Äîêóìåíò âçÿò èç êýøà ïîèñêîâîé ìàøèíû. Àäðåñ îðèãèíàëüíîãî äîêóìåíòà : http://star.arm.ac.uk/preprints/307c.ps Äàòà èçìåíåíèÿ: Tue Mar 7 13:49:27 2006 Äàòà èíäåêñèðîâàíèÿ: Mon Oct 1 22:00:35 2012 Êîäèðîâêà: Ïîèñêîâûå ñëîâà: massive stars

Workshop on Binary and Variable Stars
Gunma Astronomical Observatory, 1999
Evolutionary Constraints Imposed by Pulsations in
Extreme Helium Stars
Simon Jeery
Armagh Observatory, College Hill, Armagh BT61 9DG, Northern
Ireland
Abstract. Extreme helium stars are highly evolved luminous stellar
remnants. Their exotic surface abundances point to previous evolution
through the white dwarf sequence, followed by re-ignition due to a late
helium shell ash or to a binary merger. The existence of pulsations in
many helium stars, due to strange-mode instabilities or the Z-bump -
mechanism, provide a range of diagnostics including radii from Baade's
method and contraction rates from period changes. I review the basic
observational and theoretical properties of extreme helium star pulsations
and show how these have been used to constrain evolutionary models,
with particular reference to the cases of V652 Her and BX Cir.
1. Extreme Helium Stars
The late stages of stellar evolution are characterized by extremes. Stellar struc-
ture and surface properties change much more rapidly than during earlier phases
of evolution. A star will reach its highest luminosity and, often, its highest eec-
tive temperature shortly before it nally becomes a white dwarf. Mass-loss and
mixing may expose highly-processed material on the stellar surface, resulting in
the formation of chemically peculiar stars. The latter are distributed over most
of the Hertzsprung-Russell diagram; one of the most extreme examples is pro-
vided by the extreme helium stars (EHes) { early-type supergiants practically
void of hydrogen in their atmospheres.
The remarkable hydrogen-deciency of an EHe is demonstrated by the weak-
ness of its H line. In the case of a normal B star, such as Peg, this typically
broad line dominates the local spectrum. In the case of the extreme helium
star LSE 78, H is almost completely replaced by a blend of S iii and O ii ab-
sorption lines. The eective temperatures of these two stars are 21,500 K and
18,000 K respectively (Peters 1976, Jeery 1993), so that the ionization balance
of their photospheres will not be dissimilar. Hydrogen constitutes less than
10 5 parts by number in LSE 78. A direct consequence of the low hydrogen
abundance is that the continuum opacity, normally dominated by hydrogen, is
reduced. Although the abundances of species other than helium and carbon are
not signicantly dierent from solar, the metal line spectrum is correspondingly
magnied several fold.
This paper introduces the principal properties of extreme helium stars. S-
ince their surface compositions imply an unusual evolutionary history, I review
the principal scenarios currently considered. Stellar mass is critical to a correct
1

2
Figure 1. T g diagram for hydrogen-decient stars including RCrB
stars (: Asplund et al. 2000), EHe stars (: Jeery 1996, Pandey
1999), low gravity helium-rich sdO stars (HesdO + , : Husfeld et al.
1989), [WC] stars (: Hamann 1996, assuming M = 0:6 M ), PG1159
stars (: Werner et al. 1996), high-gravity HesdO stars (HesdO , /:
Dreizler 1993), helium-rich sdB stars (HesdB, .: Heber et al. 1988),
DO white dwarfs (4: Dreizler & Werner 1996), and DB white dwarfs
(5: Wegner & Nelan 1987). The Eddington limit, loci of constant
L=M , and hydrogen and helium main sequences (H-MS, He-MS) are
also shown.

