# Photometric analysis of the dwarf nova SU UMa based on TESS

Wei Liu<EMAIL_ADDRESS>Xiang-Dong Shi  Xiao-Hui Fang  Qi-Shan Wang  Yunnan
Observatories, Chinese Academy of Sciences, P.O. Box 110, Kunming 650216, P.R.
China  University of Chinese Academy of Sciences, No.1 Yanqihu East Rd,
Huairou District, Beijing 101408, P.R. China  Key Laboratory of the Structure
and Evolution of Celestial Objects, Chinese Academy of Sciences, P.O. Box 110,
650216 Kunming, P.R. China  School of Mathematics, Physics and Finance, Anhui
Polytechnic University, Wuhu 241000, P.R. China

###### Abstract

We report the photometric analysis of SU UMa based on the observations of the
Transiting Exoplanet Survey Satellite (TESS). TESS has released a large amount
of data, which contains the light curves of a complete superoutburst and three
normal outbursts of SU UMa. Based on the observations, the evolution of
superhumps during the superoutburst was analyzed. By using the O - C method,
the three stages were determined, and the superhump period for each stage was
calculated. The mass ratio $q=0.137(1)$ was estimated based on the stage A
superhump method. A periodic oscillation with a period of 2.17(9) days was
found in the superhump minimum O - C diagram, which is related to the
precession of the accretion disk. We investigated the frequency information of
quasiperiodic oscillations (QPOs) in the light curves. An ultralong period QPO
of 0.18 days at the time of normal outburst and two ultralong periods QPOs of
0.19 days and 0.285 days in quiescence were found. No QPO was found in the
superoutburst.

###### keywords:

photometric , dwarf novae , binary star , stars: individual (SU UMa)

††journal: New Astronomy

##  1 Introduction

Cataclysmic variables (CVs) are semicontact binary systems that contain a
white dwarf and a red dwarf (Warner, 2003). Dwarf novae (DNe) is a subtype of
nonmagnetic CVs that is currently the most abundant subgroup. The red dwarf
fills its Roche lobe and transfers mass to the white dwarf via the inner
Lagrange point. The transferred mass will form a disk around the white dwarf.
In magnetic CVs, due to the strong magnetic field of the white dwarf, the
transferred mass is trapped and moves along the magnetic field lines to reach
the poles of the white dwarf, so a complete accretion disk will not form.

SU Ursae Majoris (SU UMa) is the prototype star for a subgroup of DNe with an
orbital period of $0.07635(4)$ days (Thorstensen et al., 1986). It was thought
to be a noneclipsing binary with V magnitudes ranging from 11.3 to 15.7(Ritter
and Kolb, 2003). The mass ratio and the mass of its two components are not yet
known. Based on the ultraviolet spectra of the International Ultraviolet
Explorer, Zead et al. (2017) estimated an accretion rate of approximately
$9.8\times 10^{-13}M_{\odot}yr^{-1}$.

SU UMa-type dwarf novae (SU UMa stars) with orbital periods below the period
gap (2-3 h) show superoutbursts and normal outbursts. The outburst cycles of
SU UMa stars are indefinite. Superoutbursts last approximately ten days and
are longer than normal outbursts but have less frequency. The mechanism of
superoutbursts is considered to be the combination of disk instability and
tidal instability, which is different from normal outbursts(Osaki, 1989). A
superoutburst is usually triggered by a normal outburst. The outburst
mechanism of normal outbursts in SU UMa stars is the same as that of U Gem
stars, which are described by disk instability model (Osaki, 1974; Lasota,
2001) or mass transfer instability model (Bath, 1975). The tidal instability
of accretion disks is caused by a resonance between the orbiting secondary
star and disk particle orbits with a 3:1 period ratio (Hirose and Osaki,
1990).

