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Subsections

Appendix A: Results for individual systems

A.1 HD  5550 (= BD +65$^\circ $115 = Renson 1470)

This star had originally not been included in the CORAVEL sample because its photometric effective temperature exceeds 10 000 K. On the other hand, it was included in the sample measured with ELODIE for the survey of surface magnetic fields, which allowed us to discover its SB2 nature. The CORAVEL data show that it is a short period binary, and allow us to obtain the orbital parameters. The SB2 nature of this star is not visible with the CORAVEL instrument while it is clear with ELODIE. In addition to the better resolution of ELODIE, this might be due to the fact that CORAVEL covers only the blue wavelength range, while ELODIE is rather sensitive to the red. The star visible with CORAVEL is the less massive one (see Fig. A.1), so if significantly redder, the invisible companion could only be a red giant. This is forbidden by the short orbital period: the shortest orbital period for systems hosting a red giant is about 40 days (Mermilliod, private communication). Therefore, the more massive component must be also the hotter one, and its visibility with ELODIE is probably linked with the mask used for the correlation, which had been specifically defined for Ap stars, while the CORAVEL mask was designed from the spectrum of Arcturus. This raises the interesting possibility that both companions might be Ap stars (or possibly Am), since otherwise their metallicity would not have been sufficient to yield correlation dips. Another favorable circumstance is the rather low inclination of the system, since for an assumed mass $M_1 = 2.5 ~ M_\odot$ (for the most massive component), the inclination $i = 20.5\hbox{$^\circ$ }$ only, so that the projected rotational velocity is only 35 percent of the equatorial value. The CORAVEL data then do not allow to obtain the radial-velocity curve of the primary; on the other hand, they yield the systemic velocity which, together with the two ELODIE spectra, allow a fairly good estimate of the mass ratio (see Table A.1).


  \begin{figure}
\par\includegraphics[width=16cm,clip]{carrierf10.eps} %
\end{figure} Figure A.1: Phase-folded radial-velocity curves of the first eight binaries listed in Table 1. Full dots: CORAVEL observations; triangles: ELODIE observations.

This star is remarkable, because it is only the fifth SB2 system known among magnetic Ap stars, after HD 55719 (Bonsack 1976), HD 98088 (Abt et al. 1968; Wolff 1974), HD 59435 (Wade et al. 1996) and HD 174016-7 (Ginestet et al. 1999); HD 59435 had also been studied in the course of this survey, while a sixth case (HD 22128, see below) was discovered with ELODIE. Although HgMn stars are frequently seen in SB2 systems, this is exceptional among Si and SrCrEu stars.

A.2 HD 9996 (= BD +44$^\circ $341 = Renson 2470)

The duplicity of this B9 CrEuSi (Osawa 1965) star has first been detected by Preston & Wolff (1970) who found an orbital period of 273 days. They did not attempt to determine the orbital elements because of the poverty of the data. Scholz (1978) tried to determine the orbital elements, but the shape of the velocity curve in the vicinity of the maximum remained ill-defined. The 43 CORAVEL measurements (Table 1) confirm the 273-day period (see Fig. A.1). Thanks to the precision and homogeneity of the data, our velocity curve is more precise than the one based on the data gathered by Preston & Wolff (1970) and Scholz (1978), so that a satisfactory determination of the orbital elements is possible.

The rather large rms scatter of the residuals (1.24 km s-1) is due to the small depth of the correlation dip (3 percent). Rotation is not important, the $v\sin i$ value of the visible component is very small (<2 km s-1, see Tables 2 and A.4) and has no effect on the correlation-peak width; this is confirmed by the very long rotational period of the primary ($\sim$21 years, Rice 1988), so that even highly contrasted abundance spots could not distort the radial-velocity curve.

A.3 HD 12288 (= BD +68$^\circ $144 = Renson 3130)

This star was classified A2 CrSi by Osawa (1965). Its rotational period, known from its magnetic variability, is 34.79 days (Mathys et al. 1997). Thirty-one observations were obtained over an interval of 5949 days (Table 1), which represents about 4 orbital periods ( $P_{\rm orb}=1547$ d). The radial-velocity curve is shown in Fig. A.1. The projected rotational velocity estimated from the width of the autocorrelation dip is moderate but significant (Tables 2, A.4), but should not be considered as reliable because the effect of the magnetic field is not taken into account in this estimate. Since the Zeeman effect will always widen the dip, the $v\sin i$ values listed in Tables 2 and A.4 must be considered as upper limits to the true projected rotational velocity. If considered with this caution in mind, they are very useful.


