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1997MNRAS.285..645K
Mon. Not. R. Astron. Soc. 285, 645-650 (1997)
A new class of rapidly pulsating star - II. PB 8783
C. Koen/ D. Kilkenny/ D. O'Donoghue,2 F. Van Wyk1 and R. S. Stobie 1
'South African Astronomical ObseIVatory, PO Box 9, ObseIVatory 7935, Cape, South Africa
2Departrnent of Astronomy, University of Cape Town, Rondebosch 7700, South Africa
Accepted 1996 October 15. Received 1996 October 8; in original fonn 1996 May 9
ABSTRACT
Some 27 h of high-speed photometric monitoring of the sdB + star PB 8783 has
revealed it to be a rapidly pulsating star of the EC 14026 class. Six periodicities in the
range 120 to 135 s have been tentatively identified in the light curve. The pulsation
amplitudes of all the modes are small, mostly below 5 mmag. Spectrograms show the
star to be composite, and UBVRIJHK photometry indicates that the companion to
the subdwarf is of early-F spectral type.
Key words: binaries: general - stars: individual: PB 8783 - stars: oscillations - stars:
variables: other.
1 INTRODUCTION
In Paper I of this series (Kilkenny et al. 1997), a new class of
rapidly pulsating sdB stars, the EC 14026 stars, was
announced. To date, more than half a dozen of these stars
have been discovered. Observations of four of these are
now sufficient for publication (Kilkenny et al. 1997;
O'Donoghue et al. 1997; Stobie et al. 1997b). Three of the
well-observed EC 14026 stars were drawn from the Edinburgh-Cape (EC) Blue Object Survey (Stobie et al. 1997a),
while the fourth, the topic of this paper, is the previously
known sub dwarf PB 8783 (Berger & Fringant 1984).
In Section 2 our high-speed photometry of the star is
described, and the identification of periodicities in the data
detailed. All well-studied EC 14026 stars are composite systems, comprising an sdB star and an FIG star, probably on
the main sequence. PB 8783 is no exception to this pattern,
and in Section 3 further spectroscopic and photometric
measurements of it are described, and used to estimate
spectral types, gravities and temperatures for the component stars. Section 4 deals with the evidence in favour of the
sdB star, rather than the cooler companion, being the
source of the oscillations.
2 FREQUENCY ANALYSIS OF THE
OBSERVATIONS
During an interval of 11 d, 27.2 h of high-speed photometry
of the star were obtained. The observing log is given in
Table 1. The integration time used was 10 s in all runs
except those on JDs 9957 and 9958, when 5 s was used. The
observations were made without any filters in the light
beam. The 0.5-m telescope data were acquired with the
South African Astronomical Observatory (SAAO) Modular
Photometer and a red-sensitive photomultiplier tube; the
data obtained with the 0.75-m telescope employed the University of Cape Town (UCT) High-Speed Photometer with
a blue-sensitive tube.
We will analyse the data obtained on the two telescopes
separately. This is necessitated by the fact that the amplitudes of the variations seen in the 0.75-m data are slightly
larger than the O.5-m amplitudes. The reason for this lies in
the different spectral responses of the photomultiplier tubes
in use on the two telescopes. The reader is reminded that
the high-speed observations were obtained in white light,
i.e. with no filters in the light beam. The Sll photomultiplier
tube in the UCT High-Speed Photometer mounted on the
0.75-m telescope has an effective wavelength similar to
Johnson B, although with a much broader bandpass. The
GaAs tube in the Modular Photometer on the O.5-m telescope, on the other hand, has an even wider wavelength
response. In particular, the GaAs tube has substantial sensitivity extending to the near-infrared, whereas the blue-sensitive Sl1 tube cuts off on the redward side of the Johnson
V filter. The proportion of the cooler, hence redder, companion star measured by the GaAs tube is thus larger, causing the variations ofthe blue star to appear smaller (see also
Section 4 below).
