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3. Analysis of the photometric behaviour

Together with the newly taken and previously unpublished data in Paper I, we collected all available visual photometric data from the literature. An overview of all visual photometry of HD 45677 used in our analysis is given in Table 2 (click here). As described in Paper I, these data were transformed, as good as possible, to values in similar bands of the ``standard'' Johnson UBV and Strömgren uvby photometric systems.

The photographic magnitudes from Swings & Swings (1972) are comparable to the visual magnitude at the time the first photoelectric measurements were taken, tex2html_wrap_inline2621 (Mendoza 1958; Wampler 1968 in Swings & Allen 1971). A different effective wavelength of the photographic and photoelectric measurements will therefore not cause a large systematic difference between tex2html_wrap_inline2623 and V. For the transformation of UBV data of the Geneva system to those of the Johnson system we derived the following formulae from the absolute calibrations of both systems given by Schmidt-Kaler (1982) and by Rufener & Nicolet (1988):


The (V-I) and (V-R) colours in the Johnson system were transformed to the Cousins system using the formulae derived by Bessell (1979). Note that the Strömgren photometry of HD 45677 in Sterken et al. (1993) are not included in Table 2 (click here) because they are in fact measurements of another star. Also note that in the paper by Feinstein et al. (1976), the labels tex2html_wrap_inline2633 and tex2html_wrap_inline2635 have been interchanged in their Table 2 (click here).

The light curve for the visual magnitude in the Johnson system, further quoted as V, vs. the Julian date, JD, of HD 45677 is shown in Fig. 1 (click here). From this figure one can clearly identify a very deep minimum of long duration around 1981 (tex2html_wrap_inline2639 JD 2444500). Furthermore, superimposed on this relatively large variation rough changes between the different groups of data points and changes within such concentrations of measurements can be seen. These variations will be analyzed separately and quoted as long, intermediate and short time scale variations, respectively.

3.1. Long time scale variations/obscuration

The light curve of HD 45677 plotted in Fig. 1 (click here)a shows an asymmetric, long (tex2html_wrap_inline2643 tex2html_wrap_inline2645 44 years), and deep (tex2html_wrap_inline2647 tex2html_wrap_inline2649 1tex2html_wrap2753 6) minimum. Although in the beginning of the monitoring, around 1899, HD 45677 is rather stable, it seems to get brighter with increasing variations, from 7tex2html_wrap2755 3 with tex2html_wrap_inline2655 0tex2html_wrap2757 2 at 1900 up to 7tex2html_wrap2759 0 with tex2html_wrap_inline2661 0tex2html_wrap2761 4 around 1940. From this year on HD 45677 seems to faint which probably starts to become significant around 1950. This trend could be the beginning of the deep minimum. If we extrapolate linearly by connecting the minima of the data-points of the shorter time scale variations in Fig. 1 (click here)a, until the mean magnitude of 7tex2html_wrap2763 2 from before 1950 is reached again, we find that we expect that HD 45677 will remain increasing in brightness until about the year 2020. We believe therefore that Fig. 1 (click here)b only shows a part, including the minimum, of a variation in brightness on a time scale longer, tex2html_wrap_inline266770 years, than the one covered in our light curve.

Figure 2: Photometry of HD 45677 in the Johnson/Cousins system from 1971 to 1994

From the photoelectric measurements taken between 1971 and 1993, connected by linear interpolation to the photographic magnitudes from before, the slope of the decreasing brightness is seen steeper than the branch of increasing brightness which starts at the turning point at tex2html_wrap_inline26691981. By the extrapolation to 2020, the speeds of the brightness changes are determined to be 0tex2html_wrap2767 05 yeartex2html_wrap_inline2673 and 0tex2html_wrap2769 04 yeartex2html_wrap_inline2677 for the decreasing and increasing branches, respectively. The difference, which is significant on this time scale, means that the mechanism responsible for the increasing branch is not simply a reversed effect of the mechanism causing the decrease in brightness.

