Superhumps in Cataclysmic Binaries. XVII. AM Canum VenaticorumAuthor(s): David R. Skillman, Joseph Patterson, Jonathan Kemp, David A. Harvey,Robert E. Fried, Alon Retter, Yiftah Lipkin, and Tonny VanmunsterSource: Publications of the Astronomical Society of the Pacific, Vol. 111, No. 764 (October1999), pp. 1281-1291Published by: The University of Chicago Press on behalf of the Astronomical Society of the PacificStable URL: http://www.jstor.org/stable/10.1086/316437 .

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PUBLICATIONS OF THE ASTRONOMICAL SOCIETY OF THE PACIFIC, 111 :1281È1291, 1999 October1999. The Astronomical Society of the PaciÐc. All rights reserved. Printed in U.S.A.(

Superhumps in Cataclysmic Binaries. XVII. AM Canum VenaticorumDAVID R. SKILLMAN,1 JOSEPH PATTERSON,2,3 JONATHAN KEMP,2,3,4 DAVID A. HARVEY,5 ROBERT E. FRIED,6

ALON RETTER,7,8 YIFTAH LIPKIN,7 AND TONNY VANMUNSTER9Received 1999 June 18 ; accepted 1999 July 5

ABSTRACT. We report new photometry of the cataclysmic variable AM Canum Venaticorum, compris-ing 670 hr over 227 nights during 1992È1999. The data demonstrate conclusively that (1) the fundamentalperiod is 1051.2 s, with a well-deÐned waveform which has not changed during the four decades of study ; (2)this period wanders erratically by D0.2 s on a timescale of 3È6 months ; and (3) the light curve contains a richspectrum of periodic signals, at least 20 of them. We also report a secure detection of a photometric signal at1028.7322^ 0.0003 s, consistent with the orbital period previously hypothesized to explain the spectroscopicvariations.

The behavior of the 1051 s signal is consistent with the hypothesis of a superhump origin, and thediscovery of a signal at the presumed is yet another strong argument for this hypothesis. ApparentlyPorbsuperhumps can manufacture a very complex spectrum of photometric periods, and they can remain stablefor many thousands of cycles. But most are harmonics and sidebands of the truly fundamental clocks in thebinary, at and the diskÏs two likely periods of precessionÈat 13.36 and 16.69 hr. It is plausible that thePorblatter correspond to the periods of apsidal advance and nodal regression. The former is steadily present,evidently producing the well-known superhump. The signatures of nodal regression, primarily the 1011.4 s““ negative superhump,ÏÏ are more variable. The sideband structure of the harmonics obeys Ðrm selectionrules, which may reveal intricate details of structure in the accretion disk. And somehow all these exoticclocks manage to coexist and remain relatively stable, despite being putatively seated in the relatively sloppystructure of a disk, highly sheared and unsupported by pressure !

1. INTRODUCTION

AM Canum Venaticorum (\HZ 29) is a faint blue starwhich has inspired many visions since it was Ðrst catalogedby Humason & Zwicky (1947). Smak (1967) discovered

ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ1 Center for Backyard Astrophysics (East), 9517 Washington Avenue,

Laurel, MD 20723 ; dskillman=home.com.2 Department of Astronomy, Columbia University, 550 West 120th

Street, New York, NY 10027 ; jop=astro.columbia.edu.3 Biosphere 2 Center, Columbia University, 32540 South Biosphere

Road, Oracle, AZ 85623 ; jonathan=astro.bio2.edu.4 Visiting Astronomer, Kitt Peak National Observatory, National

Optical Astronomy Observatories, which is operated by the Association ofUniversities for Research in Astronomy, (AURA) Inc., under cooperativeagreement with the National Science Foundation.

5 Center for Backyard Astrophysics (West), 1552 West Chapala Drive,Tucson, AZ 85704 ; dharvey=comsoft-telescope.com.

6 Braeside Observatory, P.O. Box 906, Flagsta†, AZ 86002 ;captain=braeside.org.

7 Wise Observatory and Department of Astronomy, Tel Aviv Uni-versity, Ramat Aviv, Tel Aviv 69978, Israel ; yiftah=wise.tau.ac.il.

8 Current address : Astrophysics Group, Department of Physics, KeeleUniversity, Keele, Sta†ordshire ST5 5BG, England, UK;ar=astro.keele.ac.uk.

9 Center for Backyard Astrophysics (Belgium), Walhostraat 1A, B-3401Landen, Belgium; Tonny.Vanmunster=advalvas.be.

periodic photometric variations with P\ 17.5 minutes andproposed that the star is actually a cataclysmic binary withan underlying orbital period of 17.5 minutes. Faulkner,Flannery, & Warner (1972) showed that a consistent modelof this type could be developed, with the mass-losing star ahelium white dwarf of 0.04 Since then, Ðve new stars ofM

_.

this type have been discovered : GP Com (\G61-29 ;Nather, Robinson, & Stover 1981), CR Bootis (\PG1346]082 ; Wood et al. 1987), V803 Centauri (\AE 1;OÏDonoghue & Kilkenny 1989), CP Eridani (Abbott et al.1993), and HP Librae (\EC 1533.0[1403 ; OÏDonoghue etal. 1994). These stars comprise the ““ AM CVn ÏÏ class ofcataclysmic variables.

