1

No.85

Nov. 2021

ISSN 0917-2211

Variable Star Bulletin
Periodic modulations during a long outburst in V363 Lyr
Taichi Kato1
1

Department of Astronomy, Kyoto University, Sakyo-ku, Kyoto 606-8502, Japantkato@kusastro.kyoto-u.ac.jp
Received 2021 Nov. 14
Abstract

I analyzed the Kepler long and short cadence data of V363 Lyr. A period of 0.185723(8) d was persistently
detected and this is identiﬁed as the orbital period. V363 Lyr showed one long outburst accompanied byan “(embedded) precursor” during Kepler observations and modulations with a period of 0.1956(2) d, longer
than the orbital one, were detected during this outburst. There are two possible interpretations of thisperiod. The ﬁrst one is superhumps despite that V363 Lyr is far above the period gap. This interpretation
requires an evolved, undermassive secondary enabling a low mass ratio of q=0.15. The evolution of this longperiod variations, however, does not follow the standard evolution of superhumps. The second one is that theprecursor occurred when the disk reached the tidal truncation radius, as inferred from observations of IW And
stars. In this case, the long-period variations could be interpreted as a variable stream impact on a precessing
eccentric disk, which may have been formed by disturbances at the tidal truncation radius. This might lead toeﬀective removal of the angular momentum which resulted in 0.3–0.4 mag brightening following the precursor.
The fractional period excess suggests that q is just above the stability limit of the 3:1 resonance. In either
cases, the nature of the secondary and the mass ratio need to be veriﬁed by spectroscopic observations.

1

Introduction

V363 Lyr is a dwarf nova discovered by Hoﬀmeister (1967). Galkina and Shugarov (1985) studied this object
photographically. Although both authors suggested high frequency of outbursts, the interval (∼21.4 d) was ﬁrst
conﬁdently measured by CCD observations by Kato et al. (2001). Liu et al. (1999) spectroscopically conﬁrmed
this object to be a cataclysmic variable (CV). This object is included in the Kepler ﬁeld (Borucki et al. 2010;
Koch et al. 2010) and was observed as a Kepler target as KIC 7431243. Ramsay et al. (2014) reported an analysisof the 5.2 d segment and detected two periods of 4.68 hr and 4.47 hr, which I will discuss in this paper.

2

Data Analysis

The data analysis was performed practically in the same way as in Osaki and Kato (2013a,b): I used twodimensional Fourier analysis for detecting the signals and examined O − C diagrams to detect variation of theperiods.
Two sets of Kepler data for V363 Lyr are publicly available: quarter 15 (Q15) short cadence (SC) and Q16
long cadence (LC) data. Since the Q15 observations (in quiescence) covered only for 5.3 d, I primarily used thisquarter for conﬁrming the period detected in Q16. The Q16 data contained ﬁve short outbursts and one longoutburst.

2

3

Results

3.1

Identiﬁcation of two periods

I present the result of period analysis only around the frequencies of these periods. There is no candidate
frequency outside this frequency region. The results of the Fourier analysis is shown in ﬁgure 1. Two major
signals were present. These signals corresponds to the periods detected by Ramsay et al. (2014).
I examined the stability of the signal at 5.38 c/d. Almost all the segments (4 d in width), both in quiescenceand in outburst, showed the constant phase and almost constant amplitude (in ﬂux) of this 5.38-c/d signal (ﬁgure2). I conclude that this signal was coherent during the Kepler observation, and identiﬁed it to be the orbital
period (Porb ). A phase dispersion minimization (PDM: Stellingwerf 1978) analysis of the combined data set of
Q15 and Q16 yielded a period of 0.185723(8) d (ﬁgure 3). The error was estimated by methods of Fernie (1989)
and Kato et al. (2010).
A two-dimensional Fourier analysis (ﬁgure 1) clearly indicates that another signal around frequencies 5.0–
5.2 c/d was especially strong around the long outburst. Since the frequency of this signal is lower (i.e. the period
is longer) than that of Porb . Hereafter I call this signal P+ . A two-dimensional PDM analysis is also shown inﬁgure 1. In the case of V363 Lyr, PDM analysis gave a better result than least absolute shrinkage and selection
operator (Lasso: Tibshirani 1996; Kato and Uemura 2012; Kato and Maehara 2013) analysis employed in Osaki
and Kato (2013b) due to the non-sinusoidal nature of the signal and small number of points in the LC data.
The resolution of PDM analysis is intermediate between Fourier transform and Lasso analysis, and this result
can be treated as a slightly degraded version of Lasso analysis presented in Osaki and Kato (2013b) [see also anapplication of a two-dimensional PDM analysis to superhumps in Kato et al. (2021b)]. It looks like that P+ wassometimes weakly excited outside the long outburst. No evidence of the negative superhump was detected.

