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Mon. Not. R. Astron. Soc. 000, 1{15 (0000) Printed 1 November 1999 (MN L A T E X style le v1.4)
The evolution of a rapidly accreting helium white dwarf to
become a low-luminosity helium star
Hideyuki Saio 1 and C. Simon Je ery 2
1 Astronomical Institute, School of Science, Tohoku University, Sendai 980, Japan
2 Armagh Observatory, College Hill, Armagh BT61 9DG, Northern Ireland
Accepted . Received ;
ABSTRACT
We have examined the evolution of merged low-mass double white dwarfs which be-
come low-luminosity (or high-gravity) extreme helium stars. We have approximated
the merging process by the rapid accretion of matter, consisting mostly of helium, onto
a helium white dwarf. After a certain mass is accumulated, a helium shell ash occurs,
the radius and luminosity increase and the star becomes a yellow giant. Mass accre-
tion is stopped arti cially when the total mass reaches a pre-determined value. As the
helium burning shell moves inwards with repeating shell ashes, the e ective temper-
ature gradually increases as the star evolves towards the helium main sequence. When
M r
( ame) ' 0:25 M , the star enters a regime where it is pulsationally unstable. We
have obtained radial pulsation periods for these models.
These models have properties very similar to the pulsating helium star V652 Her.
We have compared the rate of period change of the theoretical models with that ob-
served in V652Her as well as its position on the HR diagram. We conclude that the
merger between two helium white dwarfs can produce a star with properties remark-
ably similar to those observed in at least one extreme helium star, and is a viable
model for their evolutionary origin. Such helium stars will evolve to become hot subd-
warfs close to the helium main sequence. We also discuss the number of low-luminosity
helium stars in the Galaxy expected for our evolution scenario.
Key words: stars: evolution, stars: helium, stars: pulsation, stars: individual
(V652 Her)
1 INTRODUCTION
The major question concerning the evolutionary origin of
extreme helium stars is whether they are the products of
single-star or binary-star evolution. Extreme helium stars
(EHes) are rare B- and A-type giant stars with extremely
low surface abundances of hydrogen (Je ery 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,
Je ery, Hill & Heber 1999).
The task of stellar evolution theory is to explain how
these stars acquired their unusual characteristics. The task
has been diфcult 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: Web-
bink 1984, Iben & Tutukov 1984) considered the accretion
of a white dwarf (WD) secondary onto a white dwarf pri-
mary, resulting in the ignition of a helium shell in the ac-
creted envelope which forces the star to expand to become
a cool giant. Subsequent evolution would follow the canon-
ical 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 re-
maining near the surface of a star at the end of AGB evo-
lution was of such a mass that a nal thermal pulse would
occur after the star had become a white dwarf, also forc-
ing the star to expand rapidly. Again, subsequent evolution
would resemble the canonical post-AGB sequence.
The LTP model has been studied extensively in re-
cent years (Iben & MacDonald 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 reproduc-
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0000 RAS

2 H. Saio & C.S.Je ery
ing a wide range of surface compositions, from s-process ele-
ments 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 & Je ery 1996). The LTP model has also been sup-
ported by the rapid evolution from WD to cool giant ob-
served in V605 Aql (Pollacco et al. 1992), FG Sge (Herbig
& 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.
Methods to study the consequences of MBWD systems
have been developed by considering evolutionary models for
accreting white dwarfs (Saio & Nomoto 1998). In these mod-
els, once suфcient accretion has occurred, nuclear reactions
are ignited in a shell and propagate into the degenerate core
via a series of mild ashes. Whilst the general properties of
such models for both CO and He WDs have been considered
(Saio & Nomoto 1998, Iben 1990), it is necessary to examine
their detailed properties within the context of observational
constraints.
It is the purpose of this paper to present evolution mod-
els for accreting helium white dwarfs with nal masses in the
range 0:5 0:8M . These models, including their pulsation
properties, are compared with observational data for low-
luminosity extreme helium stars. In doing so, it is demon-
strated that the MBWD model for the origin of EHe's is
viable in at least one highly-constrained case.
2 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; Te ) for
V652 Her which tightly constrain evolution models.
The e ective temperature log Te = 4:370  0:025
(Lynas-Gray et al. 1984) adopted here was based on ul-
traviolet 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 Je ery
et al. (1999) give a slightly higher e ective 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 Je ery 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 = 8:3  10 9 d (Kilkenny & Lynas-Gray
1982, Kilkenny et al. 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.
