Vol.0 (200x) No.0, 000–000

11institutetext:  Department of Astronomy, Beijing Normal University, Beijing
100875, China;
22institutetext: Key Laboratory of Optical Astronomy, National Astronomical
Observatories, Chinese Academy of Sciences, Beijing 100101, China;
33institutetext: School of Astronomy and Space Science, University of Chinese
Academy of Sciences, Beijing 100049, China;
44institutetext: School of Astronomy and Space Science, Nanjing University,
Nanjing 210023, Jiangsu, China

# Detecting and Monitoring Tidal Dissipation of Hot Jupiters in the Era of
SiTian

Fan Yang 112233 Wei<EMAIL_ADDRESS>2233 Xing<EMAIL_ADDRESS>11 Hui<EMAIL_ADDRESS>44 Ji-Lin Zhou 44 Su-Su Shan 2233 Jie Zheng
22 Wei-Kai Zong 11 Ming Yang 44 Yu Bai 22 Song Wang 22 Jia-Chen Zheng 11 Yu-Ru
Xu 11 Yu-Feng Li 11 You-Jun Lu 2233 Ji-Feng Liu 2233

###### Abstract

Transit Timing Variation (TTV) of hot Jupiters provides direct observational
evidence of planet tidal dissipation. Detecting tidal dissipation through TTV
needs high precision transit timings and long timing baselines. In this work,
we predict and discuss the potential scientific contribution of SiTian Survey
in detecting and analyzing exoplanet TTV. We develop a tidal dissipation
detection pipeline for SiTian Survey that aims at time-domain astronomy with
72 1-meter optical telescopes. The pipeline includes the modules of light
curve deblending, transit timing obtaining, and TTV modeling. SiTian is
capable to detect more than 25,000 exoplanets among which we expect $\sim$50
sources showing evidence of tidal dissipation. We present detection and
analysis of tidal dissipating targets, based on simulated SiTian light curves
of XO-3b and WASP-161b. The transit light curve modeling gives consistent
results within 1$\sigma$ to input values of simulated light curves. Also, the
parameter uncertainties predicted by Monte-Carlo Markov Chain are consistent
with the distribution obtained from simulating and modeling the light curve
1000 times. The timing precision of SiTian observations is $\sim$ 0.5 minutes
with one transit visit. We show that differences between TTV origins, e.g.,
tidal dissipation, apsidal precession, multiple planets, would be significant,
considering the timing precision and baseline. The detection rate of tidal
dissipating hot Jupiters would answer a crucial question of whether the planet
migrates at an early formation stage or random stages due to perturbations,
e.g., planet scattering, secular interaction. SiTian identified targets would
be constructive given that the sample would extend tenfold.

###### keywords:

planets and satellites: gaseous planets, planets and satellites: physical
evolution, planets and satellites: dynamical evolution and stability, planets
and satellites: detection

##  1 Introduction

Tidal migration is one of mechanisms that may explain why hot Jupiters occur
at such close orbits, though direct observational evidence of orbit decay is
only achieved for a single planet, namely WASP-12b, in the past decades (Patra
et al., 2017; Dawson & Johnson, 2018; Turner et al., 2021). The first data
release of Transiting Exoplanet Survey Satellite (TESS; Ricker et al., 2015)
in 2018, leads to the identification of four new candidates through TTV
detection (Dong et al., 2021; Davoudi et al., 2021; Shan et al., 2021; Yang &
Chary, 2021, submitted; Yang & Wei, 2021). TTV monitoring depends on the
timing precision and baseline length which are key technical specifications
for time-domain facilities, e.g., Zwicky Transient Facility (ZTF; Bellm et
al., 2019), Large Synoptic Survey Telescope (LSST; Ivezić et al., 2019),
Tsinghua University-Ma Huateng Telescopes for Survey (TMTS; Zhang et al.,
2020; Lin et al., 2021), Antarctic Survey Telescopes times 3 (AST3; Ma et al.,
2018; Zhang et al., 2019), and SiTian (Liu et al., 2021; Zhu et al., 2021).
The latter is aiming to tune down the false-positive probability of time-
domain signals, by implementing a global network of three-color photometric
monitoring of one-quarter of the sky at a cadence of 30min, down to a
detection limit of $V\sim 21$ mag (Liu et al., 2021).

It may suggest a TTV signal if any constant period ephemeris can not fit well
the observed timings. TTV could originate from multiple physical processes,
e.g., tidal dissipation, apsidal precession, R$\o$mer effect, and mass loss
(Ragozzine & Wolf, 2009; Valsecchi et al., 2015; Patra et al., 2017; Ou et
al., 2021). Another TTV generation process is the interaction between planets
in a multi-planet system which should cause oscillation in transit timing
residual in an observable timescale (Holman et al., 2010; Weiss et al., 2013).
However, it has been reported that a planet companion should not be close or
massive enough to induce observable TTVs for hot Jupiters (Huang et al.,
2016). Distinguishing among the above mentioned various physical origins
requires long-term high precision monitoring of transit timings continuously.

