D. Nogami¹ - M. Uemura² - R. Ishioka² - T. Kato² - K. Torii³ - D. R. Starkey⁴ - K. Tanabe⁵ - T. Vanmunster⁶ - E. P. Pavlenko^7,8 - V. P. Goranskij⁹ - E. A. Barsukova¹⁰ - O. Antoniuk^7,8 - B. Martin¹¹ - L. M. Cook¹² - G. Masi¹³ - F. Mallia¹⁴

1 - Hida Observatory, Kyoto University, Kamitakara, Gifu 506-1314, Japan
2 - Department of Astronomy, Kyoto University, Kyoto 606-8502, Japan
3 - Cosmic Radiation Laboratory, Institute of Physical and Chemical Research (RIKEN), 2-1, Wako, Saitama 351-0198, Japan
4 - DeKalb Observatory, 2507 County Road 60, Auburn, Auburn, Indiana 46706, USA
5 - Department of Biosphere-Geosphere Systems, Faculty of Informatics, Okayama University of Science, 1-1 Ridaicho, Okayama 700-0005, Japan
6 - Center for Backyard Astrophysics (Belgium), Walhostraat 1A, 3401 Landen, Belgium
7 - Crimean Astrophysical Observatory, Nauchny, 98409 Crimea, Ukraine
8 - Isac Newton Institute of Chile, Crimean Branch, Ukraine
9 - Sternberg Astronomical Institute, 119899 Moscow, Russia
10 - Special Astrophysical Observatory, Russian Academy of Sciences, Nizhnij Arkhyz, Karachaevo-Cherkesia, Russia
11 - King's University College, Department of Physics, 9125 50th Street, Edmonton, AB T5H 2M1, Canada
12 - Center for Backyard Astrophysics (Concord), 1730 Helix Court, Concord, CA 94518, USA
13 - Physics Department, University of Rome "Tor Vergata'' Via della Ricerca Scientifica, 1 00133 Rome, Italy
14 - Campo Catino Astronomical Observatory 03025 Guarcino, Italy

Abstract
An intensive photometric-observation campaign of the recently discovered SU UMa-type dwarf nova, Var73 Dra was conducted from 2002 August to 2003 February. We caught three superoutbursts in 2002 October, December and 2003 February. The recurrence cycle of the superoutburst (supercycle) is indicated to be $\sim$ 60 d, the shortest among the values known so far in SU UMa stars and close to those of ER UMa stars. The superhump periods measured during the first two superoutbursts were 0.104885(93) d, and 0.10623(16) d, respectively. A 0.10424(3)-d periodicity was detected in quiescence. The change rate of the superhump period during the second superoutburst was $1.7\times10^{-3}$ , which is an order of magnitude larger than the largest value ever known. Outburst activity has changed from a phase of frequent normal outbursts and infrequent superoutbursts in 2001 to a phase of infrequent normal outbursts and frequent superoutbursts in 2002. Our observations are negative to an idea that this star is an related object to ER UMa stars in terms of the duty cycle of the superoutburst and the recurrence cycle of the normal outburst. However, to trace the superhump evolution throughout a superoutburst, and from quiescence more effectively, may give a fruitful result on this matter.

Key words: accretion, accretion disks - novae, cataclysmic variables - stars: dwarf novae - stars: individual: Var73 Dra

1 Introduction

Dwarf novae are a class of cataclysmic variables stars (CVs), which show various types of variability originating in the accretion disk around the white dwarf (for a review, Warner 1995). Dwarf novae are further classified into three basic types of SS Cyg-type dwarf novae showing normal outbursts, Z Cam-type dwarf novae showing normal outbursts and standstills, and SU UMa-type dwarf novae showing superoutbursts as well as normal outbursts. The difference of photometric behavior in these kinds of stars including nova-like variable stars is essentially explained by the thermal-tidal disk instability scheme (for a review, e.g. Osaki 1996). Superhumps are oscillations with an amplitude of 0.1-0.5 mag and a period 1-5% longer than the orbital period ( $P_{\rm orb}$ ) observed only during long, bright (super)outbursts. The superhump is considered to be a beat phenomenon of the orbital motion of the secondary star and the precession of the tidally distorted eccentric disk (Whitehurst 1988). The eccentricity in such disks plays a key role to keep the accretion disk in the hot state to make a normal outburst evolve into a superoutburst (Osaki 1989).

