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Astron. Astrophys. 360, 627-632 (2000)

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3. Discussion

We have presented an analysis of the long-term activity of the intermediate polar DO Dra with emphasis on its outburst behaviour. The densely covered light curves enabled one to determine the course of the outbursts in this system for the first time and gave a rare opportunity to study outbursts in an intermediate polar.

A test whether the outbursts of DO Dra can be caused by the thermal instability, operating in dwarf novae (e.g. Smak 1984) can be made using the [FORMULA] diagram (Fig. 6). This diagram, based on the data from Hellier (1996), Patterson (1994), Warner (1997), Ritter & Kolb (1998) and VSNET (www.kusastro. kyoto-u.ac.jp/ vsnet/), also enables a comparison of DO Dra with other IPs (Fig. 6). [FORMULA] refers to the absolute visual magnitude. The relations between [FORMULA] and the maximum brightness of outbursts in dwarf novae and their quiescent level are plotted, too, according to Warner's (1987) Eq. (13) and Eq. (18), respectively. It can be seen that most IPs lie between these two lines. They are fainter than nova-like systems which have [FORMULA] comparable to dwarf novae in outburst (Warner 1995). [FORMULA] depends on the inclination angle i but since most IPs plotted here do not show eclipses, their i is not larger than about 70o. It can readily be seen that DO Dra is the less luminous IP among those plotted in Fig. 6 and even lies below the level of quiescent dwarf novae. Along with the weak magnetic field of the WD in DO Dra (Norton et al. 1999) and moderate i (Haswell et al. 1997) it supports the idea that the low [FORMULA] of this system is caused by quite a low mass transfer rate and not by a largely truncated disk. DO Dra therefore lies in the region which fulfils the conditions for occurrence of dwarf nova outbursts.

[FIGURE] Fig. 6. Comparison of the position of DO Dra with other intermediate polars in the [FORMULA] diagram. The filled circles denote the typical brightness of the respective IPs. Outbursts and low states are marked by empty circles and squares, respectively. GK Per lies out of range. The relation between [FORMULA] and the maximum brightness of outbursts of dwarf novae (dashed line) and their quiescent level (dot-dashed line) are plotted, too, according to Warner's (1987) Eq. (13) and Eq. (18), respectively. See Sect. 3 for details.

The decay branches remain remarkably similar for the individual outbursts of DO Dra. The properties of the cooling front which, in the framework of the thermal instability model always starts in the outer part of the disk and moves inwards, therefore remain stable for the respective events. The decay branch of the outbursts in DO Dra is faster than exponential. The observed decay rate [FORMULA] days [FORMULA] is considerably faster than that for non-magnetic dwarf novae because Eq. (3.5) in Warner (1995) predicts [FORMULA] days [FORMULA].

Width of the outbursts W in DO Dra can be compared with non-magnetic dwarf novae using the relation of van Paradijs (1983) where W is measured 2 mag below mag(max). The mean W for [FORMULA] hours is about 5.8 days (within 4.4-7.5 days). The rise of the outburst in Fig. 2 c and the upper limits of the remaining three confirm that W in DO Dra is consistent with or slightly smaller than the lower limit for W of the narrow outbursts in non-magnetic CVs and by far smaller than W of the wide outbursts in these systems.

When explaining the features of the outbursts in DO Dra, it is natural to take into account the influence of the magnetized WD on the disk. Cannizzo (1994) presented models of the decay branches for various values of the inner disk radius [FORMULA], using the viscosity parameter [FORMULA] as a function of the disk radius in the form [FORMULA]. Angelini & Verbunt (1989) used [FORMULA] independently of the radius but they modeled the full outburst light curve and [FORMULA] for two largely different values of [FORMULA]. Both approaches confirm the decrease of [FORMULA] with increasing [FORMULA]. Cannizzo's (1994) model further predicts that the decay branch ceases to be exponential with increasing [FORMULA].

