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Mon. Not. R. Astron. Soc. 341, 1141--1150 (2003)
Spectral response of the pulsationally induced shocks in the atmosphere of
BW Vulpeculae
Myron A. Smith 1# and C. Simon Jeffery 2#
1 Computer Sciences Corporation/STScI, 3700 San Martin Drive, Baltimore, MD 21218, USA
2 Armagh Observatory, College Hill, Armagh BT61 9DG
Accepted 2003 January 10. Received 2003 January 7; in original form 2002 October 11
ABSTRACT
BW Vulpeculae (BW Vul) is remarkable for exciting an extremely strong radial pulsation
mode which grows through its outer envelope and forms visible shock features in the atmo­
sphere. Material propelled upwards by the shock returns violently to the lower photosphere
where it creates a second shock just before the start of the next cycle. We have obtained
three nights of echelle data for this star over about five pulsation cycles (P = 0.201 d) in
2000 September in order to investigate the effects of atmospheric shocks on important lines
in the optical red spectrum. These lines include He I #5875 and #6678, C II ##6578--83 dou­
blet, and other moderate and high excitation lines. To these data we have added 37 archival
IUE/SWP echelle spectra obtained in 1994. We have investigated the equivalent widths and
shapes of the optical lines for evidence of inter alia lags and have compared our results to the
IUE fluxes extracted from the far­ultraviolet continuum, He II #1640, and several resonance
lines.
A comparison of He I #5875 and #6678 line profiles during the peak of the infall activity
suggests that differences in the development of a second blue lobe in the profile at this time
are due to heating and a short­lived formation of an optically thin layer above the region
compressed by the infall. This discovery and the well­known decreases in equivalent widths
of the C II doublet at the two shock phases further suggest that shock heating flattens the
atmospheric temperature gradient.
Except for evidence of wind absorption in the far blue wings of the ultraviolet resonance
lines, we find no evidence for a shock delay arriving at different photospheric strata (i.e., a
`Van Hoof effect'). Line­to­line differences in the relative strengths of double lobes can be
false indicators arising from varying degrees of desaturation of multiple lines, such as for the
red He I lines.
Key words: line: formation -- line: profiles -- shock waves -- stars: individual: BW Vul -- stars:
variables: other.
1 I NTRODUCT I ON
The # Cephei variable BW Vulpeculae (BW Vul; HR 8007,
HD 199 140; B1 V to B2 III) is in kinematic terms the largest
amplitude pulsator known in the Galaxy. Its fundamental radial pul­
sation mode (Stamford & Watson 1981; Aerts et al. 1995) is so
strongly excited as to produce discontinuous `standstill' features
in the star's light curve and, immediately following this, a longer
standstill in the radial velocity curve as well. These features result
from highly non­linear processes associated with upward propagat­
ing pulsation waves. These waves emerge into the photosphere as
# E­mail: msmith@stsci.edu (MAS); csj@star.arm.ac.uk (CSJ)
highly supersonic shocks. During the pulsation cycle, the optical
line profiles remain in absorption but undergo extreme variations in
shape and velocity. Equivalent width variations are also noticeable
at certain phases. In the often­used convention that # = 0 occurs at
light maximum (minimum radius), the radial velocity standstill be­
comes centred at # = 0.98--1.00. Line profiles exhibit double lobes
at phases just before (centred at # # 0.90), and during some cycles
just after (# # 0.06) the velocity standstill phase (e.g. Mathias et al.
1998). Adding to the complexity of description, the radial velocity
curve is sensitive to the method of measurement, the spectral and
temporal resolution of the observation, and especially to the mo­
mentary pulsational amplitude of the star, because the amplitudes
of the pulsations fluctuate by several per cent from night to night
(Crowe & Gillet 1989; Aerts et al. 1995; Mathias et al. 1998; Garnier
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1142 M. A. Smith and C. S. Jeffery
et al. 2002). The equivalent widths of some metal lines vary with
phases as a function of excitation potential (Furenlid et al. 1987).
The finite signal­to­noise ratio and temporal sampling frequency of
the International Ultraviolet Explorer (IUE) observations set prac­
tical limits on the otherwise considerable complementary ultraviolet
(UV) information that they offer to optical spectra.
Historically, controversy has surrounded the interpretations of
the profile and strength variations caused by shock waves moving
through the atmosphere of BW Vul. One of these is the so­called
`Van Hoof effect', named after its primary discoverer (Van Hoof
& Struve 1953). This characteristic is the purported phase lag be­
tween the velocity curves extracted from lines formed at different
atmospheric depths. This is thought to be the result of the finite
travel time required for a pulsational shock wave to pass through
the various line­formation strata. In a recent report, Mathias et al.
(1998) reported that double line profiles of various lines observed
near # # 0.9 and sometimes 0.1 can exhibit equal blue--red strengths
at slightly different phases.
A related issue is the cause of the line doubling itself. Odgers
(1955) and Goldberg, Walker & Odgers (1976) suggested that the
doubling occurs from velocity discontinuities below and above a
shock and suggested that this shock accelerates the line­forming
regions of the atmosphere from the lower photosphere to create a
density discontinuity. The semi­ejected `shell' coasts to some max­
imum height and returns ballistically to these lower strata. In a con­
trasting interpretation, Young, Furenlid & Snowden (1981, hereafter
YFS) suggested that turbulence and pressure effects are the chief
causes of the profile doublings at these phases. In their picture, the
standstills are caused by line formation in both a lower stationary
atmospheric region as well as an infalling zone rendered transparent
by its lower density. All these studies have pointed to the extended
displacements of the line­formation region (several per cent of a
stellar radius) and its virtual free fall from maximum to minimum
radius.
In the most recent kinematical description, Mathias et al. (1998)
and Garnier et al. (2002) have summarized the present consensus
that there are two shocks per cycle. The first, `pulsation', shock is the
result of the evolution of the upward­propagating wave which grows
in amplitude from the envelope where it is excited. As it emerges
into the atmosphere at # = 0.1, this shock has a moderately high
Mach (5--7) number, as referenced by the velocity `discontinuity'
just prior to the velocity standstill. A subsequent, `infall', shock, oc­
curring 0.8 cycles after the first, is due to the extreme compression
of the upper atmospheric strata as they fall back and catch up to
the more slowly returning layers of the lower photosphere. In this
picture, the line profiles exhibit double lobes during the main (and
often infall) shock because of the velocity jump associated with
it. Mathias et al. (1998) also note that because the density of the
atmosphere decreases monotonically outwards, the infalling region
cannot be described as a disconnected shell. In addition, they suggest
that shock progresses inward in terms of absolute (Eulerian; radius
from star centre) coordinates even as it moves outwards in mass.