Observations have revealed many more features of AMCVn. In addition to the primary photometric period of1051 s and its harmonics, the light curve also exhibits asignal at 1011 s (Solheim et al. 1984, hereafter S84 ;Patterson et al. 1992, hereafter P92 ; Provencal et al. 1995,hereafter P95 ; Solheim et al. 1998, hereafter S98). The ultra-violet spectrum shows absorption features due to N, Si, C,and He, suggesting origin in a disk or wind (P92 ; Solheim &Sion 1994). The He I lines, which dominate the visible spec-trum, show proÐle distortions repeating with a period of13.38^ 0.07 hr, a plausible signature of a precessing, eccen-

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1282 SKILLMAN ET AL.

tric accretion disk (Patterson, Halpern, & Shambrook 1993,hereafter PHS).

The photometric variations of the AM CVn stars havebeguiled many astronomers. All stars in the class show acomplex spectrum of multiperiodic signals, resembling insome respects the pulsating DB white dwarfs. Earlier westudied the hypothesis of a pulsation origin (P92), but wefound it unable to account for spectral features and thehigh-low state behavior of several members of the class. Therecent Whole Earth Telescope (WET) study (P95 ; S98)revived that hypothesis again for AM CVn, attempting toaccount for all the periods with a combination of pulsation,rotation, orbital motion, precession, and magnetism.Despite this daunting array of gadgets for producingperiods, and equally daunting author list (56) and telescopepower (10 billion photons collected), we return to debatethese matters. We are, after all, among the beguiled.

In particular, we report here on another 6 years of data,which we hope will put to rest the controversies about theperiodic signals. We also discuss, following the initial reportof Harvey et al. (1998, hereafter H98), a 1028 s signal verylikely to be the true binary period. Tracking of this signalover years may eventually reveal the direction and rate ofbinary evolution.

2. OBSERVATIONS

2.1. Data AcquisitionMost of the 1992È1994 photometry was acquired with a

CCD photometer on the ““ robotic ÏÏ 32 and 66 cm reÑectorsof the Center for Backyard Astrophysics (CBA) in Laurel,Maryland. Details of the telescope, instrument, and observ-ing procedure are given by Skillman (1981, 1993) and Skill-man & Patterson (1993). BrieÑy, on each night we obtaineda time series of di†erential magnitudes (AM [ comparison)with 1 minute integration times (usually 57 s, with theremaining 3 s for preliminary data analysis and telescopeguide corrections). For a comparison we used the star justsouth of AM CVn, for which Smak (1975) measuredV \ 12.42, B[V \ ]0.64. A ““ check star ÏÏ was observedalso, to verify the steadiness of the comparison star. Deltamagnitudes were obtained by computing the light withincircular apertures of 6A diameter.

Most CBA photometry is unÐltered, which yields aresponse over 5000È9000 with an e†ective wavelengthA�near 6400 for very blue stars such as cataclysmic vari-A�ables. This makes for extra difficulty when splicing datafrom di†erent observatories, so we try for overlaps in cover-age to establish an internal calibration. We Ðnd thatunÐltered photometry is acceptable when the starÏs signal isbroadband and does not display strong wavelength-dependent e†ects. This is deÐnitely true for AM CVn(Krzeminski 1971).

Most of the 1997È1998 data was acquired with photom-eters at other observing stations. CBA stations tended touse a similar observing procedure. Non-CBA telescopesgenerally used more traditional observing procedures(observer in attendance, Ðltered photometry, more accurateextinction correction). The distribution in longitude, fromIsrael to Arizona, enabled unambiguous identiÐcation ofaliases in the period-Ðnding enterprises discussed below.

In our standard method of data analysis, we discard thefull-frame images but retain time series consisting of theabsolute counts, as well as the delta magnitudes. Thisenables us to identify segments in which thick clouds arepresent (not otherwise known to us, since the ““ observer ÏÏ isoften asleep) and to exclude those data in subsequentanalysis. Thin clouds do not greatly compromise the data,since the CCD enables accurate sky subtraction and goodpoint-by-point removal of extinction variations.10

During 1992È1999 we accumulated 670 hr of coverageover 227 nights. The brightness measures were left in deltamagnitudes, since the actual conversion to a standard mag-nitude is difficult to know for these observations inunÐltered light. On nights of well-calibrated photometry wealways found AM CVn in the range V \ 14.10È14.20, andon the other D180 nights the star strayed less than 0.07mag from its mean brightness.

2.2. Light Curves and Nightly Power Spectra

A sample light curve is shown in the top panel of Figure1. All the high-quality light curves look the same, with adominant 525 s signal of variable amplitude (partly due tothe Ðne structure resident within it), and a weaker signal ofapproximately twice that period. To analyze the data, wecalculated the power spectrum of each nightly light curveand estimated from it the amplitude of the major periodicsignals : at 525, 1011, and 1028 s. (The latter two are notseparable in a single night, so we used longer time series todistinguish them; this has some possibility of error if theamplitude changes are faster than we can resolve.) Thisshowed that the 525 s signal is always present and changesonly slightly in amplitude (no more than a factor of 2, andusually much less). The 1011 s signal appears to show largeamplitude variations, of at least a factor of 5.

We selected 28 good nights with observations of morethan 5 hr duration and added nightly amplitude spectra to

ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ10 But not di†erential, color-dependent extinction. Because most of our

photometry is unÐltered, it contains air-mass e†ects which can in principleproduce spurious signals at 1, 2, or 3 cycles day~1. We usually do not seesuch e†ects (down to D0.03 mag), presumably because atmospheric extinc-tion is fairly gray over the CCD passband of 5000È9000 So we usuallyA� .attempt no correction for this. However, in this particular study we did seesuch an e†ect, probably because AM CVnÏs colors are so extremely blue ;so we removed low-frequency (\3 cycles day~1) trends prior to analysis.

