Astron. Astrophys. 327, 1094-1106 (1997)

4. Absolute dimensions and evolutionary status

By using the standard indices (Table 1) and the luminosity ratios for the components (Table 8) we calculate the individual standard indices given in Table 9 (uncorrected for the interstellar reddening). Combining these with unreddened indices for O7V and O9V stars from Crawford (1975), we find a colour excess of E()= , the same value obtained with the mean dereddened colours by Philip & Egret (1983). This is slightly lower than , found for V 3903 Sgr by Herbst et al. (1982), but definitely inside the errors and in better agreement with colour excesses determined for other member stars of the R association Simeis 188. The absorption (=4.28 E(), Crawford & Mandwewala 1976) is then , in full agreement with our previous estimation (Sect. 3.3.1).

Table 8. Mean elements for V 3903 Sgr.

Table 9. Individual standard indices, not corrected for reddening

We do not find any need for an anomalous law for the interstellar absorption, as Schultz & Wiemer (1975) found for HD , probably because V 3903 Sgr is not very close to the center of the Lagoon Nebula complex. Torres (1987) also assumes a normal interstellar extinction law towards NGC 6530. As there are less steps and approximations in the derivation above, we consider it to be more reliable than the former one. Taking this into account, together with bolometric corrections estimated from Popper (1980), we can use our results (Table 8) to calculate the absolute dimensions of the system and estimate its distance. The relevant results are shown in Table 10.

Table 10. Astrophysical data for V 3903 Sgr.

Fig. 5 shows both components of V 3903 Sgr (with error bars) in the vs. diagram, together with the tracks and isochrones from Claret & Giménez (1992) models for solar composition, considering mass loss and convective overshooting. The components are well represented by the models both in the tracks for the individual masses and by a unique isochrone, giving the theoretical age for the system at yrs (), practically the same age of the young cluster NGC 6530. The theoretical effective temperatures at the predicted evolutionary stages agree with the values of Table 10.

Fig. 5. Evolutionary diagram versus from Claret & Giménez (1992) and the components of V 3903 Sgr. The solid lines represent the evolutionary tracks for each mass while the other lines are the isochrones, labeled in .

The ratio is determined with an error 0.7% (Table 8), but the existing temperature calibrations for O stars are claimed to be accurate only to 5% (Hilditch et al. 1996), these being the errors quoted in Table 10. However, our results are consistent to a much higher precision: there is a common isochrone for the system, and the individual evolutionary tracks match the determined masses, even assuming temperature errors as small as 1.4% in Table 10, as shown in Fig. 5, where the error bars plotted are for the 600 K limit.

Recently (Claret 1995), a different approximation for mass loss (Nieuwenhuijzen & de Jager 1990) was introduced for models with initial masses above during the main sequence stage, and this has consequences for both components of V 3903 Sgr, mainly in their theoretical ages. As can be seen from Fig. 6, the larger mass loss of these new models place both components at the significantly younger age of 1.6 yrs ( 6.21), as compared with the age given by the 1992 models. The tracks for the calculated masses match both components at the correct theoretical temperatures and with a unique isochrone, showing again very consistent results.

Fig. 6. Evolutionary diagram versus from Claret (1995) and the components of V 3903 Sgr. The solid lines represent the evolutionary tracks for each mass while the dotted lines are the isochrones, labeled in .

4.1. Possible membership of a complex structure

The ages quoted for NGC 6530 range from =6.3 (Battinelli & Capuzzo-Dolcetta 1991, Sagar et al. 1986) to 6.5 (Strobel et al. 1992). The latter work estimates the apparent distance modulus of NGC 6530 as m -M . Using our estimation of (which yields m -M ), both these ages and distances are in a good agreement with our results.

V 3903 Sgr is off the center of NGC 6530, and this represents a projected distance of 30 pc. The diameter of NGC 6530 is ( pc, Battinelli & Capuzzo-Dolcetta 1991). Although reasonably far from the center of the cluster, the near equality of the distances and ages indicates that probably V 3903 Sgr is a member of the complex containing NGC 6530 and the Lagoon Nebula (M8).

4.2. Circularization and synchronization times

Eclipsing binary systems as close as V 3903 Sgr are good candidates for the study of internal stellar structure. One consequence of the rotational distortions is the exchange between the orbital angular momentum and the spin angular momentum due to the viscosity of the stellar material, yielding the circularization of the orbit and the synchronization of the rotation of each component. Systems with short periods systematically present both small eccentricities (Batten et al. 1989, Duquennoy and Mayor 1991, Latham et al. 1988, 1992) and synchronous rotation of its components with the orbital motion (Kreiken 1935, Swings 1936, Levato 1976, Abt and Levy 1959, Giuricin et al. 1984a, b, Schneider 1986, Tan 1986). This is a sign of tidal forces acting on the systems.

There are currently two approaches with respect to the tidal interactions on radiative stars like the components of V 3903 Sgr. According to one of them (Zahn 1975, 1977, 1984), a periodic external potential induces forced oscillations on the external radiative envelope of the star, which in turn dissipates energy near the stellar surface by radiative damping. The other interpretation treats the effect as a purely hydrodynamical mechanism (Tassoul 1987, 1988, 1990) based on large scale meridional flows.

Since tidal forces depend very sensitively on the stellar dimensions, only binary systems with absolute dimensions accurately determined are suitable to test the models. V 3903 Sgr is such a system, especially interesting not only for the massive components and their consequent rapid evolution, but for the significant difference in the components' masses, also, permitting a precise age determination by fitting an isochrone to the stars. The characteristic time scales were integrated following Claret et al. (1995, Claret and Cunha 1997): , the time when the eccentricity should vanish (circularization), and , when each component became synchronized with the orbital period. The results are given in Table 11.

Table 11. Logarithm of critical ages (yrs) for circularization and synchronization for V 3903 Sgr.

Despite the system's short age, 6.2, the actual orbital eccentricity and rotation for both components do agree very well with both formulations mentioned above. The hydrodynamical mechanism, as proposed by Tassoul, is clearly more efficient than the conventional tidal theory during the main-sequence phase, but this result must be taken with care since the very existence of this mechanism is controversial (Rieutord 1992, Rieutord & Zahn 1997).

© European Southern Observatory (ESO) 1997

Online publication: April 6, 1998
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