3
interpretation of stellar evolution, so methods for its measurement are compared.
The importance of pulsations in providing masses and other characteristics of
helium star evolution is demonstrated, with particular reference to the radial
pulsations in V652 Her and BX Cir.
2. Stellar Properties
The characteristic surface properties, eective temperature T , surface gravity
g and composition X, of EHes have been summarized by Jeery (1996). The
distribution of EHes in the T g plane is shown in Fig. 1 together with the
location of other H-decient stars, notably the putatively related RCrB stars.
It may be seen that they lie roughly along a locus given by log L=M  4, which
also corresponds to the evolution track of post-AGB stars, contracting towards
the white dwarf track. This has guided most of discussion of their evolutionary
status within the context of post-AGB evolution.
The surface compositions of EHes vary considerably from star to star, but
may be brie y summarized as follows 1 .
Hydrogen: ( 4:6 < log nH < 0:8) The fact that some hydrogen is found in
the atmospheres of nearly all EHes indicates that some remnant of the outermost
hydrogen-rich layers of the progenitor has been retained.
Helium: (0:9 < n He < 1:0) By denition, helium dominates the atmospheric
abundances.
Nitrogen: (0:4 < [N=F e] < 1:2) Nitrogen is enriched in most EHes, implying
that helium has been produced by CNO cycling. If all nitrogen comes from such
a source, it should re ect the total C+N(+O) abundances in the progenitor.
This is supported by a correlation between N and Fe abundances in EHes.
Carbon: (0:9 < [C=F e] < 2:0) Carbon is substantially enriched in nearly all
EHes, indicating the presence of material processed through 3 helium burning.
Oxygen: ( 0:6 < [O=F e] < 0:8) Since nN indicates the destruction of oxygen,
nearly all observed oxygen has probably been produced by 12 C(; ) 16 O. The
O/C ratio should therefore provide a diagnostic of conditions in the C-rich layers
of the progenitor. Observed O/C ratios do not approach the value expected in
CO cores, except in two cases (DY Cen and LSE 78).
Iron: The iron abundances fall approximately into two groups (with the excep-
tions of DY Cen and HD144941) clustered about [F e]  0:0  0:1 and [F e] 
0:9  0:2. It remains to be seen whether the bimodal distribution of iron
abundances persists to the complete EHe sample.
Consequently, any model for the origin of EHes must result in a surface
mixture which includes a remnant of the hydrogen envelope, predominantly
CNO-processed helium and a signicant quantity of 3 and 12 C+ products, as
well as reproducing the overall dimensions such as luminosity, mass and eective
temperature.
1 Abundances are referred to as (i) nX = relative abundance of species X by number, (ii) log nX
= log of above, (iii) [X] = log nX=nX , representing log abundance relative to solar and (iv)
[X=F e] = log( nX=nFe )=( nX=nFe ) , representing the same scaled to allow for the dierence
between the stellar and solar iron abundance.

