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"Stellar magnetism"

International Conference Proceedings,

1992 ,

155-157 .

O N TH E ORBITA L ECCENTRICIT Y CHANGE S I N MAGNETI C CLOS E BINAR Y SYSTEM S

I.L .

ANDRONO V

Departmen t o f Astronomy , Stat e University , Odess a 270014 , Ukrain e

ABSTRACT . eccentric if

The model of Joss et al. orbits

(1979) is generalized to the case of the The trial that
o

in magnetic binaries. axis of

eccentricity of

increases, motion

the rotational

the white dwarf and

the orbital

coincide,

or the angle between them is less than 90 ,

and decreases in the - 5)*10 (1
9

opposite case. fo r yrs of the for 71 ,
s

The characteristic times of such process are (1 rotation of the white dwarf, the and

yrs
8

"near-synchronous" the for "rapidly

- 4)* 10

rotating"

white dwarf with the

characteristic and

period

the adopted parameters of

"long-period"

"short-period"

polars.

Th e presenc e o f the magneti c field o f the whit e dwar f

(WD)

i n cataclysmi c vari bu t th e motio n o f

able s (CV) affect s no t onl y the structur e o f the accretio n flow , the stella r component s a s well . Jos s e t al .

(1979) hav e shown , that th e ohmi c dissi -

patio n o f th e Fauko t current s i n the secondary' s envelop e ma y lead t o synchronizatio n o f th e orbita l an d rotationa l motio n o f the WD . Androno v (1982, the plasm a ejectio n a t the "propelle r stage "
s

1987ab ) showe d that

i s muc h mor e efficien t mechanis m for
3

synchronizatio n wit h characteristi c time t <=10 yrs . al .

However ,

the mode l o f Jos s e t

(1979 ) ma y b e extende d t o the cas e o f eccentri c orbit s (cf. Andronov , 1983) , and T o study the

her e w e presen t th e estimate s o f the characteristic s o f suc h a process . secula r eccentricit y changes , w e used the evolutionar y expressio n

wher e P - is th e orbita l period ,

- the correspondin g angula r frequency , a -

the larg e semi-axi s of the orbit , v and E - the true an d eccentri c anomalies , respec -

155


tively, S and T - the radial and tangential part s of the disturbin g acceleration . Introducin g the "effectiv e dra g force" , on e ma y obtai n

(Andronov, 1983) , where , 1979) ,

taking into account the dissipativ e losse s (Joss e t al . ,

r is the light speed, the rotatin g binar y system,

- the angula r velocit y of the WD rotatio n in respec t to - the conductivit y of the secondary' s envelope , N - the - the

magneti c momen t of the dipole , R - the effectiv e radiu s of the secondary ,

angl e betwee n the magneti c axi s and the rotationa l axi s of WD . It is assume d that the latter is paralle l to the rotational axi s of the orbita l motion . Takin g into accoun t onl y the firs t term o f the serie s expansio n o n eccentricit y e , on e ma y obtai n

wher e

Th e

positiv e sig n is to be take n if the rotationa l an d orbita l

axe s ar e o f the sam e orientation . Fo r th e numerica l estimates , w e wil l us e the "mass-radius " relatio n to r the whit e dwarf s (Dibay and Kaplan , 1976 ) wher e Th e secondary' s radiu s (Paczynski, 1971) , thu s

Her e the orbita l perio d P is expresse d in days ,

- in seconds , the magneti c

fiel d strengt h a t the magneti c pol e - i n unit s o f 10 8 Gs . Th e characteristi c time s o f the orbital eccentricit y change s ronizatio n an d o f the synch -

fo r the two polar s a t the opposit e part s o f the "perio d gap " ar e pre -

sente d in Tabl e 1. Fo r the "short-period " systems , the secondary' s temperatur e i s usuall y smaller , a s wel l a s the total mass . Thus , the value s o f and ma y b e som e time s smaller . The

large semi-axi s o f the orbita l motio n i s changin g wit h the characteristi c time

correspondin g to the conservatio n of the total momen t of impulse .

156


Th e propose d mechanis m i s less effective , a s compare d wit h the tidal interaction , and i s compare d wit h the influenc e o f the gravitationa l radiatio n (Landa u an d Lif shitz, 1973) .

REFERENCE S

Andronov I.L.: 1982 , Preprint Ukr. Res. Inst. Sci. Tech. Inform. (UkrNIINTI ) 5901-82 . Andronov I.L.: 1983 , Proc . Conf. Young Scientists, Odess a Univ . Press , 144 . Andronov I.L.: 1987a, Astrophys. Space Sci. 131, 557 . Andronov I.L.: 1987b, Astron. Zh. 64 , 97 . Dibay E. A. , Kapla n S.A.: 1976, Dimensions and Similarity of the Astrophysical Quan tities, Moskva , Nauka , 132 (in russian) . Joss P.C., Kat z J.I. , Rappapor t S.A.: 1979, Astrophys.J. 230 , 176. Landau L.D., Lifshit z E.M.: 1973, The theory of Field, Moskva , Nauk a (in russian) . Paczynski .: 1971 , Ann. Rev.Astron.Astrophys. 9, 183. Subboti n M.F. : 1968 , Introduction to the theoretical Astronomy, Moskva , Nauka , 52 7 (in russian) .