Thus, their description reconciles the idea expressed by several pre­
vious authors that two outward­moving shocks per cycle propagate
up through the atmosphere. In this study, we adopt this view of
Mathias et al. (1998) that this shock is a natural consequence of
infall.
The elusiveness of even a qualitative interpretation of the shocks
in BWVul has slowed the necessary development of self­consistent
radiative hydrodynamical models. Early on, Stamford & Watson
(1978) posited that a large­amplitude velocity piston at the base of
the atmosphere developed into a thin, isothermal shock as it pro­
gressed through the line­formation region. Using this dynamical
model atmosphere, they constructed line profiles of Si III #4552 at
several key phases in the cycle. Profiles at phases we now call the
infall shock exhibited line doubling (albeit over only a brief inter­
val). In subsequent work, Stamford &Watson (1981) placed a large,
adiabatic sinusoidal velocity variation at the base of a grey model
atmosphere and demonstrated that an isothermal shock developed
in the line­formation region. Recently, Owocki & Cranmer (2002)
have developed hydrodynamic models that roughly simulate the ve­
locity and light variations of the pulsating star. Their models assume
strong outgoing shocks in realistic atmospheres. The shocks begin
in the envelope as a large­amplitude pulsation wave, break into a
small­amplitude shock in the lower photosphere, and evolve into an
isothermal, large­amplitude (60â in density) shock in the wind. The
results of Owocki & Cranmer (2002) show that the shock has the
effect of flattening the atmospheric density gradient well out into
the wind, thereby explaining the large range in phase over which
the shock can be traced in the UV resonance lines. As these waves
emerge into the wind, they can impact slower flows, causing re­
verse shocks and the formation of discrete absorption components
(DACs) in the far blue wings, indeed as observed in the Si IV and
C IV lines (Burger et al. 1982; Blomme & Hensberge 1985; Massa
1994).
The present paper was motivated partially by our impression that
an understanding of the shock wave properties has been hampered
by uncertainties in spectroscopic measurements and interpretation.
For example, YFS and Crowe & Gillet (1989) found widely dif­
ferent average equivalent widths for the important C II ##6578--82
lines. Yet the `large' values found by YFS during the distension
phases formed the basis of their conclusion that line doubling and
strengthening is caused by changes in atmospheric continuous opac­
ity. This suggestion, though oft­quoted, has gone untested. We also
realized in planning our programme that the existence of a Van Hoof
effect could be tested by comparing the responses of the red He I
#5875 (triplet) and #6678 (singlet) lines, which probe different col­
umn lengths through their gf difference, and also volume densities
because of the triplet line's mild sensitivity to density through the
partial metastability of its lower level. Other significant lines in the
red region are the Si II #6371 and Si III #5740 features, which to­
gether provide a measure of variations in the atmosphere's ionization
equilibrium. The echelle data we have obtained sample formation
conditions of many lines at the same time and thus can provide ac­
curate phasing information from this variable­amplitude pulsator.
This simultaneity permits us to remove past ambiguities in correlat­
ing behaviours of various lines at different epochs. A second reason
for undertaking this study is the availability of IUE data, which per­
mits a comparison of the behaviours of the wind and photospheric
lines.
2 OBSERVAT I ONS
2.1 Observations and reduction details
The optical data for this study were obtained on the nights of
2000 September 19--21 with the Sandiford echelle spectrograph
(McCarthy et al. 1993) attached by fiber optics to the Cassegrain
focus of the Struve 2.1­m telescope at McDonald Observatory.
60 observations were obtained during the interval HJD 245
1805.574--.581, 61 during HJD 245 1806.560--.856 and 48 during
245 1807.568--.916. The cross­dispersing prism in the spectrograph
was rotated to select a central wavelength of 6120 š
A and to include a
nearly continuous wavelength range (22 orders) of ##5510--6735 on
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Shocks in the atmosphere of BW Vul 1143
a CCD detector. This configuration resulted in a spectral resolution
of 45 000 and a pixel spacing of 2.8 km s -1 pix -1 . Signal­to­noise
ratios of 200--300 were typically attained in integration times of
5--6 min. The mid­observation times for the three nights are shown
in Table 1, while a line list of identified features in our spectra is
given in Table 2. The wavelengths and excitation potentials listed
are obtained from the Kurucz line library (Kurucz 1990).
The spectra were kindly reduced (background­subtracted, ex­
tracted, and flat­fielded) by Dr Chris Johns­Krull using computer
codes described by Hinkle et al. (2000) and Piskunov & Valenti
(2002). Wavelengths were determined by an interactive graphics
package that allowed a solution simultaneously in the echelle and
cross­dispersion axes (J. A. Valenti, private communication). So­
lutions were obtained by minimizing residuals between laboratory
and observed Th and Ar line wavelengths and iteratively rejecting
outliers. Corrections for terrestrial orbital and rotational velocities
were made. Rectification of echelle orders was performed by an in­
teractive polynomial fitting procedure. Orders were then spliced at
wavelengths for which flux contributions of adjoining orders were
equal. We measured the radial velocities of strong lines by cross­
correlating the lines against a reference line profile observed near
# = 0.2. Profiles at this phase are approximately symmetric and
exhibit an approximately mean width and thus lend themselves to
comparison with profiles of extrema phases. We determined true
equivalent widths of these lines and other analysed features in the
McDonald spectra by an interactive computer algorithm tailored for
this application. The program uses input wavelength ranges over
which both the continuum and the line's absorption profile are to
be extracted. The continuum level is then fixed by a specified `Nth
percentile brightest flux' among candidate fluxes in the continuum
window. The value of N, typically #80 per cent, can depend on the
presence of non­stellar features but is well suited to modification
interactively when such unwanted features appear as telluric lines,
cosmic rays, or fringing.
2.2 IUE spectra
In order to avoid uncertainties in the absolute calibration of fluxes,
we made use of 38 high­dispersion echellograms obtained with the
SWP camera through the large aperture during monitoring cam­
paigns on the star in 1994 October and November. `NEWSIPS' ex­
tractions were downloaded from the MAST 1 web­based archives.
We emphasize that our NEWSIPS­processed spectral fluxes are ex­
tracted by different algorithms than those used by Stickland & Lloyd
(2002), although the results are gratifyingly similar. Absorption line
strength indices (LSIs) were then calculated by ratioing the total
net (uncorrected for ripple distortion) flux in a narrow band cen­
tred at line centre to the total net flux in the parent echelle order.
