The Orbital Period of AM Canum Venaticorum
David A. Harvey1,
David R. Skillman2,
Robert E. Fried5, and
Center for Backyard Astrophysics
Astrophysical Journal, Letters
1 February 1998, Volume 493, Page L105
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.
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
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
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.
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.
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
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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).