 

 
Table A.1: Orbital parameters of the binaries. For each component, the second line gives the estimated standard deviations of the parameters.
Star name P $T_\circ$ (HJD e $V_\circ$ $\omega_1$ K1,2 ${\cal
M}_{1,2}\sin^3 i$ $a_{1,2}\sin i$ N (O-C)
  (days) -2 400 000)   ( ${\rm km~s^{-1}}$) ($^\circ $) ( ${\rm km~s^{-1}}$) f1($\cal M$) (106  km)   ( ${\rm km~s^{-1}}$)
HD 5550 6.82054 50988.70 0.00 -11.70 - 24.60 0.1081 2.307 2 1.13
  0.00020 0.011 fixed 0.28 - 0.82 0.0045 0.077    
                     
          - 38.43 0.0692 3.605 22  
          - 0.46 0.0036 0.043    
HD 9996 272.88 44492.34 0.532 0.97 20.17 11.12 0.0237 35.34 43 1.33
  0.20 2.24 0.023 0.22 3.35 0.29 0.0022 1.11    
HD 12288 1546.99 44480.5 0.337 -53.15 120.84 9.01 0.0982 180.5 31 0.84
  7.29 15.8 0.024 0.16 5.49 0.26 0.0089 5.5    
HD 22128 5.085564 50116.7656 0.00 15.30 - 68.40 0.786 4.784 20 1.25
  0.000070 0.0043 fixed 0.21 - 0.37 0.012 0.026    
                     
          - 73.69 0.729 5.153 18  
          - 0.55 0.010 0.038    
HD 40711 1245.6 49591.7 0.834 -11.69 314.3 7.88 0.0106 74.5 31 0.51
  4.4 6.3 0.013 0.12 2.1 0.46 0.0022 5.1    
HD 54908 17.9233 46469.96 0.286 -0.15 213.45 27.09 0.0326 6.40 21 2.58
  0.0017 0.36 0.034 0.61 6.47 1.19 0.0044 0.29    
HD 56495 27.37995 48978.40 0.1651 -7.57 224.7 44.30 1.641 16.45 32 2.45
  0.00080 0.23 0.0097 0.35 3.2 0.74 0.055 0.27    
                     
          44.7 57.75 1.259 21.44 28  
          3.2 0.81 0.044 0.30    
HD 65339 2422.04 27723.6 0.718 -2.10 5.22 12.08 0.149 280.0 181 1.72
(RV only) 2.42 14.3 0.012 0.14 1.64 0.45 0.019 11.7    
HD 73709 7.220263 49996.5352 0.00 36.51 - 30.84 0.02200 3.062 45 0.89
  0.000017 0.0093 fixed 0.13 - 0.19 0.00041 0.019    
HD 98088 5.905111 34401.387 0.1796 -8.45 314.46 73.29 1.733 5.854 88 2.34
  0.000004 0.023 0.0039 0.23 1.44 0.36 0.030 0.029    
          134.46 99.46 1.277 7.940 19  
          1.44 0.90 0.020 0.070    
HD 105680 70.0795 45991.19 0.3798 -5.13 192.6 30.75 0.1676 27.42 42 0.76
  0.0087 0.38 0.0055 0.13 1.1 0.20 0.0034 0.19    
HD 138426 11.34474 48690.398 0.512 -14.63 121.37 44.02 0.0636 5.90 20 2.04
  0.00029 0.052 0.020 0.52 2.81 1.46 0.0068 0.21    
HD 184471 429.17 46857.06 0.2017 -26.16 86.99 15.59 0.1585 90.09 36 0.51
  0.42 3.01 0.0081 0.12 2.81 0.15 0.0045 0.86    
HD 188854 8.480322 46394.223 0.2262 -29.61 23.84 41.76 0.05926 4.743 34 0.40
  0.000025 0.014 0.0024 0.07 0.64 0.10 0.00045 0.012    
HD 200405 1.635255 46999.9766 0.00 -0.974 0.00 8.44 0.0001021 0.190 34 0.63
  0.000006 0.0058 fixed 0.12 fixed 0.18 0.0000064 0.004    
HD 216533 1413.1 43752.5 0.437 -4.05 182.8 5.04 0.0137 88.1 48 0.71
  4.6 17.4 0.026 0.11 4.9 0.22 0.0019 4.0    


A.4 HD 22128 (= BD -07$^\circ $624 = Renson 5560)

This A7 SrEuMn star (Renson 1991) was found to be an SB2 system during the survey for magnetic fields carried out with ELODIE. We do not have Geneva photometry for that star, but only Strömgren photometry[*] given by Olsen (1983, 1994). The average physical parameters obtained from the $uvby\beta $ values compiled by Mermilliod et al. (1997) (assuming both components are identical) and using the calibration of Moon & Dworetsky (1985) are listed in Table A.3. From the physical parameters we obtain a typical mass ${\cal M} = 1.99 \pm 0.17~{\cal M}_\odot$, according to the models of Schaller et al. (1992). The inclination angle i may be estimated close to 48$^\circ $.

