Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://star.arm.ac.uk/~csj/papers/journal/hewd_merger.ps Äàòà èçìåíåíèÿ: Tue Aug 29 14:20:55 2000 Äàòà èíäåêñèðîâàíèÿ: Tue Oct 2 09:30:03 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: m 43

**TITLE**
ASP Conference Series, Vol. **VOLUME**, **PUBLICATION YEAR**
**EDITORS**
Helium white dwarf mergers as progeny for extreme
helium stars
C. Simon Jeery
Armagh Observatory, College Hill, Armagh BT61 9DG, N. Ireland
Hideyuki Saio
Astronomical Institute, School of Science, Tohoku University, Sendai
980-8578, Japan
Abstract. The origin of extreme helium stars poses a signicant puz-
zle for stellar astrophysics. This paper summarizes the observational data
concerning extreme helium stars in general, and one, V652 Her, in partic-
ular. One proposal involves the merger of two white dwarfs in a binary.
Here, the rapid accretion of helium onto a helium white dwarf is used to
simulate the merger of two helium white dwarfs. Helium-shell ignition
occurs at the boundary between degenerate and non-degenerate helium
after suôcient helium has been accreted, causing the star to become a
yellow giant. Thereafter, the helium-burning shell burns in to the core,
and the star contracts towards the helium main sequence where it will
appear as a subdwarf B star. About halfway through this contraction, the
model dimensions compare favourably with observations of mass, lumi-
nosity, eective temperature, surface composition, pulsation period and
pulsation period change in V652 Her. Competing models, such as the
`late thermal pulse' model for example, fail to achieve such agreemen-
t. The merged binary white dwarf hypothesis emerges, therefore, as the
preferred explanation for the origin of at least some extreme helium stars.
1. Introduction
The likely outcome of the evolution of two stars in a detached binary is a pair
of white dwarfs with masses of  0:6 M or below. Increasing numbers of such
binaries are now being discovered. With no nuclear reserves, their evolution will
be dominated by orbital decay as a consequence of gravitational radiation or
magnetic-wind braking. Although the decay timescales remain contentious, it
is reasonable to hypothesize that a substantial fraction of binary white dwarf
orbits will decay completely within a Hubble time. The less massive white
dwarf will ll a gravitational potential surface with the same potential relative
to its companion causing its surface to spill over onto its companion. Tidal
forces will take over and disrupt the less massive star, causing it to form a
disorganized envelope, from whence its companion will start to accrete material.
In loose terms, this describes the merger of two white dwarfs; a process that
should become increasingly common as the stellar population of a galaxy ages.
1

2 Jeery & Saio
This paper addresses the question of what happens when two low-mass white
dwarfs with degenerate helium cores coalesce. Its motivation is an attempt to
explain the evolutionary origin of extreme helium stars, a rare class of luminous
stars with highly processed surfaces. The results have already been published
elsewhere (Saio & Jeery 2000). Most of the details are reproduced here to
maintain the completeness of these conference proceedings.
2. Extreme Helium Stars
Extreme helium stars (EHes) are rare B- and A-type giant stars with extremely
low surface abundances of hydrogen (Jeery 1996). In most cases they are also
characterized by enhancements of CNO-processed, 3 and -capture products
and the majority have log L=M > 4 (as indicated by their surface gravities).
A few have signicantly lower L=M ratios and do not show 3 and -capture
products in their atmospheres (e.g. V652 Her, Jeery, Hill, & Heber 1999).
The major question concerning their evolutionary origin is whether they are
the products of single-star or binary-star evolution. The task has been diôcult
from the outset because, in the normal evolution of single stars from the main
sequence to the white dwarf phase, it seemed impossible to remove the hydrogen-
rich surface. Two principal hypotheses emerged during the 1980's.
