Superhumps in Cataclysmic Binaries. XXIII. V442 Ophiuchi and RX J1643.7+3402

Many cataclysmic variables of short orbital period (<4 hr) and high accretion rate (M˙>10^-9 M_⊙ yr^-1) have light curves with prominent humps slightly displaced from P_orb. These are called "superhumps" since they are particularly characteristic of dwarf novae in superoutburst. Most superhumps occur at periods slightly longer than P_orb, and have been successfully explained as due to the prograde apsidal precession of an eccentric accretion disk (Whitehurst 1988; Osaki 1989; Lubow 1991). A few, however, occur at periods shorter than P_orb; these are called negative superhumps, or occasionally nodal superhumps to emphasize their probable origin in the retrograde wobble of the disk (Harvey et al. 1995; Patterson et al. 1997; Patterson 1999; Wood, Montgomery, & Simpson 2000; Murray et al. 2002).

V442 Ophiuchi and RX J1643.7+3402 (hereafter RX 1643+34) are bright novalike variables with spectra suggestive of high M˙ and fairly short orbital periods (Hoard, Thorstensen, & Szkody 2000; Mickaelian et al. 2002, hereafter M02). So we selected them for long observing campaigns to search for superhumps. Here we report the results. In the process, we may have learned something about the SW Sextantis stars, a mysterious class of cataclysmic variables.

The spectra of RX 1643+34 reported by M02 showed a strong blue continuum with weak emission lines of high excitation. From the radial velocities of Hβ they found an orbital period of either 0.1073(2) or 0.1202(5) days, depending on the (undetermined) daily cycle count. We decided to repeat that study with sufficient baseline and density of observation to yield an accurate and unique period.

Our spectroscopy was carried out in 2002 May and June, using both telescopes at MDM Observatory on Kitt Peak. The procedures essentially followed those described by Thorstensen, Taylor, & Kemp (1998), except that in May we used the 1.3 m telescope and the Ohio State CCD spectrograph. The latter spectra covered 4200–5100 Å, with 0.8 Å pixels and a resolution of 1.9 Å FWHM. The June data consisted of a single orbit with the 2.4 m Hiltner telescope and the modular spectrograph, covering 4300–7500 Å at 2 Å pixel⁻¹ and 3.5 Å FWHM. Flux standards were observed as appropriate, but the flux calibration in May was only relative.

Figure 1 shows the mean spectrum in June, and Table 1 details the line features. The spectrum resembles that of M02, with a strong blue continuum and weak lines, typical of the most luminous novalike variables.

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We measured the apparent radial velocity of Hβ in all spectra, using a Gaussian derivative algorithm (Schneider & Young 1980). Figure 2 shows the result of a "residualgram" period search (Thorstensen et al. 1996). Because the observations span a wide range in hour angle, the velocities unambiguously determine an orbital frequency near 8.3 cycles day⁻¹. The cycle count between May and June velocities is slightly ambiguous, but the Center for Backyard Astrophysics (CBA) photometry described below in § 4 confirms the choice that best fits the velocities: P_orb = 0.120560(14) days, in agreement with one of the M02 choices. Figure 3 shows the Hβ velocities folded on P_orb, and Table 2 gives the parameters of the best‐fitting sinusoid.

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Because the star is noneclipsing and lacks secondary‐star absorptions, we do not have a fiducial marker of absolute binary phase. However, the CBA photometry shows a periodic signal at P_orb, specifically a double‐humped waveform like the classical "ellipsoidal" variation in Roche geometry. In this variation, the shallower of the two minima corresponds to "eclipse phase," i.e., inferior conjunction of the secondary. In § 4 that ephemeris is found to be

and we adopt that orbital phase convention. If this were fully trustworthy, then the emission lines lag their geometrically required schedule by 72° ± 12°. That would be of interest, since a large phase lag is one of the key indicators for the SW Sex class of cataclysmic variables (Thorstensen et al. 1991). Unfortunately, accretion structures can also produce signals at P_orb and P_orb/2, so this is merely suggestive, not reliable.¹⁹

Figure 4 shows phase‐averaged gray‐scale images of the spectra from our two observing runs, constructed using procedures described by Taylor, Thorstensen, & Patterson (1999). Hα shows an obvious high‐velocity component, similar to those seen in LS Peg (Taylor et al. 1999), V533 Her (Thorstensen & Taylor 2000), and V795 Her (Dickinson et al. 1997; Casares et al. 1996). Phase‐dependent absorption appears in He i λ4471, λ4921, and λ5015, at orbital phases 0.1<φ<0.6. He ii λ4686 shows a narrow component that moves in phase with the Balmer line cores, sharing the same phase lag.

