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Although pulsations in EHes appear to be ubiquitous, it is not
possible to summarize their properties with a single definition.
Three groups may be identified; future observations will no doubt add
to these.
V652Her variables - ``Z-bump'' pulsators. The first
discovery of pulsation in an EHe was made by Landolt (1975), who
discovered a 0.1day photometric period in V652Her, 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
, 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 flux at the lower boundary exceeds the outgoing
flux at the upper boundary, i.e. the radiation flux is blocked. This
occurs if the increase in opacity caused by the compression increases
outwards, i.e.
. The opacity
variation due to a nearly adiabatic pulsation is given as
Prior to 1990, all attempts to model the pulsation in V652Her 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 V652Her (Saio & Jeffery
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
K
(Rogers & Iglesias 1992, Seaton et al. 1994). The opacity peak due
to iron-group elements, often referred to as the ``Z-bump'', can have
a similar effect to the Heii opacity peak at lower
temperatures, particularly if the hydrogen-abundance is low. Saio
(1993) showed that a `finger of instability' exists for helium stars
with
K and which also have a sufficiently high
metallicity and luminosity, such as V652Her.
V652Her lies right in the middle of this finger of instability, as
do two other stars: HD144941 and LSS3184. If ``Z-bump'' instability
was responsible for pulsations in V652Her, then these other stars
should also pulsate with similar periods
day.
Observations of HD144941 failed to find any evidence of variations
(Jeffery & Hill 1996), but this was easily explained by its very low
metallicity
(Harrison & Jeffery 1997, Jeffery & Harrison
1997). Prompted by Saio's (1995) prediction, Kilkenny & Koen (1995)
discovered a 0.1day photometric period in LSS3184=BXCir and
with radial velocities the radial pulsations have been more fully
characterized by Kilkenny et al. (1999). The metallicities of
V652Her and BXCir have been measured as
(Jeffery et al.
1999) and
(Drilling et al. 1998) respectively.
Jeffery & Saio (1999) have explored the extent of the Z-bump
instability finger for radial and non-radial pulsations in terms of
mass, metallicity and hydrogen abundance and have shown that it is
principally quenched if metallicity is too low (
) or if
the hydrogen abundance is too high (
), for masses in the
range 0.3-0.9
. Since other hot helium-rich subdwarfs lying
close to this Z-bump finger are known, it is possible that more
V652Her variables 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, FQAqr, led to the discovery of small-amplitude
(
) photometric variations with an apparent period of
about
day (Jeffery & Malaney 1985). Subsequent observations
confirmed the variations, but the period was ambiguous (Jeffery et
al. 1986). More recently, five years worth of data demonstrated that
variations persist on a characteristic timescale of
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
(Lawson et al. 1993).
Similar properties have since been detected in a number of other EHes
including PVTel, NOSer, V2244Oph, V354Nor and V1920Cyg
(cf. Lawson et al. 1993). This group all have
K
, low surface gravities and
day
, 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
ratios. Dubbed `strange' modes, the pulsations are primarily
associated with regions of density inversion, such as the Heii
ionization zone (Saio et al. 1998). Strange modes are
characteristically different to
-modes since their frequencies
change rapidly with stellar parameters (e.g.
). For EHes and
RCrBs, two consequences noted by Saio & Jeffery (1988) are that (i)
the stability criterion is effectively provided by the
ratio,
and (ii)
and
are related approximately linearly.
The extreme non-adiabacity of EHe envelopes provides a possible
explanation 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, effectively,
lose phase coherence, even though the local characteristic timescale
will be unchanged. The failure of nonlinear
calculations of RCrB models to show limit cycles (Saio & Wheeler
1985) supports this proposal, whilst Fadeyev (1993) found considerable
disagreement between the results of linear and non-linear
calculations. Further non-linear calculations for PVTel and RCrB
variables are required.
V2076Oph variables - non-radial ``strange'' mode
pulsators. The most luminous EHes with
K are also
small-amplitude variables. The light curves of V2076Oph and
V2205Oph are considerably more complicated than those of the PVTel
variables and have shorter characteristic timescales of
day
and
day respectively (Lynas-Gray et al. 1987, Jeffery et
al. 1985). It appears that the variations are multi-periodic, and that
the characteristic timescales are longer than anticipated for radial
fundamental or first harmonic pulsations. The conclusion is that both
stars pulsate non-radially, possibly in a low-order
-mode. Radial
velocity measurements support this conclusion, with line-profile
variations in V2205Oph indicating
or 3 (Jeffery & 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 first harmonic, but a
much higher-order mode (Saio & Jeffery 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
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 V2076Oph and
V2205Oph. 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 difficulty concerns both the multi-periodicity and the extreme non-adiabacity of the pulsations. Existing observations need to be substantially 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.
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