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4 Discussion

We have shown that V Sge displayed interchanging seasons of largely different activity during the last decades. We demonstrated that regularities and trends can be found both for the general features of the light curve and for the main events. The main results can be summarized in the following way:

Intervals of the suppressed brightness variations (flat segments) interchange with intervals of the pronounced changes (active segments). The borderlines of the segments are sharp. The lengths of the segments (active versus flat) are comparable and are within about one to three, the length of a segment being several years.
The character of the brightness variations in the active segments evolves and depends on the mean level of brightness in the given segment. The low level gives rise to the separated relatively narrow outbursts while HS/LS transitions occur in segments with higher mean brightness. The system spends more time in HS than in LS and these states are more clearly resolved in the histograms for segments with high mean brightness level. This evolution is quantified by a gradual monotonic variation of skewness of the active segments. HSs are brighter than the levels of the adjacent flat segments.

The typical HS/LS variations in segments S3, S5, S7 consist of the well defined levels, separated by relatively rapid transitions with amplitude about 1 mag$_{\rm vis}$. HSs can show "fine" structure, the resulting course of HS/LS is a superposition of the well defined transitions and variations of brightness through the given state. There are no significant differences between the durations of the rise from LS and the decline from HS. With the exception of LSs in S7 the changes of the levels of the respective states are small and their courses can be considered linear. It suggests that the instability develops rapidly at the onset of the active segment (within a single episode of LS) and that the characteristics of HSs and LSs are usually kept for the whole duration of the given segment.

The HSs and LSs occur on a timescale typical for a given segment, though suggested just barely. In any case, the cycle-length near 270 days, found for the HS/LS transitions in S3 and S7, was significantly longer than in S6 (<100 days).

In the following we will confront the observed activity with the mechanisms which are physically acceptable in the respective models for V Sge. We will also make use of a comparison of the characteristics of V Sge with examples of the relevant classes of objects.

4.1 Colliding wind Algol-type binary

Comparison with the activity of the colliding wind binaries (mainly the Wolf-Rayet, WR) reveals that the amplitudes of the brightness variations in the optical are seriously discordant: changes in most WR stars are less than 0.1 mag(V) even on the time scales of decades [35, (Schmutz 1991).] There are a few exceptions-changes of the depth of the eclipse in the WR binary CV Ser by up to 0.5 mag$_{\rm y}$ [12, (Hjellming & Hiltner 1963)] and two dips 1.2 mag deep, separated by 71 years, in HD 164270 [24, (Massey et al. 1984).] However, even in these two cases the kind of activity is hardly comparable to V Sge. The character of activity in V Sge also largely differs from the Be stars, in which the circumstellar envelopes and stellar winds play a large role in the brightness variations. Their long-term variations are rather smooth (waves or broad shallow states of lower brightness), have a typical amplitude just of the order of 0.2 to 0.4 mag(V) and occur on the time scale of months and years (e.g. [26, Mennickent et al. 1994;] [10, Harmanec 1994).]

The characteristics of HSs and LSs in V Sge (distinct levels of brightness, repetition (pronounced in S7) and often rapid transitions between the states-sometimes just 4 days (Figs. 8, 9) put constraints on the underlying mechanism. The circumbinary envelope (uneclipsed light), supposed by HPSP and [22, Mader & Shafter (1997),] can only partly account for the brightness variations in HS/LS transitions. Changes of primary's radius R1 (sometimes R1 even larger than its lobe), detected by HPSP, must occur near LS, too, in order to ensure the observed amplitude. It suggests that the process in transitions between the levels of HS and LS is complex and would imply a tight interplay between the stellar components (especially the primary) and the envelope (changes of R1 near LS leading to the envelope formation). Since there is not significant difference between duration of the transitions from LS to HS and from HS to LS (Table 2), the interplay occurs on the same short time scale for both transitions and suggests a large dependence of the envelope on the current rate of the mass supply. Large abrupt changes of R1 during transitions appear unrealistic if we suppose that we see directly the photosphere of the primary. It is difficult to imagine a mechanism which would rapidly alternate radius of this star between two states to produce the brightness variations in HS/LS transitions. Moreover, radius of the lobe is a quite strict limit for the dimension of the star. Instead, we can get a plausible solution if we interpret the visible dimension of the primary not as a photosphere, but as a current radius within which its wind is optically thick. Indeed, the different levels of LSs for the various segments (e.g. Fig. 7c) rise a question when the system is really clean and quiescent and also where the real photosphere of the light-dominating primary is. It is quite possible that the primary is significantly smaller than its lobe and that we see a surrounding structure of the circumstellar matter ("pseudophotosphere"). This may reconcile the two competing models for V Sge.