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Many of these characteristics are in general accord with the SW Sex class: the high‐excitation spectrum, single‐peaked emission, apparently large phase lag, 2.9 hr P_orb, and high‐velocity components in the Balmer lines. Phase‐dependent He i absorption is also a distinguishing trait, but here appears somewhat different. The founding members of the class show a very distinctive deep absorption quite close to φ = 0.5; this has become a defining characteristic. On the other hand, the founding members were all eclipsers. This poorly understood phenomenon may depend on binary inclination, and perhaps other factors not yet explored (e.g., phase in the 4.05 day cycle discussed below, or in the years‐long cycling between negative and positive superhump). So we think the case is overall pretty good for SW Sex membership, although these issues certainly merit further study.

3.1. 1995 Campaign

We obtained 165 hr of photometry, spread over 28 nights during 1995 May 20–July 8. Most of the observations consisted of long photoelectric time series in V light, acquired with an aperture photometer mounted on the 1.0 m telescope at Cerro Tololo Inter‐American Observatory (CTIO). We used an integration time of 10 s, then subtracted the sky background and used a mean extinction of 0.15 mag per air mass to reduce the time series to counts per integration above the atmosphere. Table 3 summarizes the observations, including those of other stars studied in this paper.

Another 60 hr of coverage were obtained with CCD photometers at Tucson (35 cm telescope) and Maryland stations of the Center for Backyard Astrophysics. CBA data analysis techniques were discussed by Skillman & Patterson (1993), and yield a time series of differential magnitudes. On several nights there were overlaps with the photoelectric time series, and we used the overlap to convert the differential magnitudes to equivalent count rates in the CTIO time series. The estimated accuracy of the conversion is only ∼0.05 mag, but this enabled us to make a smooth splice and extend the time series.

A sampler of nightly light curves is shown in Figure 5. Basically all nights look alike, with two prominent features: a 3 hr wave with a full amplitude in the range 0.05–0.30 mag, and rapid flickering including apparent quasi‐periodic oscillations (QPOs) with P∼1000 s.

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To search for strictly periodic signals, we calculated power spectra of light curves from the discrete Fourier transform. The power spectrum of the 50 day light curve is shown in Figure 6, where the most obvious feature is the sharp spike at a frequency of 8.271(6) cycles day⁻¹. The peaks surrounding this signal are merely the ±1 cycle day⁻¹ aliases, and detailed comparison of the power spectrum to the spectral window reveals no nearby periodic signals passing tests of significance.

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There are also strong signals at very low frequency. In the lowest frame of Figure 7 we show an expanded view of this region, with significant peaks marked at 0.229 and 0.601 (both ±0.006) cycles day⁻¹. In the upper frames we show the power spectra of artificial time series, with injected signals at exactly these frequencies and sampled exactly like the actual data. Comparison of the upper frames with the peaks visible in the lowest frame shows that most of the variance in the low‐frequency power spectrum arises from these signals and their aliases. We also studied time series with the aliases (rather than the correct frequencies) artificially inserted, and found that they gave much poorer matches to the real power spectrum—indicating that the true frequencies are indeed 0.229 and 0.601 cycles day⁻¹ rather than any of the aliases.

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The widths of all three power‐spectrum peaks (4.37, 1.67, 0.12090 days) are consistent with the hypothesis of period constancy during the 50 day observation, but this is only provable for the latter signal.

The 8.271 cycle day⁻¹ signal occurs at a frequency consistent with ω_o + N, where ω_o is the orbital frequency (8.043 cycles day⁻¹; Hoard et al. 2000; Diaz 2001) and N is the stronger low‐frequency signal. The corresponding period is 2.85% ± 0.08% shorter than P_orb—a negative (or nodal) superhump, in the vocabulary introduced by Harvey et al. (1995).²⁰ The quantity N is then the frequency of nodal precession. The other low‐frequency signal, at 0.601 cycles day⁻¹, could possibly be the signature of a positive (apsidal) superhump. However, its detection is marginal, and we do not have a detection at the expected superhump frequency itself (at ω_o - 0.601 = 7.442 cycles day⁻¹). So that signal needs confirmation.