Non-magnetic CVs have been suggested to have a bi-modal $P_{\rm orb}$ distribution (Robinson 1983), while the gap between $\sim$ 2 h and $\sim$ 3 h seems to be filled in the case of magnetic systems (Webbink & Wickramasinghe 2002). This period gap is explained in the standard theory of the CV evolution as follows: 1) the magnetic braking, which is the mechanism of angular momentum loss, suddenly dies down when the secondary star become fully convective around $P_{\rm orb}$ $\sim 3$ h; 2) the secondary shrinks into the thermal equilibrium state and the mass transfer stops; 3) the angular-momentum loss is continued by a greatly reduced rate by the gravitational wave radiation; and 4) the secondary fills again its Roche-lobe around $P_{\rm orb}$ $\sim2$ h and the CV activity restarts (for a review, e.g. King 1988). Although most of the SU UMa-type dwarf novae are distributed below the period gap, some systems are above (TU Men: Mennickent 1995) and in the period gap (e.g. NY Ser: Nogami et al. 1998b).

The evolution scenario predicts that CVs evolve for the shorter $P_{\rm orb}$ region with the mass transfer rate ( $\dot{M}$ ) reduced, but the orbital period begins to increase after the secondary is degenerated (Kolb & Baraffe 1999; Paczynski 1971). Most SU UMa stars are believed to be on this standard path. However, a small group of most active, high- $\dot{M}$ SU UMa stars, called ER UMa stars, has been recently established near the period minimum (Nogami et al. 1995; Kato et al. 1999; Kato & Kunjaya 1995), and the evolutionary state of ER UMa stars is a serious problem (Nogami 1998).

Var73 Dra was discovered by Antipin & Pavlenko (2002) on the Moscow archive plates. Their subsequent CCD observations in 2001 August-October proved that this star is an SU UMa-type dwarf nova of R = 15.7 at the supermaximum and the recurrence cycle of the normal outburst is 7-8 days. The superhump period ( $P_{\rm SH}$ ) was measured to be 0.0954(1) day, but the possibility of its one-day alias, 0.1053 d, could not be rejected.

Var73 Dra is identified with USNO B1.0 1546-0228545 ( B1 = 15.90, R1 = 16.09), the proper motion of which is not listed in the catalog. The SIMBAD Astronomical Database does not give any cross-identification for this object other than the USNO entry.

We started an intensive photometric-observation campaign of Var73 Dra since 2002 August to reveal behavior of this newly discovered in-the-gap SU UMa-type dwarf nova. The results including two well-covered superoutbursts are reported in this paper.

2 Observations

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{4341f1.eps} \end{figure}$	Figure 1: Finding chart of Var73 Dra generated by the astronomical image-data server operated by the National Astronomical Observatory of Japan, making use of Digital Sky Survey 2 (Region ID: XP106, Plate ID: A0LI). North is up, and East is left. The field of view is $13'\times 13'$ . The numbers from 1 to 8 are given to the comparison stars in Table 1.
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The observations were carried out at ten sites with twelve sets of instruments. The log of the observations and the instruments are summarized in Table 1. Figure 1 is a finding chart where the comparison stars are marked.

All the frames obtained at Hida and Okayama, and frames at Saitama on 2002 October 14 were reduced by the aperture photometry package in IRAF, after de-biasing (Hida frames) or dark-subtraction (Okayama and Saitama frames), and flat-fielding. The Kyoto frames and the rest of the Saitama frames were processed by the PSF photometry package developed by one of the authors (TK). All frames obtained at the DeKalb Observatory, CBA Belgium, and CBA Concord were reduced by aperture photometry after dark subtraction and flat-fielding, using the AIP4WIN software by Berry and Burnell. The Crimean images were dark-subtracted, flat-fielded, and analyzed with the profile/aperture photometry package developed by one of the authors (VPG).

