The 1985 Superoutburst of U Geminorum. Detection of Superhumps

ACTA ASTRONOMICA Vol. 54 (2004) pp. 433–442

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

¢ = : ¦ :

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 characteristic 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 explained 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 challenge 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

: ¦ ℄ : ¦ ℄ : 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

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

shows the O C diagram calculated from the arbitrarily adopted preliminary

elements with constant period:

: : ¢ : JDmax 2446345 10 0 2000 E 2

The points in Fig. 4 define a clear parabola which not only confirms our earlier conclusion about period increase but also demonstrates that the superhump variations were highly coherent. The formal fit gives

: ¦ ℄ : ¦ ℄ ¢ : ¦ ℄ ¢ JDmax 2446345 2057 67 0 19671 19 E 0 0000210 12 E 3

: ¦ ℄ : ¦ ℄ : : Psh 0 19669 19 0 000213 12 JD 2446345 11 4

Using those elements to calculate phases we can now produce the composite

light curve based on all 159 data points. It is shown in Fig. 5. By ﬁtting the : sine-wave curve to the points we obtain its amplitude as A 0 16 mag which is

consistent with amplitudes shown in Fig. 3. The full amplitude of the superhump : is then 2A 0 3 mag. Vol. 54 439

Fig. 5. The composite superhump light curve based on all data points. Phases are calculated from

elements given by Eq. (3). Squares with error bars are mean points in 0:1P phase bins.

5. Onset and Disappearance of Superhumps

The data sets used in the analysis described in previous sections cover rather long time intervals, typically 10 12 days (but up to 20 days in extreme cases). This limits seriously the possibility of deﬁning the precise moments of the onset and disappearance of the superhumps. In an attempt to improve this situation we

calculated periodograms for much shorter data sets with n 30 points. From the first periodogram shown in Fig. 6a we can conclude that superhumps were clearly present already during the first few days of the superoutburst. This conclusion is strengthened by additional crude periodograms calculated from the first 20 and 10 data points which also show a broad peak corresponding to the superhump period. From JD dates corresponding to the mid-interval of those data sets, namely JD 2446348 and 346, we conclude that superhumps must have appeared not later than 2–3 days after reaching the superoutburst maximum. Turning to the end phase of the superoutburst we can see from periodograms presented in Fig. 6b–d that the superhump amplitude clearly decreased. In particu- lar, the last data set shows no trace of the superhump. The JD date corresponding to the mid-interval of this set, namely JD 2446377, implies that superhumps disappeared not later than about 4 days before the final decline.

6. “Additional Superhumps”

The last periodogram shown in Fig. 6d contains a very broad and strong peak at

: 1=P 5 55, which appears to be present also in Fig. 6c. Additional periodograms

from data sets with n 20 points show this periodicity to be only weakly present

in the set i1 i2 111 130 and clearly present in all subsequent sets. 440 A. A.

Fig. 6. Periodograms from data sets with n = 30 points. See caption to Fig. 2 for details.

Fig. 7. The composite light curve of the “additional superhump” based on data set

µ = ´ µ ´i1 i2 121 159 covering JD interval 2446366.7-81.4. Phases are calculated from elements

given by Eq. (5). Squares with error bars are mean points in 0 :2P phase bins. We analyzed all those data sets with n 20 and n 30 in the same way as it

was done in Section 4. The results can be summarized as follows. Periodic vari- : ations with P 0 18 d were present during the end phase of the superoutburst, starting around JD 2446370. In analogy with superhumps, we will call them: “ad- Vol. 54 441 ditional superhumps” (the term “late superhumps” would be more appropriate here, but it is already used for describing another type of phenomena). The elements de-

scribing moments of maxima are

: : ¢

JDmax 2446370 20 0 1806 E 5

¦ :

with the corresponding O C values being smaller than 0 01 d. : The amplitude of the “additional superhumps” increased from A 0 1 mag at

∆ : ∆ :

about t 10 days before the ﬁnal decline up to A 0 27 mag at t 2 5 days.

The composite light curve based on data set i1 i2 121 159 covering the :

interval JD 2446366.7-81.4 is shown in Fig. 7. It has an amplitude of A 0 19 mag, : or full amplitude 2A 0 4 mag. The nature of this variation and its relation to the standard superhumps remain unclear.

7. Discussion

Compared to other dwarf novae showing superoutbursts and superhumps U Gem : has the longest orbital period of Porb 4 25 hrs. Its superhump period excess is

Psh Porb

: ¦ : ε 0 130 0 014 6 Porb where “errors” refer to the observed variation of Psh . It is record large among dwarf

Fig. 8. The superhump period excess ε vs. the mass ratio q. Squares are observational data from Pat- terson (2001, Fig. 1) supplemented with U Gem. Crosses are model values resulting from numerical simulations (Murray 2000, Fig. 2). 442 A. A.

novae and the second largest after the permanent superhumper TV Col (Retter and ε Hellier 2000, Retter et al. 2003). When plotted in the log –log Porb plane U Gem and TV Col fall on a linear extension of the relation deﬁned by shorter period dwarf

novae and permanent superhumpers (Patterson et al. 2003, Fig. 20).

: : ¦

U Gem, with Porb 4 25 hrs and a well determined mass ratio q 0 364

0:017 (Smak 2001), and TV Col, with Porb 5 49 hrs and an estimated mass ratio : between q 0 62 and 0.93 (Hellier 1993), form a serious challenge to the theory

which is unable to explain the presence of superoutburst and superhumps in systems

= with long orbital periods and mass ratios q > qcrit 1 3. Very important for the theoretical interpretation is also the ε–q relation (Patter- son 2001, Fig. 1). U Gem provides an important addition to this relation (see Fig. 8) suggesting that at higher mass ratios this relation becomes non-linear. Shown also in Fig. 8 are the theoretical values of ε resulting from numerical simulations (Mur- ray 2000, Fig. 2). They also deﬁne a clear ε–q relation. Comparing it with the observational relation we must note, however, that at mass ratios higher than about 0.15 the theoretical values of ε are systematically – roughly by a factor of 2 – too large. This discrepancy forms another challenge to the theory.

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