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Astron. Astrophys. 356, 603-611 (2000)

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4. Discussion

The spectroscopic detection of the secondary component and the success of modelling the light- and velocity curves as well as the H[FORMULA] line profile supports our conclusion that HV UMa is not a short-period RR Lyr variable, but an eclipsing binary system. The physical parameters listed in Table 3 give a deep contact configuration of this binary, explaining naturally the lack of significant colour change during the light variation cycle, which would be peculiar in a pulsating variable. Since the primary minimum is due to occultation, HV UMa is a so-called W-type contact binary (systems exhibiting transit eclipses as primary minima are called A-type).

It is well known that contact binaries can be formed either from hot, early-type stars or cool, late-type stars, the latter representing the class of W UMa-type variables (see e.g. Rucinski 1993; Figueiredo et al. 1994 for reviews). The surface temperatures of W UMa-systems are usually below 7000 K, while the temperatures of early-type contact binaries show a much wider range, between 10,000 and 40,000 K. Thus, HV UMa falls into the temperature regime between 7000 and 10,000 K that is relatively rarely occupied by contact binaries. Systems like HV UMa may represent a transition population between early-type and late-type contact binaries (although even the existence of such transition is questionable). These systems lie on the boundary between radiative and convective atmospheres, at about late A - early F spectral types. Detailed studies of such systems would be important, because the formation and the structure of early-type systems having radiative envelopes and late-type contact binaries having convective envelopes is probably quite different.

The period value [FORMULA] day also indicates that HV UMa is not a typical contact system. Recent statistical studies based on the data from the OGLE microlensing survey (Rucinski 1998 and references therein) have shown that the number of contact systems strongly decreases above [FORMULA] day, and there is a well-defined limit at [FORMULA] days. Therefore, HV UMa is a member of the relatively rare "longer-period" contact binaries, although a few contact systems with [FORMULA] days definitely exist, at least close to the galactic bulge. On the other hand, there exists a period-colour relation of "normal" W UMa-stars with period [FORMULA] day, which indicates that longer period systems have bluer colour. On the plot of the empirical [FORMULA] relation (Rucinski 1983) the position of HV UMa, using the mean colour [FORMULA] (Fig. 1, assuming zero reddening) and our revised period [FORMULA] (Sect. 3.1), is close to the upper boundary of the relation, suggesting an atypical, but not peculiar contact system.

A more recent [FORMULA] diagram based on Hipparcos-parallaxes has been published by Rucinski (1997, see his Fig. 2). The position of HV UMa on this diagram was calculated assuming [FORMULA] and [FORMULA], resulting in [FORMULA]. These data show that the position of HV UMa is entirely consistent with that of involving the older [FORMULA] relation, being close to the blue short-period envelope (BSPE, Rucinski 1997), but the system is definitely redder than the upper limit defined by the BSPE, consistently with other contact binaries. Also, a rough comparison of HV UMa with other contact binaries on the [FORMULA] diagram based on OGLE-photometry (Rucinski 1998) strengthens the status of HV UMa outlined above, again, being closer to the BSPE than other systems with similar period, although the lack of observed [FORMULA] colour of HV UMa limits the reliability of this comparison at present. It can be concluded that all available measurements and pieces of information consistently support the contact binary nature of HV UMa.

The new physical parameters collected in Table 3, together with the Hipparcos-parallax ([FORMULA] mas) enable us to estimate the evolutionary status of HV UMa, provided it is indeed a contact binary with those parameters. The coordinates and the distance based on the Hipparcos-parallax indicate that HV UMa is a halo object: its distance from the galactic plane is [FORMULA] pc, which means that [FORMULA]Fe/H[FORMULA] (assumed during the analysis of the line profiles and the colour indices) may not be true. Because the spectroscopic observations presented in this paper have limited spectral range ([FORMULA] Å around 6600 Å), and this region does not contain significant metallic lines in early-type stars, the spectroscopic derivation of [FORMULA]Fe/H[FORMULA] was not possible. Thus, because of the lack of further information we assumed [FORMULA]Fe/H[FORMULA], which is not impossible for halo objects, but [FORMULA]Fe/H[FORMULA] is also likely.

The referee suggested the possibility that the low metal content of HV UMa critically affects the Stark broadening of the hydrogen lines, thus, significantly influencing the temperature derived from the H[FORMULA] profile in Sect. 3.4. We investigated this effect in detail using the pre-computed H[FORMULA] profiles by Kurucz (1979) including Stark broadening. In the left panel of Fig. 9 the dependence of the H[FORMULA] equivalent width on metallicity is plotted. For each temperature, two model sequences for [FORMULA] and 3.5 are shown. It can be seen that the decrease of the metallicity indeed affects the strength of H[FORMULA], but in this temperature range the variation of the equivalent width is governed mainly by the change of the effective temperature. The gravity (pressure) dependence is very weak. Because the equivalent width of the broad H[FORMULA] line strongly depends on the strength of the Stark wings, it is expected that the wings of the H[FORMULA] profile presented in Fig. 5 (corresponding to [FORMULA]A/H[FORMULA]) are not affected very largely by the possible lower metallicity of HV UMa, thus, the derived temperature [FORMULA] K is only slightly dependent on metal content. This is illustrated in the right panel of Fig. 9, where two model profiles corresponding to two different temperatures ([FORMULA] and 7500 K) and [FORMULA]A/H[FORMULA] i.e. significantly lower metallicity than assumed in the previous section are presented together with the observed line profile at quadrature. It can be seen that the [FORMULA] K model still gives a broader line profile than observed, while the [FORMULA] K model results in a much better agreement in the wings, very similar to the case of solar metallicity presented in Fig. 5. Note, however, that the lower metal content causes a less deep line core of H[FORMULA], thus, the problem of fitting the whole H[FORMULA] line is exaggerated when the effect of metallicity is taken into account. Nevertheless, it is concluded that the [FORMULA] km s-1 temperature derived from the wings of H[FORMULA] probably does not contain a significant systematic error due to the unknown metallicity of HV UMa.