Figure 8 shows the synchronous summations at each frequency after "prewhitening" by subtracting best fits at the other two frequencies. The semiamplitude of the negative superhump is 0.072(8) mag, and that of the underlying precession (4.37 day signal) is 0.083(12) mag. The putative apsidal precession (1.67 day signal) gives a complex light curve of low amplitude. Just for the record, the folded light curves in Figure 8 yield the ephemerides

However, we stress again that the detection at 1.67 days is merely a candidate signal.

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3.2. Data in Other Years

We carried out similar studies in 1983, 2001, and 2002. Table 3 gives the main details of these campaigns. Data reduction followed the methods discussed above. These campaigns were less extensive, but the results merit a brief report. Power spectra are shown in Figure 9; these are otherwise "dirty" but have been cleaned for the aliases of the strongest signal. The strong signal of 2001 occurred at a frequency consistent with that of 1995's negative superhump. The 2002 signal occurred at 8.294(6) cycles day⁻¹, a slightly higher frequency; in the interpretation peddled here, this corresponds to a 10% change in the underlying nodal precession frequency. The 1983 signal occurred at 7.43 ± 0.03 cycles day⁻¹. Since the latter is displaced from ω_o by -0.61 ± 0.03 cycles day⁻¹, this is an apparent apsidal superhump and gives some support for the hypothesis that the uncertain detection of 0.60 cycles day⁻¹ in the 1995 data is real.

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A similar campaign was carried out on RX 1643+34, using seven telescopes of the CBA network. This consisted of 70 nights (452 hr) of coverage during 2002 April 10–June 22. We used overlaps in coverage to calibrate between the various observatories, putting all this differential photometry on a common scale. The star remained in its "high scale," near V = 12.7, throughout the observations. A sample nightly light curve is shown in the upper frame of Figure 10. The obvious rapid oscillations, with an amplitude near 0.1 mag and a period near 0.01 days, are the dominant feature. There are also dips and slow wiggles, which suggest the orbital timescale, but they are not strictly periodic (even from one night to the next).

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The middle and lower frames of Figure 10 show the power spectrum of the season's light curve. Nightly aliasing is insignificant, because of the geographical spread of observatories (Greece, Belgium, North America, Australia). Significant detections are flagged with their frequencies in cycles day⁻¹: a 2 ω_o component at 16.594(5), and signals at 0.247(8) and 8.550(6). The latter two are, respectively, the nodal frequency N and the negative superhump frequency ω_o + N. Inset are mean waveforms at these frequencies. They are basically uninformative, except that the weak orbital waveform appears to resemble the "double sinusoid" associated with Roche‐lobe distortion of the secondary. All the waveforms are much noisier than expected for strictly periodic signals of this amplitude in a 13th magnitude star. The reason is the ceaseless din of the noisy QPO, studied in § 6 below. The rapid and erratic variations contaminate the synchronous summations, and all the telescope aperture and date analysis in the world cannot do a thing about it.

The ephemerides associated with these signals are

The observed semiamplitudes are, respectively, 0.062(1), 0.017(3), and 0.011(2) mag. It is very likely that only the orbital ephemeris has any real usefulness; the other periods, associated with disk precession, are not truly stable.

We did not find any signal at or near 9.25 cycles day⁻¹, reported by M02. A signal of the reported amplitude would have produced a power of 350 in the lowest frame of Figure 9; so neither this signal nor any of its aliases could have been present in 2002 at a semiamplitude exceeding 0.007 mag. Since the star frequently sports transient waves of similar frequency and ∼0.1 mag amplitude, we suspect that this report arises from the brevity of the observation's window on that fundamentally erratic process.

V442 Oph and RX 1643+34 are fairly good matches to the SW Sex class, characterized mainly by single‐peaked emission lines, high‐velocity S‐waves, and evidence of strong outflows varying with orbital phase (Thorstensen et al. 1991; Hellier 2000, 2001). In our study of negative superhumps, we have found a high proportion of such signals in SW Sex stars. Table 1 of Patterson (1999) lists 11 stars with negative superhumps, and seven are confirmed or likely SW Sex stars. It may well be true that the SW Sex phenomenon is linked with nodal precession.