The marked difference in amplitudes observed using the
different telescopes is the prime reason that we analyse the
two sets of observations separately. If the data were to be
treated together, the apparent decrease in the amplitude of
the variations in the 0.5-m observations (obtained entirely
subsequent to the 0.75-m observations) would resemble
© 1997 RAS
© Royal Astronomical Society • Provided by the NASA Astrophysics Data System
1997MNRAS.285..645K
646
C. Koen et al.
Table 1. Log of the high-speed photometric observations of PB 8783.
Starting Time
JD2440000+
Telescope
(metres)
Run Length
(Hours)
9955.54
9957.54
9958.45
9960.46
9961.49
9963.52
9965.47
9966.56
0.75
0.75
0.75
0.50
0.50
0.50
0.50
0.50
0.88
3.80
4.91
4.82
3.99
3.22
4.46
1.11
amplitude waning due to mode beating. We would thus
expect to identify spurious modes with frequencies close to
those truly present in the observations, were the data from
the two data sets combined.
A sample light curve is shown in Fig. 1. The variable
amplitude of the pulsations is clearly visible, and hints
strongly at interference between different modes. Thus, the
total amplitude of variation is large when the different
modes are in phase (e.g. panels four and five of Fig. 1) and
small when modes are in antiphase (e.g. the first panel of
the figure). An amplitude spectrum of the longest run
(4.9 h) is plotted in Fig. 2 (top). A highly significant peak at
a period of 122.7 s (/=8.152 mHz) is apparent. Also plotted
in Fig. 2 are the spectra of the residuals after pre-whitening
by the one (middle) and two (bottom) best-fitting sinusoids
respectively. The combination of the modes giving rise to
the highest peaks in the top two panels of Fig. 2 obviously
gives rise to the beating visible in Fig. 1, as noted above. The
bottom panel of Fig. 2 shows that there may be periodicities
remaining in the data, albeit at amplitudes at the 1 mmag
level. We searched all the runs for significant signals at
frequencies outside the range shown in Fig. 2. None were
found, with amplitudes exceeding ~ 0.7 mmag, in the frequency range 15-50 mHz. Tentative evidence for very lowfrequency signals will be discussed in Section 4.
The results of successive rounds of pre-whitening of the
0.75-m telescope data are shown in Fig. 3. The periodogram
of all the observations is plotted in the top panel. The
remaining panels show the periodograms of the residuals of
the data, after non-linear least squares fitting offrom one to
five sinusoids to the data. Initial estimates for each new
frequency were found from the position of the highest peak
in the periodogram of the residuals from fitting the previous
set of frequencies. The frequencies and amplitudes listed in
Table 2 were obtained from the last round of fitting.
For comparison, Table 2 also shows the results of fitting
six sinusoids to the somewhat longer set of O.5-m telescope
observations. The agreement between the frequencies
found in these independent data sets (different times, telescopes, photometers and observers) is encouraging. [Note
that the apparently large difference in frequency between
the two frequencies near 7.4 mHz (difference 0.012 mHz)
and 7.8 mHz (difference 0.022 mHz) can be ascribed to
their being respectively 1 and 2 cycle per day alias pairs: the
differences are therefore apparent, rather than real]. The
one striking discrepancy between the two sets of frequencies
is the doublet of 8.151 and 8.153 mHz found in the O.5-m
data, corresponding to a singlet at 8.152 mHz in the 0.75-m
-.025 f-
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45
Figure 1. A4.5-h section of the light curve ofPB 8783 (running left
to right from top to bottom), obtained during the run on
HID 244 9958. Each panel has a vertical extent of 0.08 mag. The
data have been pre-whitened by subtraction of a parabola fitted to
the full observation run.