Such indices are not true equivalent widths, but they are directly
proportional to them and increase with absorption strength. Be­
cause these indices are insensitive to continuum placement, and
(as defined herein) independent of errors in blaze function (`rip­
ple') correction, they are unambiguous measures of the absorption
for prescribed velocity limits, and they are particularly accurate
differential measures of line strength differences for an IUE time
series.
1 Multi­Mission Archive at Space Telescope Science Institute, under contract
to NASA.
Table 1. Journal of year 2000 observations (HJD -240 0000).
Night 1 Night 2 Night 3
September 17/18 September 18/19 September 19/20
51805.574 51806.560 51807.568
51805.579 51806.564 51807.578
51805.583 51806.569 51807.585
51805.588 51806.574 51807.593
51805.593 51806.579 51807.599
51805.597 51806.584 51807.604
51805.602 51806.589 51807.609
51805.607 51806.593 51807.613
51805.612 51806.600 51807.617
51805.616 51806.606 51807.621
51805.621 51806.612 51807.651
51805.625 51806.620 51807.655
51805.629 51806.626 51807.659
51805.633 51806.632 51807.754
51805.637 51806.638 51807.759
51805.643 51806.646 51807.764
51805.649 51806.653 51807.767
51805.653 51806.657 51807.771
51805.657 51806.662 51807.775
51805.661 51806.666 51807.781
51805.665 51806.671 51807.785
51805.672 51806.677 51807.789
51805.676 51806.681 51807.793
51805.680 51806.686 51807.797
51805.684 51806.691 51807.801
51805.688 51806.696 51807.805
51805.692 51806.701 51807.809
51805.696 51806.705 51807.813
51805.700 51806.710 51807.817
51805.704 51806.715 51807.821
51805.708 51806.720 51807.826
51805.715 51806.724 51807.830
51805.719 51806.728 51807.834
51805.723 51806.732 51807.838
51805.727 51806.736 51807.843
51805.731 51806.740 51807.849
51805.735 51806.747 51807.855
51805.739 51806.751 51807.860
51805.743 51806.755 51807.865
51805.747 51806.759 51807.871
51805.751 51806.764 51807.876
51805.759 51806.770 51807.882
51805.763 51806.774 51807.887
51805.768 51806.778 51807.893
51805.772 51806.782 51807.898
51805.776 51806.787 51807.904
51805.781 51806.791 51807.909
51805.785 51806.795 51807.916
51805.789 51806.798 --
51805.793 51806.803
51805.800 51806.808
51805.810 51806.813
51805.815 51806.818
51805.819 51806.822
51805.823 51806.827
51805.832 51806.832
51805.837 51806.837
51805.841 51806.842
51805.846 51806.847
51805.851 51806.851
51806.856
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1144 M. A. Smith and C. S. Jeffery
Table 2. Summary of atomic data for lines in McDonald spectra.
Wavelength Ion # (eV) log gf
5606.09 S II 13.8 0.16
5639.980 S II 14.1 0.33
5640.314 S II 13.8 0.15
5646.979 S II 14.1 0.11
5648.070 C II 20.8 -0.45
5639.980 S II 14.1 0.33
5640.314 S II 13.8 0.15
5659.956 S II 13.7 -0.07
5662.460 C II 20.8 -0.27
5666.629 N II 18.5 0.01
5676.017 N II 18.5 -0.34
5679.558 N II 18.6 0.28
5686.213 N II 18.6 -0.47
5696.603 Al III 15.7 0.23
5710.766 N II 18.6 -0.47
5722.730 Al III 15.7 -0.07
5739.734 Si III 19.8 -0.160
5747.300 N II 18.6 -1.020
5833.938 Fe III 18.6 0.616
5875.615 He I 21.0 0.73
6247.178 Al II 16.6 -0.20
6346.859 N II 23.3 -0.86
6371.371 Si II 8.2 0.00
6379.617 N II 18.5 -0.92
6562.801 H I 10.2 -0.69
6578.052 C II 14.5 0.12
6582.882 C II 14.5 -0.18
6678.154 He I 21.2 0.33
2.3 Radial velocity ephemeris
Although there is unanimity that BW Vul is monoperiodic (with
P # 0.201 043), some controversy has surrounded the `drifting'
of its pulsation period derived from data sets of different epochs.
Various authors have suggested ephemeris corrections for a quasi­
evolutionary lengthening, light travel time across a binary, and both
random and discontinuous changes for unspecified reasons. In past
years, support has built for the binarity solution with an orbital period
near 34 yr (Pigulski 1993; Odell 1994; Horvath, Gherega & Farkas
1998), although it appears possible that small random changes can
also alter the phase zero­points from time to time (Sterken 1993).
We have adopted the binary+secular­lengthening solution of Hor­
vath et al. for the light minimum phases. Light minimum is the
recommended new benchmark because it can be determined with
greater precision (Sterken 1993). To these calculated phases, we
have added 0.48 cycles (Furenlid et al. 1987; Stickland & Lloyd
2002) to reference them to the traditional zero at optical light max­
imum. This is also the approximate mid­point of the radial velocity
standstill. This ephemeris agrees to within 0.015 (±0.02) cycles of
the mid­point occurrence of the standstill in our McDonald data.
The relative phases of the 1995 IUE epoch did not match as well,
giving a difference of 0.09 cycles from this ephemeris relative to
the standstill occurrence found by Stickland & Lloyd. We have re­
ferred our # = 0 fiducial to the Stickland & Lloyd phase # = 0.10,
which takes into account that the latter authors tied their zero­point
to radial velocity maximum instead of the usual velocity standstill
criterion. 2
2 Note that the photometric standstill occurs just before the onset of velocity
standstill and is much shorter. These respective standstills last about 0.03
and 0.15 cycles (see e.g. Furenlid et al. 1987).