Combining observations from wide field transit surveys, e.g., Kepler, TESS
(Borucki et al., 2010; Ricker et al., 2015) and follow-up observations using
focused telescopes e.g., CHEOPS (Benz et al., 2021), has been proved to be
feasible in TTV detecting and related researches (Borsato et al., 2021).
Sariya et al. (2021) report TTVs of HAT-P-12b in the baseline of ten years,
using light curves from small ground-based telescopes. The transit timings of
WASP-32b are monitored and no significant TTV is found with the available data
(Sun et al., 2015). WASP-43b is reported as a candidate showing period decay
(Jiang et al., 2016) which arises wide attention and scientific discussions
(Davoudi et al., 2021; Garai et al., 2021). WASP-4b presents a significant TTV
and is furtherly explained by the R$\o$mer effect (Bouma et al., 2019, 2020).
HAT-P-25 is reported with no significant TTV which sets a limit on the
possible planet-planet interactions (Wang et al., 2018). The success in
observation in turn motivates the development of planet formation and
evolution theory (Dawson & Johnson, 2018; Wang et al., 2019; Liu & Ji, 2020).

The sample for tidal dissipation studies would be significantly enlarged in
the next decade, especially through the joint survey of ground-based
telescopes, e.g., SiTian and the next generation exoplanet space telescopes,
e.g., Habitable ExoPlanet Survey (HEPS; Yu et al., 2019, 2020), Earth 2.0
Transit Planet Survey, and shall be studied in details by ARIEL (Tinetti et
al., 2018), HABItable Terrestrial planetary ATmospheric Surveyor (HABITATS;
Wang et al., 2020).

In this work, we discuss the potential contribution of SiTian in detecting and
investigating tidal decaying hot Jupiters. We present general-purpose tools
for tidal dissipation detection, using the simulated light curves of SiTian.
The detection pipeline contains four major steps, i.e., light curve
generation, contamination light deblending, transit timing detection, and
transit timing modeling. The latter three modules are described given that
light curve generation would be integrated into SiTian science processing
pipeline (Liu et al., 2021). The paper is organized as follows. In Section 2,
we introduce the SiTian exoplanet observation strategy and the generation of
simulated SiTian light curves. In Section 3, we present the tidal dissipation
identification pipeline and apply it to the simulated light curves of
WASP-161b and XO-3b. In Section 4, we discuss the potential contribution of
SiTian in planet tidal dissipation. In Section 5, a summary is presented.

##  2 SiTian Exoplanet Observational Strategy and Simulated Transit Light
Curves Generation

SiTian is an integrated network of 1-meter telescopes, aiming at time-domain
astronomy (Liu et al., 2021). It shall produce a huge amount of the light
curves, that would contribute to time-domain researches of targets with
physical size ranging from galaxy clusters to planets (Liu et al., 2019, 2020;
Yang et al., 2022, 2020b, 2020a; Lennon et al., 2021; Wang et al., 2021; Yang
et al., 2021; Ngeow et al., 2021). Monitoring the same area of the sky
simultaneously in three bands ($u$, $g$, $i$), SiTian will deliver high
precision timing measurements, enabling detections of TTVs. The commissioning
of SiTian is expected to be before or around 2030, and the first three proto-
type equipment may start its operation in the middle of 2022.

###  2.1 SiTian Technical Specification for Exoplanet Research

SiTian will eventually accomplish with a worldwide network of 72 telescopes,
monitoring a sky area of $\sim$ 30,000 deg2 (Liu et al., 2021). The main
monitoring sky coverage is $\sim$ 10,000 deg2 which can be observed by
telescopes located in China. The typical exposure time is 1 minute, resulting
in a 5 $\sigma$ brightness limit of 21.1 mag in the $g$-band (Liu et al.,
2021). The photometric precision is expected to reach 1$\%$ for point sources
with $V=16$ mag (Liu et al., 2021), assuming the detector has a QE of 70$\%$,
read noise of 7 e-, an optical throughput of 70$\%$, filter transmission
fraction of 70$\%$, seeing of 2.5 arcsec, and night-sky brightness of 21.1 mag
arcsec-2. The applied CMOS detector GSENSE4040 has a readout noise of 3.7 e-
(Liu et al., 2021). A classic good observing site has an average night-sky
brightness around or better than 22.0 mag arcsec-2 and a median seeing size
better than 1 arcsec, for example, the Lenghu site(Deng et al., 2021), which
is the most promising major Chinese site for SiTian. Using these parameters
for calculation, the photometric precision is predicted as shown in Table 1.
The photometric precision is $\sim$ 700 parts per million (ppm) at $g$-band
and 1075 ppm at $i$-band for 12 mag targets (as shown in Figure 1). The
photometric uncertainties of sources brighter than 12 mag are dominated by
photon noise. In addition, the SiTian mission would occupy at least three
4-meter class spectroscopic telescopes for following-up observation.