Notice, in Fig. A.1, that the radial-velocity curve is very close to a circular orbit ( $e=0.0145 \pm 0.0116$). Therefore, the test of Lucy & Sweeney (1971) was applied in order to see whether this small eccentricity is significant or not. The probability p is equal to 0.69 in our case, which is much greater than the limit of 0.05 determined by Lucy & Sweeney. Thus this eccentricity of 0.0145 is not significant and is fixed to zero.

A.5 HD 40711 (= BD +10$^\circ $973 = Renson 10880)

Bidelman & McConnell (1973) classified this object Ap SrCrEu. Geneva photometry clearly confirms the peculiarity with $\Delta (V1-G) = 0.020$(the photometric data in the GENEVA system are collected in the General Catalogue - Rufener 1988 - and its up-to-date database - Burki 2002). The radial velocities are represented in Fig.  A.1. The periastron was observed again only recently, which allowed a precise estimate of the orbital period. The eccentricity is high and relatively well defined, though the exact shape of the RV curve in the vicinity of the periastron remains unknown because of the 7-weeks gap in the observations. The depth of the dip varies, while its width only shows rather marginal changes.

A.6 HD 54908 (= BD -01$^\circ $1579 = Renson 15000)

HD 54908 is a poorly studied Ap star classified A0 Si by Bidelman & McConnell (1973). In spite of a large $v \sin i = 53.6 \pm 5.34$ km s-1, the variation of the radial velocity is too large to be caused by spots and rotation ( $K = 27.47 \pm 1.14$ km s-1). However we can see the effect of a large rotational velocity on the scatter of the residuals. The twenty-one observations were obtained over an interval of 4084 days. The shape of the radial-velocity curve (Fig. A.1) is not very well defined in the vicinity of the minimum, but the period of 17.92 days is quite well determined.

 

 
Table A.2: Orbital parameters of HD 191654, assuming that the RV variations of this star is caused by orbital motion rather than by rotating abundance patches on its surface.
Star name P $T_\circ$ (HJD e $V_\circ$ $\omega_1$ K1,2 ${\cal
M}_{1,2}\sin^3 i$ $a_{1,2}\sin i$ N (O-C)
  (days) -2 400 000)   ( ${\rm km~s^{-1}}$) ($^\circ $) ( ${\rm km~s^{-1}}$) f1($\cal M$) 106  km   ${\rm km~s^{-1}}$
HD 191654 2121. 48692. 0.48 -15.72 88. 2.11 0.00140 54.0 27 0.91
  27. 50. 0.10 0.23 17. 0.24 0.00055 7.1    



 

 
Table A.3: Physical parameters of HD 22128 and HD 56495 according to their colours in the $uvby\beta $ or Geneva photometric system.
Star Photometry $T_{\rm eff} [K]$ $\log g$ [cgs] [M/H] $\log (L/L_{\odot})$ $R/R_{\odot}$ Mv $M_{\rm bol}$ $\Delta m_0$
HD 22128 $uvby\beta $ 6900 3.65 0.57 0.95 2.10 2.29 2.26 -0.052
HD 56495 $uvby\beta $ 7179 4.00 0.42 0.77 1.58 2.77 2.72 -0.032
  Geneva 7044 $\pm$ 56 4.26 $\pm$ 0.09 0.26 $\pm$ 0.08          



 

