The Orbital Period of AM Canum Venaticorum David A. Harvey1, David R. Skillman2, Jonathan Kemp3, Joseph Patterson3, Tonny Vanmunster4, Robert E. Fried5, and Alon Retter6 Center for Backyard Astrophysics Astrophysical Journal, Letters 1 February 1998, Volume 493, Page L105 Abstract We report the discovery of a strictly periodic signal at 1028.7325 ± 0.0004 s in the light curve of the cataclysmic variable AM Canum Venaticorum. This brings to an end the long search for the true binary period of this important star, which represents the latest known stage of binary star evolution. It provides a more secure and quantitative basis for testing theories of binary evolution. And it provides strong evidence in favor of the "permanent superhump" interpretation of this star, and other cataclysmic variables of extreme mass ratio. 1. Introduction AM Canum Venaticorum (= HZ 29) is a 14th-magnitude blue star which has inspired many visions since it was first catalogued by Humason & Zwicky (1947). At various times it has been interpreted as a quasar, a massive helium star, a rotating/pulsating subdwarf, and a DB white dwarf. Smak (1967) discovered periodic photometric variations with P = 1051 s, and proposed that the star is actually a cataclysmic variable with an orbital period of 1051 s. Faulkner, Flannery, & Warner (1972) developed a consistent model of this type, with the mass-losing star a helium white dwarf of 0.04 Msol. The model has survived ever since. And the star continues to command much interest, since it defines the latest known stage of binary star evolution, and is the prototype of this class (extensively discussed by Ulla 1994, and in Chapter 9.7 of Warner 1995). However, the precise value of the photometric period changes erratically from year to year, implying that it cannot be the exact orbital period (Patterson et al. 1992, hereafter P92). The signal can be interpreted as a "permament superhump" (P92), but then the question remains, what exactly is the orbital period? Despite Herculean efforts, no observation has ever revealed it. The many failures to learn Porb have clouded all discussion of the star, and have even led to doubt that it is a binary at all. Patterson, Halpern, & Shambrook (1993, hereafter PHS) found a 13.38 hr periodic distortion of the absorption-line profiles, which they interpreted as the apsidal advance ("precession") period of an eccentric disk. This is theoretically related to the superhump period through Psh-1 = Porb-1 - Pprec-1, and hence requires an orbital period of 1028.77 ± 0.25 s. So why is this putative period not seen in the light curve? That's puzzling, because ~ 5 % of the total accretion energy should be released in the "hot spot" where the mass transfer stream strikes the disk, and yet available data have suggested an upper limit of ~ 0.3 % for any signal at this period. In this paper we report that the expected signal appeared quite strongly in 1997 photometry. Examination of earlier data shows that it has appeared sporadically for years, typically near the detection limit. It has maintained a constant phase for at least 5 years, and can securely be identified as Porb. We speculate that its amplitude excursions, from 1 % to < 0.2 %, arise from episodic "wobbling" of the accretion disk. 2. Observations, Light Curves, Period-Finding We carried out long photometric observing campaigns during 1992 - 1997. Most contributing telescopes were observing stations of the Center for Backyard Astrophysics (CBA), especially the Maryland and Tucson branches (Skillman 1993, Harvey et al. 1995) with 32 cm, 35 cm, and 66 cm telescopes. The data was differential CCD photometry, which enlarged the data base by enabling use of mediocre nights, since the differential technique permits the removal of thin clouds. The latter is quite important for us because most of the telescopes are robotic, with the "observer" sound asleep. Details of observational and data reduction technique are discussed in a longer paper in preparation, but do not differ importantly from those discussed by Skillman & Patterson (1993). We observed the star for 410 hr over 154 nights. The upper frame of Figure 1 contains a sample light curve, illustrating the well-known 525/1051 s wave along with random flickering of similar amplitude. We searched each year's light curve for periodic signals. The best coverage was in 1997, which we discuss most extensively. The middle frame of Figure 1 shows the interesting regions of the power spectrum, with significant signals marked. The usual signals at 525.6 and 350.4 s are present -- the familiar harmonics of the 1051 s signal. But the surprising feature is the obvious signal at 1028.74 ± 0.02 s, in agreement with the 1028.77 ± 0.25 s period hypothesized to explain the line-profile variations. The lower frame shows the mean 1028 and 1051 s light curves. The latter is an approximate double-sinusoid with alternating broad and narrow maxima, and minima asymmetrically placed in phase. This waveform is characteristic