Some of the distinctive spectroscopic features of SW Sex stars can be reproduced by supposing that a substantial fraction of the mass‐transfer stream overflows the accretion disk (Hellier & Robinson 1994; Hellier 1996). This is a natural feature in a wobbling‐disk model, since disk wobble moves the impact point above and below the disk, varying smoothly with wobble and/or orbital phase. Disk wobble also explains naturally why a signal at ω_o + N is (nearly always) accompanied by a signal at N: because to a distant observer, the visible disk area should change on the wobble frequency N.

Unfortunately, there is no simple criterion for SW Sex membership. Most novalike variables in the 3–4 hr period range (with outliers) appear to qualify. But they also tend to be "VY Sculptoris stars," a class defined more simply by the existence of fairly well defined high and low states associated with large changes in mass transfer (Shafter 1984; Leach et al. 1999). A few novalike variables in this period range have managed to resist acquiring either label (so far). Permanent negative superhumps are actually common among all three groups, and it is still far from clear just which characteristic is causally linked to the superhumps. Since SW Sex stars have been the most extensively studied, we shall discuss that particular association in this paper. In the end, it may well turn out that all three characteristics (VY Scl, SW Sex, and permanent superhumps) are caused by a single piece of underlying physics.

All light curves of both stars show prominent activity on a timescale of ∼1000 s, with an amplitude varying from 0.03 to 0.3 mag. Each night's power spectrum shows "significant" features, but the frequencies rapidly change (on a timescale ≪1 day). This is characteristic of a signal of very low coherence. Fourier analysis is nearly blind to these strong QPOs, since it parses the time series into components of constant frequency and amplitude.

6.1. V442 Ophiuchi

Nevertheless, we pressed onward. We searched for a period by averaging power spectra of 22 long nights on V442 Oph in 1995, and (separately) 25 long nights in other years. The result is seen in Figure 11. The lower frame shows a broad QPO in the range 70–105 cycles day⁻¹. The 1995 average in the upper frame shows a similar bump, but with stronger contributions from possibly significant features at 74.0 and 89.9 (both ±1.0) cycles day⁻¹. The latter are quite weak signals, just 0.01 mag semiamplitude, much weaker than the obvious oscillations seen in the light curve.

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6.2. RX J1643.7+3402

We carried out the same search for RX 1643+34, using the 57 nights of long (>4 hr) observation. The average nightly power spectrum is shown in Figure 12 (with the lower frame rendering the same result in log‐log units). From this we learn the following:

• 1.  
  A flickering source is evident in the range 120–1000 cycles day⁻¹, with a continuum characterized by P∼ν^-2.2 ("red noise").
• 2.  
  There are features near 8 and 16 cycles day⁻¹ as discussed above; otherwise, the distribution at low frequency is flat.
• 3.  
  In the range 70–110 cycles day⁻¹ there is a strong and broad feature, the power‐spectrum counterpart of the QPO obvious in the light curve. A narrow feature at 82.8 ± 1.0 cycles day⁻¹ is superposed—a hint of a stable signal underlying the QPO. Despite its prominence in Figure 12, this is actually a very weak signal compared to the QPO. It exceeds the neighboring power by a factor of ∼2, but there are ∼25 independent frequency elements in the QPO; so in the original light curves, the candidate stable signal cannot generally be seen in the QPO's glare.

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6.3. Narrowing the Period Search

We give here a preliminary report of periodic signals found in campaigns on two other SW Sex stars. V795 Herculis and DW Ursae Majoris are well‐known members of that class (Casares et al. 1996; Shafter, Hessman, & Zhang 1988). We have been observing them sporadically over the last decade. V795 Her sported a powerful 2.8 hr photometric wave through most of the 1980s, interpreted as an apsidal superhump (Patterson & Skillman 1994, hereafter PS). This signal disappeared through 1988–1996, but by 2001 had reappeared at high amplitude. Figure 13 contains the 2002 low‐frequency power spectrum, showing a powerful superhump at 8.550(6) cycles day⁻¹. Since the orbital frequency is 9.238 cycles day⁻¹ (Shafter et al. 1990), this is evidently an apsidal superhump (ω_o - Ω in superhump terminology). The weaker signals flagged in Figure 13 occur at 2ω_o - 2Ω, 2ω_o - Ω, and 2ω_o.