 
Table A.4: Physical parameters of the binaries according to their colours in the Geneva photometric system (or in the $uvby\beta $ system for HD 22128); in the case of HD 5550, we have adopted the $T_{\rm eff}$ value estimated from the H$_\alpha $ profile observed with ELODIE near conjonction. The reddenings E(B2-G) labeled with an asterisk are determined using the maps of Lucke (1978). $v\sin i$ is obtained by a calibration of the CORAVEL correlation-dip width (Benz & Mayor 1984). The resulting $v\sin i$ is slightly less reliable than for F and cooler stars which were used for the calibration, because their effective temperature is larger and the corresponding dependance has to be extrapolated. However, the main source of uncertainty is due to disregarding the magnetic field, which implies an overestimate of $v\sin i$. The longitudinal magnetic field is taken from Babcock (1958) or more recent references. * Value given by Debernardi et al. (2000).
HD $v\sin i$ upper limits mV Hz $T_{\rm eff}$ E(B2-G)
  (km s-1)   (KG) (K)  
5550 $ 6.5\pm 1.3$ 5.967 - 11000 0.046
9996 2.0 6.379 -1.2 to 0.3 9700 0.017
12288 $ 12.5 \pm 0.4$ 7.748 -1.2 to -0.2 9378 0.175
22128A $ 15.9 \pm 0.3$ 7.595 - 7000 0*
22128B $ 16.3 \pm 0.7$   -    
40711 2.0 8.581 - 9328 0.192*
54908 $ 55.2 \pm 5.5$ 7.968 - 7483 0.031
56495A $ 25.3 \pm 2.5$ 7.654 0.21 to 0.57 7044 0*
56495B $ 12.5 \pm 2.1$ 7.654 -    
65339 $ 19.4 \pm 0.6$ 6.031 -5.4 to 4.2 8250 0.012
73709 $ 17.3 \pm 0.3^*$ 7.687 - 7831 0*
98088A $ 21.1 \pm 2.1$ 6.42 0.48 to 0.94 8043 0*
98088B $ 15.8 \pm 1.9$ 7.62   7532 0*
105680 $ 14.1 \pm 0.2$ 8.060 - 7154 0*
138426 2.0 8.546 - 8694 0.142
184471 2.0 8.980 - 8114 0.116
188854 $ 9.3 \pm 0.2$ 7.634 - 7005 0.069*
200405 $ 9.6 \pm 0.4$ 8.908 - 9624 0.101
216533 $5.7 \pm 0.3$ 7.907 -0.7 to 0.1 9000 0.120


A.7 HD 56495 (= BD -07$^\circ $1851 = Renson 15430)

This star was classified A3p Sr by Bertaud (1959), which motivated its inclusion in our sample, but Bertaud & Floquet (1967) classified it A2-F2 (Am). Its classification remains ambiguous, and it would be interesting to know its $\Delta a$ index in Maitzen's (1976) photometry. Its peculiarity index in Geneva photometry is $\Delta (V1-G) = -0.006$ only, which is typical of normal stars, but the efficiency of this index is known to be low for such cool Ap stars. This is an excentric SB2 system, whose inclination angle i remains unknown. We secured 60 points (Fig. A.1) and obtained the orbital elements listed in Table A.1.

A rough estimate of the inclination angle i and of the masses of the components can be done using $uvby\beta $ photometry[*] and the calibration by Moon & Dworetsky (1985). The physical parameters obtained are listed in Table A.3. Combining these results with the models of Schaller et al. (1992), one finds an approximate mass ${\cal M} = 1.80 \pm 0.09~{\cal M}_\odot$ and an inclination i close to 75$^\circ $.

 

 
Table A.5: Speckle observations of HD 65339 used for the simultaneous fit on the RV, speckle and parallax data. Since the errors are not given by the authors, an error of 0.01 arcsec and of $2\hbox {$^\circ $ }$ has been assumed on the separation and position angle respectively.
Epoch $\rho$ $\theta$ Source
(frac. year) (arcsec) ( $\hbox{$^\circ$ }$)  
1980.1561 0.044 336.4 McAlister et al. (1983)
1984.0526 0.093 299.6 McAlister et al. (1987)
1984.8463 0.091 307.3 Balega2 (1987)
1985.1830 0.091 306.3 Balega2 (1987)
1985.1858 0.088 308.7 Balega2 (1987)
1986.7039 0.045 328.6 Balega et al. (1989)
1986.8894 0.0339 332.44 Hartkopf et al. (1996)
1989.2267 0.063 283.1 McAlister et al. (1990)
1990.2755 0.089 293.1 Hartkopf et al. (1992)
1991.3265 0.086 303.8 Hartkopf et al. (1994)
1991.8943 0.085 306.7 Hartkopf et al. (1994)
1992.3124 0.080 310.7 Hartkopf et al. (1994)


A.8 HD 65339 (= 53 Cam = BD +60$^\circ $1105 = Renson 17910)

53 CAM is a very well studied A3 SrEuCr star (Osawa 1965). It is known as a binary by both spectroscopy and speckle interferometry. The speckle orbit was published by Hartkopf et al. (1996) and a radial-velocity curve was published by Scholz & Lehmann (1988). Combining our 46 measurements (Table 1) with those published by Scholz & Lehmann (1988), we determine the orbital parameters listed in Table A.1. The scatter of the residuals of Scholz's measurements are similar to those of CORAVEL observations alone, which appears surprising at first sight. Examining the depth and width of the correlation dip as a function of the rotational phase ( P = 8.0267 days), one clearly sees a significant variation of both quantities (see Fig. 4). The residuals around the fitted RV curve also show a variation, which is related, therefore, to the spots associated with a non-negligible $v\sin i$. 53 Cam is then a nice example of an object displaying two variations simultaneously, one due to rotation (with an amplitude of up to 7 km s-1 peak-to-peak) and the other due to a binary companion.