3 RESULTS
3.1 Radial velocities
A large number of radial velocity curves have been discussed for
BW Vul from as many optical data sets. We decided to focus on
the velocities of the red helium lines both to check our phase zero­
points and to search for cycle--amplitude differences during our
observations. Our mean nightly heliocentric radial velocities are
-7.7, -10.3 and -11.4 km s -1 . The resulting mean of -9.7 km s -1
is in excellent agreement the mean of -9.2 km s -1 given by Mathias
et al. (1998). In Fig. 1 the radial velocities are shown for He I #5875
for all three nights. It was possible to measure the equivalent widths
of the lines arising from highly excited atomic levels, but these
often were both weakened and broadened to invisibility during the
critical shock passage phases. Radial velocities are also given in
Fig. 1 for Si III #5740 and Si II #6371 (the latter can reliably be
measured only in the phase range 0.1 < # < 0.85). The silicon lines
have velocity amplitudes 5--10 per cent larger than the helium line
curves and even more striking discontinuities at the beginning of
the end of the standstill. The H# velocity curve (not shown) has
even a slightly smaller amplitude and less steep `discontinuities'
than the He I line curves do. We believe that these are effects of the
far wings of the helium and hydrogen lines, which tend to broaden
the cross­correlation function and produce artificially small velocity
differences for the line core.
In the upper halves of the Fig. 1 panels we exhibit the equivalent
widths of the Si II #6371 line over those phases outside the shock
intervals -- these are the times when the line was strong enough that
reliable centroid positions could be measured. On nights 2 and 3 we
see that the phases of velocity maximum extend slightly longer in
the Si II feature than in the He I line, causing a slight delay in the
onset of the standstill for the He I line curves. This delay seems to
be an artefact of a relatively `late' desaturation of the blue lobe of
the weaker Si II line, causing the line's centroid velocities to remain
at negative velocities for a longer time and to later phase than the
other lines measured (see Section 4.4).
Figure 1. Radial velocity in km s -1 determined from cross­correlations on
the He I #6678 (pluses), Si III #5740 (crosses) and Si II #6371 (asterisks) lines
of BW Vul for all three nights of this study, 2000 September 19--21. Note
that the He I velocities have been rescaled by factors of 1.10, 1.05 and 1.05 to
match the Si II line velocity amplitudes. The squares at the top of each panel
denote the reciprocal (with offsets of #+100) Si II equivalent widths; these
could not be measured for phases near zero when the two shocks occur.
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Shocks in the atmosphere of BW Vul 1145
Figure 2. Equivalent widths of He I #6678 with phase for the three nights
of study; offsets of -0.3 š
A and -0.6 š
A are introduced for visual clarity.
Approximate error bars are indicated.
3.2 Behaviour of the excited optical lines
3.2.1 The red He I lines
The accurate measurement of equivalent widths of lines in the BW
Vul spectrum is challenging because the positions, widths and core
depths vary dramatically over the cycle. We began our study by
investigating equivalent widths for the #5875 and #6678 lines. These
He I transitions are, respectively, analogue triplet and singlet 2P--3D
transitions, and each has excitation potentials of 21 eV. Although
variations of the neutral helium line have not yet been studied in this
star, their importance cannot be overstated because of the sensitivity
of the lines to atmospheric heating. Furenlid et al. (1987) reported
unambiguous evidence for a temperature rise from increases in the
ratio of a pair of O II and Fe III lines during the velocity­standstill
phase. Fig. 2 shows the variation of the true equivalent widths for
the He I #5875 and He I #6678 lines for all three nights. These plots
exhibit generally two maxima, the stronger of the two centred at
the occurrence of the infall shock at # # 0.90--0.95. The equivalent
width ratio of these lines is 1.13 ± 0.03 outside the `windows' of
the two shock intervals. Because the ratio of their atomic g f s is 2.5,
the observed ratio indicates that the features are very optically thick.
The ratio is virtually the same during the passage of two shocks.
3.2.2 C II ##6578, 6583 doublet and high­excitation lines
The C II ##6578, 6583 doublet is located close to the H# line and
arises from a similarly excited level of 14.4 eV. Thus, it has long
served as a conveniently accessible temperature probe for atmo­
spheres of variable B stars. We measured the true equivalent widths
of each of these lines in the same manner as the He I lines. These
are exhibited in Fig. 3, where we have represented the two lines by
different symbols and rescaled the equivalent widths of #6583 to
the slightly larger ones of #6578. Some of the scatter at like phases
arises from measurements at adjacent pulsation cycles. The gf ratio
of the components is 2. The observed ratios do not show evidence
of variations during the cycle, and their nightly means, 1.28, 1.14
and 1.16, show clearly that even though the lines are comparatively
weak they are quite optically thick.
Our C II doublet curves in Fig. 3 exhibit well­defined minima that
coincide in phase with the broad minimum found by Crowe & Gillet
Figure 3. C II ##6578, 6583 equivalent width curves for the three nights in
this study. The values for #6583 are scaled by factors of 1.3, 1.1 and 1.2 for
the three nights, respectively, to match the #6578 data.
(1989), except that the latter authors' data do not hint at a separation
in phase between the two individual shocks. The C II curves are also
very similar to those shown for the residual intensity of the H#
core discussed by Crowe & Gillet (1989). We have confirmed this
behaviour for the core of this line in our data and we have also
found that the equivalent widths extracted from small wavelength
windows centred on the core exhibit a similar behaviour. The effect
rapidly disappears and even inverts as we include more and more
contribution of the H# wings in the window. These results confirm
that the variations are produced by localized atmospheric strata.
Other moderate to high excitation lines such as N II #5710 (# =
18.5 eV) and S II #5640 (13.8 eV) produce variations similar to the
C II doublet, but the intrashock maxima for them are not always
so clearly separated in phase. For phases outside the two shock
intervals, many of the lines in our sample broaden and fade to below
our detection threshold.
3.2.3 Si II #6371 and Si III #5740 lines
The Si II #6371 and Si III #5740 lines are important because they
arise from atomic levels having the largest combined excitation and
ionization potentials of all the lines in our optical coverage, ex­
cept for the He I lines. In addition, their combined responses furnish
information on changes in the ionization equilibrium in this atmo­
sphere during the pulsation cycle. In investigating the strengths of
these lines, we found first that the Si III #5740 line shows only mild
increases of #10--50 per cent in equivalent width from night to night
during shock passage. This is because the ionization equilibrium of
silicon is roughly balanced between Si +1 and Si +2 . However, as
the dashed lines at the top of each of the panels in Fig. 1 show
(the reciprocals of the line strength are plotted), the response of the
Si II #6371 line can be quite pronounced. During the passage of the
second (pulsation) shock, the #6371 broadens and weakens so much
that its velocity centroid cannot be reliably measured. As indicated
in Fig. 1, the phases of maximum weakening do not coincide with
the shock passage but rather are delayed by 0.10 cycles after the end
of the standstill phase, when the strengths of the excited lines are
slowly decreasing.