Figure 1: The simulated and model-predicted light curves. The blue points are
the simulated SiTian light curve and the red points are binned data for
clarity. The black line shows the best-fit model light curves, while the
yellow region presents 1 $\sigma$ significance region. The fitting residuals
are shown below the light curves. The top panel refers to WASP-161b and the
bottom panel refers to XO-3b.  Table 1: The expected limiting magnitude and
photometric precision of a 1 minute single exposure for one SiTian telescope,
based on the technical specifications from Liu et al. (2021).

| $u$ | $g$ | $i$
---|---|---|---
Limiting magnitudea | 20.2 | 21.1 | 20.4
Photometric Precision at Certain Magnitude
Magnitude | $\sigma(u)$ | $\sigma(g)$ | $\sigma(i)$
16 Mag | 0.85$\%$ | 0.48$\%$ | 0.76$\%$
12 Magb | 1258 ppm | 708 ppm | 1075 ppm

Note. (a) 5 $\sigma$ limit magnitude. (b) The photometric errors of brighter
sources or longer exposure time are dominated by Poisson error.

The data will be reduced by the SiTian collaboration in two modes, i.e.,
online and offline (Liu et al., 2021). The quick data reduction, light curve
retrieval, and classification will be performed in the online mode immediately
after observation with a typical delay of 1 minute. In addition, alerts for
transient events and other interesting targets will be triggered. Full data
products, e.g. time-domain images, light curves, and target catalogs would be
available and released to the public after reducing by the offline pipeline.

The capability of an observation to detect transit signal in a planetary
system can be represented by the signal to noise ratio (S/R) as:

${\rm
S/R}=\sqrt{\frac{t_{obs}}{P}}\frac{R_{p}^{2}}{R_{\ast}^{2}}/\sigma_{total},\\\
$ (1)

where $t_{obs}$ is the total integration time for the source, $P$ the orbit
period, $R_{p}$ and $R_{\ast}$ the radius of the planet and host star,
respectively. $\sigma_{total}$ is the total uncertainty in the duration of
transit event, taking into account Poisson photon noise, uncorrected stellar
variability, and equipment noise (Borucki et al., 2010). For example, a star
with $g$=12 observed by SiTian would have a $\sigma_{total}$ of 36 ppm when
the t${}_{obs}\sim$6.5 hr, a typical transit duration of hot Jupiters (Akeson
et al., 2013; Yang et al., 2022, 2021). A typical stellar variability level
for a low variability star like Sun is $\sim$ 10 ppm on the timescale of a
planet transit (Jenkins, 2002). This stellar variability is significantly
smaller than Poisson photon noise. The $\sigma_{total}$ is $\sim 239$ ppm for
a 16 mag star in the same stacked time.

The average observation time tobs can be estimated by multiplying the survey
time and the ratio of exposure time to scanning cadence. The total field of
view (FOV) of SiTian is 600 deg2. The cadence for the main sky coverage
(10,000 deg2) is 30 minutes. Assuming 8-hour observation time per night and
300 observing nights per year, the average annual tobs is 3.3 days. For
Neptune-sized planet (3$R_{\oplus}$) orbiting $g$=12 mag stars with orbital
periods of 30 days, the average S/N is 8.2 in one year observation, superior
to the empirical exoplanet detection threshold S/R = 7.1 (Borucki et al.,
2010; Fressin et al., 2013; Christiansen et al., 2015, and references
therein). For a $g=16$ Sun-like star, the S/R for an orbiting Jupiter-sized
planet is $\sim$ 16 in one-year observation. The S/R is the same for a Neptune
orbiting an M-type star. A more detailed discussion of planet detecting rate
shall be presented in the following work, describing the pipeline of exoplanet
detecting (Yang et al. in preparation). Here, we present a simple and general
calculation.

The number of planets that can be detected by a survey depends on three
factors, i.e., the planet occurrence rate, star counts, and solid angle. The
solid angle equals to $R_{p}$/$a$, where $R_{p}$ is planet radius and $a$ is
orbital semi-major axis (Borucki et al., 2010). The planet occurrence rate is
estimated to be $\sim$ 0.15 for SiTian’s capability, based on the knowledge
and lessons gained from the Kepler mission (Howard et al., 2012; Fressin et
al., 2013; Christiansen et al., 2015).