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Figure 14 shows the average nightly power spectrum in 2002, based on the 32 nights of long coverage. A broad signal is evident near 80 cycles day⁻¹, and it may possibly resolve into components at 71.0 and 80.4 cycles day⁻¹ (each ±1). Similar results were obtained in our 1993 campaign, but at slightly different frequencies (PS).

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The power spectra of DW UMa's seasonal light curves are shown in Figure 15. In 2002 (upper frame), the dominant signal was an apsidal superhump at ω_o - Ω = 6.878(6) cycles day⁻¹. The other flagged signals, in order of increasing frequency, occurred at 2ω_o - 2Ω, 2ω_o, and 3ω_o - 2Ω. A quite different result was found in 1996 (lower frame), when the dominant signal was a nodal superhump at ω_o + N = 7.542(3) cycles day⁻¹. The other flagged signals occurred at ω_o, 2ω_o, 2ω_o + N, 3ω_o + 3N, and two other frequencies that do not appear to bear any simple relation to ω_o (but are separated by exactly ω_o).

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We give these preliminary reports here to help illustrate the common (but variable on timescales of years) presence of superhumps in SW Sex stars, and the common presence of signals at higher frequency, usually in the form of a QPO. The latter signals deserve special note, since they often show components separated by exactly ω_o. We now turn to this subject of kilosecond QPOs.

8.1. Spin and Magnetism

The presence of kilosecond QPOs is a curious phenomenon. In our many photometric campaigns on CVs, we have found them to be prominent only in confirmed or candidate SW Sex stars, and the detection rate in this class exceeds 50%. The origin of the signals remains unknown; efforts to study them are greatly hampered by the sloppiness of the QPO clock. But there are tantalizing hints in several stars that a stable signal may underlie the noise of the QPO. Available data on the QPOs are summarized in Table 4.²¹

The timescale is itself interesting. Magnetic white dwarfs in spin equilibrium should have P_spin/P_orb∼0.1 (King & Lasota 1991; Wickramasinghe, Wu, & Ferrario 1991), assuming that accretion is not primarily through a disk. Since the stars of Table 4 are all within 20% of P_orb = 3.1 hr, this identifies 1100 s as a natural value of P_spin in such binaries—in good agreement with Table 4. Is it possible that the QPOs reflect the underlying rotation of a magnetic white dwarf?

8.2. Comparison with DQ Hers

Well, maybe, but then we need to understand why the main emergent signal in quasi‐periodic, not strictly periodic. There are a few dozen CVs—known as the DQ Herculis stars or intermediate polars—which contain rapidly rotating magnetic white dwarfs (Patterson 1994; chap. 5.4 of Warner 1995). Their defining signature is a strictly periodic signal at P_spin. They have orbital periods similar to the SW Sex stars, and many have spin periods near 1000 s. So why should one binary join the DQ Her club, while another allies with the SW Sex stars?

The answer should be in some combination of magnetic field strength and accretion rate. The magnetospheric radius r_mag in CVs is given by

where μ₃₃ is the white dwarf's magnetic moment in units of 10³³ G cm³, M˙₁₆ is the mass‐transfer rate in units of 10¹⁶ g s⁻¹, and m₁ is the white dwarf mass in M_⊙. The separation a between stars is

where m is the total mass in M_⊙ and P_hr is the orbital period in hours. Thus the condition for synchronism (r_mag/a≥1, an AM Her star) is essentially

(here and below we neglect the weaker dependence on m₁ and m, since these values are usually close to 1). The great majority of AM Her stars have M˙₁₆∼1 and P_hr∼1.8, so μ₃₃≥3 is a good rule of thumb. Polarization measurements suggest a typical B∼30 MG, and for an ordinary 0.7 M_⊙ white dwarf, this implies μ = BR³ ≈ 10³⁴ g cm³; so this accords with the rule of thumb.

