o f Buda j (1996a ) ca n she d mor e ligh t o n thi s interestin g proble m i n th e future .
1

8

Conclusio n

Let u s sto p a t thi s poin t an d summariz e th e mai n result s rathe r the n pursu e th e abov e idea s deeper . W e confirme d o n a mor e elaborate d statistica l backgrou d an d large r sampl e th e findin g o f Buda j (1995 ) tha t th e physica l characteristic s o f A p binarie s depen d o n orbita l parameters . Namel y bot h (V -- G ) an d < B > increas e wit h orbita l perio d o n th e shor t perio d sid e o f th e perio d ga p whil e th e opposit e seem s tru e o n th e othe r lon g perio d side . Bot h quantitie s exhibi t eve n muc h mor e pronounce d declin e wit h eccentricit y bu t als o onl y i f th e star s wit h P < 160 ar e considered . Th e res t rathe r obe y th e reverse d rule . Thi s emphasize s th e occurrenc e o f th e perio d ga p itself ascribin g t o it , a t th e sam e time , th e rol e o f a breakin g poin t i n th e behaviou r o f fundamenta l A p characteristics .
1 e d orb

Acknowledgements . Thi s work was supporte d by th e VEGA gran t No. 1002. Par t of thi s work was done during a stay of J.B . at th e SAO and he acknowledges th e invitatio n of Dr. Yu. Balega and th e suppor t of Dr. Yu. Glagolevskij as well as th e hospitality of all SAO people.

Reference s
Abt H.A.: 1965, Astrophys . J . Suppl. Ser., 11 , 429. Abt H.A., Snowden M.S.: 1973, Astrophys. J. Suppl. Ser., 25 , 137. Babcock H.W.: 1958, Astrophys. J. Suppl. Ser., 3, 141.


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B U D A J ,

E L K IN ,

R O M A N Y U K ,

W A D E ,

Z IZ N O V S K Y ,

ZV ERKO

B a t t e n A . H . , F l e t c h e r J . M . , M a c C a r t h y D . G . : 1 9 8 9 , E i g t h C a t a l o g u e o f O r b i t a l E l e m e n t s o f S B S y s t e m s , P u b l . D o m i n i o n A s t r o p h y s . O b s . , 1 7 . B o r r a E . F . , L a n d s t r e e t J . D . : 1 9 8 0 , A s t r o p h y s . J . S u p p l . S e r . , 4 2 , 4 2 1 . B u d a j J . : 1 9 9 4 , p o s t e r a t 2 2 - n d G e n e r a l A s s e m b l y M e e t i n g , T h e H a g u e . B u d a j J . : 1 9 9 5 , i n : S t r a s s m e i e r K . G . ( e d . ) , " S t e l l a r S u r f a c e S t r u c t u r e -- P o s t e r P r o c e e d i n g s f r o m I A U S y m p . " , 1 7 6 , 1 4 7 . B u d a j J . : 1 9 9 6 a , A s t r o n . A s t r o p h y s . , ( i n p r e s s ) . B u d a j J . : 1 9 9 6 b , A s t r o n . A s t r o p h y s . , ( i n p r e s s ) . C r a m e r N . , M a e d e r A . : 1 9 8 0 , A s t r o n . A s t r o p h y s . S u p p l . S e r . , 4 1 , 1 1 1 . F l o q u e t M . : 1 9 8 3 , i n : " L e s j o u r n e e s d e S t r a s b o u r g " , V e r n e R e u n i o n , O b s e r v a t o i r e d e S t r a s b o u r g , 8 3 . G e r b a l d i M . , F l o q u e t M . , H a u c k . : 1 9 8 5 , A s t r o n . A s t r o p h y s . , 1 4 6 , 3 4 1 . G l a g o l e v s k i j Y u . V . : 1 9 9 4 , i n : Z v e r k o J . a n d Z i z n o v s k y J . ( e d s . ) , " C P a n d m a g n e t i c s t a r s " , A s t r o n o m i c a l I n s t i t u t e , T a t r a n s k a L o m n i c a , S l o v a k i a , 1 0 2 . G l a g o l e v s k i j Y u . V . : 1 9 9 6 , i n t h i s p r o c e e d i n g s . G l a g o l e v s k i j Y u . V . , R o m a n y u k I . I . , C h u n a k o v a N . M . , S h t o l ' V . G . : 1 9 8 6 , A s t r o f i z . I s s l e d . ( I z v . S A O ) , 2 3 , 3 7 . H a u c k . : 1 9 7 5 , i n : W . W . W e i s s , H . J e n k n e r , H . J . W o o d ( e d s . ) , " P h y s i c s o f A p S t a r s " , V i e n n a , 3 6 5 . H a u c k . , N o r t h P . : 1 9 8 2 , A s t r o n . A s t r o p h y s . , 1 1 4 , 2 3 . J a s c h e k C , G o m e z A . E . : 1 9 7 0 , P u b l . A s t r . S o c . P a c i f i c , 8 2 , 8 0 9 . L a n d s t r e e t J . D . , B o r r a E . F . , A n g e l J . R . P . , I l l i n g R . M . E . : 1 9 7 5 , A s t r o p h y s . J . , 2 0 1 , 6 2 4 . L e b e d e v V S . : 1 9 8 8 , P h . D . t h e s i s . L e b e d e v V . S . : 1 9 8 7 , A s t r o f i z . I s s l e d . , ( I z v . S A O ) , 2 5 , 4 1 . N o r t h P . : 1 9 8 0 , A s t r o n . A s t r o p h y s . , 8 2 , 2 3 0 . N o r t h P . : 1 9 9 4 , i n : " P r o c e e d i n g s f r o m t h e 2 5 t h w o r k s h o p a n d m e e t i n g o f E u r o p e a n w o r k i n g g r o u p o n C P s t a r s " , 3 . P r e s s W . H . , F l a n n e r y B . P . , T e u k o l s k y S . A . , V e t t e r l i n g W . T . : 1 9 8 6 , N u m e r i c a l R e c i p e s , C a m b r i d g e U n i v . P r e s s , C a m b r i d g e . P r e s t o n G . W . : 1 9 7 4 , A n n u . R e v . A s t r o n . A s t r o p h y s . , 1 2 , 2 5 7 . R e n s o n P . , K o b i D . , N o r t h P . : 1 9 9 1 , A s t r o n . A s t r o p h y s . S u p p l . S e r . , 8 9 , 6 1 . R o m a n y u k I . I . : 1 9 8 6 , P h . D . t h e s i s . S e g g e w i s s W . : 1 9 8 1 , i n : " L e s e t o i l e s d e c o m p o s i t i o n c h i m i q u e a n o r m a l e d u d e b u t d e l a s e q u e n c e p r i n c i p a l e " , I n s t . d ' A s t r o p h y s i q u e , U n i v . d e L i e g e , 1 8 3 . S e g g e w i s s W . : 1 9 9 3 , i n : D w o r e t s k y M . M . , C a s t e l l i F . , F a r a g g i a n a R . ( e d s . ) , " P e c u l i a r V e r s u s N o r m a l P h e n o m e n a i n A - t y p e a n d R e l a t e d S t a r s " , A . S . P . C . S . , 4 4 , S a n F r a n c i s c o , 1 3 7 . T a s s o u l J . L . , T a s s o u l M . : 1 9 9 2 , A s t r o p h y s . J . , 3 9 5 , 2 5 9 . W a d e G . A . , N o r t h P . , M a t h y s G . , H u b r i g S . : 1 9 9 6 , A s t r o n . A s t r o p h y s . , ( i n p r e s s ) .