Thanks to a code made available by T. Forveille and developed in Grenoble, we have fitted simultaneously the radial velocities, the speckle measurements and the Hipparcos parallax ( $\pi = 10.16 \pm 0.77$), leaving not only K1 but also K2 as an adjustable parameter in spite of the lack of RV data for the companion. The speckle measurements retained for the fit are given in Table A.5, while the results are shown in Table A.6. The "visual'' orbit is shown in Fig. A.3.

  \begin{figure}
\par\includegraphics[width=16cm,clip]{carrierf11.eps} %
\end{figure} Figure A.2: Phase-folded radial-velocity curves of the last eight binaries listed in Table 1. Full dots: CORAVEL observations; triangles: ELODIE observations.

This is the first time that such a solution is attempted for this system. The results are surprising, in that both companions appear to have the same mass, contrary to what Scholz & Lehman (1988) had found (2.5  $\cal M_\odot$ and 1.6  $\cal M_\odot$ for the primary and the secondary respectively) by combining the separate RV and speckle orbits (they used a photometric mass for the primary, since there was no good parallax value at the time). On the other hand, they are compatible with the small $\Delta m$ required for speckle observations. They also differ from the mass estimate done by Martin & Mignard (1998) on the basis of Hipparcos results, which has a large error, however. The uncertainty is very large and could be substantially reduced if the spectrum of the secondary could be observed. We could not see it on our ELODIE spectra, but this is not surprising since they were taken when both companions had almost the same radial velocity.

A.9 HD 73709 (= BD +20$^\circ $2165 = Renson 20510 = Praesepe KW 279)

HD 73709 was classified A2-A5-F0 (Am) by Gray & Garrison (1989), but was found photometrically Ap by Maitzen & Pavlovski (1987) according to the $\Delta a$ index ( $\Delta a = 0.018$). The Geneva peculiarity index gives an ambiguous answer: $\Delta (V1-G) = 0.001$ is a few thousands of magnitude larger than the average of normal stars, but is not conspicuous. It has been put lately in our programme because of its photometric peculiarity, first for magnetic field measurements, second for radial-velocity monitoring.

Two ELODIE data were taken in the course of the survey for magnetic fields, while a third one has kindly been obtained for us by Mr. Dominique Naef (Geneva Observatory) during a planet-search programme.

HD 73709 is extremely interesting because of its reliable Am classification and positive $\Delta a$: it was generally accepted that Am stars never show enhanced $\Delta a$ values (Maitzen 1976; Maitzen et al. 1998) which are characteristic of magnetic Ap stars only. Conversely, large-scale magnetic fields are generally not found in Am stars, with the probable exception of the hot Am star o Peg (Mathys 1988; Mathys & Lanz 1990). The three spectra taken with the ELODIE spectrograph consistently show a surface magnetic field of about 7.5 kG which seems very significant, in spite of a relatively large projected rotational velocity $v\sin i = 16$ km s-1 (Babel & North, in preparation).

The orbit of this star was published by Debernardi et al. (2000). However, we have 12 additional data, so we have redetermined the orbit using both published and new data (note that the data published by Debernardi et al. have not been put into the ELODIE RV system (Udry et al. 1999), so that the RV values used here are very slightly different from those published by these authors). The orbit is slightly improved.

A.10 HD 98088A (= BD -6$^\circ $3344A = Renson 28310)

This is a well-known SB2 binary hosting a magnetic Ap star of the type SrCr according to Osawa (1965). Its binary nature has been discovered by Abt (1953), who saw it only as an SB1, and the complete orbital solution of the SB2 system was given by Abt et al. (1968). These authors have shown that the spectral variations have the same period as the orbital one and that the system must, therefore, be synchronized. According to them, the spectral type of the primary is A3Vp while that of the secondary is A8V. In spite of the binary nature of this star, the Geneva photometric system "sees'' its peculiarity, with $\Delta (V1-G)=0.013$, and Maitzen's (1976) photometry is even more efficient, with $\Delta a=0.035$. Therefore, the primary is a rather extreme Ap star.

