4. The scatter curves
The mean scatter curves for HT Cas, V2051 Oph, IP Peg and UX UMa were calculated using the `single' method. A bin width of 0.01 in phase was used for all stars when calculating the smoothed light curve (see Sect. 2.2). Therefore, only flickering occurring on time scales below roughly for HT Cas and V2051 Oph, for IP Peg and for UX UMa is seen.
4.1. HT Cas
HT Cas belongs to the SU UMa subclass of CVs. In the prototypical eclipsing members of this group the light curves exhibit a strong orbital hump and the eclipse profile permits to separate the eclipse of the white dwarf and of the hot spot (OY Car: Wood et al. 1989a; Z Cha: Wood et al. 1986). In this respect HT Cas is rather unstable: An orbital hump is sometimes present; at other epochs no trace of it is visible. It is never as prominent as in OY Car and Z Cha. Similarly, the eclipse profiles may or may not show the typical structure caused by a white dwarf eclipse, followed slightly later by a hot spot eclipse (see e.g. Fig. 8 of Patterson 1981). A representative light curve and the mean of all curves studied here (normalized to a common mean count rate) are shown in Figs. 3a and 3b. There is no significant orbital hump in the mean curve, and the eclipse profile contains at most a remnant of a two-step eclipse (white dwarf and hot spot). Thus, on the average the hot spot has no significant influence on the light curve shape in the present data.
When applying the `single' method to the HT Cas light curves it was found that due to the very sudden start and end of the white dwarf eclipse ingress and egress and to the short duration of these phases the spline interpolation to the binned light curve (performed as outlined by Bruch 1996) could not follow well the eclipse ingress and egress, causing large residua in the difference curve at these phases. These translated into artificial peaks in the scatter curve. To alleviate this problem additional fiducial points for the spline interpolation were defined interactively at the beginning and end of the steep parts of eclipse ingress and egress. While this significantly reduced the height of the sharp peaks in the scatter curve, it could not remove them completely.
The resulting scatter curve, calculating the scatter in phase intervals of width 0.005 and adopting a step-width of 0.0025 (meaning that neighbouring points in the scatter curve are not independent of each other) is shown in Fig. 3c. Each point in the final scatter curve is the mean value of several individual curves. An error of ("mean error of the mean") is assigned to each point, where m is the number of individual points contributing to the mean, and is the standard deviation. The representative error bar shown in the upper left corner of Fig. 3c is the average value (= 0.097) of the errors of all data points. The dashed vertical lines are the eclipse contact phases of the white dwarf as measured by Horne et al. (1991). It is seen that - disregarding the artificial peaks occurring during eclipse ingress and egress - the minimum of the scatter curve coincides with the eclipse of the white dwarf. Thus, the flickering light source in HT Cas is well centered on the central body.
Although it may not be very significant in view of the noise in the scatter curve, the scatter eclipse appears to be V-shaped rather than flat-bottomed. If this is true it would mean that the flickering light source is a bit larger in extension than the white dwarf itself. However, it cannot be much larger because otherwise the ingress of the scatter eclipse should start earlier (and end later) than the white dwarf eclipse as the secondary star covers more and more of the region where flickering occurs. This is not seen.
There is no significant enhancement of the scatter during the phase interval in which the canonical hot spot is visible in many CVs. Thus the region of impact of the transferred matter onto the accretion disk appears not to host a flickering light source in HT Cas. The lack of any systematic trend of the scatter which phase (except for the eclipse) is formally confirmed by a Gauss fit to a histogram of the (out-of-eclipse) data points which yields a standard deviation of 0.101, almost identical to the average mean error of the data points of 0.097. This constancy of the scatter (disregarding the eclipse) is different from what is found for e.g. Z Cha (Bruch 1996), V893 Sco (Bruch et al. 2000) and IP Peg (see Sect. 4.3).
The present quantitative results are in agreement with qualitative conclusions of Patterson (1981), namely that the flickering in HT Cas originates from regions very close to the white dwarf.
