1
No.101

May 2022

ISSN 0917-2211

Variable Star Bulletin
Negative superhumps in the eclipsing Z Cam + VY Scl star ES Dra
Taichi Kato1
tkato@kusastro.kyoto-u.ac.jp
1 Department of Astronomy, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japan

Received 2022 May 02

Abstract
I analyzed All-Sky Automated Survey for Supernovae (ASAS-SN) Sky Patrol data of ES Dra and classiﬁed it to be a Z Cam star with VY Scl-type fading episodes. An analysis of Transiting Exoplanet Survey
Satellite (TESS) observations showed that this object shows shallow eclipses and that the orbital period is0.17749895(17) d. Negative superhumps with a period of 0.167830(2) d and the beat phenomenon between the
period of negative superhumps and the orbital period were detected in the TESS data between 2020 January
and March. The orbital proﬁle systematically varied depending on the beat phase and eclipses were missing
in some phases. The eclipses in ES Dra were grazing and the disk was probably not eclipsed in some phases
depending on the orientation of the tilted disk. These observations added a support to the interpretation of
the precessing, tilted disk as the origin of negative superhumps. Negative superhumps disappeared 4 d before
the VY Scl-type fading started. It was likely that the mass-transfer rate quickly dropped when negative superhumps disappeared and the decline of the total luminosity of the disk took 4 d. This provides a measurementof the time-scale of the response of the disk against a sudden decrease of the mass transfer in a VY Scl star.
Although one of standstills in ES Dra was terminated by brightening, the identity of ES Dra as an IW And
star would require further events.

1

Introduction

ES Dra was originally selected as a ultraviolet-excess object (PG 1524+622) and was conﬁrmed to be a cataclysmic
variable (CV) by spectroscopy (Green et al. 1986). The orbital period (Porb ) and the nature of this object has
much been disputed. Andronov (1991) reported weak detections of the periods 1.07(8), 0.53(3) and 0.125(3) d.
Andronov (1991) suggested a characteristic time-scale of 0.10–0.13 d. Although Ringwald (1993) suggested a spectroscopic orbital period of 0.179 d, it was ﬁnally published in Ringwald and Velasco (2012). Misselt and Shafter(1995) could not detect variations at the reported Porb from observations on two nights. In the meantime, Tonny
Vanmunster detected periods of 0.064(8) and 0.121(6) d during the 2001 June outburst.1 Combined with observations by Jerry Foote, Vanmunster claimed to detect superhumps with a period of 0.1267(20) d and ES Dra wasonce considered as an SU UMa-type dwarf nova above the period gap. Baklanov et al. (2001) reported ∼20-dvariations with an amplitude of 1.6 mag. Baklanov et al. (2001) suggested that the object is a novalike variable.
Ringwald and Velasco (2012) published a radial-velocity study giving Porb =0.17660(6) d and a spectral typeof M2±1 for the secondary. Ringwald and Velasco (2012) used American Association of Variable Star Observers(AAVSO) observations and concluded it to be a Z Cam star after the identiﬁcation of standstills in 1995 and2009. Simonsen et al. (2014) reached the same conclusion by showing a standstill in 2012 January to August.
1 <https://www.cbabelgium.com/cv_2001/Dra_ES_jun_2001.html>.

2

Table 1: Orbital period of ES Dra from TESS data
Interval BJD−2400000
58711–58737
58738–58763
58870–58982
59419–59446
59607–59636

2

TESS sector
S15
S16
S21–24
S41
S48

Period (d)0.17746(4)0.17750(2)0.177491(8)0.17752(1)0.17749(2)Amplitude (mag)
0.006
0.015
0.013
0.014
0.008

Long-term variation

I used All-Sky Automated Survey for Supernovae (ASAS-SN) Sky Patrol data (Shappee et al. 2014; Kochanek et al.
2017) and I conﬁrmed that ES Dra is indeed a Z Cam star (vsnet-chat 8114).2 Although the 2017 standstill was
terminated by brightening (outburst), not by fading as in ordinary Z Cam stars (see e.g. Szkody and Mattei
1984), the importance of this ﬁnding was not recognized at that time. In 2020, I noticed two fading episodes(2019 August and 2020 April) in the ASAS-SN data and concluded that this object is a Z Cam + VY Scl star(vsnet-chat 8473).3 This classiﬁcation has been adopted in AAVSO Variable Star Index (VSX: Watson et al.
2006). The long-term behavior based on the ASAS-SN data is shown in ﬁgures 1 and 2.

