# Physical Parameters of 11,100 Short-Period ASAS-SN Eclipsing Contact
Binaries

Xu-Zhi Li(李旭志) CAS Key Laboratory for Research in Galaxies and Cosmology,
Department of Astronomy, University of Science and Technology of China, Hefei,
230026, China  School of Astronomy and Space Sciences, University of Science
and Technology of China, Hefei, 230026, China  Qing-Feng Zhu(朱青峰) CAS Key
Laboratory for Research in Galaxies and Cosmology, Department of Astronomy,
University of Science and Technology of China, Hefei, 230026, China  School of
Astronomy and Space Sciences, University of Science and Technology of China,
Hefei, 230026, China  Deep Space Exploration Laboratory, Hefei 230088, China
Xu Ding(丁旭) Yunnan Observatories, Chinese Academy of Sciences, 396
Yangfangwang, Guandu District, Kunming, 650216, Yunnan, 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  Center for
Astronomical Mega-Science, Chinese Academy of Sciences, 20A Datun Road,
Chaoyang District, Beijing 100012, P. R. China  Xiao-Hui Xu(徐小慧)  CAS Key
Laboratory for Research in Galaxies and Cosmology, Department of Astronomy,
University of Science and Technology of China, Hefei, 230026, China  School of
Astronomy and Space Sciences, University of Science and Technology of China,
Hefei, 230026, China  Hang Zheng(郑航)  CAS Key Laboratory for Research in
Galaxies and Cosmology, Department of Astronomy, University of Science and
Technology of China, Hefei, 230026, China  School of Astronomy and Space
Sciences, University of Science and Technology of China, Hefei, 230026, China
Jin-Sheng Qiu(邱锦盛)  CAS Key Laboratory for Research in Galaxies and Cosmology,
Department of Astronomy, University of Science and Technology of China, Hefei,
230026, China  School of Astronomy and Space Sciences, University of Science
and Technology of China, Hefei, 230026, China  Ming-Chao Liu(刘明超) Yunnan
Observatories, Chinese Academy of Sciences, 396 Yangfangwang, Guandu District,
Kunming, 650216, Yunnan, P. R. China  University of the Chinese Academy of
Sciences, Yuquan Road 19, Shijingshan Block, Beijing, 100049, P. R. China

###### Abstract

Starting from more than 11,200 short-period (less than 0.5 days) EW-type
eclipsing binary candidates with the All-Sky Automated Survey for Supernovae
(ASAS-SN) V-band light curves, we use MCMC and neural networks (NNs) to obtain
the mass ratio ($q$), orbital inclination ($incl$), fill-out factor ($f$) and
temperature ratio ($T_{s}/T_{p}$). After cross-matching with the Gaia DR3
database, the final sample contains parameters of 2,399 A-type and 8,712
W-type contact binaries (CBs). We present the distributions of parameters of
these 11,111 short-period CBs. The mass ratio ($q$) and fill-out factor ($f$)
are found to obey log-normal distributions, and the remaining parameters obey
normal distributions. There is a significant period-temperature correlation of
these CBs. Additionally, the temperature ratio (${T_{s}}$/${T_{p}}$) tends to
increase as the orbital period decreases for W-type CBs. There is no
significant correlation between them for A-type CBs. The mass ratio and fill-
out factor ($q-f$) diagram suggest there is no significant correlation between
these two parameters. A clear correlation exists between the mass ratio and
radius ratio. The radius ratio increases with the mass ratio. Moreover, the
deep fill-out CBs tend to fall on the upper boundary of the
$q$$-$${R_{s}}$/${R_{p}}$ distribution, while the shallow fill-out CBs fall on
the lower boundary.

Eclipsing binary stars(444) — Contact binary stars(297) — Fundamental
properties of stars(555)

##  1 Introduction

Contact binary systems (CBs) are close binaries in which both components fill
their Roche lobes and share a common envelope (Kuiper, 1941; Kopal, 1959;
Lucy, 1968a, b). Previous studies have revealed that CBs whose components have
similar temperatures (Kuiper, 1941) are caused by the exchange of energy and
mass transfer through the common envelope (Webbink, 2003; Yakut & Eggleton,
2005).

