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Subsections

   
4 Binary SPBs

In the following three subsections, we present the results of the mass/inclination and frequency procedure for the binaries.

   
4.1 Double-lined binaries

4.1.1 HD 123515 - HR 5296 - HIP 69174


  \begin{figure}
\par\resizebox{8.8cm}{!}{\rotatebox{0}{\includegraphics{H36752a.p...
...
\resizebox{8.8cm}{!}{\rotatebox{0}{\includegraphics{H36752d.ps}}}\end{figure} Figure 2: The different steps of subsequent prewhitening for the 4 accepted intrinsic frequencies (from top to bottom) $\nu _1$ = 0.68528(10)  $\rm {c~d^{-1}}$, $\nu _2$ = 0.65929(10)  $\rm {c~d^{-1}}$, $\nu _3$ = 0.72585(10)  $\rm {c~d^{-1}}$, and $\nu _4$ = 0.55198(10)  $\rm {c~d^{-1}}$ of HD 123515. Left: The modified Scargle periodograms for the first velocity moment <v>4130 derived from the observed $\lambda \lambda $ 4130 Å Si II line, the Geneva B data, and the HIPPARCOS ${\rm H_p}$ data of HD 123515. The dashed and dotted lines correspond respectively to the 1% FAP-level and the 3.7 S/N-level. Right: The corresponding phase plots with the accepted intrinsic frequency. The dots are the observed data while the full line represents the best sinusoidal fit.


 

 
Table 2: Overview of the characteristics of the accepted intrinsic frequencies in the different data-sets of HD 123515. For the meaning of the different symbols, we refer to the text. The amplitudes for which 0 is in the asymptotic 95% confidence interval are given in italic. The full table for all colours and velocity moments is only available in electronic at the CDS via anonymous ftp to cdsarc.u-strasbg.fr (130.79.125.5) or via http://cdsweb.u-strasbg.fr/cgi-bin/qcat?J/A+A/393/965
data-set $\sigma$ Ai $\phi_i$ $\sigma _{\rm res}$ $\sigma _N$
$\nu _1$ = 0.68528(10)  $\rm {c~d^{-1}}$
<v>4130 ( $\rm {km~s^{-1}}$) 3.69 3.54(34) 0.50(2)    
B (mmag) 22.3 19.6(6) 0.241(5)    
$H_{\rm p}$ (mmag) 21.2 20.9(12) 0.203(9)    
$\nu _2$ = 0.65929(10)  $\rm {c~d^{-1}}$
B (mmag)   13.6(5) 0.875(7)    
$H_{\rm p}$ (mmag)   10.9(13) 0.819(21)    
$\nu _3$ = 0.72585(10)  $\rm {c~d^{-1}}$
<v>4130 ( $\rm {km~s^{-1}}$)   1.91(36) 0.15(3) 1.93 0.54
B (mmag)   11.0(6) 0.967(8)    
$H_{\rm p}$ (mmag)   11.9(11) 0.947(18)    
$\nu _4$ = 0.55198(10)  $\rm {c~d^{-1}}$
B (mmag)   6.1(6) 0.43(1) 10.1  
$H_{\rm p}$ (mmag)   7.8(12) 0.25(3) 9.4 6.2


HD 123515 ( mV = 5.96) is double-lined spectroscopic binary with $P_{\rm orb}$ = 26.036(4) d and e= 0.264(7) (Paper I). With our spectra, we derive a mass-ratio of M2/M1 = 0.629(8), and hence M2 $\approx$ 1.9(1) $M_{\odot }$ and $i \approx$ 54$^{\circ}$. All these observations are compatible with a main-sequence A 6 component.