DQ Her stars have moderately well formed disks, and disks have outer radii of ∼0.35a. So the magnetospheres cannot extend out any farther than ∼0.3a. From equations (4) and (5) this implies

Now a few DQ Her stars have M˙ and P_orb comparable to the AM Her stars, and in those cases equation (7) requires a quite low field, far below those of the AM Her stars. But DQ Her stars have 〈P_orb〉 ≈ 4 hr, and M˙ rises sharply with P_orb, so things get more complicated. Let us specialize to P_orb = 3.5 hr, since that is the regime of interest here. Then equation (7) reduces to μ₃₃≤0.8 M˙^1/2₁₆.

But most DQ Her stars have M˙ near (1–3) × 10¹⁷ g s⁻¹, suggesting μ₃₃≤3, or lower than the AM Her stars. This also agrees with the lack of strong circular polarization in DQ Her stars, and the magnetic moments inferred from the assumption of spin equilibrium (see Table 2 and § 11 of Patterson 1994). These arguments teach us that most DQ Her stars are too weakly magnetic to be a plausible ancestor for AM Her stars (King & Lasota 1991; Wickramasinghe et al. 1991). But several observational clues—very blue colors, weak emission, high excitation, and line profiles suggestive of strong winds—suggest that SW Sex stars may have significantly higher M˙. With high M˙, high values of μ can exist even for asynchronous rotators.

These ideas are summarized in Figure 16. The main parameters are μ and M˙; for simplicity and definiteness we eliminate P_orb by using an empirical M˙(P_orb) relation (Fig. 7 of Patterson 1984, with M˙₁₆ fixed at 1 below the period gap). AM Her stars then must live in the upper left, above the synchronism line. DQ Her stars must live below that line, but above the lower line where the magnetospheric radius is 3R_wd (since below that, a well‐channeled flow to the white dwarf surface is unlikely). "Nonmagnetics" (mostly dwarf novae) live below that lower line.

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The upper right region of Figure 16 is perhaps the most interesting, because stars of high μ and high M˙ are possible ancestors of AM Her stars. The latter constitute ∼20%–50% of all CVs, but are very strongly clustered at short P_orb and low M˙. A few DQ Her stars—especially those with measurable polarization and relatively long spin periods—might later become AM Her stars. But the ancestors should have μ>10³⁴, and this is best sought at high M˙, where synchronism is destroyed and hard X‐rays are not produced (accounting for the stars' absence in previous surveys of magnetic CVs). These could be SW Sex stars. Some outer disk should still be present, to account for the superhumps; but it may be sufficiently slim, or tilted, that some of the mass‐transfer flow impacts more or less directly onto the magnetosphere.

So the suggestion is that SW Sex stars contain magnetic white dwarfs drowned by a high accretion rate. If yet identified, the actual rotation periods could be the shorter of the two precise periods cited in Table 4.

8.3. QPOs among Confirmed DQ Her stars

8.4. X‐Rays and Magnetic Channeling

Magnetic white dwarfs in CVs are normally associated with strong and pulsed hard X‐ray emission at P_spin. Yet SW Sex stars are very weak X‐ray sources, with F_x/F_opt typically ∼0.01, among the weakest of any class of CV (Richman 1996). Can this be reconciled with the assumption of strong magnetism?

Yes, probably it can. Magnetic CVs often spill much of their accretion luminosity into the EUV/soft X‐ray, partly because high density in the accreting gas enables the gas to avoid the shock above the magnetic pole and deposit accretion energy directly in the white dwarf (Kuijpers & Pringle 1982; Woelk & Beuermann 1993). Frank, King, & Lasota (1988) estimate the critical density to occur at 10⁻⁷ g cm⁻³, and King & Lasota (1991) calculate that accreting gas at the surface must have a minimum density given by

where P₃ is the spin period in units of 10³ s. Thus for a 1000 s spin period, the transition to EUV/soft X‐ray occurs at μ₃₃ = 10, or B = 30 MG for an ordinary 0.7 M_⊙ white dwarf. This is a plausible dipolar field strength, indeed a typical field for an AM Her binary.

However, this cannot be the whole story, because strictly periodic signals are not seen at any wavelength. A more promising "pulsar" model could release much of the accretion energy at the outer edge of the magnetosphere, where a natural clock is provided by white dwarf spin but heavily buffeted by the orbital timescales in (and response timescales in) the accreting gas. Some of this gas is likely to be ejected, but some should be accreted too, in order to provide the long‐term heating required by the high white‐dwarf temperatures observed in quiescent SW Sex stars.