Je ery et al. (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 ni-
trogen, indicating that it primarily comprises the residue
of CNO-processed material. There is some residual hydro-
gen,  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 char-
acterized 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 these observations,
Je ery (1984) constructed models of a 0.7 M mass helium
star contracting towards the helium main-sequence. Whilst
able to reproduce the observed properties of V652 Her suc-
cessfully, it was diфcult to account for the initial conditions
adopted for the evolution sequence { a `helium-rich horizon-
tal branch' model { within single-star evolution theory.
The LTP model introduced above provides an attrac-
tive 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 degenerate carbon-oxygen core. For such stars, the lu-
minosity is determined principally by the core mass (Jef-
fery 1988). Detailed models of thermally-pulsing post-AGB
stars (Blocker & Schonberner 1997) with masses 0.625 and
0:836 M have luminosities log L=L  3:8 and 4.2 re-
spectively. A somewhat older model for a 0:553 M post-
AGB star exhibiting a late thermal pulse was given by
Schonberner (1983). The pulse drives the star through a red
loop in the HR diagram and, in the range log Te = 4:3 4:4,
the star achieves luminosities log L= L  3:15 and 3.4
on the expanding and contracting branches, respectively.
The rates of period change at these locations would be, for
P = 0:108 day, approximately dP=dn = +3  10 7 d and
dP=dn = 6  10 8 d.
None of these models is consistent with the observed di-
mensions of V652 Her. Following the most recent measure-
ment of log g (Je ery et al. 1999), the allowed mass and
luminosity ranges (1) are M=M = 0:57 0:84 and
log L=L = 2:91 3:15. These are not fully independent,
since either limit on the measured radius (from Baade's
method, Lynas-Gray et al. 1984) leads to equivalent lim-
its on M / gR 2 and L / R 2 T 4 . At best, if M=M = 0:57,
then log L= L = 2:91 is 0.5 dex lower than the luminosity
of the 0.55 M LTP model on its contracting branch.
Pulsation properties place even tighter constraints upon
the dimensions of V652 Her (Je ery & Saio 1999). Thus, for
example, if the luminosity were only as high as log L=L =
3:15, the observed pulsation period would require the mass
to be greater than 0.9 M , in direct confrontation with the
spectroscopic properties. The implication is therefore that
V652 Her cannot have a degenerate CO core and that an
alternative evolutionary model must be found.
3 EVOLUTION MODELS
We have calculated evolutionary models starting with a
low-mass white dwarf rapidly accreting helium-rich mate-
rial (Y = 0:98; Z = 0:02). For the initial accretion phase,
which is considered as a rough approximation of the merg-
ing 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. Ini-
tial masses (M i ) of white dwarfs considered are 0.3 M and
0.4 M . The accretion was stopped when the total mass in-
creased to a pre-determined nal mass. Considering that the
nal mass should be smaller 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 ,
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Merged binary white dwarf evolution 3
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)
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 e ective temperature (upper panel).
The abscissa presents time after the rst helium ignition. The
initial mass is 0.4 M for both cases.
6000 8000
0.3
0.4
0.5
0.6
Figure 3. The location of convective regions during accretion of
helium by a 0.4 M helium white dwarf. The convective zones
in the interior occur during helium shell ashes. The extent of
the surface convection zone re ects the e ective temperature at
the surface. The zones are only shown for each timestep in the
model sequence; the gaps between models are longer between than
during shell ashes.
and M f = 0:6 and 0.5 M for M i = 0:3 M . The compu-
tational method is the same as in Saio & Nomoto (1998)
except that opacities have been obtained from OPAL95 ta-
bles (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 evolution-
ary tracks for the other cases are similar. The triple-alpha
reaction is ignited at Mr = 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 en-
velope, 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. Evolu-
tionary tracks after the accretion phase are shown by solid
(M f = 0:7 M ) 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 repeat-
ing shell ashes as described by Saio & Nomoto (1998).
Figure 2 shows the temporal variation of the mass coor-
dinate of the helium-burning shell, Mr( ame), and the ef-
fective temperature. Each ash phase corresponds to each
sudden change in Mr( ame) in Fig 2 (see also Fig 3). As
the ame moves inward, the e ective temperature increases
gradually, although it uctuates due to shell ashes. When
Mr( 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 Mr  0:25 M , and about 10 6 y
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0000 RAS, MNRAS 000, 1{15

4 H. Saio & C.S.Je ery
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.
We note that the accretion rate, 1  10 5 M yr 1 , is
considerably higher than any considered for HeWDs by Saio
& Nomoto (1998). Considerable mass is accumulated before
the star leaves the yellow giant region. For the models of Saio
& Nomoto (1998) signi cant mass accumulated only after
the star approaches the helium zero-age main sequence.
