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O n possibl e stratificatio n o f chemica l element s wit h dept h i n th e atmosphere s o f C P star s
I.I . Romanyuk , G.P . Topilskay a
Specia l Astrophysica l Observator y o f th e Russia n AS , Nizhni j Arkhy z 357147 , Russi a

Abstract . Differen t problem s concerne d wit h th e stratificatio n o f ment s wit h dept h ar e described . Result s o f investigatio n o f vertica l CV n obtaine d b y differen t author s o f C r i n th e well-know n sta r A stud y o f th e vertica l stratificatio n o f rare-eart h elemen t i n futur e i s proposed .

chemica l ele stratificatio n i s compared . investigation s

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Introductio n

For lon g i t ha s persistentl y bee n attempte d t o inquir e int o th e matte r o f distributio n o f chemica l element s i n th e atmosphere s o f C P star s wit h depths , for i t i s o f grea t theoretica l importance . Th e present-da y scienc e canno t admi t chemica l anomalie s i n C P star s t o represen t th e chemica l com positio n o f th e whol e sta r - thes e mus t b e o f surfac e nature . Bu t wha t th e characteristi c dept h o f occurrenc e o f variou s anomalie s i n star s o f different type s i s - thi s depend s o n a grea t numbe r o f parameter s an d mechanism s an d i s determine d ambiguousl y a s a resul t o f complicate d theoretica l calculations . Therefor e th e proble m o f actua l processe s o f separatio n o f chemica l element s i n th e atmosphere s o f C P stars , ca n b e resolve d o n th e basi s o f observations . However , t o pick from ob servation s th e informatio n o n th e dept h o f concentratio n o f chemica l elements , on e needs , firstly, high-qualit y spectra l dat a wit h low noise , hig h resolution , secondly , accurat e value s o f atomi c pa rameter s o f spectra l lines , especially , oscillato r strengths , thirdly , accurat e theoretica l calculation s o f spectra , takin g int o accoun t th e magneti c field, inhomogeneou s distributio n o f element s over th e surfac e an d othe r individua l propertie s o f ever y star . All thes e requirement s ar e difficult t o meet , therefor e th e obtaine d observationa l result s ar e often ambiguous . A condense d surve y o f variou s technique s o f spectra l analysi s whic h ca n b e helpful i n solvin g th e proble m wa s presente d a t th e las t meetin g o f th e magneti c sta r investigator s (Zboril , 1994) . Her e w e will analyz e th e attempt s o f different author s t o investigat e th e dept h distributio n o f chemica l element s i n th e atmospher e o f on e o f th e well-studie d C P stars , CVn , stat e ou r assumption s concernin g som e peculiaritie s o f it s spectru m an d plan s o f it s furthe r investigation .

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I s ther e inhomogeneit y i n th e distributio n o f iro n pea k element s CVn ? i n th e uppe r layer s o f

Th e iron-pea k element s i n th e atmosphere s o f th e Si-Cr-E u magneti c sta r CV n ar e largel y overabundant , b y 1-3 orders , an d thei r abundance s var y wit h phas e (Cohen , 1970 ) i.e . th e element s ar e inhomogeneousl y distribute d ove r th e surfac e o f th e star . Mappin g o f th e surfac e distributio n o f Ti , Cr , F e i n CV n ha s bee n performe d b y Khokhlov a an d Pavlov a (1983) . W e kno w four paper s i n whic h attempt s hav e bee n mad e t o deriv e th e distributio n o f thes e element s wit h dept h i n th e atmosphere . Romanyu k e t al . (1992 ) studie d th e distributio n o f iron , whil e Khokhlov a an d 170