HD 123515 is one of the 7 SPB-prototypes introduced by Waelkens (1991) for which he found 4 intrinsic photometric frequencies: $\nu _{1,{\rm p}}$ = 0.68521  $\rm {c~d^{-1}}$, $\nu _{2,{\rm p}}$ = 0.65928  $\rm {c~d^{-1}}$, $\nu _{3,{\rm p}}$ = 0.72861  $\rm {c~d^{-1}}$, and $\nu _{4,{\rm p}}$ = 0.45834  $\rm {c~d^{-1}}$. With our data, also 4 intrinsic frequencies are found: $\nu _1$ = 0.68528(10)  $\rm {c~d^{-1}}$, $\nu _2$ = 0.65929(10)  $\rm {c~d^{-1}}$, $\nu _3$ = 0.72585(10)  $\rm {c~d^{-1}}$, and $\nu _4$ = 0.55198(10)  $\rm {c~d^{-1}}$. $\nu _{1,{\rm p}}$ and $\nu _{2,{\rm p}}$ correspond to $\nu _1$ and $\nu _2$ while  $\nu _{3,{\rm p}}$ and $\nu _{4,{\rm p}}$ are aliases of respectively $\nu _3$ and $\nu _4$. The modified Scargle periodograms and the best theoretical sinusoidal fits to the data after subsequent prewhitening are shown from top to bottom in Fig. 2. The amplitudes of the 4 intrinsic frequencies clearly exceed both the 1% FAP-level and the 3.7 S/N-level in the Geneva data. In the other data-sets, this is only the case for $\nu _1$. The 4 frequencies are all present in the $H_{\rm p}$ variations, but they are found in a different order ($\nu _1$, $\nu _3$, $\nu _2$, $\nu _4$). Without the Geneva data, we would not have been able to pin-point the physical frequencies from the different candidate frequencies with an amplitude exceeding the 1% FAP-level. In the spectroscopic variations, no evidence for $\nu _2$ or $\nu _4$ is found. After prewhitening the Geneva data with $\nu _1$, $\nu _2$, $\nu _3$, and $\nu _4$, there are still several frequencies whose amplitude exceeds both significance levels, of which $\nu _5$ = 0.68817(10)  $\rm {c~d^{-1}}$ is one of the best candidates. However, there is no reason to prefer this candidate to another. Therefore, $\nu _5$ will not be considered during the modelling.

The amplitudes and phases for the fits with the four accepted intrinsic frequencies are given in Table 2, together with the original standard deviation $\sigma$, the residual standard deviation $\sigma _{\rm res}$, and the level of mean error of the observations $\sigma _N$ (when available) of the different data-sets. Here, only the properties of the accepted intrinsic frequencies in the <v>, Geneva B and HIPPARCOS $H_{\rm p}$ data are given. The properties in the other velocity moments and the other Geneva filters are additionally given in the full table, which is only available electronically. The observed frequency spacings between $\nu _1$, $\nu _2$, $\nu _3$ and $\nu _4$ are small, which may point towards membership of a frequency multiplet. The frequency splitting induced by the effect of stellar rotation on high-order g-mode pulsations is, in a good approximation, given by:

 
$\displaystyle \nu_{l,m} \simeq \nu_{l,0} - m \left( 1 - \frac{1}{l(l+1)} \right...
...frac{4l(l+1)[2l(l+1)-3]-9}{2l^2 (l+1)^2 [4l(l+1)-3] } + \theta(\nu^3_{\rm rot})$     (1)

(Dziembowski & Goode 1992), where $\nu_{l,0}$ denotes the pulsation frequency in the corotating frame, $\nu_{l,m}$ the observed pulsation frequency, and $\nu_{\rm rot}$ the rotation frequency of the star. If we assume synchronisation ( $\nu _{\rm orb}$ = $\nu_{\rm rot}$ = 0.038410  $\rm {c~d^{-1}}$), we find an equatorial rotation velocity of some 4  $\rm {km~s^{-1}}$ and the observed frequency spacings between $\nu _1$, $\nu _2$, $\nu _3$ and $\nu _4$ would be compatible with a septuplet structure. The overal line broadening is indeed small for the star (Aerts et al. 1999) and the pulsational broadening is relatively large. Hence, such a rotation velocity is feasible. However, we cannot take this suggestion of a septuplet for granted as the orbit is still quite eccentric and the separation between the stars is too large for tidal effects to be very efficient.

4.1.2 HD 140873 - HR 5863 - HIP 77227


  \begin{figure}
\par\resizebox{8.8cm}{!}{\rotatebox{0}{\includegraphics{H36753.ps}}}\end{figure} Figure 3: Same as Fig. 2, but for the accepted intrinsic frequency $\nu _1$ = 1.1515(8)  $\rm {c~d^{-1}}$ of HD 140873.

In Paper I we showed that HD 140873 ( mV = 6.24) is a double-lined spectroscopic binary with $P_{\rm orb}$ = 38.927(4) d and e = 0.731(6). We derive a mass-ratio of M2/M1 = 0.50(1), and hence M2 $\approx$ 1.8(1) $M_{\odot }$ and $i \approx$ 53$^{\circ}$. These observations are compatible with an A 7 V secondary.

