Astron. Astrophys. 333, 205-218 (1998)

4. Discussion and conclusions

The primary K0 giant of HD 185510 has been found to be quite active both at photospheric and chromospheric level. Our light curves of the three years are asymmetric with the decrease from the maximum to the minimum steeper than the rise from the minimum to the maximum. However, the main feature is a hump just before the maximum clearly defined in the 1993 light curve, which gradually disappears in 1994 and 1995. A similar feature characterizes the Hooten & Hall (1990) light curve, while the asymmetry at the maximum appears reversed in Lloyd Evans & Koen (1987) observations. The change in the asymmetry is accompanied by a decrease in the maximum and minimum levels, and therefore in the mean magnitude. A similar behaviour is reported by Balona et al. (1987), who observed, in 1987, a magnitude mean level brighter than in the 1979-1981 session.

Mean parameters of present and previous light curves are reported in Table 4. A synthesis of the available V light curves of HD185510, grouped for homogeneous time intervals and authorship is shown in Fig. 11. The general behaviour of the light curves is characterized by a deep steady minimum at phase and a variable feature around phase superimposed to the maximum light. In the currently accepted hypothesis that the light changes are due to unevenly distributed starspots on the K0 giant, the detection of a constant rotation period reveals the presence of a long lasting preferential active longitude, the main one more stable at phase and the variable one in the opposite hemisphere, which appears and disappears from time to time and moves also in longitude by about 70-90^o.

Table 4. Rotational V light curve parameters.

Fig. 11. V light curves of HD 185510 at various epoches. Phase are reckoned from the new photometric ephemeris = 2447315.826 + 26.2342 E

Small changes in the spots distribution driven by differential rotation, decay and appearance of spots groups at different latitudes could account for the different rotation period in short time intervals and the phase shifts in some individual rotational light curve, the shift in the Lloyd Evans & Koen light curve phase being the most striking case.

The H emission shows a clear modulation with the rotation period (upper panel in Fig. 10a and b). The obvious anticorrelation displayed by the H emission curve with respect to the photometric light curve, seems to indicate a clear spatial correlation of chromospheric active regions with the photospheric spotted regions, frequently observed in active RS CVn binaries (Catalano et al. 1996). We therefore assume that the H excess emission is mainly or completely due to chromospheric emission plages as also indicated by the Mg II emission seen at all orbital phases (Balona et al. 1987).

4.1. The evolutionary stage of the hot component

Jeffery & Simon (1997) concluded that on the basis of the Ly- solution HD185510B could be a helium dwarf because of the high gravity , while from the photometric solution it would be identified as a sdOB star. Our values of the mass, radius and effective temperature lead us to place HD185510B (Fig. 12) close to the lower boundary of the sdB stars (Heber 1986, Moehler et al. 1990) in the log  -log g diagram. The subluminous B and OB stars are considered extended horizontal branch (EHB) stars, which behave like helium main sequence stars, whose mass is constrained around 0.5 . This average value has been mainly defined by the analysis of EHB stars in NGC 6752 (Heber 1986). HD185510B would be the first sdB star whose mass has been unambiguously determined, but its value M=0.3 is significantly smaller than the typical sdB star mass.

Fig. 12. The position of HD 185510B in the log  -log g diagram (thick cross; solution for ). The location of the zero-age horizontal branch for Y=0.3 and a helium core mass of 0.4691 (Sweigart 1987), an extrapolated extended horizontal branch (dashed line), the helium main sequence and the subdwarf OB stars adapted from Moehler et al. (1990) are indicated. The first part of the evolutionary track for a 0.296 helium star from Iben & Tutukov (1986) model [I-T] is represented by a thin line. The point D indicates the first shell helium flash.

Mengel et al. (1976) suggested that the sdB stars might be formed in close binary systems if Roche lobe overflow occurs during the core helium flash.

The question of how helium dwarfs are formed was first addressed by Kippenhahn, Kohl & Weigert (1967), who followed the Roche lobe filling phase of a primary of 2 and a secondary of 1 . The primary fills its Roche lobe for the first time after it has exhausted hydrogen at its center and has developed an electron degenerate helium core of mass 0.23 . The final remnant dwarf would be only slightly more massive, by 0.03 , than the helium core.

