Superhumps and Accretion-Disk Precession in TT Arietis David R. Skillman1, David A. Harvey2, Joseph Patterson3, Jonathan Kemp3, Lasse Jensen4, Robert E. Fried5, Gordon Garradd6, Jerry Gunn7, Liza van Zyl8, Seiichiro Kiyota9, Alon Retter10, Tonny Vanmunster11, and Paul Warhurst12 Center for Backyard Astrophysics Astrophysical Journal, Letters 10 August 1998, Volume 503, Page L67 Abstract We have been conducting a long-term (1988–1998) photometric study of the novalike variable TT Arietis. The main periodic signal in the star's light curve normally occurs at a period which varies but averages ~0.1329 d, about 3.5% shorter than the orbital period of the binary. In 1997 this signal disappeared, and was replaced by a stronger signal 8.5% longer than the orbital period. This new wave strongly resembles the "superhumps" commonly seen in SU UMa-type dwarf novae during superoutburst. In superhump parlance, we could say that a negative superhump was replaced by a positive superhump (P > Porb). This could signify the development of an eccentric instability in the accretion disk. The two superhumps probably signify two types of disk precession: apsidal advance and nodal regression. TT Ari is an excellent candidate for observational studies which probe the origin of superhumps. 1. Introduction Normally at magnitude 10.5–11, TT Arietis is one of the brightest cataclysmic variables. Good accounts of early studies were given by Smak & Stepien (1969, 1975), Shafter et al. (1985), and Thorstensen, Smak, and Hessman (1985). Photometry on timescales of minutes to hours has also been extensively reported (Udalski 1988, Tremko et al. 1996, Kraicheva et al. 1997, Andronov et al. 1998). The star is famous for occasional drops to a low state at V = 17, which earn it membership in the "VY Scl" class of CVs. The long-term light curves were discussed by Fuhrmann (1981) and Wenzel et al. (1992), and spectroscopy at these various states was described by Shafter et al. (1985). TT Ari shows a great variety of photometric periods, and we have been studying these signals intensively since 1988, with ~700 hr of coverage over 200 nights. In the main our results are consistent with those previously reported: a 20-minute quasi-periodic oscillation, and a signal which averages ~0.1329 d and wanders slightly and erratically in period from year to year. But in 1997–8, we saw an altogether new feature, a very strong modulation at 0.14926±0.00006 d. This "positive superhump" is probably a signature of an eccentric accretion disk. Here we report the recent photometry. 2. Observations In 1997–8 we organized a campaign of global photometry, with the telescopes of the Center for Backyard Astrophysics (CBA; Skillman 1993, Harvey et al. 1995). We observed for 195 hr over 57 nights, with details given in Table 1. Each telescope acquired a time series of differential photometry, in V light or unfiltered. Comparison of simultaneous data of each type showed no measurable differences in hump amplitude or timing, but small constant offsets due to the fact that each telescope/detector operates at a slightly different effective wavelength. We removed these offsets prior to analysis. The star remained near its usual high-state brightness at V = 10.9, and displayed a light curve which looked familiar: rapid flickering with a dominant timescale near ~20 min, and a wave of period roughly 3 hr. A 30-hour light curve with nearly continuous coverage is shown in Figure 1. (Here the flickering is not easily evident, but is actually present at its usual amplitude.) On closer inspection, we found to our surprise that the star's humps occurred at an unfamiliar period. For detailed period search we used a central 18-d segment (JD 50784–50801) where the observations were maximally dense. The power spectrum is shown in Figure 2, indicating a powerful signal at 6.702 c/d (P = 0.14921±0.00008 d). Inset in Figure 2 is the average waveform. There is an obvious pattern of rapid rise and slow decline, as is usually found in the common superhumps of dwarf novae. No clear evidence of period change was found throughout the year, and all timings were consistent with the ephemeris Maximum light = HJD 2450771.470 + 0.14926(5) E. The power spectrum of Figure 2 shows only a lone peak, with the surrounding bumps due merely to the windowing of the time series. We removed the powerful signal from the time series and studied the residual for any periodic signals. None were found, to a limit of 0.023 mag full amplitude. Marked in Figure 2 are the locations of the orbital period and the photometric period prior to 1997, and no signal was found there to a limit <0.017 mag full amplitude. We also searched for periodic signals at low frequency (P > 1 d). Only