In the past, HD 140873 has been used as a standard star for different photometric systems (e.g. Taylor 1986; Paunzen et al. 1997). However, from our data-sets it is clear that we are dealing with an intrinsic variable. For most of our data-sets of HD 140873, the two highest peaks in the output of the frequency search algorithms correspond to $\nu _{1}^{\prime}= 0.1487$(8)  $\rm {c~d^{-1}}$ and $\nu _1$ = 1.1515(8)  $\rm {c~d^{-1}}$ (Fig. 3). The 3.7 S/N-level is only exceeded in the Geneva data. $\nu _{1}^{\prime}$ and $\nu _1$ are each others 1  $\rm {c~d^{-1}}$ alias frequency, but $\nu _1$ is the intrinsic one since only evidence for $\nu _1$ is found in the $H_{\rm p}$ variations. Although there are still some peaks reaching the 1% FAP-level in the $H_{\rm p}$ data and in some filters of the Geneva data after prewhitening with $\nu _1$, the current data-sets are insufficient to unambiguously designate additional intrinsic frequencies. In Table 3, we give an overview of the characteristics of $\nu _1$.

   
4.2 Single-lined binaries with eccentric orbits


 

 
Table 3: Same as Table 2, but for the accepted intrinsic frequency of HD 140873.
data-set $\sigma$ Ai $\phi_i$ $\sigma _{\rm res}$ $\sigma _N$
$\nu _1$ = 1.1515(8)  $\rm {c~d^{-1}}$
<v>4128 ( $\rm {km~s^{-1}}$) 3.62 4.02(47) 0.80(2) 2.14 2.0
B (mmag) 15.4 17.7(19) 0.51(2) 9.5  
$H_{\rm p}$ (mmag) 13.4 16.8(12) 0.27(1) 6.6 5.1


4.2.1 HD 24587 - HR 1213 - HIP 18216


  \begin{figure}
\par\resizebox{8.8cm}{!}{\rotatebox{0}{\includegraphics{H36754.ps}}}\end{figure} Figure 4: Same as Fig. 2, but for the accepted intrinsic frequency $\nu _1$ = 1.1569(6)  $\rm {c~d^{-1}}$ of HD 24587.

The "mass/inclination'' procedure applied to the eccentric 459(4) day orbit (see Paper I) of HD 24587 ( mV = 4.63) leads to a lower limit of approximately 2.6 $M_{\odot }$ for M2. If the secondary is a main-sequence star, this would imply that we are dealing with an early A-type companion. However, synthetic spectra show that a B 6 V + A 0-2 V binary system is double-lined, which is not seen in our spectra. The only way out is to assume a neutron star companion, which implies that the system has undergone a phase of mass-transfer through Roche lobe overflow and has survived the supernova explosion.

Mathys et al. (1986) were the first to detect light variations for HD 24587. They found a frequency 0.5786  $\rm {c~d^{-1}}$ and concluded that the light curves resemble those of many chemically peculiar stars (hereafter "CP stars'') whose variations are due to the non-homogeneous distribution of elements on the stellar surface. HD 24587 was listed as a suspected CP star in the "General Catalogue of Ap and Am stars'' (Renson et al. 1991). However, the spectroscopic study of Leone & Catanzaro (1998) led to the conclusion that HD 24587 presents chemical elements which are only slightly underabundant with respect to main sequence stars. Moreover, the observed EW values are constant and consistent with the effective temperature. These observations are confirmed by Catanzaro et al. (1999), who concluded that HD 24587 is not a CP star.


 

 
Table 4: Same as Table 2, but for the accepted intrinsic frequency of HD 24587.
data-set $\sigma$ Ai $\phi_i$ $\sigma _{\rm res}$ $\sigma _N$
$\nu _1$ = 1.1569(6)  $\rm {c~d^{-1}}$
<v>4128 ( $\rm {km~s^{-1}}$) 1.99 2.1(2) 0.92(2) 1.37 0.50
<v>4121 ( $\rm {km~s^{-1}}$) 2.53 2.2(3) 0.86(2) 1.98  
B (mmag) 10.12 7.3(10) 0.59(2) 8.60  
$H_{\rm p}$ (mmag) 7.95 7.9(8) 0.40(2) 5.66 4.6