Superhumps are periodic brightness variations in SU UMa stars with periods a
few percent longer than the orbital period. They generally appear during the
plateau of superoutbursts, which originate from the resonance between the
elliptical disk and binary orbit (Whitehurst, 1988). According to the
envolution of the superhump period ($P_{sh}$) of SU UMa stars, Kato et al.
(2009) divided superhumps into three distinct stages: a longer superhump
period in the early envolutionary stage (stage A), varying periods in the
middle stage (stage B), and a shorter superhump in the final stage (stage C).
They later developed the stage A superhump method to estimate the mass ratio
of binary stars based on their superhump period of stage A and orbital period
(Kato and Osaki, 2013). Based on the photometric observations of the April
1989 superoutburst of SU UMa, Udalski (1990) discovered superhumps with a
period of 113.4 min (0.07875 d) during the late stages of the superoutburst.
The January 2010 superoutburst was observed by Kato et al. (2010), but only a
mean period of stage B of 0.07907(3) d was obtained. Unlike superhumps,
negative superhumps are periodic light modulations with a period a few percent
shorter than the orbital period, which has not been detected in SU UMa. They
originate from a retrogradely precessing tilted accretion disk and are
produced by the transit of the accretion steam impact spot across the face of
the tilted disk (Wood and Burke, 2007). Superhumps are slightly similar to
negative superhumps, but the mechanisms of their generation are completely
different. Imada et al. (2012) discovered superhumps in a normal outburst in
January 2012.

The intervals of superoutbursts (supercycles) are longer than those of normal
outbursts. SU UMa exhibits normal outbursts at intervals generally ranging
from 5–33 days, and the supercycle is approximately 160 days (Patterson, 1979;
Szkody and Mattei, 1984; Imada et al., 2013). Superoutbursts are unpredictable
and last from ten to dozens of days, so it is difficult to obtain their
complete light curve. Supercycles can also reflect the material transfer rate
from the companion to the accretion disk.

Quasiperiodic oscillations (QPOs) are a common phenomenon in the light curves
of CVs (Patterson et al., 1977). They are short-time-scale modulations in
light curves that refer to the luminosity variation with time ranging from 50
to 1000 seconds (Woudt and Warner, 2002). QPOs are difficult to recognize
because of their low coherence and short coherence time. In previous studies,
based on ground-based telescopes, the QPOs during quiescence and normal
outbursts in SU UMa were discussed. A QPO with period of $\sim 0.0481(4)$ days
during the rising stage of a normal outburst was found (Imada et al., 2013).
Since no superoutburst was observed, their discussion was not comprehensive
enough.

In this paper, we present light curve studies of SU UMa. Section 2 introduces
the observations and data of SU UMa. Section 3 shows the analysis of the
evolution of the superhump during the superoutburst. Based on this, we
constrained some system parameters of this system. The O - C analysis of the
superhump minimum is presented in Section 4. QPOs and their variations are
investigated and discussed in Section 5. Section 6 contains a conclusion.

##  2 The observations and data

The data were taken from the Transiting Exoplanet Survey Satellite (TESS)
(Ricker et al., 2015). The main mission of TESS is to search for exoplanets
via transit detection. Many outbursts of DNe were observed. Continuous
monitoring allows us to study the properties of superhumps better than ground-
based telescopes. The photometric observations by TESS were described in
barycentric julian date (BJD) and the flux of electron/s. The data were
downloaded from the Mikulski Archive for Space Telescopes (MAST) data archive
111https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html. Two sectors’
data were obtained from 25 December 2019 to 19 January 2020 and from 31
December 2021 to 27 January 2022 with a cadence time of 120 seconds. Every
sector has a one-day gap for transferring data back. The detectors attached to
TESS are sensitive from 600 nm to 1000 nm. SAP data were adopted in this work.
To identify the amplitude of outbursts and superhumps more easily, we
transferred the SAP flux to the relative magnitude and set the magnitude in
quiescence to 0. All light curves of SU UMa are shown in the top panel of Fig.
1. The light curves of a complete superoutburst and 3 normal outbursts are
observed, and two shoulders occur at the presuperoutburst. The interval
between the peaks of the later two consecutive normal outbursts is 15 days.

Figure 1: The top panel shows light curves from TESS, which are shown in
relative magnitude and Barycentric Julian Date (BJD). The relative magnitude
was calculated by the formula $\Delta mag=-2.5log_{10}(sap\\_flux)+6$. Panels
a, b, c, and d show the enlargement of the data in each rectangle marked in
the top panel after the removal of global trend . The orbital phases were
calculated by the orbital period 0.07635 .