Convective regions occur above the helium-burning
shell during shell ashes and at the surface during the most
redward excursion of the evolutionary tracks (Fig. 3). 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 he-
lium main sequence pass near the position of V652 Her. The
luminosity of models in inter- ash phases around the posi-
tion of V652 Her is mainly determined by the mass interior
to the helium-burning shell, i.e., Mr( ame). This is the rea-
son 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 (Je ery 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 nor-
mal extreme helium stars. This property seem to appear in
the luminosity-frequency histogram for extreme helium stars
shown by Je ery (1996).
4 RADIAL PULSATIONS
Since many extreme helium stars show pulsations, and since
the primary comparison 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 evolu-
tionary tracks and obtained complex eigenfrequencies us-
ing the linear non-adiabatic radial pulsation code described
by Saio (1995). The real part of the eigenfrequency gives
the period, and the imaginary part gives the stability of
the mode. 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 Te  4:43 and the rst overtone is over-
stable in the range 4:34  log Te  4:43 for M f = 0:7 M .
These ranges are almost independent of M f . Near the posi-
tion of V652 Her, both fundamental and rst overtone pulsa-
tions are overstable in the linear analysis. However, the rst
overtone 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; Je ery & 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.
0.05 0.1 0.15 0.2
­1.5
­1
­0.5
0
0.5
1
Figure 4. 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).
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 numerical di erentiation.
Figure 4 shows the period change (in days) per cycle (n),
dP=dn = P (dP=dt), as a function of period P for the over-
stable 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.
The position of V652 Her in the P dP=dn plane is
shown in Fig. 4 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 . Table 1 shows the properties of
those models which have a period of P = 0:108d for all the
cases considered in this paper. In this table t is the time past
after the mass accretion stopped, and d 2 P=dn 2 the second
time derivative of the period. In some cases, the period of
V652 Her is realized more than once during its evolution be-
cause of expansion/contraction due to helium shell ashes
(see Fig. 4). Table 1 shows that all the models have sur-
face gravities consistent with spectroscopic analysis by Jef-
fery et al. (1999). Although the rst solution of 0.5 M and
the third solution of 0.6 M with M i = 0:4 M give values
of dP=dn consistent with observation, the luminosities and
the e ective temperatures are slightly lower than those of
V652 Her determined by Lynas-Gray et al. (1984). The lu-
minosity and the e ective temperature are consistent with
the cases of 0.7 M and 0.8 M with M i = 0:4 M .
In addition to the cases M f = 0:5 M and M f = 0:6 M
with M i = 0:4 M , a model having a mass slightly larger
than 0.5 M with M i = 0:3 M would also have the observed
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0000 RAS, MNRAS 000, 1{15

Merged binary white dwarf evolution 5
Table 1. Period change rates when P = 0:108d
M=M t(10 4 yr) log L=L log T e log g dP
dn (d) d 2 P
dn 2
(d)
M i = 0.4 M
0.50 4.1 2.766 4.337 3.67 -1.26E-08 1.05E-14
0.50 4.3 2.679 4.315 3.67 9.70E-09 5.02E-15
0.50 5.4 2.834 4.355 3.68 -2.14E-08 1.31E-14
0.50 5.9 2.691 4.318 3.67 9.92E-09 2.38E-15
0.50 7.0 2.853 4.359 3.67 -1.61E-08 -4.14E-15
0.50 8.1 2.711 4.323 3.67 3.94E-09 -6.07E-17
0.50 8.8 2.836 4.355 3.67 -3.02E-09 7.39E-17
0.60 5.0 2.801 4.330 3.69 -6.89E-09 1.85E-15
0.60 6.7 2.751 4.317 3.69 3.31E-09 2.29E-16
0.60 7.8 2.849 4.341 3.68 -8.06E-09 1.39E-15
0.7 6.1 2.921 4.347 3.70 -5.24E-09 6.37E-16
0.8 4.6 3.006 4.358 3.72 -3.43E-09 2.62E-16
M i = 0.3 M
0.50 0.3 3.012 4.401 3.68 -1.47E-08 5.39E-15
0.60 1.3 2.929 4.362 3.69 -2.53E-09 8.24E-17
V652 Her: Lynas-Gray et al. (1984), Kilkenny et al. (1996), Je ery et al. (1999)
0.7 3.03 4.370 3.68 -8.3E-09 1.7E-14
0.05 0.1 0.15 0.2
­1.5
­1
­0.5
0
0.5
1
Figure 5. The second time derivative of the period versus period
for 0.7 and 0.6 M (M i = 0:4 M ) cases. The crossed square
indicates the observed period and second derivative for V652 Her
(Kilkenny et al. 1996).
dP=dn (Table 1). We should note, however, that the time
since the termination of accretion is very short ( <  10 4 y) for
M i = 0:3 M . This is because the rst helium ignition occurs
relatively deep at Mr = 0:28 M and consequently when the
e ective temperature is higher. Such a short interval after
the accretion phase might con ict with the absence of any
infrared excess around V652 Her (Lynas-Gray & Kilkenny
1986).