All our data-sets point towards the same intrinsic frequency: $\nu _1$ = 1.1569(6)  $\rm {c~d^{-1}}$ (Fig. 4). The corresponding frequency peaks in the modified Scargle periodograms clearly exceed the 1% FAP-level and (almost) reach the 3.7 S/N-level. After prewhitening with $\nu _1$, some peaks still reach the 1% FAP-level in the $H_{\rm p}$ data and the velocity moments. However, there is no reason to prefer one candidate above the other. Although we cannot clearly identify more than one intrinsic frequency in our data-sets, the remaining standard deviations $\sigma _{\rm res}$ (Table 4) are still rather high and point towards multi-periodicity. We find no evidence for variations with (sub)harmonics of $\nu _1$. These observations are in favour of the classification of HD 24587 as an SPB. However, $\nu _1$ is twice the frequency found by Mathys et al. (1986) and the observed average EW of the Si II profiles is relatively small compared to those of other target stars with similar temperature (Fig. 1). These observations are in their turn in favour of the earlier classification of HD 24587 as a CP star.

The variability induced by spots can (but need not) be quite different for different spectral lines as far as amplitudes, phases and harmonics are concerned. We therefore additionally studied the time behaviour of the 4121 Å He I profile, which is also situated within in the observed wavelength range. Just like for the moments derived from the Si II profiles, variations with $\nu _1$ are obviously present in <v> and <v3>, but they are less pronounced in the variations of the EW and <v2>. Again, we find no evidence for the appearance of (sub)harmonics of $\nu _1$, nor of other frequencies. The behaviour of the Si II doublet and the He I line is therefore similar, and so does not rule out a pulsation model.

In Table 4, an overview of the characteristics of $\nu _1$ is given. From our data-sets, it is not clear if the observed variations of HD 24587 are induced by stellar pulsation or by rotation modulation, or perhaps both. We are currently performing additional spectroscopic observations to disentangle the variable nature of this star in full detail.

4.2.2 HD 53921 - HR 2674 - HIP 34000


 

 
Table 5: The orbital parameters for HD 53921. The "Si II'' and "4132.5 Å'' column give the orbit as found in the radial velocities derived from respectively the Si II-doublet and the 4132.5 Å feature.
    Si II 4132.5 Å
$P_{\rm orb}$ (d) = 338(2) 340(3)
$v_{\gamma}$ ( $\rm {km~s^{-1}}$) = 9.9(3)  
$t(\tau)$ (HJD) = 50498(4) 50500(5)
e = 0.63(6) 0.43(8)
$\omega$ ($^{\circ}$) = 302(15) 283(11)
K ( $\rm {km~s^{-1}}$) = 3.2(3) 8.5(4)
$a \sin i$ (AU) = 0.077 0.24
$f(M)\ ($$M_{\odot }$) = 0.0005 0.016
rms ( $\rm {km~s^{-1}}$) = 1.302 0.173



  \begin{figure}
\par\resizebox{8.8cm}{!}{\rotatebox{0}{\includegraphics{H36755.ps}}}\end{figure} Figure 5: Observed radial velocities versus orbital phase of HD 53921. The primary component data are given by black dots (CAT data) and grey squares (CORALIE data). The observed radial velocities derived from the observed $\lambda \lambda $ 4130 Å Si II doublet (top) and the $\lambda \lambda $ 4132.5 Å feature (bottom) are given together with the theoretical velocities defined by the orbital elements for the primary as given in Table 5 (full lines). In both panels, phase zero corresponds to periastron passage.

HD 53921 ( mV = 5.64) is known as a close visual binary with two B-type components (Corbally 1984). It has never been proven nor ruled out that the visual components are physically bound. This object was listed as a suspected spectroscopic binary in Paper I.