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SUPERHUMPS IN CATACLYSMIC BINARIES. XVII. 1283

FIG. 1.ÈTop panel : Sample light curve of AM CVn, obtained fromCBA-East. The 525 s (164.4 cycles day~1) signal is occasionally visibleamid the noise. All light curves look pretty much the same! Bottom panel :The mean amplitude spectrum from the 28 longest/best nights. SigniÐcantfeatures are labeled with their frequency in cycles day~1, with an averageerror of 0.5 cycles day~1. The two signals of highest frequency are onlybarely ““ signiÐcant ÏÏ in an unbiased period search, but their precise agree-ment with harmonics in the high-resolution spectrum described in Table 2establishes their reality. The signals marked with a cross, at 105.8 and 299.2cycles day~1, are also ““ signiÐcant ÏÏ but are discussed separately herebecause we could not Ðnd any plausible relation between them and themajor clocks in the binary.

obtain a mean. This is shown in the bottom panel of Figure1, where signiÐcant features are labeled with their fre-quencies in cycles day~1. The typical error is 0.5 cyclesday~1. Aside from the strong signal at 85.3 cycles day~1,the other labeled features are harmonics of the fundamentalat 82.2 cycles day~1 (unseen during single nights, butobvious in the seasonal power spectra described below). Butthe features marked with a cross, occurring at 105.8 and299.2 cycles day~1, clearly are not. They pass signiÐcancetests and are certainly real since they have been detected inother data sets (P92 and P95), but we consider them separa-tely here because they are transient, not necessarily coher-ent, and with no clear relationship to the major clocks in thelight curve. They will be discussed in ° 8.

2.3. Tracking the Strong Signals through OÔC Analysis

Although the periodic structure of AM CVn is complex, itis always dominated by the 525 s signal. Thus we canmeasure for this signal an accurate phase on nearly everynight of observation. (Since the true period is 1051 s and thewaveform is slightly asymmetric, the Ðt to 525 s can intro-duce an error of 0.02 cycles ; but this is smaller than ourtypical measurement error, so we deemed it acceptable.)Timings of 525 s minimum light during 1992È1999 are givenin Table 1.

Figure 2 shows yearly O[C diagrams for the thesetimings. These give an accurate basis for evaluating preciseperiods, because the slopes measure the departure from the

FIG. 2.ÈSeasonal O[C diagrams for the 525 s signal, relative to a test period of 525.60 s. The vertical and horizontal scaling is the same in all panels, andthe Ðrst timing in each deÐnes phase 0.0 or 1.0. The timings are listed in Table 1. The freehand curve helps visualize the large drifts in phase, which occur on atimescale of D4È12 months (with some smaller drifts occurring more rapidly).

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1284 SKILLMAN ET AL.

TABLE 1

TIMINGS OF 525 s MINIMA

HJD 2,400,000]

48746.5534 49140.5628 50540.3259 50640.5769 50944.6321 51265.606348749.5643 49149.5782 50559.6960 50641.5555 50945.0575 51266.810548754.5649 49150.5758 50563.9668 50642.5536 50945.6293 51268.636548755.5619 49152.5594 50568.6637 50825.8067 50946.2496 51274.603348765.5634 49153.5691 50570.6472 50853.7132 50946.6329 51274.646348771.5739 49154.5664 50571.6444 50855.7882 50947.5579 51279.524848783.5591 49155.5583 50573.5428 50856.8224 50948.7014 51283.527748794.5704 49162.5598 50573.6646 50882.5140 50949.5464 51285.559448795.5614 49163.5630 50574.6686 50891.8395 50950.6355 51294.259348802.5634 49164.5602 50575.6237 50896.3400 50951.6391 51294.642049041.7055 49166.5622 50576.5421 50899.7104 50952.6308 51295.256649043.6702 49447.6101 50576.6520 50901.7483 50953.5611 51295.548749048.6704 49450.5905 50579.6023 50902.6725 50955.5627 51295.621449061.6810 49459.5447 50580.5453 50903.7003 50970.6911 51296.248049062.6788 49463.5531 50589.7381 50913.6348 50972.6926 51297.252149072.6664 49467.5799 50590.2735 50914.6692 50973.7014 51297.684249077.7570 49469.5444 50590.6448 50915.6298 50974.6516 51297.774849081.5836 49472.6880 50591.2477 50915.5880 50974.6993 51298.255949084.6008 49482.5920 50591.5508 50916.6093 50976.6641 51298.669949091.6081 49483.5649 50592.2452 50917.5949 50977.6742 51299.539049096.6140 49486.5635 50593.2481 50927.6187 50980.6303 51300.652649101.5286 49493.7414 50617.2623 50931.5417 50981.6218 51327.255149105.5852 49494.5692 50617.6576 50932.5578 50981.6579 51327.619349109.5332 49494.7269 50618.2533 50937.2475 50985.5874 51328.227549115.5430 49501.5579 50618.7098 50938.2390 51211.9861 51328.642349117.5506 49517.5618 50619.2577 50938.6404 51219.0423 51329.736549122.5625 49526.5705 50620.2677 50939.6255 51221.9980 51337.601849128.5542 50526.6728 50620.7180 50940.6353 51223.8592 51338.563549129.5826 50527.6404 50621.2655 50941.6331 51252.8130 51339.561149136.5843 50529.6054 50622.2631 50942.6308 51256.651549138.5556 50537.6905 50623.2544 50943.6222 51262.7773

adopted test period of 525.600 s. The curvature in O[Cshows that it is not a strictly periodic signal, but drifts on atimescale of months (D20,000 cycles). Over the historicalrecord, the period has ranged erratically from 525.52 to525.65 s. In all cases, we found that the period as deducedfrom the sloping O[C agreed with that deduced from thepower spectrum, indicating the reliability of both. TheO[C curvature over a timescale of a few months has beendiscussed many times previously (Patterson et al. 1979,hereafter P79 ; P92 ; Patterson et al. 1993 ; H98), although ithas also been denied on numerous occasions (S84 ; P95 ;S98). It would certainly be good if the world would recog-nize this simple truth : the 525 s phase drifts on a timescale ofmonths.

