Negative superhumps in the eclipsing Z Cam + VY Scl star ES Dra

ES Dra was originally selected as a ultraviolet-excess object (PG 1524$+$622) and was confirmed to be a cataclysmic variable (CV) by spectroscopy (Green et al. 1986). The orbital period ($P_{\rm orb}$) 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 $P_{\rm orb}$ 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.¹¹1 $<$https://www.cbabelgium.com/cv_2001/Dra_ES_jun_2001.html$>$. Combined with observations by Jerry Foote, Vanmunster claimed to detect superhumps with a period of 0.1267(20) d and ES Dra was once considered as an SU UMa-type dwarf nova above the period gap. Baklanov et al. (2001) reported $\sim$20-d variations 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 $P_{\rm orb}$=0.17660(6) d and a spectral type of M2$\pm$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 and 2009. Simonsen et al. (2014) reached the same conclusion by showing a standstill in 2012 January to August.

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).²²2 $<$http://ooruri.kusastro.kyoto-u.ac.jp/mailarchive/vsnet-chat/8114$>$. 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).³³3 $<$http://ooruri.kusastro.kyoto-u.ac.jp/mailarchive/vsnet-chat/8473$>$. 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.

I also analyzed Transiting Exoplanet Survey Satellite (TESS) observations (Ricker et al. 2015).⁴⁴4 $<$https://tess.mit.edu/observations/$>$. The full light-curve is available at the Mikulski Archive for Space Telescope (MAST⁵⁵5 $<$http://archive.stsci.edu/$>$. ). I used six high level science products (HLSP) sectors between 2019 August 15 and 2022 February 25 (figures 3, 4). I obtained $P_{\rm orb}$ for different states using 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 and S48 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

$${\rm Min(BJD)}=2459148.9510(7)+0.17749895(17)E.$$

(1)

As will be shown later, this object showed negative superhumps between 2020 January and March and the orbital profile was variable depending on the presence/absence of negative superhumps. The mean orbital profiles in different states are shown in figure 5. When negative superhumps were completely absent, the orbital profile was 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 than those of orbital humps and the hump phase defined by $P_{\rm orb}$ 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 $P_{\rm orb}$ 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 $P_{\rm orb}$. The S15 and S24 curves in this figure correspond to the epochs when the object experienced fading episodes (figure 2). It was most likely that the disk shrunk and eclipses disappeared. The orbital profile resembled that of ellipsoidal variation, consistent with a VY Scl star in low state.

A PDM analysis of the segment BJD 2458870–2458940 yielded a period of negative superhumps of 0.167830(2) d. The beat period with $P_{\rm orb}$ (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 shown in figure 7. Although eclipses were present in most beat phases, they were not apparent for $\phi$=0.50–0.75.

The fractional superhump deficit for negative superhumps is $\epsilon^{-}$ = $-$5.4%, which is a typical value for this $P_{\rm orb}$ (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 the precessing, 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 $\phi$=0.50–0.75 suggests that the part of the disk facing the secondary was most distant from the secondary when the secondary passes in front of the disk in this beat phase and was most difficult to eclipse. This variation of the eclipse depth depending on the beat 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 the decrease 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.

Assuming a standard Roche-filling secondary, the mass of the secondary ($M_{2}$) is expected to be 0.35$M_{\odot}$ (Knigge 2006). The spectral type (M3.3) is in agreement with M2$\pm$1 by Ringwald and Velasco (2012). The white dwarf in ES Dra is not expected to be particularly massive as judged from the absence of high excitation lines (Ringwald and Velasco 2012). Assuming an average-mass white dwarf ($M_{1}$=0.81$M_{\odot}$) for CVs (Pala et al. 2022), the mass ratio is expected to be $q=M_{2}/M_{1}=0.43$. The $K_{1}$ 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 radius

$$r_{\rm tidal}=\frac{0.60}{1+q},$$

(2)

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$\pm$0.5^∘. This value is most dependent on the disk radius and $i$=64^∘ is the best for a disk radius of 0.38$A$.

The $K$ velocity of the emission ($K_{\rm em}$=134$\pm$11 km s^-1) in Ringwald and Velasco (2012) is slightly larger than the value expected for these system parameters. If the emission line exactly traces the motion of the primary ($K_{\rm em}=K_{1}\sin i$), the best parameters are $M_{1}$=0.53$M_{\odot}$ and $i$=61^∘. It is well-known that such an ideal case is rarely achieved, and we would better rely on the first solution until $M_{1}$ or $q$ is independently measured.

Using Gaia EDR3 (Gaia Collaboration et al. 2021), the absolute magnitude $M_{V}$ 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

$$\Delta M_{v}(i)=-2.5\log_{10}\left[(1+\frac{3}{2}\cos i)\cos i\right],$$

(3)

is 0.19–0.35 mag. By adopting $i$=62.0^∘, the corrected $M_{V}$ for standstill and outburst peak are $+$5.5 and $+$4.7, respectively.

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

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.

IW And, Z Cam, LS Cam, ES Dra, SU UMa, VY Scl

We provide two forms of the references section (for ADS and as published) so that the references can be easily incorporated into ADS.