Our observational facts for the outbursts in DO Dra (decay faster than exponential and faster than predicted for non-magnetic dwarf novae) are in good agreement with both above-mentioned models of outbursts in disks with the missing inner region. These facts further imply that despite the low field strength (Norton et al. 1999) the magnetosphere of the WD in DO Dra is not fully compressed during the outburst and the central region of the disk is still missing. Mass accretion during the outburst therefore is not large enough to diminish the Alfven radius down to the surface of WD and the matter is supposed to be still channelled onto its pole(s). Also the small W of the outbursts in DO Dra is in accordance with Angelini & Verbunt's (1989) model for outbursts in disk with large [FORMULA]. These facts may suggest that the crude assumption made by Angelini & Verbunt (1989) that [FORMULA] remains the same in quiescence and during outburst is not far from true in the case of DO Dra.

We determined the mean [FORMULA] of the outbursts in DO Dra over the last 63 years to be about 870 days. The cycle-to-cycle variations of [FORMULA] are significantly smaller than the full amplitude of the [FORMULA] variations, apart from the last two outbursts which may suggest an increase of [FORMULA]. Position of DO Dra in the [FORMULA] diagram (Fig. 11 in Paper I) places this system well above the location of all dwarf novae having 3 hr[FORMULA] day. The exceptionally long [FORMULA] along with the short duration of outbursts in DO Dra can be interpreted in terms of the thermal instability which starts in the inner region of the disk with missing central part (inside-out outburst), following the model of Angelini & Verbunt (1989). Their model showed that if the inner disk region is missing in quiescent IP, a higher critical density must be achieved to initiate the transition of the disk to the hot state in comparison with non-magnetic CV; longer [FORMULA] is therefore needed.

Mag(max) of DO Dra is consistent with Warner's (1987) relation for maxima of outbursts in non-magnetic dwarf novae (his Eq. (13)) (Fig. 6). The magnetic field of the WD in this system therefore does not lower much the visual luminosity at the outburst maximum. Again, following the models of Angelini & Verbunt (1989) it points to the inside-out type of outburst. The visual luminosity at maximum of outburst is supposed to come mostly from the middle region of the disk and is thus less dependent on the missing inner region.

There is no apparent trend in the variations of the quiescent level between the neighbouring outbursts of DO Dra. Instead, the slow component of these fluctuations, having quite a large amplitude (almost 1 [FORMULA]), can roughly be described as waves on the time scale of tens to hundreds days, that is much shorter than [FORMULA]. It is not well known yet if these waves are tightly related to interaction of matter with the magnetic field of the WD but they are uncommon for most dwarf novae (WW Cet is a rare exception; Ringwald et al. 1996). On the other hand, they are similar to the dwarf nova HT Cas (Robertson & Honeycutt 1996) which is a suspected IP (Warner 1995).

Let us compare the outbursts of DO Dra with those reported for several other confirmed IPs. The outbursts in TV Col and V 1223 Sgr have a lower amplitude (about 2 mag), a much shorter duration (1 day or less) and much faster decay rate ([FORMULA] and 0.21 days [FORMULA], respectively (Schwarz et al. 1988, van Amerongen & van Paradijs 1989). Both systems are significantly more luminous than DO Dra (Fig. 6). Outbursts of EX Hya ([FORMULA] days) have [FORMULA] consistent with that of non-magnetic dwarf novae with the corresponding [FORMULA] (Bailey 1975). Hellier & Buckley (1993) discussed these three IPs thoroughly (including their spectral changes over outburst) and concluded that their outbursts are caused by mass transfer bursts from the secondary instead of thermal instability.

In conclusion, our analysis has shown that the photometric parameters of outbursts of DO Dra, in conjunction with the deviating position in the [FORMULA] diagram and the weak magnetic field are consistent with the thermal instability in accretion disk with the missing inner region.

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© European Southern Observatory (ESO) 2000

Online publication: August 17, 2000