We tried the same analysis on the 1011 s signal, butwithout much success. Nightly timings could not be trusted,because of amplitude changes and interference from thesignals at 1028 and 1051 s. A reliable timing could usuallybe obtained over fairly long baselines ([8 days), but thenthe number of timings became too sparse. We learned thatthe mean period of the 1011 s signal is fairly constant at

1011.41^ 0.03 s, but the signal does drift in phase on atimescale of a few months (some much faster drifts wereseen, but they may have arisen from contamination bynearby signals).

The stability of a clock process is sometimes character-ized by the rate of period change The phase wanders ofP0 .the 525 s signal in AM CVn correspond to P0 \ ^2 ] 10~8.But the mean period has not wandered more than 0.1 s in 35years, which corresponds to The stability ofoP0 o\ 10~10.the 1011 s clock appears to be comparable, subject to theuncertainties cited above.

2.4. Detailed Power Spectra

We created a single time series for each observing seasonand calculated the power spectra with a discrete Fouriertransform. Some of the results are shown in Figures 1 and 2of H98, illustrating the general pattern : signals at 1028,1011, 525, and 350 s. During 1997 and 1998, we obtainedcoverage which was both long ([100 days) and global,

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SUPERHUMPS IN CATACLYSMIC BINARIES. XVII. 1285

giving high frequency resolution and freedom from aliasing.Coverage of good quality was also obtained during 1978and 1999. In Figures 3 and 4 we present power spectra ofthe most densely sampled portions of these 4 years. Theyhave been lightly ““ cleaned ÏÏ by removing the windowpattern of the strongest signals, in order to aid in dis-tinguishing noise from aliasing (difficult with multiperiodicsignals). SigniÐcant detections are marked with their fre-quencies in cycles day~1.

The strongest signal always occurred at 164.39 cyclesday~1 (P\ 525.6 s), with a full amplitude of 0.024 mag.This is simply the Ðrst harmonic of the fundamental fre-quency of 82.19 cycles day~1, which reached easy visibilityin the power spectrum of 1997 and 1998 and was dimlyespied in other years (and always clearly evinced by theconsistent and stable 1051 s waveform). We will refer to that

signal as the ““ positive superhump.ÏÏ The other strong signaloccurred at 85.43 cycles day~1, which we call the ““ negativesuperhump.ÏÏ

During each year, signiÐcant sidebands were detectednear the positive superhump and its higher harmonics (outto the sixth). Based on the arguments given by H98(essentially phase stability), we interpret 83.987 cycles day~1as the orbital frequency u. Many signals were spaced by1.80 cycles day~1, which we designate as ). Others werespaced by 1.44 cycles day~1, which we designate as N.

The many detections are related by simple rules. Onefamily is simply u itself and its Ðrst harmonic. The second isgiven by nu[ m), where m\ 1, . . . , n ; we consider all ofthese to be manifestations of the positive superhump. Thethird is given by any of these signals ]N, manifestations ofthe negative superhump. In Table 2 we present a summary

FIG. 3.ÈHigh-resolution power spectra of the light curve during the densest coverage of 1978 and 1997. Most signiÐcant features are labeled with theirfrequencies in cycles day~1. Uncertainties are typically 0.1/B cycles day~1, where B is the baseline in days (indicated at the top of the Ðgure). The spectra havebeen cleaned by removing the aliases of the labeled signals. The principal signal at 164.38 cycles day~1 rises to a power of 340 in 1978 and 160 in 1997. Sincethat signal is reliably of 0.024 mag full amplitude, other signals can calibrated with the relation powerP (amplitude)2.

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1286 SKILLMAN ET AL.

FIG. 4.ÈPower spectra in 1998 and 1999. See Fig. 3 legend. The principal signal at 164.39 cycles day~1 rises to a power of 450 (in 1998) and 250 (in 1999).

of these detections, including also the signals detected bythe WET observation in 1990.

Only subsets of each year were used in the detailed periodÐnding, because maximum density of observation is criticalto overcome aliasing. But we also used the full D100 nightbaselines for each year, to reÐne the frequency measures andespecially to verify the exactitude of the ““ modeidentiÐcations ÏÏ in Table 2. Within the measurement errorof 0.002 cycles day~1, all the identiÐcations were found tobe exact.

The amplitudes of the ) sidebands follow a characteristicpattern too. The simple harmonics of the fundamental(nu[ n)) are always the strongest in each family, and theamplitudes generally drop down to the nu[ ) component.With this rule in mind, it then seems possible that all per-mitted components may be present (i.e., none are clearlymissing for reasons other than the expected low amplitude).But the strength of the ) sidebands is highly variable. Theywere easy to see during most years, but practically invisible

during 1997, when the only strong sidebands were thesimple harmonics of the positive superhump. Ironically,1997 was the year of best coverage !

In ° 6 we shall interpret all the [) signals as arising fromapsidal precession of the accretion disk, and all the ]Nsignals as arising from nodal precession of the disk.

2.5. Mean Light Curves of the Periodic Signals

Figure 5 shows yearly mean light curves of the 1051 ssignal, the positive superhump. The waveform is very con-sistent, an ““ asymmetric double sinusoid ÏÏ with minima at0.000 (by deÐnition) and 0.545^ 0.011. This waveform hasnot changed since SmakÏs original discovery in 1962 photo-metry.