The `merged binary white dwarf model' (MBWD: Webbink 1984; Iben &
Tutukov 1984) considered the accretion of a white dwarf (WD) secondary onto
a white dwarf primary, resulting in the ignition of a helium shell in the accreted
envelope which forces the star to expand to become a cool giant. Subsequent
evolution would follow the canonical post-AGB contraction to the white dwarf
track, in the case of a CO+He WD merger, or contraction to the helium main-
sequence { possibly giving a subdwarf B star { in the case of He+He WD merger
(Iben 1990).
The `late thermal pulse' model (LTP: Iben et al. 1983) considered what
would happen when the helium layer remaining near the surface of a star at the
end of AGB evolution was of such a mass that a nal thermal pulse would occur
after the star had become a white dwarf, also forcing the star to expand rapidly.
Again, subsequent evolution would resemble the canonical post-AGB sequence.
The LTP model has been studied extensively in recent years (Iben & Mac-
Donald 1995; Blocker & Schonberner 1997) and used to discuss the origins of
various hydrogen-decient stars. Part of the success of LTP models has been
due to the very large degree of freedom allowed in reproducing a wide range of
surface compositions, from s-process elements in RCrB stars (Bond, Luck, &
Newman 1979; Lambert & Rao 1994) to very high C and O concentrations in
PG1159 and [WC] stars (Werner, Heber, & Hunger 1991; Leuenhagen, Heber, &
Jeery 1996). The LTP model has also been supported by the rapid evolution
from WD to cool giant observed in V605 Aql (Pollacco et al. 1992), FG Sge (Her-
big & Boyarchuk 1968) and V4334 Sgr (Duerbeck & Benetti 1996), all of which
are hydrogen-decient to some extent. However another part of the success of
the LTP model may have been due to the absence of detailed numerical MBWD
models. In particular the LTP model cannot account for all EHes, especially the
low-luminosity EHe V652 Her.

He white dwarf mergers 3
3. V652 Her
V652 Her is an exceptional helium star. It rst attracted attention because of
the discovery of radial pulsations with a period of 0.108 d (Hill et al. 1981).
These pulsations have provided remarkably precise dimensions (M; L; R; T e )
for V652 Her which tightly constrain evolution models.
The eective temperature log T e = 4:370  0:025 (Lynas-Gray et al. 1984)
adopted here was based on ultraviolet spectrophotometry. Baade's method was
used by the same authors to determine the radius and hence the luminosity
log L=L = 3:03 0:12. We note that Jeery et al. (1999) give a slightly higher
eective temperature for V652 Her. With a spectroscopic measurement of the
surface gravity, the stellar mass has then been obtained directly, as 0:7 +0:4
0:3 M
by Lynas-Gray et al. (1984) and 0:69 +0:15
0:12 M by Jeery et al. (1999).
The pulsations have provided yet more constraints on evolution models since
the period was found to be decreasing at a rate dP=dn = 8:310 9 d (Kilkenny
& Lynas-Gray 1982; Kilkenny, Lynas-Gray, & Roberts 1996) commensurate with
a secular contraction. Kilkenny et al. (1996) have also measured the second
derivative of the period, d 2 P=dn 2 = 1:7  10 14 d.
The earliest observations of pulsation were extremely challenging since, as
for  Cepheids, no excitation mechanism for driving the pulsations could be
found. It was only the introduction of the OPAL opacities (Rogers & Iglesias
1992) that provided an explanation for why V652 Her should pulsate at all. The
existence of an instability \nger" due to high opacity from iron-group elements
at temperatures around 10 5 K in hydrogen-decient stars with T e  23 000 K
was discovered by Saio (1993). The same opacity source drives  Cepheid pulsa-
tions. Subsequently, Fadeyev & Lynas-Gray (1996) were able to construct non-
linear pulsation models which reproduced the radial-velocity and light curves
of V652 Her with substantial precision. Their best models were obtained with
M = 0:72 M , T e = 23 500 K, L = 1062 L , and Z = 0:0156.
For any highly evolved star, the surface chemical composition provides a
fossil record of the previous evolution, although it may be diôcult to decode.