##  3 Analysis of Superhump maxima

Superhumps can always be seen during superoutbursts of SU UMa stars. The 2020
January superoutburst was completely observed by TESS except for a one-day gap
(see Fig. 2). The superoutburst lasts approximately 19.5 days with an
amplitude of approximately 2.5 magnitude, which is 3 times longer than a
normal outburst. We removed the superoutburst trend in the light curve by
using the locally weighted scatter plot smoothing (LOWESS) method. According
to the detrended light curves, the changes in amplitude of superhumps can be
viewed directly (as panel b of Fig. 2). The superhump takes approximately one
day from its appearance to full amplitude , remains for approximately two
days, and then begins to decrease and gradually disappear.

Table 1: Superhump period of SU UMa Stage | E | BJD-2457000 | Period (d) | error(d)
---|---|---|---|---
A | 0-20 | 1846.80-1848.45 | 0.08013 | 0.00004
B | 20-72 | 1848.45-1852.55 | 0.07920 | 0.00002
C | 73-100 | 1852.55-1854.86 | 0.07886 | 0.00004

Using the quadratic polynomial fitting method, we obtained the light maximum
times of superhumps. only the light maximum times from BJD 2458846 to 2458854
were taken because of the low signal-to-noise ratio at the beginning and end
of the superoutburst. Based on the generalized Lomb-Scargle method (Lomb,
1976; Scargle, 1982; Press and Rybicki, 1989), the mean period of the
superhumps was derived as 0.079281(1) days. The ephemeris of superhumps can be
written as

$T_{max}=BJD2458846.8326(11)+0.079281(1)\times E,$ (1)

where BJD2458846.8326(11) is the initial epoch, and E is the cycle number of
superhumps. According to the ephemeris and the light maximum times, the O - C
values were obtained.

The O - C diagram is shown in panel c of Fig. 2. After a linear correction,
typical stages A, B, and C appear in panel d of Fig. 2. According to the
linear fit, the mean superhump period was revised to 0.079164(9) days. Stages
A, B, and C can be clearly distinguished from this O - C diagram (as
identified in Fig.2). Table 1 lists the information of each stage. The
evolution of the superhumps can also be seen in Fig.3. After the superhump
reaches its full amplitude, it gradually shows a second hump after cycle 40,
as seen in Fig.3 as well as in panel c of Fig.1. Two purple lines in Fig.3
show the trend of the light maximum phases with cycles. The trend corresponds
to stages A, B, and C as the O - C distribution in panel d of Fig.2.

The stage A superhump method proposed by Kato and Osaki (2013), a dynamical
method that relies only on celestial mechanics, was adopted to calculate the
mass ratio. Using the orbital period and the stage A superhump period, the
fractional superhump excess in frequency is

$\epsilon^{\ast}=1-\frac{P_{orb}}{P_{sh}},$ (2)

where $P_{orb}$ is orbital period and $P_{sh}$ is superhump period. For stage
A, $P_{sh}=0.08013(4)$, $\epsilon^{\ast}=0.04717(4)$ . The dynamical
precession rate, $\omega_{dyn}$ in the disk can be expressed by (see Kato et
al. (2016)):

$\frac{\omega_{dyn}}{\omega_{orb}}=\frac{q}{\sqrt{1+q}}[\frac{1}{4}\frac{1}{\sqrt{r}}b_{3/2}^{(1)}]$
(3)

where $r$ is the dimensionless radius measured in units of binary separation
$a$ and $q$ is the mass ratio (M2/M1). $\frac{1}{2}b_{s/2}^{(j)}$ is the
Laplace coefficient

$\frac{1}{2}b_{s/2}^{(j)}=\frac{1}{2\pi}\int_{0}^{2\pi}\frac{cos(j\phi)d\phi}{(1+r^{2}-2rcos\phi)^{2}}.$
(4)

During stage A, it is considered that the superhump wave is confined to the
3:1 resonance, and $r$ can be described as

$r_{3:1}=3^{(-2/3)}(1+q)^{-1/3}.$ (5)

This $\omega_{dyn}/\omega_{orb}$ is equal to the fractional superhump excess
in frequency ($\epsilon^{\ast}$). According to these equations, the mass ratio
of $q=0.137(1)$ is derived.

The orbital period-mass ratio relation of CVs is shown in Fig. 4. The black
dashed line and red line represent the standard and revised evolution tracks
of CVs (Knigge et al., 2011). The blue dots represent other CVs, the data of
which are listed in Kato (2022). As the mass ratio $q$ of SU UMa derived
above, we put the data of SU UMa on this picture. As seen from the figure, the
q-value is slightly lower than the model predictions. SU UMa is in the middle
stage of the evolution of a short-period ($P_{orb}$ below the period gap) CV
and evolving toward a shorter orbital period. It will take a long time to
evolve to its period minimum.