4.2. V2051 Oph
Even disregarding the strong flickering activity, V2051 Oph has the most unstable light curve of all stars considered here. During most cycles, a hump is clearly present. However, its amplitude is quite variable, and in some cycles it all but vanishes. Moreover, its phase is not stable: While in most cycles its maximum occurs before the eclipse (as is expected for an orbital hump caused by the hot spot) sometimes it coincides with the eclipse or wanders to even later phases. Moreover, with a considerable frequency an intermediate hump appears roughly half a cycle before (or after) the principle hump.
The latter, however, disappears in the mean light curve which is shown together with a representative individual curve in of Figs. 4b and 4a, respectively. The mean hump is located at its canonical phase and has a moderate amplitude (as compared to e.g. Z Cha, Wood et al. 1986, or IP Peg, Sect. 4.3). Note also that in contrast to other eclipsing systems with prominent humps the end of the hump occurs even before the onset of the eclipse. However, this is only true for the mean curve and may be quite different in individual cycles. The mean eclipse profile differs from that of HT Cas (Sect. 4.1). It does not show the sudden eclipse ingress and egress of the white dwarf (although this may still be visible in individual light curves; Warner & Cropper 1983) but is more gradual. This, together with the round eclipse bottom, points towards a higher contribution of the accretion disk which is never totally eclipsed in this system. During an exceptionally low state of V2051 Oph Baptista et al. (1998) were able to measure the contact points of white dwarf eclipse ingress and egress. The corresponding phases are indicated by the dashed vertical lines in Fig. 4.
The scatter curves for the individual light curves were calculated as in the case of HT Cas. The resulting mean curve is shown in Fig. 4c. The average error of the data points of 0.064 is shown in the lower right corner. The eclipse is similar to that observed in HT Cas but - due to the much larger number of individual light curves and the absence of the problems with the steep eclipse ingresses and egresses - much better defined. In particular, the scatter eclipse is coincident with the white dwarf eclipse and definitely narrower than the disk eclipse. Thus, also in this system the flickering light source is located very close to the white dwarf while the outer parts of the accretion disk to not take part in the flickering to a perceptible degree.
In contrast to HT Cas, however, the scatter curve shows evidence that flickering occurs also to a certain degree at the location of the impact of the transferred matter onto the accretion disk: the scatter is clearly elevated at the phases when the orbital hump is visible. This is formally confirmed by the standard deviation of 0.080 of a Gauss fit to the histogram of the out-of-eclipse data points which is larger than their average mean error of 0.064. This hot spot flickering can also explain the apparent slight asymmetry of the scatter eclipse: it remains visible for a short time even after the white dwarf is already eclipsed, causing a slightly more gradual eclipse ingress, but is invisible when the central star emerges from the eclipse, explaining the steeper scatter eclipse egress. This behaviour of the flickering in V2051 Oph is identical to that of Z Cha during quiescence as measured by Bruch (1996).
The present results are in excellent agreement with those of Warner & Cropper (1983). They concluded "that in V2051 Oph the flickering is probably in general generated in the inner disk region with only a minor contribution from the hot spot".
4.3. IP Peg
The light curves of IP Peg differ strongly from those of HT Cas and V2051 Oph. As an example the B light curve (Stiening system) of 1992, November 27, is shown in Fig. 5a. It is dominated by an exceptionally strong hump which reaches a peak flux approximately three times as high as the flux at phase where the hump is invisible. The eclipse is characteristically structured: A steep part of the ingress caused by the white dwarf ingress is followed by a more gradual part due to the hot spot ingress. Unlike in the classical SU UMa systems OY Car and Z Cha, however, white dwarf and hot spot ingress cannot be separated. The white dwarf egress is in most cycles discernible as a discrete step in the light curve. Somewhat later a second step marks the egress of the hot spot.
In view of the variations of the location of the hot spot in the system the corresponding contact phases are not very stable as was shown by Wood et al. (1989b). The lateral dashed lines in Fig. 5 represent the mean first and last hot spot eclipse contacts as measured in the present light curves. The central line marks the mean white dwarf egress phase determined by Wood et al. (1989b).
