11institutetext:  Instituto de Astrofísica e Ciências do Espaço, CAUP, Rua das
Estrelas, PT4150-762 Porto, Portugal
11email<EMAIL_ADDRESS>22institutetext: Departamento de Fisica e
Astronomia, Faculdade de Ciências, Universidade do Porto, Rua do Campo Alegre
687, PT4169-007 Porto, Portugal

# Measuring the orbit shrinkage rate of hot Jupiters due to tides

N. M. Rosário, Measuring the orbit shrinkage rate of hot Jupiters due to
tidesMeasuring the orbit shrinkage rate of hot Jupiters due to tidesMeasuring
the orbit shrinkage rate of hot Jupiters due to tidesMeasuring the orbit
shrinkage rate of hot Jupiters due to tides S. C. C. Barros , Measuring the
orbit shrinkage rate of hot Jupiters due to tidesMeasuring the orbit shrinkage
rate of hot Jupiters due to tidesMeasuring the orbit shrinkage rate of hot
Jupiters due to tidesMeasuring the orbit shrinkage rate of hot Jupiters due to
tides O. D. S. Demangeon , Measuring the orbit shrinkage rate of hot Jupiters
due to tidesMeasuring the orbit shrinkage rate of hot Jupiters due to
tidesMeasuring the orbit shrinkage rate of hot Jupiters due to tidesMeasuring
the orbit shrinkage rate of hot Jupiters due to tides N. C. Santos , Measuring
the orbit shrinkage rate of hot Jupiters due to tidesMeasuring the orbit
shrinkage rate of hot Jupiters due to tidesMeasuring the orbit shrinkage rate
of hot Jupiters due to tidesMeasuring the orbit shrinkage rate of hot Jupiters
due to tides

(Received July 15, 2022 / Accepted October 20, 2022)

###### Abstract

Context. A tidal interaction between a star and a close-in exoplanet leads to
shrinkage of the planetary orbit and eventual tidal disruption of the planet.
Measuring the shrinkage of the orbits will allow for the tidal quality
parameter of the star ($Q^{\prime}_{\star}$) to be measured, which is an
important parameter to obtain information about stellar interiors.

Aims. We analyse data from the Transiting Exoplanet Survey Satellite (TESS)
for two targets known to host close-in hot Jupiters, which have significant
data available and are expected to have a fast decay: WASP-18 and WASP-19. We
aim to measure the current limits on orbital period variation and provide new
constrains on $Q^{\prime}_{\star}$ for our targets.

Methods. We modelled the transit shape using all the available TESS
observations and fitted the individual transit times of each transit. We used
previously published transit times together with our results to fit two
models, a constant period model, and a quadratic orbital decay model, using
Markov chain Monte Carlo (MCMC) algorithms.

Results. We obtain new constrains on $Q^{\prime}_{\star}$ for both targets and
improve the precision of the known planet parameters with the newest
observations from TESS. We find period change rates of $(-0.11\pm 0.21)\times
10^{-10}$ for WASP-18b and $(-0.35\pm 0.22)\times 10^{-10}$ for WASP-19b and
we do not find significant evidence of orbital decay in these targets. We
obtain new lower limits for $Q^{\prime}_{\star}$ of $(1.42\pm 0.34)\times
10^{7}$ in WASP-18 and $(1.26\pm 0.10)\times 10^{6}$ in WASP-19, corresponding
to upper limits of the orbital decay rate of $-0.45\times 10^{-10}$ and
$-0.71\times 10^{-10}$, respectively, with a 95% confidence level. We compare
our results with other relevant targets for tidal decay studies.

Conclusions. We find that the orbital decay rate in both WASP-18b and WASP-19b
appears to be smaller than the measured orbital decay of WASP-12b. We show
that the minimum value of $Q^{\prime}_{\star}$ in WASP-18 is two orders of
magnitude higher than that of WASP-12, while WASP-19 has a minimum value one
order of magnitude higher, which is consistent with other similar targets.
Further observations are required to constrain the orbital decay of WASP-18
and WASP-19.

###### Key Words.:

planets and satellites: dynamical evolution and stability – planets and
satellites: fundamental parameters – planet-star interactions – techniques:
photometric

##  1 Introduction

In 1995, 51 Pegasi b became the first exoplanet discovered orbiting a solar-
like star (Mayor & Queloz, 1995). It is a massive planet, about half the mass
of Jupiter, with a short period, orbiting close to its host star. These
planets, now known as hot Jupiters due to their size and high temperature,
have been found around several systems and provide an astronomical laboratory
for our physical models of planetary formation and evolution, as well as
planet-star interaction. Hot Jupiters are an uncommon presence around Sun-like
stars when compared to smaller planets (Howard et al., 2012; Wright et al.,
2012; Johnson et al., 2010), and the circumstances of their formation and
evolution are still not completely understood (e.g. Dawson & Johnson, 2018).
Due to their size and short period, these planets have a high signal-to-noise
ratio (S/N), making it easier to obtain data on them and turning hot Jupiters
into an important source of information regarding the physics of planet
formation and evolution.

Due to the proximity to their host star, hot Jupiters are strongly affected by
tidal forces. In cases where the rotation of the star is not synchronised with
the orbital period of the planet, a transfer of angular moment occurs, leading
to an increase in the rotation of the star and a shrinkage of the planet’s
orbit. This effect, known as tidal decay (Counselman III, 1973; Levrard et
al., 2009; Matsumura et al., 2010), gives important information about the
tidal interaction between a planet and star and helps to constrain stellar
physics through the tidal quality factor $Q^{\prime}_{\star}$. This parameter
measures the efficiency of the energy dissipation during tidal interactions
and is related to the propagation of tidal oscillations inside the star
(Ogilvie & Lin, 2007; Ogilvie, 2014). According to the theory developed by
Zahn (1975, 1977), larger stars with convective cores and radiative envelopes
are expected to have a less efficient dissipation and, therefore, a larger
value of $Q^{\prime}_{\star}$.

Other physical processes can, in the short term, result in a shift in period
that is similar to tidal decay: apsidal precession (Miralda-Escudé, 2002; Heyl
& Gladman, 2007; Jordán & Bakos, 2008; Ragozzine & Wolf, 2009) and the
presence of external bodies affecting their orbits (Gibson et al., 2009,
2010). Apsidal precession is the rotation of the ascending node along the
orbital plane and as such, this effect is periodic and does not lead to a
long-term decay of the orbit. Additionally, a change in period may arise from
gravitational effects from nearby companions disturbing the orbit. An example
of this effect is reported by Triaud et al. (2017) in their study of the
system architecture of WASP-53 and WASP-81. Turner et al. (2021a) have
recently suggested that the orbit of WASP-4b (Wilson et al., 2008) may also be
changing because of another companion nearby.

WASP-12b, a hot Jupiter orbiting a late F-type star, was the first target
confirmed as having a decaying orbit caused by tidal interactions (Patra et
al., 2017; Maciejewski et al., 2018; Turner et al., 2021b; Wong et al., 2022).
It orbits its star with a period of $1.09$ days, and has a mass of $1.5\
M_{\mathrm{J}}$ and a radius of $1.90\ R_{\mathrm{J}}$. Its orbit is shrinking
at a rate of $29.81\pm 0.94$ ms $\mathrm{yr^{-1}}$, leading to a decay
timescale of $3.16\pm 0.10$ Myr. The tidal quality factor of
$Q^{\prime}_{\star}=(1.50\pm 0.11)\times 10^{5}$ is thought to be on the lower
side of the predicted values (Wong et al., 2022).

Despite being one of the prime targets to measure tidal decay (Patra et al.,
2020), so far there is still no evidence towards a decaying period in
WASP-18b, with Maciejewski et al. (2020) placing a lower limit for
$Q^{\prime}_{\star}$ of $3.9\times 10^{6}$ at 95% confidence level. The value
is of the same order of magnitude as the ones found by Shporer et al. (2019)
and Patra et al. (2020), which also investigated this system. WASP-19b (Hebb
et al., 2009), which is one of the shortest period hot Jupiters reported to
date (0.78 days), is also an interesting target for tidal decay studies.
Several authors have studied this system (e.g. Hellier et al., 2009; Tregloan-
Reed et al., 2013; Espinoza et al., 2019; Petrucci et al., 2020) and Patra et
al. (2020) found statistically significant evidence towards a decreasing
period, with $\dot{P}=dP/dt=(-2.06\pm 0.42)\times 10^{-10}$. However, WASP-19
is a highly active star, leading to distortions in the light curves thought to
be caused by star spots (Tregloan-Reed et al., 2013; Espinoza et al., 2019).
The result by Petrucci et al. (2020), discarding tidal decay in WASP-19,
contradicts these previous results, finding a value of $\dot{P}=0.0114\pm
0.74\times 10^{-10}$ consistent with zero, and increases the importance of
continuing observations of this system.

In this paper, we present our analysis of the Transiting Exoplanet Survey
Satellite (TESS; Ricker et al., 2014) data concerning two hot Jupiters
expected to show orbital decay, WASP-18b and WASP-19b. We aim to search for
signs of tidal decay on these targets and to measure the current constrains on
the tidal decay parameters, which allow us to better understand the migration
mechanisms of hot Jupiters and the reasons behind the decaying orbits.

We describe our target systems and the process of target selection in Sect. 2.
In Sect. 3, we present the TESS data and the pre-processing of the light
curves. The transit analysis is listed in Sect. 4 and in Sect. 5 we describe
our transit timing variation (TTV) and orbital decay models. We present and
discuss the results of the TTV analysis in Sect. 6 and provide a short summary
of the current status of orbital decay studies in other systems in Sect. 7.
Finally, a summary and conclusion is presented in Sect. 8.

