The ellipsoidal model suggested for this star by
Hill et al. (1976) must
be ruled out on the grounds of two strong pieces of evidence: the dramatic
changes shown by the light curves from 1969 to 1992 and the light-colour
correlations obtained just from the data presented by these authors. In a short
period binary star, the tidal strain cannot disappear for years, yielding the
flat light curve observed by
Garrido et al. (1983), and then become again
visible. On the other hand, an ellipsoidal variable would appear redder at
the light minima than at the light maxima: the effective temperature in two
arbitrary points on the surface of a distorted star in radiative equilibrium
fulfils the relation 
, where
g1 and g2 are the respective gravity values. The heating
produced by the presence of the companion (often misleadingly called
reflection effect) can cause changes only on the side facing the
secondary component. The contrary follows from the colour curves obtained from
Dominion's simultaneous multifilter measurements. In Fig. 11 (click here) we can compare a
light curve (
(55), in the top of the figure) with a colour curve
(
, in the middle), both phased with the previously
determined frequency of 0.09918 d -1 : luminosity and colour temperature
increase upwards. The periodic component of the 
curve
(bottom of the figure), which has been isolated resorting again to the MPDM
method (Bossi & La Franceschina 1995), shows an intermediate phase shift.
Figure 11: (55) light curve (top), colour
curve (in the middle) and periodic component of the
curve (bottom). All these series of data, obtained from the photometry published
by Hill et al. (1976), are phased with a frequency
of 0.09918 d -1 . Luminosity and colour temperature increase upwards
The negative correlation which we observe between luminosity and colour temperature could in principle be consistent with an eclipsing binary mechanism. It would entail an eclipsing body hotter than the eclipsed one both in the primary and in the secondary light minimum; however, the strong rotational distortion of the Be object could make it plausible at first glance: a companion with an intermediate temperature between the equatorial belt of the primary star and the average of its projected figure, if put into an ad hoc orbit, would meet this requirement. Nevertheless, a quantitative model fitting proves a hopeless task: the temperature range on the surface of 14 Lac, as it has been evalued in the preceding section, is very far from explaining the colour variations implied by the data of Hill et al. (1976). Moreover, a comparison of the equatorial radius to the orbital separation leads us to exclude a simple succession of eclipses as the mechanism responsible of the observed light changes. On the other hand, the absence in the light curves of horizontal stretchs between eclipses cannot be due to the tidal strains: as stated above, it would not agree with the observed light-colour correlations. Besides, we can neglect the effect of tidal strains on the basis of simple dynamical considerations. The upper limit of the gravity perturbation due to tide is given by the expression:
We can easily verify that, assuming P 
10 days,
not even the presence of a supermassive black hole would cause at the equator
of 14 Lac more than a 
2% gravity perturbation.
Figure 12: Fraction of the total measured V light ascribable to a secondary star
whose radius fulfils Eq. (2) as a function of its spectral type
The fraction of the total measured V light ascribable to a secondary star whose
radius fulfils Eq. (2) is shown in Fig. 12 (click here). As can be immediately realized,
only the tidal deformation of an F0 companion could in theory reproduce the
scale of the observed variations. Another strong constraint must be laid down
on the angle 
between the view line and the
orbital plane: small values (
) would result in
deep eclipses (up to 
in V), high values
(
) would reduce both the rotational luminosity
modulation of the secondary body and the projected component of its orbital
motion below the observed thresholds. In spite of these narrow boundaries, the
assumption of a strongly deformed companion as the source of the light
variations would have the advantage of an at least qualitative consistency with
our light-colour correlations: such object would contribute the 28%
of the total V light against the 19% and the 11% of the
B and U lights respectively. Nevertheless, also this variant of the ellipsoidal
model is ruled out by the observations of
Garrido et al. (1983). In fact,
if we combine the photometry presented by these authors with our spectroscopy,
we are led to assign the companion star to a spectral type not far from K0.
Figure 13: Our 
curve (top) compared to the nightly mean intensities
of the H
emission component A), of the H shell nucleus
B), of the (FeI?) line visible at 6613 Å C) and of the probable
HeI
shell nucleus D). All the data are phased with a frequency
of 0.0982 d -1
If the light curve of 14 Lac proves inconsistent with simple duplicity effects,
it seems to make up for it correlating with the considerable changes shown in
the same time scale by all the circumstellar components of our spectra,
including the very peculiar line visible at 6613 Å (as we have seen,
it can neither originate in the photosphere of the B star nor belong to the
spectrum of a companion): in Fig. 13 (click here) our curve
is compared to the
nightly mean intensities of these features. Therefore, nothing remains except
for us to ascribe the variability observed in this star to circumstellar
phenomena. Moreover, our data indicate a complex shell structure: to the
light decrease during the secondary minimum corresponds an intensity rise of
the circumstellar H components, while the line at
6613 Å and the HeI shell nucleus undergo
simultaneous intensity falls.
This result does not diminish the relevance of a probable duplicity. As can be clearly seen, duplicity is likely to play an important rôle in the modulation of the circumstellar effects: the gravitational perturbation due to the presence of a second body breaks any symmetry in the envelope of a shell star causing observable changes characterized by its orbital period.