Moreover Iben & Tutukov (1986) discussed the formation and evolution of a helium-degenerate white dwarf of mass 0.3 , i.e. just the mass of HD 185510B. Although the detailed model calculation is made for an initial mass of 1 it applies to any other model of initial mass less than 2.3 , which forms an electron-degenerate helium core before the ignition of helium and which fills its Roche lobe for the first time when the core mass reaches a value of 0.3 . The evolutionary track of the remnant, which undergoes two hydrogen flashes before reaching the final white dwarf cooling track passes close to the location of HD 185510B during the first cooling phase prior to the first flash (point D in Fig. 12, where the most relevant points of the 0.3 remnant evolution from Iben & Tutukov(1986) model are reported in the log  -log g plane together with the location of sdB and sd stars). The evolution time to the first cooling phase is rather short, only about 3 years. This short time evolution, as already pointed out by Jeffery et al. (1992), is inconsistent with the evolution stage of the original secondary HD 185510A, which with an increased mass of 2.24 would reach the present giant stage of spectral class K0 III/IV in about 5.6 years (Iben 1967).

According to the various models the evolutionary characteristics of the system after the mass loss are almost entirely determined by the mass of the helium core at the onset of the mass loss phase. Where, in the case of HD 185510B, a degenerate helium core of 0.3 has been formed, as predicted by Iben & Tutukov (1986), or the core-helium ignition mass has been exceeded leading to a sdB star near the ZAEHB (Heber 1986, Moehler et al. 1990) it is difficult to state. The actual system parameters of HD 185510 and the condition that the primary has filled its Roche lobe for the first time when the helium core mass reached a value of 0.3 places important constraints on the initial parameters and on the mass loss behaviour.

Any interpretation of the evolutionary status of HD 185510B must also take into account the apparent evolved status of the original secondary component and of the dynamical evolution of the system as a consequence of the mass loss from the primary. In order to attempt to estimate the initial parameters of the system, we have made some simple calculations of the parameter evolution under different conditions of mass loss. Starting with the present period, mass and separation we have computed the initial system parameters using the formulae = constant for mass loss from the system and = constant for mass transfer, which also imply angular momentum conservation. The Roche lobe radius, following Paczyski (1971), has been computed as:

where a is the system separation and the mass ratio.

In Fig. 13 we report the evolution of the Roche lobe radius as a function of the remaining mass of the original primary for the conservative case (only mass transfer) and mass transfer plus 10% and 14% mass loss. The comparison with the radius for the appropriate mass (Bertelli et al. 1986) at the core-hydrogen exhaustion (dash-dot line) shows that in the conservative case (curve a) Roche lobe overflow is expected during the shell Hydrogen burning, leading to a typical case B mass transfer, while the addition of only 10% mass loss would lead to Roche lobe radius at the limit of case B overflow (curve b). A 14% mass loss (curve c) produces a sizable shrinking of the orbit and therefore a Roche lobe radius smaller than that at the core hydrogen exhaustion, i.e. a case A overflow with a possible common envelope phase.

Fig. 13. Evolution of the Roche lobe radius of the original primary of HD 185510 during mass loss as a function of the remaining mass M1. Curves are labelled as follows: a) conservative case, b) 10% mass loss from the system, c) 14% mass loss. The dash-dot line represent the radius values at the core-hydrogen exaustion for the various masses from Bertelli et al. (1986).

4.2. The asynchronism problem

As we have confirmed, the giant component of HD185510 is asynchronoulsy rotating, with a rotation period longer than the orbital one. Fekel & Eitter (1989) examined 114 chromospherically active binaries from the first edition of the Catalog of Active Binaries (Strassmeier et al. 1988) and found that 19 systems, i.e. about 17%, including HD 185510 are definitely asynchronous. The fraction of asynchronous rotators increases with the orbital period, being between 86% and 100% for a period longer than 70 days. We have updated the Fekel & Eitter list with more recently determined rotation periods and noticed that about the 50% of the asynchronous systems (11 out of 23) have rotation periods longer than the orbital one. We have investigated the dependence of the asynchronism on the various system parameters. Adopting the ratio / as asynchronism parameter we have found that systems with a small mass function tend to have asynchronism parameter values 1, i. e. rotation period longer than the orbital one, and values 1 for log f(m) . However, the best correlation is exhibited by the semimajor axis of primary star orbit, , mesured in units of the star radius. Fig. 14, where the asynchronism ratio is plotted as a function of , shows a linear dependence of the / ratio on , with stars of smaller rotating slower than synchronous. These results can be interpreted as follows. Small a₁ values indicate large mass ratios with the primary component of larger mass and consequently small mass function. In turn a small mass function means either a low mass companion or a long orbital period and therefore a large separation. The low mass of the companion and the large separation make the tidal effect inefficient to bring the giant primary to co-rotation in a time scale comparable to the evolution time of the star.