 

 
Table A.6: Orbital parameters of HD 65339 obtained with a simultaneous fit on the RV, speckle and parallax data.
Star name P $T_\circ$ (HJD e $V_\circ$ $\Omega_1$ $\omega_1$ i K1,2 ${\cal
M}_{1,2}$ a1,2 $\pi$
  (days) -2 400 000)   ( ${\rm km~s^{-1}}$) ($^\circ $) ($^\circ $) ($^\circ $) ( ${\rm km~s^{-1}}$) ( $\cal M_\odot$) (106 km) (mas)
HD 65339 2418.9 27738.8 0.742 -1.94 116.80 7.30 134.3 12.33 1.49 275.1 10.2
(RV+speckle) 2.41 15.6 0.013 0.13 1.31 1.37 4.4 0.41 0.66   1.0
                12.13 1.52 270.5  
                3.25 0.33    



  \begin{figure}
\par\resizebox{8cm}{!}{\includegraphics[angle=-90,width=9.5cm]{carrierf12.eps}}\end{figure} Figure A.3: Orbit of the system HD 65339 projected on the sky, as fitted to both radial velocities and speckle measurements simultaneously. The axes are labeled in arcseconds. The error bars have been chosen in an arbitrary way because they are not given by the authors.

A very interesting feature of HD 98088 is that, in spite of its relatively short orbital period, it has a significant eccentricity, so that one may expect an apsidal motion to take place. According to Wolff (1974), only marginal evidence for such a motion could be found over a time base of 20 years, and new observations should be done 20 to 30 years later to settle the question, the expected period of the apsidal motion being 500 to 700 years. Because of this expectation, we reobserved the system with CORAVEL in the spring of 1998. Bad weather prevented us to obtain a dense coverage of all phases, but 17 observations of the primary and 8 of the secondary could be done. The period could be refined to

\begin{displaymath}%
P = 5.905111 \pm 0.000004 ~{\rm days}.
\end{displaymath} (A.1)

The $\omega$ angle has not changed in a significant way since about 30 years, since we find $\omega_1=314.25\pm 3.66 \hbox{$^\circ$ }$, while the combined literature data for the epochs 1953-1973 give $\omega_1=314.41\pm 1.09 \hbox{$^\circ$ }$ according to Wolff (1974). We verified this result with our code, which gives practically the same value but a larger uncertainty ( $\omega_1=314.47\pm 1.60 \hbox{$^\circ$ }$, for the primary RV curve alone). If the period of the apsidal motion was 700 years as suggested by Wolff (1974), then the argument of the periastron should have changed by $18\hbox{$^\circ$ }$ in 35 years, so we should have found $\omega_1\sim 332.5 \hbox{$^\circ$ }$. This is five $\sigma$ away from our result, so we conclude that the apsidal motion can only be much slower, with a period probably longer than a millenium. If one imposes $\omega_1=332.5\hbox{$^\circ$ }$, the fit of the CORAVEL observations is clearly worse, with an rms scatter of the residuals of 3.83 km s-1 instead of 2.74 km s-1 (for both components); the difference is more visible on the RVcurve of the primary ( $\sigma_{{\rm res}}=3.89$ km s-1 instead of 2.35). Combining all published data with the CORAVEL ones, and after a correction $\Delta RV=-1.14$ km s-1 to the latter for a better consistency, we obtain a very good curve with $\omega_1=314.46 \pm 1.44 \hbox{$^\circ$ }$ (Fig. A.2).
 

 
Table A.7: Physical parameters of both components of the spectroscopic system HD 98088A, inferred from photometric temperatures and Hipparcos parallax.
Parameter primary secondary
MV 0.87 2.07
$\log~(T_{{\rm eff}})$ $3.905\pm 0.016$ $3.877\pm 0.017$
$\log~(L/L_\odot)$ $1.60\pm 0.09$ $1.10\pm 0.09$
M ($M_\odot$) $2.261\pm 0.093$ $1.755\pm 0.085$
R ($R_{\odot}$) $3.27\pm 0.43$ $2.10\pm 0.28$
$\log g$ (cgs) $3.76\pm 0.10$ $4.04\pm 0.11$
$R\sin i=\frac{P\cdot v\sin i}{50.6}$ ($R_{\odot}$) $2.46\pm 0.25$ $1.84\pm
0.22$
$R=R\sin i/\sin~(66\hbox{$^\circ$ })$ $2.70\pm 0.27$ $2.02\pm 0.24$
d (pc) $129\pm 13$