Changes in photometric colour indices are measurable, but relatively small compared to the ones in V. Figure 2 show the light curves in both visual magnitude and colours in the Johnson/Cousins photometric system over the last 20 years. From these figures it is easily seen that, superimposed on variation on smaller time scales, the U-B and B-V colours have shown a trend of getting redder during the last 20 years by about 0tex2html_wrap2771 1, during the phase of increasing brightness. The scatter in the data of these colours is too large to follow this trend during the obscuration phase as well, but an indication of this behaviour can be seen in the B-V colour.

The opposite colouring, getting bluer, is seen for V-R and V-I during the period of increasing brightness.

Table 2: Visual photometric data of HD 45677 from the literature

3.2. Short time scale variations/flickering

To understand the way the intermediate variations are distributed it is better first to explain the short time scale variations, i.e. to study whether they are caused by obscurations or brightenings. Short time scale variations are seen in the lightcurve as dense groups of data points. The typical time scales vary from several days to several hours, depending on the monitoring programmes. They can be easily studied by constructing light curves and colour-magnitude diagrams over several short periods during the last twenty years. #P&Pérez et al. (1993) suggested the presence of short time scale ``pulse-like'', or ``flickering'', type of variations, characteristic of instabilities in accretion flows.

We examined light curves and colour-magnitude diagrams of several datasets obtained within several days, which are denoted in Fig. 1 (click here)b as A-E. UBV and Strömgren data of Feinstein et al. (1976), sets A and B respectively, are shown in Fig. 3 (click here). As can be seen from this figure, HD 45677 shows irregular minima and maxima of which the time scale seems to be up to days, see plot B1 of Fig. 3 (click here). These ``pulse-like'' variations from night to night, and their colours clearly indicate a dependence on magnitude: the blue colours, U-B, u-v and v-b are getting redder as the magnitude decreases but then colours like B-V and b-y become bluer. A better example of the ``pulse-like'' behaviour and their colour effects are seen in the same figure for the transformed Geneva colours of Gilbert (1994), set C, and the BV observations of Halbedel (1989), set D (see next section). At decreasing brightness the U-B colour of sets A and C gets redder while B-V becomes bluer again. The amount of the getting redder seems to increase slightly towards the blue, i.e. most strongest in u-v. Even in the colours U-B and v-b the getting bluer is significant higher than the getting redder in the b-y and B-V colours. The Walraven data in Table 1 (click here) of Paper I confirms this behaviour.

Figure 3: The short time scale variations expressed in light curves and in colour-magnitude diagrams for the datasets taken in 1972, set A (UBV data of Feinstein et al. 1976); 1975, set B (uvby data of Feinstein et al. 1976); 1981, set C (Gilbert 1994) and 1993, set E (Table 2 (click here))

Figure 3: continued. The intermediate time scale variations expressed in light curves and in colour-magnitude diagrams for the datasets taken between 1986 and 1993, set D, by Halbedel (1989 and 1991), Sitko et al. (1994) and from Paper I

3.3. Intermediate time scale variations/semi periodic

The intermediate time scale variations, with typical time scales of a few years, were studied and found to be semi-periodic by Halbedel (1989). However, the monitoring from 1899 to 1969 by Swings & Swings (1972) indicated no presence of clear periodicity on such time scales.

A clear representation of these changes, in the photoelectric data, are only given beyond JD tex2html_wrap_inline28132446000. Before this, HD 45677 was not monitored sufficiently regular. The empty intervals in the lightcurve (Fig. 1 (click here)b) are the reason for the difficulties to explain these variations by Halbedel (1989) and Feinstein et al. (1976). Producing colour-magnitude diagrams for the intermediate time scale variations is not easy because of the different photometric systems used for the measurements. However, using the BV data from Halbedel (1989, 1991), Sitko et al. (1994) and from Paper I, which extend over several similar years, a slight relation is seen between B-V and V (Fig. 3 (click here)). Superimposed on the short time scale variations and their colour dependencies a reddening is seen with decreasing brightness. Because of the lack of other colours measured over such time intervals their effects are not known.

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