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Topilskay a (1992 , furthe r KhT ) an d Zverk o an d Ziznovsk y (1994 , ZZa ; 1995 , ZZb ) studie d th e distributio n o f chromium . I n th e las t thre e paper s th e chromiu m distributio n wa s investigate d from th e sam e lines o f C r I I o f th e 30-t h multiplet , whic h wer e locate d i n th e wing s o f . Th e result s wer e contrary : Kh T establishe d tha t th e inhomogeneit y distributio n o f chromiu m i n th e uppe r atmospher e layer s i s inconsisten t wit h observations , wherea s ZZ(a,b ) foun d i t t o decreas e i n th e uppe r atmosphere . Le t u s compar e th e result s i n detail . Kh T use d photographi c spectr a take n a t th e 6 m telescop e wit h D = 1.3 /m m maximu m chromium , , = 0.25 . Th e Kuruc z (1979 ) mode l wit h th e parameter s T = 4.0 , z = 0 wa s use d i n th e analysis , equivalen t width s o f isolate d line s o f C r I I wit wer e calculate d usin g th e progra m KONTU R (Leushi n an d Topilskaya , 1986 ) an d th e observe d
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a t th e phas e o f 11500K , l g g = h v = 2.0 km/ s compare d wit h .
t

ZZ a worke d wit h retico n spectr a wit h D = 8.5 /mm , S/ N = 350 ou t o f phas e o f maximu m chromium , = 0.8 . The y use d th e sam e mode l bu t calculate d b y th e progra m ATLA S 9 (Kurucz , 1993) , th e analysi s wa s mad e b y th e syntheti c spectru m metho d usin g th e progra m SYNSPE C (Hybeny , 1987) , takin g th e atomi c dat a fro m th e lis t o f Kuruc z (1993) . I n bot h work s th e whol e analysi s wa s mad e i n th e LT E approximation . W e measure d th e observe d equivalen t width s o f th e lines use d i n ZZ a fro m th e fragmen t o f th e spectru m availabl e i n literatur e an d compute d for the m th e chromiu m abundanc e an d effective depth s o f lin e formatio n usin g th e procedur e tha t wa s applie d i n KhT . A t th e sam e tim e w e repeate d th e calculation s wit h fro m KhT . Th e onl y distinctio n wa s tha t w e calculate d th e lin e C r I I 437 6 a s th e double t o f C r I I 4876.4 0 an d C r I I 4876.4 7 an d too k int o accoun t th e blendin g o f CrI I 4856.1 9 wit h T i 4855.9 1 , l g g f = -1.32 , l g Ti / = -5.95 . Thi s mad e th e agreemen t wit h th e observe d better . All th e result s ar e give n i n Tabl e 1 an d Fig.l . Ou r ne w computation s confirme d th e result s obtaine d previousl y b y Kh T an d ZZa : th e chromiu m abundanc e doe s no t chang e a t depth s from fro m Kh T an d decrease s outwar d accordin g t o fro m ZZa . Thus , th e reaso n for 0.01 t o 0.3 i n th e discordanc e o f th e result s lies no t i n th e difference o f th e procedure s applie d b y Kh T an d ZZa , bu t i n th e difference i n observationa l data . Thi s i s well represente d i n Fig.2 : decrease s wit h decreasin g distanc e o f th e lines C r I I from th e center . Ther e migh t b e tw o cause s o f th e discrepancies : 1 ) different chromiu m distributio n wit h dept h i n different area s o f th e surfac e o f CVn ; 2 ) differences i n calibratio n o f spectr a (photographi c spectr a -- density/intensit y relation ,


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retico n -- relativel y shor t segmen t o f spectr a an d uncertaintie s o f drawin g th e continuum) . Th e pape r o f ZZb , wher e th e analysi s o f CV n wa s performe d from spectr a a t six different phases , did no t clea r u p th e situatio n either : simila r result s wer e obtaine d for all phase s -- th e chromiu m abundanc e decrease s outward , bu t th e phas e = 0.25 , whic h wa s examine d i n KhT , wa s lackin g i n ZZb . Unfortunately , th e qualit y o f spectra l dat a i n ZZ b wa s somewha t worse , S/N ~ 150 , an d thi s i s a likely caus e o f th e scatte r o f chromiu m abundance s fro m different lines , s o th e possibl e relationshi p betwee n th e abundanc e an d dept h i s smeare d b y thi s spread . Th e pape r o f ZZ b i s mor e remarkabl e becaus e fou r star s wer e analyze d usin g th e sam e procedure , bu t onl y for CVn , afte r averagin g th e dat a obtaine d a t all phases , th e chromiu m abundanc e wa s foun d t o decreas e outward . Thre e othe r star s -- Sirius , Veg a an d UM a -- did no t sho w an y dept h stratificatio n o f chromium . Th e detaile d analysi s o f th e tw o paper s allows th e conclusio n t o b e draw n tha t th e metho d o f analysi s o f th e line s o f on e multiplet , whic h ar e locate d i n th e wing s o f H lin e ca n b e use d for diagnostic s o f distributio n o f a n elemen t wit h dept h i n th e atmosphere . Th e level o f theoretica l calculatio n -- th e accurac y o f constructio n o f mode l atmosphere s an d computatio n o f theoretica l