3 Results

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{long.ps} \end{figure}$	Figure 2: Long-term light curve of Var73 Dra drawn with the Kyoto data only. The campaign was started at the decline phase of an outburst. Three superoutbursts were observed approximately around HJD 2 452 560, 2 452 620, and 2 452 680. A normal outburst was recorded around HJD 2 452 650.
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The long-term light curve is shown Fig. 2. During our monitoring, Var73 Dra gave rise to three superoutbursts: the first was in the rising phase on HJD 2 452 551, the second began on some day between HJD 2 452 611 and HJD 2 452 615 (see Table 1), the precursor of the third superoutburst was caught on HJD 2 552 674. This fact proves the supercycle of Var73 Dra to be $\sim$ 60 days. While two normal outbursts were caught at the start and around HJD 2 452 650 in the long-term light curve shown in Fig. 2, our observations reject the possibility of the recurrence cycle of the normal outburst shorter than 13 days, since no outburst was found for at least 11 days after the end of the first normal outburst (Table 1).

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{q2.ps} \end{figure}$	Figure 3: a) PDM Theta diagram of a period analysis of the quiescence data between 2002 August 30 and October 3 (see text). A period of 0.10424(3) d is pointed. b) The quiescence light curve folded by the 0.10424-d period after subtracting the daily average magnitude from the data.
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To search periodic variability in quiescence, a period analysis by the Phase Dispersion Minimization (PDM) method (Stellingwerf 1978) was performed for the data obtained between 2002 August 30 and October 3, after excluding points over 3 $\sigma$ far from the daily mean magnitude and subtracting the daily mean magnitude from the daily data sets. Figure 3 exhibits the resultant theta diagram. The sharp peak points to the period of 0.10424(3) d. The error of the period was estimated using the Lafler-Kinman class of methods, as applied by Fernie (1989). The folded light curve has a peak around $\phi=0.0$ and a marginal secondary peak around $\phi=0.65$ .

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{hida.ps} \end{figure}$	Figure 4: Superhumps observed at the Hida observatory on 2002 October 13 ( upper panel) and 14 ( lower panel). The typical error bars are drawn near the upper-left corner.
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$\begin{figure} \par\includegraphics[width=8.4cm,clip]{super3.ps} \end{figure}$	Figure 5: a) PDM theta diagram for superhumps observed during the first superoutburst. The best estimated superhump period is 0.104885(93) d. b) Superhump light curve folded by the superhump period, after subtracting the mean magnitude from each data set.
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Figure 4 shows examples of superhumps observed during the first superoutburst. After selecting data sets with errors small enough to use for the period analysis (indicated by " $\bigcirc$ '' in Table 1) and subtracting the mean magnitude from each data set, we applied the PDM period analysis to the processed data sets. The theta diagram and the mean superhump light curve is given in Fig. 5. The superhump period of 0.104885(93) d we obtained affirms the longer candidate proposed by Antipin & Pavlenko (2002), and assures that Var73 Dra is an in-the-gap SU UMa-type dwarf nova with the second longest $P_{\rm SH}$ , next to TU Men (Stolz & Schoembs 1984), almost equal to that of NY Ser (Nogami et al. 1998b).

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{shmax1.ps} \end{figure}$	Figure 6: O-C diagram of the timings of the superhump maxima in Table 2. The calculated timings are given by Eq. (1). The parabolic curve is based on Eq. (2).
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We extracted the timings of the superhump maxima by fitting the average superhump light curve in Fig. 5. The results are listed in Table 2. The cycle count E was set to be 0 at the first superhump maximum measured. A linear regression and a parabolic fit to the times give the following equations:

$\begin{displaymath}HJD_{\rm max} = 61.847(1) + 0.10468(15)\times(E-8), \end{displaymath}$

(1)

$\displaystyle HJD_{\rm max}=61.847(3) + 0.10468(18)\times(E-8) + 0.000003(56)\times(E-8)^2.$

(2)

Figure 7 displays the result of the PDM period analysis for the data obtained during the second superoutburst and the average superhump light curve. We used the data marked by " $\bigcirc$ '' in Table 1 also for this second $P_{\rm SH}$ analysis. The superhump period of 0.10623(16) is slightly longer than that during the first superoutburst. No apparent signal of a secondary hump around the phase of 0.5 is seen.