##  2 Target selection

In order to work with the most relevant targets we looked at several hot
Jupiters that orbit close to their stars. We mainly focussed on the expected
orbital decay rate of those planets in order to explore the most promising
candidates. Patra et al. (2020) plotted the scaled orbital semi-major axis
$a/R_{\star}$ against the planet-to-star mass ratio
$M_{\mathrm{p}}/M_{\star}$, two quantities that are proportional to the decay
rate according to the current orbital decay models, and they provided several
cutoffs based on the decay rate for a constant $Q^{\prime}_{\star}$ in a
population of cold and hot stars brighter than $V=14.5$. We followed the
approach taken in that paper and started by looking at a sample of 12 targets,
six candidates orbiting hot stars ($T_{\mathrm{eff}}>6000$ K) and six orbiting
cold stars, with an expected decay rate of $dP/dT<10^{7}$ yrs for a
$Q^{\prime}_{\star}=10^{6}$.

We then looked at the targets that have been observed by TESS in more than one
season and whose data were not already published, so as to be able to obtain
the maximum amount of transits and therefore obtain the best possible
constrain on the orbital decay parameters. We also looked at the previous
available data from other observations to ensure the data span a large enough
timescale to possibly detect a change in period. For example, HATS-18 (Penev
et al., 2016) would seem promising with the previous criteria; however, the
lack of previous data makes it hard, if not impossible, to properly search for
period changes. WASP-4 (Wilson et al., 2008) and WASP-43 (Hellier et al.,
2011), for example, would also make for good targets in this study; however,
orbital decay analyses using the available data from TESS were recently
published (WASP-4: Turner et al., 2021a; WASP-43: Davoudi et al., 2021).

According to Patra et al. (2020), it is expected that planets around colder
stars have a faster tidal dissipation due to their larger convective
envelopes. Therefore, it can be important to investigate tidal decay around
both hot and cold stars. Given the previous criteria and taking stellar
temperature into account, we looked into the best candidates orbiting a hot
star and the best candidates orbiting a cold star. From the original sample,
WASP-18 is shown to be one of the most promising candidates for tidal decay
thanks to its high $M_{\mathrm{p}}/M_{\star}$ ratio. Furthermore, it was
observed by TESS in a total of four sectors, which gives us a good amount of
data to work with, and it has been the subject of several decay studies and
previous observations (e.g. Shporer et al., 2019; Maciejewski et al., 2020).
WASP-19 is one of the most promising targets among cold stars. It has
available data from TESS in two sectors and has been studied for several years
(e.g. Mancini et al., 2013; Espinoza et al., 2019), with observations from
different instruments in both photometry and spectroscopy, in part due to the
high stellar activity that is present in the star. The additional TESS data
may also provide new input to understand the effect of the activity in the
orbital decay studies.

###  2.1 WASP-18

WASP-18b (Hellier et al., 2009; Southworth et al., 2009) is a massive hot
Jupiter with a mass of 11.4 $M_{\mathrm{J}}$ and a radius of 1.20
$R_{\mathrm{J}}$, orbiting its star on a period of 0.94 days. The star,
WASP-18, is a bright ($V=9.30$) F-type star with a mass of 1.46 $M_{\sun}$, an
effective temperature of 6431 K, and an estimated age of 1 Gyr (Patra et al.,
2020). Several authors have looked at this system before to try to find
evidence of tidal decay since, according to theoretical models, WASP-18b
should be one of the fastest decaying targets we know of, in part due to its
large mass relative to the star. However, Wilkins et al. (2017) initially
found no evidence of rapid decay. McDonald & Kerins (2018) included an early
transit for Hipparcos and found a weak (1$\sigma$) sign of decay, but one must
take the high uncertainty in the timing of the Hipparcos transit into account.
With the first TESS observations for WASP-18, in Sectors 2 and 3, new
constrains have been found in the tidal decay parameters, with Shporer et al.
(2019) and Maciejewski et al. (2020) reporting results consistent with the
findings of Wilkins et al. (2017), with the new data not showing enough
evidence to confirm the decay of the orbit of WASP-18b. With two additional
TESS sectors and a 2-year gap between observations, we expect to add an
additional constraint to the tidal decay parameters and strengthen the
evidence towards the presence or absence of rapid decay.

###  2.2 WASP-19

WASP-19b (Hebb et al., 2009) is a Jupiter-sized planet with 1.14
$M_{\mathrm{J}}$ and 1.4 $R_{\mathrm{J}}$ orbiting an active solar-type G-star
with around 10 Gyr, a mass of 0.9 $M_{\sun}$, and an effective temperature of
5460 K. It is one of the shortest-period hot Jupiters discovered so far, with
a period of 0.78 days, and it was surpassed recently by the discovery of
TOI-2109 with a period of 0.67 days (Wong et al., 2021). With the high amount
of activity reported, WASP-19 is an interesting but challenging target to
measure orbital decay. Several authors have obtained WASP-19b transits (e.g.
Mancini et al., 2013; Espinoza et al., 2019), and Patra et al. (2020) added
their own transits to previous data and found strong evidence of decay, with a
period change rate of $-6.50\pm 1.33$ ms yr-1. However, they suspect stellar
activity is causing systematic errors and the result may be misleading. This
evidence is further weakened by Petrucci et al. (2020), who include several
more recent transits from the literature and from their own observations and
show evidence towards a constant period, with a value of $\dot{P}=0.015\pm
0.96$ ms yr-1 consistent with zero. Despite this, they provide an upper limit
for $\dot{P}$ of -2.294 ms yr-1. The newest TESS observations might shed some
new light on WASP-19b and the true nature of its orbital period and help to
clarify the behaviour of this hot Jupiter.

Figure 1: Plot of the PDC light curves of WASP-18 with NaNs and quality
flagged points removed. Moving median filter over 32 points shown in red.
Incomplete transits are shown near the gaps that separate the two physical
orbits of the spacecraft.

Figure 2: Plot of the PDC light curves of WASP-19 with NaNs and quality
flagged points removed. Moving median filter over 32 points shown in red.
Long-term trends can be observed in both sectors, most likely due to stellar
activity or uncorrected systematic errors.

##  3 TESS data

###  3.1 Observations

WASP-18 (TIC 100100827) was observed by Camera 2 of TESS with a 2 minute
cadence in Sector 2 (from 2018 August 22 to 2018 September 20), Sector 3 (from
2018 September 20 to 2018 October 18), Sector 29 (from 2020 August 26 to 2020
September 21), and Sector 30 (from 2020 September 23 to 2020 October 20). A
total of 92 transits were extracted from the observations.

WASP-19 (TIC 35516889) was observed with the same cadence by Camera 2 of TESS
in Sector 9 (from 2019 February 28 to 2019 March 26) and Sector 36 (from 2021
March 07 to 2021 April 01). We extracted 56 transits from the observations.

The TESS light curves were downloaded through the Mikulski Archive for Space
Telescopes (MAST) portal111https://mast.stsci.edu/. For the analysis performed
in this work, we use the Presearch Data Conditioning Simple Aperture
Photometry (PDCSAP) curves, which remove long-term non-astrophysical trends
from the data and reduce systematic errors (Smith et al., 2012, 2017).

The data files include a quality parameter that indicates data points that
have been affected by anomalous events such as attitude tweaks, momentum
dumps, firing of thrusters, and other events (Tenenbaum & Jenkins, 2018). We
removed all non-zero quality flagged data points from our light curve to
ensure reliable data and removed all NaN values caused by poor instrumental
behaviour, but long-term trends are still present in the initial curves,
especially in WASP-19 (Fig. 2). This may be caused by the high stellar
activity of WASP-19 (Hebb et al., 2009; Espinoza et al., 2019; Wong et al.,
2020), as well as some uncorrected systematic trends, and additional
corrections are described in Sect. 3.2.

Some incomplete transits are seen in Figs. 1 and 2, especially near the gaps
in the middle which separate the two physical orbits from TESS. During the
light curve processing described in Sect. 3.2, these incomplete transits were
discarded, since the lack of a complete transit does not allow for a precise
derivation of the transit timing (Barros et al., 2013).

###  3.2 Stellar activity correction

As mentioned before, stellar activity is a likely cause of the trends shown in
WASP-19 data (Fig. 2). To take the effect of stellar activity and spots into
account, we assume the maximum flux to correspond to the minimum amount of
stellar spots. We applied a moving median filter over 32 points to each light
curve and found the maximum median flux over all light curves in each target.
We then used this value as the normalisation constant to obtain the relative
flux. We also considered the maximum of each sector light curve for
normalisation instead of the overall maximum, but the difference in the final
result was not significant and we decided to keep the original approach. It
is, however, important to note that this does not correct for spot occultation
events (e.g. Barros et al., 2013).

The normalised curve was then split into individual transits. For that, we
started by flagging the data points within three transit durations of the mid-
transit time and by splitting the light curves into individual segments,
removing the remaining data between transits, which allowed for an easier
capture of short-term trends near the transits while minimising the influence
of long-term trends. We applied a detrending model using a low-order
polynomial and used the Bayesian information criterion (BIC) to find the
optimal polynomial order for each segment. The vast majority of the individual
light curves favoured a first-order polynomial trend, with only a few
exceptions in WASP-18 favouring a second-order model. We normalised each
individual transit light curve to an out of transit level of 1 using the
obtained best-fit coefficients.