Taking the advantage of the high spatial resolution of $\sim$ 1 arcsec, and
considering the number density of bright stars, SiTian is planned to monitor
the galactic plane for exoplanet research. There are about 6.5 million stars
brighter than 12 mag in the galactic plane with galactic longitude $b$ between
0∘ and 20∘ (Robin et al., 2003). This leads to an expected planet detection of
25,000 if applying an average solid angle of 2.5$\%$ (Akeson et al., 2013).
The expected detected planet would thereby be 250 per year, assuming 1$\%$
SiTian time is allocated for bright sources. We note that the blending of
nearby sources is correctable (cf. details in Section 2.2) for bright target
transit observation (Yang et al., 2022, 2021, 2021). Thereby, monitoring
crowded stars in the Galactic plane is an efficient strategy for SiTian to
detect transit planets.

The expected number of stars with $g\sim$15-17 mag and with absolute $b$
between 20 and 40 ∘ is $\sim$ 1 million(Robin et al., 2003). The occurrence of
Jupiter-sized planets around Sun-like stars is about 0.06 (Fressin et al.,
2013), which implies the detection of 1500 Jupiter size exoplanets orbiting
Sun-like stars by SiTian. In addition, about 1400 Neptune size exoplanets
orbiting M-type star are expected to be detected, considering the small size
of M-type stars and their large abundance of $\sim$ 70$\%$ (Chabrier, 2003).

The detection of these 2900 exoplanets around faint stars are byproducts of
SiTian’s main scientific objectives. We emphasize that with only 1$\%$
observing time on bright stars, SiTian may discover additional 2500 exoplanets
in ten-year observation and up to 25000 planets with 10$\%$ time.

###  2.2 SiTian Data for Transit Timing Analysis and Simulated Transit Light
Curves

The proposed SiTian Mission would significantly extend the sample size of
exoplanets. The expected multiple timing measurements of these newly
discovered targets from SiTian may already allow a transit timing analysis.
Meanwhile, SiTian’s main survey or follow-up discretionary program of the
known planets with reported timing observation and TTV evidence will provide
opportunities for a full TTV study of these targets. The planet identification
package will detect exoplanet candidates and provide their preliminary orbital
and planetary parameters (Yang et al., in preparation). For the research of
TTV, it is necessary to build a specialized package to obtain more precise
transit parameters, especially the transit timings. The potential targets for
the pipeline include already-known hot Jupiters and new transiting hot
Jupiters detected from the SiTian survey. Below we describe our simulation of
SiTian’s capability on the study of TTV and tidal dissipation.

The deblending of the light curve is crucial for the transit planet survey
programs with poor spatial resolution and is particularly important for
studies relying on high precision transit depth measurements (Yang et al.,
2022, 2021). We note that the high spatial resolution and sampling are one of
the major advantages of SiTian.

We model and remove the blending light from the unsolved sources in the
vicinity of the target for the TESS image which has a pixel size of 21 arcsec
(Yang et al., 2022). Firstly, the correlation between the fraction of blended
light and the distance of the contaminating star to the target is built. The
step-by-step description of blending-distance correlation is available in our
previous work (Yang et al., 2022). With this relation, one can calculate the
contamination fraction of every source and their sum is the total blending
fraction. The calculation needs external information from the Gaia catalog
(Gaia Collaboration et al., 2018) on the flux and position of individual stars
inside the aperture of the target star.

The deblending method that we have developed delivers TESS brightness highly
consistent the Gaia brightness (Yang et al., 2022). The derived transit depths
are consistent within 1$\sigma$ with those given by the TESS Pre-Search Data
Conditioning (PDC; Smith et al., 2012) modules for the comparison samples
(Yang et al., 2022, 2021). The deblending package has been provided as a
general-purpose software 111https://github.com/sailoryf/TESS_Deblending/, and
will be used for the deblending and correction of the SiTian light curves.

For this purpose, we first simulate the “observed” SiTian $g$-band light
curves of two hot Jupiters with the host star of 12 mag. The sampling interval
is set as 1 minute with the input observational uncertainty of 708 ppm (as
shown in Table 1). The input parameters are set as the same as those of
WASP-161b and XO-3b, which shows TTV evidence (Yang & Chary, 2021, submitted;
Yang & Wei, 2021). For each source, we simulate 1000 transit light curves. The
light curves are all set with a total observation time of 8 hours. The
simulation light curves are de-trended by a polynomial fit to the several-hour
out-of-transit baseline data, which is shown to be a valid approach in (Yang
et al., 2022, 2021, 2021).