Most of the eclipsing CBs are EW-type eclipsing binary systems according to
the morphological classification of light curves (Molík, 1998; Li et al.,
2020). Therefore, to understand the formation and evolution of CBs, EW-type
eclipsing binaries are generally studied. The well-known period-luminosity-
color (PLC) relations (Eggen, 1967; Rucinski, 1994; Chen et al., 2016, 2018b;
Mateo & Rucinski, 2017; Jayasinghe et al., 2020a; Qian et al., 2017, 2020) of
CBs are established by using different passband photometric data of EW-type
eclipsing binaries. The PLC relations are different between early- and late-
type CBs (Jayasinghe et al., 2020a), and the PLC relations of different types
of CBs have been extensively studied (Graczyk et al., 2011; Pawlak et al.,
2016; Rucinski, 1994; Chen et al., 2016, 2018a, 2018b; Mateo & Rucinski, 2017;
Jayasinghe et al., 2020a; Qian et al., 2017, 2020). In previous studies,
early-type and late-type CBs are usually separated on the basis of their
period. Late-type CBs generally have a period of less than 0.5 days and are
much more numerous than early-type CBs. Chen et al. (2018a) defined the late-
type CBs to have orbital periods $\log(P/d)\leqslant 0.25$, but Jayasinghe et
al. (2020a) think that a period separation of $\log(P/d)\leqslant 0.30$ is a
better choice. In this paper, we focus on late-type CBs, which are usually
short-period CBs. Currently, statistical studies of CBs (Qian et al., 2017;
Zhang et al., 2019; Sun et al., 2020; Jayasinghe et al., 2020a; Ren et al.,
2021; Latković et al., 2021; Debski, 2022) are becoming increasingly important
thanks to the development of time-domain survey projects, e.g., the Catalina
Sky Survey (CSS; Drake et al., 2009, 2014), the Wide-field Infrared Survey
Explorer (WISE; Wright et al., 2010; Chen et al., 2018b), the Northern Sky
Variability Survey (NSVS; Woźniak et al., 2004; Gettel et al., 2006), the
Asteroid Terrestrial-impact Last Alert System (ATLAS; Heinze et al., 2018; Ren
et al., 2021), the Optical Gravitational Lensing Experiment (OGLE; Udalski et
al., 1992, 1994; Soszyński et al., 2016), the Zwicky Transient Facility (ZTF;
Bellm et al., 2019; Chen et al., 2020), the All-Sky Automated Survey for
Supernovae (ASAS-SN; Pojmanski, 1997; Paczyński et al., 2006; Jayasinghe et
al., 2018, 2019a), and some Space-based surveys like $Hipparcos$ (Esa, 1997) ,
$Kepler$ (Prša et al., 2011; Conroy et al., 2014; Kirk et al., 2016), $TESS$
(Prša et al., 2022) and $Gaia$ (Mowlavi et al., 2017, 2023).

The ASAS-SN (Shappee et al., 2014; Jayasinghe et al., 2018, 2019a, 2019b,
2020b, 2021; Christy et al., 2023) is an automatic time-domain photometric sky
survey project that currently consists of 24 telescopes distributed around the
globe. More details can be seen on the websites 111https://www.astronomy.ohio-
state.edu/asassn/index.shtml. The ASAS-SN photometric down to V $\sim$17 mag
collected $\sim$2000 to over 7500 epochs of V-band observations per field. The
ASAS-SN Variable Stars Database222https://asas-sn.osu.edu/variables has
revealed $\sim$688,000 variable stars, $\sim$78,000 of which are classified
EW-type eclipsing binaries.

In this paper, we use the ASAS-SN V-band photometric light curves of EW-type
eclipsing binaries to study short-period CBs. In section 2, we describe the
sample selection and light curve analysis methods. In section 3, we give the
parameter distribution and some discussion of these CBs. Finally, the summary
and conclusion are presented in section 4.

##  2 Sample Selection and Analysis of the Light Curves

###  2.1 Sample Selection

We used the ASAS-SN Variable Stars Database for target selection (Shappee et
al., 2014; Jayasinghe et al., 2018, 2019a, 2019b, 2020b, 2021). There are a
total of 78,503 EW-type eclipsing binaries in the ASAS-SN Variable Stars
Database. We search the short-period (less than 0.5 days) CB candidates under
the following conditions. Based on the mean magnitude distribution of ASAS-SN
(Jayasinghe et al., 2018), we select targets with mean V-band magnitude less
than 15 mag, this includes the vast majority of targets. We also select
targets with amplitudes greater than 0.2 mag because many ellipsoidal variable
stars have amplitudes less than 0.2 mag and they are often mistaken for low-
amplitude EW-type eclipsing binaries (Dal & Sipahi, 2013; Li & Liu, 2021;
Skarka et al., 2022). The Laflfler-Kinman string length (LkSL) statistic
(Lafler & Kinman, 1965; Clarke, 2002) is a measure of scatter in the light
curve of periodic variables. We used LKSL Statistic $\leqslant$ 0.1 to select
the light curves of EW-type eclipsing binaries with good data quality. The
class probabilities are given by Jayasinghe et al. (2018, 2019a), which are
derived from a random forest classifier. They recommended that a class
probability of $>$ 0.9 is the best classification. Under these conditions, we
selected 11,282 candidate targets. We downloaded ASAS-SN V-band light curve
data from the ASAS-SN Variable Stars Database for these 11,282 targets, of
which 4 targets had no data, and 11,278 targets had valid data.