Fortunately, this system has a rather good Hipparcos parallax of $\pi = 7.75\pm 0.76$ mas, so that the radii of its components can be estimated. From the observed apparent magnitude V1+2=6.107 (Rufener 1988) and from the magnitude difference $\Delta V=1.2$ (Abt et al. 1968) one gets the individual apparent magnitudes V1=6.42 and V2=7.62 which give the absolute magnitudes MV1=0.87 and MV2=2.07 using the Hipparcos parallax. From the spectral types A3 and A8 proposed by Abt et al. (1968), a first guess of the effective temperatures is given by the calibration of Hauck (1994): $T_{{\rm eff1}}=8275$ K and $T_{{\rm eff2}}=7532$ K. Another guess can be done from the (B2-G) index of Geneva photometry, according to the calibration of Hauck & North (1993): one has first to subtract the typical Geneva colours of the companion (assuming an A8V star) to the observed ones in order to get (B2-G)1=-0.455, which corresponds to $T_{{\rm eff1}}=8043$ K. Note that (B2-G)1 is not very sensitive to the assumption made on the companion, since it differs by only 0.023 mag from the observed value (B2-G)1+2=-0.432. Adopting this effective temperature for the primary, an interpolation in the evolutionary tracks of Schaller et al. (1992) for an overall solar metallicity yields the physical parameters listed in Table A.7. It is interesting to notice that the mass ratio obtained in this way is $q=0.776\pm 0.049$, which is compatible to better than one sigma with the dynamical mass ratio $q_{\rm dyn}=0.737\pm 0.008$.

Also listed in Table A.7 are the radii estimated from the CORAVEL projected rotational velocities assuming a negligible Zeeman broadening, from the spin period (synchronization makes it equal to the orbital one) and from $i=66\hbox{$^\circ$ }$. The latter value is obtained from $M_1\sin^3i=1.733\pm 0.030$ with the mass of the primary interpolated in the evolutionary tracks. It is almost identical with $i=67\hbox{$^\circ$ }$ proposed by Abt et al. (1968). The radii obtained through the projected rotational velocities are compatible with those obtained from the Hipparcos luminosity and photometric effective temperatures, in the sense that error bars overlap. The agreement is perfect for the secondary, but much less satisfactory for the primary, even though the difference is less than twice the largest sigma. An attempt has been made to impose the dynamical mass ratio $q_{\rm dyn}=0.737$ and interpolate in the evolutionary tracks the pair of stars whose magnitude difference is compatible with it. Maintaining the assumption of an A8V companion, we get in this way $\Delta V=1.54$ and $M_1=2.30\pm .09$, $M_2=1.69\pm .08~M_\odot$, $R_1=3.42\pm 0.45$, $R_2=1.86\pm 0.25~R_\odot$. The magnitude difference appears a bit large compared with the estimate of Abt et al. (1968) and the radius of the primary turns out to be even larger, making the discrepancy more severe compared to the radius estimated from the rotational velocity.

The number of CORAVEL measurements is too small to conclude about the possible variability of the depth and width of the correlation dip of the primary.

A.11 HD 105680 (= BD +23$^\circ $2423 = Renson 30570)

This star was listed A3p SrSi? by Bertaud (1959), which motivated its inclusion in the sample, and as A3-F2 by Bertaud & Floquet (1967). The radial-velocity curve is very well defined (see Fig. A.2). We secured 42 points over an interval of 2966 days. In spite of a relatively large $v\sin i$, the rms scatter of the residuals is small. Unfortunately, the classification remains ambiguous; $\Delta (V1-G) = 0.004$ suggests a mild peculiarity, but it is not large enough to exclude that it may be an Am star instead of an Ap.

A.12 HD 138426 (= BD -18$^\circ $4088 = Renson 39420)

This poorly known star has been classified Ap SrCr(Eu) by Houk & Smith-Moore (1988). Its photometric peculiarity is just significant in the Geneva system ( $\Delta (V1-G)= 0.010$) and it is clearly an SB1 binary with a relatively short period. The $v\sin i$ is very small (<2.4 km s-1) and neither the depth nor the width of the correlation dip seems to vary. Figure A.2 shows a phase diagram of the radial velocities. The residual scatter is rather large, but the most discrepant points (at phases 0.48 and 0.56) were observed in the run of March 1997 where technical problems prevented the data to be registered on tape, so that it has not been possible to evaluate their quality.

A.13 HD 184471 (= BD +32$^\circ $3471 = Renson 50890)

This star was classified A9 SrCrEu by Bertaud & Floquet (1974). A total of 36 measurements have been made over almost 3500 days (Table 1), which clearly define a 429-day period (see Fig. A.2). The residuals are very small thanks to a small $v\sin i$ (<2 km s-1) and a well contrasted dip.

A.14 HD 188854 (= BD +46$^\circ $2807 = Renson 52220)

Ap or Am, according to different authors, its spectral type is not well determined. HD 188854 was listed as A7 CrEu by Bertaud & Floquet (1974), but also as A5-F0 (Bertaud & Floquet 1967). No $\Delta a$ photometry has been published for it, and the Geneva index $\Delta (V1-G) = -0.002$ does not allow us to conclude, especially as it is among the coolest existing Ap stars. The radial-velocity curve is well determined with a $\sigma{\rm (O-C)}$ of 0.51 km s-1 only (see Fig. A.2).