Jeery et al. (1986, 1999) have shown that the extremely helium-rich surface
of V652 Her is > 1 dex underabundant in carbon and oxygen and  1 dex
overabundant in nitrogen, indicating that it primarily comprises the residue of
CNO-processed material. There is some residual hydrogen,  1% by numbers,
but no evidence of any helium-burning products. The abundances of other
elements are typically solar, and the surface composition may be characterized by
mass fractions of hydrogen, helium and metals as X = 0:0017; Y = 0:9825; Z =
0:0158.
In an attempt to interpret some of the earliest estimates of these quanti-
ties, Jeery (1984) constructed models of a 0.7 M mass helium star contracting
towards the helium main-sequence. Whilst able to reproduce the observed prop-
erties of V652 Her successfully, it was diôcult to account for the initial conditions
adopted for the evolution sequence { a `helium-rich horizontal branch' model {
within single-star evolution theory.
The LTP model introduced above provides an attractive alternative because
it can, in principle, be ne-tuned to match many combinations of observables.
However, its principal property is that of a helium-burning shell around a degen-

4 Jeery & Saio
4.8 4.6 4.4 4.2 4 3.8
­2
0
2
4
Figure 1. Evolutionary tracks starting with an accreting white dwarf
of 0.4 M . The accretion was stopped when the total mass became
0.5 M (dotted line) or 0.7 M (solid line). The dashed line indicates
the part in which accretion is switched on. The square with error bars
shows the approximate position of V652 Her (Lynas-Gray et al. 1984)
erate carbon-oxygen core. Models with such properties are entirely inconsistent
with the observations of V652 Her (Saio & Jeery 2000).
4. Evolution Models
We have calculated evolutionary models starting with a low-mass white dwarf
rapidly accreting helium-rich material (Y = 0:98; Z = 0:02). For the initial
accretion phase, which is considered as a rough approximation of the merging
process of a double white dwarf system, we have adopted an accretion rate of
1  10 5 M yr 1 , which is about a half of the Eddington limit accretion rate
for white dwarfs. Initial masses (M i ) of white dwarfs considered are 0.3 M
and 0.4 M . The accretion was stopped when the total mass increased to a
pre-determined nal mass. Considering that the nal mass should be smaller

He white dwarf mergers 5
4 4.5 5 5.5 6
0
0.1
0.2
0.3
0.4
3.8
4
4.2
4.4
4.6
Figure 2. Evolutionary changes of the position of helium burning
shell (lower panel) and the eective temperature (upper panel). The
abscissa presents time after the rst helium ignition. The initial mass
is 0.4 M for both cases.
than 2M i , we have adopted nal masses of M f = 0:8; 0:7; 0:6 and 0.5 M for
M i = 0:4 M , and M f = 0:6 and 0.5 M for M i = 0:3 M . The computational
method is the same as in Saio & Nomoto (1998) except that opacities have been
obtained from OPAL95 tables (Iglesias & Rogers 1996).
Figure 1 shows evolutionary tracks for the cases of M f = 0:5 M and 0.7 M
with M i = 0:4 M . The evolutionary tracks for the other cases are similar.
The triple-alpha reaction is ignited at M r
= 0:413 M when the total mass
has increased to 0.466 M (for M i = 0:3 M these quantities are 0.278 M and
0.5 M , respectively). It led to a shell- ash with a peak nuclear luminosity of
7:7  10 7 L (4:2  10 5 for M i = 0:3 M ). As the released energy migrates
into the envelope, the radius as well as luminosity increases so that the star
becomes a yellow giant in  10 3 yr. Accretion is stopped when the total mass
reaches a pre-determined nal mass, which occurs during the yellow-giant phase.
Evolutionary tracks after the accretion phase are shown by solid (M f = 0:7 M )

6 Jeery & Saio
and dotted (0.5 M ) lines in Fig. 1, while the accretion phase is shown by a
dashed line. The position of V652 Her is also shown.