3.2

Development of P+

The long outburst had a shoulder (precursor) followed by a brighter outburst. This phenomenon in SS Cyg stars
is also referred to as an “embedded precursor” by Cannizzo (2012). During the precursor, humps recurring with
Porb were recorded. After BJD 2456352 (two days after the peak), P+ humps appeared.
I measured the times of maxima of these humps in the light curve by the template ﬁtting method described in
Kato et al. (2009) after removing the trend of the outburst by locally-weighted polynomial regression (LOWESS:
Cleveland 1979). I used the raw light curve (without subtraction of the orbital signal) in ﬁgure 4. The times ofmaxima are listed in table 1. As shown in ﬁgure 4, the variations during the precursor can be identiﬁed as theorbital signal. After the precursor, the object brightened by 0.3–0.4 mag. No clearly periodic variations weredetected for 2 d. The amplitudes of P+ were small (∼0.04 mag) and there was no signiﬁcant variation of theperiod. The proﬁle of P+ was slightly asymmetric (ﬁgure 6).

4Discussion

4.1

Comparison with superhumps in SU UMa stars

As we have seen, V363 Lyr showed both the orbital signal and the P+ signal longer than Porb during the long,bright outburst. These P+ variations may look similar to superhumps in SU UMa stars, which have periods a
few percent longer than Porb and are considered to arise from the precession of an eccentric accretion disk whose
deformation is excited by the 3:1 resonance (Whitehurst 1988; Hirose and Osaki 1990; Lubow 1991).
There are, however, a number of features diﬀerent from superhumps in ordinary SU UMa stars. They are:
• The orbital period is too long [0.185723(8) d] for a typical SU UMa star [see e.g. Warner (1995) for classicalstatistics], although some long-Porb dwarf novae are classiﬁed as SU UMa stars (see e.g. Kato et al. 2021a).
• The ratio between the durations of the long outburst (12 d for the entire outburst, 6 d after the long period
appeared) and other outbursts (5 d) is small compared to other SU UMa stars.
• Superhumps in SU UMa stars usually show O − C variations (Kato et al. 2009). P+ in V363 Lyr, however,
did not show such a variation.
• In many SU UMa stars, superhumps start to appear during the precursor (Osaki and Kato 2013a,b). In
V363 Lyr, P+ appeared much later (2 d after the end of the precursor).

3

16

17

18

19

6.0
5.8
5.6
5.4

Porb

5.2
5.0
4.8
6.0
5.8
5.6
5.4

Porb

5.2
5.0
4.8
56320

56330

56340

56350

56360

56370

56380

56390

Figure 1: Two-dimensional power spectrum of the Kepler long cadence light curve of V363 Lyr. (Upper:) Kepler
Light curve. (Middle:) Power spectrum. The width of the sliding window and the time step used are 5 d and
0.5 d, respectively. A Hanning window function was used. A signal (P+ ) with a period longer than Porb appeared
during the long outburst. (Lower) Two-dimensional PDM analysis. The width of the sliding window and thetime step used are 5 d and 0.5 d, respectively. Dark colors represent signals (lower θ in the PDM statistics).
The orbital signal was present except during the long outburst. The signal of P+ was strongest during the longoutburst.