The spacing of high‐frequency components by exactly ω_o and 2ω_o, observed in at least four SW Sex stars, is another tantalizing clue. This first made us think of the DQ Her stars, where this spacing is very common due to the reprocessing of pulsed X‐rays/UV in the secondary (and other structures fixed in the orbital frame). Does this structure indicate a stable underlying clock? No, not necessarily. More accurately, it suggests that the secondary sees a fairly strong incident flux pulsed (in fact, sweeping prograde) at the same period that we observe—and then reprocesses it at the lower sideband. Several variants on this can easily occur from the specific geometry, discussed for DQ Her stars by Warner (1986). This pulsed signal must be strong, or its daughter signal at the lower sideband would be invisible; but it is unlikely to be coherent, since the signal we observe is not. It should, however, be just as coherent as the parent signal, since the reprocessor follows a strict clock (the orbit).

So far, the only real evidence cited here for magnetism is the kilosecond QPOs. While these appear to be characteristic of SW Sex stars, and are merrily clustered near 0.1P_orb, they still do not amount to compelling evidence since the timescales are rough and quite possibly characteristic of the disk (sans magnetism) as well. What other evidence might exist?

There are two ne plus ultra indicators of magnetically channeled accretion. One is periodic circular polarization, the usual credential for AM Her classification. And indeed, this has been recently reported for two SW Sex stars (Rodriguez‐Gil et al. 2001a, 2001b). But the observed periodic term is quite weak (∼0.2%) and the data are not yet sufficiently extensive to establish stability, even over a few nights. (In other words, this could be yet another manifestation of the QPO.) It is possible that future observations of this type will clinch the matter, but the needed evidence is not yet in.

The other indicator is a period of demonstrably high phase stability in the photometry (at any wavelength, but X‐ray and optical are the most common and likely). This is the usual credential for DQ Her classification. Over hundreds of nights, we have tried very hard to find such a period in SW Sex stars. We have even succeeded in identifying candidate signals consistent with strict phase stability over ∼30 nights (AH Men, V795 Her, DW UMa). However, the resultant signal is so weak that when we split it into a dozen independent segments, the QPO noise dominates and the evidence for phase stability disappears or becomes ambiguous. So this effort is still not conclusive. To achieve success, we need

• 1.  
  to observe one of these stars even more assiduously;
• 2.  
  to find a wavelength less contaminated by the QPO; or
• 3.  
  to get lucky and find one of these stars in a state of low (but detectable) accretion and low QPO activity.

Since our main research instrument is a network of very small telescopes, only the first is typically feasible for us; but we recommend all three approaches to everyone!

To explain negative superhumps with regressing nodes, we should understand what makes the disk non‐coplanar with the orbit. The most well studied process for warping the disk invokes the effect of radiation on the inner disk (Iping & Petterson 1990; Pringle 1996; Maloney, Begelman, & Nowak 1998). This works well for luminous X‐ray binaries but requires very strong radiation from the central object, and hence is probably not relevant for these white dwarfs of modest luminosity. Also possible is a dynamical instability at the 3:1 resonance in the disk. Lubow (1992) discovered and studied this instability, but concluded that its weakness and slow growth rate made it unlikely to be important; Murray & Armitage (1998) reached a similar conclusion.

Another possibility (of course) is magnetism. An inclined magnetic dipole centered on the white dwarf breaks the azimuthal asymmetry and provides a path vertically out of the disk plane. Detailed studies of this geometry have been presented in the context of X‐ray binaries (Lai 1999) and T Tauri stars (Terquem & Papaloizou 2000); these have shown that an inner‐disk warp can be created and lead to a global retrograde precession. Murray et al. (2002) alternatively invoke magnetism of the secondary and obtain the same result, with a large warp situated in the outer disk (see their Fig. 4 for a vivid illustration).