[FIGURE] Fig. 9. Effect of metallicity on the H[FORMULA] line profile. Left panel: the dependence of the H[FORMULA] equivalent width on the metallicity for three temperatures (labeled) and two [FORMULA] values (4 and 3.5) for each temperature. Right panel: comparison of the H[FORMULA] of low metallicity models (for [FORMULA] and 7500 K) with the observed profile.

As was mentioned in Sect. 3.4, the colour excess of HV UMa is [FORMULA]. This is supported by the effective temperature derived spectroscopically (discussed above) and photometrically (from observed and tabulated Strömgren indices), because both methods resulted in a consistent value. The negligible reddening is also in agreement with the statement that HV UMa belongs to the halo population.

At first glance, the absolute geometric parameters collected in Table 3 would indicate that the HV UMa system consists of main-sequence components: both stars have [FORMULA] and the mass and radius values of the primary are also similar to those of a main sequence star (the secondary is oversized in relation to its mass, typical of contact systems). However, the surface temperatures and luminosities indicate that HV UMa is probably an evolved object. First, the combined absolute magnitude of the system based on parallax measurement and [FORMULA] results in [FORMULA] mag, where the large error is due to the uncertainty of the Hipparcos-parallax. Using tabulated bolometric corrections, the total luminosity of the system is [FORMULA]. Second, the luminosities of the components are [FORMULA] and [FORMULA] for the primary and secondary, respectively, giving [FORMULA] for the combined luminosity, which is within the error of the distance-based total luminosity estimated above. However, both of these luminosities are much less than the expected luminosity [FORMULA] of a main sequence star with [FORMULA] (Lang 1991). Moreover, this kind of main sequence star would have [FORMULA] K, much higher than the surface temperature of HV UMa. Therefore, the primary component of HV UMa is too cool and too faint for its mass if it is assumed to be a main sequence object.

The agreement with a class III giant star having [FORMULA] for [FORMULA] is much better. The temperature of such giant star is [FORMULA] K which is not very far from the surface temperature of HV UMa. Taking into account the energy transfer between the components in the contact binary (assuming that the total luminosity of the system is due to the energy production of only the more massive primary component), the corrected effective temperature of the primary component is [FORMULA] K. The radius and the surface gravity of this giant star, [FORMULA] and [FORMULA], also agrees well with the derived parameters of HV UMa. Therefore, the comparison of empirical and theoretical values of the physical parameters suggests that the primary component of HV UMa is an evolved object, probably a IV-III class subgiant, or giant star. Because W UMa stars are generally accepted to belong to the old disk population (e.g. Rucinski 1993, 1998), it is reasonable that a long-period contact system, containing a more massive primary than most of other W UMa systems, is significantly evolved from the main sequence. Therefore, the evolved status of HV UMa qualitatively agrees with the age of other contact binaries.

It is interesting to compare the direct empirical absolute magnitude of HV UMa derived above ([FORMULA] mag) with the prediction of the period-colour-luminosity relation of W UMa stars calibrated by Rucinski & Duerbeck (1997) as [FORMULA]. Using the same estimated [FORMULA] index as above, the predicted absolute magnitude for HV UMa becomes [FORMULA] mag, which agrees with the empirical value within the errors. Note, that the deviation of some of the calibrating W UMa stars in the sample of Rucinski & Duerbeck (1997) from the value predicted by this relation is as large as [FORMULA] mag (see Fig. 4 in Rucinski & Duerbeck 1997), therefore the difference between the observed and the predicted absolute magnitude of HV UMa does not make this system discrepant with respect to other contact binaries. On the other hand, it is a bit surprising that the relation that is mainly based on main sequence objects gave such a good prediction for the more evolved HV UMa system. This agreement is probably limited to the particular range on the HR-diagram close to the position of HV UMa, and may not hold on for more evolved systems with [FORMULA] day. Very few known contact systems exist above the [FORMULA] day period value, as recently discussed by Rucinski (1998), this lack of systems also gives a natural limit for the applicability of this relation for longer periods.

The separation of the components in the HV UMa system and the evolved physical state of the primary may suggest that this contact system formed during a case B mass transfer. This may also give a reasonable explanation for the poor thermal contact [FORMULA] K between the components. Model computations of the formation of contact binaries via evolution induced mass transfer from the more massive component (Sarna & Fedorova 1989) predict large amount of temperature excess ([FORMULA] K) at the moment of reaching the contact configuration. The result that the eclipse depths of HV UMa can be modelled with only such high temperature excess may indicate that this contact system formed only recently and did not have enough time to reach better thermal contact. Note, that the temperature excess in W UMa-type contact binaries is usually considered unphysical, because the lack of the colour index variation suggests very good thermal contact for late-type stars. The physically consistent model of the eclipse depths of W UMa-stars contains large starspots on the surface of one or both components (e.g. Hendry et al. 1992). However, in the case of HV UMa with [FORMULA] K, the presence of such starspots is less likely, thus, the eclipse depths of this system may indeed mean a 900 K temperature difference between the secondary and the primary.

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Online publication: April 10, 2000