4
3. Evolution Models
Several scenarios have been proposed to account for the depletion of surface
hydrogen in extreme helium stars. Those which may be successful in producing
extremely hydrogen-poor surfaces are the following:
Case BB mass transfer in a binary. Following main-sequence evolution, a red
giant star in a close binary system may expand to ll its Roche lobe. Transfer-
ring mass to the less massive companion (Case B) will reduce but not remove the
H-rich envelope. If core-helium burning is completed before the secondary com-
pletes its main-sequence evolution and the primary expands to the giant region
for a second time, then a further phase of mass transfer (case BB) can complete-
ly remove the H-rich envelope, exposing CNO-processed helium (Plavec 1973,
Schonberner & Drilling 1983). Although Iben & Tutukov (1984) used this model
to account for the EHes, the latter are not binaries (Jeery et al. 1987). Case
BB mass transfer does account successfully for the observations of hydrogen-
decient binaries such as  Sgr and KSPer.
Final helium-shell ash in a post-AGB star. The model proposed by Iben et al.
(1983) derives from evolutionary calculations of post-AGB stars. At some point
during contraction from the AGB to the white dwarf (WD) track, some models
were found to experience a late thermal pulse { or helium-shell ash. The energy
output of this last shell ash causes large-scale mixing and a brief expansion of
the envelope to giant dimensions. Strong evidence that such late shell ashes
do occur comes from three objects, V652 Aql, FG Sge and V4334 Sge, all of
which have been observed to evolve from faint blue star to a red supergiant
on timescales of 3 { 50 years. In the case of V652 Aql, contraction after the
shell ash to the WD track was also rapid. Recently, more detailed evolutionary
calculations have been carried out for WDs which experience a late shell ash
(Herwig et al 1999). The post-expansion tracks have been compared favourably
with observations of other H-decient objects including some central stars of PN
([WC] stars) and very hot pre-WDs (PG1159 stars). All of these objects have
a surface carbon abundance of  10% or greater. If the nal shell- ash model
successfully explains such stars, the question is whether it can also explain EHes,
with  1% carbon abundances and apparently slower evolutionary timescales.
Merger of CO and He white dwarf. While most proposed models for EHes invoke
post-AGB evolution, the model introduced by Webbink (1984) is completely d-
ierent. A binary system with appropriate initial masses and orbital separation
can evolve to the point where both stars are WDs, one being a carbon-oxygen
WD of  0:6 M , the other a helium WD of 0.3{0.4 M , with an orbital period
in the range 1{10 hours. Over a long interval, the orbital angular momentum can
be reduced by a combination of gravitational-wave radiation and magnetic-wind
braking to the point at which the less massive WD lls its Roche lobe. Tidal
disruption will follow on a dynamical timescale, the WD being transformed in-
to a thick disk around the more massive companion. Accretion from the disk
onto the surviving WD creates a star with a degenerate CO core and a helium
envelope. Depending on the accretion rate, helium may be ignited either explo-
sively (slow accretion) or quiescently (fast accretion), resulting in either a type

5
Ib supernova or a helium giant (Iben & Tutukov 1985). Numerical models for
the mergers of two CO WDs and two He WDs have been computed (Saio &
Nomoto 1998, Saio & Jeery 2000), but the CO+He case has yet to be treated
successfully.
Other models. Schonberner (1986) discusses a variety of unsuccessful models
which have been proposed at one time or another. Only the nal- ash and
WD-merger models currently seem capable of reproducing most of the observed
properties of EHes.
4. Masses
To test whether any evolutionary model is correct, reliable tests are required.
These include a detailed comparison between models which predict evolution
tracks and surface composition for a given stellar mass and accurate observa-
tions of stellar compositions and dimensions. Stellar compositions, temperatures
and gravities can be measured relatively simply, but measuring mass is less s-
traightforward. There are three principal approaches.
Spectroscopic Mass M S . Suppose some physical mechanism connects the mass
M of the star to its luminosity L, such as the mass-luminosity relation for main-
sequence stars or a core-mass shell-luminosity relation for shell-burning stars.
From spectroscopy and model atmospheres, the eective temperature T and
surface gravity g of the star can be measured. Since L=M / T 4 =g, then the
spectroscopic mass M S of the star may be deduced using an appropriate M L
relation (e.g. Jeery 1988).
Pulsation Mass MP . Stellar pulsations provide much more powerful tools for
determining stellar masses. Fortuitously, pulsations appear to be common a-
mongst EHes (see next section). The most straightforward approach is provided
by pulsation periods  obtained from photometry. Linear theory provides theo-
retical pulsation periods for stellar models of given M;T and L. In conjunction
with spectroscopic measurements of T and g,  can provide an estimate of the
pulsation mass MP .
Direct Mass MD . In some cases, it may be possible to measure the angular
radius () and radial velocity (v) of a pulsating stars throughout the pulsation
cycle. v may be integrated to yield the total radius change ôR. ô= gives the
relative radius change. The stellar radius R is then given by R = ôR=(ô=).
Following Baade (1926) and combining the radius with g from spectroscopy and
model atmospheres yields the direct mass MD / g=R 2 .
5. Pulsation Properties
Although pulsations in EHes appear to be ubiquitous, it is not possible to sum-
marize their properties with a single denition. Three groups may be identied;
future observations will no doubt add to these.