##  4 Transit analysis

Table 1: System stellar parameters for each target, with WASP-18 parameters obtained from Shporer et al. (2019) and WASP-19 parameters obtained from Mancini et al. (2013). Limb-darkening coefficients for the quadratic model ($u_{1}$ and $u_{2}$) were estimated with LDTk (Parviainen & Aigrain, 2015) using the $T_{\mathrm{eff}}$, $\log g$, and $\mathrm{[Fe/H]}$ from the references. Parameter | WASP-18 | WASP-19
---|---|---
$R_{\star}(R_{\sun})$ | $1.26\pm 0.04$ | $1.018\pm 0.021$
$M_{\star}(M_{\sun})$ | $1.46\pm 0.29$ | $0.935\pm 0.045$
$T_{\mathrm{eff}}$ (K) | $6431\pm 48$ | $5460\pm 90$
$\log g$ | $4.47\pm 0.13$ | $4.432\pm 0.013$
$\mathrm{[Fe/H]}$ | $0.11\pm 0.08$ | $0.14\pm 0.11$
$u_{\mathrm{1}}$ | $0.361712\pm 0.000917$ | $0.435405\pm 0.001394$
$u_{\mathrm{2}}$ | $0.158463\pm 0.001641$ | $0.132505\pm 0.002214$

The transits were modelled using the model from batman (Kreidberg, 2015) and
we split our analysis into two parts. First we performed a fit of all transits
aiming to obtain the transit parameters. We put together all individual
segments already detrended and fit for reference time $T_{\mathrm{0}}$, period
$P$, planet-to-star radius ratio $r_{\mathrm{p}}/R_{\star}$, scaled orbital
semi-major axis $a/R_{\star}$, orbital inclination $i$, and the two limb-
darkening coefficients of the quadratic model $u_{\mathrm{1}}$ and
$u_{\mathrm{2}}$. Circular orbits with fixed $e=0$ and $\omega=90\degree$ were
used in all analyses. The circularisation timescale for WASP-18b is around 15
Myr, while WASP-19b has a value around 2 Myr; both are at least an order of
magnitude lower than the estimated system ages. Because of this, we expect the
eccentricity to be zero in both planets, unless external perturbations occur.
Nevertheless, we also fitted a model with varying eccentricity using Gaussian
priors, and compared the fits using the BIC. We found that the circular models
were strongly preferred (with a lower BIC) over the eccentric models.
Therefore, we assumed a circular model for all the remaining analyses in this
paper.

We used a quadratic limb-darkening model with values estimated with the Limb-
Darkening Toolkit (LDTk, Parviainen & Aigrain, 2015) using the effective
temperature ($T_{\mathrm{eff}}$), gravity ($\log g$), and metallicity
($\mathrm{[Fe/H]}$) of each star. The stellar parameters as well as the
initial limb-darkening values can be found in Table 1.

Figure 3: Best-fit model for WASP-18b phase-folded light curve of all TESS transits.  Figure 4: Best-fit model for WASP-19b phase-folded light curve of all TESS transits. Table 2: System parameters and priors used in the transit modelling. Parameter | Prior | Derived Value
---|---|---
WASP-18b |  |
$T_{\mathrm{0}}$ (BJD) | $\mathcal{U}(2458021.125,2458023.125)$ | $2458022.125237(37)$
$P$ (days) | $\mathcal{U}(0.44145,1.44145)$ | $0.941452397(44)$
$r_{\mathrm{p}}/R_{\star}$ | $\mathcal{U}(0.04776,0.14776)$ | $0.09765\pm 0.00017$
$a/R_{\star}$ | $\mathcal{U}(1.0,5.0)$ | $3.456\pm 0.017$
$i\ (\degree)$ | $\mathcal{U}(60,90)$ | $83.58^{+0.25}_{-0.24}$
$u_{\mathrm{1}}$ | $\mathcal{N}(0.361712,0.1)$ | $0.300\pm 0.020$
$u_{\mathrm{2}}$ | $\mathcal{N}(0.158463,0.1)$ | $0.159\pm 0.037$
WASP-19b |  |
$T_{\mathrm{0}}$ (BJD) | $\mathcal{U}(2456020.704,2456022.704)$ | $2456021.70386(50)$
$P$ (days) | $\mathcal{U}(0.28884,1.28884)$ | $0.78883896(14)$
$r_{\mathrm{p}}/R_{\star}$ | $\mathcal{U}(0.09233,0.19233)$ | $0.14541^{+0.00070}_{-0.00077}$
$a/R_{\star}$ | $\mathcal{U}(1.0,5.0)$ | $3.533^{+0.039}_{-0.037}$
$i\ (\degree)$ | $\mathcal{U}(60,90)$ | $79.17^{+0.33}_{-0.31}$
$u_{\mathrm{1}}$ | $\mathcal{N}(0.435405,0.1)$ | $0.403^{+0.061}_{-0.062}$
$u_{\mathrm{2}}$ | $\mathcal{N}(0.132505,0.1)$ | $0.118^{+0.084}_{-0.082}$

We used a Markov chain Monte Carlo (MCMC) algorithm based on the emcee
ensemble sampler in Python (Foreman-Mackey et al., 2013) for the transit
analysis. We defined a number of walkers of 4 times the number of fitted
parameters over 10000 steps and discarded the burn-in before retrieving the
results from the posterior distributions. We defined uniform priors for all
parameters except the limb-darkening coefficients, for which we defined
Gaussian priors centred in the values from LDTk with a conservative standard
deviation of 0.1. The results of the transit analysis and the best-fit
parameters are listed in Table 2 together with the used priors. We obtained
updated planetary and transit parameters for both targets with good agreement
with the parameters obtained previously.

For the second part of the analysis, we fitted the mid-transit times of each
transit separately. We fixed the previously obtained value for $P$,
$u_{\mathrm{1}}$, and $u_{\mathrm{2}}$, allowing $r_{\mathrm{p}}/R_{\star}$,
$a/R_{\star}$, and $i$ to float with Gaussian priors defined by the posteriors
from the previous analysis. A uniform prior was used for the mid-transit time
$T_{\mathrm{mid}}$. We used the same MCMC approach as for the first part of
the analysis, with a number of walkers equal to 4 times the number of free
parameters over 5000 steps for each transit, discarding burn-in, and included
a first-degree polynomial trend in the fit to propagate detrending errors in
all curves. In this analysis we obtained precise timings for all TESS transits
currently available, which are listed in Tables LABEL:w18_times and
LABEL:w19_times together with previously obtained transits and their origin
paper.

Sectors 2 and 3 of WASP-18 have been analysed previously by Shporer et al.
(2019) and Maciejewski et al. (2020). Our results agree with the ones from
Maciejewski et al. (2020) within 0.5-1$\sigma$ for the period and radius and
2$\sigma$ for $a/R_{\star}$ and inclination. Shporer et al. (2019) considered
a non-zero eccentricity for their analysis and did not fit the limb-darkening
parameters, which leads to a more significant deviation from our results, with
a 3$\sigma$ agreement in radius but a deviation of 2-3% in $a/R_{\star}$ and
inclination.

The radius of WASP-19b significantly deviates from previous works. Espinoza et
al. (2019) compare their results with the ones from Hebb et al. (2009),
Tregloan-Reed et al. (2013), and Mancini et al. (2013) with good agreement;
however, Wong et al. (2020) used sector 9 of TESS and found an increase of
10-15% in the transit depth, reporting a value of 23240 ppm against 20258 ppm
as reported by Espinoza et al. (2019). We ran individual fits of sectors 9 and
36 and found that between both sectors there is a significant difference of
around 3% in depth, with 21590 ppm in sector 9 and 20996 ppm in sector 36.
While our transit depth estimation is not as far from the previous ones as the
one from Wong et al. (2020), we still find an increase of over 4% in depth
comparing our value with Espinoza et al. (2019) using both TESS sectors (21145
ppm), and over 6% if we use sector 9 only. Wong et al. (2020) suggest that an
increase in stellar spots on the surface during sector 9 measurements is the
cause for the apparently bigger radius. Our smaller difference when only using
sector 9 data may therefore arise from our initial correction with individual
transit segments and posterior normalisation, which was aimed to minimise the
effect of spots. The different values obtained for sector 36 and the fact that
the remaining parameters all agree with Espinoza et al. (2019) in ¡1$\sigma$
levels suggests stellar activity is indeed high and is causing significant
variations in the transit depths when using TESS data.

##  5 Timing and orbital decay analysis

The main goal of our paper is to better constrain tidal decay in promising
targets. We used our derived transit times from TESS together with other
transit times from the literature to look for TTVs in WASP-18b and WASP-19b.
All timings are listed in Tables LABEL:w18_times and LABEL:w19_times,
referencing the original paper where the transit was first reported. However,
Maciejewski et al. (2020), while compiling all previous transits of WASP-18b,
ran new photometric analyses of the majority of the reported transits. Several
transits from TRESCA used by Petrucci et al. (2020) were excluded from the
WASP-19 TTV analysis. While they correspond to recent observations, we
verified the normalised residuals of those times against a constant period
model and found a high amount of scatter and high uncertainties when compared
to TESS transits. Since the data are contemporary with the more precise TESS
transits, we decided not to include them in the analysis.

In order to study the period variations in both targets, we estimated the time
of each individual transit as a function of the epoch using a linear and a
quadratic model. The linear model assumes a circular orbit with a constant
period as

$T_{\mathrm{mid}}=T_{\mathrm{0}}+P\times E$ (1)

where $T_{\mathrm{0}}$ is the reference mid-transit time ($E=0$), $P$ is the
orbital period, and $E$ is the epoch number counted from $T_{\mathrm{0}}$. The
quadratic model includes an additional term, taking a uniform period change
into account as

$T_{\mathrm{mid}}=T_{\mathrm{0}}+P\times E+\frac{1}{2}\dot{P}\times P\times
E^{2}$ (2)

where $\dot{P}=dP/dT$ is the rate of change in orbital period given by its
derivative over time.