Some additional spectra were taken in November 1998 with the CORALIE spectrograph attached to the Euler telescope situated at La Silla (Chile). The radial velocities and the corresponding weights for the orbital solution determination were obtained from the $\lambda \lambda $ 4130 Å Si II-doublet in a similar way as for the CAT data (see Paper I). The simultaneous use of the CAT and CORALIE data results in the orbit as shown in the upper panel of Fig. 5. The corresponding parameters are given in the "Si II'' column of Table 5. This orbital solution was tested by considering radial velocities derived from a small unidentified feature near 4132.5 Å. These radial velocities were determined by a Gaussian approximation of the line profile after subtraction of the mean central wavelength 4132.583 Å. No weights are used. The resulting orbit is shown in the lower panel of Fig. 5. The corresponding parameters are given in the "4132.5 Å'' column of Table 5. Both sets of orbital parameters are in agreement, except for e and K. The 4132.5 Å-amplitude is a factor 2.5 larger than the Si II-amplitude. Since the velocity shifts of the Si II doublet and the 4132.5 Å feature are always in the same direction, they cannot originate from different components of the same spectroscopic binary. We therefore suggest that the observed Si II lines result from the superposition of the Si II lines of both components of the visual binary, and that one of these two visual components is a spectroscopic binary with an eccentric orbit of about 340 d. This suggestion also gives a natural explanation for the discrepancy between the observed EW values and the effective temperature of HD 53921 (Fig. 1).

The mass/inclination procedure applied to the "4132.5 Å'' orbit leads to a lower limit of 25$^{\circ}$ for i and of 0.65 $M_{\odot }$ for M2. The spectra were shifted according to the "Si II'' orbit in an attempt to be able to study the intrinsic variability of HD 53921 afterwards.


  \begin{figure}
\par\resizebox{8.8cm}{!}{\rotatebox{0}{\includegraphics{H36756.ps}}}\end{figure} Figure 6: Same as Fig. 2, but for the accepted intrinsic frequency $\nu _1$ = 0.6054(6)  $\rm {c~d^{-1}}$ of HD 53921.


 

 
Table 6: Same as Table 2, but for the accepted intrinsic frequency of HD 53921.
data-set $\sigma$ Ai $\phi_i$ $\sigma _{\rm res}$ $\sigma _N$
$\nu _1$ = 0.6054(6)  $\rm {c~d^{-1}}$
<v>4128 ( $\rm {km~s^{-1}}$) 1.91 2.01(23) 0.66(2) 1.33 1.3
B (mmag) 9.2 9.6(8) 0.25(1) 6.4  
$H_{\rm p}$ (mmag) 8.7 8.7(7) 0.19(2) 5.4 5.2


All our data-sets of HD 53921 agree upon the first intrinsic frequency: $\nu _1$ = 0.6054(6)  $\rm {c~d^{-1}}$ (Fig. 6). After prewhitening with $\nu _1$, none of the frequency peaks in the modified Scargle periodograms reach the 1% FAP-level nor the 3.7 S/N-level. This is not surprising, since $\sigma _{\rm res}$ is already close to $\sigma _N$ in all data-sets. In Table 6, we give an overview of the characteristics of $\nu _1$.

4.2.3 HD 74560 - HR 3467 - HIP 42726


  \begin{figure}
\par\resizebox{8.8cm}{!}{\rotatebox{0}{\includegraphics{H36757a.p...
...
\resizebox{8.8cm}{!}{\rotatebox{0}{\includegraphics{H36757e.ps}}}\end{figure} Figure 7: Same as Fig. 2, but for the 5 accepted intrinsic frequencies $\nu _1$ = 0.64472(9)  $\rm {c~d^{-1}}$, $\nu _2$ = 0.39578(9)  $\rm {c~d^{-1}}$, $\nu _3$ = 0.44763(9)  $\rm {c~d^{-1}}$, $\nu _4$ = 0.82281(9)  $\rm {c~d^{-1}}$, and $\nu _5$ = 0.63567(9)  $\rm {c~d^{-1}}$ of HD 74560. For $\nu _2$, <v2> is given instead of <v>.

HD 74560 ( mV = 4.82) is one of the brightest objects of the IC 2391 cluster which is situated at about 150 pc and is approximately $3.63\times10^7$ years old (Mermilliod 1981). In our spectra, HD 74560 reveals itself as a single-lined spectroscopic binary with an eccentric orbit of 8.378(1) days (Paper I). The application of the mass/inclination procedure leads to a lower limit on i and M2 of respectively 10$^{\circ}$ and 0.25 $M_{\odot }$.

HD 74560 is an SPB prototype for which Waelkens (1991) detected two well established photometric pulsation frequencies: $\nu _{1,{\rm p}}$ = 0.64472  $\rm {c~d^{-1}}$ and $\nu _{2,{\rm p}}$ = 0.60772  $\rm {c~d^{-1}}$. Two candidates for a third intrinsic frequency were also given, but the physical one could not be determined due to severe aliasing.