Fig. 3 indicates that there are variations in shock heating and of
the inequality of amounts of heating between the two shocks. We
can see this, first, in the amplitude variations in the shocks (as judged
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1146 M. A. Smith and C. S. Jeffery
by the sharpnesses and depths of the C II minima) and, secondly, in
the variation of the strengths of the Si II line and other moderate
excitation lines, e.g. S II #5640. These diagnostics generally imply
that the temperature increase associated with the pulsational wave
is the stronger of the two shocks. This is contrary to the inequality
of the shock jumps (Fig. 1; see also Mathias et al. 1998). We also
note that the phase of equivalent width minimum is delayed by 0.07--
0.08, both with respect to the line's radial velocity minimum (Fig. 1)
and relative to the C II equivalent width minimum at # = 0.1.
3.3 Ultraviolet lines
Except for the He II 1640­ š
A line (`helium H#', # exc = 41 eV), the
UV lines used in this analysis are all resonance lines. To varying
degrees, the latter lines have components formed both in the static
line­forming region (upper photosphere) and the accelerating wind.
We will treat these lines in order of likely formation depth, starting
from the He II feature, and work our way up through ionization
potential out into the wind.
3.3.1 He II #1640
Fig. 4 depicts the extracted UV continuum (UVC; representing
##1800--1905) light curves from the 37 available large­aperture
IUE/SWP spectra obtained in 1994, together with the extracted line
strength index created from ratios of fluxes within about ±1.6 š
A of
the He II line centre to all the other net (ripple uncorrected) fluxes in
the echelle order containing the line. The detailed shape of the UVC
curve is in excellent agreement with the two plots constructed by
Stickland & Lloyd (2002) from essentially the same data. The curve
shows a broad, asymmetric maximum which may be an underre­
solved rendition of two peaks apparent in the line strength curves
at # = 0.9 and 0.1. This double­peaked structure is completely un­
resolved in optical light curves (cf. figure 3 of Stickland & Lloyd
2002). Note also that the scatter is small and does not seem to re­
flect the obvious cycle­to­cycle differences at some phases in the
radial velocity curves. The He II #1640 absorption curve is morpho­
logically very similar to the UVC curve. The curves extracted from
the blue and red halves of the profile are in turn identical to one
another. A slight kink is visible in the He II curve at # # 0.05--0.25
Figure 4. UVC fluxes at ##1850 (diamonds) and line strength index for
He II #1640 (crosses). The latter, denoted LSI, is defined in Section 2.2. UVC
fluxes are plotted relative to the mean, but 0.7 units are subtracted from the
He II LSI to separate the curves. Symbols for data above # = 1.0 are repeated
and rendered small. The dashed line through the He II curve is a reference
sinusoid; the solid line is a compressed/stretched curve around the sinusoid
(see text). Note the slight kink in the descending He II curve in the # range
0.05--0.25.
Figure 5. UVC fluxes at ##1850 (diamonds) and line strength indices
for the Al III #1855, Si III #1206 and Si IV #1394 resonance lines. The line
strengths are obtained from the central profile within about ±0.8 š
A of the
line centre and refer to the strength of the continuum. In the case of Si III and
Al III the indices are inverted because the line responds oppositely from the
other features. Error bars are indicated.
and is also reproduced in the UVC curve (Fig. 4). For clarification
we overplot two curves in Fig. 4. The first is a simple sine curve
(dashed line), and the second (solid line) is a sine curve that has been
compressed/stretched in the first and second quadrants. No matter
how we choose a fitted curve to the observed values (from three
different pulsation cycles) the dip and bump features fall outside the
error limits. Because these features are also visible in the two UVC
curves of Stickland & Lloyd, these are undoubtedly real.
3.3.2 Resonance lines of moderately excited ions:
Al III, Si III and Si IV
Fig. 5 depicts the UVC and absorption curves for the lines Al III
#1855, Si III #1206 and Si IV #1394. We have inverted the Al III and
Si III curve in these plots to facilitate a comparison among all four
curves. Curves extracted from the blue halves of the Si III and Si IV
lines have 10--20 per cent larger amplitudes than the red halves
but otherwise are similar. Note first that the Si III curve weakens
(rises) more quickly than Si IV strengths during the phase interval
0.7--0.9. [This Si III behaviour is closely tracked by the multiplet UV
4 Si III lines formed in the photosphere near #1300 and discussed
by Stickland & Lloyd (2002).] The increased sensitivity of the Si III
lines is probably a consequence of their arising from atoms of a
subordinate ion stage. To within measurement errors, these lines
(and C IV #1548 red half, see below) track the phase of the UVC
and He II #1640 curves quite closely.
Note also that as we proceed to more highly ionized species (from
Al III through to Si IV), the maximum absorptions of the excited
ions extend over longer and longer intervals. Fig. 6 demonstrates
that their long­lived character continues for the C IV #1548 and
N V #1238 (blue half only) features. For these lines, we see that
this plateau extends to # # 0.4, which is some 0.3 cycles after the
shock passes through the photospheric line­formation regions of
C IV and N V. Experimentation with extractions along the C IV profile
indicates that as we include more and more blue wing (wind absorp­
tion) in the measurement, the onset and extension of the maximum­
strength phase shifts to later and later phases. Thus, this appearance
of the shock as a long­lived feature in the wind is responsible for the
positive phase shift of the `C IV blue' and `N V blue' curves relative
to the `C IV red' plot in this figure.
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Shocks in the atmosphere of BW Vul 1147
Figure 6. UVC fluxes (diamonds) and line strength indices for Si IV #1394,
C IV #1548 and N V #1238, either blue or red portions of the profile, as
indicated. The windows sampled are about ±0.8 š
A around the line centre.
Error bars are indicated.
4 D I SCUSS I ON
4.1 `Phase lags' reinterpreted
The combination of optical and UV resonance line results requires
a picture which integrates the effects of the pulsation and infall­
generated shocks. Figs 4, 5 and 6 record the differences in UV line
responses with increasing ionization potential. Massa (1994) has
depicted the acceleration of C IV, Si IV and Si III in grey­scale IUE
1979 spectra. These spectra show that the wind features start 0.1
cycles after the passage of the pulsation wave through the photo­
sphere. The photospheric and wind components of C IV are at times
co­mingled, but otherwise there is no hint of a graduated response
through the photosphere. Rather, there seem to be separate responses
from two discrete `photospheric' and `wind' regions. In particular,
continuum fluxes and lines of high excitation, such as He I, He II
and Si III, show no perceptible phase differences in their velocity
or line strength responses. Even the line strength minima of the
moderate excitation C II doublet (# = 14 eV) seem to coincide with
the appearance of the shocks just prior to and following the end of
the velocity standstill. These lines collectively span a large range in
excitation. Lines arising from less excited levels than 14 eV, such
as the resonance lines of Al III or moderate excitation lines of Si III
(Stickland & Lloyd 2002), cannot be measured precisely enough in
IUE spectra to search for phase lags with respect to the optical lines.