5
10
FREQUENCY (mHz)
15
Figure 2. Top panel: the amplitude spectrum of the longest observational run. Middle panel: the amplitude spectrum of the residuals obtained after pre-whitening the observations by the
best-fitting sinusoid with a frequency determined by the position of
the peak in the top panel. Bottom panel: the amplitude spectrum of
the residuals after pre-whitening the observations by the two bestfitting sinusoids, with frequencies determined by the positions of
the two peaks in the top two panels. Note the different vertical
scales of the different panels.
© 1997 RAS, MNRAS 685, 645-650
© Royal Astronomical Society • Provided by the NASA Astrophysics Data System
1997MNRAS.285..645K
A new class of rapidly pulsating star - II
647
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QI)
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FREQUENCY (mHz)
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Figure 4. A comparison of the amplitude spectra of the residuals
of a five-frequency fit to the 0.75-m data (bottom panel), and a sixfrequency fit to the O.5-m data (top panel) .
.5
5
10
FREQUENCY (mHz)
15
Figure 3. As for Fig. 2, but referring to all the observations
acquired on the 0.75-m telescope, and pre-whitening by up to five
sinusoids. Note the different vertical scales of the different
panels.
Table 2. Frequencies and amplitudes of sinusoids fitted to the
observations by a non-linear least squares method.
Combined 0.75m Runs
Frequency Period Amplitude
(mmag)
(mHz)
(sec)
8.152
122.67
9.1
8.092
7.442
8.291
7.861
123.58
134.37
120.61
127.21
4.1
1.5
1.2
0.8
Combined 0.5m Runs
Frequency Period Amplitude
(mHz)
(sec)
(mmag)
8.151
8.153
8.093
7.454
8.291
7.883
122.68
122.65
123.56
134.16
120.61
126.86
4.7
2.8
2.2
1.2
1.1
0.8
data. This may be due to the longer time-base of the O.5-m
data, namely 6 d, as opposed to the 3 d spanned by the
0.75-m data: the implication is that the frequency resolution
in the former data set is half of that in the latter. In numerical terms, Av ~ 4 !!Hz for the 0.75-m observations, which
does not allow resolution of features 1.5!!Hz apart
(Loumos & Deeming 1978).
The amplitude spectra of the final residuals (Le. after prewhitening by five and six sinusoids respectively) of the two
sets of observations are compared in Fig. 4. Inspection of
this diagram shows a striking agreement in frequency of the
two largest peaks, between the two periodograms. It would
appear that the star may be pulsating in more modes than
those listed in Table 2, with very low amplitudes (below
0.7 mmag). The largest periodogram peaks are close to 7.44
and 8.09 mHz.
3 PHYSICAL PARAMETERS OF THE
BINARY COMPONENTS
PB 8783 was discovered to be a blue star by Berger & Fringant (1984). According to these authors, spectra of the star
showed' ... shallow Balmer lines ... and a moderate Kline';
they conclude that PB 8783 is ' ... intermediate between HB
and sdB or composite'. Fig. 5 shows a 3.5-A resolution
spectrum of PB 8783. Moderately strong Balmer lines on a
blue continuum are evident. The Ca II K line is as strong as
the Balmer lines, suggestive of a mid- to late-A star. However, the Balmer lines and the Balmer jump are too shallow
for such an interpretation. As will be seen below, this can be
understood if the observed spectrum is the sum of cooler
and hotter components.
A few UBV(RI)c measurements of the star were obtained
using the O.5-m telescope; the results are V = 12.32,
U-B= -0.65,B-V=0.13, V-R=O.13 and V-I=0.27,
the accuracy of the values being of the order of 0.01 mag.
The latter two measurements were made in the Cousins
system. A single Stromgren uvby measurement is available:
y=12.31, b-y=O.lO, v-b=0.19, u-b=0.35. Kilkenny
(1995) described the star as 'apparently reddened'. Two
infrared photometric measurements were also acquired;
mean brightnesses are J=11.89, H=11.69 and K=11.68.
The accuracies of these values probably range from about
0.03 mag in J to 0.1 mag in K.
