The 1985 Superoutburst of U Geminorum. Detection of Superhumps
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ACTA ASTRONOMICA Vol. 54 (2004) pp. 433–442 The 1985 Superoutburst of U Geminorum. Detection of Superhumps by Józef Smak N. Copernicus Astronomical Center, Polish Academy of Sciences,ul. Bartycka 18, 00-716 Warsaw, Poland e-mail: [email protected] and ElizabethO. Waagen American Association of Variable Star Observers, 25 Birch Street, Cambridge, MA 02138, USA email: [email protected] Received November 9, 2004 ABSTRACT Superhumps are detected in the AAVSO light curve of the 1985 superoutbursts of U Gem. They appeared not later than 2–3 days after reaching maximum and disappeared not later than about : 4 days before the final decline. The superhump period was Psh 0 20 d and increased at a rate 4 ¢ = : ¦ : of dP=dt 2 10 . The corresponding superhump period excess was ε 0 130 0 014 . The full : amplitude of the superhumps was 2A 0 3 mag. During the last ten days of the superoutburst additional periodic variations were also present. : : : Their period was 0 18 d and their full amplitude grew from 2A 0 2 mag to 0 5 mag. U Gem, together with the permanent superhumper TV Col (Retter et al. 2003), form a challenge to the theory which is unable to explain superoutburst and superhumps in systems with long orbital = = periods and mass ratios q > qcrit 1 3. Another challenge to the theory comes from a comparison of the theoretical ε–q relation resulting from numerical simulations (Murray 2000) with its obser- : ε vational counterpart: for q > 0 15 the model values of are systematically – by a factor of 2 – too large. Key words: Stars: dwarf novae – novae, cataclysmic variables – Stars: individual: U Gem 1. Introduction Superoutbursts are common phenomenona in dwarf novae of the SU UMa type with ultra-short orbital periods (cf. Warner 1995, Osaki 1996). One of their char- acteristic features are the superhumps with periods which are few percent longer than the orbital period (cf. O’Donoghue 2000, Patterson 2001). Superhumps are 434 A. A. also present in several stationary accretion cataclysmic binaries – the “permanent superhumpers” (cf. O’Donoghue 2000, Patterson 2001). According to the commonly accepted theory (cf. Osaki 1996, Murray et al. 2000, Murray 2000) superhumps and superoutbursts are explained in terms of the tidally driven eccentric instability which occurs – due to 3:1 resonance – in the outer parts of the accretion disk. The original version of the theory (Whitehurst 1988, Hirose and Osaki 1990) predicted this instability to occur in systems with = mass ratios q < qcrit 1 4, i.e., in systems with very short orbital periods. This ex- plained nicely the occurrence of superoutbursts and superhumps in SU UMa stars. Further investigations, including those involving numerical simulations, increased = the value of the critical mass ratio up to qcrit 1 3 (cf. Murray et al. 2000, Mur- ray 2000 and references therein). This appeared to be sufficient to explain also the presence of superhumps in permanent superhumpers with orbital periods up to : : ¦ : 4 hours, including UU Aqr with Porb 3 92 hrs and q 0 30 0 07 (Patterson : 2001). Only the case of the dwarf nova TU Men, with P 2 81 hrs, continued to remain somewhat unclear due to the uncertain determinations of its mass ratio : giving a broad range of values ranging from q 0 33 to 0.45 (Mennickent 1995). A major challenge to the theory was produced recently by the discovery (Retter : and Hellier 2000, Retter et al. 2003) that TV Col, with Porb 5 49 hrs and an : estimated mass ratio between q 0 62 and 0.93 (Hellier 1993), is a permanent ε : superhumper with a large superhump period excess 0 154. U Gem, with its 1985 superoutburst (Mattei et al. 1991), orbital period Porb : ¦ : 4:25 hrs and mass ratio q 0 364 0 017 (Smak 2001), formed actually a chal- lenge to the theory even before it was formulated. Remarkably, however, it has only seldom been discussed in this context (e.g., Kuulkers 1999, Smak 2000). Instead it was common to interpret the “1985 event” as “an unusually long outburst” (Mason et al. 1988) or “a long outburst” (Cannizzo et al. 2002). The aim of the present paper is to report the detection of superhumps during that “1985 event” thereby providing definite proof to its superoutburst nature and strengthening the challenge to the theory. 