Based on the semiempirical donor tracks proposed by Knigge et al. (2011) and
the orbital period, the donor mass was estimated as $0.138(1)M_{\odot}$. With
$q=0.137(1)$ , the mass of the white dwarf is estimated to be
$M_{1}=1M_{\odot}$.

Figure 2: The panel a shows light curve of the superoutburst, and the red line
represents the superoutburst trend. The relative magnitude was caculated by
the formula $\Delta mag=-2.5log_{10}(sap\\_flux)+6$. Panel b shows the
detrended light curve, we can see the amplitudes variation from the panel
directly. Panel c shows the O - C diagram of the superhumps and the linear fit
of the O - C data. Panel d shows the revised O - C diagram of the superhumps.
Figure 3: The superhump phase is calculated by equation 1 and shifted
afterward by 0.5 phases. The color bar represents the superhump cycle. Two
purple lines show the trend of the maximum with cycles. The trend corresponds
to stages A, B, and C. Figure 4: Mass ratio–period relation of CVs. The blue
points shown are mass ratio and period form literature (Kato, 2022). The data
of the red dot is obtained in this work. The black dashed line shows the
standard model for CV evolution. The red solid line shows the evolution of
donor properties along the revised model track (Knigge et al., 2011).

##  4 Analysis of Superhump minimum

The superhumps show clear superhump minima in the plateau of the superoutburst
from BJD 2458847 to 2458858.7, which last approximately 11.7 days and longer
than the superhump maxima (8 days). They show a much higher signal-to-noise
ratio (SNR) than the superhump maxima and disappear much later. As shown in
panel c of Fig. 1, the superhump minimum profile changes with the outburst,
which rapidly disappears in the postsuperoutburst stage. A high SNR superhump
minimum was selected as the initial epoch of the ephemeris. According to the
quadratic polynomial fitting method, the times of superhump minima were
obtained. We obtained a mean period of 0.079252 days by the light minima
times. Taking the mean period, the ephemeris can be written as follows:

$T_{min}=BJD2458847.03549(9)+0.079252\times E.$ (6)

From the equation, the O - C diagram was obtained, which is shown in the
bottom panel of Fig. 5.

The O - C diagram shows a downward parabolic shape, and a sinusoidal variation
occurs from BJD 2458848.5 to 2458853. The superhump minima O - C diagram is
similar to that of the superhump maxima; both are parabolic with an opening
downward, except that the superhump minima O - C exhibits a distinct
sinusoidal variation at the peak of the superoutburst. The variation lasts
approximately $4.5$ days which is shorter than the duration of the superhumps.
We used a sine function to fit the variation, and a period of 2.17(9) days was
obtained.

Precession of the accretion disk widely occurs during superoutbursts of SU UMa
stars with a period of several days. The O - C variation occurs at the time of
accretion disk precession, and the cycle is similar, which implies that the O
- C variation period (2.17(9) days) may be due to the precession of the disk.
To verify whether this variation is related to precession, we calculated the
period of precession using the orbital period ($P_{orb}=0.07635$) and the mean
superhump period ($P_{sh}=0.079164(9)$ days) given above. According to the
formula,

$\frac{1}{P_{prec}}=\frac{1}{P_{orb}}-\frac{1}{P_{sh}},$ (7)

the period of precession is derived as $P_{prec}=2.15$ days, which is only
0.02 days shorter than the O - C variation. Considering the variation in the
period of the superhump and precession , we believe that the 2.17(9)-day
variation is related to the precession of the accretion disk. The O - C method
may be a new tool to determine the period of precession.

##  5 Investigation of quasiperiodic oscillations

QPOs are obvious during outbursts in some CVs (e.g., EM Cyg (Liu et al., 2021)
and HS 2325+8205 (Sun et al., 2023)), but not obvious during quiescence. They
are mostly on the order of tens of seconds to thousands of seconds. QPOs are
presented in the light curves of SU UMa clearly, as shown in panel d in Fig.
1. In particular, it is obvious in quiescence but not in outbursts.