Figure 6 shows yearly mean light curves for the 1011 and1028 s signals. The former is consistently a very pure sinus-oid (no harmonics in the power spectrum). The 1028 s wave-

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SUPERHUMPS IN CATACLYSMIC BINARIES. XVII. 1287

TABLE 2

PERIODIC SIGNALS DETECTED BY YEAR

Periodic Signal 1978 1990 1997 1998 1999

u[ 2)[ N . . . . . . . ] ]u[ ) . . . . . . . . . . . . . . ] ] ]u . . . . . . . . . . . . . . . . . . . . ] ] ] ]u] N . . . . . . . . . . . . . . ] ] ] ]2u[ 2) . . . . . . . . . . . ] ] ] ] ]2u[ ) . . . . . . . . . . . . . ] ] ] ]2u[ )] N . . . . . . . ] ] ]2u . . . . . . . . . . . . . . . . . . ] ]3u[ 3) . . . . . . . . . . . ] ] ] ] ]3u[ 2) . . . . . . . . . . . ] ]3u[ ) . . . . . . . . . . . . . ] ] ] ]3u[ )] N . . . . . . . ]4u[ 4) . . . . . . . . . . . ] ] ] ]4u[ 3) . . . . . . . . . . . ] ] ]4u[ 2) . . . . . . . . . . . ] ]4u[ 2)] N . . . . . . ] ]5u[ 5) . . . . . . . . . . . ] ] ] ]5u[ 4) . . . . . . . . . . . ]6u[ 6) . . . . . . . . . . . ] ] ]

NOTE.ÈListed here are years with very sensitive detection limits.Even fairly cursory coverage usually shows signals with u andu] N, and 2u[ 2) and 3u[ 3) are always seen. The indepen-dent frequencies are u\ 83.987 cycles day~1, )\ 1.785È1.801cycles day~1, and N \ 1.436È1.440 cycles day~1.

form has an irregular maximum but a characteristic 0.01mag dip, which provides the basis for the timing studyreported in ° 3.

3. THE 1028 s SIGNAL

The 1997 data were mildly interesting for the total disap-pearance of the 1011 s signal. But this conferred a secondarybeneÐt which proved to be much more interesting : the easyvisibility of a 1028 s signal. This signal, reported earlier byH98, led us to search carefully for its presence in other timeseries. After subtracting the usually stronger 1011 s signal,we found that the 1028 s signal is nearly always present,with a full amplitude averaging D0.01 mag. This can beseen in Figures 3, 4, and 6 ; but a signal of similar amplitudeand waveform appears to be present in all the data.

A search yielded 13 independent timings of minimumlight for the 1028 s signal. Table 3 reports these timings, andFigure 7 reduces them to an O[C diagram with a testperiod of 1028.7322 s. The Ðt is acceptable within measure-ment limits (rms scatter of 0.04 cycles, or 0.016 cycles for theyearly means), certifying that the clock is stable over the 7year baseline. Timings obey the ephemeris

minimum light \ HJD 2,448,742.5610(4)

] 0.011906623(3)E . (1)

FIG. 5.ÈMean waveforms of the 1051 s signal during three observingseasons. Two cycles are shown for clarity. The small asymmetry in thewaveform, with minima at phase 0.00 and 0.54, is present in all large datasets.

FIG. 6.ÈThe left panels show mean waveforms of the 1011 s signal,consistent with a pure sinusoid. The right panels show mean waveforms ofthe 1028 s signal, with a periodic 0.01 mag dip.

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1288 SKILLMAN ET AL.

TABLE 3

TIMINGS OF 1028 s MINIMA

HJD 2,400,000 ]

48742.5612 50617.5923 51211.995249041.7147 50855.7963 51252.809650526.6726 50938.6413 51292.662050570.3826 50945.631050589.7425 50977.6733

The period is stable with In view of thisoP0 o\ 2 ] 10~12.stability, it seems reasonable to consider as established theinterpretation of this signal as the true orbital period.

4. THE 1051 s SIGNAL, ONCE MOREWITH FEELING

Doubts have been raised over whether the fundamentalperiod of the dominant wave is 1051 or 525 s. All previousauthors have settled on 1051 s, except for P95 and S84. Theyearly 1051 s light curve repeats with great Ðdelity, illus-trated in Figure 5 and showing the asymmetrically placedminima. All large data sets (Smak 1967 ; Ostriker & Hesser1968 ; Krzeminski 1971 ; P92 ; P95) show this asymmetry ; itdeÐnes primary minimum and proves beyond doubt thatthe fundamental period is 1051 s.

This conclusion is simple and certain, but that has notspared it from criticism and rejection (P95 ; S84). We hopethat the power spectrum peaks in Figures 3 and 4 will bringthis dispute to an end.

5. COMPARISON WITH THE WHOLE EARTHTELESCOPE RESULTS

Very di†erent conclusions were reached by the authors ofthe two WET papers (P95 ; S98). They concluded that the525 s clock was nearly stable in phase, increasing its period

FIG. 7.ÈO[C diagram for the minima of the 1028 s signal, relative toeq. (1), which is the horizontal line. The Ðt is acceptable within measure-ment error, certifying the stability of the underlying clock. (All points areindependent, but many nights are used to measure each timing, to over-come the signalÏs weakness and contamination by other frequencies.)

very slowly with This led them toP0 \ ]1.7] 10~11.pursue models invoking pulsation, rotation, and orbitalclocks, in order to account for such high stability. Yet theliterature contains clear evidence (Fig. 2 of this paper ;Fig. 15 of Patterson et al. 1993 ; Fig. 3 of P79 and H98) thatlarge phase changes occur on a timescale of merely months.Where did the WET analysis go astray?

