L105

The Astrophysical Journal, 493:L105L108, 1998 February 1q 1998. The American Astronomical Society. All rights reserved. Printed in U.S.A.

THE ORBITAL PERIOD OF AM CANUM VENATICORUM

David A. Harvey,1,2 David R. Skillman,1,3 Jonathan Kemp,1 Joseph Patterson,1 Tonny Vanmunster,1,4

Robert E. Fried,1,5 and Alon Retter1,6

Received 1997 October 22; accepted 1997 November 24; published 1998 January 14

ABSTRACT

We report the discovery of a strictly periodic signal at s in the light curve of the cataclysmic1028.7325 5 0.0004variable AM Canum Venaticorum. This brings to an end the long search for the true binary period of this importantstar, which represents the latest known stage of binary star evolution. It provides a more secure and quantitativebasis for testing theories of binary evolution. And it provides strong evidence in favor of the permanentsuperhump interpretation of this star and other cataclysmic variables of extreme mass ratio.

Subject headings: accretion, accretion disks novae, cataclysmic variables stars: individual (AM Canum Venaticorum)

1. INTRODUCTION

AM Canum Venaticorum (5HZ 29) is a 14th magnitudeblue star that has inspired many visions since it was first cat-aloged by Humason & Zwicky (1947). At various times, it hasbeen interpreted as a quasar, a massive helium star, a rotating/pulsating subdwarf, and a DB white dwarf. Smak (1967) dis-covered periodic photometric variations with s andP 5 1051proposed that the star is actually a cataclysmic variable withan 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 . The model hasM,survived ever since. And the star continues to command muchinterest, since it defines the latest known stage of binary starevolution, and is the prototype of this class (extensively dis-cussed by Ulla 1994, and in Warner 1995, chap. 9.7). However,the precise value of the photometric period changes erraticallyfrom year to year, implying that it cannot be the exact orbitalperiod (Patterson et al. 1992, hereafter P92). The signal canbe interpreted as a permanent superhump (P92), but then thequestion remains: what exactly is the orbital period? DespiteHerculean efforts, no observation has ever revealed it. Themany failures to learn have clouded all discussion of thePorbstar 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 pro-files, which they interpreted as the apsidal advance (preces-sion) period of an eccentric disk. This is related theoreticallyto the superhump period through and hence21 21 21P 5 P 2 Psh orb precrequires an orbital period of s. So why is this1028.77 5 0.25putative period not seen in the light curve? That is puzzling,because 5% of the total accretion energy should be releasedin the hot spot where the mass transfer stream strikes thedisk, and yet available data have suggested an upper limit of0.3% for any signal at this period.

In this Letter, we report that the expected signal appeared

1 Center for Backyard Astrophysics, Department of Astronomy, Pupin Phys-ics Laboratories, Columbia University, 550 West 120th Street, New York, NY10027; jonathan@astro.columbia.edu, jop@astro.columbia.edu.

2 1552 West Chappala Drive, Tucson, AZ 85703; comsoft@primenet.com.3 9517 Washington Avenue, Laurel, MD 20723; cbaceo@clark.net.4 Walhostraat 1A, 3401 Landen, Belgium; tvanmuns@innet.be.5 Braeside Observatory, P.O. Box 906, Flagstaff, AZ 86002; captain@

braeside.org.6 Wise Observatory and Department of Astronomy, Tel Aviv University,

Ramat Aviv, Tel Aviv 69978, Israel; alon@wise.tau.ac.il.

quite strongly in 1997 photometry. Examination of earlier datashows that it has appeared sporadically for years, typically nearthe detection limit. It has maintained a constant phase for atleast 5 years and can be identified securely as . We speculatePorbthat its amplitude excursions, from 1% to less than 0.2%, arisefrom episodic wobbling of the accretion disk.

2. OBSERVATIONS, LIGHT CURVES, PERIOD FINDING

We carried out long photometric observing campaigns during19921997. Most contributing telescopes were observing sta-tions of the Center for Backyard Astrophysics (CBA), espe-cially the Maryland and Tucson branches (Skillman 1993; Har-vey et al. 1995) with 32, 35, and 66 cm telescopes. The datawere differential CCD photometry, which enlarged the databaseby enabling us to use mediocre nights, since the differentialtechnique permits the removal of thin clouds. The latter is quiteimportant for us because most of the telescopes are robotic,with the observer sound asleep.