Fig. 14. Asynchronism parameter as a function of the semiaxis of the orbit of the more massive component in units of its radius

Habets & Zwaan (1989) have computed the rotation evolution of two systems similar to HD 185510, with low mass evolved secondary component, i.e. AY Cet and  And. They show that during the evolution out of the ZAMS the angular rotation rate of the present primary decreases because of the increase of the moment of inertia and because of magnetic braking, as soon as the convective envelope sets in. The star can spin down to a frequency below the orbital frequency before the tidal interaction becomes strong enough to bring the star in synchronous rotation. They estimate the synchronization time scale according to Zahn (1977) and Campbell & Papaloizou (1983) as

where q= and F is a dimensionless structure constant. The observed dependence of the asynchronism coefficient on is consistent with predictions, i.e. systems with lower mass function (longer orbital periods, larger separation) have on the average a larger asynchronism factor because the synchronization time is much longer.

Let us analyse now the rotational evolution of HD 185510A. Adopting the structure constant k given by Rutten & Pylyser (1988) and the present radius, we estimated that the moment of inertia between the main sequence, i.e. the end of mass accretion, and the present evolutionary status has increased by a factor of 80. This means that, if angular momentum is conserved, the star at the ZAMS spins with an equatorial velocity 260 km/s, which is quite large for a normal 2.25 star. However, we have to consider that such high rotational velocity, at the end of the mass transfer, may be the result of accretion of about 1 of high angular momentum. If tidal interaction and magnetic bracking is included, according to the rotational evolution model for a 2 star by Habets & Zwaan (1989) HD 185510A should be already in co-rotation. The slight asynchronism observed for HD 185510A and the larger one for  And = 2.7) seems to indicate that the time scale of the tidal interaction is significantly longer than predicted by Zahn (1977) and Campbell & Papaloizou (1983). Tassoul (1987) and Tassoul & Tassoul (1992) proposed a pure hydrodynamical mechanism for synchronization and circularization of binaries which predicts shorter time scales than the friction theory of Zahn (1977), therefore in more disagreement with our case.

If one has to give credit to Habets & Zwaan (1989) calculations, the still observed asynchronism of the K0 III component of HD 185510 should indicate that the mass transfer phase has ended only by a few 10⁷ years and that the time scale evolution of the gaining mass stars is rather different from that of a single normal star, to which we have referred the evolutionary status of HD 185510A. In the case of short period binaries, as likely HD 185510 was before the beginning of the mass exchange (P= - ), the time scale for the mass transfer is so short that the companion could not be able to accrete all the mass, but will expand to form a giant envelope overflowing its Roche lobe (Iben & Tutukov 1986). The system passes through a common envelope phase, in which some matter, lost by the donor and of the order of 10 % according to the period evolution scenario of Fig. 13, is flowing out of the binary system. Unfortunately, there are not detailed models describing the very complex evolution of the common envelope phase and of the envelope expansion. In any case, the present temperature and luminosity of the remnant of the original primary star in HD 185510 do not sufficiently excite potential fluorescence of surrounding material to make it observable as a planetary nebula. However, the material may be cold enough to account for the large infrared excess observed by IRAS (Busso et al. 1988). This view would agree with the apparent evolution of the donor as a sdB in the EHB, or near the first hydrogen shell flash according to Iben & Tutukov (1986) model.

We would like to summarize the result of the present work stressing the following aspects:

Although HD 185510 is not a typical RS CVn, the giant K0 III component exhibits significant evidences of magnetic activity both at photospheric and chromospheric level.

Physical parameters of the two components have been improved through a more complete light curve and accurate solution.

The new values of the temperature and gravity classify HD 185510B as a B subdwarf about 10⁷ years old. In order to comply with this short evolution time, the cooler giant component should have evolved through a common envelope out-of-equilibrium phase. A mass loss from the system of the order of 10-15%, the signature of which could be the IR excess observed by IRAS (Busso et al. 1988), is then required.

© European Southern Observatory (ESO) 1998

Online publication: April 15, 1998
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