6
V652 Her variables { \Z-bump" pulsators. The rst discovery of pulsation in an
EHe was made by Landolt (1975), who discovered a 0.1 day photometric period
in V652 Her, and by Hill et al. (1981), who measured the radial velocity curve
and demonstrated the variations were due to radial pulsation. The pulsation
is strictly periodic with regular light and radial-velocity curves. The discovery
enabled Lynas-Gray et al. (1984) to deduce a direct mass MD = 0:7 +0:4
0:3 M ,
whilst Kilkenny & Lynas-Gray (1982) discovered that the pulsation period was
shrinking in a manner consistent with a secular contraction. These properties
will be examined later.
Radial pulsations are mostly driven by the  mechanism. This occurs in a
zone which gains thermal energy as it is compressed and loses thermal energy
as it expands. A zone gains thermal energy if the incoming radiation ux at
the lower boundary exceeds the outgoing ux at the upper boundary, i.e. the
radiation ux is blocked. This occurs if the increase in opacity caused by the
compression increases outwards, i.e. d[ô]=dr > 0. The opacity variation due to
a nearly adiabatic pulsation is given as
ô = @
@
ô + @
@T
ôT =

@
@

d
dT

ad
+ @
@T

ôT :
Therefore, neglecting the spatial variation of ôT , d[ô]=dr > 0 when ôT > 0
(i.e. compression) is an approximate formal condition for -mechanism driving
in nearly adiabatic pulsations. The occurrence of strong opacity peaks at an
appropriate depth in the stellar envelope is an important criterion for such pul-
sations. In classical Cepheids, with T  7; 000 K, driving is provided by the
He ii opacity peak at  40; 000 K.
Prior to 1990, all attempts to model the pulsation in V652 Her found the
star to be stable. While stars hotter than the classical Cepheid instability strip
could show radial pulsations, this was only true if they were considerably more
luminous than V652 Her (Saio & Jeery 1988, see below). This problem was
overcome with the calculation of stellar opacities which more correctly included
the contribution of iron-group elements at temperatures around 210 5 K (Rogers
& Iglesias 1992, Seaton et al. 1994). The opacity peak due to iron-group ele-
ments, often referred to as the \Z-bump", can have a similar eect to the He ii
opacity peak at lower temperatures, particularly if the hydrogen-abundance is
low. Saio (1993) showed that a `nger of instability' exists for helium stars with
T  20 000 K and which also have a suôciently high metallicity and luminosity,
such as V652 Her.
V652 Her lies right in the middle of this nger of instability, as do two other
stars: HD144941 and LSS 3184. If \Z-bump" instability was responsible for
pulsations in V652 Her, then these other stars should also pulsate with similar
periods  0:1 day. Observations of HD144941 failed to nd any evidence of
variations (Jeery & Hill 1996), but this was easily explained by its very low
metallicity Z = 0:0003 (Harrison & Jeery 1997, Jeery & Harrison 1997).
Prompted by Saio's (1995) prediction, Kilkenny & Koen (1995) discovered a
0.1 day photometric period in LSS3184=BX Cir and with radial velocities the
radial pulsations have been more fully characterized by Kilkenny et al. (1999).
The metallicities of V652 Her and BX Cir have been measured as Z = 0:016
(Jeery et al. 1999) and Z = 0:007 (Drilling et al. 1998) respectively.