Comparing the two models using the BIC allowed us to look for a significant
detection of a period change. The derivative over time is related to the star
tidal quality factor $Q_{\star}$, which corresponds to the rate of energy
dissipation due to tidal interactions (Goldreich & Soter, 1966). The larger
the value of $Q_{\star}$, the lower the tidal dissipation efficiency is. We
used a parametrisation for $Q_{\star}$ from the tidal interaction model by
Zahn (1977)

$Q^{\prime}_{\star}=\frac{3Q_{\star}}{2k_{\star}}$ (3)

where $k_{\star}$ is the stellar Love number, which measures how much of the
star’s density is concentrated in its core and is related to its response to
tidal forces. This leads to a relationship between $Q^{\prime}_{\star}$ and
$\dot{P}$

$Q^{\prime}_{\star}=-\frac{27}{2}\pi\left(\frac{M_{\mathrm{p}}}{M_{\star}}\right)\left(\frac{a}{R_{\star}}\right)^{-5}\dot{P}^{-1}$
(4)

where $M_{\mathrm{p}}/M_{\star}$ is the planet-star mass ratio and
$a/R_{\star}$ is the scaled orbital semi-major axis. Planets similar to
WASP-18b, with a high planet-star mass ratio, are very good candidates for
tidal decay studies.

We assumed Gaussian priors for $T_{\mathrm{0}}$ and $P$, using the previous
best-fit values and uncertainties, and a uniform prior for $\dot{P}$,
$\mathcal{U}(-10,2)$. We ran an MCMC analysis with the emcee code using all
available transit times $T_{\mathrm{mid}}$ to fit for the value of $\dot{P}$
and refine $T_{\mathrm{0}}$ and $P$. We ran the model over 32 walkers with
10000 steps each, discarding burn-in.

##  6 Results and discussion

The results for the TTV fits are listed in Table 3. We compared the BIC values
of the linear and quadratic models, with the linear model being favoured for
both targets (-4.09 against 0.73 for WASP-18b and -3.91 against 0.85 for
WASP-19b), suggesting there is still no significant evidence towards a change
in orbital period. The best-fit quadratic models are plotted in Figs. 6 and 7.

Figure 5: Plot of the posterior distribution of $\dot{P}$ from the quadratic
ephemerides fit of WASP-18b (upper) and WASP-19b (lower) TTVs. While it is
clear the distribution of WASP-18 is centred at a non-zero value, it still
includes zero in its 68% confidence interval. On the other hand, in the
distribution for WASP-19b, we see zero is absent from the 1$\sigma$ confidence
level, but present at a 2$\sigma$ level. Figure 6: Transit difference (O-C)
against the epoch, counted from the initial reference time for WASP-18b.
Previous results from the literature (see Table LABEL:w18_times for reference)
are shown in dark red while our results from TESS are shown in orange. The
blue line shows the fitted TTV model with the blue shaded area showing the
error margin for $\dot{P}$. The residuals show no signs of additional small-
scale structures and most are compatible with zero within 1$\sigma$. Upper
plot: Complete view of all the transits used in the fit. Middle plot: Zoom of
the transit timings of TESS Sectors 2 and 3. Bottom plot: Zoom of the transit
timings of TESS Sectors 29 and 30. Figure 7: Same as Figure 6, but for
WASP-19b. The points from previous data are plotted in dark red and listed
with references in Table LABEL:w19_times. As with WASP-18b, we did not find
any additional signals in the residuals, with most being compatible with zero
at 1$\sigma$. Upper plot: Complete view of all the transits used in the fit.
Middle plot: Zoom of the transit timings of TESS Sector 9. Bottom plot: Zoom
of the transit timings of TESS Sector 36. Table 3: Best-fit results for our
TTV analysis, with the linear constant period model and the quadratic model of
orbital decay. We note that $Q^{\prime}_{\star}$ is given as a lower limit
with a 95% confidence level with the corresponding upper limit of $\dot{P}$.

| Constant Period
---|---
Target |  $T_{\mathrm{0}}$ (BJD) |  $P$ (days)
WASP-18 | 2458022.125226(16) | 0.941452407(14)
WASP-19 | 2456021.703698(20) | 0.788839004(13)

| Decay Quadratic Model
---|---
Target |  $T_{\mathrm{0}}$ (BJD) |  $P$ (days) | $\dot{P}$ |  $\dot{P}$ upper limit |  $Q^{\prime}_{\star}$ lower limit
WASP-18 | 2458022.125234(22) | 0.941452400(20) | $(-0.11\pm 0.21)\times 10^{-10}$ | $<-0.45\times 10^{-10}$ | $>(1.42\pm 0.34)\times 10^{7}$
WASP-19 | 2456021.703704(21) | 0.788839038(25) | $(-0.35\pm 0.22)\times 10^{-10}$ | $<-0.71\times 10^{-10}$ | $>(1.26\pm 0.10)\times 10^{6}$

Table 4: Comparison of $\dot{P}$ and $Q^{\prime}_{\star}$ values from recent works. All upper or lower limits were evaluated at a 95% confidence level (2$\sigma$). Source | $\dot{P}$ | $Q^{\prime}_{\star}$
---|---|---
WASP-18b |  |
This work | $(-0.11\pm 0.21)\times 10^{-10}$ | $>(1.42\pm 0.34)\times 10^{7}$
Maciejewski et al. (2020) | $(0.11\pm 1.17)\times 10^{-10}$ | $>3.9\times 10^{6}$
Patra et al. (2020) | $(-1.2\pm 1.3)\times 10^{-10}$ | $>(1.7\pm 0.4)\times 10^{6}$
Shporer et al. (2019) | $(-0.60\pm 2.18)\times 10^{-10}$ | $>1.73\times 10^{6}$
WASP-19b |  |
This work | $(-0.35\pm 0.22)\times 10^{-10}$ | $>(1.26\pm 0.10)\times 10^{6}$
Petrucci et al. (2020) | $<-0.73\times 10^{-10}$ | $>(1.23\pm 0.231)\times 10^{6}$
Patra et al. (2020) | $(-2.06\pm 0.42)\times 10^{-10}$ | $=(5.0\pm 1.5)\times 10^{5}$

We see from Table 3 and Fig. 5 that the $\dot{P}$ value for WASP-18b is still
far from showing evidence of decay, being comfortably compatible with zero at
1$\sigma$ and thus favouring a constant period. The most recent studies of
WASP-18b by Shporer et al. (2019), Maciejewski et al. (2020), and Patra et al.
(2020) report values consistent with these findings, with the ones of the
latter being the closest to a varying period with $\dot{P}=(-1.2\pm 1.3)\times
10^{-10}$. WASP-18b has a relatively high planet-star mass ratio, which makes
it one of the main targets for observing tidal decay. Wilkins et al. (2017)
estimated a minimum of $Q^{\prime}_{\star}>10^{6}$ at 95% confidence; this
value was only slightly improved by Shporer et al. (2019) and Maciejewski et
al. (2020) using TESS data (see Table 4). We are able to improve upon the
minimum value of $Q^{\prime}_{\star}$ with the additional transits from
Sectors 29 and 30 by an order of magnitude compared to previous works. Despite
the increased precision, we did not detect evidence of tidal decay in the
orbit of WASP-18b and so we derived a lower limit of
$Q^{\prime}_{\star}>(1.42\pm 0.34)\times 10^{7}$ at 95% confidence,
corresponding to a $\dot{P}$ upper limit of $-0.45\times 10^{-10}$. From our
result of $Q^{\prime}_{\star}$, the estimated spiral in-fall timescale is
around $5\times 10^{7}\ \mathrm{yr}$, which is longer than originally
expected. For comparison, WASP-12b, the only planet with confirmed tidal decay
so far has a corresponding $Q^{\prime}_{\star}=(1.50\pm 0.11)\times 10^{5}$
(Wong et al., 2022), which is two orders of magnitude lower than the minimum
value we found for WASP-18. WASP-12 is also an F-type star, with an effective
temperature of 6150 K, with a mass similar to WASP-18. If we assume Eq. (4) to
be correct and $Q^{\prime}_{\star}$ to be the same for the same type of stars,
WASP-18b should have a faster decay than WASP-12b, due to the planet-star mass
ratio (which is 10 times higher). The absence of significant decay in WASP-18b
so far shows that despite the similar stellar type and mass,
$Q^{\prime}_{\star}$ is significantly different between the systems,
suggesting the tidal dissipation processes may differ within stars of a
similar type.

WASP-19b shows a decay rate different from zero at a 1$\sigma$ level (Table 3
and Fig. 5). Comparing our results with the ones obtained by Patra et al.
(2020), our value of $Q^{\prime}_{\star}$ is higher than theirs by almost an
order of magnitude, with our $\dot{P}$ absolute value being almost 6 times
smaller, deviating from theirs by more than 7$\sigma$. Since we are unable to
confirm the detection of a period change, we derived a lower limit for
$Q^{\prime}_{\star}$ of WASP-19 of $(1.26\pm 0.10)\times 10^{6}$ at a 95%
confidence level, corresponding to an upper limit of $\dot{P}<-0.71\times
10^{-10}$. Petrucci et al. (2020) include additional transits that appear to
discard a change in the period of WASP-19b. As mentioned before, we opted to
leave this data set out of our analysis due to the high scatter in the transit
times and the higher normalised residuals we found in them, with several
outliers showing up near the TESS observations. We opted to include only the
new data from TESS for this reason. It is important to note that Petrucci et
al. (2020) derived a value of $\dot{P}$ that favours the absence of orbital
decay, listing an upper limit for the decay rate and a lower limit for
$Q^{\prime}_{\star}$ (see Table 4). These inconsistent results and the high
stellar activity of WASP-19 make it a challenge to obtain significant
conclusions. As we have discussed before, the transit depth found in TESS
transits is significantly higher than reported before by previous authors
(Hebb et al., 2009; Tregloan-Reed et al., 2013; Mancini et al., 2013; Espinoza
et al., 2019). Wong et al. (2020) suggest that star spots are at fault for
this difference, but they were unable to find spot-crossing events in
individual transits. The effect has also been studied in detail by Tregloan-
Reed et al. (2013), who found anomalies in two consecutive light curves due to
spots. Espinoza et al. (2019) claim that WASP-19 shows rotational variability
that is caused by giant spots that impact the observations. Patra et al.
(2020) suggest that there are indications that the stellar activity is causing
systematic errors affecting transit times, which is further addressed by
Petrucci et al. (2020), citing the uncertainty in the inclination parameter as
the main cause of errors in transit times. Therefore, while the results may
seem promising, the uncertainties caused by stellar activity indicate that one
should use caution regarding the confirmation or when ruling out tidal decay
in WASP-19. The system is expected to be observed by the CHaracterising
ExOplanet Satellite (CHEOPS) soon, which may shed some new light on the
physical processes behind this system.

