Results

We show, in the histograms of Figure 1, the distributions in phase of and rates of detection for the RS CVn, EA2, ETB groups. These are formed by dividing the number of registered detections by the total number of observation entries in each 0.1 interval of phase. The phase sampling is fairly uniform in these phase bins for the binary groups studied.

 
Figure 1: Distribution in phase of detections of RS CVn stars (top) classical Algols (middle) and early type pairs (bottom).

Easiest to deal with, perhaps, is the ETB group, which is consistent with no particular phase preference for detections, although the sample is too small for reliable statistics (only 15 detections).

The detections of the RS CVn stars also appear to be without very strong phase linking, although there is more variation than goes with a purely random distribution. If we include V711 Tau, sums of the 3 detection rates, comparing with the mean rate (0.44) for the whole set, indicate a probability of about 21% that the observed phase distribution could correspond to a random example of one which is intrinsically uniform. However, V711 Tau is detected essentially at all phases. If this diluting effect is removed, the phase distribution of the remaining, more distant RS CVn detections becomes distinctly less uniform. This distribution is illustrated in Figure 1 (top). (V711 Tau is considered later in Figure 3.) The probability of the distribution of Figure 1 (top) being a random example from a uniform source drops to about 1.3%, according to the sum of its deviations from the mean, tested with the function for 9 degrees of freedom (cf. e.g. Conover, 1980).

The outburst detection rate's variation with phase , shown in Figure 1 (top), is adequately modelled, for a Poisson distribution of deviations from the model's predictions, by a three element Fourier series, of the form (phase shifts in degrees)

The detection rates for the Algol systems in Figure 1 also show some departure from uniform, however, the small numbers in the data set imply correspondingly large error bars. A test indicates only a little more than even chance (54%) of a non-uniform parent distribution for this sample. The observed EA2 detections' trend is well represented by:

which is effectively within its broad errors of the formula used for the RS CVn stars.

The RS CVn and Algol binaries were explored as a single class by combining their detection statistics. Relevant data are summarized in Table 1. Results are shown diagrammatically in Fig. 2. This distribution of 3 detections of the combined groups satisfies:

There is an improvement in the quality of the 3 term Fourier representation over Equation (1), and testing indicates a probability of just about 1% that this data sample is drawn from a uniform parent distribution. This 2-harmonic Fourier representation is shown as the dotted curve in Figure 2. We can thus reasonably infer that the observed phase distribution of the rates of microwave detections for Algol and RS CVn binaries is consistent with their sharing certain key underlying physical similarities bearing on the flux generation.

Table 1: Summary of 3 detection statistics for RS CVn and Algol binaries: their combined observations and detections, the average detection incidence per bin for the whole set suitably `normalized' to the number of observations in each phase bin, the detection rate (detections/observations), probable (Poissonian) errors and deviations from a uniform incidence. The values are derived from squaring the difference of the two numbers in the 7th and 8th columns, and dividing by the latter entry.

Phase	Observations			3 detections			Norm'ed	Detect.	Error
bin	RS's	Al's	Sum	RS's	Al's	Sum	incidence	rate
0.05	35	12	47	9	3	12	15.6	0.255	0.073	0.83
0.15	49	9	58	17	2	19	19.3	0.328	0.075	0.00
0.25	57	8	65	31	1	32	21.6	0.492	0.087	5.01
0.35	49	19	68	28	7	35	22.6	0.515	0.087	6.80
0.45	48	18	66	13	8	21	21.9	0.318	0.069	0.03
0.55	45	10	55	11	2	13	18.3	0.236	0.066	1.53
0.65	39	14	53	9	2	11	17.6	0.208	0.063	2.78
0.75	35	6	41	6	0	6	13.6	0.146	0.060	4.24
0.85	49	11	60	18	3	21	19.9	0.350	0.076	0.06
0.95	42	8	50	15	2	17	16.6	0.340	0.082	0.01
							Av. 18.7			20.99

 
Figure 2: Distribution in phase of detections of RS CVn stars + Algols

The most effective Algol performer in the sample -- Lib -- (detected in 75% of observations) appears to accentuate the heterogeneity of emission with phase. All 13 flux measurements above 12 mJy are within 0.16 of phases 0.45 and 0.95; 92% are within 45 and 62% are within 35 of these phases. The sampling rate of the 28 observations is not too uniform, however. Even so, there are five observations in both the 0.3-0.4 and 0.4-0.5 phase ranges, but the accumulated flux in the latter bin is four times that of the former.

