Astron. Astrophys. 354, 881-891 (2000)

5. Discussion

These new observations enable us to discuss the binary frequency, the (e, ) relation, and the nature of the secondaries.

5.1. Mutiplicity

Several spectroscopic and photometric surveys have been made to classify the bright stars in the Praesepe and in Hyades clusters. Therefore we can consider that all Am stars have been detected, nineteen in total, in the two open clusters. Ten orbits were derived from the present observations. Among the nineteen Am stars, twelve have orbital elements, one uncertain orbital elements and two evidences of orbital motion without orbital elements (see Table 1). For the other four, we have only unconclusive evidence of their duplicity.

KW 276 is presumed to have long-term radial-velocity variations stars (Raboud & Mermilliod 1998). Abt & Willmarth (1999) did not observe significant change in radial-velocity during their observations, which argues for the very long-term radial-velocity variations.

KW 286 could be presumed to have long-term radial-velocity variations. Wilson & Joy (1950) published a mean radial velocity of 27.8 km s^-1 and McDonald (Hill 1978) observed a mean radial velocity of 38.4 km s^-1.

vB 74 Abt & Levy (1985) consider a constant radial-velocity for this star of about 40 km s^-1. But the old data of Frost et al. (1929) give a mean radial-velocity of about 25 km s^-1. It is however not possible to derive any definitive conclusion about vB 74 binarity.

vB 107 has no clear evidence of radial velocities variations, all the available radial-velocity data (Frost et al. 1929, Stilwell 1949) are old and of limited precision, which again precludes any definitive conclusion to be drawn.

Thus if we consider only the certain orbital elements, the rate of Am binary is 63%. Among the nineteen Am stars, only two have no evidence of radial-velocity variations. This would imply a rate of binary of 90%. Another point which must be underlined is that some binary systems, like vB 83, need accurate radial-velocities measurements to determine satisfactory orbital elements. So an evidence of a single Am star could only be expected for vB 74 and vB 107.

Finally the number of quadruple-, triple-, double-, single systems is 1:2:14(10+4?):(2?). The numbers between brackets represent the uncertain numbers, for instance there are 10 certain SB and 4 suspected SB (KW 276, KW 286, vB 67 and vB 112), which represents 14 SB1. And the two possible non-binary stars are vB 74 and vB 107. But we cannot exclude that the nineteen Am stars in the Praesepe and Hyades clusters are all binaries.

5.2. Calibration of rotational velocity

Benz & Mayor (1984) have already studied the rotational velocities obtained with CORAVEL. But this study was based on late-type dwarfs. To estimate the influence of parameters such as temperature and microturbulence on the rotation-velocity calibration, we compare the rotational velocities observed with CORAVEL and those found in the literature (Fig. 14). The maximum rotational velocities, which could be measured by CORAVEL is about 60 km s^-1. Up to 40 km s^-1 the literature and the CORAVEL measurement are in good agreement. Only one observation shows a significant difference (KW 224 open square in Fig. 14). McGee & al. 1967 observe a V of 60 km s^-1 and CORAVEL gives 44.0 km s^-1. The CORAVEL value is a mean of three observations, which is not enough to have a good precision for large rotators, i.e. the mean error for this value is 16.98 km s^-1. Nordström et al. (1997) have already pointed out that CORAVEL rotational velocities for values larger than 40 km s^-1 are overestimated.

Fig. 14. Comparaison of CORAVEL and literature rotational velocities.

Therefore we can consider up to 40 km s^-1 that CORAVEL observations of rotational velocities are also reliable for Am stars.

5.3. Distribution of the periods and eccentricities, circularisation of short period binaries

The eccentricity distribution is strongly dependent on the orbital period (Duquennoy & Mayor 1991). Two different regions could be distinguished in a (e, ) plane (Fig. 15). Systems with periods shorter than 10 days have 0.05, while 0.3 are obtained for 10 days. Our cut-off period P (about 10 days) is in good agreement with the value found by Matthews & Mathieu (1992).

Fig. 15. Distribution of the eccentricity as a fonction of the period.

For , the binaries are circularized, mainly as a result of pre-main sequence processes (Zahn & Bouchet 1989). For three of them (filled circles in Fig. 15, KW 279, vB 38 and vB 45) the orbit is circular. The two other stars with non-zero eccentricities are the two multiple systems (open circles in Fig. 15, KW 40 and vB 169). This finding confirms that the presence of a third companion will maintain a small eccentricity in the short period binary, even if its orbital period is long (Mazeh 1990). During the circularization process and the synchronization phase between the orbital period and the rotational period, the rotation will be modified. In the case of Am stars, the rotational velocity will slow down from the typically large value for A stars ( km s^-1), to a few tens km s^-1.

The inclination i of the orbital plane for the synchronised stars, which is assumed to be parallel to the inclination i of the star rotation, can be determined by comparing the observational rotation velocity () and the synchronised rotational velocity (), derived from the orbital period and the radius. The radius of each star is calculated from the T_eff and the corresponding luminosity L. The effective temperature (Table 5) is obtained for KW 279 in Hui-Bon-Hoa et al. (1997) and for KW 40, vB 45 in Hui-Bon-Hoa & Alecian (1998). For vB 38 and vB 169 we must use the photometric estimation. Therfore we have corrected the photometric values of T_eff (Künzli et al. 1997) by the differences of T_eff calculated from the spectroscopic and photometric methods at same values of (B-V). Thus we have coherent values of T_eff. The luminosity is calculated using the apparent magnitude (Table 5), the Hipparcos parallaxes for the Hyades stars and the distance modulus for the Praesepe stars (Mermilliod 1999). Only the apparent magnitude of vB 169 must be corrected to take into account that the apparent magnitude is the sum of all system's stars. Thus we have added (Fekel 1980). The value of i, for vB 169, calculated with this method is in good agreement with the inclination obtained through the orbital parameters determination.

Table 5. Inclination of the orbit i

For vB 45 the inclination in Table 5 is assumed to be 90^o considering the error of the observational rotational velocity. On the basis of these observations, the inclinations are probably not correlated in an open cluster.

For log 1 (squares in Fig. 15), binaries are not circularized (0.3 0.6) and not synchronized. Two new long orbital period Am binaries stars were found (KW 538 and vB 130) increasing the range of periods in the e - log P diagram. Long period Am binaries are probably more numerous than usually expected, but past observing campaigns (Abt 1961, 1985) were not long enough to detect them. In addition the correspondingly smaller amplitudes require sufficient radial-velocity precision. Therefore the gap in the orbital period distribution (OPD) (Budaj 1997) may result from bias in the sample.

The Am stars in the Praespe and Hyades open clusters do not represent a large enough sample to perform a significant statistical study of the OPD and to determine a reliable value of the mean eccentricity of non-synchronised system.

© European Southern Observatory (ESO) 2000

Online publication: February 25, 2000
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