WASP-161b is a hot Jupiter orbiting an F6-type star every 5.41 days (Barkaoui
et al., 2019) and is reported to bear significant TTV related to tidal
dissipation (Yang & Chary, 2021, submitted). The giant planet has a mass
($M_{p}$) of 2.49$\pm$0.21$M_{J}$ and a radius ($R_{p}$) of $1.14\pm
0.06R_{J}$. The host star has a mass of 1.39$\pm$0.14$M_{\odot}$, a radius of
$1.71\pm 0.08R_{\odot}$. Applying a combined-fit to both the radial velocity
curve and the TESS 2-minute cadence light curve, Yang & Chary (2021,
submitted) has an orbital eccentricity of $e$ = 0.34$\pm$0.03, an inclination
of 89.58$\pm$0.28, and a semi-major axis in stellar radii ($a/R_{\ast}$) of
6.57$\pm$0.45 (Yang & Chary, 2021, submitted). In addition, a significant TTV
is reported by combining the TESS observation and the archival timing
measurements.

XO-3b is an another hot Jupiter with significant TTVs (Shan et al., 2021; Yang
& Wei, 2021). The planet-star system has an orbit period ($P_{orb}$) of 3.19
days, an $a$ of 4.95$\pm$0.18, an inclination of 84.20$\pm$0.54, and an $e$ of
0.27587${}^{+0.00071}_{-0.00067}$ (Winn et al., 2008; Bonomo et al., 2017;
Stassun et al., 2017). The planet has an $M_{p}$ of 11.70$\pm$0.42$M_{J}$ and
an $R_{p}$ of 1.217$\pm$0.073$R_{J}$. The host star has an $M_{\ast}$ of
1.213$\pm$0.066$M_{\odot}$ and an $R_{\ast}$ of 1.377$\pm$0.083$R_{\odot}$.

When simulating the observed light curve, and performing light curve model
fitting, we used the classic planet transit model assuming a Keplerian orbit
from Mandel & Agol (2002). The parameters include $R_{p}/R_{\ast}$,
$a/R_{\ast}$, transit mid-point $T_{C}$, inclination, the argument of
periapsis, the time of periapse passage, the longitude of the ascending node,
and quadratic limb darkening coefficients (a1 and a2). The limb darkening
coefficients are inserted from limb darkening models, depending on the stellar
type of the host star and observational band (Claret, 2000; Claret & Bloemen,
2011; Yang et al., 2021, 2021). We set the transit midpoint as the time zero
reference for comparison purposes. Examples of synthetic light curves for
WASP-161b and XO-3b are as shown in Figure 1. The blending light from sources
nearby is negligible given that no comparable sources within 10′′ are detected
and SiTian data has a pixel resolution of 1′′.

Figure 2: The posterior distribution obtained from the MCMC fitting to the
simulated light curves of WASP-161b (top), XO-3b (bottom). The dashed lines in
the diagonal histograms give the 1 $\sigma$ regions. The corner plot uses the
routine from Foreman-Mackey (2016).

##  3 The pipeline for Tidal Dissipation Candidates Identification

Our pipeline to search for the tidal dissipation candidates is firstly
developed for the TESS data, including four main modules: the light curve
generation and detrending, the light curve deblending from contamination by
additional stars inside the aperture, transit timing determinations, and
multi-epoch timing analysis. The light curve generation and detrending will be
performed by the SiTian data reduction pipeline (Liu et al., 2021) which
should be more specializing for SiTian data. We have described light curve
deblending in Section 2.2. Below, we describe timing obtaining, and timing
modeling modules in detail. Our pipeline is based on the usage of functions
from NumPy (Harris et al., 2020), Astropy (Astropy Collaboration et al.,
2013), EXOFAST (Eastman et al., 2013), and PYMC (Patil et al., 2010). NumPy
and Astropy provide basic statistics and astronomical calculations. EXOFAST
utilize the transit model from Mandel & Agol (2002). PYMC furnishes the Markov
Chain Monte-Carlo (MCMC) technique.

###  3.1 Modeling Transit Light Curve and Obtaining Transit Timing

The Markov Chain Monte-Carlo technique (Patil et al., 2010; Foreman-Mackey et
al., 2013), or alternatively, the multimodal nested sampling algorithms
(MULTINEST; Feroz et al., 2009) are widely used for the fitting to transit
light curves. These two methods have been compared in previous work and the
results obtained are consistent (Yang et al., 2021). In our pipeline, we
currently use the MCMC method and may add the MULTINEST method as an option in
future versions.

The fitting procedure applies the Mandel & Agol (2002) model assuming
Keplerian orbit, to generate theoretical transit light curves. All parameters
involved in light curve generation are set as free parameters. Uniform priors
ranging through the whole reasonable space are used for all these parameters,
except for the limb darkening coefficients, which use Gaussian priors with a
$\sigma$ of 0.05. The central priors of the limb darkening coefficients are
dependent on stellar spectral types and can be inferred via interpolation of
the classic limb darkening model (Claret, 2000; Claret & Bloemen, 2011; Yang
et al., 2021). The spectral types of the planet host stars can be found from
Gaia catalogs. The induced uncertainties in our work can be up to a few
percent in radius ratios and are not significant for the timing study (Yang et
al., 2021).

