The Duplicity of the SX Phoenicis Star CY Aquarii

Ai-Ying ZHOU and Jian-Ning FU

Beijing Astronomical Observatory, Chinese Academy of Sciences,
China. E-mail:

New photoelectric times of maximum light of the large amplitude SX Phoenicis star CY Aquarii are analyzed together with the times of maximum light in the literature. The general shape of the fitted curve of the observed minus calculated (O-C) times of maximum light suggest the duplicity of the variable star, which causes the long-term period variations in the light-time. The period changes of CY Aqr are probably a consequence of a continuously increasing period combined with the light-time effect in a binary system. The secondary companion is less massive. Some of spectroscopic orbital elements are derived from the O-C diagram.

Figure 1: The O-C diagram of CY Aqr (cycles).

For understanding the cause of the period variations of CY Aqr, previous parabolic and straight-line segments fits of (O-C) values made by many authors may be inappropriate. As a check of the light-time effect which may possibly be responsible for the period changes, we have attempted a new orbital solution using trigonometric functions to fit all data points. 483 individual times of maximum light are found in the literature. We suggest the variation in the times of maximum light is subject to the light travel time across the binary orbit of CY Aqr. Taking following (for the case with e=0) as an estimate of times:

where P is the pulsation period; PB is the orbital period, PB=1/f; Delta t=a*sin i/c, the projected light travel time, and phi is a phase shift (Barnes and Moffett 1975, Garrido et al. 1979). Consequently, the long-term variation in the time of light maximum is mathematically equivalent to a single-lined spectroscopic binary with parameters: a1*sin i = Delta t * c = 1.4731 AU; K1=(2 * pi * a1 * sin i)/PB = 0.7036 km/sec, mean velocity of the primary star (CY Aqr) projected on the orbit;

where CY Aqr has mass m1. As these values are not unreasonable for a binary and bearing in mind the difficulties of the question that abrupt changes in period occur, we adopt for further discussion the interpretation that the variation in time of maximum is caused by a light travel effect in a binary.

Figure 2: Solutions to the mass function given in Eq. 2 for various choices of sin i .

The possibility that CY Aqr is a spectroscopic binary immediately leads to the hope that a mass can be determined. In Figure fig:CYAqr5f we show the relationship between the masses of the two companions for assumed values of the orbital inclination. The curve for i=90 sets a lower limit to m2 at each m1. Recent results given by McNamara et al. (1996) indicated: m1=1.06Mo, Mv=2.5. For this mass value of the primary star m2 rounds 0.15Mo. The companion must be fainter than CY Aqr by about 8.8 mag. We stress that, the binary model seems to us to be the most plausible interpretation of the variable times of maximum light. It remains only a reasonable hypothesis until new confirming data are available. The simplest and most easily accomplished test is to examine the radial velocity of CY Aqr for the low 1.4 km/sec amplitude predicted by the model. However, the very low K1 value may prevent observers from detecting the unseen companion. The light-time effect is naturally augmented by the absence of amplitude modulation in the light curve with the 62.36 years period which is too long to test its reality by the short period covered by the observations (nearly just one cycle). New observations in the future are required to test our hypothesis. It is so allowed to inspect the variable in the future.


Barnes, T. G. and Moffett, T. J. 1975, AJ, 80, 48
Garrido, R., Alfaro, E. J., Quintana, J. M. and Saez, M. 1979, A AS, 36, 51
McNamara, D. H., Powell, J. M., and Joner, M. D. 1996, PASP, 108, 1098