The timings of the superhump maxima were obtained for this superoutburst as before (Table 3). A linear regression to these timings yields the following ephemeris:

$\begin{displaymath}HJD_{\rm max} = 20.2513(55) + 0.10768(44)\times(E-26). \end{displaymath}$

(3)

$\displaystyle HJD_{\rm max} = 20.2654(25) + 0.10756(16)\times(E-26) - 0.0000893(95)\times(E-26)^2.$

(4)

$\begin{figure} \par\includegraphics[width=8.8cm,clip]{super2.ps} \end{figure}$	Figure 7: a) PDM theta diagram for superhumps observed during the first superoutburst. The best estimated superhump period is 0.104885(93) d. b) Superhump light curve folded by the superhump period, after subtracting the mean magnitude from each data set.
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4 Discussion

4.1 Two superhump periods

We obtained two superhump periods: 0.104885(93) d during the first superoutburst (hereafter $P_{\rm SH}$ 1), and 0.10623(16) d during the second superoutburst (hereafter $P_{\rm SH}$ 2). The difference between $P_{\rm SH}$ 1 and $P_{\rm SH}$ 2 must result from differences of the observed phase in the course of the superoutburst.

The first superoutburst is estimated to have attained to its maximum brightness at HJD 2 452 552.0 ( $\pm$ 1.0) from Table 1. The data used for the $P_{\rm SH}$ 1 analysis were therefore taken between the 6( $\pm$ 1)th day and the 14( $\pm$ 1)th day from the supermaximum. In the case of the second superoutburst, the maximum of the outburst was reached somewhen between HJD 2 452 611.0 and 2 452 615.0. Thus the data used for the $P_{\rm SH}$ 2 analysis were taken between the 4( $\pm$ 2)th day and the 9( $\pm$ 2)th day from the onset. Therefore the "mid'' day of the observed phase during the second superoutburst (the 7( $\pm$ 2)th day) is earlier than that during the first superoutburst (the 10( $\pm$ 1) day). The extremely large change rate observed during the second superoutburst can easily yield the difference between two superhump periods.

It should be also noted that $P_{\rm SH}$ seemed to decrease with a larger rate in an earlier phase. This trend is suggested by the fact that the change rate of $P_{\rm SH}$ 2 was derived from the superhump-maximum times between 4( $\pm$ 2)th day and 10( $\pm$ 2)th day, in contrast to that that of $P_{\rm SH}$ 1 was derived from the timings of the superhump maximum between 9( $\pm$ 1)th day and 10( $\pm$ 1)th day from the supermaximum.

4.2 Orbital period

We photometrically detected coherent modulations with a period of 0.10424(3) d in quiescence. This period is slightly shorter than the superhump periods $P_{\rm SH}$ 1 and $P_{\rm SH}$ 2, and is naturally attributed to the orbital period. Confirmation by spectroscopic observations is, however, desired since our quiescence data contain large errors and the actual error of the period derived is perhaps larger than the noted one statistically calculated. The orbital period of 0.10424 d is the second longest among those of SU UMa stars with the orbital period measured, next to 0.1172 d of TU Men (Mennickent 1995), and places Var73 Dra at the midst of the period gap.

The superhump excess $\epsilon$ (= $(P_{\rm SH}-P_{\rm orb})/P_{\rm orb})$ is 0.6% for $P_{\rm SH}$ 1 or 1.9% for $P_{\rm SH}$ 2, respectively. It is generally known that there is a robust relationship that the superhump excess smoothly increases with $P_{\rm orb}$ (see e.g. Patterson 1998). This relationship is well explainable in the disk instability model in that a large superhump excess suggests a large accretion-disk radius in a long- $P_{\rm orb}$ system with a large mass ratio ( $q = M_{\rm 2}/M_{\rm 1}$ ). While Var73 Dra is expected to have $\epsilon \sim 5{-}7$ % from this relation, the derived values of $\epsilon$ corresponds to those of SU UMa stars with a period about 0.06 d. This implies that Var73 Dra has a small mass ratio, although theoretical calculations on the CV evolution propose a high mass ratio for a CV in the period gap (e.g. Howell et al. 2001). Var73 Dra may be the first object which breaks the $\epsilon$ - $P_{\rm orb}$ relation. (Patterson (1998) discusses this relationship after correction of $P_{\rm SH}$ , taking period changes into account, to the value 4 days after superhump emergence. The same correction does not have significant effect on our results.) This problem urges spectroscopic determination of q as well as $P_{\rm orb}$ . Note that the modulations in quiescence may be attributed to permanent superhumps, as discussed later.