In fact, we find that in order to see any obvious indication of a phase
lag after the passage of the excited lines we must search in the far
blue wings of the resonance lines. Perhaps this should not be a sur­
prise. According to the simulations of Owocki & Cranmer (2002),
the UV absorption features form over length­scales much longer
than the effective depth of the static line­formation region. Thus,
there is ample column length over which shock­induced features
can develop.
If there are no phase delays among the excited optical lines, what
are we to make in Fig. 1 of the apparent phase delay of 0.07--0.08
after the Si II #6371 curve? We believe the key here is that Si +1 is
a trace atmospheric ion, which is therefore sensitive to temperature
and not that its mean line­formation region is so high in the atmo­
sphere that it takes the shock a finite time to reach it. Consider as
a more plausible circumstance that the formation regions of most
optical lines largely overlap. The so­called `delayed' weakenings of
the Si II feature may more easily represent the subsequent passage
of a cooler medium. We have in mind the post­shock region which
is cooler and more tenuous than the shock interface (Liberman &
Velikovich 1986). A strong post­shock rarefaction is clearly visible
in the hydrodynamic simulations of Owocki & Cranmer (2002) and
indicates a rough `half­wavelength' of #0.25 cycles. From this result
we might anticipate the effects of a rebound shock having approxi­
mately this delay. Altogether, we can speculate that the marginally
visible kinks in the UVC and He II strength curves at # # 0.23 are
produced by a small temperature enhancement due to the rebound. In
this picture the abrupt­appearing end of the UVC maximum would
be the result of particles entering the cooled post­shock flow.
4.2 Blue wing strengthenings (moderate velocities)
To gain some insight into the cause of the equivalent width variations
of the red He I lines exhibited in Fig. 2, we examined the shapes of
the two lines as a function of phase. Fig. 7 illustrates that the cause
of the equivalent width maximum of #5875 at # = 0.9 on each
night is a strengthening of the blue wing. In these plots we exhibit
this fact by multiplying the depth of #6678 on the blue wing (and
also extreme red wing) by a factor of 1.4 to 1.8. Fig. 7 shows that
blue wings of #6678 scaled by these factors indeed replicate the
#5876 absorptions at this phase. We see this phenomenon over a
total range of 0.08--0.10 cycles centred on radial velocity maximum
(# # 0.91) on each of the three nights. In these various examples,
the limiting line­depth scaling factor appears to be about 2.0. As this
is also the gf ratio of the lines, it is likely that these extra absorptions
are due to the medium at negative velocities being optically thin to
He I line radiation. An alternative possibility, that the excess arises
from metastability of #5875, is implausible because no such excess
absorption is present in this line during the distension (low­density)
phases at # # 0.5.
If temperature variations cause the changes in the blue wings of
the He I lines, there should be a similar response in the inner blue
wing of the C IV doublet members -- the cores of the Si IV lines are too
Figure 7. Profile for the red #5876 (dashed) and #6678 (solid) He I lines,
which have an atomic gf ratio of 2.5:1, at a phase near # = 0.90 on each of
three nights. This ratio is ameliorated slightly by a wavelength dependence
of continuous opacity. Thus, we have also depicted the #6678 feature scaled
by a factor of 2 (dotted line), as well as this same feature (thick dot­dashed)
scaled by the indicated scale factor given next to the solid dot. This figure
suggests that the `excess absorption' of the blue segment of both lines is
due to optical thinness of the line at negative velocities. The lines seem to
be strictly optically thin (ratio of 2) up to about -30 km s -1 on `night 3'
(September 21).
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1148 M. A. Smith and C. S. Jeffery
Figure 8. Montage of C IV profiles (#1550 overplotted on to #1548) at # #
0.9, showing the optical thinness of the low velocity blue wing at this phase.
The observations, SWP 52 644­5 & SWP 52 880, were taken in 1994 -- the
first two on HJD 244 9650.2 and the third on HD 244 9679.8.
broad to demonstrate this. Fig. 8 implies that the absorption­scaling
argument is likely to be valid, i.e. that an excess absorption at about
-100 km s -1 of the line centre is caused by an optically thin column
at these shifted wavelengths. (By `excess', as for the He I lines in
the previous figure, we refer to the absorption in the blue wing of
the stronger #1548 line relative to #1550.) The grey­scales of Massa
(1994, see Fig. 3) exhibit this same effect -- as a low­velocity `spur'
occurring #0.1 cycles before the wind acceleration manifests itself
at more negative velocities.
4.3 C II line strength variations
The reader will recall that YSF first drew attention to C II varia­
tions during the cycle of BW Vul and posited that the C II variations
were the result of the lines growing anomalously strong outside
the shock phases. To test this assertion, we have synthesized the
C II doublet with the Hubeny SYNSPEC (Hubeny, Lanz & Jeffery
1994) line synthesis code using Kurucz (static!) model atmospheres.
For an atmosphere having T eff = 23 000 K, log g = 4,
and# t =
5 km s -1 , we found an equivalent width of 0.22 š
A, for #6578 and
a #6578/#6583 ratio of 1.14. We obtain nearly identical results for
log g = 3. These values compare well with our mean observed
#6578 equivalent width value of 0.235 ± 0.015 š
A for phases out­
side the shocks and with the corresponding mean observed ratio of
1.19. Our modelling also shows that the strengths of these lines are
quite insensitive to changes in temperature in the domain 20 000--
25 000 K. The models do not confirm the speculation by YSF that
changes in atmospheric density play a strong role in determining the
line strength changes during the cycle. Of course, the line strengths
will increase appreciably with any microturbulence that might ac­
company the shocks, so this would not explain the decrease during
these phases. The upshot of these calculations is that the decreases
in C II strengths observed at shock phases cannot be due to simple
changes in atmospheric temperature or density. Thus, our results
suggest that the question to pose is not `why are the C II strengths
large during the non­shock phases?', but rather `why do the C II
strengths decrease to smaller values than they should have dur­
ing shock phases?' The question is critical to a discussion of the
shocks in BW Vul's atmosphere because the effects of temperature
increases are obvious for other lines but lead to a contradiction for
the response of the C II features. Adding additional turbulence from a
shock would make the disagreement worse by forcing the predicted
absorptions to be larger.
