Although the available information about the systems V 700 Cyg and AW Vir
is based only on photometry and spectral classification, the adopted
spot models fit satisfactorily the observed light curves. The two minima
have unequal depths, and a temperature difference of a few hundred degrees
between the components is expected. The final solution yields a temperature
difference 
between the components of V 700
Cyg, and 
between those of AW Vir.
According to our W-type solution, the larger and more massive component
of both systems is also the cooler one, while the smaller and less massive
is the hotter component.
The thermal-decoupling degree, defined as 
(Lipari &
Sistero 1988), where 
corresponds to the temperature of the larger
and more massive component and 
to that of the smaller and less massive
one, yields values -0.07 and -0.05 for V 700 Cyg and AW Vir,
respectively. These values place the two systems among the W-type
systems in Figs. 2 (click here) and 3 (click here) of
Lipari & Sistero (1988). In the previous
expression for DT we have replaced, according to our W-type solution,
and 
.
We succeeded to model the light curves of V 700 Cyg by invoking two cool spots on the larger (cooler, more massive) component, while for AW Vir one cool spot on the larger (cooler, more massive) component, was sufficient to obtain a satisfactory fit to the observations. As far as the uniqueness of our model is concerned, it should be pointed out that solutions with different spot combinations may equally well fit the observations. According to Maceroni et al. (1990) and Maceroni & van't Veer (1993) this is a general problem of light curve fitting with spot models. On the basis of this argument, we tried to use the simplest model with a physical meaning.
Given that a unique solution can hardly be obtained for partially
eclipsing systems with unknown spectroscopic mass-ratio, we can invoke
an independent check of the quality of the derived (unspotted and spotted)
solutions by considering the residuals for each light curve. Barone et
al. (1993) pointed out that, according to the Chauvenet hypothesis, at
least 
of the points should be in the band defined by the
statistical error lines 
, where 
is given by Eq. (7) of
Barone et al. (1993). In the case of V 700
Cyg we find 
for B and 
for V. For the unspotted solution (with phase intervals 0.13 -
0.24 and 0.61 - 0.82 excluded) 
of the 
points in
B and 
in V lie inside the statistical error lines. When
the whole light curve is considered, the Chauvenet hypothesis is not
fulfilled. In the spotted solution (where all the points are included)
of the 
points in B and 
of the points in V
are within the error lines. Therefore, both the unspotted and spotted
solutions fulfill the Chauvenet hypothesis marginally making thus both
solutions acceptable.
In the case of AW Vir, the error lines are 
in B and 
in V. Similarly, for the
unspotted solution (with phase interval 0.60-0.78 excluded) 
of the 
points in B and 
in V lie inside the error
lines: if we consider the whole light curve, the corresponding
numbers are 
and 
in B and V, respectively. For the
spotted solution 
of the 
points in B and 
in
V are within the statistical error lines. These data indicate that
both solutions, the unspotted and spotted one, are acceptable, since
both fulfill the Chauvenet hypothesis.
After our study had been submitted, a photometric analysis of AW Vir was published by Lapasset et al. (1996). They used the WD code to analyse their B,V light curves, which do not show noticeable asymmetries or irregularities. An unspotted solution was found on the basis of the best fit, which formally corresponds to an A-type configuration, although the values of some physical parameters - mass-ratio, degree of contact and spectral type - are typical for W-type systems. The authors conclude they are unable to assess unambiguously the subtype of this system by photometric evidence only. Since their identification of minimum I and II is the same as in the present paper, we are confident to say that AW Vir oscillates between states of DT between 0 and a negative value.
Our solution is based on B,V light curves, obtained 7 years before the observations of Lapasset et al. They clearly show a brightness deficiency in the phase interval 0.60 - 0.78, and require the application of a spot model. Our W-type solution is based not only on the best fit, but also on the similarity of some basic physical parameters of AW Vir to those typical for W-type systems. Despite the different subtypes found in the two analyses, the geometrical elements (inclination and relative radii) are very similar in the two solutions (see Table 5 (click here)). Lapasset et al. assumed a spectral type G0 for the primary component on the basis of UBV colours; since the photometric data given in their Table 2 are apparently misprinted, it is difficult to judge whether this spectral type is to be preferred over MacDonald's (1964) spectral classification.
Three-dimensional pictures of the spotted models of V 700 Cyg and AW Vir are shown in Figs. 9 (click here) and 10 (click here). Cross-sectional surface outlines of the two systems with their inner and outer critical Roche surfaces are shown in Figs. 11 (click here) and 12 (click here).
Figure 9: A three-dimensional model of V 700 Cyg for phases 0.25 (upper plot)
and 0.75 (lower plot)
Figure 10: A three-dimensional model of AW Vir for phases 0.25 (upper plot)
and 0.75 (lower plot)
Figure 11: Cross-sectional surface outline of V 700 Cyg (dashed line). The
solid lines are the Roche critical surfaces.
Figure 12: Cross-sectional surface outline of AW Vir (dashed line). The
solid lines are the Roche critical surfaces
The present results are based on photometry only, since no radial velocities of the systems exist so far. Nevertheless it is interesting to speculate on the evolution status by using the absolute parameters of the systems. These were computed by the LC program of the WD code and standard relations, where the parameters found in the spotted solutions were used as input parameters, and are listed in Table 5 (click here).
The absolute elements were used to estimate the evolutionary status of the two systems by means of the mass-radius (MR), mass-luminosity (ML) and HR diagrams of Hilditch et al. (1988), who showed that the mass-radius diagram is the principal indicator of the evolutionary state. The primary components of V 700 Cyg and AW Vir lie in the region between ZAMS and TAMS, which is occupied by the primaries of other W-type W UMa systems. The position of V 700 Cyg, quite close to the TAMS, indicates that this system is somewhat evolved while AW Vir is rather unevolved. In both cases, the secondary component lies in the region where other secondaries of W-type W UMa systems are found, and has a larger radius than expected for the ZAMS mass (Hilditch et al. 1988).
The derived W-type solutions, supported by the thermal-decoupling degree of the systems, successfully reproduce the observations and are consistent with the MR, ML and HR diagrams of Hilditch et al. (1988). But more definite conclusions about the evolutionary status of V 700 Cyg and AW Vir can only be drawn by means of additional photometric and spectroscopic observations of the systems.
Acknowledgements
We are especially grateful to Wenxian Lu for taking a spectrum of V 700 Cyg on short notice. We thank W. Van Hamme for useful discussions, the referee, F. van't Veer, for his comments on the manuscript, and H. Busch for communicating data from the Hartha Circular. The 3-D pictures and cross-sectional surface outlines were made by D.H. Bradstreet's Binary Maker 2.0. H.W.D. was supported by a ESO Senior Visitor fellowship.