The rates of change of the fundamental and overtone periods of SX Phe

Long-Term Changes in the Periods of SX Phe

“…These parameters enable us to calculate the best estimates of P 0 and P 1 at epoch, and the rates of change (assumed constant) of these periods, using the methods described in Coates, Halprin & Thompson (1982), which we now summarise.…”

“…Measurements of the periods of SX Phe and their rates of change have been reported by several authors, for example Stock et al (1972), Elst (1973), Coates et al (1979), Coates, Halprin & Thompson (1982) and . The derived long-term rates of change of these periods from quadratic fits to O-C data appear not to be constant, but this may be due to a constant long-term period increase or decrease being masked by much larger short-term changes.…”

The beat-curve approach applied to AEUMa

“…The following summarises the methods given by Coates et al (1982) and Landes et al (2007) to derive periods at epoch and their (constant) rates of change using the beat-curve approach.…”

“…Full details of this beat-curve analysis are given in Coates et al (1979Coates et al ( , 1982, but in summary, changes in the mean level, or estimate of (O-C) for the season (B) and phase of the sinusoidal curve δ, reflect changes in the fundamental and beat periods of the star, from which changes in the overtone period can be derived. In addition, as noted in Landes et al (2007), the relative phase of the changes in B and in δ may allow us to exclude a light-time effect in a binary as an explanation in cases where (O-C) is changing sinusoidally.…”

“…The long-term graph of (O-C) versus time can then be used to determine the period and its rate of change. Methods of determining the secondary period usually involve Fourier analysis of relatively complete sets of photometric data.We show that the beat-curve method, e.g., Elst (1973), Coates et al (1979Coates et al ( , 1982 is an alternative approach also worth considering. The offset of the beat curve usually yields a more precise value of (O-C) for a season than a simple average does, the phase of the beat curve leads to an estimate of the secondary period without the need for intensive photometry, and the amplitude of the beat curve provides information about the relative amplitudes of the modes of oscillation of the star.…”