Table 5: Summary of the status of the main targets of orbital decay studies
from the literature. Minimum values of $Q^{\prime}_{\star}$ given at a 95%
confidence level, with the exception of WASP-103 which has a confidence level
of 99.7%.

Target | Type |  $T_{\mathrm{eff}}$ (K) | Age (Gyr) |  $M_{\star}/M_{\sun}$(a) | $\dot{P}$ | $Q^{\prime}_{\star}$ | Reference
---|---|---|---|---|---|---|---
WASP-18 | F | 6431 | $\approx 1$ | 1.46(29) | $(-0.10\pm 0.21)\times 10^{-10}$ | $>(1.42\pm 0.34)\times 10^{7}$ | This work
WASP-19 | G | 5460 | $\approx 10$ | 0.935(41) | $(-0.35\pm 0.22)\times 10^{-10}$ | $>(1.26\pm 0.10)\times 10^{6}$ | This work
WASP-12 | F | 6150 | $\approx 2$ | 1.434(11) | $(-9.45\pm 0.30)\times 10^{-10}$ | $=(1.50\pm 0.11)\times 10^{5}$ | Wong et al. (2022)
WASP-4 | G | 5400 | $\approx 7$ |  $1.37(18)$ (b) | $(-7.33\pm 0.23)\times 10^{-10}$ | $=(5.1\pm 0.9)\times 10^{4}$ | Turner et al. (2021a)
WASP-43 | K | 4195 | $>0.2$ | 0.717(25) | $(-1.11\pm 0.22)\times 10^{-10}$ | $>(4.01\pm 1.15)\times 10^{5}$ | Davoudi et al. (2021)
WASP-103 | F | 6013 | $\approx 5$ | 1.21(11) | $(3.6\pm 1.6)\times 10^{-10}$ |  $>(3.3\pm 1.15)\times 10^{6}$(c) | Barros et al. (2022)
KELT-16 | F | 6250 | $\approx 3$ | 1.211(46) | $(-3.36\pm 4.15)\times 10^{-10}$ | $>(1.9\pm 0.8)\times 10^{5}$ | Mancini et al. (2021)
(a) Patra et al. (2020)
(b) Bouma et al. (2019)
(c) 99.7% confidence level

##  7 Tidal decay in other systems

There are several other targets that are interesting for tidal decay studies
due to the characteristics of their stars and the predicted tidal decay rate
they present. As mentioned before, WASP-12b has already been confirmed as
having a decaying period due to tides and WASP-4b has also shown signs of a
rapid change in period; although, the reason for that change is still unclear
(Turner et al., 2021a). Systems such as WASP-43 (Hellier et al., 2011),
WASP-103 (Gillon et al., 2014), and KELT-16 (Oberst et al., 2017) have also
been subject of tidal decay analyses. In Table 5, we present a summary of the
current status of orbital decay studies for these targets and a comparison
with our results.

WASP-18 presents a lower limit of $Q^{\prime}_{\star}$ that is higher than the
measured value for WASP-12 and WASP-4, indicating that the orbit of WASP-18b
might be decaying slower. Some systems have a minimum value of $\approx
10^{5}$, which is consistent with the measured value in WASP-12. According to
the values we collected, KELT-16 and WASP-43 appear to be good candidates to
show tidal decay. WASP-43 has the added interest of being a K-type star,
unlike the other promising targets, making it an important test subject for
the measurement of $Q^{\prime}_{\star}$ in colder stars. We note that
WASP-103b has been recently found to show a hint of an increase in period,
with new transits obtained by CHEOPS indicating that perhaps tidal decay is
not the dominant factor in the period change of the planet (Barros et al.,
2022). It is still possible to obtain a lower limit for $Q^{\prime}_{\star}$,
shown in Table 5, since a negative $\dot{P}$ cannot be excluded within a 99.7%
confidence level. The minimum $Q^{\prime}_{\star}$ found by Barros et al.
(2022) is higher than previously found (e.g. Patra et al., 2020). WASP-4b
shows the fastest decay to date; however, the $Q^{\prime}_{\star}$ value it
shows is lower than expected by theory, making it still uncertain if the
change in period is caused by tidal decay or not.

Theoretically, one could assume that the same type of stars would share
similar values of $Q^{\prime}_{\star}$. However, the different values found,
differing by as much as two orders of magnitude, indicate that even within
stars of similar spectral types and ages similar to WASP-12 and WASP-18,
stellar physics may vary significantly. The better constraining of
$Q^{\prime}_{\star}$ is crucial to address the reasons behind the different
$Q^{\prime}_{\star}$ values and to give us new information about stellar
interiors.

##  8 Summary

We performed an analysis of two hot Jupiters expected to show signs of orbital
decay due to a tidal interaction: WASP-18b and WASP-19b. We analysed all the
available sectors from TESS obtained for both targets between 2019 and 2021
and obtained updated planet parameters. We refined the planetary and transit
parameters obtaining a good agreement with previous reports for WASP-18b. For
WASP-19b, our parameters agree with Espinoza et al. (2019) at a 1$\sigma$
level; however, we found that the transit depth (and the planet radius)
differs significantly with TESS data, with an increase of 6%. This is likely
to be caused by stellar variability as proposed by several authors. We
attempted to correct the light curves to account for the effect of the non-
occulted star spots but, nevertheless, the transit depth varies even between
the two TESS sectors we analysed (3%).

We further obtained transit times for all the available TESS observations and
used our results, together with previous timings, to look for signs of orbital
decay. We found no statistically significant evidence of decay in either
targets, with the linear model being favoured by the BIC. On WASP-18b, we
derived a new minimum value of $Q^{\prime}_{\star}$ of $(1.42\pm 0.34)\times
10^{7}$ at 2$\sigma$, which is two orders of magnitude higher that the value
of WASP-12. We found a negative $\dot{P}$ within $1\sigma$ for WASP-19b, but
the results are likely influenced by possible systematic errors induced by
stellar activity that is unaccounted for and they are not statistically
significant. We derived a lower limit for $Q^{\prime}_{\star}$ of $(1.26\pm
0.10)\times 10^{6}$ at 2$\sigma$.

We found that $Q^{\prime}_{\star}$ ranges from at least between $10^{5}$ and
$10^{7}$ for selected F- and G-type stars, indicating that tidal dissipation
works differently even within similar stars. Most of the mentioned targets are
to be observed by TESS and CHEOPS in the future and those observations may be
able to help improve the constrains on $Q^{\prime}_{\star}$ and find out more
about the tidal decay process and the physics involved in tidal dissipation.

###### Acknowledgements.

This work was supported by FCT – Fundação para a Ciência e a Tecnologia
through national funds and by FEDER through COMPETE2020 – Programa Operacional
Competitividade e Internacionalizacão by these grants: UID/FIS/04434/2019,
UIDB/04434/2020, UIDP/04434/2020, PTDC/FIS-AST/ 32113/2017 and
POCI-01-0145-FEDER-032113; PTDC/FIS-AST/28953/2017 and
POCI-01-0145-FEDER-028953; PTDC/FIS-AST/28987/2017 and
POCI-01-0145-FEDER-028987; UIDB/04564/2020, UIDP/04564/2020, PTDC/FIS-
AST/7002/2020, POCI-01-0145-FEDER-022217 and POCI-01-0145-FEDER-029932. N.M.R.
acknowledges support from FCT through grant DFA/BD/5472/2020. O.D.S.D. is
supported in the form of work contract (DL 57/2016/CP1364/CT0004) funded by
national funds through FCT. This paper includes data collected by the TESS
mission. Funding for the TESS mission is provided by the NASA’s Science
Mission Directorate. We acknowledge the use of public TESS data from pipelines
at the TESS Science Office and at the TESS Science Processing Operations
Center. Resources supporting this work were provided by the NASA High-End
Computing (HEC) Program through the NASA Advanced Supercomputing (NAS)
Division at Ames Research Center for the production of the SPOC data products.
Some of the data presented in this paper were obtained from the Mikulski
Archive for Space Telescopes (MAST). STScI is operated by the Association of
Universities for Research in Astronomy, Inc., under NASA contract NAS5-26555.
Support for MAST for non-HST data is provided by the NASA Office of Space
Science via grant NNX13AC07G and by other grants and contracts.

