The results of Chapter 6 represent the first search for multiple periodic structure of a major subset of the RS CVn systems, using a rigorous numerical approach appropriate to unevenly-spaced gapped data. As stated in Chapter 1, the main emphasis of this dissertation concerns the proper characterization of RS CVn binary light curves and how this information can be used to constrain the current models for the systems. The global characteristics of the spectral analysis and the ensuing model constraints are discussed in section 7.1. This dissertation concludes with section 7.2, which discusses possible future observations, suggested improvements in the APT observing program and the future of the TISAN software package.
Of the 36 sources analyzed, five show no signs of short term periodicity and one system, RZ Eri, was too sparsely observed to draw any definite conclusions. Two of the five null detections, 33 Psc and AE Lyn, had detectable periodic structure in the past, although the level of 33 Psc may be below the sensitivity limits of my analysis. The remaining two sources, 53 UMa and BH CVn, both show enticing evidence for long term (>500 days) variability.
Of the thirty positive detections, twenty display evidence for multiple periodic structure, with one source, HD 136901, having three distinct periods. Prior to this work only BM Cam, II Peg, HR 7428, V711 Tau and V1764 Cyg were known to show such structures, although ER Vul and l And are known to be best fit by the canonical two component starspot model (see Sections 5.30 and 5.32).
Of the eleven singly periodic systems, only EI Eri shows evidence for period variability, although V478 Lyr does shows a clear change in amplitude. Of the multiple periodic systems, seven show evidence for period variations, with associated changes in amplitude and phase. Those systems that show multiple periodic structure are clearly more active. It is remotely possible that I am seeing a selection effect because the multiply periodic systems were observed 7% longer with only 0.03% fewer observations than the average of all the systems, as opposed to the singly periodic systems observed for a 11% shorter time period with 9% fewer observations. The null detection systems have 18% more observations than the average over a time span that is 3% shorter.
In trying to understand the mechanisms behind the variability, it is constructive to examine the global characterizations of the periods and phases found for the systems. Figure 7-1 shows the photometric period plotted against the orbital value and Figure 7-2 is the same plot in terms of frequency. Those sources for which the periodic structure was attributed to eclipse, ellipticity or reflection have been removed.
It is clear that there is a definite preference for photometric variations with time scales near the orbital and half orbital periods. This effect is particularly strong for the shorter period systems, as can be seen from the frequency plot, and becomes less pronounced for periods longer than about 20 days. If this preferential period effect is considered in terms of synchronous rotation, then the results are not surprising since synchronization should be more pronounced in the shorter period systems as a result of the stronger tidal coupling from the close proximity of the stars.
The fact that there is a strong tendency for the photometric periods to fall into two regions indicates that starspots cannot be distributed randomly about the surface of the stars. If spot distributions were random, I would expect to detect secondary periods at arbitrary fractions of the primary photometric value. A plot of the inverse of the smaller vs. longer period for the fourteen systems that show multiple periodic structure not attributable to eclipses, reflection or ellipticity is shown in Figure 7-3. This plot is clearly linear with a slope of 2.025, a correlation coefficient of R2 = 0.999857 and an RMS error of 0.00452. This strong linearity indicates that multiple spot groups, or active regions, preferentially appear in pairs. No exceptions are observed in my analysis.
The evidence for pairs of spots groups would tend to lend support to the concept of active longitude belts. In this model, active regions preferentially appear in relatively stationary zones of longitude approximately 180° apart. In terms of the photometric variability, these structures would generate two periods, with one being half the other as is seen for these sources. The phases however, should also coincide. The absolute phase differences for all the periods found for the fourteen sources plotted in Figure 7-3 are shown in the line graph of Figure 7-4 in ascending order. It is clear that there is no preferential phase separation. Thus, although spot groups do appear in pairs, they are arbitrarily separated in phase. This type is structure is highly reminiscent of the well known pattern of leading and trailing sunspots visible on the solar photosphere.
The subject of differential rotation is an outstanding problem in RS CVn research. Although my evidence for near synchronization as a function of orbital period is strong, the characterization of possible differential rotation is difficult. If differential rotation is present, I would expect to observe fractional changes in the photometric periods, as is observed in one-third of the positively detected systems. If the period variations are solely a result of migrating spots on a differentially rotating star, there should be a correlation between the change in the photometric period and the orbital value as a result of synchronization effects. No such correlation is observed.