Well, it is certainly not from data quality ; their data is ofhigher quality than ours. Nor is it from di†erences in howthe minima are timed ; both sets cover the 1992 observingseason and yield periods (525.62 s) and phases in full agree-ment.11

The WET analysis was problematic because their dis-tribution of observations in time was too sparse. The onlyepisodes of dense coverage spanned D15 days, and Figure 2shows that AM CVn is pretty stable over so short an inter-val (2500 cycles). Having found that apparent stability, theythen assumed stability over longer timescales, reduced theirdata to mean yearly timings, and noted that with an appro-priate choice of cycle count, the six such timings fell on asmooth curve giving But this can onlyP0 \ ]1.7] 10~11.be fortuitous, because their ephemeris has no predictivevalue. That ephemeris gives a near-constant period of525.618 s, implying that all panels of Figure 2 should givethe same straight-line slope as the star exhibited in 1992 ;but inspection of Figure 2 shows that the slope actuallychanges erratically and D1000 times faster. In order to trackthe phase of the 525 s clock, one needs steady coverage overweeks to months, and this was lacking in the WET data.

The other curious feature of the WET analysis is theirrejection of 1051 s as the fundamental period of photo-metric variation. But the power spectrum peaks in Figures 3and 4, and the stable 1051 s waveform seen in Figure 5 (aswell as all other seasons of good coverage), establish 1051 sbeyond any doubt.

6. SUPERHUMPS IN AM CVn

6.1. The Positive (Apsidal?) SuperhumpWhitehurstÏs breakthrough discovery (Whitehurst 1988)

led to a series of studies which established the theory that

ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ11 This is a key point, perhaps, after recent fusillades. P95 vigorously

propose that the only reliable way to time the 525 s clock is to use largesegments of data which span all phases of the 13.4 hr cycle, in order tominimize contamination by Ðne structure in the 525 s clock. But this isonly formally true. Our data consist mostly of much shorter spans, and theobserved night-to-night scatter of timings is only 30È40 s, implying thatthis is an upper limit to the systematic error introduced by using shortobservations. The same is true of our earlier timings (P92 ; P79), and indeedof everyoneÏs timings. Since our random (measurement) error alone isabout this size, the true systematic error is still lower. As further illustra-tion, we note that all our nightly 1992 observations, averaging just 2.6 hr inlength, yield timings in agreement with the seasonal mean timing from thecontemporaneous data of P95. In short, this is not an important worry.

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SUPERHUMPS IN CATACLYSMIC BINARIES. XVII. 1289

accretion disks in dwarf novae can su†er eccentric insta-bilities at the 3 :1 orbital resonance (Osaki 1989 ; Lubow1991 ; King & Whitehurst 1991). Torque from the orbitingsecondary then leads to precession, at a rate ), of the line ofapsides, and periodic tidal stressing of the disk occurs at arate u[ ), causing a photometric wave known as a super-hump.12 P92 suggested that this also caused the 1051 s wavein AM CVn. The PHS absorption-line skewness period of13.38^ 0.07 hr suggested a periodic eccentricity e†ect, butthis can be linked to a 1051 s superhump only if the truebinary period is 1028.77^ 0.25 s, a signal then unreportedin the light curve. The existence and properties of the 1028 ssignal, described by H98 and in ° 3 above, now provide the““ smoking pistol ÏÏ needed to believe the apsidal-precessioninterpretation of the absorption-line skewness period (andthe associated superhump theory). With sPorb\ 1028.7322and s, the precession period shouldPsh\ 1051.08È1051.30vary in the range 13.30È13.44 hr, since in prograde precess-ion the periods are related by

1Psh

\ 1Porb

[ 1Pprec

. (2)

This agrees with the PHS measurement and the photo-metric measure of the sideband splittings (13.37 hr ; P95).The fact that the precession frequency always appears as[) in the sideband splittings presumably reÑects the sign(prograde) of the apsidal precession.

Di†erentiation of equation (2) leads to a connectionbetween and the required namely,P0 sh P0 prec,

P0 prec \ [APprec

Psh

B2P0 sh . (3)

Thus the observed impliesP0 sh\ 2 ] 10~8 P0 prec \ 4This is about 500 times smaller than inferred] 10~5. P0 prec

from superhump observations in dwarf novae, perhapsbecause the disk is thermally much more stable (in andM0viscosity) in AM CVn.

6.2. The Negative (Nodal?) Superhump

The 1011 s signal must have a di†erent story. About adozen cataclysmic variables have been found with persistentphotometric periods less than (reviewed by PattersonPorb1999). We have labeled these waves as negative superhumpsto signify the sign of their period excess over A few,Porb.

ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ12 It is not exactly true that this comes from apsidal precession,

however. The disk should undergo a large change in shape during thesuperhump cycle, in response to the dynamical forcing from the secondary.Simpson & Wood (1998) give a lucid discussion of this, complete withpictures. There is never any true ellipse and thus no true or exact line ofapsides ; ““ apsidal precession ÏÏ is only a convenient shorthand.

including AM CVn, show negative superhumps whichcoexist with positive superhumps. Coexistence, along withthe restriction to upper sidebands (]N rather than [N),suggests an origin in a di†erent type of precession : namely,a wobble of the disk plane backward with respect to theorbit. The stream-disk geometry then recurs with a fre-quency u] N, where N is the wobble frequency.

In one version of this idea, the light could come fromdirect infall energy. In another, it could arise from the e†ectof reprocessing in the secondary. Disk wobble can removethe diskÏs own obstruction of light reaching the secondary,and thereby boost the incident ÑuxÈcausing periodic emis-sion at the upper precessional sideband (u] N), since thedisk-secondary geometry repeats at that frequency. Thehighly sinusoidal waveform tends to favor the idea ofperiodic illumination of the secondary.

