Application to HT Cas

In the previous section it was shown that in the case or artificial light curves with well defined properties both methods yield the expected results within their respective limitations. Now, the 'ensemble' method will be applied to real light curves of the dwarf nova HT Cas (the application of the 'single' method to the same data will follow in Sect. 4.1).

Since HT Cas does not show a strong orbital hump, and since the effect of an unsuitable choice of on the scatter eclipse is limited, the entire light curve with the exception of the eclipses ( ) was used to define . The resulting curve is shown in Fig. 2c. It has no resemblance with the corresponding curve calculated with the 'single' method (Sect. 4.1, Fig. 3). In particular, no trace of a scatter eclipse is visible. Quite on the contrary! This can be understood regarding the three exemplary light curves of HT Cas (binned in phase for clarity but not altered concerning their count rates) in Fig. 2b. The count rates out of eclipse are not proportional to those at the minima. Thus, the basic assumption of the 'ensemble' method is violated. This is underlined by the relation between the reference count rate and the count rate at eclipse minimum shown in Fig. 2a (here, the data points representing the light curves shown in the middle frame are ringed). It is obvious that both quantities are not proportional to each other but only loosely correlated.

  

Figure 2: a Count rates of the light curves at HT Cas at eclipse bottom as a function of the out-of-eclipse count rate. The ringed data points correspond to the light curves shown in the next frame. b Three light curves of HT Cas, binned in phase for clarity but unaltered concerning the count rates. c Scatter curve of HT Cas calculated using the 'ensemble' method.

In principle the violation of the basic assumption could be due to the fact that the light curves are expressed in count rates rather than in fluxes. As was detailed in Sect. 2.1 the method assumes that long term variations at a given phase scale linearly with the reference count rate. In the present context variations of the count rates may be due to real long term variations as well as to different instrumental setups. The latter would cause the same relative variation at all phases while for the former the relative variations can be phase dependent. Thus, mixing real long term variations and such due to instrumental effects causes a superposition of two different equations of the kind (see Sect. 2.1), resulting in an apparently enhanced scatter.

Although this effect may contribute to the failure of the 'ensemble' method in the present case it is certainly not the principle reason. The strongly variable eclipse depth in HT Cas with respect to the out-of-eclipse light level is independent of the absolute value of the count rates and would clearly lead to a strong scatter during eclipse even if the light curves were expressed in fluxes.

Application of the 'ensemble' method to light curves of UX UMa (Sects. 3 and 4.4) led to a similar failure.