###  2.2 Neural Network and MCMC Algorithm Model

Due to the development of time-domain photometric survey projects around the
world, a large number of CB light curves have been released. It would be
clearly impractical to use the Wilson-Devinney (Wilson & Devinney, 1971;
Wilson, 1990; Van Hamme & Wilson, 2007; Wilson et al., 2010; Wilson, 2012) or
PHOEBE (Prša et al., 2016) programs to derive the parameters of all these CBs.
Prša et al. (2008) and Ding et al. (2021) used machine-learning methods to
derive the parameters of detached binaries and contact binaries, respectively.
These methods can speed up parameter derivation but cannot obtain the
corresponding parameter errors.

In this work, we use the neural network (NN) and the Markov chain Monte Carlo
(MCMC) algorithm following the work in Ding et al. (2021, 2022) to derive the
parameters of contact binaries. The NN model is trained with a set of light
curves generated by Phoebe and known input parameters. Then, combined with the
MCMC algorithm, the posterior distributions of the parameters can be quickly
obtained. We used Phoebe to generate two sets (with or without the third
light) of synthetic light curves as samples. The third light is one value for
each light curve, representing the effect of the third body on the system as
an equivalent result. In this step, the filter band is set to $V$ because this
work uses the ASAS-SN V-band data. The number of training light curves without
and with the influence of the third light are 346,741 and 344,104,
respectively. We select 10$\%$ of them as the test set. The model without the
influence of the third light achieves a precision of 0.00045 magnitude in
generating the light curves, while the model with the influence of the third
light achieves a precision of 0.0002 magnitude in generating the light curves.
Both models achieve a precision in generating the light curves that is less
than 0.001 magnitude. Then, two models are obtained by training on the two
sets of sample data. These two trained completed models can generate light
curves according to the parameters of the CBs.

###  2.3 Analysis of the Light Curves

We downloaded ASAS-SN V-band light curve data from the ASAS-SN Variable Stars
Database. We also obtained the period and primary eclipse time $T_{0}$. Then,
we phased these data and turned them into phase-magnitude data. To determine
the fundamental photometric parameters of these ASAS-SN short-period CBs, the
light curves were analyzed by using the NNs and MCMC algorithms.

We apply the two obtained models (with or without the third light) to obtain
the parameters of the phased ASAS-SN light curves. Before using the models, we
calculate the temperature for these CBs based on the given period-temperature
relationship by Jayasinghe et al. (2020a) as follow:

$T_{eff}=6598+5260*\log_{10}(P/0.5)K.$ (1)

We use the parameter of goodness-of-fit ($R^{2}$) to evaluate the relevant
results. The goodness-of-fit ($R^{2}$) is calculated based on the light curves
generated by Phoebe and the original phased ASAS-SN light curves. If one
target fits better under the third light model and the luminosity ratio of the
third light

$L_{3}/(L_{1}+L_{2}+L_{3})\geqslant 0.2,$ (2)

we consider the third light present and use the third light fitting model. The
non-third-light model was used for the rest of the cases.

We have listed four example targets, the observations and best-fitting
solutions of the light curves are displayed in Figure 1. We select all targets
with goodness-of-fit ($R^{2}$) greater than 0.8, with a total of 11,145 short-
period ASAS-SN CBs. The sky distribution of the short-period CBs in ASAS-SN,
colored by their period, is shown in Figure 2.

Figure 1: The blue dots represent the phased ASAS-SN light curves. Using the
NNs and MCMC algorithm model to obtain the posterior distribution of the
parameters as the input parameters. The red line represent the light curves
generated by the NNs model with the input parameters. The green X line and
symbol represent the light curves generated by Phoebe using the same input
parameters. Top row: two example targets used the non-third-light model to get
the parameters. Bottom row: two example targets used the third light model to
get the parameters, and the luminosity ratio of the third light are about
68$\%$ and 27$\%$, respectively. Figure 2: Projected distribution of the
11,145 short-period ASAS-SN contact binaries in equatorial coordinates (Hammer
projection). The points are colored by period. The red line indicates the
Galactic plane.

###  2.4 Final sample

Based on the analysis with the machine learning method (NN and MCMC algorithm
model), we obtained the system parameters of ASAS-SN short-period CBs. The
initial effective temperature of the first substar ($T_{1}$) is calculated by
the period-temperature relationship (Jayasinghe et al., 2020a). The orbital
inclination ($incl$), mass ratio ($q$), temperature ratio ($T_{2}/T_{1}$),
fill-out factor ($f$), third light ratio ($l_{3}$) and corresponding errors
are derived by the machine learning method. The relative radii of the two
substars ($r_{1}$, $r_{2}$) and luminosity ratio ($L_{2}/L_{1}$) are
determined by Phoebe.

We define mass ratio as values between 0 and 1, with the more massive star
being the primary star and the less massive star being the secondary star.
Thus, when the derived mass ratio ($q$) is greater than 1, we take the
reciprocal as the final mass ratio. Similarly, the reciprocal of the
temperature ratio $T_{2}/T_{1}$ and luminosity ratio $L_{2}/L_{1}$ should be
$T_{s}/T_{p}$ and $L_{s}/L_{p}$, respectively. The radius $r_{1}$, $r_{2}$
should be exchanged as $R_{s}$, $R_{p}$, and the rest of the parameters do not
need to be changed.