4(BJD−2400000)
56307 (Q)1000

56326 (S)56332 (Q)800

56338 (S)56344 (Q)600

56353 (L)56361 (Q)56366 (S)400

56371 (Q)56376 (S)200

56381 (Q)56387 (S)

0
−0.5

0.0

0.5

1.0

1.5

Figure 2: Variation of the proﬁle of the 5.38-c/d signal. Each phase-averaged light curve was constructed from
4-d Kepler observations centered on the dates shown in the ﬁgure. The phase= 0 and period were deﬁned as BJD
2456351.979 and 0.185723 d, respectively. The days 56307, 56332, 56344, 56361, 56371 and 56381 correspond toquiescence (Q in the ﬁgure); the days 56326, 56338, 56366, 56376 and 56387 correspond to short outbursts (S).
The day 56353 corresponds to the long outburst (L). Only except during the long outburst, the 5.38-c/d signal
was detected with a constant phase and almost constant amplitudes (in ﬂux).

5

1.0

Θ

0.9

0.8

0.7

4.8

5.0

5.2

5.4

5.6

5.8

40

20

0

−20

−40
−0.4

−0.2

0.0

0.2

0.4

0.6

0.8

1.0

1.2

1.4

Figure 3: PDM analysis of V363 Lyr of the entire data. Upper: PDM analysis. The sharp signal at 0.18572 d is
Porb . Lower: mean proﬁle of the orbital signal.

6

Original

16.0

16.5

After subtractionof the orbital signal

17.0

17.5

56348

56350

56352

56354

56356

Figure 4: Long outburst of V363 Lyr. The light curve of original observations (upper) and the light curve after
subtraction (in ﬂux) of the mean orbital signal are shown. The latter light curve was shifted by 0.5 mag. This
long outburst had a shoulder (precursor) followed by a brighter outburst. Semi-regular variations were visible
during the precursor, which can be interpreted as the orbital signal. Two days after the object reached the peakbrightness, P+ humps appeared.

7

−20

0

20

40

60

80

0.06

0.04

0.02

0.00

−0.02

0.10
0.08
0.06
0.04
0.02
0.00

16

17

18

19

344

346

348

350

352

354

356

358

360

362

Figure 5: O − C diagram of humps during the long outburst in V363 Lyr. (Upper:) O − C diagram. The maxima
for E ≤ 8 refer to the orbital signal (see text). P+ appeared around E = 20. I used a period of 0.19585 d for
calculating the O −C residuals. (Middle:) Amplitudes of P+ humps. (Lower:) Light curve. The data were binned
to 0.065 d.

8

θ
1.0

0.8

0.6

0.4

P=0.19560

0.2
0.175

0.180

0.185

0.190

0.195

0.200

0.205

0.210

(d)

−0.05

0.00

0.05

−0.5

0.0

0.5

1.0

1.5

Figure 6: PDM analysis of V363 Lyr during the long outburst when long-period variations were apparent (BJD
2456352–2456356.5). Upper: PDM analysis. I analyzed 100 samples which randomly contain 50% of observations
and the result is shown as a form of 90% conﬁdence intervals in the resultant PDM θ statistics. The signal at
0.1956 d corresponds to P+ . Lower: mean proﬁle of P+ variations.

9

Table 1: Times of maxima in V363 Lyr during the long outburst
E
max∗
error
O − C†
N‡
0 56347.8869
0.00810.03518
1 56348.0537
0.00500.006570.01072 56348.2533
0.00217
3 56348.4395
0.00270.00168
4 56348.6354
0.00640.00228
5 56348.8280
0.0027−0.00067
6 56349.0188
0.0060−0.00518
7 56349.2000
0.0069−0.01938−0.02497
8 56349.3897
0.004420 56351.7762
0.00580.0175
7
21 56351.9316
0.0088−0.02248
22 56352.1433
0.0075−0.0060
8
23 56352.3538
0.01280.00918
24 56352.5455
0.00870.0055
6−0.01148
25 56352.7240
0.002926 56352.9225
0.0071−0.00828
27 56353.1165
0.0040−0.00967
28 56353.3083
0.0129−0.01317
29 56353.5087
0.0037−0.00818
30 56353.6995
0.0068−0.01268−0.00348
31 56353.9040
0.005432 56354.1002
0.0099−0.00268
33 56354.3044
0.00260.0063834 56354.4917
0.0075−0.0018835 56354.6966
0.00840.0078836 56354.8981
0.00480.014080.013337 56355.0928
0.00508
38 56355.2868
0.01100.01207
39 56355.4779
0.00580.0077840 56355.6742
0.00490.0087
741 56355.8557
0.0036−0.0052742 56356.0531
0.0032−0.00317∗
BJD−2400000.
†
Against max = 2456347.8519 + 0.195341E.
‡
Number of points used to determine the maximum.