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absorptio n line s an d fragment s o f syntheti c spectr a -- make s i t possibl e t o obtai n reliabl e results , given accurat e atomi c parameter s o f lines . However , for thi s t o b e done , furthe r improvemen t o f accurac y o f spectra l dat a an d allowanc e for inhomogeneou s distributio n o f element s ove r th e sta r surfac e ar e needed . CV n wa s studie d i n th e pape r o f Th e distributio n o f iro n abundanc e i n th e atmospher e o f Romanyu k e t al . (1992 ) fro m th e line s F e I an d F e I I locate d o n bot h side s o f th e Balme r jum p a t tw o phases : =0. 0 an d =0.5 . Th e wor k wa s don e usin g photographi c spectr a take n a t BT A wit h D = 6.7 /mm . I t turne d ou t tha t a t bot h phase s th e iro n abundanc e increase s i n th e uppe r atmospheri c layers . Th e accurac y o f thi s resul t i s no t hig h becaus e o f th e unreliabl e lin e oscillato r strength s i n th e blu e regio n o f th e spectrum , stron g lin e blendin g an d uncertaint y i n th e plo t o f th e continuum , whic h i s invisibl e du e t o th e larg e numbe r o f atmospheri c lines , although , i n orde r t o improv e th e accuracy , th e analysi s wa s mad e usin g 3 spectr a a t phase s close t o 0. 1 an d 4 spectr a a t phase s close t o 0.5 . Not e tha t i f on e compare s th e resul t o f th e wor k describe d abov e wit h th e result s o f th e presen t from ZZ(a,b) , iro n will tur n ou t t o concentrat e paper , whic h ar e obtaine d fro m chromiu m wit h i n th e atmospher e o f CV n quit e unlik e chromium : th e iro n abundanc e a t a dept h = --1.5 i s highe r tha n a t = --0.1 , bot h insid e an d outsid e th e spot , wherea s th e chromiu m abundanc e outsid e th e spo t i s lowe r a t = --1.0 tha n a t = --0.5. I t seem s t o u s tha t despit e th e grea t difficulties i n th e analysi s o f line s o n bot h side s o f th e Balme r jump , thi s metho d ha s th e advantag e tha t i n thi s wid e spectra l regio n on e ca n find a comparativel y larg e numbe r o f line s o f different chemica l element s suitabl e for analysis . I t woul d b e o f grea t interes t t o chec k th e chromiu m distributio n wit h dept h fro m line s o n bot h side s o f th e Balme r jum p a t different phases .

3

O n possibl e investigatio n o f vertica l stratificatio n o f rare-eart h element s i n th e atmosphere s o f C p star s