As expected, the U - B index clearly shows the presence
of a very blue star, while most of the other indices are
consistent with a much redder star. We thus attempted to
explain the photometry as the sum of two spectra using the
relation
F V =(r1 /d)2S 1 (T1, v) + (r2/d)2S2(T2' v),
where r1, r2, T1, T2 are the radii and effective temperatures of
the blue and red stars, respectively, and d is the distance to
the system. We fitted this function to the fluxes in uby and
UBVRIJHK obtained by converting the magnitudes using
© 1997 RAS, MNRAS 685, 645-650
© Royal Astronomical Society • Provided by the NASA Astrophysics Data System
1997MNRAS.285..645K
648
C. Koen et al.
PB 8783
3600.0 3800.0 4000.0 4200.0 4400.0 4600.0 4800.0 5000.0
8.0
8.0
6.0
6.0
4.0
4.0
2.0
2.0
0.0
0.0
3600.0 3800.0 4000.0 4200.0 4400.0 4600.0 4800.0 5000.0
Figure 5. Spectrogram of PB 8783. The ordinate is FA in erg
the calibrations listed in Bessell (1979) for UBVRI, Fabregat
& Reig (1996) for uvby and Wilson et al. (1972) for IHK.
Our initial approach was to use blackbody distributions for
SI(Ti> v) and Sz(Tz, v). These are obviously incapable of
reproducing the Balmer jump. The U - B colour (as well as
Figs 5 and 6) indicates that there is a significant Balmer
jump, so the U flux was excluded from the blackbody fitting
procedure. The uvby data were also not included in the
blackbody fitting but were rather used as a check on the
consistency of the photometry.
The results of the fitting revealed a tight correlation
between TI and Tz in the sense that for larger values of Tz,
larger values of TI are required [along with a concomitant
decrease in the scaling factors (ri/dY and (rz/d)Z]. Three
sample fits yielded values for (Ti> Tz) of (20 000 K., 5750 K),
(24500 K., 6000 K), (36000 K., 6250 K); these sample fits are
illustrated in the top panel of Fig. 6. The blackbody curves
of the blue and red stars (with appropriate scaling) for these
three sample fits are shown in this panel (temperatures
appear next to the corresponding curves). The sum of the
contributions is also shown as the curves passing through
the observed BVRIIHK fluxes (these three curves are
indistinguishable except for log l < 3.6). The correlation
between the blue and red star temperatures can be understood as arising from the need for the blue star contribution
to decrease at short wavelengths (log l < 3.8) as the red star
contribution increases. This can only be achieved if the blue
star temperature increases and its radius decreases. We
note also that the high temperature of the red star precludes
the use of the Allard et al. (1994) flux ratio diagrams to
identify accurately the properties of the two stars. Particularly, examination of their fig. 8 shows that the sdB and red
star flux ratio sequences are virtually parallel for spectral
types of the red star earlier than G8, so that small changes in
the orientation of the required connecting line between the
sequences cause large changes in the identification of the
stellar types.
S-I
cm- 2 A-I. The abscissa is wavelength in A.
Log (Wavelength)
3.40
3.80
4.20
o
o
o ~~~~--------------------~
'"
C'I
o
.no
o
:J(T)
...........
C
LL
o
3.40
3.80
4.20
Log (Wavelength)
Figure 6. Fits of blackbody curves (top panel) or Kurucz model
atmospheres (bottom panel) to the UBVRIJHK (filled squares) and
Stromgren uvby (filled triangles) measurements of PB 8783. The
ordinate is F, in erg S-I cm- 2 Hz- t • The absicssa is loglo of the
wavelength in A. Numerical annotation refers to the temperatures
of the corresponding curves. See text for more details.