We cross-matched the CBs with Gaia DR3 (Gaia Collaboration et al., 2023) using
a matching radius of 5.0 arcsec to obtain the temperature of the primary stars
($T_{p}$). Finally, we matched a total of 11,111 targets, of which 9,621 could
obtain the temperatures ($T_{eff}$) from Gaia DR3. For the remaining 1490
targets, we still use the calculated temperature by the period-temperature
relationship (Jayasinghe et al., 2020a) as the primary star temperature. The
final parameters for these CBs are given in the attached table in catalog
format. The information listed in Table 1 is an introduction to the contents
of catalog-1.

Table 1: Contents of the catalog-1 with 11,111 CBs Num | Label | Units | Explanations
---|---|---|---
1 | name |  | ASAS-SN Name
2 | RA | $\circ$ | RA (J2000)
3 | Dec | $\circ$ | DEC (J2000)
4 | Period | day | Orbital period
5 | $T_{p}$ | $K$ | Effective temperature of the primary star
6 | $incl$ | $\circ$ | Orbital inclination
7 | $\sigma_{i}$ | $\circ$ |  Uncertainty in $incl$
8 | $q$ |  |  Mass ratio, $q=\frac{m_{s}}{m_{p}}\leqslant 1$
9 | $\sigma_{q}$ |  |  Uncertainty in $q$
10 | $f$ |  |  Fill-out factor. $f=\frac{\Omega_{in}-\Omega}{\Omega_{in}-\Omega_{out}}$,
|  |  |  where $\Omega_{in}$ and $\Omega_{out}$ are the inner and outer Lagrangian surface potential values,
|  |  |  surface potential $\Omega$ $=$ $\Omega_{1}$ $=$ $\Omega_{2}$.
11 | $\sigma_{f}$ |  |  Uncertainty in $f$
12 | $T_{s}/T_{p}$ |  | Temperature ratio
13 | $T_{s}$ | $K$ | Effective temperature of the secondary star
14 | Type |  | CBs subtype classification (A or W)
15 | $R_{p}$ |  | Relative radius of the primary star
16 | $R_{s}$ |  | Relative radius of the secondary star
17 | $L_{s}/L_{p}$ |  | Luminosity ratio
18 | $l_{3}$ |  |  Third light ratio $l_{3}=L_{3}/(L_{1}+L_{2}+L_{3})$
19 | $R^{2}$ |  | Goodness of fit
20 | DR3Name |  | Gaia DR3 ID
21 | $T_{eff}$ | $K$ | Effective temperature from Gaia DR3

##  3 Parameter distribution and Discussion

In the previous section, we obtained physical parameters of 11,111 ASAS-SN
short-period CBs. The physical parameters include orbital period ($Period$),
temperatures of the primary stars and the secondary stars ($T_{p}$, $T_{s}$),
mass ratio ($q$), orbital inclination ($incl$), fill-out factor ($f$),
temperature ratio ($T_{s}/T_{p}$), relative radii of the two substars
($R_{p}$, $R_{s}$), luminosity ratio ($L_{s}/L_{p}$). Here, we show the
distribution of each parameter.

###  3.1 Parameter distribution

Figure 3 show the distribution of orbital periods ($p$), temperature ($T_{p}$,
$T_{s}$), temperature ratio ($T_{s}/T_{p}$), orbital inclination ($incl$),
fill-out factor ($f$), mass ratio ($q$) and relative radius ($R_{p}$, $R_{s}$)
for the 11,111 ASAS-SN short-period CBs. The period distribution of ASAS-SN
short-period CBs peaks at approximately 0.35 d, which is slightly shifted from
the typical distribution of short-period EW-type eclipsing binaries with a
peak at 0.31 d (Qian et al., 2020; Jayasinghe et al., 2020a). This may be
caused by the fact that some short-period ellipsoidal variable stars are
usually classified as EW-type eclipsing binaries. Ellipsoidal variable stars
and low amplitude EW-type eclipsing binaries are not easily distinguished
directly by light curves (Dal & Sipahi, 2013; Li & Liu, 2021; Skarka et al.,
2022). However, in this paper, the selection of our sample with amplitudes
greater than 0.2 mag, which has led to the early exclusion of many ellipsoidal
variable stars that have been misclassified as low amplitude EW-type eclipsing
binaries.