Although the different data-sets of HD 74560 lead to periodograms and $\theta$-statistics showing very prominent alias peaks, they all result in the same first intrinsic frequency, $\nu _1$ = 0.64472(9)  $\rm {c~d^{-1}}$ (Fig. 7). After prewhitening the different data-sets with $\nu _1$, four additional frequencies are clearly found in the residual variations in the seven Geneva filters: $\nu _2$ = 0.39578(9)  $\rm {c~d^{-1}}$, $\nu _3$ = 0.44763(9)  $\rm {c~d^{-1}}$, $\nu _4$ = 0.82281(9)  $\rm {c~d^{-1}}$, and $\nu _5$ = 0.63567(9)  $\rm {c~d^{-1}}$. Apart from $\nu _1$, none of the frequencies coincides with those found by Waelkens (1991), although $\nu _2$ is close to the 1  $\rm {c~d^{-1}}$ alias of $\nu _{2,{\rm p}}$. The sequence in which the frequencies is given is somewhat arbitrary since their importance in the different filters is not always the same and their amplitudes are very alike. We followed different "prewhitening'' orders, but they all lead to the same set of frequencies. $\nu _6$ = 0.60778(9)  $\rm {c~d^{-1}}$ and $\nu _6$' = 1.60510(9)  $\rm {c~d^{-1}}$ are found as the best candidates for the sixth intrinsic frequency in the Geneva variations after having prewhitened with $\nu _1$, ..., $\nu _5$. Our Geneva data do not allow us to choose as the blue filters are dominated by $\nu _6$ while the red ones by $\nu _6$'. Moreover, no evidence for either of the candidates is found in the other data-sets. Note that Waelkens (1991) found $\nu _6$ as second frequency in the subset he had at his disposal. Although we do not include $\nu _6$ for interpretations, we propose it as the best candidate for the sixth intrinsic frequency.

In the HIPPARCOS data there are a lot of frequencies with an amplitude exceeding only the 1% FAP-level after prewhitening with $\nu _1$. The three best candidates, 0.0197(6)  $\rm {c~d^{-1}}$, 0.0520(6)  $\rm {c~d^{-1}}$, and 0.0844(6)  $\rm {c~d^{-1}}$, have longer periods than the expected pulsation periods in SPBs, but they can all be connected with $\nu _{\rm orb}$ = 0.11936(1)  $\rm {c~d^{-1}}$ by peaks in the window function. We therefore prewhitened the residual $H_{\rm p}$ data with a fourier fit including $\nu _{\rm orb}$ and its first harmonic. However, the signal at 0.0197(6)  $\rm {c~d^{-1}}$ does not disappear (Fig. 7, lower panel). Besides this unexplained low frequency, one of the many frequencies with an amplitude exceeding the 1% FAP-level is 0.6359(6)  $\rm {c~d^{-1}}$, which is equal to $\nu _5$ within the frequency resolution. After prewhitening with $\nu _5$, there are still several frequencies with a similar amplitude exceeding the 1% FAP-level, but no evidence for one of the candidates is found in the other data-sets. Therefore, we are not able to determine a third intrinsic frequency in the $H_{\rm p}$ data of HD 74560.

After having prewhitened the velocity moments with $\nu _1$, the best candidates in <v>, <v2> and <v3> do not coincide. For <v2>, 0.3961(6)  $\rm {c~d^{-1}}$ and 0.6069(6)  $\rm {c~d^{-1}}$ are found in the list of the frequencies with an amplitude exceeding the 1% FAP-level (Fig. 7, second panel from top). They are close to respectively $\nu _2$ and $\nu _6$. $\nu _6$ does not fit the residual second moment with an acceptable quality, while a pulsation model with $\nu _2$ has the same quality as the best candidates of <v2>. We therefore accept $\nu _2$ to be present in the moments. After prewhitening <v2> with $\nu _2$, no additional frequencies can be retained. In Table 7, we give an overview of the characteristics of the five accepted frequencies. For $\nu _1$ and $\nu _5$ to be members of the same frequency multiplet, the rotational frequency $\nu_{\rm rot}$ should be close to 0.01  $\rm {c~d^{-1}}$, leading to an equatorial rotation velocity of only 1.6  $\rm {km~s^{-1}}$. This is hard to reconcile with the total line broadening of about 45  $\rm {km~s^{-1}}$ (Aerts et al. 1999), as the pulsational broadening of the star is small.