a subset of CBA data could be used for this purpose, because calibration uncertainties among the many telescopes create the possibility of spurious signals. However, the well-calibrated data yield a strong limit of no periodic signal exceeding 0.06 mag full amplitude in the period range 1–8 d. A minor but interesting question is: what happened to the 20-min QPO when the 3-hr signal changed its period so drastically? At first glance, Figure 1 shows no clear evidence of the 20-min signal which has been so obvious in previous photometry. But this is merely due to the coarser time resolution in the figure. When we studied the individual nights we found signals near 20 min which danced wildly about in frequency, the customary signature of the QPOs. The mean nightly power spectrum (not shown) gave a broad bump centered at P = 23±3 min. 3. Discussion and Prospects Cataclysmic variables of short orbital period are known to display "superhumps" — photometric waves with a period slightly discrepant from Porb. These are ubiquitous and well-known in the case of SU Ursae Majoris-type dwarf novae (Warner 1995). But they are also common in bright CVs (MV < +6) with Porb < 3.5 hr. Most of these have a period slightly exceeding Porb — "positive" superhumps, since the period excess is positive. The fractional period excess of positive superhumps correlates strongly with Porb, as first remarked by Stolz & Schoembs (1984). This is illustrated in Figure 3, where the 43 dwarf novae are shown anonymously and other CVs are identified by name (Table 1 of Patterson 1998). The orbital period of TT Ari is 0.13755 d (Cowley et al. 1975, Thorstensen et al. 1985). The star appears near the upper right, with a fractional period excess of 0.085. This clearly fits well with the trend. It seems very likely that the newly apparent wave in TT Ari is a positive superhump, of the same type as the others represented in Figure 3. These waves are thought to arise from the development of an eccentric instability in the accretion disk (Whitehurst 1988, Osaki 1989, Lubow 1991), which then precesses under the gravity of the orbiting secondary. If the line of apsides advances with a period Pprec, then the secondary transits that line with a period slightly longer than Porb, namely Psh, where (1 / Psh) = (1 / Porb) – (1 / Pprec). This is identified as the superhump period. The actual mechanism for generating the superhump light is not yet known. It could be the periodic tidal stresses in the disk, or the periodic variation in the infall distance of the mass-transfer stream. In TT Ari, this implies an apsidal precession period of 1.76 days. No photometric signal is expected, or seen, at that period. But the superhump is rather strong in TT Ari, and it should be powered by eccentricity. So we expect to see asymmetric absorption lines, with the asymmetry migrating with P = 1.76 d back and forth across the line profile like a see-saw (see Figures 6 and 12 of Patterson, Halpern, & Shambrook 1993). Because the star is very bright with the higher Balmer lines strongly in absorption, this is a practical measurement which can sensitively test the eccentric-disk model for positive superhumps. What about the signal that disappeared — the "negative" superhump that rippled through the light curve during 1962–1994 and showed an average period excess of –.035? Can this come from apsidal precession also? It does not seem likely. The reason is that among the ~9 CVs showing negative superhumps, at least three (V503 Cyg: Harvey et al. 1995; AM CVn: Harvey et al. 1998; V603 Aql: Patterson et al. 1997) show positive and negative superhumps simultaneously. It is hard enough to understand how a differentially rotating, fluid disk can manage one well-defined precession frequency, let alone two of the same type! It seems much more likely that the negative superhump arises from a different type of precessional motion, and a worthy candidate is accretion-disk wobble. If something can drive the disk out of the orbital plane, then the torque from the secondary will cause the disk to wobble backwards; the nodes will regress, causing the geometry between disk and secondary to recur on a period slightly less than Porb (the negative superhump). We know of no spectroscopic test of the wobbling-disk theory, but there is a photometric test: assuming the disk to be not too close to face-on, there should be a photometric signal at the wobble frequency itself, due to the periodic variation of disk area. Indeed, a search for this expected nodal-precession signal at 4.0 d was the goal of our recent observing effort. The disappearance of the negative superhump thwarted the enterprise. But a search is warmly recommended whenever the negative superhump