Figure 3: Distribution of orbital periods (period), temperature ($T_{p}$,
$T_{s}$), temperature ratio ($T_{s}/T_{p}$), orbital inclination ($incl$),
fill-out factor ($f$), mass ratio ($q$) and relative radius ($R_{p}$, $R_{s}$)
for the 11,111 ASAS-SN short-period CBs. The period distribution have a peak
around 0.35 d. The temperature distribution of primary and secondary stars
peaks at approximately 5750 $K$ (the red short dashed lines) and 6000 $K$ (the
green short dashed lines), respectively. The orange short dashed lines
represents a temperature ratio of 1, the left side represents the A-type CBs
and the right side represents the W-type CBs. The distributions of the orbital
period, temperature ($T_{p}$, $T_{s}$), temperature ratio ($T_{s}/T_{p}$),
inclination ($incl$) and relative radius ($R_{p}$, $R_{s}$) roughly obey
normal distributions (the blue solid line), the distributions of the mass
ratio ($q$) and the fill-out factor ($f$) obey log-normal distributions (the
red solid line).

The temperature distribution of ASAS-SN short-period CBs peaks at
approximately 5750 $K$ (the red short dashed lines) for the primary star and
6000 $K$ (the green short dashed lines) for the secondary star. The peak of
the secondary star temperature is higher than the peak of the primary star
temperature, as can also be seen from the temperature ratio distribution.
Traditionally, CBs have been classified into two subtypes based on
temperature: A-type and W-type (Binnendijk, 1970). In A-type the more massive
star is hotter, while in W-type the more massive star is cooler. Our sample
contains 2,399 A-type and 8,712 W-type CBs.

The orbital inclination distribution indicates that most CBs have orbital
inclinations larger than $50^{\circ}$, which is likely due to selection
effects, and CBs with high orbital inclination are more easily observed.
Another reason is that our method is more reliable when used to fit targets
with orbital inclinations greater than $50^{\circ}$ (Ding et al., 2021). The
fill-out factor distribution of ASAS-SN short-period CBs indicates that CBs
generally have shallow fill-out. The mass ratio distribution indicates that
both extremely low mass ratio ($q\leqslant 0.1$) and large mass ratio
($q\geqslant 0.7$) CBs are less frequent.

Very interestingly, according to the distribution of these short-period CB
parameters, we find that only the distributions of the mass ratio and the
fill-out factor obey log-normal distributions, while the rest of the
parameters roughly obey normal distributions. We are confident that this is
related to the evolution of contact binaries, but more simulation work is
needed to confirm this.

###  3.2 Period-Luminosity-Color Relations

Figure 4 is a 2D kernel density graph. There is a clear correlation between
the orbital period and the temperature of the primary star. The period-
temperature relationship is actually the well-known period-color relationship
or the so-called period-luminosity-color (PLC) relations (Eggen, 1967;
Rucinski, 1994; Chen et al., 2016, 2018b; Mateo & Rucinski, 2017; Jayasinghe
et al., 2020a; Qian et al., 2017, 2020). Most CBs are located in a banded
region rather than a simple linear PLC. This is related to the evolution of
the common envelope of CBs, where the fill-out factor affects the PLC (Qian et
al., 2020).

Figure 4: The 2D kernel density graph between the orbital period and the
temperature of the primary stars. It is show a clear correlation between the
orbital period and the temperature of short-period CBs (usually are the late-
type CBs), the longer the period, the higher the temperature.

###  3.3 Period and Subtype CBs Evolution

We plot the 2D kernel density graph between the orbital period and the
temperature ratio, as shown in Figure 5. The period-temperature ratio seems to
have some trend of correlation, as shown by the black line with arrows in
Figure 5. As shown in Figure 5, there are far more W-type samples than A-type
samples in the short-period CBs. For A-type CBs, there is no significant
relationship between the temperature ratio and period, similar to a random
distribution; however, for W-type CBs, the temperature ratio tends to increase
as the orbital period decreases. This suggests that the evolution of A-type
CBs is different from that of W-type CBs. Perhaps this could indicate that
A-type CBs may be less evolved and suggest that W-type CBs evolved from A-type
CBs (Li et al., 2020; Zhang et al., 2020). Currently, the formation and
evolution of CBs are still open issues (Yakut & Eggleton, 2005; Gazeas &
Stȩpień, 2008; Li et al., 2007, 2008; Stȩpień, 2009; Yıldız, 2014; Qian et
al., 2017, 2018; Jiang, 2020; Maceroni & van’t Veer, 1996; Awadalla & Hanna,
2005; Eker et al., 2006; Gazeas & Niarchos, 2006; Yildiz & Doğan, 2013).

Figure 5: The 2D kernel density graph between the orbital period and the
temperature ratio. The green short dashed lines represent the temperature
ratio as 1. The upper and lower parts of the short dashed lines represent the
W-type and the A-type CBs, respectively.

Figure 6 shows the correlation between the orbital period and the temperature,
mass ratio, orbital inclination and fill-out factor. This shows that they do
not have a good correlation with the period, except for temperature. In
addition, we find that the temperature, mass ratio, orbital inclination and
fill-out factor are independently distributed from each other. There is no
correlation among them.

