The light curve analysis of both systems is quite difficult for the following reasons: (a) no spectroscopic mass-ratio is known, (b) the light curves show significant anomalies with O'Connell effect, and (c) the systems exhibit partial eclipses.
The light curves of V 700 Cyg reveal brightness
fluctuations mainly around the maxima. The O'Connell effect is
observed in both light curves and the magnitude difference between the
two maxima is MaxII - MaxI = 
on the average for both
light curves. A small deficiency of light is noted in the phase interval 0.13 - 0.24, mainly in the B band. The difference between the two
minima is 
in B and 
in V.
The light curves of AW Vir show brightness
disturbances not only around the maxima, but also at other phases.
A decrease in brightness is present in both B and V light
curves in the phase interval 0.60 - 0.78 and a small excess of light is
seen in both curves in the phase interval 0.39 - 0.46. Other minor light
variations are present in other phase intervals. A small O'Connell effect
is observed in both light curves. The magnitude difference between the two
maxima is MaxII - MaxI = 
on the average for both light curves.
The difference between the two minima is about 
in B
and 
in V.
With such anomalies in the light curves, the analysis of both systems is quite difficult. We tried to model the light curves by invoking spots on one or both components. The need to place cool (sunspot-like) and/or hot spots on the components of contact binaries to explain the light curve anomalies and the O'Connell effect, has been suggested by several investigators (e.g. Binnendijk 1960; Hilditch 1981; Linnell 1982; Van Hamme & Wilson 1985; Milone et al. 1987; van't Veer & Maceroni 1988, 1989; Maceroni et al. 1990).
The light curve analysis was carried out by using the most recent
(1993) version of the Wilson-Devinney (Wilson 1990) synthetic light
curve code, which has the capacity of automatically adjusting the
spots. In order to reduce computational time and to smooth the scatter
around the maxima, normal points were formed from the individual
observations and assigned weights equal to the number of observations
per normal. The normal points of V 700 Cyg are given in Table 3 and
those of AW Vir in Table 4 (both tables are available from
cdsarc.u-strasbg.fr). The mean standard deviation for normal points in
B and V are 
and 
for V 700 Cyg, and 
and 
for AW Vir, respectively. Care has been taken
to ensure a faithful resemblance of the normal points to the actual
shape of the minima.
We proceeded to the unspotted solution by assuming that there are no spots on the components of the systems. Therefore the unperturbed parts of the light curves were used. In accordance with the light curve anomalies mentioned before, the observations in the phase intervals 0.13 - 0.24 and 0.61 - 0.82 were not included in the case of V 700 Cyg, while those in the interval 0.60 - 0.78 were omitted in the case of AW Vir.
In the following, the subscripts h and c refer to the hotter and
cooler component, respectively. The shape of the light curve minima
shows partial eclipses, so that we do not know a priori whether the
systems belong to A or W type. In both cases the deeper primary
minimum indicates that the hotter star is eclipsed at primary minimum.
Therefore, the subscripts 1 and 2 in the DC program (with phase of
conjunction 
) are identical with h and c, respectively.
A preliminary set of input parameters for the DC program was obtained
by the Binary Maker 2.0 program (Bradstreet 1993). The DC program was
used in mode 3. In the subsequent analysis the following assumptions
were made:
Case V 700 Cyg:
A mean surface temperature 
according to the spectral
type G5V; bolometric albedos 
and gravity darkening
coefficients 
were assigned values typical for stars with
convective envelopes; limb darkening coefficients 
in B
and 
in V were taken from Al-Naimiy's (1978) tables;
bolometric linear limb darkening coefficients 
were taken
from Van Hamme (1993); third light was assumed to be 
.
Case AW Vir:
A mean surface temperature 
according to the spectral
type F8V; bolometric albedos and gravity darkening coefficients were
assigned the same values as for V 700 Cyg; limb darkening coefficients
in B and 
in V were taken from
Al-Naimiy's tables; bolometric linear limb darkening coefficients
were taken again from Van Hamme (1993);
third light was
assumed to be 
.
