HERVY ELEMENT ABUNDANCES PREDICTED BY RADIATIVE SUPPORT THEORY IN
THE ATMOSPHERES OF HOT WHITE DWARFS
P. Chayer, G. F o n t a i n e , and F. Wesemael
Departement de Physique, Universite de Montreal
The surface composition of a white dwarf evolves as a result of t h e
of several mechanisms, the most important of which being g r a v i t a t i o n a l
interaction
s e t t l i n g . In
the early phases of the e v o l u t i o n , theory shows that s e l e c t i v e r a d i a t i v e
levitation
can o c c a s i o n a l l y defeat s e t t l i n g a n d , t h u s , prevent the formation of a p r i s t i n e
hydrogen (helium) atmospheric
Michaud 1979; V a u c l a i r ,
Vauclair,
sharp metallic
in the
stars
alike
essential
the
features
resulting
motivation
atmospheres
investigations
of
of hot
from
and
Greenstein 1979). The e x c i t i n g
ultraviolet
the
work
for further
white
pure
layer in a hot DA (non-DA) white dwarf (Fontaine and
of
spectra
of
several
investigators
theoretical
investigations
dwarfs. Additionnal
DA white
dwarfs
several
impetus
carried
out
by
hot
discovery
DA and
has
provided
of r a d i a t i v e
comes
from
Bruhweiler
the
levitation
the
of
non-DA
in
continuing
and Kondo
which
have already r e v e a l e d a most i n t e r e s t i n g observational p a t t e r n of heavy elements in
these stars (Bruhweiler 1985). Moreover the recent a v a i l a b i l i t y of t h e o r e t i c a l
lent widths of s e l e c t e d a s t r o p h y s i c a l l y
white
dwarfs
(Henry,
Shipman,
and
important u l t r a v i o l e t
Wesemael
1985)
metal
makes
a
lines
equiva-
in hot
comparison
DA
between
theory and observations - i n at least t h i s t y p e of s t a r s - a timely and useful
exer-
cise.
We have r e c e n t l y completed a d e t a i l e d
radiative support
DA and non-DA
i n v e s t i g a t i o n of the effects
of
selective
on C, N, 0 , and Si in model atmospheres and envelopes
of
white dwarfs. For each of these elements, and for a large
of models, we have d e r i v e d
the
abundance profiles
as a f u n c t i o n
both
number
of d e p t h
which
are obtained by assuming an equilibrium between g r a v i t a t i o n a l s e t t l i n g and r a d i a t i v e
l e v i t a t i o n . The bulk of our c a l c u l a t i o n s
only,
i.e. in regions
approximation
radiative
which
forces
are formally v a l i d
in o p t i c a l l y
below t h e Rosseland p h o t o s p h e r e . This
has
in white
been
dwarfs
used
so
far
(Vauclair,
in
the
Vauclair,
few
is the
same
investigations
and Greenstein
thick
layers
level
of
devoted
to
1979;
Morvan,
Vauclair, and V a u c l a i r 1986). Radiative a c c e l e r a t i o n s have also been computed for a
small subset of models t a k i n g into account the effects of r a d i a t i v e transfer in o p t i cally thin
layers and the n o n - u n i f o r m abundance profile
As in the
case of hot
B subdwarfs discussed
on the s y n t h e t i c
by Bergeron
et
aJ.
spectra.
(1988), we
find
that the n o n - u n i f o r m i t y of the equilibrium abundance d i s t r i b u t i o n of an element s u p -
253
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ported by radiative levitation does not generally lead to line profiles and strengths
which are markedly different from the line profiles and strengths obtained under the
assumption of a uniform distribution with a value of the abundance equal to that of
the non-uniform model at the Rosseland photosphere. The full results of our investigation will be presented elsewhere (Chayer et eJ. 1988). In this short communication, we restrict ourselves to some sample results.
Fig.1 (Fig.2) shows the equilibrium abundance profiles for Dfl (non-Dfl) models
with M/M @ -0.6. Note that the envelope parameters have been taken from the evolutionary tracks of Vinget, Lamb, and Van Horn (1988); the gravity therefore decreases (as it should) with increasing effective temperature. As compared to cosmic
abundance ratios, only underabundances of C, N, 0 , and Si can be supported by
radiative levitation in the outermost layers of Dfl white dwarfs with M/M @ -0.6. The
qualitative behavior of the equilibrium abundance profile is the same for C, N, and
0 . In particular, note that the surface abundance decreases monotonically with
decreasing effective temperature for these elements. At high effective temperatures,
there are two reservoirs supported by radiative forces. These two reservoirs are
separated by a layer in which the dominant ionization state is that of the noble
gas configuration which implies that radiative support is considerably reduced there.