 

 
Table 7: Same as Table 2, but for the accepted intrinsic frequencies of HD 74560.
data-set $\sigma$ Ai $\phi_i$ $\sigma _{\rm res}$ $\sigma _N$
$\nu _1$ = 0.64472(9)  $\rm {c~d^{-1}}$
<v>4128 ( $\rm {km~s^{-1}}$) 2.90 2.85(27) 0.36(2)    
B (mmag) 16.30 16.8(4) 0.038(4)    
$H_{\rm p}$ (mmag) 13.63 14.3(10) 0.00(1)    
$\nu _2$ = 0.39578(9)  $\rm {c~d^{-1}}$          
<v>4128 ( $\rm {km~s^{-1}}$)   1.11(27) 0.54(4) 1.81 0.47
B (mmag)   4.8(4) 0.38(1)    
$\nu _3$ = 0.44763(9)  $\rm {c~d^{-1}}$          
B (mmag)   3.8(4) 0.59(2)    
$\nu _4$ = 0.82281(9)  $\rm {c~d^{-1}}$          
B (mmag)   4.1(4) 0.29(2)    
$H_{\rm p}$ (mmag)   4.8(10) 0.34(3)    
$\nu _5$ = 0.63567(9)  $\rm {c~d^{-1}}$          
B (mmag)   3.5(4) 0.58(2) 8.4  
$H_{\rm p}$ (mmag)   6.0(8) 0.55(3) 6.8 4.7


4.2.4 HD 177863 - HR 7241 - HIP 93887

HD 177863 ( mV = 6.28) is a fixed double system (Schrijver 1997). HD 177863A and HD 177863B are separated by 0.70 arcsec and they have a magnitude difference of approximately three. From now on, we drop the "A'' in the name of the component A of the visual binary. The mass/inclination procedure applied to the eccentric 11.9154(9) day orbit derived in Paper I provides us a lower limit on i of 35$^{\circ}$ and restricts M2 between 1-2 $M_{\odot }$.

HD 177863 is one of the SPB-prototypes for which Waelkens (1991) determined two pulsation frequencies, $\nu _{1,{\rm p}}$ = 0.84068  $\rm {c~d^{-1}}$ and $\nu _{2,{\rm p}}$ = 0.90167  $\rm {c~d^{-1}}$. Although we are dealing with strong aliasing, there is no doubt that $\nu _1$ = 0.84059(10)  $\rm {c~d^{-1}}$ is the main intrinsic frequency in the variations of our data-sets (Fig. 8). Note that $\nu _1$ is close to ten times the orbital frequency $\nu _{\rm orb}$ = 0.083925(6)  $\rm {c~d^{-1}}$ (Paper I). Willems & Aerts (2002) showed that this mode is a resonantly excited l=2 mode through the time-varying tidal potential.

After prewhitening with $\nu _1$, there are still frequencies with an amplitude exceeding the 1% FAP-level and 3.7 S/N-level in all data-sets. The residual variations in the velocity moments do not lead to convincing candidate frequencies. In the residuals of the Geneva data, the best candidates are $\nu _2$ = 0.10108(10)  $\rm {c~d^{-1}}$, $\nu _2$' = 0.90166(10)  $\rm {c~d^{-1}}$ and $\nu _3$ = 1.00525(10)  $\rm {c~d^{-1}}$. $\nu _2$' corresponds to $\nu _{2,{\rm p}}$ and $\nu _2$ is its (1  $\rm {c~d^{-1}}$+ 1  $\rm {c~y^{-1}}$- $\nu $) alias. With the Geneva photometry only, it is hard to decide upon the reality of the candidates, since their relative importance depends on the considered filter. However, $\nu _2$ is found in the $H_{\rm p}$ data and is therefore accepted as second intrinsic frequency in the photometric data-sets. Note that $\nu _2$ is much lower than the theoretically expected pulsation frequencies for SPBs. It is not related to the orbital frequency $\nu _{\rm orb}$ either. The origin of this variation is therefore not clear. Finally we mention that, after additional prewhitening with $\nu _2$, the two frequencies $\nu _3$ and 2.00797(10)  $\rm {c~d^{-1}}$ become the best candidates in the Geneva data. We refer to Table 8 for an overview of the characteristics of the intrinsic frequencies of HD 177863.