Details of observational and data reduction technique arediscussed in a longer paper that is in preparation, but thesedetails do not differ importantly from those discussed by Skill-man & Patterson (1993). We observed the star for 410 hr over154 nights. The top panel of Figure 1 contains a sample lightcurve, illustrating the well-known 525/1051 s wave along withrandom flickering of similar amplitude.

We searched each years light curve for periodic signals. Thebest coverage was in 1997, which we discuss most extensively.The middle panels of Figure 1 show the interesting regions ofthe power spectrum, with significant signals marked. The usualsignals at 525.6 and 350.4 s are presentthe familiar harmonicsof the 1051 s signal. But the surprising feature is the obvioussignal at s, in agreement with the1028.74 5 0.02

s period hypothesized to explain the line pro-1028.77 5 0.25file variations.

The bottom panels show the mean 1028 and 1051 s lightcurves. The bottom right panel is an approximate double si-nusoid with alternating broad and narrow maxima, and minimaasymmetrically placed in phase. This waveform is characteristicof all large data sets (Ostriker & Hesser 1968; Smak 1975;P92; Provencal et al. 1995), and this agreement proves beyonda 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 otheryears of recent coverage. During 1993 and 1994, there was astrong signal at 1011.40 and 1011.44 s (50.03 s), a period

L106 HARVEY ET AL. Vol. 493

Fig. 1.Top panel: a sample light curve of white-light CBA photometry. Each point is a 60 s integration. The 525 s variations are occasionally but barelyvisible in the raw light curve. Middle panels: power spectrum of the 1997 light curve. Significant peaks are marked with their period in seconds. The signals at525.65 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. Bottom left panel: 1997 light curvesummed 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 themain signal (although most of the power is clearly at the first harmonic, 525 s). Bottom right panel: 1997 light curve summed at 1028.733 s.

frequently, although intermittently, seen in previous photom-etry (Solheim et al. 1984; P92; Provencal et al. 1995). Thesame region in 1992 shows a signal at 1004.6 s or one of itsaliasesone of which occurs at 1028.7 s. Subtraction of thestrong 1011 s signal from the 1993 light curve gave a residualtime series dominated by a signal at 1028.7 s.

Do these represent the same signal seen so strongly in 1997?We studied the time series and found that the signals agreedin period, phase, and waveform. Timings of minimum lightwere found compatible with a unique long-term ephemeris atconstant period:

Minimum light

5 HJD 2, 448, 742.5610(2) 1 0.011906626(5)E.

Hence, it seems very likely that these are earlier apparitionsof 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, asthe true orbital period of the binary and even given ephemerideswith a slowly increasing period. But that cannot be correct,

because that signal changes period erratically on short times-cales. This is illustrated in Figure 3, which shows O2C dia-grams during the 1993 and 1997 observing seasons and estab-lishes that the phase wanders on timescales of just a few months(20,000 cycles). This instability excludes an interpretation as

and is principally what led to the permanent superhumpPorbinterpretation of the light curve (P92).

Most of the other well-documented periods in the light curve(350, 262, 210, and 175 s) are simply harmonics of the un-derlying 1051 s variation. The one exception is the signal at1011.4 s, which is noncommensurate with any other signal andis sometimes quite strong. Presumably this cannot be the true

, because that would predict a line skewness period of 7.4Porbhr, whereas the data of PHS gave P 5 13.38 hr. That surpriseled to the prediction that the actual orbital period is

s, a signal that seemed to be embarrassingly1028.77 5 0.25invisible in the light curve.