of all large data sets (Ostriker & Hesser 1968, Smak 1975, P92, Provencal et al. 1995) and this agreement proves beyond doubt that the fundamental photometric period is 1051 s (whereas most of the power is at 525 s, the first harmonic). Figure 2 shows low-frequency power spectra from the other years of recent coverage. During 1993 and 1994, there was a strong signal at 1011.40 and 1011.44 s (± 0.03 s), a period frequently though intermittently seen in previous photometry (Solheim et al. 1984, P92, Provencal et al. 1995). The same region in 1992 showed a signal at 1004.6 s or one of its aliases -- one of which occurs at 1028.7 s. Subtraction of the strong 1011 s signal from the 1993 light curve gave a residual time series dominated by a signal at 1028.7 s. Do these detections at 1028.7 s represent the same signal seen so strongly in 1997? We studied the time series and found that the signals agreed in period, phase, and waveform. Timings of minimum light were found compatible with a unique long-term ephemeris at constant period: Minimum light = HJD 2,448,742.5610(2) + 0.011906626(5) E . Hence it seems very likely that these are earlier apparitions of the signal seen easily in 1997. 3. Discussion Several studies (Provencal et al. 1995, Solheim et al. 1984) have interpreted the strongest photometric signal, at 525 s, as the true orbital period of the binary, and even given ephemerides with a slowly increasing period. But that cannot be correct, because that signal changes period erratically on short timescales. This is illustrated in Figure 3, which shows O - C diagrams during the 1993 and 1997 observing seasons, and establishes that the phase wanders on timescales of just a few months (~ 20000 cycles). This instability excludes an interpretation as Porb, and is principally what led to the "permanent superhump" interpretation of the light curve (P92). Most of the other well-documented periods in the light curve (350 s, 262 s, 210 s, 175 s) are simply harmonics of the underlying 1051 s variation. The one exception is the signal at 1011.4 s, which is noncommensurate with any other signal and is sometimes quite strong. Presumably this cannot be the true Porb, because that would predict a line skewness period of 7.4 hrs, whereas the data of PHS gave P = 13.38 hr. That surprise led to the prediction that the actual orbital period is 1028.77 ± 0.25 s, a signal which seemed to be embarrassingly invisible in the light curve. But the 1028 s signal does exist in the light curve, providing the "smoking pistol" needed to identify Porb and complement the other evidence that the main periodic signal is a superhump arising from apsidal advance of the accretion disk. While there are several possible mechanisms which can produce a photometric signal at Porb, the most natural one relies on the gravitational energy released at the "bright spot" where the mass-transfer stream strikes the accretion disk. In steady-state accretion onto a white dwarf, ~ 5 - 10 % of the total accretion energy should be liberated there. Because the bright spot is at the edge of the disk, it radiates freely in the outward direction, whereas radiation emitted inward is absorbed and re-radiated in the azimuthally symmetric disk. Thus the bright spot is a natural flashlight which shines outward and wheels at the orbital period. In an edge-on binary it should create a signal of a few percent amplitude. The effect disappears entirely at i = 0 °, but in AM CVn should still be obvious at the moderately high binary inclination required by the breadth of the absorption lines. So that provides a natural way to understand the orbital signal. But it's surprising that the amplitude changes so much, by at least a factor of 5, even though the star's brightness never wanders more than 0.1 mag from its long-term mean of V = 14.15. This is hard to accept if the signal arises from something as basic as the gravitational energy in the bright spot. Similar variability afflicts the 1011 s signal, and that too is unexplained. Below we propose a unified explanation of these changes. PHS speculated that the 1011 s signal was a "negative superhump" (so-called because P is slightly less than Porb), arising from the retrograde precession of a tilted accretion disk. The idea is that if the disk somehow comes out of the orbital plane, gravity from the secondary will force it to precess retrograde, so the stream-disk geometry recurs not at Porb but at a slightly shorter period. Discovery of a 1028 s orbital period certainly raises the plausibility of this idea. We could explain the amplitude variations of the negative superhump and orbital signals by invoking episodic retrograde precession. When the disk is coplanar with the orbit, a normal bright spot results with P = Porb. When disk tilt occurs (possibly due to the 3:1 vertical instability discussed by Lubow 1992), the mass-transfer stream will overflow the disk edge and strike the disk farther in. The location of that impact point changes with the negative superhump period. This predicts that 1028 and 1011 s are basically alternatives, depending on whether there is disk tilt. That does not require that they absolutely exclude each other, nor that they should be of identical maximum amplitude when seen (because, for example, the proposed orbital mechanism is inclination-dependent, whereas the proposed 1011 s mechanism is independent of i). But it does imply that the signals should be generally anticorrelated, and should never be seen together at high amplitude. 