There are generally much more frequent measurable fluxes of RS CVn stars than the EA2 or ETB groups. Thus, V711 Tau gives a >3 detection in 98% of cases, while Cap, at only 1/3 of the distance ( 12 pc), achieves this in only 1/6 of its observations. Slee et al. (1987) showed, however, that the increased detection rate of RS CVn stars is influenced by their greater spatial incidence than classical Algols. The median brightness temperatures of Algols were found to be several times higher than those of RS CVn stars by Slee et al. (1987), while the median distance of that sample of Algols was about 50% greater. There is, however, considerable overlap in the emission characteristics of the two groups, the Algols' surface fluxes falling within the range of that of the RS CVn stars, though it should also be noted that 4.6 times as many observations of RS CVn stars as Algols were made altogether.

The four eclipsing RS CVn stars (V 1379 Aql, RZ Eri, SZ Psc and CF Tuc) have a slightly smaller median surface flux than the remaining 12 non-eclipsing ones, but their mean 3 detection rates are essentially the same (0.33 for the eclipsers, as against 0.35 (excluding V711 Tau) for the non-eclipsers). The mean distances and distance ranges of these two groups are sufficiently comparable as to indicate that there is no effective way of statistically discriminating between eclipsing and non-eclipsing RS CVn binary emission effects in our data. The very frequent detections of the low-inclination (33) RS CVn binary V711 Tau might favour polar visibility as a factor in detectability, but this is not verified on the basis of any simple statistical correlation with flux levels and non-eclipses. The radio-bright and relatively near V711 Tau shows occasionally very large and apparently randomly distributed emissions superposed over what appears as a more steady background. This background variation also suggests a phase dependency, maximizing towards phases 0.4 and 0.9 (Figure 3).

 
Figure 3: (upper) Distribution of flux measurements with phase for V711 Tau (HR 1099); (lower) distribution of accumulated relative S/N values for V711 Tau. The 6 highest values have been removed to show any trend to the `background' emission.

From averaging the full detection rates of the RS CVn stars, including now the non-detections for the remaining 32 stars of Slee et al. (1987), we estimate that for a typical RS CVn star at a distance of about one hundred pc about one observation in three would result in a positive detection with the set-up used in the Parkes survey. The mean distance of the 16 RS CVn stars studied in this paper is 155pc. There is a great variation in the absolute detectabilities of different systems, however; for example, the well-known eclipsing binary CF Tuc (HIPPARCOS distance 86pc) was detected on about one in four observations, as against one in seven for IN Vel, which is six times more distant. Indeed, the detections seem to include some selection effect which reflects a disproportionate influence of unusually active remote RS CVn stars.

Proceeding similarly, we find the 3 detection expectancy of a classical Algol, at a hundred pc, to be about 0.2. The 8 Algols in this study have an average distance some 1.3 times greater than the RS CVn systems, though the overall range of distances of EA2 stars is comparable to the RS CVns (few tens to several hundreds of pc). It is worth noting that Algol detection probability, in our data, is enhanced by a factor of 1.8 in the phases ranges 0.4-0.5 and 0.9-1.0 over the remainder of the phase cycle.

Referring back again, briefly, to the ETB detections: the rate is very heterogeneous in this small selection. For example, the relatively near Cap has a 3 detection incidence of 0.17, while V822 Aql, at some 680 pc distance, has a 3 detection rate of 0.22. The latter binary has a very early type (B3) primary, and is photometrically classified as an EB (strong tidal distortions) binary (Kholopov, 1985), despite its 5.3 day period. It may then well resemble Lyrae, or a massive Algol at the early stages of its interaction history. Overall, the detection rate for the ETBs appears about half that of the classical Algols.

© Copyright Astronomical Society of Australia 1997