The MCMC algorithm omits some first steps as burn-in and applies a number of
iterations for probability statistics. More iteration should more likely give
an effective MCMC fitting. However, the numbers of the omitted steps and the
applicable steps linearly relate to the consuming time of MCMC fitting. In
practice, we show that 30,000 as burn-in numbers and 50,000 as applicable
steps are high enough for the TESS light curve fitting (Yang et al., 2021,
2021).

An investigation has been performed for the simulated SiTian light curves, to
determine the threshold of the chain steps for securing stable MCMC results.
For each of WASP-161b and XO-3b, 100 light curves are generated using their
reported parameters as input, respectively. We then fit the light curves and
monitor the stability of the MCMC results for the 100 run. The monitoring
shows that the MCMC fitting turns stable when 10,000 steps are used as burn-in
and 20,000 steps are used as analysis. Considering possible extra fluctuation
due to the diversity of planet parameters and light curve quality in real
applications, we apply 30,000 as burn-in and 50,000 for a statistic in the
pipeline. We note that a tenfold-length chain will be used for high priority
sources which already show tidal dissipation evidence, for example, WASP-161
b, and XO-3 b. The probability statistics of their parameters are shown in
Figure 2.

The MCMC fitting obtains a $T_{C}$ of 0.00027$\pm$0.00031 days (0.39$\pm$0.44
minutes) for WASP-161b and a $T_{C}$ of 0.00010$\pm$0.00022 days
(0.14$\pm$0.32 minutes) for XO-3b, consistent with the input $T_{C}$ of 0. We
apply further simulations to investigate whether the MCMC fitting is robust.
We generate another 1000 light curves for each planet and fit them
individually. The resulting distributions are well consistent within 1$\sigma$
to the MCMC derived distributions in fitting one particular light curve.
Taking $T_{C}$ as example, the distributions are 0.00000$\pm$0.00038 days
(0$\pm$0.54 minutes) for WASP-161b, and 0.00001$\pm$0.00027 days
(0.01$\pm$0.39 minutes) for XO-3b, as shown in Figure 3. Therefore, we
conclude that the MCMC fitting gives precise timing measurement and the timing
precision obtained for the simulated SiTian light curve is $\sim$ 0.5 minutes
for a single transit observation.

Figure 3: The distribution of the best-fit $T_{C}$ values of the 1000
simulated light curves. Upper panel for WASP-161 b and lower for XO-3 b. The
vertical dash lines show the input value of 0.

###  3.2 Transit Timing Modeling and Tidal Dissipation Identification

For hot Jupiters, observed TTV signal can be accounted for by various
mechanisms, e.g., tidal dissipation, apsidal precession, R$\o$mer effect,
multi-planet interaction, and mass loss. Exploring these physical processes is
among the main scopes of SiTian for the exoplanet research. The apsidal
precession scenario can be identified or rejected by studying the shape of the
light curve (Jordán & Bakos, 2008; Antoniciello et al., 2021; Yang & Wei,
2021). For the mass-loss case, the TTV signal is dependent on the mass rate
and amplitude, which can be well constrained by orbital parameters. The
R$\o$mer effect can be tackled by long-term radial velocity monitoring of the
host star, or high-resolution imaging search for stellar-mass companion(Siverd
et al., 2018; Yang et al., 2021).

In principle, a TTV signal induced by tidal dissipation should persist a
constant period derivative, which can be easily spotted out from transit
timing data using our developed pipeline (as shown in Figure 4).

Figure 4: The archival timings (black points) and the predicted new SiTian
timing observations (red diamonds) of WASP-161b (top) and XO-3b (bottom). The
black horizontal line gives the best fitted constant period model. The red
dashed curve presents tidal dissipation models as described by Yang & Chary
(2021, submitted); Yang & Wei (2021) with the yellow region showing 1 $\sigma$
region encompassing 68$\%$ archival timings. The simulated SiTian data are to
be taken in 2022, 2027, and 2032, which can effectively distinguish between
the linear and the quadratic models.

As predicted by the tidal dissipation model, timing variation follows a
quadratic function of the transit epochs (Patra et al., 2017; Yang & Chary,
2021, submitted):

$t_{\mathrm{tra}}(N)=t_{0}+NP+\frac{1}{2}\frac{dP}{dN}N^{2},\\\ $ (2)

where $t_{\mathrm{tra}}(N)$ is the timing of Nth transit, $t_{0}$ is the zero
point.