4. Summary 1. We report a photometric signal which bears all the earmarks of the long-sought orbital period. The period is 1028.7325 ± 0.0004 s, stable during 1992 - 1997. Study of timings over a 10 - 20 yr baseline should reveal changes as small as P-dot ~ 10-12, the approximate level predicted by stellar evolution. 2. This agreement with the Porb required by PHS furnishes an additional strong piece of evidence in favor of the permanent-superhump theory of the 1051 s signal (and, for that matter, in favor of the precessing-disk theory of the periodic skewness signal in the absorption lines). It also provides evidence mildly supportive of the wobbling-disk theory of the 1011 s signal, mainly because it establishes a Porb slightly longer than 1011 s. For a particularly simple model (the "bright-spot" model) of the 1011 and 1028 s signals, we predict an anticorrelation in the signal amplitudes. 3. With Porb reasonably secure, AM CVn can now be more reliably and quantitatively used as a bellweather of binary-star evolution. It may also be an appropriate target for future gravitational-wave experiments, some of which may reach greater sensitivity by exploiting a known precise period. And it seems an excellent testing ground for theories of precession in accretion disks, since it provides two types of superhump, at least one of the corresponding precession periods, and the very low flickering amplitude which greatly aids study of periodic signals. How wonderful it is that such things arrive from small backyard telescopes, toiling patiently with all nearby astronomers safely neutralized and asleep! We thank the Research Corporation for its generous support of the CBA through grant RC-GG0084 to Columbia University. Also essential was support from the National Science Foundation (AST96-18545). __________ 11552 West Chappala Drive, Tucson, AZ 85703; comsoft .at. primenet.com 29517 Washington Avenue, Laurel, MD 20723; cbaceo .at. clark.net 3Department of Astronomy, Columbia University, 550 West 120th Street, New York, NY 10027; jonathan, jop .at. astro.columbia.edu 4Walhostraat 1A, 3401 Landen, Belgium; tvanmuns .at. innet.be 5Braeside Observatory, P. O. Box 906, Flagstaff, AZ 86002; captain .at. braeside.org 6Wise Observatory and Department of Astronomy, Tel Aviv University, Ramat Aviv, Tel Aviv 69978, Israel; alon .at. wise.tau.ac.il References Faulkner, J., Flannery, B.P., & Warner, B. 1972, ApJ, 175, L79. Harvey, D., Skillman, D.R., Patterson, J., & Ringwald, F.A. 1995, PASP, 106, 551. Humason, M.L. & Zwicky, F. 1947, ApJ, 105, 85. Lubow, S. 1992, ApJ, 398, 525. Ostriker, J.P. & Hesser, J.E. 1968, ApJ, 153, L151. Patterson, J., Sterner, E., Halpern, J.P., & Raymond, J.C. 1992, ApJ, 384, 234 (P92). Patterson, J., Halpern, J.P., & Shambrook, A.A. 1993, ApJ, 419, 803 (PHS). Provencal, J. et al. 1995, ApJ, 445, 927. Skillman, D.R. 1993, Sky & Telescope, 85, 83. Skillman, D.R. & Patterson, J. 1993, ApJ, 417, 298. Smak, J.I. 1967, Acta Astr., 17, 255. Smak, J.I. 1975, Acta Astr., 25, 371. Solheim, J.-E., Robinson, E.L., Nather, R.E., & Kepler, S.O. 1984, A&A, 135, 2. Ulla, A. 1994, SSRV, 67, 241. Warner, B. 1995, Cataclysmic Variable Stars (Cambridge U.: Cambridge). Figure Captions Figure 1. Upper frame, a sample light curve of white-light CBA photometry. Each point is a 60-s integration. The 525 s variations are occasionally but barely visible in the raw light curve. Middle frame, power spectrum of the 1997 light curve. Significant peaks are marked with their period in seconds. The signals at 525.65 and 350.43 s are just the usual harmonics of the main signal, but the signal at 1028.74 s appears to be a new feature. Lower left frame, 1997 light curve summed at 1051.30 s. The double-humped waveform agrees in detail with all previous studies, indicating that 1051.3 s is indeed the fundamental period of the main signal (although most of the power is clearly at the first harmonic, 525 s). Lower right frame, 1997 light curve summed at 1028.733 s. Figure 2. Power spectra in 1992 - 1994, with significant peaks marked with their periods in seconds. A 1011 s signal, markedly absent in 1997, dominates the low-frequency regime in 1993 and 1994. The 1992 data is highly aliased, but one of the acceptable aliases occurs at 1028.7 s, the period seen strongly in 1997. Figure 3. O - C diagram of the 525 s timings in 1993 and 1997. The curvature, shown by best-fit cubics, demonstrates that the clock wanders on a timescale of ~ 20000 cycles (a few months).