Each of these theories has a specific observational point in its favor:

• 1.  
  All the observed negative superhumps are "permanent," i.e., endure for months to years. None grow or decay rapidly, as the positive superhumps (famous in dwarf novae) are wont to do. Thus a slow growth rate is not necessarily disqualifying.
• 2.  
  White dwarf magnetism is demonstrably present through X‐ray pulses in two negative superhumpers (TV Columbae and V709 Cassiopeiae), and is arguable on the basis of QPO evidence in most of the others (cataloged here and in Table 1 of Patterson 1999).
• 3.  
  Secondary‐star magnetism is always plausible in CVs, since these are cool, rapidly rotating stars. The magnetism in such stars could well have built‐in 5–20 yr timescales, which might explain the slow transitions between negative and positive superhumps.

In view of the subtleties raised by these points, however, and in view of the need to steer our other results through to proper publication, we now quickly escape, and leave these issues as fodder for intrepid theorists!

• 1.  
  We report spectroscopy of RX 1643+34, showing a blue continuum, weak emission lines of high excitation, high‐velocity components in the Balmer lines, and phase‐dependent He i absorption. The orbital period is 0.120560(14) days. These basically establish its membership in the SW Sex class of cataclysmic variables.
• 2.  
  We report long photometric campaigns on RX 1643+34 and V442 Oph, another SW Sex star. Both stars show negative superhumps, with periods, respectively, 3.2% ± 0.2% and 2.9% ± 0.2% shorter than P_orb. A positive superhump is also possible in V442 Oph, with a period 8.2% ± 0.6% longer than P_orb.
• 3.  
  Both stars show photometric signals at the beat frequency between orbit and superhump. This follows the usual pattern seen in negative superhumpers (N, ω_o, ω_o + N). V442 Oph may also show the beat frequency between orbit and positive superhump (i.e., a signal at Ω).
• 4.  
  We also briefly report long photometric campaigns on two other SW Sex stars, V795 Her and DW UMa. The former showed a return of its positive superhump, unseen since the 1980s, and the latter showed powerful superhumps that changed sign (from negative to positive) between 1996 and 2002.
• 5.  
  These superhump detections follow the patterns familiar from studies of dwarf novae (e.g., Fig. 1 of Patterson 1999). Thus they furnish good evidence that SW Sex stars have disks. The point is of some importance, since other evidence is somewhat ambiguous (single‐peaked and uneclipsed emission lines, peculiar eclipse waveform).
• 6.  
  It is possible that the signal at N arises directly from the varying area of a wobbling disk. Assuming that retrograde nodal precession is the underlying phenomenon, the signal at ω_o + N occurs at the frequency with which disk‐secondary geometry recurs. Thus the origin of the superhump could be as simple as heating of the secondary by radiation from the disk (which reaches the secondary relatively unimpeded, since the disk is not coplanar).
• 7.  
  We see long‐term variability in the superhump behavior of essentially all the SW Sex stars, and candidates, we observe over a baseline ≥6 yr. The stars tend to linger for years at a time in states of positive, negative, and no superhumps. Since superhumps and line profiles both reflect deep properties of the disk (maybe even the same deep property), it would be fascinating to know if the spectroscopic signatures followed suit. Repeated spectroscopic studies in different superhump states would be of high interest.
• 8.  
  Three of the four stars show strong kilosecond QPOs, and three of the four show a two‐peak structure with components separated by ω_o and 2ω_o. Other examples are given in Table 4. These could represent DQ Her type rotation periods, with the lower frequency signal attributed to reprocessing of pulsed flux in structures fixed in the orbital frame. This raises two questions: why are the emergent signals quasi‐periodic rather then periodic, and why is the high‐energy pulsed flux hidden from direct observation? We discuss these issues without resolution. But among magnetic CVs, this is a plausible outcome when high M˙ is coupled with high B. The SW Sex stars could be ancestors of AM Her stars, spun up to kilosecond periods and drowned by a high accretion rate. If true, this would fill an important gap in the understanding of CV evolution.
• 9.  
  Of really critical interest would be observations in different luminosity states, because that provides a good chance to be rid of the vexing QPO.
• 10.  
  So there are some whispers of white dwarf magnetism: QPOs near 0.1P_orb, some evidence for underlying stable signals, frequency spacing by ω_o and 2ω_o, polarimetry, negative superhumps suggesting disk wobble, and the need for a still unidentified class of high‐B stars to provide an ancestor channel for AM Her stars. These appear now to warrant a few pages in a scientific journal. But the really important work lies ahead: compelling evidence for magnetism, and a theory to weave all these interesting threads into a coherent whole!