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##  Appendix A Additional tables

Table 6: WASP-18b transit times with epochs calculated from reference time $T_{\mathrm{0}}=2458022.1249563$. Values marked with an asterisk were derived by Maciejewski et al. (2020) using the source light curve. Epoch |  $T_{\mathrm{mid}}$ (BJD) | Residuals | Band-pass | Light Curve Reference
---|---|---|---|---
$-10150$ | $2448466.365700^{*}$ | $+0.0328^{*}$ | $-0.0209^{*}$ | I | Hipparcos, ESA (1997)
$-4784$ | $2453518.21258^{*}$ | $+0.00842^{*}$ | $-0.00666^{*}$ | I | Pojmanski (1997)
$-4304$ | $2453970.113611^{*}$ | $+0.000782^{*}$ | $-0.000815^{*}$ |  $0.4-0.7\ \mu$m | Butters et al. (2010)
$-3881$ | $2454368.347146^{*}$ | $+0.000748^{*}$ | $-0.00077^{*}$ |  $0.4-0.7\ \mu$m | Butters et al. (2010)
$-3566$ | $2454664.905676^{*}$ | $+0.000582^{*}$ | $-0.000576^{*}$ |  $0.4-0.7\ \mu$m | Hellier et al. (2009)
$-3565$ | $2454665.84803^{*}$ | $+0.000629^{*}$ | $-0.00064^{*}$ |  $0.4-0.7\ \mu$m | Hellier et al. (2009)
$-3122$ | $2455082.910597^{*}$ | $+0.000598^{*}$ | $-0.000634^{*}$ | V | Southworth et al. (2009)
$-3121$ | $2455083.852439^{*}$ | $+0.000315^{*}$ | $-0.000302^{*}$ | V | Southworth et al. (2009)
$-3120$ | $2455084.793919^{*}$ | $+0.000243^{*}$ | $-0.000244^{*}$ | V | Southworth et al. (2009)
$-3119$ | $2455085.734997^{*}$ | $+0.000267^{*}$ | $-0.000263^{*}$ | V | Southworth et al. (2009)
$-3118$ | $2455086.677153^{*}$ | $+0.000344^{*}$ | $-0.00035^{*}$ | V | Southworth et al. (2009)
$-3068$ | $2455133.7472^{*}$ | $+0.001181$ | $-0.001181$ | I | Cortés-Zuleta et al. (2020)
$-3067$ | $2455134.6914^{*}$ | $+0.001181$ | $-0.001181$ | I | Cortés-Zuleta et al. (2020)
$-3066$ | $2455135.6331^{*}$ | $+0.001181$ | $-0.001181$ | I | Cortés-Zuleta et al. (2020)
$-2975$ | $2455221.3042$ | $+0.0001$ | $-0.0001$ |  $3.6\ \mu$m | Maxted et al. (2013)
$-2751$ | $2455432.1897$ | $+0.0001$ | $-0.0001$ |  $4.5\ \mu$m | Maxted et al. (2013)
$-2710$ | $2455470.7885$ | $+0.0004$ | $-0.0004$ | I+z | Maxted et al. (2013)
$-2707$ | $2455473.6144$ | $+0.0009$ | $-0.0009$ | I+z | Maxted et al. (2013)
$-2621$ | $2455554.5786$ | $+0.0005$ | $-0.0005$ | I+z | Maxted et al. (2013)
$-2604$ | $2455570.584$ | $+0.00045$ | $-0.00048$ | I+z | Maxted et al. (2013)
$-2348$ | $2455811.597^{*}$ | $+0.004097$ | $-0.004097$ | I | Cortés-Zuleta et al. (2020)
$-2279$ | $2455876.5559$ | $+0.0013$ | $-0.0013$ | z’ | Maxted et al. (2013)
$-1196$ | $2456896.1478$ | $+0.0008$ | $-0.0008$ |  $1.1-1.7\ \mu$m | Wilkins et al. (2017)
$-814$ | $2457255.7832$ | $+0.0003$ | $-0.00029$ | z | Wilkins et al. (2017)
$-746$ | $2457319.801$ | $+0.00039$ | $-0.00038$ | z | Wilkins et al. (2017)
$-726$ | $2457338.6296^{*}$ | $+0.00106^{*}$ | $-0.00108^{*}$ | r’ | Kedziora-Chudczer et al. (2019)
$-725$ | $2457339.572103^{*}$ | $+0.000516^{*}$ | $-0.000506^{*}$ | r’ | Kedziora-Chudczer et al. (2019)
$-388$ | $2457656.84078$ | $+0.000972$ | $-0.000972$ | I | Cortés-Zuleta et al. (2020)
$-387$ | $2457657.78359$ | $+0.000972$ | $-0.000972$ | I | Cortés-Zuleta et al. (2020)
$-386$ | $2457658.72404$ | $+0.000972$ | $-0.000972$ | I | Cortés-Zuleta et al. (2020)
$-353$ | $2457689.79147^{*}$ | $+0.00075$ | $-0.00075$ | z’ | Patra et al. (2020)
$5$ | $2458026.83186^{*}$ | $+0.001042$ | $-0.001042$ | R | Cortés-Zuleta et al. (2020)
$353$ | $2458354.45787421$ | $+0.0001575586$ | $-0.0001564676$ |  $0.6-1.0\ \mu$m | TESS S2
$354$ | $2458355.39930413$ | $+0.0001488504$ | $-0.0001511559$ |  $0.6-1.0\ \mu$m | TESS S2
$355$ | $2458356.34067383$ | $+0.0001539404$ | $-0.0001580069$ |  $0.6-1.0\ \mu$m | TESS S2
$356$ | $2458357.28222453$ | $+0.0001567581$ | $-0.0001626202$ |  $0.6-1.0\ \mu$m | TESS S2
$357$ | $2458358.22349873$ | $+0.0001580067$ | $-0.0001633241$ |  $0.6-1.0\ \mu$m | TESS S2
$358$ | $2458359.16513058$ | $+0.0001620091$ | $-0.0001548205$ |  $0.6-1.0\ \mu$m | TESS S2
$359$ | $2458360.10662774$ | $+0.0001524249$ | $-0.0001600427$ |  $0.6-1.0\ \mu$m | TESS S2
$360$ | $2458361.04803607$ | $+0.0001606493$ | $-0.0001632962$ |  $0.6-1.0\ \mu$m | TESS S2
$361$ | $2458361.98969784$ | $+0.000163606$ | $-0.000161472$ |  $0.6-1.0\ \mu$m | TESS S2
$362$ | $2458362.93133366$ | $+0.0001485966$ | $-0.0001554287$ |  $0.6-1.0\ \mu$m | TESS S2
$363$ | $2458363.87260354$ | $+0.0001581918$ | $-0.0001603849$ |  $0.6-1.0\ \mu$m | TESS S2
$364$ | $2458364.81376481$ | $+0.0001590161$ | $-0.0001616745$ |  $0.6-1.0\ \mu$m | TESS S2
$365$ | $2458365.75526545$ | $+0.0001551888$ | $-0.0001560597$ |  $0.6-1.0\ \mu$m | TESS S2
$366$ | $2458366.69709569$ | $+0.0001624828$ | $-0.0001675395$ |  $0.6-1.0\ \mu$m | TESS S2
$369$ | $2458369.52125913$ | $+0.0001696489$ | $-0.000165043$ |  $0.6-1.0\ \mu$m | TESS S2
$370$ | $2458370.46275328$ | $+0.0001658185$ | $-0.0001689851$ |  $0.6-1.0\ \mu$m | TESS S2
$371$ | $2458371.40401605$ | $+0.0001579167$ | $-0.0001617904$ |  $0.6-1.0\ \mu$m | TESS S2
$372$ | $2458372.34537126$ | $+0.0001652232$ | $-0.0001639084$ |  $0.6-1.0\ \mu$m | TESS S2
$373$ | $2458373.28731853$ | $+0.0001626426$ | $-0.0001615565$ |  $0.6-1.0\ \mu$m | TESS S2
$374$ | $2458374.22820482$ | $+0.0001543535$ | $-0.0001656061$ |  $0.6-1.0\ \mu$m | TESS S2
$375$ | $2458375.16979404$ | $+0.0001626522$ | $-0.0001585855$ |  $0.6-1.0\ \mu$m | TESS S2
$376$ | $2458376.11125522$ | $+0.0001772189$ | $-0.0001689486$ |  $0.6-1.0\ \mu$m | TESS S2
$377$ | $2458377.05267219$ | $+0.0001583615$ | $-0.0001536757$ |  $0.6-1.0\ \mu$m | TESS S2
$378$ | $2458377.99447371$ | $+0.000163249$ | $-0.00015706$ |  $0.6-1.0\ \mu$m | TESS S2
$379$ | $2458378.93575739$ | $+0.0001563332$ | $-0.0001569462$ |  $0.6-1.0\ \mu$m | TESS S2
$380$ | $2458379.87716368$ | $+0.0001624613$ | $-0.0001570392$ |  $0.6-1.0\ \mu$m | TESS S2
$381$ | $2458380.8188868$ | $+0.0001584449$ | $-0.0001654274$ |  $0.6-1.0\ \mu$m | TESS S2
$387$ | $2458386.46725968$ | $+0.0001516065$ | $-0.0001555054$ |  $0.6-1.0\ \mu$m | TESS S3
$388$ | $2458387.40884281$ | $+0.0001566545$ | $-0.0001593569$ |  $0.6-1.0\ \mu$m | TESS S3
$389$ | $2458388.35020331$ | $+0.0001558977$ | $-0.000153218$ |  $0.6-1.0\ \mu$m | TESS S3
$390$ | $2458389.29167884$ | $+0.0001504402$ | $-0.0001515723$ |  $0.6-1.0\ \mu$m | TESS S3