It was found in previous works that timings of WASP-161b and XO-3b
significantly favor a quadratic function model than linear models (Yang &
Chary, 2021, submitted; Yang & Wei, 2021). We present the predicted SiTian
timing measurements of WASP-161b and XO-3b in 2022, 2027, and 2031 (as shown
in Figure 4). Transit midpoints are generated according to Equation 2. We
recalculate BICs to estimate the evidence among different models. The
$\Delta$BIC of WASP-161b and XO-3b is 8.8, 383 obtained from archival timings,
favoring a quadratic model compared to a linear model. The $\Delta$BIC of
WASP-161b and XO-3b between linear and quadratic models would be larger than
5.5$\times$105 and 1.8$\times$104, favoring quadratic models.

Adding the future SiTian measurements is shown to be highly capable of
distinguishing the difference between the constant period model and the period
decaying model. In our tidal dissipation detection module, a target with the
BIC difference between the best fit quadratic model and the best fit linear
model larger than 5 will be flagged as a candidate planet with tidal
dissipation. These candidates shall be further studied and verified by follow-
up observations including more transit epochs measuring and radial velocity
monitoring.

We present timings and following-up strategy of KELT-19Ab as an example.
KELT-19Ab is reported to hold a maximum stellar acceleration of 4 m s-1 yr-1
caused by the binarity of its host star (Siverd et al., 2018). Applying the
relation between the stellar acceleration and transit period derivative from
Bouma et al. (2020), the transit period would present a derivative of 5.32 ms
yr-1. Shan et al. (2021) report a possible but not significant period
derivative of 112$\pm$94 ms yr-1.

Timings obtained from SiTian would potentially distinguish these different
scenarios. SiTian timing predictions are obtained following the same process
as described above with planet parameters taken from (Siverd et al., 2018).
The timing would present a difference at $\sim$ 1.5 minutes in 2022 between a
linear and a quadratic model obtained from archival timings available (as
shown in Figure 5). The difference would be significant when one has timings
in 2027 and 2031. The $\Delta$BIC obtained from archival timings between
linear and quadratic models is 2.1, slightly favoring a quadratic model. It
would derive a $\Delta$BIC of 1963 until 2031 if the observational timings are
as predicted by the quadratic model (seen in Figure 5). Moreover, the stellar
acceleration would be detectable with SiTian observation in 2031. It would
reveal a 1-minute difference between the constant period and the stellar
acceleration models. The period derivative due to acceleration is taken from
Shan et al. (2021).

Figure 5: Timings of KELT-19Ab with symbols the same to Figure 4. The green
line presents the period derivative caused by stellar acceleration calculated
by Shan et al. (2021).

Moreover, long-term transit observation can also help to discriminate between
possible TTV origins. Planets in a multi-planet system are usually not massive
and close enough to each other to cause TTVs with an amplitude larger than 10
minutes (Holman et al., 2010; Huang et al., 2016). Therefore, it may rule out
the possibility of the multi-planet origin, if either a monotonic TTV or a
large TTV amplitude is observed, as shown in Figure 4. For another important
arguing possible origin, apsidal precession, the transit duration variation
(TDV) should be more significant than TTV (Pál & Kocsis, 2008; Ragozzine &
Wolf, 2009). The TDV can be obtained by modeling the transit light curves as
well. No evidence of TDV in the archival data is found for WASP-161b and XO-3b
(Yang & Chary, 2021, submitted; Yang & Wei, 2021). We expect that the SiTian
project may provide additional observation on TDV.

##  4 discussion

The observed TTV signal and its interpretation are highly dependent on the
data quality of timing observation. Any unexpected factors in deriving the
transit timing parameters may change the period derivative (detailed example
in Yang & Chary, 2021, submitted; Shan et al., 2021), and thus leads to
different explanations. Therefore, long-baseline transit monitoring with high
precision is crucial for enhancing understanding of the tidal dissipation
process.

We have introduced the capacity of SiTian in modeling the tidal dissipation of
WASP-161b and XO-3b (as shown in Figure 4). For them, we have scheduled multi-
epoch transit observations from 2022 with the SiTian prototype telescopes. In
addition, continuous observation of at least one transit per five years is
proposed. This observation would improve the accuracy and robustness of the
period derivative, which is important for modeling the dissipation process for
these two benchmark planets.

The migration is believed to be the reason that giant gas planets can exist at
such en-close orbit (Dawson & Johnson, 2018). The migration is probably due to
one of the two scenarios: tidal migration that loses angular momentum by e.g.,
planet scattering, stellar companion scattering, and secular interaction (Wu &
Lithwick, 2011; Naoz et al., 2011); or migration due to disk friction in the
early stage of planet formation (Lin et al., 1996). A high eccentricity system
showing period decaying favors the former model (Yang & Chary, 2021,
submitted; Yang & Wei, 2021). Also, the tidal dissipation occurrence rate
should be higher for the former model. It is likely that both migration
mechanisms may contribute separately to different sources, or even act in the
same source while in different evolutionary stages.