A wobbling disk is very good for ““ explaining ÏÏ the photo-metric signals, but the underlying physics is still obscure.Difficulties in understanding how the disk can come out ofthe orbital plane have been discussed by Lubow (1992) andMurray et al. (1999).

7. THE PRECESSION PERIODS THEMSELVES

Table 2 makes it clear that ) and N, which we haveinterpreted as precession frequencies, are fundamentalclocks in the binary. Yet they are revealed only through thesplitting of sidebands, not by direct detection in the powerspectrum. Why should that be?

In part it may arise from difficulties with the data. MostCBA data are unÐltered, leading to uncorrected second-order extinction e†ects which are periodic with periods near1 day. We remove these to study the 80È500 cycle day~1signals, but the low-frequency search must contend withthem. Therefore, with data afflicted by extinction and thestarÏs intrinsic and probably random variability, we haveonly fairly coarse upper limits for signals at ) and N. Wenever found any signal greater than 0.05 mag full amplitudeat ). This may well be a consequence of its origin in apsidaladvance. The advancing motion of the apsides does notgenerate light in any obvious way (whereas the periodic diskstressing with u[ ) is obvious). And in the 32 other starswhere we have studied positive superhumps, we have neverseen a signal at the putative frequency of apsidal advance.

Near N, we found possible detections at D0.07 magamplitude, but also upper limits below 0.05 ; the case issufficiently weak that we prefer to quote an upper limit of0.08 mag full amplitude. This is somewhat surprising,because as the disk plane wobbles, one certainly expects amodulation of the presented disk area with N. In order tosatisfy the upper limit, a simple wobble of the full disk musthave an amplitude of less than 4¡ (assuming a binary incli-nation near 45¡). If the wobble occurs in only a portion ofthe disk, then larger amplitudes are possible.

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1290 SKILLMAN ET AL.

8. OTHER SIGNALS

During 1978 and 1998, a signal appeared near 79 cyclesday~1, with some power also at or near the second harmo-nic. It was transient, weak, and not necessarily at an exactlyrepeating frequency (this was too difficult to ascertain). So itis still premature to assimilate this conÐdently into a modelfor AM CVn.

Nevertheless, having spent a lot of time pushing buttonsto make the frequency identiÐcations in Table 2, we didnotice that the 2 years of relatively strong detection with aprecise frequency measurement yielded 78.95 cycles day~1,consistent with u[ 2)[ N. In order to accommodate thisinto the ““ [) and ]N ÏÏ rule cited above, we might chooseto write this as u[ )[ ()] N). This can make sense interms of the model in ° 6, since in inertial space u[ ) is thefrequency of one physical event (apsidal passage, resultingin a system brightening) and )] N is the frequency ofanother (intersection of the apses with the nodes). It is thennatural to have a [ ()] N) sideband, since the )] Nevent moves prograde around the binary.

Additional signals were found near 106 and 299 cyclesday~1, marked with a cross in Figure 1. These signals areweak, but surely real, since they have been reported in otherdata sets (P92 ; P95). We could not Ðnd any plausible con-nection between these frequencies and the major frequenciesin the binary. We do not have Ðrm information about thecoherence of these signals, but high-resolution powerspectra in their vicinity did not yield sharp peaks ; thisfailure usually implies poor coherence. Since the signals areweak, transient, and possibly of low coherence, we knowlittle about them and thus conÐne ourselves to only a briefmention. Nevertheless, it would certainly be nice to under-stand them someday.13

9. SUMMARY

1. We report 6 new years of photometry, demonstratinganew that the main photometric period is 1051.2 s and thatit drifts by D0.2 s on a timescale of 4È12 months. Thearguments are essentially those presented by P92, but theyare repeated here in more detail because they have beenvigorously disputed by the Whole Earth Telescope paper(P95).

2. The 1051 s period is consistent with interpretation as asuperhump in a precessing accretion disk. But the periodic

ÈÈÈÈÈÈÈÈÈÈÈÈÈÈÈ13 The same is true for the 26 s signal reported by P92, another ““ extra ÏÏ

signal not explicable in terms of disk precession. However, the period andcoherence of this signal are quite plausible for ““ dwarf nova oscillations ÏÏ(Patterson 1981 ; Warner 1995, chap. 8.6), a fairly common syndrome ofcataclysmic variables accreting at a high rate.

signal in the skewness of absorption lines requires that theorbital period be 1028.77 ^ 0.25 s, and it was puzzling thatno signal at that period was reported in the photometry.Close analysis of the data, reported here and by H98, showsthis signal to be persistently present during 1992È1999, withstable phase and a precise period of 1028.7322(2) s. Thisappears to be the true binary period of AM CVn.

3. Global observing campaigns in 1997 and 1998 showedintricate Ðne structure in the power spectrum. Twenty dif-ferent periodic signals are present, but most can be rep-resented as linear combinations of three basic frequencies :u\ 83.987 cycles day~1, )\ 1.80 cycles day~1, andN \ 1.44 cycles day~1. Apparitions of ) are in the formnu[ m), where n is any integer and m\ 1, . . . , n. Appar-itions of N are displaced by ]N from any detected signal.These are generally consistent with the hypothesis that ) isthe frequency of prograde apsidal precession and N is thefrequency of retrograde nodal precession.

4. The 1051 s period (““ apsidal superhump ÏÏ) wanderswith implying a precession period chang-oP0 oD 2 ] 10~8,ing with The latter is D500 times smalleroP0 oD 4 ] 10~5.than typically inferred from the superhumps of dwarf novae,presumably because the disk conditions in AM CVn are farmore stable than those of dwarf novae.