7
Jeery & Saio (1999) have explored the extent of the Z-bump instability
nger for radial and non-radial pulsations in terms of mass, metallicity and hy-
drogen abundance and have shown that it is principally quenched if metallicity
is too low (Z <  0:002) or if the hydrogen abundance is too high (X >  0:5), for
masses in the range 0.3{0.9 M . Since other hot helium-rich subdwarfs lying
close to this Z-bump nger are known, it is possible that more V652 Her vari-
ables remain to be discovered.
PVTel variables { radial \strange" mode pulsators. One of the brightest EHes,
PVTel was considered to show irregular brightness and radial velocity variations
on timescales of weeks, months and years (Walker & Hill 1985). More systematic
observations of another EHe, FQ Aqr, led to the discovery of small-amplitude
( 0 m : 1) photometric variations with an apparent period of about 21 day (Jeery
& Malaney 1985). Subsequent observations conrmed the variations, but the pe-
riod was ambiguous (Jeery et al. 1986). More recently, ve years worth of data
demonstrated that variations persist on a characteristic timescale of  21 day,
but with no long-lasting coherent period (Kilkenny et al. 1999). These variations
are accompanied by small-amplitude velocity variations of a few km s 1 (Lawson
et al. 1993).
Similar properties have since been detected in a number of other EHes
including PVTel, NO Ser, V2244 Oph, V354 Nor and V1920 Cyg (cf. Lawson et
al. 1993). This group all have 8 000  T=K  15 000, low surface gravities and
7  = day  25, where  here represents the characteristic timescale.
Variability of similar character but longer  has been recorded in RCrB
stars and associated with radial pulsations for some time. These pulsations are
reviewed by Lawson & Kilkenny (1996). Whilst RCrB pulsators are relatively
cool, EHes are considerably hotter than, for examples, classical Cepheids. Lying
to the blue of the classical instability strip, their pulsations are a consequence
of the extremely non-adiabatic conditions in the envelopes of stars with high
L=M ratios. Dubbed `strange' modes, the pulsations are primarily associated
with regions of density inversion, such as the He ii ionization zone (Saio et al.
1998). Strange modes are characteristically dierent to -modes since their
frequencies change rapidly with stellar parameters (e.g. M;T ). For EHes and
RCrBs, two consequences noted by Saio & Jeery (1998) are that (i) the stability
criterion is eectively provided by the L=M ratio, and (ii)  and T are related
approximately linearly.
The extreme non-adiabacity of EHe envelopes provides a possible expla-
nation for their quasi-periodic behaviour. If the start and end states for each
pulsation cycle are not identical, each cycle will not resemble the previous cycle
exactly in either amplitude or duration. Over time, the oscillation will forget
its history or, eectively, lose phase coherence, even though the local charac-
teristic timescale will be unchanged 2 . The failure of nonlinear calculations of
RCrB models to show limit cycles (Saio & Wheeler 1985) supports this propos-
al, whilst Fadeyev (1993) found considerable disagreement between the results
of linear and non-linear calculations. Further non-linear calculations for PVTel
2 This is actually the description of chaotic behaviour in a mechanical system.