The adjustable parameters were in both cases: the phase of conjunction
, the inclination i, the temperature 
, the non-dimensional
potential 
, the monochromatic luminosity 
and
the mass-ratio 
. The quantity 
was adjusted only in the
first few iterations, since it showed no tendency to vary significantly.
The lack of a spectroscopic mass-ratio for both systems led us to search
for the solution with several fixed values for the mass-ratio q in the
range 0.2 - 4.
The values of q<1 correspond to a transit at the primary (A-type system)
and those of q>1 to an occultation (W-type system).
The lowest values of the sum 
of
the weighted squares of the residuals occured at q=0.8 and q=1.6 for the
case of V 700 Cyg and at q=0.8 and q=1.2 for AW Vir, with almost equal
values in both cases for each system.
Figures 3 (click here) and 4 (click here) show the fit parameter 
as a function
of the mass-ratio q. The range in q for V 700 Cyg is 0.4 - 2.8,
since for values of q outside this range no convergent acceptable
solution could be obtained.
Figure 3: V 700 Cyg: The fit parameter 
as a function of the mass-ratio q
Figure 4: AW Vir: The fit parameter 
as a function of the
mass-ratio q
In order to find the final unspotted solution we continued the
analysis by applying the DC program for the above values of q,
treating q as a free parameter. The solutions for V 700 Cyg
converged to q=0.8895 and q=1.5699 with values of 
0.0330 and 0.0319, respectively. In the case of AW Vir the solutions
converged to q=0.8006 and q=1.2222 and the corresponding values
of 
were found to be 0.0210 and 0.0202.
Of these two solutions (A and W-type for each system), we finally
adopted the W-type solutions
by taking into account (a) the better fit of the W-type solution
and (b) the large mass-ratio of the A-type solution,
which would be unusual for an A-type system. In all DC solutions, the
method of subsets (Wilson & Biermann 1976) was used because of the
strong correlation between the adjustable parameters. The parameters
i and q were always taken in separate subsets, since
in many cases q and i can be combined in such a way that the
quality of the solution becomes good for a large range of mass-ratios.
The results of the unspotted solution for both systems are given in Table
5 (click here). In Figs. 5 (click here) and 6 (click here), the corresponding theoretical light curves are
shown as dashed lines.
Figure 5: Normal points and theoretical B and V light curves
of V 700 Cyg. Dashed lines: unspotted solution; Solid lines: spotted solution
Figure 6: Normal points and theoretical B and V light curves of AW Vir.
Dashed lines: unspotted solution; Solid lines: spotted solution
| V 700 Cyg | V 700 Cyg | AW Vir | AW Vir | AW Vir | |||||||||||
| Parameter | unspotted | spotted | unspotted | spotted | unspotted solution | ||||||||||
| solution | solution | solution | solution | (Lapasset et al. 1996) | |||||||||||
 |  |
 |
 |  | |||||||||||
| i (degrees) |  |  |
 |  |  | ||||||||||
 | 0 | . |  | 0 | . |  | 0 | . |  | 0 | . |  | 0 | . |  |
 (K) |  |  |
 |
 |  | ||||||||||
 (K) |  |  |
 |
 |  | ||||||||||
  | 0 | . |  | 0 | . |  | 0 | . |  | 0 | . |  | 0 | . |  |
  |  |  |
 |  |  | ||||||||||
 |  |  |
 |  | 1 | . | 48 | ||||||||
 (B) |  |  |
 |  | 0 | . | 585 | ||||||||
 (V) |  |  |
 |  | 0 | . | 584 | ||||||||
  (B) | 0 | . |  | 0 | . |  | 0 | . |  | 0 | . |  | 0 | . |  |
  (V) | 0 | . |  | 0 | . |  | 0 | . |  | 0 | . |  | 0 | . |  |
  (bolo) | 0 | . |  | 0 | . |  | 0 | . | 
| 0 | . |  | |||
| % overcontact | 26% | 27% | 9% | 8% | 2.1% | ||||||||||
 (pole) |  |  |
 |  | 0 | . | 332 | ||||||||
 (side) |  |  |
 |  | 0 | . | 348 | ||||||||
 (back) |  |  |
 |  | 0 | . | 383 | ||||||||
 (pole) |  |  |