Figure 6: The 2D kernel density graph between the orbital period and the
temperature, mass ratio, orbital inclination and fill-out factor. There are no
certain correlations between orbital period with mass ratio, orbital
inclination and fill-out factor.

###  3.4 q-f Diagram

Figure 7 shows the correlation between the mass ratio and fill-out factor of
ASAS-SN short-period CBs. As shown in Figure 3 and discussed in section 3.1,
we find that the distributions of the mass ratio and the fill-out factor obey
log-normal distributions. The correlation between the mass ratio and the fill-
out factor is weak, as shown in Figure 7. However, we can also find much
useful information in the $q-f$ diagram.

In recent decades, there have been several studies on deep, low-mass ratio
contact binaries (DLMRCBs) with mass ratios and fill-out factors of $q<0.25$
and $f>50\%$ (Yang & Qian, 2015; Zhou et al., 2016; Li et al., 2021, 2022),
corresponding to the upper left region in Figure 7. Model calculations suggest
that these DLMRCBs will finally merge into single stars, such as blue
stragglers or FK-Com-type stars (Stepien, 2006; Stępień, 2011). V1309 Sco, the
only observed sample, was a DLMRCB before the merge and was recently found as
a blue straggler (Tylenda et al., 2011; Zhu et al., 2016; Ferreira et al.,
2019). Recently, Gazeas et al. (2021) and Loukaidou et al. (2022) led a
project focusing on DLMRCBs. They find that low mass-ratio systems seem more
likely to eventually merge into single fast-roating stars. Our DLMRCB samples
are located in the upper left region in Figure 7, and they should also be
candidates for merging.

As shown in Figure 7, there is no clear correlation between the mass ratio and
fill-out factor. However, it show the upper limit of the fill-out factor
increases as the mass ratio decreases, as shown by the green solid line in the
figure, which is consistent with our previous results (Li et al., 2020). In
the previous study we had a sample of only 380 $Kepler$ CBs, this time we have
a much larger sample.

We can also see in Figure 7 that there are very few samples in the upper right
region that contain CBs with a deep fill-out factor and high mass ratio
($q>0.25$ and $f>50\%$). The common convective envelope-dominated mechanism
(Liu et al., 2018) can explain the presence of short period, deep fill-out
factor and high mass ratio CBs. According to the CCE-dominated mechanism, $P$
will becomes very short when $f$ is large at a high value of $q$.

Figure 7: The 2D kernel density graph between the mass ratio and fill-out
factor of ASAS-SN short-period CBs. The red horizontal short dashed lines and
vertical short dashed lines represent fill-out factor of 0.5 and mass ratio of
0.25, respectively. The green solid line indicates the trend between mass
ratio ($q$) and fill-out factor ($f$). There are very few sample in the upper
right region, thus CBs with deep fill-out factor, high mass ratio are more
worthy of attention and study.

###  3.5 Mass ratio - radius ratio Relationship

The mass-radius relation ($M-R$) and mass-luminosity relation ($M-L$) of the
primary and secondary stars of CBs have been studied by many authors (Yakut &
Eggleton, 2005; Li et al., 2008; Yildiz & Doğan, 2013; Li et al., 2020;
Latković et al., 2021). The $M-R$ relation of a CB system is significantly
different from that of a single zero main sequence star. An approximate
relation between the radii and masses of the components is
$\frac{R_{s}}{R_{p}}=q^{0.46}$ (Kuiper, 1941), while for the zero main
sequence star the relation is $\frac{R_{s}}{R_{p}}=q^{0.6}$ (Lucy, 1968a).

We used the obtained data to fit the $q$ $-$ ${R_{s}}$/${R_{p}}$ relation, and
the results are shown as the red solid line in Figure 8 as
${R_{s}}$/${R_{p}}$=$q^{0.435}$, which is very close to the results in Kuiper
(1941). The relationship between ${R_{s}}$/${R_{p}}$ and $q$ is monotonically
increasing overall, but with dispersion at all $q$-value locations. We fit the
upper and lower bounds of this region, as shown in the black and magenta solid
lines in Figure 8. The black solid line has a relation of
${R_{s}}$/${R_{p}}$=$q^{0.38}$, while the magenta solid line has
${R_{s}}$/${R_{p}}$=$q^{0.48}$. We find that the upper bound region is the
deep fill-out CBs and the lower bound region is the shallow fill-out CBs. This
suggests that the radius ratio is related to the fill-out factor of CBs for
the same mass ratio (Yakut & Eggleton, 2005).

Figure 8: Mass-radius Relationship of our short-period CBs. The red solid line
represents the best fitting result as ${R_{s}}$/${R_{p}}$=$q^{0.435}$. The
black solid line represents the fitting result as
${R_{s}}$/${R_{p}}$=$q^{0.38}$ for the upper bound, and the magenta solid line
represents the fitting result as ${R_{s}}$/${R_{p}}$=$q^{0.48}$ for the lower
bound. The upper bound region is the deep fill-out CBs and the lower bound
region is the shallow fill-out CBs.