10

4.2

Can P+ be growing superhumps?

In many SU UMa-type dwarf novae, superhumps start to appear during the precursor (if there is a precursor)
or a few to several days after the start of the superoutburst (if there is no precursor). This reﬂects when the
3:1 resonance starts to develop (Osaki 2005). During this growing phase of superhumps, superhump periods(PSH ) are longer and this phase is referred to as stage A (Kato et al. 2009). It is interpreted that during thegrowing phase of superhumps, the eccentric part of the disk is conﬁned to the region near the 3:1 resonance(Osaki and Kato 2013b; Kato and Osaki 2013) and that the period reﬂects the dynamical precession rate at the
3:1 resonance. As the region of the eccentric part reaches the inner part of the disk, the pressure eﬀect slows
down the precession rate (stage B). In many SU UMa-type dwarf novae, stage B superhumps are seen near the
peaks of superoutbursts.
P+ in V363 Lyr has a period of 0.1956(2) d (ﬁgure 6), which is 5.3% longer than Porb . This period corresponds
to a fractional superhump excess in frequency ϵ∗ ≡ 1 − Porb /PSH = 0.0514(10). If we consider that P+ variationsin V363 Lyr reﬂect the dynamical precession rate at the 3:1 resonance, this value corresponds to a mass ratio of
q=0.152(3) (Kato and Osaki 2013). The mass of the secondary inferred from this mass ratio is too small for an
object with Porb =0.18572 d. The mass, MV and MK ofthe secondary for this period on the standard evolutionary
sequence of CVs are 0.39M⊙ , +10.2 and +5.9, respectively (Knigge 2006). Even a Chandrasekhar-mass whitedwarf gives q=0.28, which cannot explain the observation.
There remains a possibility that the secondary in V363 Lyr is undermassive for Porb . Such a system shouldhave an evolved secondary such as QZ Ser (Thorstensen et al. 2002), CRTS J134052.1+151341 (Thorstensen 2013)
and ASASSN-18aan (Wakamatsu et al. 2021). The quiescent absolute magnitudes of V363 Lyr are MV =+7.5 andMK =+4.4 [using 2MASS (Cutri et al. 2003) and Gaia parallax (Gaia Collaboration et al. 2021)]. These values arebrighter than those of main-sequence stars on the standard evolutionary sequence of CVs, and the secondary inV363 Lyr may indeed be evolved. For comparison, quiescent absolute magnitudes are MV =+10.5 and MK =+7.2
for QZ Ser, MV =+8.4 and MK =+5.9 for CRTS J134052.1+151341 and MV =+8.4 and MK =+6.0 for ASASSN18aan. If the secondary is indeed evolved in V363 Lyr, P+ might be attributed to superhumps arising from the 3:1
resonance. If this is the case, the diﬀerence in the behavior of superhumps from other SU UMa stars would require
an additional explanation since the corresponding q value is normal for an SU UMa star and textbook evolutionof superhumps is expected. Spectroscopic determination of the secondary type and radial-velocity measurements
are needed.

4.3

Could P+ be stream impact on a precessing eccentric disk?