© 1997 RAS, MNRAS 685, 645-650
© Royal Astronomical Society • Provided by the NASA Astrophysics Data System
1997MNRAS.285..645K
A new class of rapidly pulsating star - II
As mentioned above, it is clear from Figs 5 and 6 that
there is a substantial Balmer jump observed in PB 8783. In
order to include this extra information in the fitting, Planck
functions were replaced by model atmospheres from
Kurucz (1992) to represent Sl (Tl> v) and Sz(Tz, v). For the
red star logg=4 models were used, while for the blue star
logg=5 models were used (a little lower than typical values
of logg for sdB stars). The model spectra with temperatures
closest to 36 000 and 6250 K are shown in the lower panel of
Fig. 6, along with the sum of these two curves. It is evident
that the sum of these two curves has far too much flux
compared with the observed U and u fluxes. In addition, the
sum has a steeper gradient across the optical region than the
observed BVRI fluxes: the observed I flux is slightly, but
significantly, too large (the errors on the UBVRI fluxes are
smaller than the plotted symbols). In order to explain the
size of the Balmer jump, it is clear that the blue star temperature must be reduced (so that its Balmer jump
increases) or the red star temperature increased (for the
same effect).
In order to obtain quantitative estimates, a least squares
fit to the fluxes was performed for T1 ranging from 20000 to
40 000 K and Tz ranging from 5250 to 8250 K. Because of
the extra complexity involved in using those blue photometric fluxes that include strong absorption features,
especially the Balmer jump, only the ubyVRIJHK fluxes
were used in these fits. As with the blackbody fits, a tight
correlation between T1 and Tz was found, with Tz about
649
1000 K hotter than previously to account for the Balmer
jump. Only three points on the (Tl> Tz) grid searched gave
acceptable solutions: (20000 K, 6500 K), (24 000 K,
6750 K) and (33000 K, 7000 K).
The correct point on this one-parameter family of solutions was identified using the strength of the Ca II K line: as
the temperature of the red star increases from 6500 to
7000 K, the Ca II K line increases in strength. In addition,
the contribution of the red star to the flux at 4000 A
increases relative to that of the blue star. A tight constraint
on the red star temperature is thus obtained: the strength of
the observed Ca II K line (Fig. 5) could only be explained by
the (33 000 K, 7000 K) solution. This fit is illustrated in Fig.
7 and is in satisfactory agreement with all observed fluxes.
Much hotter temperatures can be ruled out because the
slope of the composite spectrum across the BVRI bands is
steeper than observed. From examination of the quality of
fits obtained by varying the temperatures in the region of
the optimal solution, we estimate errors of 200 and 2000 K
for Tz and T1 respectively.
From the fit of the Kurucz models, the ratio of the fluxes
at 5500 A (the effective wavelength of the V band) was
found to be 2.81. Mv for main-sequence stars of T z = 7000 K
(spectral type Fl) is 3.3 (Lang 1992), implying that, if both
components are at the same distance, Mv of the blue star is
4.4. Heber (1986: tables 6 and 8) finds that the sdB star
SB 446 has a temperature of 33500 K and Mv = 4.4. The
assumption that PB 8783 is a physical binary is therefore
Log (Wavelength)
0
o
3 . 40
3.70
4.00
4.30
T1: 33000
R1: 0.17
G1:
5.7
T2: 7000
R2: 1. 44
816
d:
CO
o
...
0
-~
.
0",,"
~
...........
::l
C
LLo
o
C\.I
o
o~__~____~__~__~____;===~=d
o
3.40
3.70
4.00
4.30
Log (Wavelength)
Figure 7. Best-fitting Kurucz model atmospheres to the ubyVRIJHK fluxes. The UBVRIIHK fluxes appear as filled squares and the
Stromgren uvby fluxes as filled triangles. The model for the blue star has a temperature of 33 000 K, that for the red star has a temperature
of 7000 K. Other details as for Fig. 6.
