This bright A2 Sr star was already known as an SB1 system. Its rotational period, known from its photometric variability, is 69.43 days (Rakosch & Fiedler 1978). Renson (1966) found an orbital period of 106.3 days and published the radial-velocity curve, but not the orbital parameters. A total of 107 measurements have been made over almost 5000 days (Table 6), which confirms the 106 days period (see Fig. 1). However, the residuals are larger than expected from the precision of the measurements, and follow a very clear trend (see Fig. 2). The presence of a third component is certain, although its period is so long that we could not cover even one cycle. The orbital parameters of the primary are given in Table 1. This is the second spectroscopic triple system known among Ap stars, after the SiMg star HD 201433 whose periods are much shorter (see the catalogue of Tokovinin 1997).
The Hipparcos parallax of this star is mas (Perryman et al. 1997); this translates into a distance d=232 pc, after having applied a Lutz-Kelker correction (Lutz & Kelker 1973) which takes into account the exponential decrease of stellar density in the direction perpendicular to the galactic plane. On the other hand, the visual absorption estimated from Geneva photometry is Av = 0.13. Assuming a contribution of about 0.23 magnitudes of the companions to the visual magnitude of the system, the apparent magnitude of the primary alone is V=6.92, and finally we obtain an absolute magnitude for this component. Adopting K (Adelman et al. 1995) and interpolating in the evolutionary tracks of Schaller et al. (1992) for a solar metallicity Z=0.018 (and for a moderate overshooting distance ), one obtains , (g in cgs units) and .Although the uncertainties are fairly large, the primary is evolved and on the verge of leaving the Main Sequence; it is satisfying that our small value agrees with the spectroscopic estimate of Adelman et al. (1995) who gave .
|Figure 4: Radial-velocity curve of HD 137909 including data published by Kamper et al. (1990), by Neubauer (1944) and by Oetken & Orwert (1984). A correction of has been added to the values of Neubauer. The period is days|
Thanks to the Hipparcos satellite, CrB has now a very precise parallax
mas which allows to compute the linear semi-major axis of the relative orbit from the angular semi-major axis obtained by speckle
interferometry ( mas). Since the inclination angle
of the orbit is known from speckle
interferometry and the quantity is known from CORAVEL
measurements, the semi-major axis of the absolute orbit of the companion can be
The HR diagram is shown in Fig. 6. Strangely enough, the agreement between the observed location of CrB and the evolutionary track at the observed dynamical mass is very poor: both the primary and the secondary (if we rely on ) appear overluminous compared to the evolutionary tracks drawn for their mass. Considered alone, the primary might well be at the very tip of the blue hook at the core-hydrogen exhaustion phase, which would reconcile within one its observed and theoretical locations in the HR diagram. Its logarithmic age might then be 9.05 dex instead of 8.9. However, the secondary (indicated in Fig. 6 as a dot arbitrarily placed along the abcissa on the isochrone ) seems overluminous as well, making the puzzle more complicated but also more interesting, and certainly well worth further investigations. Unfortunately, it is not possible to test completely the position of the secondary because of its unknown colours. Such an information would be most interesting to test the idea of Hack et al. (1997) that the companion might be a Boo star with K, although such a hypothesis appears difficult to maintain in view of Fig. 6.
|Figure 6: HR diagram of CrB. The ZAMS, TAMS and evolutionary tracks interpolated for the observed masses are shown as solid lines, while those interpolated for the masses appear as broken lines. The dotted lines indicates the isochrones at and 9.05 (t in years)|
The semi-major axis of the orbit of the binary's photocenter is given in the Hipparcos and Tycho Catalogues (Perryman et al. 1997). This allows an independant test of the magnitude difference : assuming the photocenter to be defined by E1 x1 = E2 x2, where E1 and E2 are the respective brightnesses of the components in the passband and x1, x2 the distances of the components to the photocenter such that x1+x2=a1+a2=a, one obtains au, on the basis of Tokovinin's (one has a0= a1-x1). This is in rough agreement (within three sigmas) with au given in the Hipparcos catalogue. Our estimate assumes a companion with K and takes into account the colour equation between and V (Vol. 2, p. 59 of Perryman et al. 1997) which leads to . Increasing by about 0.2 magnitudes would bring perfect agreement. Unfortunately, Tokovinin (1985) do not give any error estimate on .
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