2. AAVSO Light Curve The superoutburst of U Gem which took place in October-November 1985 was beautifully covered by the AAVSO observers. The resulting light curve (Mattei et al. 1991) is shown in Fig.1. The superouburst lasted for a record-long 42 days. The : maximum, at m 9 0 mag, was reached on JD 2446344.5 and was followed by the “flat-top” part, with its characteristic slow decline, extending up to JD 2446381.5, i.e., for about 37 days. In preparation for further analysis we represent the slow decline within the “flat-top” with a straight line : ¦ ℄ · : ¦ ℄ ´ : µ ´ µ m 9 000 38 0 0371 19 JD 2446344 0 1 Vol. 54 435 and calculate the residuals which are shown in the bottom part of Fig. 1. As can be : seen the scatter is very large – the formal dispersion being σ 0 26 mag. Fig. 1. Top: The AAVSO light curve of the 1985 superoutburst of U Gem. The line shows the linear fit given by Eq. (1). Bottom: The residuals. There are several reasons why the search for periodicities in the residuals could appear almost hopeless. The original magnitudes m are given only to within 0.1 mag. Observations are distributed in time non-uniformly: there are 6-hr gaps corresponding to the day-time hours in North America. Of the 187 data points within the 37-day “flat-top” only 159 – with JD’s given with accuracy of 0.01 day (or better) – can be used in the analysis. On the average then there are only 4–5 data points per day or less than one point per orbital period. In view of this it is not surprising that during nearly 20 years since that superouburst no attempt was made to analyze these data. 3. Periodograms We begin by calculating the periodogram based on all data points. It is shown in Fig. 2(a). At first sight the situation may appear not very encouraging. Nevertheless : we note that the highest peaks are the double peak near 1 =P 5 0 and its two = ¦1c d aliases. Could they represent any real periodicity? 436 A. A. Fig. 2. a Periodogram from all data. b–g Examples of periodograms from data sets with n = 60 points. They are identified with current numbers of data points and corresponding JD intervals. The vertical scale shows the amplitude (in magnitudes) of the sine-wave signal at a given frequency. To answer this question we calculated periodograms based on smaller data sets consisting of, respectively, n 50, 60 and 70 data points. Each data set is identified µ with the current number of the first and last point ´i1 i2 , with i1 being increased in successive sets by 10; for example (31–80) is the third set with n 50. Al- together then periodograms were obtained for 33 data sets. Prior to calculating the periodograms the linear trend within each data set was removed. It should be added, however, that this was not crucial for the results: periodograms calculated from uncorrected ∆m values were in fact very similar. Vol. 54 437 Examples of periodograms for n 60 are presented in Fig. 2b–g. They clearly : show that (1) the peak near 1 =P 5 0 is always present, (2) it is usually the highest peak in the periodogram, and (3) its position is systematically shifted, indicating that the corresponding period is increasing with time. 4. Superhump Periods and Amplitudes In the next step all data sets were analyzed by fitting to them – via the least squares solution – the sine-wave curve and thereby determining its parameters: the period, the amplitude and the phase (moment) of maximum, together with their Fig. 3. Superhump periods and amplitudes are plotted against time. Crosses, triangles and squares represent data sets with, respectively, n = 50, 60 and 70 data points. JD corresponds to the mid- interval of a given data set. The line in the upper plot corresponds to Eq. (4). 438 A. A. formal errors. Note that the term “amplitude” and its numerical values A refer here to the amplitude of the sine-wave curve, while the full amplitude is, of course, 2A. As in the case of periodograms, the linear trend within each data set was removed prior to the solution. Results, shown in Fig. 3, can be summarized as follows. The : : superhump period increased from Psh 0 197 d at JD 2446350 to Psh 0 203 d at JD 2446371; note that those JD’s refer to the mid-intervals of the first and last data : sets. The amplitude appears to have changed slightly between A 0 10 mag and : A 0 16 mag (see Section 5 for further discussion). ´ µ Fig. 4. The O C diagram. Symbols are the same as in Fig. 3. The O C values are from linear elements given by Eq. (2). The parabola corresponds to the elements given by Eq. (3). The moments of maxima could then be used to determine the elements. Fig. 4 µ shows the ´O C diagram calculated from the arbitrarily adopted preliminary elements with constant period: µ : · : ¢ : ´ µ JD´max 2446345 10 0 2000 E 2 The points in Fig. 4 define a clear parabola which not only confirms our earlier con- clusion about period increase but also demonstrates that the superhump variations were highly coherent.