returns. Possible detections have already been reported by Semeniuk et al. (1987) and Kraicheva et al. (1997). Do we understand why the star retired one of its superhumps and activated the other? Certainly not. No noticeable changes in spectrum or mean brightness accompanied this event. In 1997–8 the full amplitude was 0.22 mag, with no measurable change over the 115-day campaign. We hope to track the amplitude excursions of these signals over the years, and hope that theorists will study the growth and decay timescales of accretion-disk precession, following the work of Lubow (1991, 1992). We thank Richard Thompson and Darragh O'Donoghue for contributions to the observing campaign. And we thank the Research Corporation and the NSF for their support of the CBA and our research on cataclysmic variables. __________ 19517 Washington Avenue, Laurel, MD 20723; cbaceo .at. clark.net 21552 West Chappala Drive, Tucson, AZ 85703; dharvey .at. comsoft-telescope.com 3Department of Astronomy, Columbia University, 550 West 120th Street, New York, NY 10027; jop, jonathan .at. astro.columbia.edu 4Sondervej 38, DK-8350 Hundslund, Denmark; teist .at. image.dk 5Braeside Observatory, Post Office Box 906, Flagstaff, AZ 86002; captain .at. braeside.org 6Post Office Box 157, Tamworth NSW 2340, Australia; gjg .at. mpx.com.au 71269 North Skyview Drive, East Peoria, IL 61611; jgunn .at. mtco.com 8Department of Astronomy, University of Cape Town, Private Bag, Rondebosch 7700, Cape Town, South Africa; vanzyl .at. uctvms.uct.ac.za 91-401-810 Azuma, Tsukuba, Ibaraki 305-0031, Japan; pfg00474 .at. niftyserve.or.jp 10Wise Observatory and Department of Astronomy, Tel Aviv University. Current address: Astrophysics Group, Department of Physics, Keele University, Keele, Staffordshire ST5 5BG, England, United Kingdom; ar .at. astro.keele.ac.uk 11Walhostraat 1A, B-3401 Landen, Belgium; Tonny.Vanmunster .at. advalvas.be 12Department of Physics, University of Auckland, Private Bag 92019, Auckland, New Zealand; pwar022 .at. phy.auckland.ac.nz References Andronov, I. et al. 1998, AJ, in press Cowley, A.P., Crampton, D., Hutchings, J.B., & Marlborough, J.M. 1975, ApJ, 195, 413 Fuhrmann, B. 1981, MVS, 9, 14 Harvey, D., Skillman, D.R., Patterson, J., & Ringwald, F.A. 1995, PASP, 106, 551 Harvey, D.A., Skillman, D.R., Kemp, J., Patterson, J., Vanmunster, T., Fried, R.E., & Retter, A. 1998, ApJ, 493, L105 Kraicheva, Z., Stanishev, V., Iliev, L., Antov, A., & Genkov, V. 1997, A&AS, 122, 123 Lubow, S. 1991, ApJ, 381, 268 Lubow, S. 1992, ApJ, 398, 525 Osaki, Y. 1989, PASJ, 41, 1005 Patterson, J. 1998, PASP, submitted Patterson, J., Halpern, J., & Shambrook, A. 1993, ApJ, 419, 803 Patterson, J., Kemp, J., Saad, J., Skillman, D.R., Harvey, D., Fried, R., Thorstensen, J.R., & Ashley, R. 1997, PASP, 109, 468 Semeniuk, I., Schwarzenberg-Czerny, A., Duerbeck, H., Hoffmann, M., Smak, J., Stepien, K., & Tremko, J. 1987, Ap&SS, 130, 167 Shafter, A.W., Szkody, P., Liebert, J., Penning, W.R., Bond, H.E., & Grauer, A.D. 1985, ApJ, 290, 707 Skillman, D.R. 1993, Sky & Telescope, 85, 83 Smak, J. & Stepien, K. 1969, in Non-Periodic Phenomena in Variable Stars, ed. L. Detre (Academy: Budapest), p. 355 Smak, J. & Stepien, K. 1975, Acta Astr., 25, 379 Stolz, N. & Schoembs, R. 1984, A&A, 132, 187 Thorstensen, J.R., Smak, J., & Hessman, F.V. 1985, PASP, 97, 437 Tremko, J., Andronov, I.L., Chinarova, L.L., Kumsiashvili, M.I., Luthardt, R., Pajdosz, G., Patkos, L., Roessiger, S., & Zola, S. 1996, A&A, 312, 121 Udalski, A. 1988, Acta Astr., 38, 315 Warner, B. 1995, Ap&SS, 226, 187 Wenzel, W., Hudec, R., Schult, R., & Tremko, J. 1992, Contr. Astr. Obs. Skalnate Pleso, 22, 69 Whitehurst, R. 1988, MNRAS, 232, 35 Figure Captions Figure 1. Long light curve of TT Ari on 17/18 December 1997, showing the persistent superhump. This signal continued throughout the 115-day observing season, with no obvious changes in period or amplitude. The well-known 20-minute quasiperiodic signal is present too, but at this scale masquerades as noise in the light curve. Figure 2. Power spectrum of an 18-day segment with dense coverage (JD 2450784–801). A single peak appears at P = 0.14921(9) d, with the surrounding small bumps arising merely from the windowing of the time series. Arrows point to null detections at the orbital period and the photometric period familiar from studies during 1962–1994. Inset is the mean waveform at the 0.14921 d period. Figure 3. Empirical correlation of the fractional period excess with Porb, for positive superhumps. Filled squares are dwarf novae, and open circles with explicit names are other types of cataclysmic variables. TT Ari, at the upper right, fits well with the trend — supporting its membership in this family of stars.