The helium-burning shell moves inward with repeating shell ashes as de-
scribed by Saio & Nomoto (1998). Figure 2 shows the temporal variation of the
mass coordinate of the helium-burning shell, M r
( ame), and the eective tem-
perature. Each ash phase corresponds to each sudden change in M r
( ame) in
Fig 2. As the ame moves inward, the eective temperature increases gradually,
although it uctuates due to shell ashes. When M r
( ame)  0:25M , the star
enters the instability region on the HR diagram for radial pulsations. It takes
about 10 5 yr for the ame to reach M r  0:25 M , and about 10 6 y to reach the
center. The evolution timescale becomes longer as the star get closer to the
helium zero-age main sequence. Since only 10% or less of helium is burnt during
a shell ash, the star has a structure similar to that of a helium main-sequence
star when the ame reaches the center.
Convective regions occur above the helium-burning shell during shell ashes
and at the surface during the most redward excursion of the evolutionary tracks.
Only the rst ash was strong enough for the shell convection zone to reach close
to the surface.
Figure 1 shows that evolutionary tracks toward the helium main sequence
pass near the position of V652 Her. The luminosity of models in inter- ash
phases around the position of V652 Her is mainly determined by the mass interior
to the helium-burning shell, i.e., M r
( ame). This is the reason why our models
have a luminosity insensitive to the total mass and much lower than those of
post-AGB models with the same total masses (Jeery 1988, Saio 1988).
Thus the `merged binary white dwarf' hypothesis for the progenitors of low-
luminosity extreme helium stars satises the requirement for the position on the
HR diagram. This scenario predicts that the luminosity of the low-luminosity
extreme helium stars is distinctively lower than that of normal extreme helium
stars. This property seem to appear in the luminosity-frequency histogram for
extreme helium stars shown by Jeery (1996).
5. Radial Pulsations
Since many extreme helium stars show pulsations, and since the primary compar-
ison target V652 Her shows well-dened radial pulsations with a secular period
change, these can be used as a further strong constraint on the evolutionary
models.
We have calculated envelope models along the evolutionary tracks and ob-
tained complex eigenfrequencies using the linear non-adiabatic radial pulsation
code described by Saio (1995). Helium-rich stellar envelopes around the location
of V652 Her on the HR diagram are known to be unstable against pulsation due
to the Z-bump kappa-mechanism (Saio 1993). The fundamental radial mode is
overstable in the range 4:26  log T e  4:43 and the rst overtone is overstable
in the range 4:34  log T e  4:43 for M f
= 0:7 M . These ranges are almost
independent of M f
. Near the position of V652 Her, both fundamental and rst
overtone pulsations are overstable in the linear analysis. However, the rst over-
tone component has not been detected in the observed light and velocity curves
(Lynas-Gray et al. 1984; Lynas-Gray & Kilkenny 1986; Hill et al. 1981; Jeery

He white dwarf mergers 7
0.05 0.1 0.15 0.2
­1.5
­1
­0.5
0
0.5
1
Figure 3. The rate of period change versus period for 0.7 and 0.6 M
cases, where dP=dn is the period change per cycle in days. The crossed
square indicates the observed period and the period change rate of
V652 Her (Kilkenny et al. 1996).
& Hill 1986), nor in nonlinear models by Fadeyev & Lynas-Gray (1996). It may
mean that the amplitude of the rst overtone is very small, or that the heavy
element abundance of V652 Her is smaller than 0.02 so that the rst overtone is
stable.
Since we now know the age and pulsation period at any point along an
evolutionary track, we can obtain the rate of period change dP=dt by simple nu-
merical dierentiation. Figure 3 shows the period change (in days) per cycle (n),
dP=dn = P (dP=dt), as a function of period P for the overstable fundamental
mode. The cases of M f
= 0:6M and 0:7M with M i = 0:4 M are shown.
As seen in this gure, dP=dn changes sign during the evolution in the Z-
bump instability region. In an inter- ash phase the star contracts so that the
period decreases (dP=dn < 0) while in a ash phase the envelope expands and
hence dP=dn > 0.