4.2 Accreting white dwarf primary

The characteristics of activity of V Sge in segments S3, S5, S7 (the semi-regular interchanging HSs and LSs, separated by rapid transitions) closely follow those observed in CVs of the VY Scl class. For example, clusters of LSs, sometimes replaced by extended intervals of almost stable brightness near the high state, commonly occur in V 442 Oph, S 193 [4, (Garnavich & Szkody 1988 and 1992)] and KR Aur [19, (Liller 1980).] V Sge only differs in the level of the flat segments with respect to HSs in the active segments. HSs are slightly brighter than the adjacent flat segments in V Sge while brightness of HSs is equal to or lower than the level of seasons of the flat curve in S 193 and V 442 Oph. Activity of the supersoft X-ray binary RX J0513.9 - 6951 [1, (Alcock et al. 1996)] is the most similar case to V Sge. The alternating HSs and LSs in RX J0513.9 quite resemble those in V Sge (segment S7), scaled 1.7 times down. Low states in the VY Scl-type CVs are caused by a temporary reduction of the mass transfer rate $\dot m$ (e.g. [36, Shafter et al. 1985).] The amount of matter outflowing from the loser strongly depends on the position of its photosphere with respect to the Roche limit and also on the current conditions near the $L_{\rm 1}$ point. It means that large changes of $\dot m$ can easily be obtained. Both the time scales and the course of the HS/LS behaviour in V Sge are consistent with the response of the mass accreting WD to variations of $\dot m$. This argument is strongly supported by the X-ray variations of V Sge during different optical states, reported by [8, Greiner & van Teeseling (1998).]

The structure of HSs and LSs in V Sge can be resolved in some cases. The light curve, especially in S7, often displays a peak after recovery from LSs. This peak is followed by a decline of brightness through the episode of HS, which is completed by a rapid transition back into LS. On the other hand, a slow brightening through LS is seen in some cases. [20, Livio & Pringle (1994)] and [17, King & Cannizzo (1998)] offered an explanation for the occasional reduction of $\dot m$ in the VY Scl-type CVs by the magnetic field of a spot, appearing in the vicinity of the $L_{\rm 1}$ point of the late-type loser. It explains the episodic character of LSs but because it supposes solar-type spots it can work only for the cool stars with the convective outer layer (COL). However, in the case of V Sge it is very unlikely that the photosphere of its mass-losing secondary is cooler than about 7200 K, when COL sets in. The mass ratio q=3.8 (HPSP) and the geometrical considerations (Paper I) imply its mass and radius typical for mid to late BV star. In addition, the course of HS/LS brings one even more conclusive evidence against the spot theory in V Sge. There is no reason that after disappearance of the spot the brightness should return to a higher level than before the episode of LS and give rise to the peak.

On the other hand, the course of HS/LS strongly resembles what would be expected in the case of instability when the system tries to find a steady state, but is forced to alternate between the high and low levels of brightness. High luminosity of V Sge even in LSs implies that $\dot m$ is still above the critical value, which does not allow the thermal instability to occur. It suggests that the disk remains in the hot state and allows to relate changes of the brightness and $\dot m$ directly [37, (Smak 1989).] The recent model for the irradiation-driven instability (hereafter IDI) of the outer layer of the loser [49, (Wu et al. 1995)] offers a promising mechanism. It makes use of the degree of filling of loser's lobe x, the mass transfer rate y, temperature of WD (accreting star) $\theta$ and indirectly also temperature z of the loser's photosphere facing the accreting star (all parameters being normalized values). IDI allows to obtain double-valued y for a distinct range of x and $\theta$ (their Fig. 1b).

IDI solves the main observed characteristics of activity in V Sge. The two levels of HS and LS and the rapid transitions between them can be interpreted as a direct product of the two-level $\dot m$. Brightness of V Sge also often slowly declines through HS and increases again during LS, in accordance with the predicted course of the mass transfer rate in the IDI model. Moreover, this model allows $\dot m$ to vary even if the radius of the loser stays constant, because the growing dimensions of the disk (especially in the vertical direction) in epoch of the high $\dot m$ shield the loser from further irradiation. It makes the HS/LS transitions even more easy. Since the striking differences in the orbital modulation between HS and LS (HPSP, [28, Patterson et al. 1998)] imply large changes of the distribution of the circumstellar matter in V Sge, the variable degree of irradiation of the loser can be invoked. The promising mechanisms for the striking change of the orbital modulation are the modified disk with high rim [27, (Meyer-Hofmeister et al. 1997;] [34, Schandl et al. 1997)] and/or wind emanating from the luminous disk [31, (Proga et al. 1998;] [9, Hachiya et al. 1998).] They both can lead to a large increase of the dimension of the primary, when $\dot m$ enhances.

The facts, that the difference between the mean levels of the neighbouring active and flat segments is much smaller than the amplitude in the active segments (Fig. 5ab) and that the HSs are brighter than the levels of the adjoining flat segments (Fig. 7c) can be clarified, if the behaviour in the active segments is understood as a perturbation of relatively stable mass outflow from the loser, which occurs in the flat segments. The IDI model predicts that both double-valued y and single-valued y can co-exist and that the system can really alter between stable and unstable mass transfer, for example if $\theta$ varies.

Evolution of the character of the brightness variations from outbursts to HS/LS transitions is quantified by a gradual variation of skewness. It suggests that these seemingly different brightness variations in V Sge are a product of a single mechanism and that the kind of activity just depends on the mean level of brightness in the given segment. We can offer an explanation for this evolution in the framework of IDI, if we include the long-term increase of x. The value of the mass outflow rate from the loser depends on its temperature z (determined by $\theta$) and x. Only variations of $\theta$ suffice for modulation of y inside a given segment. The value of x then would determine the mean properties of activity inside the segment while a slow increase of x from segment to segment may account for the evolution of activity.

The advantage of the model with the accreting WD and the irradiation- driven instability is that the activity and its evolution can be driven by just relatively small variations of the parameters of the mass-losing secondary, which are able to lead to large changes of $\dot m$.

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