But the 1028 s signal does exist in the light curve, providingthe smoking gun needed to identify and complement thePorbother evidence that the main periodic signal is a superhumparising from apsidal advance of the accretion disk. While thereare several possible mechanisms that can produce a photometricsignal at , the most natural one relies on the gravitationalPorbenergy released at the bright spot where the mass transfer

No. 2, 1998 ORBITAL PERIOD OF AM CVn L107

Fig. 2.Power spectra in 19921994, with significant peaks marked withtheir periods in seconds. A 1011 s signal, markedly absent in 1997, dominatesthe 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 stronglyin 1997.

Fig. 3.O2C diagram of the 525 s timings in 1993 and 1997. The curvature,shown by best-fit cubics, demonstrates that the clock wanders on a timescaleof 20,000 cycles (a few months).

stream strikes the accretion disk. In steady state accretion ontoa white dwarf, 5%10% of the total accretion energy shouldbe liberated there. Because the bright spot is at the edge of thedisk, it radiates freely in the outward direction, whereas radi-ation emitted inward is absorbed and reradiated in the azi-muthally symmetric disk. Thus, the bright spot is a naturalflashlight that shines outward and wheels at the orbital period.In an edge-on binary, it should create a signal of a few percentamplitude. The effect disappears entirely at , but in AMCi 5 0CVn, it should still be obvious at the moderately high binaryinclination required by the breadth of the absorption lines.

So that provides a natural way to understand the orbitalsignal. But it is surprising that the amplitude changes so much,by at least a factor of 5, even though the stars brightness neverwanders more than 0.1 mag from its long-term mean of V 5

. This is hard to accept if the signal arises from something14.15as basic as the gravitational energy in the bright spot. Similarvariability afflicts the 1011 s signal, and that too is unexplained.We propose a unified explanation of these changes.

PHS speculated that the 1011 s signal was a negative su-perhump (so-called because P is slightly less than ), arisingPorbfrom the retrograde precession of a tilted accretion disk. Theidea 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 but at a slightlyPorbshorter period. The discovery of a 1028 s orbital period cer-tainly raises the plausibility of this idea.

We could explain the amplitude variations of the negativesuperhump and orbital signals by invoking episodic retrogradeprecession. When the disk is coplanar with the orbit, a normalbright spot results with . When disk tilt occurs (possiblyP 5 Porbbecause of the 3:1 vertical instability discussed by Lubow1992), the mass transfer stream will overflow the disk edgeand strike the disk farther in. The location of that impact pointchanges with the negative superhump period. This predicts that1028 and 1011 s are basically alternatives, depending onwhether there is a disk tilt. That does not require that theyabsolutely exclude each other, nor that they should be of iden-tical 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 anticor-related and should never be seen together at high amplitude.

4. SUMMARY

1. We report a photometric signal that bears all the earmarksof the long-sought orbital period. The period is

s, stable throughout 19921997. A study1028.7325 5 0.0004of timings over a 1020 yr baseline should reveal changes assmall as , the approximate level predicted by stellar212P 10evolution.

2. This agreement with the required by PHS furnishesPorban additional strong piece of evidence in favor of the permanentsuperhump theory of the 1051 s signal (and, for that matter,in favor of the precessing disk theory of the periodic skewnesssignal in the absorption lines). It also provides evidence mildlysupportive of the wobbling disk theory of the 1011 s signal,mainly because it establishes a slightly longer than 1011Porbs. For a particularly simple model (the bright-spot model) of

L108 HARVEY ET AL. Vol. 493

the 1011 and 1028 s signals, we predict an anticorrelation inthe signal amplitudes.

3. With reasonably secure, AM CVn can now be morePorbreliably and quantitatively used as a bellwether of binary starevolution. It may also be an appropriate target for future grav-itational wave experiments, some of which may reach greatersensitivity by exploiting a known precise period. And it seemsan excellent testing ground for theories of precession in ac-cretion disks, since it provides two types of superhump, at leastone of the corresponding precession periods, and the very low

flickering amplitude that greatly aids the study of periodic sig-nals. How wonderful it is that such things arrive from smallbackyard telescopes, toiling patiently with all nearby astron-omers safely neutralized and asleep!

We thank the Research Corporation for its generous supportof the CBA through grant RC-GG0084 to Columbia University.Support from the National Science Foundation (AST 96-18545)was also essential.

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