8 Jeery & Saio
V652 Her
Pulsations at surface
Helium­rich envelope
Helium­burning shell
Degenerate helium core
The helium­burning shell burns inwards through the
degenerate core and the star shrinks to become a blue giant
After core helium­burning, the star contracts to become a
begins; the star is then a hot subdwarf
The burning­shell reaches the center and core­burning
... and then a helium white
to become a red giant ...
More massive star evolves
Two normal main­sequence stars
Second star becomes a
... and then a helium white dwarf
The binary orbit decays because of gravitational radiation ...
until the slightly less massive white dwarf is swallowed up by
its more massive companion
Helium from the the lower­mass white dwarf is heated
at the core/envelope boundary, nuclear reactions begin
and the new star expands to become a yellow giant
carbon/oxygen white dwarf
dwarf
red giant ...
Figure 4. Illustration of the merged-binary white dwarf evolution
model for V652 Her (Saio & Jeery 2000).
The position of V652 Her in the P dP=dn plane is shown in Fig. 3 by a
crossed square. The observed rate of change agrees with the theoretical value
for M f
= 0:6 M for M i
= 0:4 M .
The measured second derivative of the period d 2 P=dn 2 is much higher (by
a factor of 10 2 ) than indicated by those theoretical models which do reproduce
dP=dn, although the sign is right. The cause of the discrepancy is not clear.
One possible explanation may be that the location of the helium-shell ash in
the P d 2 P=dn 2 plane is sensitive to the initial conditions and nal mass. It
appears that d 2 P=dn 2 varies suôciently both during and between helium-shell
ashes that a closer agreement is possible.
6. Discussion
We have calculated rapidly accreting white dwarf models as a rough approxi-
mation for what would be expected when a low-mass double white dwarf binary
system coalesce.

He white dwarf mergers 9
Several short-period low-mass double white dwarf systems are known to
exist (Saer, Liebert, & Olszewski 1988; Bragaglia et al. 1990; Marsh, Dhillon,
& Duck 1995; Marsh 1995; Moran, Marsh, & Bragaglia 1997; Holberg et al.
1995). The mass of the primary component of such a system is estimated to be
similar to or less than 0.4 M , and the secondary mass is comparable with it.
These white dwarfs should consist of mostly helium because the core helium ash
does not occur unless the helium core mass becomes about 0.45 M . Nelemans
et al. (2000) have reconstructed their possible previous evolution from binaries
with initial masses of  2 + 2 M . On reaching the WD+WD stage, such a
binary system loses angular momentum due to gravitational wave emission or
magnetic-eld interaction so that the separation decreases gradually. If the
secondary mass is comparable with the primary, when the secondary lls its
critical Roche lobe, a runaway mass transfer to the primary is expected to lead
to the coalescence of the binary system. Among the known double white dwarf
systems, three systems have periods short enough to coalesce within the Hubble
time (Marsh 1995, Marsh et al. 1995; Moran et al. 1997). These systems are
candidates for the progenitors of our models which make the merging scenario to
produce low-luminosity extreme helium stars viable. A synopsis of the complete
evolutionary history that is emerging for V652 Her is given in Fig. 4.
The merger frequency of double HeWD systems in the Galaxy is theoret-
ically estimated to be  0:006 yr 1 by Han (1998), and  0:02 yr 1 by Iben,
Tutukov, & Yungelson (1997). The known low-luminosity helium stars have ef-
fective temperatures in a range of 4:3  log T e  4:5 (Jeery 1996). It takes
 6  10 4 yr for a merged star to evolve in this temperature range (Fig. 2).
Combining the evolution time and the above estimates for the merger frequen-
cy, we obtain  4  10 2 10 3 for the number of the low-luminosity helium stars
in the Galaxy.