   
4.3 Single-lined binaries with circular orbits

4.3.1 HD 92287 - HR 4173 - HIP 52043


  \begin{figure}
\par\resizebox{8.8cm}{!}{\rotatebox{0}{\includegraphics{H36758a.p...
...
\resizebox{8.8cm}{!}{\rotatebox{0}{\includegraphics{H36758b.ps}}}\end{figure} Figure 8: Same as Fig. 2, but for the 2 accepted intrinsic frequencies $\nu _1$ = 0.84059(10)  $\rm {c~d^{-1}}$, and $\nu _2$ = 0.10108(10)  $\rm {c~d^{-1}}$ of HD 177863. For $\nu _2$, the Geneva U filter is given instead of the Geneva B filter.


 

 
Table 8: Same as Table 2, but for the accepted intrinsic frequencies of HD 177863.
data-set $\sigma$ Ai $\phi_i$ $\sigma _{\rm res}$ $\sigma _N$
$\nu _1$ = 0.84059(10)  $\rm {c~d^{-1}}$
<v>4130 ( $\rm {km~s^{-1}}$) 3.16 3.82(47) 0.19(2) 1.89 1.3
B (mmag) 15.6 20.6(5) 0.835(4)    
$H_{\rm p}$ (mmag) 16.4 19.9(11) 0.856(10)    
$\nu _2$ = 0.10108(10)  $\rm {c~d^{-1}}$
B (mmag) 15.6 3.3(5) 0.68(3) 6.1  
$H_{\rm p}$ (mmag) 16.4 5.9(10) 0.66(4) 6.5 6.4


HD 92287 ( mV = 5.88) is a member of the Carina OB-association (Kaltcheva 1998). Before our study, no line profile variations were reported and HD 92287 was not known as a spectroscopic binary yet. The application of the mass/inclination procedure to the 2.90457(7) day circular orbit as given in Paper I leads to a lower limit on i and M2 of respectively 30$^{\circ}$ and 1.3 $M_{\odot }$. At periastron, both components approach to about 10 $R_{\odot }$.

HD 92287 was already known as a suspected photometric variable for 20 years (Rufener & Bartholdi 1982). Although Waelkens & Rufener (1985) reported $\nu_{\rm p}$ = 0.6812  $\rm {c~d^{-1}}$ as candidate frequency in their photometric data, they omitted this object from their target list. In Paper I, we showed that $\nu_{\rm p}$ is close to the first harmonic of the orbital frequency $\nu _{\rm orb}$ = 0.344236(1)  $\rm {c~d^{-1}}$. Therefore, we classified HD 92287 as an ellipsoidal variable.

  \begin{figure}
\par\resizebox{8.8cm}{!}{\rotatebox{0}{\includegraphics{H36759.ps}}}\end{figure} Figure 9: Same as Fig. 2, but for the accepted intrinsic frequency $\nu _1$ = 0.21480  $\rm {c~d^{-1}}$ of HD 92287.

After prewhitening the orbital variations, all data-sets point towards the same main intrinsic frequency: $\nu _1$ = 0.21480(7)  $\rm {c~d^{-1}}$ (Fig. 9). Note that $\nu _1$ is smaller than $\nu _{\rm orb}$, i.e. the pulsation mode in this star has an observed pulsation period which is longer than the orbital period. The variations with $\nu _1$ in <v>4128 are non-sinusoidal, which is not surprising since we are dealing with a non-spherical star. After prewhitening with $\nu _1$, none of the data-sets reveal convincing candidate frequencies with an amplitude exceeding the 1% FAP-level and/or the 3.7 S/N-level. However, $\sigma _N$ is not reached yet by $\sigma _{\rm res}$ in any of our data-sets. In Table 9, an overview of the characteristics of the accepted intrinsic frequency is given.


 

 
Table 9: Same as Table 2, but for the accepted intrinsic frequency of HD 92287.
data-set $\sigma$ Ai $\phi_i$ $\sigma _{\rm res}$ $\sigma _N$
$\nu _1$ = 0.21480(7)  $\rm {c~d^{-1}}$
<v>4128 ( $\rm {km~s^{-1}}$) 4.95 4.85(59) 0.07(2) 3.41 2.6
B (mmag) 13.7 11.3(7) 0.77(1) 7.1  
$H_{\rm p}$ (mmag) 12.0 7.7(9) 0.79(2) 6.6 5.5



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