For Te<40,000K, only the outer reservoir can be supported. The behavior of the surface abundance of Si is qualitatively different because that element goes through
its noble gas configuration in the surface layers for the effective temperatures
illustrated here. Thus, small traces of silicon can be supported at the photosphere
of 0.6 M@ Dfl white dwarf models with T e )75,000K, no support is possible in the
range 75,OOOIQTe>50,OOOK, and silicon can again reappear at the surfaces of cooler
white dwarfs.
The surface abundances of the four elements considered all decrease monotonically with decreasing effective temperature in models of non-Dfl white dwarfs (Fig.2).
Fit high effective temperatures (T J75,000K), slight overabundances of N can pollute
the atmospheres of these stars, but, otherwise, underabundances are predicted.
These are generally smaller than in the case of hot Dfl stars. However, the appearance of a superficial helium convective zone around Teas65,000K plays against
radiative support in the cooler objects because radiative levitation can only be
effective at the base of the convection zone where ionization is more complete and
bound-bound absorption becomes less important. Below Te%35,0OOK, radiative support
becomes totally negligible in the atmospheric layers of He-rich white dwarfs. The
formation of a helium convection zone also prevents Si from reappearing at lower
effective temperatures; no Si is predicted in the atmospheres of 0.6 M Q non-Dfl
white dwarfs with T e <85,000K.
The results of our extensive calculations should be eventually used in a detailed comparison of the predictions of radiative support theory with the observations.
Currently, such a comparison remains quite limited because detailed abundance
analyses have been carried out for only three hot white dwarfs: the Dfl stars Volf
254
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1346 and Feige 24 and the DO object PG 1034+001. Chayer et al. (1987) have
demonstrated that there are large discrepencies between the predicted and observed
C abundances for both Feige 24 and PG 1034+001. They suggest that another mechanism (such as a weak wind) possibly interferes with settling and radiative levitation
in these hot objects, fit the very least, it appears that the idea of a simple equilibrium between gravitationel settling and radiative support does not pass the test
in these stars.
Further evidence in that direction is gained by using the sample of some 20
bright, hot Dfl white dwarfs currently being investigated by Bruhweiler and Kondo.
Pending the final results of their detailed studies, Bruhweiler (1985) has nevertheless
announced a most interesting observational pattern of heavy elements in hot Dfl
stars: while no features are detected (at the 15 mA level) in high-resolution IUE
spectra of a minority of objects, only Si features are observed for stars with
Te<40,000K in the rest of the sample, and features of Si, C, and N ar& observed in
the hotter stars. This qualitative pattern can be contrasted to the predictions of
radiative support theory. As an illustrative example, we have used the predicted
abundances at the Rosseland photosphere of our 0.6 M@ Dfl models to derive the
strenghts of several spectral features which are accessible in the /UE window. In
this process, we have used the equivalent widths computed in the spectrum synthesis study of Henry, Shipman, and Vesemael (1985). The results are shown in Fig.3
which puts in evidence the predicted equivalent width of a given spectral line as a
function of effective temperature. Oxygen features have not been considered by
Henry, Shipman, and Vesemael (1985) because they are only of relevance to effective temperatures higher than that of the hottest known Dfl white dwarf in the /OF
spectral range. Even adopting a very conservative detection limit of 100 mfl, we
find that the observed abundance pattern is not reproduced as carbon features for
example would still be easily detectable in Dfl white dwarfs with Te<40,000K.
Coupled to the fact that no features are observed in some of the Dfl objects in
the Bruhweiler and Kondo sample, this suggests very strongly that the predictions
of simple radiative support theory are inadequate. Ve note that the absence of
metallic spectral features in some of the hot Dfl stars observed with the /UE in the
high resolution mode is usually blamed on known (or expected) higher gravities in
these stars. Preliminary inspection of our detailed results indicates that, while the
expected photospheric abundances are indeed reduced in higher gravity objects,
spectral features should still be detectable.
The main conclusion of this paper is that simple radiative support theory fails
to explain the observed abundance pattern of heavy elements in hot white dwarfs.