Now, let us estimate from observational data the number of low-luminosity
helium stars in the Galaxy. Combining the known number of RCrB and HdC
stars ( 30) with the distribution in the Galaxy, Lawson et al. (1990) have
estimated that  200 300 RCrB and HdC stars exist in the Galaxy. That is,
multiplying the observed number with a factor of  10 yields the actual number
of RCrB and HdC stars in the Galaxy. Compared with RCrB/HdC stars, the
low-luminosity helium stars are about 10 times fainter in bolometric luminosity
and  30 times in visual luminosity because of the bolometric correction. It
means that the volume in which low-luminosity helium stars are observed in the
Galaxy is  30 times smaller than in the case of RCrB/HdC stars, if both distri-
butions are more or less planar. Therefore, multiplying the observed number of
low-luminosity helium stars by  300 yields a rough estimate for the number in
the Galaxy. We know four low-luminosity helium stars in the above temperature
range; V652 Her, LSS 3184 (Drilling, Jeery, & Heber 1998), LSIV+6 ô 2 (Jef-
fery 1998), and HD 144941 (Harrison & Jeery 1997). Combining this number
with the above multiplying factor yields  10 3 for the number of low-luminosity
helium stars in the Galaxy, which is surprisingly consistent with the number
predicted from the merged white-dwarf scenario.
The surface composition of V652 Her, consisting of CNO-processed helium
and no helium-burning products (Jeery et al. 1999), is consistent with our
models. Since the rst ash was so strong, the outer boundary of the convective

10 Jeery & Saio
0.3 + 0.4 Msun
tidal disruption of secondary
helium envelope expansion after helium­shell ignition
Not To Scale
accreting helium white dwarf
The evolution of a rapidly
formation of Keplerian disk (~50s)
accretion onto primary
helium envelope with degenerate
development of non­degenerate
helium core
Figure 5. Conceptualisation of the merger of two helium white dwarfs.
shell reached close to the surface. In the convective shell, 3% (by mass) of the
helium was converted to carbon. However, the enhanced carbon abundance has
been covered by further accretion of helium. Since the subsequent shell ashes
were weak and hence the convective shell was thin, helium burning products
were not mixed into the atmosphere.
The low-luminosity extreme star LSS 3184 has very similar properties (T e
and log g) to V652 Her (Drilling et al. 1998) and pulsates with a period of 0.106
d (Kilkenny et al. 1999). Drilling et al. (1998) have shown that its atmosphere
contains CNO-processed matter and carbon from helium burning. Such a chem-
ical composition would result from a merger model if the mass accreted after the
end of the initial helium ash is small; i.e. if the mass of LSS 3184 is smaller than
that of V652 Her and around 0.5 M . There is observational support for this
conjecture. Woolf & Jeery (2000) used Baade's method to measure its radius
as R = 2:3  0:1 R . Together with the surface gravity log g = 3:35 determined
by Drilling et al. (1998), LSS 3184 has a mass M = 0:42  0:12 M .
A more puzzling problem is that V652 Her retains a small concentration of
hydrogen ( 0:2% by mass, Jeery et al. 1999). In a non-turbulent spherically
symmetric merging process, the accreted material would settle on top of any
residual hydrogen envelope possessed by the progenitor white dwarf. The real
merging process is turbulent and three-dimensional, so that substantial mixing
will occur. For example, some of the hydrogen could be expelled outwards
during the initial dynamical phase to settle later on the surface of the merged
product, or substantial mixing could occur throughout the surface layers during
the merger process. Only  10 3 M of hydrogen-rich material in the progenitor
system, mixed through the product envelope, would be required to explain the
hydrogen observed in V652 Her. Two-dimensional calculations which include

He white dwarf mergers 11
some surface hydrogen on the white dwarfs, consider what mixing processes
occur during initial mass transfer, and follow the surface hydrogen abundance
through the complete accretion/shell- ash process are required before the surface
abundances can be used as nal arbiters of the evolution question.