3

Orbital period and proﬁleI also analyzed Transiting Exoplanet Survey Satellite (TESS) observations (Ricker et al. 2015).4 The full lightcurve is available at the Mikulski Archive for Space Telescope (MAST5 ). I used six high level science products(HLSP) sectors between 2019 August 15 and 2022 February 25 (ﬁgures 3, 4). I obtained Porb for diﬀerent statesusing the Phase Dispersion Minimization (PDM, Stellingwerf 1978) method after removing long-term trends by
locally-weighted polynomial regression (LOWESS: Cleveland 1979). The errors of periods by the PDM method
were estimated by the methods of Fernie (1989) and Kato et al. (2010). The results are shown in table 1. A
PDM analysis of the entire segments as a whole did not yield a unique period. This was due to the variation of
the orbital proﬁle as discussed later. Shallow eclipses were seen following the orbital hump in S16, S21–24 andS48 and I obtained a unique period of 0.1774992(2) d after combination of these segments. The orbital period
was reﬁned using the Markov-Chain Monte Carlo (MCMC)-based method introduced in Kato et al. (2010). The
resultant ephemeris is
Min(BJD) = 2459148.9510(7) + 0.17749895(17)E.
(1)
As will be shown later, this object showed negative superhumps between 2020 January and March and theorbital proﬁle was variable depending on the presence/absence of negative superhumps. The mean orbital proﬁlesin diﬀerent states are shown in ﬁgure 5. When negative superhumps were completely absent, the orbital proﬁlewas that of a dwarf nova with a shallow eclipse showing an orbital hump at phase 0.8 (S16, S41 and S48). When
negative superhumps were prominent, the hump moved to a diﬀerent phase (S21–23 NSH). This result would,
however, give a somewhat artiﬁcial impression since the amplitudes of negative superhumps were larger thanthose of orbital humps and the hump phase deﬁned by Porb may not be very adequate. This curve, however,indicates that the eclipses were present at the correct orbital phase even during the phase of negative superhumps
and conﬁrms the validity of Porb determined in this study. This variation of the proﬁle was the reason why a
PDM anlysis of the entire data set did not yield a unique Porb . The S15 and S24 curves in this ﬁgure correspondto the epochs when the object experienced fading episodes (ﬁgure 2). It was most likely that the disk shrunk andeclipses disappeared. The orbital proﬁle resembled that of ellipsoidal variation, consistent with a VY Scl star in
low state.

2 <http://ooruri.kusastro.kyoto-u.ac.jp/mailarchive/vsnet-chat/8114>.
3 <http://ooruri.kusastro.kyoto-u.ac.jp/mailarchive/vsnet-chat/8473>.
4 <https://tess.mit.edu/observations/>.
5 <http://archive.stsci.edu/>.

3

13
14
15
16
17
18
56350
13

56400

56450

56500

56550

56600

56650

56700

56750

14
15
16
17
18

56800

56850

56900

56950

57000

57050

57100

57150

13
14
15
16
17
18

57200

57250

57300

57350

57400

57450

57500

57550

57600

13
14
15
16
17
18

57650

57700

57750

57800

57850

57900

57950

58000

Figure 1: Long-term light curve of ES Dra using ASAS-SN V -band data (1). Both states with dwarf nova outbursts and standstills were recorded. The long standstill starting on BJD 2457406 was terminated by brightening(arrow in the fourth panel).

4

13
14
15
16

18

ASAN−SN g

ASSN−SN V

17
58050

58100

58150

58200

58250

58300

58350

58400

58450

13
14
15
16
17

S15 S16

18
58450
13

58500

58550

58600

58650

58700

58750

58800

58850

14
15
16
17
18

NSH
S21 S22 S23 S24
58900

58950

59000

59050

59100

59150

59200

59250

13
14
15
16
17
18

S41
59300

59350

59400

59450

S48
59500

59550

59600

59650

59700

Figure 2: Long-term light curve of ES Dra using ASAS-SN data (2). Two fading episodes following standstills
are shown by the arrows. The horizontal bars represent TESS sectors. The red horizontal bar represents theinterval when negative superhumps (NSH) were present in the TESS data.