Stratificatio n o f rare-eart h element s i n th e atmosphere s o f C p star s deserve s specia l attention . Ther e ar e muc h evidenc e tha t ion s o f rare-eart h element s i n th e atmosphere s o f peculia r star s ar e concentrated , a s a rule , i n ver y shar p spot s tha t coincid e wit h th e pole s o f magneti c dipol e (for instance , Floquet , 1979) . Th e atmospher e dept h i n C p star s i s onl y 0.1 % o f thei r diameter , therefor e th e non-unifor m distributio n o f element s ove r th e surfac e strongl y affects th e result s o f investigatio n o f stratificatio n wit h depth . Examinin g th e lines o f rare-eart h element s wit h a wavelengt h large r o r smalle r tha n 364 6 at different phase s o f th e rotatio n cycle , on e ca n deriv e ne w importan t information , provide d tha t th e informatio n i s interprete d b y th e mode l atmosphere s whic h tak e int o accoun t th e two-dimensiona l non-uniformity . I n orde r t o avoi d th e uncertaintie s associate d wit h inaccurat e estimate s o f oscillato r strengths , temperatur e an d othe r effects, i t i s mos t intelligen t t o us e for analysi s th e line s o f on e multiplet , whic h ar e forme d fro m sublevel s o f th e sam e level whic h hav e simila r excitatio n potentials . I t woul d b e goo d luc k t o find a rare-eart h elemen t multiplet , on e par t o f whic h woul d hav e > 3646 , th e othe r -- < 3646 . I n th e table s o f Moor e (1945 ) w e hav e foun d th e secon d multiple t o f G d II , whic h complie s wit h thes e requirements . Th e dat a o n th e lilies o f thi s multiple t ar e give n i n Tabl e 2 . I n th e column s o f Tabl e 2 ar e presented : lin e wavelengt h ( ) , lin e intensitie s (bot h take n from Moor' s (1945 ) tables) ; fou r subsequen t column s follow from th e Vienn a Atomi c Lin e Databas e (VALD , Piskuno v e t al. , 1995) : logarithm s o f oscillato r strength s (lg gf ) , Land e factor s (z) , excita tio n potential s (eV ) an d centra l dept h o f G d I I lines for a typica l peculia r sta r wit h th e effective


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temperatur e T = 10000 , th e abundanc e o f G d II = Remembe r tha t som e th e Balme r series) : H (9 ) = 3835.39 ; H (10 ) H(12 ) = 3750.12 ; H (13 ) H(15 ) = 3711.95 .
e

acceleratio n o f gravit y l g g = 4. 0 an d G d I I abundanc e =-8.1 . (I n VALD -10.9 2 i s adopte d a s normal. ) o f th e lines indicate d ar e i n th e wing s o f hydroge n lines (hig h member s o f = 3797.90 ; H (11 ) = 3770.63 ; = 3734.37 ; H (14 ) = 3721.96 ;

A s i s seen , som e line s o f th e secon d multiple t o f G d I I (3768.39 ; 3796.37 ) will b e difficult t o measure , becaus e the y ar e actuall y locate d i n th e core s o f hydroge n lines . Tabl e 2 demonstrate s tha t th e line s o f th e secon d multiple t o f G d I I mus t b e observabl e i n peculia r star s (provide d tha t th e abundanc e o f G d I I i s 2- 3 time s highe r tha n tha t o f solar) . A detaile d stud y i s th e matte r o f th e future , howeve r som e consideration s ca n b e state d even now . I n rea l peculia r star s th e line s o f rare-eart h element s ar e strongl y variable . Th e line s o f th e sam e multiple t mus t sho w synchronou s variabilit y whic h expedite s th e identification . O n th e basi s o f th e result s o f different author s a conclusio n ca n b e draw n tha t th e intensit y o f th e G d I I line s i n CV n i n th e regio n o f spectru m shortwar d th e Balme r jum p i s lower . I f th e CV n regularit y i s confirmed , thi s ma y impl y tha t th e abundanc e o f G d I I i n th e atmosphere s o f decrease s outward . Certainly , on e ha s t o mak e accurat e measurement s o f equivalen t widt h o f th e secon d multiple t o f G d I I i n th e spectr a obtaine d a t different phase s o f th e rotatio n perio d o f th e star . Onl y the n ca n definit e conclusion s b e made . I t seem s t o u s tha t ne w high-precisio n observation s o f peculia r star s will call for ne w mode l at mosphere s allowin g for th e two-dimensiona l non-uniformit y i n th e distributio n o f chemica l element s for interpretatio n o f results . Thi s proble m i s ver y involved . However , i t i s onl y b y investigatio n o f vertica l stratificatio n o f chemica l compositio n an d magneti c fiel d i n th e atmosphere s o f peculia r star s tha t on e ca n attemp t t o understan d th e mechanis m producin g anomalies .


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