We have attempted to anticipate some of the processes likely to occur during
the merger process (Fig. 5). These have been partially preempted by Benz et
al. (1990) in their models for the merger of 0.9 and 1.2 M white dwarfs. At
the point where tidal disruption occurs, material from the secondary would be
dispersed to form a thick Keplerian disk around a degenerate core in hydrostatic
equilibrium. This process takes palce on a dynamical timescale,  50s in the
case of the simulation by Benz et al. (1990). The material in the disk will be
fully mixed. Viscous forces will drag most of the material from the Keplerian
disk onto the surface of the primary. Some material may reach escape velocities
and be ejected from the disk. Turbulent ow or shear-mixing at the star/disk
boundary may provide some mixing between the primary core and the accreted
material. As the accreted mass increases, the envelope will expand to exceed
the disk radius just after helium-shell ignition. At this point the remnant disk
continues to orbit within the stellar envelope. Assimilation into the expanding
star will continue until all Keplerian material has been captured.
Following expansion to giant dimensions, contraction through shell- ashes
and passage through the Z-bump instability zone, the subsequent evolution of
our mass-accreted helium white dwarf models will bring them to the helium
main sequence where they will appear as hot subdwarfs. With masses slightly
greater than 0:5 M , and hydrogen-poor surfaces, they might be expected to
appear as subdwarf O or B stars.
Subdwarf B stars are generally recognized to be helium main-sequence stars
with masses in the region of 0.5 to 0.6 M . However, they have very hydrogen-
rich atmospheres and are extremely numerous. The scarcity of He+He WD
binaries and the helium-rich surfaces of their descendants probably excludes
them as normal sdB progenitors.
On the other hand, a small number of helium-rich subdwarf B stars has
been detected in low-dispersion surveys (e.g. Green, Schmidt, & Liebert 1986).
Practically nothing is known about these stars at present beyond their general
spectral characteristics (Jeery et al. 1997). If they are also the products of
mass-accreted WD evolution then, because the contraction time between helium-
shell ignition and the helium main sequence ( 10 6 y) is very short compared with
the helium main-sequence lifetime ( 10 8 y) there should be many more such
subdwarfs than extreme helium stars like V652 Her and LSS 3184, as appears to
be the case.
7. Conclusion
We have examined the merged binary white dwarf hypothesis for the origin of
low-luminosity (or high-gravity) extreme helium stars. We have approximated
the merging process by spherical rapid accretion onto a low-mass helium white
dwarf. We have found that the evolutionary path of such a model passes close to
the position of the low-luminosity helium star V652 Her. We have obtained the
pulsation periods and their time derivatives for models along the evolutionary

12 Jeery & Saio
tracks. We have found that the observed period and period change rate for
V652 Her as well as its position on the HR diagram would be reproduced by a
model with an initial mass slightly less than 0.4 M and a nal mass between
0.6 M and 0.7 M . The observed second derivative of the period and the surface
hydrogen abundance in V652 Her are both larger than the values predicted in our
models; further detailed modeling should indicate that these discrepancies can
be resolved. We have also found that the predicted number of low-luminosity
helium stars in the Galaxy is consistent with observation.
We conclude that the merged binary white dwarf hypothesis, as represented
by an accreting helium white dwarf model, provides a viable explanation for the
evolutionary origin of at least some extreme helium stars. These helium stars
will evolve to become hot subdwarfs close to the helium main sequence.
Acknowledgments
This research has been supported by the British Council through Collaborative
Research Grant TOK/880/41/4 and by the Department of Education in North-
ern Ireland through a grant to the Armagh Observatory. The author is grateful
to the conference organizers for a travel grant.
References
Benz W., Bowers R.L., Cameron A.G.W, Press W.H., 1990, ApJ 348, 667
Blocker T., Schonberner D., 1997, A&A, 324, 991
Bond H.E., Luck R.E., Newman M.J., 1979, ApJ, 233, 205
Bragaglia A., Greggio L., Renzini A., D'Odorico S., 1990, ApJ, 365, L13
Drilling J.S., Jeery C.S., Heber U., 1998, A&A 329, 1019
Duerbeck H.W., Benetti S., 1996, ApJ, 468, L111
Fadeyev Yu.A., Lynas-Gray A.E., 1996, MNRAS, 280, 427
Green R.F., Schmidt M., Liebert J., 1986, ApJS, 61, 305
Han Z., 1998, MNRAS, 296, 1019
Harrison P.M., Jeery C.S., 1997, A&A, 323, 177
Herbig G.H., Boyarchuk A.A., 1968, ApJ, 153, 397
Hill P.W., Kilkenny D., Schonberner D., Walker H.J., 1981. MNRAS, 197, 81
Iben I.,Jr. 1990, ApJ, 352, 215
Iben I.,Jr., Kaler J.B., Truran J.W., Renzini A., 1983, ApJ, 264, 605
Iben I.Jr., McDonald J., 1995, in Koester D., Werner K., eds., White Dwarfs.
