4 The P₂-P₁ relationship

In Fig. 3 we show what we consider the most surprising result of this paper. The P₂ and P₁ periods seems to be correlated. All five deviant points correspond to single-wave light curves, so it is possible that the true orbital period has been missed by a factor 2. The value $2\times P_{1}$ is also indicated in the figure. A linear least squares fit passing by zero gives:

P₂ = 35.17(75) P₁ (2)

with a correlation coefficient 0.97 and standard deviation of 28 days. The existence of such a relationship suggests that the phenomenon causing the long-term oscillation could be directly related to the binary nature of the system.

Figure 3: The long-term period P2versus the short-term period P1. The errors in P1 are smaller than the used symbols. Dashed horizontal lines connect two possible solutions for stars with single-wave short-term light curve. The linear fit given by Eq. (2) is also shown.

Figure 4: The primary radius in units of the the binary separation for the Algols shown by Richards & Albright 1999 (filled circles). The circularization radius, the tidal truncation radius and the 3:1 resonance radius, all of them in units of the binary separation, are shown as a function of the mass ratio. Theoretical expressions for these quantities have been taken from Warner (1995). It is possible that only Algols with very low mass ratios could maintain (precessing) accretion discs beyond the 3:1 resonance.