A.15 HD 200405 (= BD +47$^\circ $3256 = Renson 55830)

This A2 SrCr (Osawa 1965) star had already been announced as having the shortest orbital period known among all Bp and Ap stars (North 1994), with a period of only 1.635 days. A survey of the literature has not denied this claim: the few binaries with a period shorter than 3 days in Renson's (1991) catalogue either owe their spectral peculiarity to another physical cause like in situ nucleosynthesis (HD 93030, an "OBN" star according to Schönberner et al. 1988 and HD 49798, an O6 He star), or are misclassified (HD 25833, a normal B4V star according to Gimenez & Clausen 1994), or do not have a typical Bp, Ap peculiarity (HD 124425, F7 MgCaSr in Renson's catalogue; HD 159876, F0IIIp in the Hipparcos Input Catalogue but A5-F1 $\delta$ Del? in Renson's, and Am, A7/A9/F3 according to Abt & Morrell 1995); finally, the A2 CrEu star HD 215661B is not a binary: only the A component of this visual system is an Algol-type binary.

HD 200405 is a bona fide Ap star also from the photometric point of view: Geneva photometry shows it is peculiar, with $\Delta(V1-G)=0.021$, and Maitzen's peculiarity index $\Delta a=0.038$ on average (Schnell & Maitzen 1995).

The inclination angle i of the orbital plane of HD 200405 must be very small, according to the value of $a_{1} \sin i$ and of the mass function (Table A.1), unless the companion is a brown dwarf. The radial-velocity curve is shown in Fig. A.2. The orbit is circular (e = 0). This object is especially interesting, since it is exceptional: all other binaries with a magnetic Ap component have orbital periods longer than 3 days. If tidal effects tend to wash out the chemical peculiarity of the components, as suggested by this lower limit, then one has to explain how HD 200405 has been able to remain an Ap star in spite of significantly large tides.

Another way to interpret this radial-velocity curve would be to assume that HD 200405 has a very small, highly contrasted spot with enhanced abundance of iron-peak elements (whose lines are selected by the CORAVEL mask); in such a case, rotation alone might be responsible for a sinusoidal curve, if both the inclination i of the rotational axis and the angle between the rotation and spot axes are such that the spot remains visible during the whole cycle. However, such a situation appears extremely improbable, since one does not see any variation in the intensity of the correlation dip, nor in its width or depth, which should occur because of the varying aspect of the spot. Likewise, the radial velocity of the H$_\alpha $ line measured once with ELODIE is compatible with the CORAVEL RV curve, while one would rather expect it to remain at the "systemic" velocity. Furthermore, the spot hypothesis would imply an apparent $v\sin i \approx 0$ km s-1 (the radial velocity of every point in the spot being practically the same), while we obtain $v\sin i = 9.5\pm 0.4$ and $7.9\pm 0.2$ km s-1 using respectively CORAVEL and ELODIE: a small spot could never give rise to such a high value (the effect of the magnetic field has been removed in the ELODIE estimate). Therefore, HD 200405 holds the record of the shortest orbital period known.

A.16 HD 216533 (= BD +58$^\circ $2497 = Renson 59810)

This A1 SrCr star (Osawa 1965) was already known as an SB1 system. Floquet (1979) found an orbital period of 16.03 days, using the radial velocity of the Ca  II K line.

A total of 48 measurements have been made over almost 6225 days. The 16.03-day period does not fit at all our radial velocities. We find a much longer period P = 1413 days (see Fig. A.2), which should be considered as more reliable. It seems that Floquet was too confident in her assumption of an homogeneous distribution of ionized calcium on the surface of the star, and that the RV variation she observed was in fact due to a spot. The rotational period of this star, 17.2 days, is indeed very close to the "orbital'' one found by Floquet (1979), although not identical.

Acknowledgements
This work was supported in part by the Swiss National Fondation for Scientific Research. The reduction of the data were made by the late Dr. Antoine Duquennoy and by SU. We thank the numerous observers who have contributed to this survey, especially Dr. J.-C. Mermilliod and Mr. Bernard Pernier. We also thank Dr. Noël Cramer, who had initiated the CORAVEL measurements of some bright Ap stars. We thank Dr. Thierry Forveille for having shared his ORBIT code for orbital elements determination from visual and RV data. This research has made use of the SIMBAD database, operated at CDS, Strasbourg, France. It was supported by the Swiss National Science Foundation.


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