5

S15

13.4
13.6
13.8
14.0
14.2
58715

58720

58725

58730

58735

13.6

S16

13.8
14.0
14.2
14.4
58740

58745

58750

58755

58760

58765

14.6

S21

14.8
15.0
15.2
15.4
58870

58875

58880

58885

58890

13.8

58895

S22

14.0
14.2
14.4
14.6
58900

58905

58910

58915

58920

58925

Figure 3: TESS light curve of ES Dra (1). The data were binned to 0.01 d. The numbers following S represent
the TESS sector numbers. The magnitudes were deﬁned as −2.5 log10 (ﬂux/15000) + 10. Beat phenomenon witha period of 3 d was present in S21 and S22.

6

14.0

S23

14.2
14.4
14.6
14.8
58930

58935

58940

58945

58950

58955

13.4

S24

13.6
13.8
14.0
14.2
58955

58960

58965

58970

58975

58980

S41
13.8
14.0
14.2
14.4
59420

59425

59430

59435

59440

59445

S48

13.4
13.6
13.8
14.0
59610

59615

59620

59625

59630

Figure 4: TESS light curve of ES Dra (2). See ﬁgure 3 for explanation.

59635

7

0.00

S15

S16

0.05

S21−23 (NSH)

S24
0.10

S41+48

−0.4

−0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Figure 5: Mean orbital proﬁles of ES Dra. The ephemeris in equation (1) was used. The numbers following S
represent TESS sector numbers (see ﬁgure 2). S21–23 (NSH) represents the interval when negative superhumps
were detected. S24 includes a short segment of S23 when negative superhumps were absent.

84Negative superhumps

A PDM analysis of the segment BJD 2458870–2458940 yielded a period of negative superhumps of 0.167830(2) d.
The beat period with Porb (3.08 d) is clearly visible in the TESS light curve (ﬁgure 6). The variation of orbital
proﬁles depending on the beat phase (i.e. orientation of the disk to the observer assuming a tilted disk) is shownin ﬁgure 7. Although eclipses were present in most beat phases, they were not apparent for ϕ=0.50–0.75.
The fractional superhump deﬁcit for negative superhumps is ϵ− = −5.4%, which is a typical value for this Porb
(Wood et al. 2009). It is widely believed that negative superhumps arise from the variable release of the potential
energy when accreting on a precessing, tilted disk (Wood et al. 2000; Murray et al. 2002; Wood and Burke 2007).
Recent detailed analysis of Kepler observations provided a strong support to this interpretation (Kimura et al.
2020; Kimura and Osaki 2021). ES Dra showed a clear beat phenomenon and this is also a support to theprecessing, tilted disk as the origin of negative superhumps. A similar case has also been reported using TESS
observations of LS Cam (Stefanov 2022; Rawat et al. 2022). Eclipses in ES Dra are grazing and the secondary
only eclipses the outermost part of the disk. The absence of eclipses in for ϕ=0.50–0.75 suggests that the partof the disk facing the secondary was most distant from the secondary when the secondary passes in front of thedisk in this beat phase and was most diﬃcult to eclipse. This variation of the eclipse depth depending on thebeat phase also supports the precessing, tilted disk as the interpretation of negative superhumps.
The disappearance of negative superhumps when the object entered the low state was probably caused by thedecrease of the mass-transfer rate. Negative superhumps disappeared 4 d earlier than the fading episode started(see ﬁgure 8). It was possible that the mass-transfer rate quickly dropped and the spot on the disk disappeared
4 d before the total luminosity of the disk started to decline.