$\begin{figure} \par\includegraphics[width=8.4cm,clip]{shmax2.ps} \end{figure}$	Figure 8: O-C diagram of the timings of the superhump maxima in Table 3. The calculated timings are given by Eq. (3). The parabolic curve is based on Eq. (4).
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4.3 Derivative of the superhump period

Until mid 1990s, the superhump period was considered to monotonically decrease, or at least be constant, after full development (see e.g. Warner 1985; Patterson et al. 1993). This phenomenon was basically explained in the disk instability scheme by that the precession frequency of the eccentric accretion disk decreases due to shrinkage of the disk radius Osaki (1985), or propagation of the eccentric wave to the inner disk Lubow (1992). Elongation of $P_{\rm SH}$ was, however, first observed during the 1995 superoutburst of AL Com (Nogami et al. 1997). Following this discovery, similar behavior has been found in several SU UMa stars: V485 Cen (Olech 1997), EG Cnc (Kato et al. 1997), SW UMa (Semeniuk et al. 1997; Nogami et al. 1998a), V1028 Cyg (Baba et al. 2000), WX Cet (Kato et al. 2001a), and HV Vir (Kato et al. 2001b). These stars are, however, concentrated around the period minimum in the $P_{\rm orb}$ distribution, and SU UMa stars with relatively long $P_{\rm orb}$ have been confirmed to show $P_{\rm SH}$ decrease with a similar rate of $\dot{P}_{\rm SH}/P_{\rm SH}$ $\sim$ $-5 \times 10^{-5}$ (see Kato et al. 2003c). Very recently, Kato et al. (2003c) reported large negative derivatives of $P_{\rm SH}$ in V877 Ara ( $\dot{P}_{\rm SH}/P_{\rm SH}$ $= -1.5(\pm0.2) \times 10^{-4}$ , $P_{\rm SH}$ = 0.08411(2) d) and KK Tel ( $\dot{P}_{\rm SH}/P_{\rm SH}$ $= -3.7(\pm0.4) \times 10^{-4}$ , $P_{\rm SH}$ = 0.08808 d), and pointed out a diversity of $\dot{P}_{\rm SH}/P_{\rm SH}$ in long-period SU UMa-type dwarf novae.

We revealed that $\dot{P}_{\rm SH}/P_{\rm SH}$ in Var73 Dra during the second superoutburst was still about one order of magnitude larger than these two records. Kato et al. (2001a) and Kato et al. (2003c) proposed a possibility that $\dot{P}_{\rm SH}/P_{\rm SH}$ is related to the mass transfer rate: SU UMa stars with larger $\dot{P}_{\rm SH}/P_{\rm SH}$ tend to have larger mass transfer rates, and those with $\dot{P}_{\rm SH}/P_{\rm SH}$ close to and smaller than zero have small $\dot{M}$ . The quite short supercycle length of about 60 d suggests a high $\dot{M}$ in the present object (discussed later), which may support this possiblity. It should be, however, worth noting that Kato et al. (2003a) found $\dot{P}_{\rm SH}/P_{\rm SH}$ $\sim0$ in BF Ara, an SU UMa star supposed to have a rather large $\dot{M}$ .

4.4 Outburst behavior

The three superoutbursts we caught suggests that Var73 Dra steadily repeats superoutbursts with a supercycle of $\sim$ 60 d. This value is shorter than the shorterst one known so far in usual SU UMa stars (89.4 d in BF Ara: Kato et al. 2003a), and close to 19-50 d of ER UMa stars.

The disk instability model predicts that the supercycle is shorter in an SU UMa-type star with a highter $\dot{M}$ . Reproduction of the light curves of ER UM stars was successfully done by Osaki (1995a) by assuming a mass transfer rate about ten times higher than that in ordinary SU UMa stars (see also Osaki 1995b), although it has not still been clear why ER UMa stars have such high mass transfer rate (Nogami 1998). Var73 Dra is expected to also have a very high mass transfer rate because of its extraordinary short supercycle (Ichikawa & Osaki 1994). This condition may be achieved if this star is in the short, high- $\dot{M}$ phase just after getting semi-detached and starting mass transfer. This interpretation provides an explanation to the problem on the evolutionary status of this star that mass transfer is supposed to be stopped (or seriously reduced) for evolution in the period gap in the currently standard evolution theory.