4.4 Physical effect of the shocks on the He I and C IV lines
If enhancements of neither temperature nor turbulence can explain
the line weakening, let us consider instead the effect of a flattening
of the temperature gradient with atmospheric depth, particularly in
the construct of a local thermodynamic equilibrium (LTE) Milne--
Eddington atmosphere. In this formulation the strengths of weak
lines should simply be proportional to the gradient dT /d# . To in­
terpret the enhanced absorptions in the blue wings of the He I lines
(and possibly C IV) at # = 0.9, we should also consider the heating
effects from infall of material above where a line is being formed.
At this phase, upper strata are returning toward the surface at nearly
free­fall velocities (Furenlid et al. 1987). Strata just below them fall
slightly more slowly, and so on, down to the fully­braked stationary
layers. These combined decelerations produce compression over a
broad range of layers. The result of this pile up is a conversion of
differential flow velocity to local heating. Indeed, this effect can be
observed as the first maximum of the UVC and He II line strength
curves at # = 0.85--0.1 (i.e. at velocity maximum) and by the disap­
pearance of the cool­gas diagnostic, Si II #6371, at the same times.
Heating will increase the number of atoms in excited states and thus
should permit new optically thin absorption to appear in the excited
He I lines. This absorption is formed in a still­falling column which
is still high enough in the atmosphere to be optically thin to an exter­
nal observer. Most of the initial column density will be concentrated
near the shock, so the lobe will appear at near­rest velocities. As this
pile up proceeds, the threshold column density needed for visibility
will recede (moving upward, in Eulerian coordinates), permitting
the optically thin absorption in the profile to grow toward positive
velocities until it runs into and merges with the optically thick red
lobe. The process ceases when the deepest layers essentially at rest
become optically thick to the observer. At this point, just after phase
0.0, the entire profile becomes optically thick over a broad distri­
bution of line velocities, both from the still­falling column and the
strata at rest at the bottom. The standstill phase ends quickly as the
material in the falling column is suddenly exhausted -- the optical
depth turns thin and to zero very quickly at wavelengths in the red
lobe of the profile.
During the infall phase, the velocity gradient can be expected to
increase among the superficial, cooler layers, causing proportionally
more heating there. Thus, the weakening of the C II doublet (first
dip in Fig. 3) is consistent with a flattening of the gradient of the
atmospheric temperature and line source functions. 3 Indeed, in the
expectation of accompanying increased turbulence, it seems difficult
to understand how the weakening could arise in any other way. The
second dip of the C II curve features coinciding with the passage
of the pulsation shock can be explained by a more fundamental
characteristic: the shock has a tendency to be more nearly isothermal
than in the pre­shock atmosphere.
The above picture is sketched qualitatively in Fig. 9. This illustra­
tion depicts the evolution of the stellar radius (top) and the absorption
profiles (bottom) during five phases (#), including one just before
and one just following the primary shock passage interval. These
line shapes may be compared to those in Fig. 7 or figure 1 of Mathias
et al. (1998) and are additionally indicated as having blueshifted,
redshifted and/or stationary components. The five central panels
3 A fact which may bear on this discussion is that to reproduce UV spec­
trophotometic signatures from line aggregates in BW Vul's IUE/SWP cam­
era spectra, Smith (2001) found it necessary to impose arbitrarily an artificial
steepening of the temperature gradient for a simulated model atmosphere at
minimum light phase. This is equivalent to imposing a flattening of the
gradient in the maximum light phase, as suggested from this optical study.
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Shocks in the atmosphere of BW Vul 1149
Figure 9. Schematic illustration of the formation of the He I #5876 line
profile as it evolves through radius minimum. The top panel suggests the
overall behaviour of the stellar radius. The five bottom panels approximate
the apparent line profile (F(#)) at five specific phases (#). The centre of
each panel corresponds to the rest wavelength of the line (tick marks). The
composite line profiles (solid lines) are decomposed into blueshifted (black
rectangle) and redshifted (/ shading) and optically thick components, and
the unshifted optically thin component (â shading). The five vertical panels
in the centre illustrate (i) the relative positions (z: horizontal lines) and (ii)
motions (vectors) of six specific Lagrangian zones in the atmospheres, (iii)
the position relative to these layers where the monochromatic optical depth
# (#) # 1 (black dotted line), and (iv) the location where each component
of line absorption is likely to be strongest (shaded rectangles). Thus, for
# = 0.86, the optically thin stationary component (â shading) is formed
below the optically thick redshifted component (/ shading). These profiles
should be compared with those in Fig. 7, and also with fig. 1 of Mathias et al.
(1998). This figure is available in colour in the online version of the journal
on Synergy. In the online version of the figure, the redshifted components
(/ shading) are coloured red, the unshifted components (â shading) are
coloured green and the blueshifted component (solid) is coloured blue.
show a representation of several notional `layers'. From left to right,
these are shown to be falling inwards (arrows), and then arrested and
reversed by material moving upwards from beneath. Compression
gives rise to heating and a flattening of the temperature gradient.
In turn, this gives rise to absorption in optically thin layers (# =
0.86), represented by a shaded rectangle (â). Other line compo­
nents are also represented, displaced according to whether they are
formed in outflowing (blueshifted, solid), stationary (no shift, â
shaded) or infalling (redshifted, / shaded) material. The zero ve­
locity reference position or, equivalently, the rest wavelength for
the absorption line is marked at the bottom of each panel. On
the basis of observations presented here, a dashed line indicates
where the atmosphere becomes optically thick across the line profile
(# # = 1). Whether absorption lines are formed in optically thick or
thin layers is suggested by their proximity to this curve. In any case,
while admitting the omission of critical details of transfer of pho­
tons across the profile as the line as it turns optically thick, it appears
possible that we can understand the formation of the excess opti­
cally thin absorption in the blue wing of the He I lines as well as the
weakening of the temperature­sensitive C II and Si II lines.
Suffice it to say that in contrast to the infall shock the heating
associated with the infall shock in our picture will extend over a
broader range of strata in the atmosphere at any given moment than
heating from the primary shock. If the UVC and He II and Si II line
curves are to be taken as diagnostics of atmospheric heating, the
pulsation shock is more impulsive and liberates more heat per unit
time than the infall shock. In contrast, according to the equivalent
width curves of Si II #6371, the heating from the infall shock not
only lasts longer, but by differing amounts from cycle to cycle. This
suggests that the details of this heating are driven by the strength
of the earlier pulsation wave. Also, as noted in Section 3.2.3, the
velocity jump criterion leads to the opposite inequality of apparent
shock strengths, with the radial velocity jump to the standstill (infall
shock) being typically larger than the jump at the end of the stand­
still (primary shock). Because the velocity and equivalent width
variations measure different types of shock properties, this apparent
disagreement of the inequalities need not be a contradiction to the
model.