$391$ | $2458390.23329699$ | $+0.000153637$ | $-0.0001603253$ |  $0.6-1.0\ \mu$m | TESS S3
$392$ | $2458391.17449162$ | $+0.0001584431$ | $-0.0001643114$ |  $0.6-1.0\ \mu$m | TESS S3
$393$ | $2458392.11599167$ | $+0.0001552277$ | $-0.0001539209$ |  $0.6-1.0\ \mu$m | TESS S3
$394$ | $2458393.05747866$ | $+0.0001625986$ | $-0.0001583644$ |  $0.6-1.0\ \mu$m | TESS S3
$395$ | $2458393.99897112$ | $+0.0001548479$ | $-0.0001582581$ |  $0.6-1.0\ \mu$m | TESS S3
$396$ | $2458394.94021869$ | $+0.0001668753$ | $-0.000169203$ |  $0.6-1.0\ \mu$m | TESS S3
$398$ | $2458396.82307126$ | $+0.0001512507$ | $-0.0001505658$ |  $0.6-1.0\ \mu$m | TESS S3
$399$ | $2458397.76447778$ | $+0.000146889$ | $-0.0001459783$ |  $0.6-1.0\ \mu$m | TESS S3
$400$ | $2458398.70654418$ | $+0.0001594393$ | $-0.0001563517$ |  $0.6-1.0\ \mu$m | TESS S3
$401$ | $2458399.64746347$ | $+0.0001560997$ | $-0.0001559248$ |  $0.6-1.0\ \mu$m | TESS S3
$402$ | $2458400.58901982$ | $+0.0001530252$ | $-0.0001545594$ |  $0.6-1.0\ \mu$m | TESS S3
$403$ | $2458401.53082095$ | $+0.0001507412$ | $-0.0001534252$ |  $0.6-1.0\ \mu$m | TESS S3
$404$ | $2458402.47208663$ | $+0.0001577229$ | $-0.0001532313$ |  $0.6-1.0\ \mu$m | TESS S3
$405$ | $2458403.41355656$ | $+0.0001517973$ | $-0.0001556871$ |  $0.6-1.0\ \mu$m | TESS S3
$406$ | $2458404.35498739$ | $+0.0001610387$ | $-0.0001595482$ |  $0.6-1.0\ \mu$m | TESS S3
$407$ | $2458405.29600312$ | $+0.0001597197$ | $-0.0001557732$ |  $0.6-1.0\ \mu$m | TESS S3
$1133$ | $2459088.79056522$ | $+0.0001600377$ | $-0.000157913$ |  $0.6-1.0\ \mu$m | TESS S29
$1134$ | $2459089.73230357$ | $+0.00016285$ | $-0.0001653548$ |  $0.6-1.0\ \mu$m | TESS S29
$1135$ | $2459090.67382584$ | $+0.0001615088$ | $-0.000156747$ |  $0.6-1.0\ \mu$m | TESS S29
$1136$ | $2459091.61540082$ | $+0.0001579316$ | $-0.0001647125$ |  $0.6-1.0\ \mu$m | TESS S29
$1137$ | $2459092.55650709$ | $+0.000163614$ | $-0.0001653631$ |  $0.6-1.0\ \mu$m | TESS S29
$1138$ | $2459093.49800326$ | $+0.0001791626$ | $-0.000182826$ |  $0.6-1.0\ \mu$m | TESS S29
$1139$ | $2459094.43932496$ | $+0.00016946$ | $-0.0001692725$ |  $0.6-1.0\ \mu$m | TESS S29
$1140$ | $2459095.38106862$ | $+0.0001587269$ | $-0.0001569717$ |  $0.6-1.0\ \mu$m | TESS S29
$1141$ | $2459096.322251$ | $+0.0001754$ | $-0.0001693464$ |  $0.6-1.0\ \mu$m | TESS S29
$1142$ | $2459097.26367608$ | $+0.0001623146$ | $-0.000163599$ |  $0.6-1.0\ \mu$m | TESS S29
$1143$ | $2459098.20530848$ | $+0.0001658825$ | $-0.0001709083$ |  $0.6-1.0\ \mu$m | TESS S29
$1148$ | $2459102.91287775$ | $+0.0001981444$ | $-0.0001957247$ |  $0.6-1.0\ \mu$m | TESS S29
$1149$ | $2459103.85470132$ | $+0.0001778397$ | $-0.0001803071$ |  $0.6-1.0\ \mu$m | TESS S29
$1150$ | $2459104.79555654$ | $+0.0001625176$ | $-0.0001631086$ |  $0.6-1.0\ \mu$m | TESS S29
$1151$ | $2459105.73693338$ | $+0.0001674303$ | $-0.0001728937$ |  $0.6-1.0\ \mu$m | TESS S29
$1152$ | $2459106.67848308$ | $+0.0001915787$ | $-0.0001836274$ |  $0.6-1.0\ \mu$m | TESS S29
$1153$ | $2459107.61998804$ | $+0.0001852554$ | $-0.0001908498$ |  $0.6-1.0\ \mu$m | TESS S29
$1154$ | $2459108.56109682$ | $+0.0001617988$ | $-0.0001577111$ |  $0.6-1.0\ \mu$m | TESS S29
$1155$ | $2459109.50246742$ | $+0.0001534618$ | $-0.0001552651$ |  $0.6-1.0\ \mu$m | TESS S29
$1156$ | $2459110.44401564$ | $+0.0001615148$ | $-0.0001572489$ |  $0.6-1.0\ \mu$m | TESS S29
$1157$ | $2459111.38546737$ | $+0.0001939066$ | $-0.0001912813$ |  $0.6-1.0\ \mu$m | TESS S29
$1162$ | $2459116.09285056$ | $+0.0001631719$ | $-0.0001617505$ |  $0.6-1.0\ \mu$m | TESS S30
$1163$ | $2459117.03434091$ | $+0.000159676$ | $-0.0001590436$ |  $0.6-1.0\ \mu$m | TESS S30
$1164$ | $2459117.97587372$ | $+0.0001570867$ | $-0.0001617813$ |  $0.6-1.0\ \mu$m | TESS S30
$1165$ | $2459118.91736845$ | $+0.0001536699$ | $-0.0001490039$ |  $0.6-1.0\ \mu$m | TESS S30
$1166$ | $2459119.85879866$ | $+0.0001564968$ | $-0.0001585761$ |  $0.6-1.0\ \mu$m | TESS S30
$1167$ | $2459120.80037428$ | $+0.0001553485$ | $-0.0001542201$ |  $0.6-1.0\ \mu$m | TESS S30
$1168$ | $2459121.74156424$ | $+0.0001554497$ | $-0.0001566477$ |  $0.6-1.0\ \mu$m | TESS S30
$1169$ | $2459122.68320566$ | $+0.0001682892$ | $-0.0001619783$ |  $0.6-1.0\ \mu$m | TESS S30
$1170$ | $2459123.62416204$ | $+0.0001632229$ | $-0.0001626586$ |  $0.6-1.0\ \mu$m | TESS S30
$1171$ | $2459124.56604724$ | $+0.0001482321$ | $-0.0001548794$ |  $0.6-1.0\ \mu$m | TESS S30
$1172$ | $2459125.50752307$ | $+0.0001542799$ | $-0.0001514558$ |  $0.6-1.0\ \mu$m | TESS S30
$1173$ | $2459126.44901138$ | $+0.0001535523$ | $-0.0001585222$ |  $0.6-1.0\ \mu$m | TESS S30
$1178$ | $2459131.15613401$ | $+0.0001649443$ | $-0.000162974$ |  $0.6-1.0\ \mu$m | TESS S30
$1179$ | $2459132.09748432$ | $+0.000152724$ | $-0.0001505922$ |  $0.6-1.0\ \mu$m | TESS S30
$1180$ | $2459133.03891429$ | $+0.000160387$ | $-0.0001600435$ |  $0.6-1.0\ \mu$m | TESS S30
$1181$ | $2459133.98016695$ | $+0.0001660438$ | $-0.0001685588$ |  $0.6-1.0\ \mu$m | TESS S30
$1182$ | $2459134.92223374$ | $+0.0001939714$ | $-0.000202803$ |  $0.6-1.0\ \mu$m | TESS S30
$1183$ | $2459135.86338806$ | $+0.000181922$ | $-0.000183373$ |  $0.6-1.0\ \mu$m | TESS S30
$1184$ | $2459136.80530221$ | $+0.0001828732$ | $-0.0001829882$ |  $0.6-1.0\ \mu$m | TESS S30
$1185$ | $2459137.74616908$ | $+0.0001570621$ | $-0.000162082$ |  $0.6-1.0\ \mu$m | TESS S30
$1186$ | $2459138.6877949$ | $+0.0001539593$ | $-0.0001510713$ |  $0.6-1.0\ \mu$m | TESS S30
$1187$ | $2459139.62954128$ | $+0.0001504001$ | $-0.000146267$ |  $0.6-1.0\ \mu$m | TESS S30
$1188$ | $2459140.57066808$ | $+0.0001572311$ | $-0.000159404$ |  $0.6-1.0\ \mu$m | TESS S30
$1189$ | $2459141.51195794$ | $+0.0001686196$ | $-0.0001678828$ |  $0.6-1.0\ \mu$m | TESS S30
Table 7: WASP-19b transit times with epochs calculated from reference time $T_{\mathrm{0}}=2456021.70389628$. Epoch |  $T_{\mathrm{mid}}$ (BJD) | Residuals | Bandpass | Light Curve Reference
---|---|---|---|---
$-1580$ | $2454775.3372$ | $+0.0015$ | $-0.0015$ | z | Hebb et al. (2009)
$-1578$ | $2454776.91566$ | $+0.00019$ | $-0.00019$ | H | Anderson et al. (2010)
$-1527$ | $2454817.14633$ | $+0.00021$ | $-0.00021$ | H | Lendl et al. (2013)
$-1042$ | $2455199.73343$ | $+0.00083$ | $-0.00083$ | Clear | Tifner F. (TRESCA)