This simple view, however, faces a difficulty of lack of the normal outburst in Var73 Dra. We caught two superoutbursts and two normal outbursts in the course of monitoring. The recurrence cycle of the normal outburst and the supercycle are estimated to be over 13 days and $\sim$ 60 days, respectively. In contrast, the normal-outburst recurrence cycle is expected to be $\sim$ 8 days for an SU UMa star with a supercycle of 60 days based on the model reviewed by Osaki (1996).

The normal-outburst cycle was, however, 7-8 d by Antipin & Pavlenko (2002) from their observations in 2001 August-October. The supercycle at that time was longer than at least 70 d, judging from Fig. 3 in Antipin & Pavlenko (2002). These facts clearly indicate a chage of the outburst activity between 2001 and 2002. Similar changes have been reported in recent years, such as in DI UMa (Fried et al. 1999), SU UMa (Kato 2002; Rosenzweig et al. 2000), V1113 Cyg (Kato 2001), V503 Cyg (Kato et al. 2002), and DM Lyr (Nogami et al. 2003). Among these stars, only DM Lyr showed an anti-correlation: the recurrence cycle of the normal outburst decreased, and the supercycle increased, while Var73 Dra showed a reverse anti-correlation: the recurrence cycle of the normal outburst increased, and the supercycle decreased. Such behavior cannot be explained by variations of the mass transfer rate due to e.g. the solar-type cycle of the secondary star (e.g. Ak et al. 2001). Nogami et al. (2003) proposed for DM Lyr that a machanism to reduce the number of the normal outbursts may work when the superoutbursts more frequently occur and another mechanism to shorten the recurrence time of the normal outburst may work when the superoutburst less frequently takes place. The same idea may be applicable to Var73 Dra. Closer monitoring to avoid to miss rather faint normal outbursts (>15 mag) is needed to check variabilities of the recurrence cycles of the normal outburst and superoutburst.

4.5 Related to ER UMa stars?

Two problems regarding ER UMa stars to be solved are the extraordinary large mass transfer rates for their short orbital periods and the evolution path, as mentioned above. One of the keys to the problems is the discovery of ER UMa counterparts with longer $P_{\rm orb}$ .

Whether Var73 Dra is an object related to ER UMa stars is an interesting subject. While the supercycle of $\sim$ 60 d is certainly very close to those of ER UMa stars, our observations give a negative support to this question in terms of the duty cycle of the superoutburst and the recurrence cycle of the normal outburst. The duration of the superoutburst of Var73 Dra is at most 15 d (Table 1), a normal one for an SU UMa system, and the duty cycle of the superoutburst in one supercycle is $\sim$ 25%, while the duty cycle is 30-50% in ER UMa stars. The normal outburst is 1 or at most a few in one supercycle, quite infrequent for an ER UMa analog.

New interpretations on how ER UMa stars most frequently give rise to superoutbursts have been recently published, which are based on the disk instability scheme, but assuming decoupling of the thermal and tidal instability (Hellier 2001), or the effects of irradiation (Buat-Ménard & Hameury 2002). Both models predict superhumps observed in quiescence. The modulations observed here in quiescence may be superhumps, which could give a solution to the problem that the superhump excess in Var73 Dra is too small for this long $P_{\rm orb}$ . A small mass ratio is, however, a basic assumption in both models. Measurement of the orbital period and the mass ratio in this system has a significant effect also on this matter.

Kato et al. (2003b) discovered a peculiar behavior of superhumps in ER UMa which is a phase shift of 0.5 before entering the plateau phase of the superoutburst. They interpreted that the (normal) superhumps are seen at the very early phase of the superoutburst, and the modulations observed during the plateau phase correspond to "late'' superhumps in SU UMa stars. It is important to trace the superhump evolution throughout a superoutburst, to clarify whether the superhumps in Var73 Dra exhibit the normal SU UMa-type behavior or the ER UMa-type one.

In-the-gap SU UMa-type dwarf nova, Var73 Dra with a supercycle of about 60 days