Since P+ was seen during the middle-to-late phase of the outburst, this variation might be attributed to (traditional) late superhumps (Haefner et al. 1979; Vogt 1983; van der Woerd et al. 1988), which arise from the stream
impact on an eccentric disk.
The dynamical precession rate of an eccentric disk can be obtained by the method in Hirose and Osaki(1990); Kato and Osaki (2013) and the disk radius can be estimated by equating the theoretical precession ratewith the observed ϵ∗ . The results for various q values are listed in table 2. I used the formula of the tidal
truncation radius
0.60(1)
rtidal =1+q
in Paczyński (1977). and Lubow-Shu (or circularization) radiusrLS = 0.488q −0.464(2)from Lubow and Shu (1975). The value q=0.15 corresponds to subsection 4.2 (assuming that P+ is growing or
stage A superhumps). The values q=0.25 or q=0.30 correspond to the limit of the 3:1 tidal instability. The value
q=0.476 corresponds to a secondary star on the standard evolutionary sequence of CVs (Knigge 2006) and an
average-mass white dwarf 0.82M⊙ in CVs (Zorotovic et al. 2011).
In cases for q < 0.30 the radius of the 3:1 resonance is inside rtidal and the tidal instability due to the
3:1 resonance can occur. In these cases, an eccentric disk is expected to form by the tidal instability andthe identiﬁcation P+ as (traditional) late superhumps is possible. This interpretation, however, requires an
explanation why ordinary superhumps before the appearance of late superhumps were not observed. In all cases,
the estimated radii are far outside rLS and they are achievable. For q > 0.30, however, eccentric deformation of
the disk by the 3:1 resonance is not expected and there is a need for a diﬀerent mechanism.

11

Table 2: Disk radius estimated from the precession rateq
Disk radius∗ Truncation radius∗ Radius of 3:1 resonance∗
0.15
0.462
0.52
0.459
0.20
0.413
0.50
0.453
0.25
0.377
0.48
0.447
0.30
0.348
0.46
0.441
0.35
0.325
0.44
0.435
0.476†
0.283
0.41
0.422
∗
Unit: binary separation.
†
Assuming a standard secondary and an average mass white dwarf.

4.4

Lubow-Shu radius∗
0.118
0.103
0.093
0.085
0.079
0.069

Possible deformation of the disk for a high-q system

If the true mass ratio is too large to hold the 3:1 resonance within the tidal truncation radius, V363 Lyr is not an
SU UMa star. Kato and Hambsch (2021) recently proposed an interpretation that embedded precursors in longoutbursts of SS Cyg stars may correspond to a phenomenon when the disk radius reaches the tidal truncation
radius. This interpretation originated from direct observations of the variation of the disk radius (M. Shibata et
al. in preparation) in an IW And star (Simonsen 2011; Kato 2019). If this is indeed the case in the precursor
in V363 Lyr, P+ may be a previously undescribed phenomenon which is excited when the disk reaches the tidal
truncation radius. In IW And stars, standstills are terminated by brightening and this would require a mechanismof eﬀective removal of angular momentum at the tidal truncation radius (see Kimura et al. 2020; Kato et al. 2021b;
M. Shibata et al. in preparation). It would not be surprising if intersections of orbits in the disk near the tidal
truncation radius (Paczyński 1977) cause disturbances and lead to eccentric deformation of the disk (which isdesired for the late-superhump type interpretation) and eﬀective removal of the angular momentum. As seen intable 2, the estimated disk radius is much smaller than rtidal for larger q values. This mechanism to produce
P+ would only be acceptable in V363 Lyr for a narrow range of q which does not allow the 3:1 resonance to occur
but enables the disk radius suﬃciently close to rtidal . Brightening by 0.3–0.4 mag after the precursor in V363
Lyr is probably the result of eﬀective removal of the angular momentum (just as in superoutburst in SU UMastars, Osaki 1989), and P+ observed in V363 Lyr could be a manifestation of the disturbances around the tidal
truncation radius.

Acknowledgments
I thank the Kepler Mission team and the data calibration engineers for making Kepler data available to the
public. This work was supported by JSPS KAKENHI Grant Number 21K03616.

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VSOLJ
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Editor Seiichiro Kiyota
e-mail: skiyotax@gmail.com