 |  | 0 | . | 391 | ||||||||
 (side) |  |  |
 |  | 0 | . | 414 | ||||||||
 (back) |  |  |
 |  | 0 | . | 446 | ||||||||
 | 0 | . | 0319 | 0 | . | 0338 | 0 | . | 0202 | 0 | . | 0157 | |||
 | 0 | . | 60 | 0 | . | 84 | |||||||||
 | 0 | . | 92 | 1 | . | 11 | |||||||||
 | 0 | . | 86 | 0 | . | 95 | |||||||||
 | 1 | . | 04 | 1 | . | 08 | |||||||||
 | -0 | . | 13 | 0 | . | 08 | |||||||||
 | -0 | . | 08 | 0 | . | 10 | |||||||||
 assumed. | |||||||||||||||
Inspection of Figs. 5 (click here) and 6 (click here) reveals that the theoretical ``unspotted''
light curves do not fit satisfactorily the
observations (normal points). The disagreement for V 700 Cyg is relatively
small in the phase regions before MaxI and around MaxII, while the
disagreement for AW Vir is severe around MaxII (O'Connell effect).
In order to take care of the decrease of brightness in the above phase
intervals
in both systems, a spotted solution was carried out by adopting the
simplest spot model with a physical meaning, i.e. by assuming that the
systems have cool spots on the primary component of the same nature as
solar magnetic spots (Mullan 1975). Two cool spots were placed on the
primary (larger, more massive and cooler) component of V 700 Cyg and
one cool spot on the primary (larger, more massive and cooler)
component of AW Vir. The Binary Maker 2.0 program was used to obtain
the best fit by adjusting the spot parameters: the latitude b, the
longitude l, the angular radius R and the temperature factor 
Once the best fit was obtained, the DC program was used to derive the
final solution. At this stage of the solution the DC program (1993
version) was used to adjust some of the spot parameters (longitude,
angular radius and temperature factor) together with the system
parameters i, 
, 
, q and 
. Because of
convergence problems with a simultaneous adjustment of all parameters,
we employed the method of subsets in the sense: system parameters,
spot parameters, system parameters etc. (Van Hamme, private
communication). The differential corrections were computed until the
corrections became smaller than their probable errors. A few more
iterations were always performed after obtaining a convergent solution
to ensure its stability. The final results of the spotted solution of
V 700 Cyg and AW Vir are given in Table 5 (click here), and the corresponding
theoretical light curves are shown as solid lines in Figs. 5 (click here) and 6 (click here),
respectively. The final spot parameters for the two systems are given
in Table 6 (click here). The final spotted solution for V 700 Cyg (where the spots
were adjusted) places the two spots on the primary in positions where
both are visible at phase 0.0 and hence should introduce perturbations
in that phase region. These perturbations are quite small, of the
order of the statistical error lines (see Sect. 5 for a discussion),
because the temperature factor of the spots are very close to
unity. The 
differences between the observed and calculated
points for the unspotted and spotted solutions for the two systems are
shown in Figs. 7 (click here) and 8 (click here), respectively.
Figure 7: The light curve 
residuals for V 700 Cyg in B and
V band. Crosses refer to unspotted solution; asterisks refer to spotted
solution
Figure 8: The light curve 
residuals for AW Vir in B and V
band. Crosses refer to unspotted solution; asterisks refer to spotted
solution
| V 700 Cyg | V 700 Cyg | AW Vir | |||||||
| parameter | spot 1 | spot 2 | spot 1 | ||||||
| b (degrees) | 90 | 90 | 80 | ||||||
| l (degrees) | 241.77 |  | 6.41 | 123.20 |  | 4.58 | 309.51 |  | 4.98 |
| R (degrees) | 20.16 | | 0.84 | 19.60 | | 1.07 | 14.56 | | 0.32 |
 | 0.945 | | 0.005 | 0.952 | | 0.006 | 0.720 | | 0.028 |