At least one other mechanism must interfere with gravitational settling and radiative
levitation in such objects. Ve note that the studies of Bruhweiler and Kondo (1981,
1983) already point to a very natural candidate: the presence of weak winds. The
work of these investigators strongly suggests that the outermost layers of very hot
white dwarfs are permeated with a wind which eventually dies out with cooling. It is
important to point
out that such winds do not need t o , and indeed cannot, be
255
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very l a r g e . This is because abundance anomalies (the large underabundances usually
observed in white dwarfs) cannot be b u i l t if the wind v e l o c i t y
the
diffusion
velocities
of various
s p e c i e s , Michaud
is much larger
(1987) finds
somewhat
than
weak
3X10"' 6 M^yr" 1 for the maximun mass loss rate allowing c h e -
c o n s t r a i n t s of 3X10"" -
mical sedimentation and s e t t l i n g in white dwarfs. Ve note that a mass loss rate as
small as 10' 2 1 M @ yr~' can s t i l l play havoc with the p r e d i c t e d surface abundances in
presence
of
radiative
o u t e r reservoirs
s u p p o r t . For example, we
of C and N are opened at
cannot
help
the surface
that
the
of a Dfl white dwarf
but
notice
and
c o u l d e a s i l y be emptied by such a wind in the hot phases of the e v o l u t i o n
fit
the same time the reservoir of Si is not opened at the surface
in a
(Fig.1).
significant
e f f e c t i v e temperature r a n g e . Hence, it is strongly tempting to speculate that first C
and
then
N are
very
hot
phases
caught
totally
expelled
of the
from the
e v o l u t i o n , while
photosphere
Si
investigation
of the
interaction
the
visible
on g r a v i t y for the effects
e n v i s i o n e d . Whether or not t h i s s p e c u l a t i v e s c e n a r i o
detailed
Dfl white
"hides" below
by the effects of wind and becomes e v e n t u a l l y
of the e v o l u t i o n , fl dependance
of
dwarfs
surface
in the
in
until
later
the
it
is
phases
of winds is also
easily
is at all c o r r e c t rests with a
between s e t t l i n g , r a d i a t i v e
levitation,
and
mass loss in hot white dwarfs. Ve have embarked on such a p r o j e c t and will report
our results in due t i m e .
This work was supported by NSERC Canada, and by a E.VJ?. Steacie
Fellowship
t o one of us (GF).
Bergeron, P., Vesemael, F., M i c h a u d , G., and F o n t a i n e , G. 1988,Ap.
Bruhweiler, F.C. 1985, Bull.
Amer.
Astron.
Soc.,
Bruhweiler, F.C., and Kondo, Y. 1981, Ap.
J.
Bruhweiler, F.C., and Kondo, Y. 1983, Ap.
J.,
(Letters),
Colloquium
No.
95,
The Second
in press.
2 4 8 , L123.
269, 657.
Chayer, P., F o n t a i n e , G., Vesemael, F. and M i c h a u d , G. 1987, in
fl.
J.,
17, 5 5 9 .
Conference
on Faint
IAU
Blue
Stars,
G. D. Philip, D. S. Hayes and J . L i e b e r t , e d s . , L. Davis Press,
S c h e n e c t a d y , p. 6 5 3 .
Chayer, P., F o n t a i n e , G., V e s e m a e l , F. and M i c h a u d , G. 1988, in p r e p a r a t i o n .
F o n t a i n e , G., and M i c h a u d , G. 1979, Ap.
Henry, RB£.,
M i c h a u d , G. 1987, in
Faint
J.,
231, 826.
Shipman, H I . , and Vesemael, F. 1985, Ap.
Blue
IAU Colloquium
Stars,
fl.
No.
95,
The Second
J.
Suppl.,
5 7 , 145.
Conference
on
G. D. P h i l i p , D. S. Hayes and J . L i e b e r t ,
e d s . , L. Davis Press, S c h e n e c t a d y , p. 2 4 9 .
M o r v a n , E., V a u c l a i r , G., and V a u c l a i r , S. 1986, Astr.
Ap.,
V a u c l a i r , G., V a u c l a i r , S., and Greenstein, JJ_. 1979, Astr.
163, 145.
Ap. , 8 0 , 7 9 .
V i n g e t , D £ . , Lamb, D.Q., and Van Horn, H J 1 . 1988, in p r e p a r a t i o n .
256
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at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0252921100099656
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C II (1335 A j , C III (1176 A ] , C IV (1250 A ) , N V (1240 A ) ,
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at https://www.cambridge.org/core/terms. https://doi.org/10.1017/S0252921100099656
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