COMMISSION 27 OF THE I.A.U. INFORMATION BULLETIN ON VARIABLE STARS Number 3264 Konkoly Observatory Budapest 18 November 1988 HU ISSN 0374 - 0676 ON THE ORBITAL PERIOD OF FO AQUARII Patterson and Steiner (1983) identified the 13th magnitude cataclysmic variable FO Aquarii is the optical counterpart of the X-ray source H2215-086, and found strictly coherent large-amplitude pulsations in the light curve, with a period of 21 minutes. In addition they found a shallow modulation recurring at the same period with which the emission lines move, which appeared to be 0.1650 days. This period has been adopted as the fundamental orbital period in all later studies, but we shall see below that it is probably incorrect, being a 24-hour alias of the true orbital period. Tables 1 and 2 contain all available information on the two signatures of the orbital motion: the timings of "orbital dips" in the light curve, and the timings of inferior conjunction of the emission-line source as revealed by radial velocity studies. The photometric data are sufficient to establish that the dips follow one of the following ephemerides: (a) Minimum light = JDHel 244782.867 + 0.202060d E (b) Minimum light = JDHel 244782.888 + 0.168017d E In Table 1 we give cycle counts and O-C residuals for the timings under each of these alternatives. The O-C diagrams are shown in Figure 1, which shows that ephemeris (a) provides an excellent fit with an rms scatter of only 0.03 cycles, while ephemeris (b) is much less satisfactory, with an rms scatter of 0.09 cycles. Still a third cycle count, corresponding to P= 0.1680466 d, was suggested as a possibility by Semeniuk and Kaluzny (1988), but Figure 1 shows that this is not possible. This evidence strongly favors the longer period. Normally we would consider this evidence decisive, but the three spectroscopic timings given in Table 2, supply contrary evidence. They occur at a consistent orbital phase according to ephemeris (b), but not according to ephemeris (a). This strongly favors the shorter period. We can envision 3 solutions to this confusing problem: TABLE 1 Orbital "dips" in the light curve ephemeris (a) ephemeris (b) Time Obs. E O-C E O-C Source (JD 2,440,000+) (cycles) (cycles) 4782.871 KPNO 0 +.02 0 -.10 Patterson and Steiner 1983 4787.914 KPNO 25 -.02 30 -.09 Patterson and Steiner 1983 4789.938 KPNO 35 -.01 42 -.04 Patterson and Steiner 1983 4790.953 KPNO 40 +.02 48 +.00 Patterson and Steiner 1983 4791.969 KPNO 45 +.05 54 +.05 Patterson and Steiner 1983 4834.801 CTIO 257 +.02 309 -.03 Patterson and Steiner 1983 4873.789 KPNO 450 -.02 541 +.02 Patterson and Steiner 1983 4881.673 KPNO 489 -.01 588 -.05 Patterson and Steiner 1983 4882.685 KPNO 494 +.00 594 -.03 Patterson and Steiner 1983 5117.881 ESO 1658 -.01 1994 -.20 Pakull 1986 5505.029 UKIRT 3574 -.00 4298 +.02 Sherrington, James & Bailey 1984 5613.733 KPNO 4112 -.02 4945 +.01 This paper 5919.867 KPNO 5627 +.04 6767 +.05 Mateo 1965 5929.142 AAO 5673 -.06 6822 +.25 Berriman et al. 1986 (6931.64) KPNO 7962 +.01 9575 +.11 This paper (6682.64) CTIO 9402 +.02 11307 -.10 Semeniuk and Kaluzny 1988 6684.655 CTIO 9412 -.00 11319 -.10 Semeniuk and Kaluzny 1988 6685.665 CTIO 9417 -.00 11325 -.09 Semeniuk and Kaluzny 1988 6695.574 CTIO 9466 +.03 11384 -.12 This paper 6704.625 McDonald 9699 -.01 11652 +.02 Shafter and Macry 1987 TABLE 2 - Times of inferior conjunction of emission lines ephemeris (a) ephemeris (b) Time Obs. E O-C E O-C Source (JD 2,440.000+) (cycles) (cycles) 4791.939 McGraw-Hill 45 -.10 54 -.13 Williams 1981 4822.939 Lick 446 -.23 536 -.04 Shafter and Macry 1987 5915.475 