##  4 Summary and Conclusions

In this paper, we present the physical parameters of 11,111 short-period (see
catalog-1) eclipsing contact binaries from the All-Sky Automated Survey for
Supernovae (ASAS-SN) based on a machine learning method with neural networks
(NNs) and Markov chain Monte Carlo (MCMC) algorithms. Based on the Gaia DR3
database, statistical work was performed for these ASAS-SN short-period CBs.
Our main results and conclusions are summarized below.

1\. After cross-matching with the Gaia DR3 database, our final sample
contained 11,111 CBs, with a period less than 0.5 d, they were classified into
two subtypes: 2,399 A-type and 8,712 W-type CBs.

2\. We present the distributions of parameters of these short-period CBs,
where the distributions of the mass ratio ($q$) and fill-out factor ($f$) are
found to obey log-normal distributions, and the remaining parameters obey
normal distributions.

3\. There is a clear correlation between the orbital period and the
temperature of short-period CBs, which is the well-known period-luminosity-
color (PLC) relations.

4\. Different subtypes of CBs seem to have different period and temperature
ratio relationships. For A-type CBs, there is no significant correlation
between the temperature ratio and period, similar to a random distribution;
however, for W-type CBs, the temperature ratio tends to increase as the
orbital period decreases. This likely suggests that the evolution of A-type
CBs is different from that of W-type CBs.

5\. The $q-f$ diagram indicated that there is no significant correlation
between the mass ratio and fill-out factor. However, it can be seen that the
fill-out factor increases as the mass ratio decreases.

6\. The mass ratio - radius ratio ($q$ $-$ ${R_{s}}$/${R_{p}}$) diagram
indicated that there is a clear correlation between the mass ratio and radius
ratio, the radius ratio increases with the mass ratio. And this correlation is
also related to the fill-out factor of CBs, the deep fill-out CBs fall on the
upper boundary of the $q$$-$${R_{s}}$/${R_{p}}$ distribution, while the
shallow fill-out CBs fall on the lower boundary.

This work is supported by the National Key Research and Development Program of
China (2023YFA1608100), the Anhui Provincial Natural Science Foundation
(2308085QA35), the Strategic Priority Research Program of the Chinese Academy
of Sciences (No. XDB 41000000), the China Postdoctoral Science Foundation
(2021M703099) and the Fundamental Research Funds for the Central Universities.
This work made use of data from the ASAS-SN Variable Stars Database
(https://asas-sn.osu.edu/variables). ASAS-SN is funded in part by the Gordon
and Betty Moore Foundation through grants GBMF5490 and GBMF10501 to the Ohio
State University and funded in part by the Alfred P. Sloan Foundation grant
G-2021-14192. This work has made use of the cross-match service
(http://cdsxmatch.u-strasbg.fr/#tab=xmatch&) provided by CDS, Strasbourg.

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<EMAIL_ADDRESS><EMAIL_ADDRESS><EMAIL_ADDRESS>
# Towards View-based Development of Quantum Software

Joshua Ammermann  KIT
Institute of Information Security and Dependability (KASTEL)
Karlsruhe
Germany  Wolfgang Mauerer  Technical University of Applied Sciences Regensburg
and Siemens Technology
Regensburg/Munich
Germany  Ina Schaefer  KIT
Institute of Information Security and Dependability (KASTEL)
Karlsruhe
Germany

###### Abstract

Quantum computing is an interdisciplinary field that relies on the expertise
of many different stakeholders. The views of various stakeholders on the
subject of quantum computing may differ, thereby complicating communication.
To address this, we propose a view-based quantum development approach based on
a Single Underlying Model (SUM) and a supporting quantum Integrated
Development Environment (IDE). We highlight emerging challenges for future
research.

###### keywords:

Quantum Computing, View-based Development, Integrated Development Environment

##  1 Introduction

Quantum computing is an interdisciplinary field that draws upon expertise
ranging from the concrete quantum mechanical effects to the systematic
development of quantum software. Many different stakeholders, each with a
distinct background, are involved, such as mathematicians, physicists,
engineers, and computer scientists. The mental models of stakeholders and
their preferred view on quantum computing and programming may differ, which
presents a significant challenge in terms of interdisciplinary collaboration.
Stakeholders want to work with their preferred view of a quantum program while
being supported by a model- and view-based approach that combines mutual
views.