5. We also study the episodic appearances of the 1011 ssignal (““ nodal superhump ÏÏ). This is considerably more dif-Ðcult because the amplitude varies by a factor of at least 5.The mean period was fairly well determined at1011.42^ 0.03 s. We did not succeed in tracking the phasecontinuously over long intervals with unambiguous cyclecount. The clock stability is comparable to that of the 1051s clock, but it could be somewhat higher or lower.

6. The apsidal superhump suggests an origin in tidalstresses in the disk. The nodal superhump probably arisesbecause disk wobble moves the periodic signature of struc-tures Ðxed in the binary frame (the secondary star and themass-transfer stream) from u to an upper orbital sidebandu] N, just as local solar heating of the Earth occurs not onthe sidereal year but on the upper orbital sideband, thetropical year. But the origin of disk wobble is still unknown.The relative power in the various components of the apsidalsuperhump is not yet understood either, but the study ofSimpson & Wood (1998) suggests that this may be a usefulprobe of detailed structure in the accretion disk.

7. Despite its venerable history, the star still o†ers a Ðnetarget for timing studies. The wanderings of the 1051/525and 1011 s clocks should be anticorrelated, if the precess-ions are driven by the same agent (the secondary) ; presentdata do not establish this. There are three other periodicsignals (at 810, 289, and 26 s) that we have not properlyexplained. And the putative precession periods themselvesremain undetected in photometry. An extensive photo-metric campaign with larger aperture and better calibrationwould remove some of the shortcomings implicit in our

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SUPERHUMPS IN CATACLYSMIC BINARIES. XVII. 1291

network of very small telescopes, working usually inunÐltered light.

We thank the NSF for Ðnancial support through grantAST 96-18545 and especially the Research Corporation for

explicit support of the CBA, which has been somewhatorphaned in the world of science funding. We hope thispaper gives a glimpse into the power of periodic studiesmade feasible by a network of small backyard telescopes,aided by CCDs, computers, and tenacious humans.

REFERENCESAbbott, T. M. C., Robinson, E. L., Hill, G. J., & Haswell, C. A.

1993, ApJ, 399, 680Faulkner, J., Flannery, B. P., & Warner, B. 1972, ApJ, 175, L79Harvey, D. A., Skillman, D. R., Kemp, J., Patterson, J., Vanmun-

ster, T., Fried, R. E., & Retter, A. 1998, ApJ, 493, L105 (H98)Humason, M. L., & Zwicky, F. 1947, ApJ, 105, 85Krzeminski, W. 1971, in IAU Colloq. 15, New Directions and New

Frontiers in Variable Star Research, ed. W. Strohmeier (Vero†.Remeis-Sternw. Bamberg, Vol. 9, No. 100), 78

Lubow, S. 1991, ApJ, 381, 259ÈÈÈ. 1992, ApJ, 398, 525Murray, J., Armitage, P., Warner, B., & Wickramasinghe, D. 1999,

in Disk Instabilities in Close Binary Systems, ed. S. Minishige &J. C. Wheeler (Tokyo : Univ. Academy Press), 83

Nather, R. E., Robinson, E. L., & Stover, R. 1981, ApJ, 244, 269OÏDonoghue, D., & Kilkenny, D. 1989, MNRAS, 236, 319OÏDonoghue, D., Kilkenny, D., Chen, A., Stobie, R. S., Koen, C.,

Warner, B., & Lawson, W. A. 1994, MNRAS, 271, 910Osaki, Y. 1989, PASJ, 41, 1005Ostriker, J. P., & Hesser, J. E. 1968, ApJ, 153, L151Patterson, J. 1981, ApJS, 45, 517ÈÈÈ. 1999, in Disk Instabilities in Close Binary Systems, ed.

S. Minishige & J. C. Wheeler (Tokyo : Univ. Academy Press), 61Patterson, J., Halpern, J. P., & Shambrook, A. A. 1993, ApJ, 419,

803 (PHS)

Patterson, J., Robinson, E. L., Nather, R. E., & Handler, F. 1979,ApJ, 232, 819 (P79)

Patterson, J., Sterner, E., Halpern, J. P., & Raymond, J. C. 1992,ApJ, 384, 234 (P92)

Patterson, J., Thomas, G., Skillman, D. R., & Diaz, M. P. 1993,ApJS, 86, 235

Provencal, J. L., et al. 1995, ApJ, 445, 927 (P95)Simpson, J. C., & Wood, M. A. 1998, ApJ, 506, 360Skillman, D. R. 1981, S&T, 61, 71ÈÈÈ. 1993, S&T, 85, 83Skillman, D. R., & Patterson, J. 1993, ApJ, 417, 289Smak, J. I. 1967, Acta Astron., 17, 255ÈÈÈ. 1975, Acta Astron., 25, 371Solheim, J.-E., et al. 1998, A&A, 332, 939 (S98)Solheim, J.-E., Robinson, E. L., Nather, R. E., & Kepler, S. O.

1984, A&A, 135, 1 (S84)Solheim, J.-E., & Sion, E. M. 1994, A&A, 287, 503Warner, B. 1995, Cataclysmic Variable Stars (Cambridge : Cam-

bridge Univ. Press)Whitehurst, R. 1988, MNRAS, 232, 35Whitehurst, R., & King, A. R. 1991, MNRAS, 249, 25Wood, M. A., Winget, D. E., Nather, R. E., Hessman, F. V.,

Liebert, J., Kurtz, D. W., Wesemael, F., & Wegner, G. 1987,ApJ, 313, 757

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