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Astron. Astrophys. 359, 998-1010 (2000)

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5. Discussion and conclusions

The term "flickering" has never been well defined. In particular, it is not clear whether variations occuring on time scales of hours (or orbital time scales) and those on minute time scales should be regarded as different aspects of the same phenomenon. If this is the case one might expect that the time scales on which the individual events of the flickering develop are drawn from a common, albeit unkown distribution function. If, on the other hand, variations on largely different time scales are due to different physical mechanisms the respective durations will in general be drawn from different distribution functions.

While the statistical superposition of many events makes it impractical to determine the distribution functions directly, a look at the auto-correlation-functions (ACFs) of CV light curves might be helpful. Therefore the ACFs of several hundred light curves of dozens of CVs have been calculated. In the majority of them a common feature can be discerned more or less clearly. As examples, the upper three frames of Fig. 7 contain exemplary light curves with their respective ACFs of three different systems. All ACFs show a narrow central maximum 2 with a half width of several minutes at its base (the exact value can vary between [FORMULA]3 minutes and [FORMULA]20 minutes and appears to be characteristic for each system). This maximum is superposed on a broader base which itself may be structured (but note that ACF structures on times scales not short compared to the duration of the light curve are easily dominated by the accidential presence of randomly distributed features occuring on such longer time scales).

[FIGURE] Fig. 7. Representative light curves of three cataclysmic variables and an artificial flickering curve (left hand frames) together with their respective auto-correlation-functions (right hand frames).

The distinction between the narrow maximum and the broad base suggests that variations with different distributions functions for their respective time scales are superposed. In order to test if this conclusion is reasonable an artificial light curve was constructed which consists of a superposition of two ensembles of flares with different distribution functions concerning their amplitudes and time-scales. The light curve is shown together with its ACF in the lower frame of Fig. 7. The structure of the ACF is very similar to that of the ACFs of the real light curves. While this is not a rigorous proof that the variations in CV light curves are in fact governed by events drawn from different distribution functions, it lends credibility to this conjecture.

If this is true variations on different time scales must be expected to be due to different physical mechanisms. They should therefore not be labelled by the same term. I suggest to use the term "flickering" only for those variations which cause the above mentioned narrow maximum in the ACFs.

These ideas have some bearing on the interpretation of the results of Sect. 4: The lack of sensitivity for variations on time scales longer than the bin width of the smoothed light curves was mentioned in Sect. 2.2 as the main disadvantage of the `single' method. However, even if the `single' method does not see the bulk of the power of the flickering (which is emitted in flares occurring in general on time scales longer than the acceptable bin width) it is sensitive to variations drawn from the same distribution of time scales. Therefore, unless variations drawn from different parts of the distribution are not co-spatial, the part of the flickering sampled by the `single' method is representative for the entire flickering in terms of its location.

It is striking that in all of the present cases as well as in Z Cha (Bruch 1996) (with the exception of the superoutburst state) and V893 Sco (Bruch et al. 2000) the phases of start and end of the scatter eclipse coincide to within the resolution of the scatter curves with eclipse ingress and egress of well defined light sources in the respective systems, be it the white dwarf or the hot spot. This is true also for V2051 Oph and UX UMa where the mean light curves do not show sharp ingress or egress features at these phases, lending confidence that the scatter eclipses are not caused by some hidden effect of the adopted method.

These results leave little doubt as to the place of origin of the flickering. It can arise in two regions: The innermost accretion disk including the boundary layer and the surface of the white dwarf itself (the phase resolution of the scatter curves does not permit to distinguish these regions), and the region of impact of the stream of matter transferred from the secondary star upon the accretion disk. The relative strength of what might be termed hot spot flickering and white dwarf flickering (Bruch 1996) can vary from one object to the other. Whereas in HT Cas the hot spot does not contribute perceptibly to the flickering, in V2051 Oph, UX UMa as well as in Z Cha (Bruch 1996) and V893 Sco (Bruch et al. 2000) hot spot flickering is not negligible. In IP Peg this contribution even dominates the flickering while the white dwarf flickering is all but absent.

Let us assume that at phases away from the orbital hump only the white dwarf flickering (which may be termed [FORMULA]) is visible in the scatter curves. Around hump maximum both, white dwarf flickering and hot spot flickering (termed [FORMULA]), are superposed. Assuming both contributions to be independent the scatter at hump maximum is then [FORMULA]. Determining the average of the scatter in the corresponding curves at phases away from the hump and around hump maximum then permits to calculate the ratio [FORMULA]. Similarly, the mean system brightness during out-of-hump phases, [FORMULA], is due to all light sources except the hot spot, while during hump maximum it is the sum of the hot spot brightness, [FORMULA], and [FORMULA]. Measuring the brightness levels in the mean light curves (no calibration is required because only ratios are of interest here) during the respective phase intervals yields the ratio [FORMULA], i.e. the hot spot flux relative to the flux due to all other light sources of the system. In Fig. 8, [FORMULA] is plotted as a function of [FORMULA] for the stars investigated in this study as well as for Z Cha and V893 Sco. The data for the latter two stars were taken from Bruch (1996) and Bruch et al. (2000), respectively.

[FIGURE] Fig. 8. Ratio of the scatter due to hot spot and white dwarf flickering as a function of the brightness ratio of the hot spot and other light sources in six CVs.

Not unexpectedly, Fig. 8 suggests a general rise of the relative contribution of the hot spot flickering with increasing amplitude of the orbital hump. However, the scatter of the data points is substantial, emphasizing the peculiar behaviour of the individual CVs. Therefore, the formal linear least squares fit, shown as a dashed line in Fig. 8, should only be regarded as an approximate representation of the increase of the relative hot spot flickering strength with the hump amplitude. This is the more so since it obviously depends heavily on the point in the upper right corner which corresponds to IP Peg.

Warner & Nather (1971) first stated that the hot spot flickering might be due to unsteady mass transfer from the secondary star. The question as to why it is unsteady has not yet been addressed and will also not be discussed in more detail here. I content myself in speculating that variations in the upper atmosphere of the red dwarf may cause more or less material to pass through the L1 point. Oscillations similar in nature to solar oscillations, occurring on time scales of minutes, might be responsible. Alternatively (as the referee pointed out) shocks and turbulences could be generated by the impact of the transferred matter on the accretion disk and thus cause flickering even if the mass transfer rate is constant.

Concerning the white dwarf flickering the situation is similar. It has been presumed by Bruch (1992) that unsteady accretion out of the inner disk onto the white dwarf surface could be responsible. However, it is unclear which physical mechanism might cause such instabilities. Lyubarskii (1997) has outlined a scenario of how small scale disk instabilities could possibly cause flickering. It is planned to pursue these ideas further in order to verify if they can lead to an explanation for the white dwarf flickering.

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Online publication: July 13, 2000