There are some established concepts and tools that support one or more views
of quantum computing. Such views include mathematical formulas (linear
algebra), quantum circuits, and Quantum Programming Languages (QPLs). Many
QPLs are embedded in a classical host language (e.g., Qiskit is embedded in
Python), so they can reuse its tooling. For other languages such as Q# [Sv18]
a Visual Studio Code plugin is available as part of the Azure Quantum
Development Kit111https://github.com/microsoft/qsharp. While this tooling
provides comfortable editors (e.g., with syntax highlighting), it lacks
support for adequate quantum views other than the QPL. Q-UML [Pé22] extends
the Unified Modeling Language (UML) with quantum elements, such as quantum
classes or variables, but fails to address quantum-specific characteristics
adequately [AY23]. First Integrated Development Environments (IDEs) for
quantum software are under development.
Quirk222https://github.com/Strilanc/Quirk and IBM
Composer333https://quantum.ibm.com/composer both provide a circuit editor,
while IBM Composer has an additional OpenQASM / Qiskit view, but only supports
one-way-editing for Qiskit code. The QuantumPath IDE [HPP22] provides disjoint
annealing, circuit, and code editors. The Classiq IDE [Mi22] provides a high-
level description in a quantum modeling language that can be synthesized into
circuits, but this is merely a unidirectional transformation. Thus, existing
IDEs still mostly support only one-way-editing / unidirectional
transformations between views. These are not sufficient to support a
collaborative workflow between an interdisciplinary group of stakeholders.

In classical software engineering, a model is an abstraction of a real system
towards specific aspects of interest. Model-based techniques use models as the
central artifact, facilitating the creation of domain-specific views and
languages [WB23]. View-based development techniques allow the organization and
generation of different views through the use of a (Virtual) Single Underlying
Model (V-SUM) [Me20]. A V-SUM ensures consistency of underlying model(s) and
derived views, and enables collaborative editing. These techniques are being
adopted in interdisciplinary fields, such as cyber-physical systems [Re23],
and appear suitable for addressing the needs of the interdisciplinary field of
quantum computing.

A comprehensive approach to view-based development of quantum software is yet
to be established. Such an approach enables stakeholders to view and edit
different views, which will be held consistent automatically. Thus, the
research challenge is: How can a view-based approach to quantum software
development be defined and realized?

##  2 View-based Quantum Development Approach

Figure 1: View-based Quantum Development approach relying on a Q-SUM

We propose a View-based Quantum Development approach based on the V-SUM to
comprise different views of quantum computing suitable for stakeholders with
varying backgrounds. Fig. 2 shows the approach based on the Quantum Single
Underlying Model (Q-SUM), a V-SUM [Me20] tailored for quantum software, as the
central artifact. This model contains cross-disciplinary information such as
mathematical descriptions, quantum circuits, and program code. The Q-SUM
allows information to be kept consistent between views, while quantum-specific
views can be created dynamically via projection. Also, only the integration
into the Q-SUM is required, for instance, when adding support for a new QPL.
Quantum Assembly (QASM) can be used as an interface to quantum compilers that
handle optimization for the specific quantum hardware. This approach reuses
existing concepts from view- and model-based development and takes advantage
of their benefits.

Figure 2: Vision of an IDE for the View-based Quantum Development approach

##  3 Quantum IDE for the View-based Quantum Development Approach

A View-based Quantum Development approach requires tool support in order to be
applicable in practice. We propose a Quantum IDE based on the Q-SUM for the
collaborative view-based development of quantum software. Fig. 2 depicts how
we envision such an IDE. A rich circuit editor 1 and QPL editor 2 should be
provided for editing of quantum circuits and quantum program code
respectively. Our IDE addresses open research questions in quantum software
identified by [AY23]: encapsulation, abstraction, modularity, and quantum
platform independence. Standard gates and more complicated building blocks of
quantum software (e.g., a diffusion operator) could be accessed from a library
3. The creation of user-defined blocks and the composition of building blocks
should also be possible. An inspector 4 should provide a mathematical
description and allow configuration of the mapping of connections (e.g.,
quantum variables as parameters) for a selected building block. The execution
5 of the modeled quantum software on quantum hardware and the simulation and
inspection of the system state at different points in time should be
supported. For this constraints on the simulation and execution of quantum
software must be considered. The IDE vision is a representative example based
on currently employed means of abstraction, but finding appropriate
abstractions is an important part of the endeavor. For example, one might
consider a diagrammatic language [Co10] alternatively to the circuit
representation.

##  4 Research Challenges

Realizing this View-based Quantum Development approach with a supporting IDE
will require solving the following research challenges: The conceptual
challenge is the design of the Q-SUM that manages the consistency of different
views of quantum software based on existing view- and model-based
technologies. To design such a model, it is necessary to identify and analyze
the various possible views, and their respective benefits and drawbacks. The
design has to be extensible to integrate existing and future QPLs and support
design patterns, best practices, modularity, and compositionality.
Implementation challenges are the design and implementation of the IDE using a
selection of state-of-the-art tooling, and the integration of external quantum
simulators and interfaces to quantum hardware. For the evaluation of the
Q-SUM, use case scenarios have to be defined and the capabilities of the
approach have to be evaluated against them. Finally, a user study with domain
experts should be conducted to rate the usability of our approach and its
supporting IDE.

## Acknowledgements

This work has been supported by the German Ministry for Education and Research
in project QuBRA under Grant No.: 13N16303, and in TAQO-PAM under Grant No.:
13NI6092.

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