The general character of the short term variations of IP Peg is different from that of other CVs. Significant variations above the noise level are only seen during the presence of the orbital hump, suggesting that the hot spot is the culprit. This is confirmed by the more formal scatter analysis.
The mean scatter curve of IP Peg (Fig. 5b) was measured in the same way as in the previous cases. Since it is based on only three light curves the noise is particularly large. For the same reason it is not sensible to derive formal errors in the way done for the other stars in this study. Nevertheless there is no doubt that it is significantly different from the corresponding curves for the other stars. The strong increase of the scatter at the phases when the orbital hump is visible indicates that the flickering in IP Peg is dominated by the hot spot. In contrast to Z Cha (Bruch 1996) and V2051 Oph (Sect. 4.2) where the scatter eclipse ends with the white dwarf eclipse even if the hot spot continues to be eclipsed, there is no significant increase of the scatter of IP Peg when the white dwarf eclipse ends. The scatter only increases when the hot spot emerges from the eclipse (the single high point just at white dwarf egress is an artifact due to the same effect which produces the spurious peaks in the HT Cas scatter curve; see Sect. 4.1).
Recognizing that the scatter at phases when the hot spot is invisible is as small as during eclipse centre indicates that in this particular system the accretion disk/white dwarf contributes practically nothing to the total flickering.
Since these conclusions are based on only three light curves, they may not be as firm as concerning the other stars of this study. However, it does not appear likely that the light curves used here which are very similar to each other are wholly atypical for IP Peg.
4.4. UX UMa
Due to the longer orbital period the phase coverage of the presently available light curves of UX UMa is not as complete as for the other stars in this study. Therefore, the phase range for the present investigations is restricted to . A representative individual light curve and the mean of all normalized curves are shown in Figs. 6a and 6b, respectively (note that the discontinuity in the mean curve close to phase is an artifact caused by a light curve with a particularly low light level after eclipse which contributes to the mean only at phases ). The broadness of the eclipse and the rounded bottom suggests that the eclipsed body is extended (the accretion disk) and that it is never fully eclipsed. This agrees with the low orbital inclination of determined by Baptista et al. (1995), which is just high enough to cause grazing eclipses of the white dwarf. Using UV light curves, Baptista et al. (1995) could also measure the white dwarf eclipse ingress and egress phases which are marked in Fig. 6 by dashed vertical lines. The eclipse contains an extended wing at egress, a feature introduced by the retarded eclipse egress of the hot spot. The presence of the latter is also visible in eclipse maps of UX UMa (Baptista et al. 1995).
The mean scatter curve, calculated in the same way as in the previous cases, is shown in Fig. 6c. The average mean error of the data points (upper right corner of Fig. 6c) is 0.125. Although the scatter curve is rather noisy there is no doubt about the presence of an eclipse. Once again, its boundaries agree remarkably well with those of the white dwarf eclipse, indicating that in UX UMa (as in HT Cas and V2051 Oph) the flickering light source is located very close to the central body. Using the orbital inclination of , a mass ratio of 1 (Baptista et al. 1995) and taking into account the distorted shape of the Roche-lobe filling secondary star it is found that the secondary star eclipses the accretion disk on the far side only out to 4.4 white dwarf radii. Therefore, the flickering light source - at least a significant part of it - must be located within this distance for a sharply confined flickering eclipse to occur. In view of the scatter of the curve and the unknown contribution of residual noise (Bruch 1996) no attempt is made here to quantify this statement. However, the extremely rapid eclipse egress permits an even considerably narrower distribution of the flickering around the white dwarf. The apparently more gradual eclipse ingress and the slightly enhanced scatter before the eclipse (the Gauss fit to the histogram of all out-of-eclipse points yields a standard deviation of 0.185, significantly larger than the average mean error of 0.125) may also in this case indicate a hot spot contribution to the total flickering.
© European Southern Observatory (ESO) 2000
Online publication: July 13, 2000