8
and RCrB variables are required.
V2076 Oph variables { non-radial \strange" mode pulsators. The most luminous
EHes with T > 20 000 K are also small-amplitude variables. The light curves of
V2076 Oph and V2205 Oph are considerably more complicated than those of the
PVTel variables and have shorter characteristic timescales of 0:7 1:1 day and
3 9 day respectively (Lynas-Gray et al. 1987, Jeery et al. 1985). It appears
that the variations are multi-periodic, and that the characteristic timescales
are longer than anticipated for radial fundamental or rst harmonic pulsations.
The conclusion is that both stars pulsate non-radially, possibly in a low-order
g-mode. Radial velocity measurements support this conclusion, with line-prole
variations in V2205 Oph indicating m = 2; l = 2 or 3 (Jeery & Heber 1992).
Linear radial pulsation theory indicates that these stars should be unstable
to strange-mode pulsations. However, the most unstable radial mode is no longer
similar to the fundamental or rst harmonic, but a much higher-order mode
(Saio & Jeery 1988). Glatzel & Gautschy (1992) investigated non-adiabatic
non-radial pulsations in a limited helium star evolution sequence, and found
strange-mode instabilities at temperatures up to the limit of their study at
T  20 000 K. The similar appearance of the instabilities for radial and non-
radial pulsations suggests that non-radial strange-modes may be responsible
for the variability in V2076 Oph and V2205 Oph. However the models used by
Glatzel & Gautschy (1992) are less evolved than these stars are likely to be. An
important experiment will be to perform linear non-radial pulsation analyses for
any evolution models constructed to explain the origin of these EHes.
A major observational diôculty concerns both the multi-periodicity and the
extreme non-adiabacity of the pulsations. Existing observations need to be sub-
stantially improved both in sampling rate and duration in order to fully resolve
the frequency structure of the light curves. However, if the quasi-periodicity of
radial pulsations in cooler stars extends to the hotter non-radial counterparts,
frequency analyses of long data trains will be doomed from the outset. The
observation and modelling of non-radial pulsations in extremely luminous stars
(including EHes) presents a major challenge for astrophysics.
6. V652 Her and Merged Binary White Dwarf Models
As already indicated, V652 Her is an important EHe star because its relative-
ly short pulsation period and large amplitude pulsations allow its overall di-
mensions to be determined with high precision. The pulsation properties have
been determined from visual and ultraviolet spectrophotometry and from spec-
troscopy by Landolt (1975), Hill et al. (1981), Lynas-Gray et al (1984) and
Jeery & Hill (1986). The simple saw-tooth shape of the radial-velocity curve
implies that the pulsation can be divided quite simply into a short impulse phase
lasting < 0:1 cycles, followed by a near free-fall phase for the remainder of the cy-
cle. Combining these data, Lynas-Gray et al. (1984) obtained a direct measure-
ment of the radius R = 2:0  0:2 R and mass MD = 0:7 +0:4
0:3 M . A renement
of the measurement of g led Jeery et al. (1999) to obtain MD = 0:690:15 M ,
with T = 24 450  500 K, log g = 3:68  0:05 (cgs) and L  10 3 L . In contrast
to most EHes, V652 Her is nitrogen rich and carbon and oxygen poor, implying

9
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 2. Illustration of the merged-binary white dwarf evolution
model for V652 Her (Saio & Jeery 2000).
that its surface is predominantly CNO-processed. The period change discovered
and rened by Kilkenny & Lynas-Gray (1982,1984) and Kilkenny et al. (1996)
translates into a contraction rate _
R=R  2:10 4 yr 1 , together with nonlinear
terms 
R and ...
R .
With a lower luminosity and a purely CNO-processed surface, the evolu-
tionary status of V652 Her has long been regarded as possibly quite dierent to
most EHes. Jeery (1984) constructed a set of highly articial \helium horizon-
tal branch models" in which a 0.5 M helium-burning core was surrounded by
an envelope with a very low hydrogen abundance. Because of the low hydrogen-
abundance, the luminosity of the H-burning shell at the core-envelope interface
was very high and the star evolved rapidly towards the helium main-sequence.
Whilst able to match M; L; T ; _
R and surface composition, these models could
only suggest a possible structure for V652 Her, rather than explain its origin.