KPNO 5605 +.30 6741 -.09 Mateo 1985 [FIGURE 1] Figure 1. O-C diagram of the orbital dips, relative to three candidate ephemerides. The scatter about ephemeris (a) is by far the least, suggesting that it is the correct choice. [FIGURE 2] Figure 2. Dependence of dip timings on observatory longitude. No dependence is seen for ephemeris (a), but ephemeris (b) shows a systematic trend with longitude - in agreement with the solid line, which shows a trend expected if a cycle count error is present. (1) The photometric period is really 0.20206 days, but the spectroscopic period is slightly different sufficient to cause the inconsistent O-C residuals in Table 2. (2) Both photometric and spectroscopic periods are really 0.168017 days, but the uncertainties in the timings conspired by accident to give a substantially better fit to the longer, incorrect period. (3) Both periods are really 0.20206 days, but at the time of Mateo's (1985) spectroscopy, the dominant emission-line source switched from its normal location by ~180 deg. While none of these can be entirely excluded, we suspect that (3) is the correct answer. The accreting white dwarf in the system is a strong X-ray source which may cause a significant emission-line luminosity from the secondary and/or the hot spot region, due to the reprocessing of X-rays. This would be significantly out of phase with the motion of the accretion disk, normally the site of emission lines in cataclysmic variables. It's possible that a small rise in X-ray luminosity might shift the dominant role in the emission lines away from the accretion disk. In principle, it might be possible to find the orbital frequency by finding an optical modulation at the sideband frequency (nu_x-nu_orb) caused by X-ray heating of surfaces fixed in the orbital frame. Such a modulation appears to be intermittently present, seen in the power spectra published by Patterson and Steiner (1983; P=1370 +/- 15 sec) and Semeniuk and Kaluzny (1988; P=1374 +/- 4 or 1351 +/- 4 sec). The 0.168 d orbital period predicts P_SIDE = 1373 sec, while the 0.202 d orbital period predicts P_SIDE = 1352 sec. Hence this evidence, though far from conclusive, slightly favors the shorter period. A better test, in our opinion. is to look for a systematic dependence of the O-C residuals on the observer's terrestrial longitude. Figure 2 shows that such an effect does exist with ephemeris (b), but not with ephemeris (a). As Figure 2 demonstrates, the observed sign and magnitude of the effect provides strong support for the hypothesis we favor, that ephemeris (a) is correct. Finally, it's worth noting that any lingering uncertainty about the photometric period could be dispelled by a single, high-quality timing obtained in Europe, Africa or Asia. This will break the 24-hour alias which is the root of the problem. JOSEPH PATTERSON Department of Astronomy Columbia University New York, New York 10027 U.S.A. References: Berriman, G., Bailey, J., Axon, D.J., and Hough, J.H. 1986, M.N.R.A.S., 223, 449. [BIBCODE 1986MNRAS.223..449B ] Mateo, M. 1985, in Ninth North American Workshop on Cataclysmic Variables, ed. P. Szkody, p. 80. Pakull, M. 1986, priv. comm. Patterson, J. and Steiner, J.E. 1983, Ap.J. (Letters), 264, L61. [BIBCODE 1983ApJ...264L..61P ] Semeniuk, I. and Kaluzny, J. 1988, Acta Astr., in press. [BIBCODE 1988AcA....38...49S ] Shafter, A.W. and Macry, J.D. 1987, M.N.R.A.S., 228, 193. [BIBCODE 1987MNRAS.228..193S ] Sherrington, M.R., Jameson, R.F. and Bailey, J. 1984, M.N.R.A.S., 210, 1P. [BIBCODE 1984MNRAS.210P...1S ] Williams, G. 1981, private communication.