The changes in the photometric period are associated with variations in the amplitude of the distortion wave, which would indicate the growth and decay of spot groups. Thus, I suspect that the observed period variations are primarily a result of the growth and decay of pairs of spot groups, separated arbitrarily in phase, on differentially rotating stars.
The analysis in this dissertation indicates that the characteristics of the photometric distortion waves of RS CVn systems can be described by their spectral content and that the light curve can be used as a probe into the activity cycles of these systems. The spectral analysis techniques are clearly best suited to the regular period systems where the orbital period is short compared to the activity time scales and long in terms of the observing frequency.
The quality of the data from the APT could be greatly improved. Currently, the APT observes all objects in ten second intervals. If the system were, instead, to observe down to a predefined statistical noise level of 0.001m, then the errors in the analysis would be greatly reduced giving better insight into the physical interpretations of the results. The limit of three decimals of precision is also a large limiting factor. With the classical analysis techniques, which are graphical in nature, this precision is adequate. However, the modified Scargle periodogram is known to be capable of extracting signals from data with a signal to noise ratio as low as 0.3 (Horne and Baliunas 1986), which would allow for the clear detection of a signal with a full amplitude as low as 0.006m with the current error of 0.01m. An additional factor for the APT would be to more carefully choose the sources to be observed. Observing a system with an orbital period near 0.5 days at a frequency of one day, as is the case for ER Vul, is not terribly useful in the search for photometric period, amplitude and phase variability.
The work from this dissertation can be followed up immediately with the APT data from 1985 to 1988. With this additional data, the sources that show dramatic changes in period, amplitude and phase can be better described and the suspected long term variations in the sources such as 53 UMa and BH CVn can be confirmed (or refuted).
The details of the differential rotation structure for these systems is still not well defined. The sampling frequency of the APT precludes the separation of individual observation sets down to three or four orbital cycles. It is only with closely spaced, long term observations that the suspected differential rotation effects can be characterized for the individual systems. Lastly, I want to say a few words about the future of the TISAN software package. Without TISAN, the analysis for this dissertation would not have been possible, as is evident from the handful of publications dealing with the analysis of APT data. However, TISAN is still a serial processing package. With the advent of the 80286/80386 based workstations, such as the IBM PS/2 systems, a fully multitasking analysis environment can be developed. With a windows based operating system, the environment would become system independent and would allow for greater flexibility in the display of the data. I therefore intend to develop TISAN under the Microsoft Windows Presentation Manager (OS/2) which will take full advantage of the capabilities of these next generation systems.
Figure 7-1
Photometric vs. Orbital Period
Figure 7-1 is a plot of the photometric vs. the orbital period. Those sources for which the periodic structure was attributed to eclipse, ellipticity or reflection have been removed. This plot shows the general tendency of even the long period systems to prefer photometric periods near the orbital and half-orbital values.
Figure 7-2
Photometric vs. Orbital Frequency
Figure 7-2 is a plot of the photometric vs. the orbital frequency. Those sources for which the periodic structure was attributed to eclipse, ellipticity or reflection have been removed. This plot is the complement of Figure 7-1 since plotting the inverse of the periods emphasizes the shorter period systems. This plot clearly shows the strong tendency of the shorter period systems toward synchronization.
Figure 7-3
Higher vs. Lower Photometric Frequency
Figure 7-3 is a plot of the inverse of the shorter photometric period to the inverse of the longer photometric period for those systems with multiple periodic structure not attributable to eclipse, ellipticity or reflection. The strong linearity (R2 = 0.999857) for these fourteen systems indicates that multiple spot groups, or active regions, preferentially appear in pairs.
Figure 7-4
Delta Phase of Minima in Ascending Order
Figure 7-4 is a line graph of the differences between the phase of minima, sorted in ascending order, for the systems plotted in Figure 7-3. The phases are adjusted, modulo one, so the phase difference always lies between 0 and 0.5. If a preferential phase distribution were present, horizontal lines would appear at those locations. The phases show a clear uniform distribution.
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Copyright (c) 1988-1997, Eric R. Nelson, Ph.D.