To investigate QPOs in the light curves, the generalized Lomb-Scargle method
(Lomb, 1976; Scargle, 1982; Press and Rybicki, 1989) was adopted. The light
curves in quiescence from BJD 2459585 to 2459593 and in normal outburst from
BJD 2459580 to 2459585 were used to detect the QPOs. Before producing the
Lomb-Scargle periodogram, the light curves were detrended by the LOWESS
method. In normal outbursts, the trend of the outbursts in the light curve
should be removed. In the quiescence, there is still the overall trend in the
light curve that needs to be removed, as seen in the top panel of Fig. 1. The
periodograms and detrended light curves are shown in Fig. 6. The periodgrams
show two peaks at 0.285 and 0.19 days in quiescence and the strongest peak at
0.18 days in a normal outburst. We also conduct QPO detection on other
quiescence and outbursts of these light curves, and the results are basically
the same. At the time of the superoutburst, the QPO was not detected. The
amplitude of the QPO in quiescence is significantly higher than that in normal
outbursts. The QPO signal of 0.18 days in the normal outbursts is close to the
0.19-day signal in quiescence. Their mechanisms of generation may be the same,
and both quiescence and normal outbursts are present in this system. The QPO
of 0.285 days exists only at the time of quiescence, which is approximately 4
times the orbital period. The mechanism by which they arise is currently
unclear. These QPOs mainly appear in quiescence and disappear in outbursts,
their timescales are much longer than those of previous QPOs, and their
amplitudes are larger.

Figure 5: The top panel shows the compete superoutburst and the LOWESS fit of
the light curve. The relative magnitude was caculated by the formula $\Delta
mag=-2.5log_{10}(sap\\_flux)+6$. The middle panel shows the Residuals of the
LOWESS fit, we can see the variation of the amplitude from the panel directly.
The bottom panel shows the O - C analysis of the superhump minima, and the
green line is the sine fit of the O - C variation. Figure 6: The left and
right top panels show the detrended light curve in quiescence and a normal
outburst, respectively. The bottom panels show the Lomb-Scargle periodogram
derived by using the Corresponding light curve in the top panel.

##  6 Conclusion

Superoutbursts of SU UMa have been observed many times (e.g., Szkody and
Mattei (1984); Udalski (1990); Kato et al. (2010)), but only a partial light
curve of a superoutburst has been obtained, and the evolution of the superhump
during the superoutburst cannot be well studied. It is difficult to observe a
complete light curve of a superoutburst, and due to the TESS mission, we were
able to obtain such high-precision and continuous light curves. Based on the
light curves of SU UMa observed by TESS, we analyzed the evolution of
superhumps during the 2019 December superoutburst, which shows typical stages
A, B, and C. We derived a mean superhump period of 0.079164(9) days and a
stage A superhump period of 0.08013(4) days. The mass ratio $q=0.137(1)$ is
estimated by the stage A superhump method. The donor mass and white dwarf mass
are estimated as $M_{2}=0.138(1)M_{\odot}$ and $M_{1}=1M_{\odot}$,
respectively.

We also investigated the period evolution of the superhump minimum by the O -
C method, and the distribution of O - C shows a parabolic shape with an
opening downwards, which is slightly different from that of the superhump
maxima O - C diagram. A periodic oscillation with a period of 2.17(9) days
exists at the top of the parabola. Using the relationship among $P_{prec}$,
$P_{sh}$ and $P_{orb}$, we verified that 2.17(9) days coincides with the
precession cycle and that the 2.17(9)-day oscillation is related to the
precession. This shows that the O - C method may be a new tool to obtain the
period of precession.

QPOs were found in quiescence and normal outbursts, but not in the
superoutburst. An ultralong period of 0.18 days of QPO was found at the time
of a normal outburst, and two ultralong periods of QPOs of 0.19 days and 0.285
days were found in quiescence. These QPOs are unexpected because they have
longer periods and higher amplitudes and are more pronounced in quiescence.

## Acknowledgements

This work was supported by the National Natural Science Foundation of China
(Nos. 11933008, 12103084), and the basic research project of Yunnan Province
(Grant No. 202301AT070352), and the Natural Science Foundation of Anhui
Province (2208085QA23). This paper includes data collected by the TESS
mission, which are publicly available from the Mikulski Archive for Space
Telescopes (MAST). Funding for the TESS mission is provided by the NASA
Science Mission Directorate.

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