Interestingly, the system parameters of the five reported tidal dissipation
exoplanets show obvious diversity (Patra et al., 2017; Dong et al., 2021;
Davoudi et al., 2021; Yang & Wei, 2021; Yang & Chary, 2021, submitted).
Extending the available sample crucial for further statistic investigations.
Using the methods introduced by Dong et al. (2018); Zhu & Dong (2021), we are
performing statistic analysis to find possible relationships between the
eccentricity, orbital radius or semi-major axis, obliquity, metallicity, and
planet-multiplicity with no conclusive results yet due to the limited sample
size.

A large number of candidate systems with evidence of tidal dissipation may be
discovered or identified by SiTian, which will be of great importance for
understanding tidal migration. The detection number depends on the real
occurrence rate of planets with tidal dissipation, which is one of the most
important questions to answer by future observations, e.g. SiTian. The current
fraction of such systems is 5 out of more than 4000. We note that planets
other than hot Jupiters bearing tidal dissipation should be rarer. We expect
to discover $\sim$ 50 new tidal dissipation star-planet systems taking into
account at least one order of magnitude larger sample size. Moreover, other
targets showing TTV signals but caused by other mechanisms such as planet-
planet interactions, apsidal precession, will be identified by our pipeline as
byproducts.

For targets with high scientific interests, following-up observation would be
promptly scheduled with the SiTian 4-meter class spectroscopic following-up
telescopes (Liu et al., 2021). The following-up observation would give us
information of e.g., host star properties, binarity, and planet multiplicity.
In addition, future advanced facilities will provide important opportunities
for deep investigations. For example, the HABItable Terrestrial planetary
ATmospheric Surveyor (HABITATS), which is a proposed mission for a 4-6 meter
space telescope aiming at modeling the atmospheric features of exoplanets down
to Earth-like planets(Wang et al., 2020). The high-precision transmission
spectra from HABITATS will help us understand the atmosphere properties of
tidal dissipation targets, including the composition, thermal structures,
inflation, and escape. This information shall yield a comprehensive
understanding of the undergoing physical processes in the tidal dissipating
sources.

##  5 Summary

We describe a pipeline for tidal dissipation detection as software preparation
for the ongoing SiTian survey which is expected to have the first light of the
three prototype telescopes in the middle of 2022. The SiTian survey will have
72 telescopes in total with full installation till 2030 (Liu et al., 2021). We
have estimated SiTian’s capability for detecting exoplanets, based on its
technical parameters. SiTian is expected to discovery 5,000 to 25,000 new
exoplanets. Assuming a similar tidal dissipation occurrence, there would be
$\sim$ 50 hot Jupiters showing tidal dissipation evidence.

The pipeline for tidal dissipation detection has modules of light curve
deblending, transit light curve modeling, and timing modeling for tidal
dissipation detection. The light curve deblending is based on our developed
algorithm for TESS light curve deblending (Yang et al., 2022). For each
target, a relationship between the contamination fraction and the distance to
the target will be built, based on the brightness and position measurements
for individual stars from the GAIA catalog (Gaia Collaboration et al., 2018),
and then corrected to obtain “uncontaminated” light curves for SiTian.

We set the reported period decaying candidates of WASP-161b and XO-3b as
examples to describe our pipeline and the contribution of SiTian data. We
simulate SiTian light curves for WASP-161b and XO-3b with a photometric
precision of $\sim$ 700 ppm in 1-minute cadence, estimated from SiTian’s
technical parameters. The MCMC technique is applied when modeling transit
light curves. We show that our transit timing measurement has a precision of
0.5 minutes for a single transit observation.

We conclude that the inclusion of SiTian data shall provide key evidence to
discriminate between various TTV origin models. For WASP-161b and XO-3b, a
tidal dissipation origin seems to be the most likely explanation. The proposed
future SiTian measurements shall significantly improve the model confidence
and robustness.

We thank SiTian Collaboration for the support in preparing this work. The work
made use of the NASA Exoplanet Archive
222https://exoplanetarchive.ipac.caltech.edu/index.html (Akeson et al., 2013).
We would like to thank Jin-Ping Zhu for the careful reading and constructive
suggestions. We thank Bo Zhang for the helpful discussion. Fan Yang and Su-Su
Shan are supported by funding from the Cultivation Project for LAMOST
Scientific Payoff and Research Achievement of CAMS-CAS. Xing Wei acknowledges
National Natural Science Foundation of China (NSFC; No.11872246, 12041301),
and the Beijing Natural Science Foundation (No. 1202015). Wei Wang is
supported by the National Natural Science Foundation of China (NSFC) grants
No. 11988101, 42075123, the National Key RD Program of China No.
2019YFA0405102, and the science research grants from the China Manned Space
Project with NO. CMS-CSST-2021-B12.

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