5

System parameters and absolute magnitude

Assuming a standard Roche-ﬁlling secondary, the mass of the secondary (M2 ) is expected to be 0.35M⊙ (Knigge2006). The spectral type (M3.3) is in agreement with M2±1 by Ringwald and Velasco (2012). The whitedwarf in ES Dra is not expected to be particularly massive as judged from the absence of high excitation lines(Ringwald and Velasco 2012). Assuming an average-mass white dwarf (M1 =0.81M⊙ ) for CVs (Pala et al. 2022),
the mass ratio is expected to be q = M2 /M1 = 0.43. The K1 velocity of the primary is expected to be 112 km
s−1 . Assuming that the disk of ES Dra in high state (in standstill) has a radius reaching the tidal truncation
radius0.60
rtidal =(2),
1+q
in unit of the binary separation (A) (Paczyński 1977), and assuming an optically thick standard disk, the observed
eclipse could be best modelled by an inclination of i=62.0±0.5◦ . This value is most dependent on the disk radius
and i=64◦ is the best for a disk radius of 0.38A.
The K velocity of the emission (Kem =134±11 km s−1 ) in Ringwald and Velasco (2012) is slightly larger thanthe value expected for these system parameters. If the emission line exactly traces the motion of the primary(Kem = K1 sin i), the best parameters are M1 =0.53M⊙ and i=61◦ . It is well-known that such an ideal case israrely achieved, and we would better rely on the ﬁrst solution until M1 or q is independently measured.
Using Gaia EDR3 (Gaia Collaboration et al. 2021), the absolute magnitude MV at standstill (in average) is+5.7 and peaks of dwarf nova outbursts reach +4.9. For an object with i=61–64◦ , the eﬀect of inclination[]
3∆Mv (i) = −2.5 log10 (1 + cos i) cos i ,(3)2
is 0.19–0.35 mag. By adopting i=62.0◦ , the corrected MV for standstill and outburst peak are +5.5 and +4.7,
respectively.

6Standstill terminated by brightening

The phenomenon of a standstill terminated by brightening (outburst) in 2017 May is a signature of an IW And
star (Simonsen 2011; Hameury and Lasota 2014; Kato 2019). As described in Kato (2019), typical IW And stars
show a tendency of recurrence of this phenomenon which is frequently followed by a dip and subsequent damping
oscillations. Such a cycle has not been yet apparent in ES Dra and it would be interesting to see whether this

9

14.1

14.2

14.3

14.4
58898

58900

58902

−0.2

0.0

58904

58906

58908

0.6

0.8

58910

58912

−0.02

0.00

0.02

−0.4

0.2

0.4

1.0

1.2

1.4

Figure 6: Negative superhumps in ES Dra. (Upper:) Example of TESS light curve. Both short-period modulations (negative superhumps) and the 3-d beat period were present. (Lower:) Proﬁle of negative superhumps.
The zero phase and the period were deﬁned as BJD 2458905.118 and 0.167830 d, respectively.

10

φ=0.00−0.250.0

φ=0.25−0.50

0.1

0.2

φ=0.50−0.75

φ=0.75−1.00

0.3

0.4

−0.4

−0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Figure 7: Variation of orbital proﬁles of ES Dra during the phase of negative superhumps. The beat phases ϕwere determined using the epoch of BJD 2458905.118 (see ﬁgure 6) and the beat period of 3.08096 d. The orbital
phases were deﬁned by equation (1).

11

14.2
14.4
14.6
14.8

58930

58935

58940

58945

58950

58930

58935

58940

58945

58950

0.020
0.015
0.010
0.005
0.000

Figure 8: Light variation and amplitude of negative superhumps when ES Dra entered a VY Scl-type low state.
(Upper:) TESS light curve. (Lower:) Amplitude of negative superhumps. The values were obtained for 3-dsegments considering the beat phenomenon. The amplitude reached almost zero on BJD 2458943. The fading
started on BJD 2458947.

12
object shows cyclic behavior in future as in typical IW And stars or the 2017 May event was a sporadic one andits resemblance to the IW And-type phenomenon was superﬁcial.

Acknowledgements
This work was supported by JSPS KAKENHI Grant Number 21K03616. The author is grateful to the ASAS-SN
and TESS teams for making their data available to the public. I am grateful to Naoto Kojiguchi for helping
downloading the TESS data.

List of objects in this paper
IW And, Z Cam, LS Cam, ES Dra, SU UMa, VY Scl

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e-mail: skiyotax@gmail.com