© 1997 RAS, MNRAS 685, 645-650
© Royal Astronomical Society • Provided by the NASA Astrophysics Data System
1997MNRAS.285..645K
650 C. Koen et al.
well justified. In addition, we can assume, in contrast to
other studies of sub dwarf binaries (e.g. Allard et al. 1994,
Theissen et al. 1995) where the red star is of later type and
consequently more luminous than a main-sequence star,
that the red star in PB 8783 is on the main sequence. Using
the radius of a main-sequence star of the same effective
temperature, the distance of the system and the radius of
the blue star can be estimated. Assuming further that the
blue star has a mass of 0.5 M 0 , typical of sdB stars (Saffer et
al. 1994), loggl can be estimated. The resulting values
are: '2 = 1.4 ± 0.1 R 0 , 'I = 0.17 ± 0.03 R 0 , d = 800 ± 120 pc,
loggl =5.70 ± 0.15. The wavelength range spanned by the
spectrum in Fig. 5 is too short for it to serve as an additional
check on the derived physical parameters of the stars. However, the values for Tl> T2 and loggl are consistent with
those found from the absorption line profile analysis of
O'Donoghue et al. (1997). The quoted errors should not be
regarded as being statistically independent of each other, as
the relevant quantities are correlated. Note that the above
analysis neglects interstellar reddening (although at the
high galactic latitude of PB 8783 this may not be a serious
oversight) and has used models with Population I composition. The parameters derived above should therefore be
treated with appropriate caution.
4 WHICH STAR IS THE PULSATOR?
Although it is more likely that the more compact star, i.e.
the sdB star, is the source of the oscillations, this should not
be taken for granted. One method of establishing which star
gives rise to the pulsations is to determine the amplitude as
a function of wavelength. PB 8783 was observed on two
nights successively in the U and V filters for ~ 10 oscillation
cycles in each filter. Interchange of measurements through
the two filters, and then interpolation of the mean amplitude, was necessary in order to remove statistically the
effect of amplitude variations arising from beating. The
result was a ratio of amplitudes Au/Av= 4.2. The decomposition of the fluxes from the red and blue stars derived in
the last section yield UI =2.04 x 10- 25 , VI = 1.15 X 10- 25
(blue star); and UI = 1.02 X 10- 25 , V2=3.23 X 10- 25 (red
star). This implies that UI/VI = 1.8, whereas U2JV2 = 0.32; it
is thus clear that the sdB star is the source of the rapid
pulsations.
A great many stars of the spectral type of the cooler star
in the PB 8783 pair are known to be b Scuti pulsators, with
typical periods of a few hours. We therefore examined the
low-frequency parts of our amplitude spectra for excess
power. There are indeed similar features at frequencies of
about 54 and 135 JlHz (periods of 5.1 and 2.1 h) in the
periodograms of the 0.5- and 0.75-m data, but these are not
so pronounced as to be entirely convincing. The problem is,
of course, that the inevitable slow drifts in atmospheric
transparency that affect our data have the same time-scales
as b Scuti variations.
5 CONCLUSIONS
The periodicities identified in our observations of PB 8783,
ranging from 120 to 135 s, extend the range of periods seen
in the BC 14026 stars to below 130 s (cf. Kilkenny et al.
1997, O'Donoghue et al. 1997, Stobie et al. 1997b). Furthermore, it appears that PB 8783 has a particularly rich oscillation spectrum, making the star an attractive proposition for
well-constrained pulsation modelling.
Being the brightest of the known BC 14026 stars, fairly
accurate absolute photometry of PB 8783 was obtained
from the U up to the K band. This photometry allowed the
determination of the temperatures of the component stars
to within quite narrow limits. Furthermore, estimates of the
distance of the system and the gravity of the subdwarf star
were made which were found to be in accord with parallel
studies.
ACKNOWLEDGMENTS
The authors are grateful to Fred Marang (SAAO) and
to Kristen Larson (Rensselaer Polytechnic) for obtaining
some of the photometry discussed in the paper.
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