10
Other highly articial models in the horizontal-branch family have been con-
structed, notably by Sweigart (1997), but fail to provide either a hydrogen-poor
surface or a self-consistent explanation of their origin. Similarly, no \nal- ash"
models have been computed which match the observed properties of V652 Her.
Saio & Nomoto (1998) made the rst successful models for the merger of
two carbon-oxygen white dwarfs, and prompted Saio & Jeery (2000) to attempt
models for the merger of two helium white dwarfs. Following orbital decay, the
less massive white dwarf in a double-degenerate suers total tidal disruption
on a dynamical timescale; the debris forms a thick disk around the surviving
white dwarf. The latter then accretes matter from the disk until the envelope is
suôciently massive that nuclear reactions, in this case 3 burning, are initiated
at the core-envelope interface. At this point, the star expands to become a cool
helium giant. Heating of the core surface by the nuclear-burning shell, or ame,
lifts the local electron-degeneracy so that the ame migrates inwards. Because
the ame migration proceeds stepwise, the surface evolution follows a series of
loops of increasing T and decreasing L, until the ame reaches the core centre,
whereupon the star assumes the structure of a helium main-sequence star or hot
subdwarf. A schematic of the evolution is shown in Fig. 2.
The evolution sequence for a 0.476 M helium white dwarf accreting 0.233 M
helium-rich debris passes exactly through the observed locus for V752 Her. To
within the numerical uncertainty of the calculations, this model also has the
correct pulsation properties,  and _
. As yet, the higher order terms 
R and ...
R
(Kilkenny et al. 1996) cannot be reproduced.
Table 1. Mass estimates (in M ) for PVTel variables from (i) spec-
troscopy M S using the M c L s relation from Jeery (1988), (ii) pul-
sation periods MP (Saio & Jeery 1988) and (iii) direct measurement
MD (Jeery et al. 2000).
Star M S MP MD
HD168476=PV Tel 0.95 0.85 0.82
BD+1 ô 4381=FQ Aqr 1.09 0.93 0.03
LSIV{1 ô 2=V2244 Oph 0.66 0.94 0.76
7. Direct Masses for BX Cir and PVTel Variables
The discovery of BX Cir with properties very similar to V652 Her and the sub-
sequent analysis of its light and velocity curves gave Kilkenny et al. (1999) the
opportunity to derive its radius using Baade's method. However, in conjunction
with the Drilling et al. (1998) value for log g, their results yielded MD = 0:15 M ,
a value that is diôcult to accept. A new study using AAT echelle spectroscopy
and HST spectrophotometry promises to revise this value upwards (Woolf &
Jeery, in preparation).
Measuring MD for the PVTel variables poses considerable diôculties. Since
the pulsations are not strictly regular, comparing angular and radial variations

11
Figure 3. The ultraviolet and radial velocity behaviour of
HD168476=PV Tel (from Jeery et al. 2000). From top to bottom,
the four panels show the variation of T e , , F IUE and v. Superim-
posed on each is a sine curve; the period for all four ts is indicated in
the top panel, the phase and amplitude were obtained from an inde-
pendent least-squares t to each set of data (solid curves). The dashed
curve represents the product of the ts  2 T e
4 scaled to the same mean
value as F IUE .

12
requires that observations be obtained simultaneously. Moreover the radial-
velocity amplitudes are small, the periods are long, and ultraviolet photometry
is essential. In spite of these constraints, Jeery et al. (2000) succeeded in
obtaining nearly contiguous ultraviolet photometry and radial velocities (v) of
three PVTel variables. Analysis of the UV photometry provides measures of
T ;  and . Fitting  and v with sine curves provides estimates of their mean
amplitudes, and hence their mean radii. The data for PVTel is shown in Fig. 3.
These provided remarkably convincing estimates of MD in two cases, albeit with
signicant errors. The failure of the method in the third case (FQ Aqr) could
be a consequence of its low T , but highlights the fact that the data are far from
ideal. It is interesting to compare the three masses M S ; MP ; MD for the three
PVTel variables in our sample (table 1).
8. Summary
The highly-processed surfaces of extreme helium stars point to an extremely
unusual evolutionary history. In order to test candidate theories it is necessary
to make reliable measurements of, in particular, stellar masses. Three methods
are available; all depend on a measurement of the surface gravity g. The spec-
troscopic mass M S requires a suitable mass-luminosity relation. The pulsation
mass MP is obtained from a pulsation period and linear pulsation theory, and
the direct mass MD is provided directly by the pulsation properties.
Data now exists to provide direct masses for ve EHes. That for V652 Her
is well established and agrees well with evolution models involving the merger
of two helium white dwarfs. The result demonstrates that pulsations are an
essential and successful tool for determining the evolutionary origin of extreme
helium stars.
Direct masses for PVTel and V2244 Oph agree well with the spectroscopic
and pulsation masses, although much may be done to reduce the errors. Further
painstaking observations and analyses are also required for BX Cir and FQ Aqr.
Acknowledgments
The author is grateful to the organizers of the Workshop on Binary and Vari-
able Stars for their kind invitation to give this review, and to Hideyuki Saio
and Vincent Woolf for their critical comments on the manuscript. The British
Council and the Japanese Society for the Promotion of Science have sponsored
some of the research reviewed through their UK { Japan Exchange Programmes
in Science & Technology.
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