5 CONCLUS I ONS
Our primary results may be summarized as follows. From optical
radial velocities we find:
(i) The cycle­to­cycle change of radial velocity amplitudes is
confirmed in our data (Section 3.1). These variations may explain
occasional differences in standstill attributes (e.g. their mean radial
velocity).
(ii) At # # 0.9, the anomalously strong blue lobes in the He I
#5876 and #6678 lines produce departures of the velocity curve
relative to curves extracted from weaker lines which suggest that the
differences in onset of the first velocity discontinuity are attributable
to this profile peculiarity (Section 3.1).
From UV data we conclude:
(iii) UVC flux and He II line strength curves track each other and
the red halves of various resonance lines well. There seems to be
no systematic phase difference between them, suggesting that for
practical purposes they are formed at nearly the same atmospheric
depth (Section 3.3; Fig. 4).
(iv) These same two curves with phase depart from sinusoidal
form, in particular showing a kink just after the passage of the pri­
mary shock (Fig. 4).
From optical line strengths we find:
(v) The C II doublet and Si II #6371 weaken during shocks,
i.e. they do not become anomalously strong at other phases
(Section 3.2.1, Fig. 3).
(vi) The C II doublet strength ratio remains strongly optically­
thick­like during shock passage; the lines do not desaturate
(Section 3.2.2).
(vii) The blue lobes of the He I lines grow during the infall shock
phases (Fig. 7). This is consistent with their being in an optically
thin column, even though these atoms are at rest velocity and are
likely at the deeper layers of the infall process (cf. Fig. 9).
(viii) The C IV and Si IV lines seem to show similar blue­lobe
effects at these phases (Section 4.4).
(ix) Transient blue lobes clearly can form in some lines more
strongly than others, whether for reasons of temperature sensitiv­
ity or line strength. This can masquerade as a phase­delay through
atmospheric strata (a `Van Hoof effect').
Points (v)--(vii) suggest that both infall heating and differen­
tial velocities through the atmosphere are critical in producing the
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1150 M. A. Smith and C. S. Jeffery
double lobes during shock passages. [Our explanation has some
commonality and differences with both the models of YFS and
Mathias et al. (1998)]. The heating during the infall shock is likely
to be distributed across a range of atmospheric layers, which would
produce the shallow temperature slope (relative to the slope in a
static B star atmosphere) required to explain simultaneously the
weakening of the C II doublet lines and the strengthening of the blue
lobes of the He I lines. The quantitatively similar heating implied
by the C II and Si II lines weakenings likewise suggests a tendency
of the temperature gradient to become shallow as well. We hope
to carry out future work to evaluate what temperature gradients are
needed to fit the C II and He I line/lobe strengths and to learn what
is required of ab initio hydrodynamic atmospheric models.
ACKNOWLEDGMENTS
We wish to express our thanks to the members of the McDonald
TAC for their granting of three nights of 2.1­m telescope time. We
are also grateful to Dr Chris Johns­Krull for his reductions of the
McDonald data to echellogram format. We thank Dr Jeff Valenti
for the loan of his interactive wavelength calibration program and
Mr Anthony Valenti for his time and instructions on the use of this
program.
REFERENCES
Aerts C., Mathias P., Van Hoolst T., De Mey K., Sterken C., Gillet D., 1995,
A&A, 301, 781
Blomme R., Hensberge H., 1985, A&A, 148, 97
Burger M., de Jager C., van den Oord G. H., Sato N., 1982, A&A, 107,
320
Crowe R., Gillet D., 1989, A&A, 211, 365
Furenlid I., Young A., Meylan T., Haag C., Crinklaw G., 1987, ApJ, 319,
264
Garnier D., Nardetto N., Mathias P., Gillet D., Fokin A. B., in Aerts C.,
Bedding T., Christensen­Dalsgaard J., eds, ASP Conf. Ser. Vol. 259,
Radial &Nonradial Pulsations as Probes of Stellar Physics. Astron. Soc.
Pac., San Francisco, p. 206
Goldberg B. A., Walker G. A. H., Odgers G. J., 1976, AJ, 81, 433
Hinkle K., Wallace L., Valenti J., Harmer D., eds, 2000, Visible & Near­
Infrared Atlas of the Arcturus Spectrum. Astron. Soc. Pac., San Francisco
Horvath A., Gherega O., Farkas L., 1998, Rom. A. J., 8, 89
Hubeny I., Lanz T., Jeffery S., 1994, Newslett. Anal. Astron. Spectra, 20, 30
Kurucz R. L., 1990, Trans. IAU, 20B, 169
Liberman M. A., Velikovich A. L., 1986, Physics of Shock Waves in Gases
and Plasmas. Springer­Verlag, Berlin
Massa D., 1994, Ap&SS, 221, 113
Mathias P., Gillet D., Fokin A. B., Cambon T., 1998, A&A, 339, 525
McCarthy J. K., Sandiford B. A., Boyd D., Booth J., 1993, PASP, 105, 881
Odell A. P., 1994, Inf. Bull. Variable Stars, 4138
Odgers G. J., 1955, Pub. Dom. Ap. Obs., 10, 215
Owocki S. P., Cranmer S. R., 2002, in Aerts C., Bedding T., Christensen­
Dalsgaard J., eds, ASP Conf. Ser. Vol. 259, Radial and Nonradial
Pulsations as Probes of Stellar Physics. Astron. Soc. Pac., San
Francisco, p. 512
Pigulski A., 1993, A&A, 274, 269
Piskunov N. E., Valenti J. A., 2002, A&A, 385, 1095
Smith M. A., 2001, ApJ, 562, 998
Stamford P. A., Watson R. D., 1978, Publ. Astron. Soc. Aust., 3, 273
Stamford P. A., Watson R. D., 1981, Proc. Astron. Soc. Aust., 4, 210
Sterken C., 1993, A&A, 270, 259
Stickland D., Lloyd C., 2002, Observatory, 122, 33
Van Hoof A., Struve O., 1953, PASP, 65, 158
Young A., Furenlid I., Snowden M. S., 1981, ApJ, 245, 998 (YFS)
This paper has been typeset from a T E X/L A T E X file prepared by the author.
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