Springer, Berlin, p.48
Iben I.Jr., Tutukov A., 1984, ApJS, 55, 335
Iben I.,Jr., Tutukov A., Yungelson L.R., 1997, ApJ, 475, 291
Iglesias C.A., Rogers F.J., 1996, ApJ, 464, 943
Jeery C.S., 1984, MNRAS, 210, 731
Jeery C.S., 1988, MNRAS, 235, 1287

He white dwarf mergers 13
Jeery C.S., 1996, in Jeery C.S., Heber U., eds., ASP Conf. Ser. Vol.96,
Hydrogen Decient Stars. Astron. Soc. Pac., San Francisco, p.152
Jeery C.S., 1998, MNRAS, 294, 391
Jeery C.S., Drilling J.S., Harrison P.M., Mohler S., Heber U., 1997, A&AS,
125, 501
Jeery C.S., Hill P.W., 1986, MNRAS, 221, 975
Jeery C.S., Hill P.W., Heber U., 1986, In IAU Coll. 87, Hydrogen Decient
Stars and Related Objects, ed. K. Hunger, D. Schonberner, N.K. Rao,
(Dordrecht, Reidel), 101
Jeery C.S., Hill P.W., Heber U., 1999, A&A, 346, 491
Jeery C.S., Saio H., 1999, MNRAS, submitted
Kilkenny D., Koen C., Jeery C.S., Hill N.C., O'Donoghue D., 1999, MNRAS,
310, 1119
Kilkenny D., Lynas-Gray A.E., 1982. MNRAS, 198, 873
Kilkenny D., Lynas-Gray A.E., Roberts G., 1996, MNRAS, 283, 1349
Lambert D.L., Rao N.K., 1994, JApA 15, 47
Lawson W.A., Cottrell P.L., Kilmartin P.M., Gilmore A.C., 1990, MNRAS, 247,
91
Leuenhagen, U., Heber U., Jeery C.S., 1994, A&AS, 103, 445
Lynas-Gray A.E., Kilkenny D., 1986, in Hunger K., Schonberner D., Rao N.K.,
eds., Hydrogen Decient Stars and Related Objects. D. Reidel, Dor-
drecht, p.117
Lynas-Gray A.E., Schonberner D., Hill P.W., Heber U., 1984, MNRAS, 209, 387
Marsh T.R., 1995, MNRAS, 275, L1
Marsh T.R., Dhillon V.S., Duck S.R., 1995, MNRAS, 275, 828
Moran C., Marsh T.R., Bragaglia A., 1997, MNRAS, 288, 538
Pollacco D.L., Lawson W.A., Clegg R.E.S., Hill P.W., 1992, MNRAS, 257, 33P
Rogers F.J., Iglesias C.A., 1992, ApJS, 79, 507
Saio H., 1988, MNRAS, 235, 203
Saio H., 1993, MNRAS, 260, 465
Saio H., 1995, MNRAS, 277, 1393
Saio H., Jeery C.S., 2000, MNRAS, 313, 671
Saio H., Nomoto K., 1998, ApJ, 500, 388
Saer R.A., Liebert J., Olszewski E.W., 1988, ApJ, 334, 947
Schonberner D., 1983, ApJ, 272, 708
Webbink R.F., 1984, ApJ, 277, 355
Werner K., Heber U., Hunger K., 1991, A&A, 244, 437
Woolf V.M., Jeery C.S., 2000, 358, 1001