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in recent years , white dwarf stars are receiving increasing attention .
the theoretical relationship between the mass and radius of a white dwarf is important in interpreting some of the observational results .
m - r relation was first defined by chandrasekhar ( 1939 ) .
later hamada and salpeter ( 1961 ) obtained numerical models for different core compositions by considering a fully degenerate configuration ( zero - temperature ) because of their higher densities ( @xmath1-@xmath2 g @xmath3 ) .
a real wd is not a zero - temperature object .
the inclusion of hydrogen envelope increases the radius depending on the amount of hydrogen present which is not known with certainty ( koester , 1987 ; hamada and salpeter , 1961 ) .
hamada and salpeter ( 1961 ) mentioned that for massive wds ( @xmath0 @xmath4 0.7 ) non degenerate envelope is rather insignificant .
benvenuto and althaus ( 1998 ) in their recent studies also concluded that thick h envelopes increase the radii especially in the case of low mass wds .
the recent studies on the relation of m - r for the wds are those of wood ( 1990 ) , vennes et al .
( 1995 ) and althaus and benvenuto ( 1997 , 1998 ) .
vennes et al .
( 1995 ) computed static m - r relation for masses between 0.4 @xmath0 and 0.7 @xmath0 assuming non zero temperature effects .
they assumed the luminosity is proportional to the mass which works for cool wds but their results are in the range of high effective temperatures .
as althaus and benvenuto ( 1997 ) mentioned , luminosity is not proportional to a constant for hot wd interiors because of neutrino emission .
one must include neutrino cooling which causes larger radii for wds .
neutrino losses are important especially for masses greater than 0.4 @xmath0 ( see fig.11 of althaus and benvenuto , 1997 ) .
the purpose of this study is to present the effect of neutrino emission at finite temperatures .
we considered fully degenerate configuration for wds with pure helium composition to obtain m - r relation for masses greater than 0.4 @xmath0 with neutrino emission taken into account as well . in section 2
we describe the procedure that we follow . in section 3
we present and discuss the results and compare the obtained m - r relation with the other results .
our stellar wd models are calculated on the assumption that the wd is spherically symmetric and in hydrostatic equilibrium .
then , four stellar structure equations that must be satisfied by this structure are integrated outward with runga - kutta iteration tecnique . for the equation of state , we followed the procedure given by althaus and benvenuto ( 1997 ) for a dense plasma in which the electrons are strongly degenerate at a finite temperature , that is we included in the equation of state coulomb interaction , thomas - fermi deviation from uniform charge distribution of the electrons and the exchange contribution to the free energy at finite temperature .
as far as neutrino losses are concerned we considered photo neutrino process ( itoh et al . , 1989 ) ,
plasma neutrino process ( itoh et al . , 1989 ; itoh et al . , 1992 ) and neutrino bremstrahlung for the liquid phase ( itoh and kohyama , 1983 ) .
for the conductive opacities we used the analytic fits given by itoh et al .
( 1983 ) for high densities .
in this paper , we give the first results of our white dwarf models including neutrino emission , that is m - r relations of the fully degenerate helium wds for masses greater than 0.4 @xmath0 are presented .
figure 1 . shows the m - r relations for helium wds calculated by hamada and salpeter ( 1961 ) , althaus and benvenuto ( 1997 ) , vennes et al .
( 1995 ) and our results . in this figure , plus sign shows our results obtained at the temperature @xmath5= @xmath6 k using the density values given in table 1a of hamada and salpeter ( 1961 ) for helium core ( cross sign shows the results of hamada and salpeter ) .
the difference in mass and radius is about 1% .
as seen from the figure the static mass - radius relations are modified by thermal effects and neutrino emission particularly for wds of low mass .
these thermal effects and neutrino emission can cause deviations from the zero temperature m - r curve which are almost of the same order as hamada - salpeter corrections to the standard chandrasekhar m - r curve .
we repeated the calculations for a different central temperature @xmath5= 5x@xmath6 k. the resulting data is also shown ( circle sign ) in the figure .
the increase in @xmath5 causes the curve to shift upward for the masses smaller than 0.7 @xmath0 .
we plot on the same figure also the results of althaus and benvenuto ( 1997 ) for zero temperature ( star sign ) and for @xmath5= 5x@xmath6 k helium wd models ( full box sign ) .
the models of vennes et al .
( 1995 ) for masses smaller than 0.7 @xmath0 are shown by open box sign .
their models have larger radii than the other models plotted in the same figure due to the high effective temperature ( 49000 k ) they used which means higher central temperature .    in our calculations with internal temperature of 5x@xmath6 k , we found r=0.015 @xmath7 for 0.5 @xmath0 wd . the effective temperature of 0.5 @xmath0 wd star can be assigned to be in the range 17x@xmath8 - 17.5x@xmath8 k using the results of atweh and eryurt - ezer ( 1991 ) for the lower boundary of convection zone of helium wds in the case of strong convection .
they give the depth of convection zone for this effective temperature range between 30 and 60 km .
therefore , about 7% difference in the radii of 0.5 @xmath0 wds at the mentioned interior temperature , between our study and the study of althaus and benvenuto , is not due only to the absence of helium atmosphere in our study but also due to neglecting star s thermal history .
detailed evolutionary models are necessary for better interpretation of observations of wds .
we would like to thank prof .
d. eryurt - ezer for her suggestions in this study .
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fig.1 . mass - radius diagram for pure helium white dwarfs . plus and empty circles are the results of the present study for central temperatures of @xmath6 k and 5x@xmath6 k , respectively .
star and full box signs show the results of althaus and benvenuto ( 1997 ) for zero - temperature and @xmath5= 5x@xmath6 k wd stars , respectively . also shown
are the data of hamada and salpeter ( 1961 ) ( cross sign ) and vennes et al .
( 1995 ) ( empty box sign ) .
we studied the static mass - radius relation of white dwarf stars with masses greater than 0.45 @xmath0 . 
 we assumed pure degenerate helium interiors at a finite temperature with luminosity - mass ratio due to neutrino energy loss . 
 we compared the obtained m - r relation with those of other writers .    
 key words : stars : white dwarfs , stars : interiors    20.5 cm 14.5 cm