As table 1 indicates, the e ective temperature and the
luminosity for P = 0:108 d tend to be higher for smaller M i .
An initial mass slightly less than 0.4 M may be better for
the progenitor of V652 Her. We infer that the best model,
in terms of dP=dn and the position on the HR diagram,
would be obtained by adopting an initial mass slightly less
than 0.4 M and a present mass between 0.6 M and 0.7 M ,
which is consistent with spectroscopic estimates.
Table 1 shows that 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 discrep-
ancy is not clear. One possible explanation may be that the
location of the helium-shell ash in the P d 2 P=dn 2 dia-
gram is sensitive to the initial conditions and nal mass. It
appears that d 2 P=dn 2 varies suфciently both during and be-
tween helium-shell ashes that a closer agreement is possible
(Fig. 5).
5 DISCUSSION
We have calculated rapidly accreting white dwarf models as
a rough approximation for what would be expected when a
low-mass double white dwarf binary system coalesce. Sev-
eral short-period low-mass double white dwarf systems are
known to exist (Sa er, 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
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0000 RAS, MNRAS 000, 1{15

6 H. Saio & C.S.Je ery
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 . Such a
binary system loses angular momentum due to gravitational
wave emission 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 coales-
cence 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 sce-
nario to produce low-luminosity extreme helium stars viable.
The merger frequency of double HeWD systems in the
Galaxy is theoretically 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 e ec-
tive temperatures in a range of 4:3  log Te  4:5 (Je ery
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 frequency, 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 num-
ber 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 esti-
mated 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 vol-
ume 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 distributions 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 et al.
1998), LSIV+6 ф 2 (Je ery 1998), and HD 144941 (Harrison
& Je ery 1997). Combining this number with the above mul-
tiplying 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
(Je ery et al. 1999), is consistent with our models. Since
the rst ash was so strong, the outer boundary of the con-
vective shell reached close to the surface. In the convective
shell, 3% (by mass) of the helium was converted to car-
bon. 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 at-
mosphere (Fig. 3).
Another low-luminosity extreme star, LSS 3184, has
very similar properties ( Te 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) has shown
that its atmosphere contains CNO-processed matter and
carbon from helium burning. Such a chemical 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.
The surface gravity of LSS 3184 ( log g = 3:35) determined
by Drilling, Je ery & Heber (1998) is smaller than that of
V652 Her (log g = 3:68  0:05) determined by Je ery et al.
(1999). This may indicate that LSS 3184 has a mass smaller
than that of V652 Her.
A more puzzling problem is that V652 Her retains a
small concentration of hydrogen ( 0:2% by mass, Je ery
et al. 1999). In a non-turbulent spherically symmetric merg-
ing process, the accreted material would settle on top of
any residual hydrogen envelope possessed by the progeni-
tor 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 sur-
face of the merged product, or substantial mixing could oc-
cur throughout the surface layers during the merger process.
Only  10 3 M of hydrogen-rich material in the progeni-
tor system, mixed through the product envelope, would be
required to explain the hydrogen observed in V652 Her. Two-
dimensional calculations which include some surface hydro-
gen 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.
Following their passage through the Z-bump instabil-
ity zone, the subsequent evolution of our mass-accreted he-
lium 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 sur-
faces, they might be expected to appear as subdwarf O or
B stars.
Subdwarf B stars are generally recognized to be he-
lium 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 sub-
dwarf 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 (Je ery 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.
6 CONCLUSION
We have examined the merged binary white dwarf hypothe-
sis for the origin of low-luminosity (or high-gravity) extreme
c
0000 RAS, MNRAS 000, 1{15

Merged binary white dwarf evolution 7
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 he-
lium star V652 Her. We have obtained the pulsation periods
and their time derivatives for models along the evolution-
ary 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 be-
tween 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; fur-
ther detailed modeling should indicate that these discrepan-
cies can be resolved. We have also found that the predicted
number of low-luminosity helium stars in the Galaxy is con-
sistent with observation.
We conclude that the merged binary white dwarf hy-
pothesis, 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.
ACKNOWLEDGEMENTS
This research has been supported by the British Coun-
cil through Collaborative Research Grant TOK/880/41/4
and by the Department of Education in Northern Ireland
through a grant to the Armagh Observatory.
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