$-976$ | $2455251.79657$ | $+0.00014$ | $-0.00014$ | r-Gunn | Tregloan-Reed et al. (2013)
$-975$ | $2455252.58544$ | $+0.0001$ | $-0.0001$ | r-Gunn | Tregloan-Reed et al. (2013)
$-971$ | $2455255.74077$ | $+0.00012$ | $-0.00012$ | r-Gunn | Tregloan-Reed et al. (2013)
$-966$ | $2455259.68448$ | $+0.00033$ | $-0.00033$ | Clear | Coloque J. (TRESCA)
$-948$ | $2455273.88282$ | $+0.00062$ | $-0.00062$ | Clear | Evans P. (TRESCA)
$-916$ | $2455299.12768$ | $+0.00055$ | $-0.00055$ | Clear | Curtis I. (TRESCA)
$-871$ | $2455334.6254$ | $+0.00021$ | $-0.00021$ | R | Mancini et al. (2013)
$-866$ | $2455338.56927$ | $+0.00023$ | $-0.00023$ | I+z’ | Lendl et al. (2013)
$-847$ | $2455353.55659$ | $+0.00024$ | $-0.00024$ | R | Mancini et al. (2013)
$-834$ | $2455363.81131$ | $+0.00041$ | $-0.00041$ | BB | Milne G. (TRESCA)
$-828$ | $2455368.54285$ | $+0.00212$ | $-0.00212$ | R | Mancini et al. (2013)
$-611$ | $2455539.72327$ | $+0.0003$ | $-0.0003$ | I-Cousins | Lendl et al. (2013)
$-573$ | $2455569.69826$ | $+0.00036$ | $-0.00036$ | I+z’ | Lendl et al. (2013)
$-556$ | $2455583.10979$ | $+0.00089$ | $-0.00089$ | Clear | Curtis I. (TRESCA)
$-554$ | $2455584.68693$ | $+0.00024$ | $-0.00024$ | r’ | Lendl et al. (2013)
$-554$ | $2455584.68684$ | $+0.00019$ | $-0.00019$ | I+z’ | Lendl et al. (2013)
$-542$ | $2455594.15188$ | $+0.00168$ | $-0.00168$ | R | Mancini et al. (2013)
$-533$ | $2455601.25164$ | $+0.00071$ | $-0.00071$ | R | Mancini et al. (2013)
$-531$ | $2455602.83138$ | $+0.00046$ | $-0.00046$ | I+z’ | Lendl et al. (2013)
$-528$ | $2455605.19414$ | $+0.0018$ | $-0.0018$ | R | Mancini et al. (2013)
$-526$ | $2455606.77464$ | $+0.00022$ | $-0.00022$ | z’ | Lendl et al. (2013)
$-525$ | $2455607.56241$ | $+0.00033$ | $-0.00033$ | I+z’ | Lendl et al. (2013)
$-506$ | $2455622.55057$ | $+0.00026$ | $-0.00026$ | I+z’ | Lendl et al. (2013)
$-504$ | $2455624.12787$ | $+0.00142$ | $-0.00142$ | R | Mancini et al. (2013)
$-493$ | $2455632.80612$ | $+0.00025$ | $-0.00025$ | r’ | Lendl et al. (2013)
$-464$ | $2455655.68222$ | $+0.00045$ | $-0.00045$ | I+z’ | Lendl et al. (2013)
$-445$ | $2455670.66976$ | $+0.00064$ | $-0.00064$ | I+z’ | Lendl et al. (2013)
$-436$ | $2455677.77038$ | $+0.00195$ | $-0.00195$ | R | Mancini et al. (2013)
$-422$ | $2455688.81201$ | $+0.00333$ | $-0.00333$ | R | Mancini et al. (2013)
$-421$ | $2455689.60276$ | $+0.0003$ | $-0.0003$ | R | Mancini et al. (2013)
$-417$ | $2455692.75674$ | $+0.00255$ | $-0.00255$ | R | Mancini et al. (2013)
$-416$ | $2455693.54639$ | $+0.00013$ | $-0.00013$ | R | Mancini et al. (2013)
$-403$ | $2455703.79933$ | $+0.00411$ | $-0.00411$ | R | Mancini et al. (2013)
$-402$ | $2455704.59078$ | $+0.00034$ | $-0.00034$ | R | Mancini et al. (2013)
$-397$ | $2455708.53495$ | $+0.00015$ | $-0.00015$ | R | Mancini et al. (2013)
$-171$ | $2455886.81234$ | $+0.00208$ | $-0.00208$ | R | Mancini et al. (2013)
$-159$ | $2455896.27611$ | $+0.0021$ | $-0.0021$ | R | Mancini et al. (2013)
$-135$ | $2455915.2098$ | $+0.00065$ | $-0.00065$ | R | Mancini et al. (2013)
$-130$ | $2455919.15485$ | $+0.00103$ | $-0.00103$ | R | Mancini et al. (2013)
$-126$ | $2455922.30966$ | $+0.00555$ | $-0.00555$ | R | Mancini et al. (2013)
$-28$ | $2455999.616301$ | $+0.00007$ | $-0.00007$ | HK | Bean et al. (2013)
$0$ | $2456021.70374$ | $+0.000085$ | $-0.000085$ | HK | Bean et al. (2013)
$10$ | $2456029.5925$ | $+0.00035$ | $-0.00035$ | r’ | Lendl et al. (2013)
$15$ | $2456033.53645$ | $+0.00014$ | $-0.00014$ | g’ | Mancini et al. (2013)
$15$ | $2456033.53651$ | $+0.00007$ | $-0.00007$ | r’ | Mancini et al. (2013)
$15$ | $2456033.53643$ | $+0.00007$ | $-0.00007$ | i’ | Mancini et al. (2013)
$15$ | $2456033.53652$ | $+0.00009$ | $-0.00009$ | z’ | Mancini et al. (2013)
$53$ | $2456063.51174$ | $+0.0003$ | $-0.0003$ | I+z’ | Lendl et al. (2013)
$397$ | $2456334.87208$ | $+0.00053$ | $-0.00053$ | Clear | Evans P. (TRESCA)
$910$ | $2456739.547178$ | $+0.000046$ | $-0.000046$ | White light | Espinoza et al. (2019)
$957$ | $2456776.622511$ | $+0.000066$ | $-0.000066$ | White light | Espinoza et al. (2019)
$1464$ | $2457176.563965$ | $+0.000094$ | $-0.000094$ | White light | Espinoza et al. (2019)
$2250$ | $2457796.591441$ | $+0.000061$ | $-0.000061$ | White light | Espinoza et al. (2019)
$2316$ | $2457848.654791$ | $+0.000068$ | $-0.000068$ | White light | Espinoza et al. (2019)
$2326$ | $2457856.543042$ | $+0.000111$ | $-0.000111$ | White light | Espinoza et al. (2019)
$952$ | $2456772.67789$ | $+0.00052$ | $-0.00052$ | I+z’ | Patra et al. (2020)
$1933$ | $2457546.53025$ | $+0.00038$ | $-0.00038$ | I+z’ | Patra et al. (2020)
$3244$ | $2458580.69724$ | $+0.0004$ | $-0.0004$ | I+z’ | Patra et al. (2020)
$3198$ | $2458544.41098726$ | $+0.0005096953$ | $-0.0005161792$ |  $0.6-1.0\ \mu$m | TESS S9
$3199$ | $2458545.19909857$ | $+0.0004676348$ | $-0.0004776159$ |  $0.6-1.0\ \mu$m | TESS S9
$3200$ | $2458545.98899546$ | $+0.000459334$ | $-0.0004546766$ |  $0.6-1.0\ \mu$m | TESS S9
$3201$ | $2458546.77724425$ | $+0.0004526817$ | $-0.0004699151$ |  $0.6-1.0\ \mu$m | TESS S9
$3202$ | $2458547.56694414$ | $+0.0004957815$ | $-0.0005057116$ |  $0.6-1.0\ \mu$m | TESS S9
$3203$ | $2458548.35481158$ | $+0.0004678426$ | $-0.0004630053$ |  $0.6-1.0\ \mu$m | TESS S9
$3204$ | $2458549.14425338$ | $+0.0004675586$ | $-0.0004538751$ |  $0.6-1.0\ \mu$m | TESS S9
$3205$ | $2458549.93228826$ | $+0.0004875952$ | $-0.0004723997$ |  $0.6-1.0\ \mu$m | TESS S9
$3206$ | $2458550.72132794$ | $+0.0004917443$ | $-0.0004904705$ |  $0.6-1.0\ \mu$m | TESS S9
$3207$ | $2458551.51006035$ | $+0.0005079718$ | $-0.000499857$ |  $0.6-1.0\ \mu$m | TESS S9
$3208$ | $2458552.29893896$ | $+0.000491923$ | $-0.0004829233$ |  $0.6-1.0\ \mu$m | TESS S9
$3209$ | $2458553.08800457$ | $+0.000490958$ | $-0.0004977896$ |  $0.6-1.0\ \mu$m | TESS S9
$3210$ | $2458553.87691279$ | $+0.000444077$ | $-0.0004363738$ |  $0.6-1.0\ \mu$m | TESS S9
$3211$ | $2458554.66571083$ | $+0.0004551007$ | $-0.0004432428$ |  $0.6-1.0\ \mu$m | TESS S9
$3212$ | $2458555.45433949$ | $+0.0004878705$ | $-0.0004864196$ |  $0.6-1.0\ \mu$m | TESS S9
$3215$ | $2458557.82151997$ | $+0.0005212972$ | $-0.0005195209$ |  $0.6-1.0\ \mu$m | TESS S9
$3216$ | $2458558.609454$ | $+0.0004931412$ | $-0.000493327$ |  $0.6-1.0\ \mu$m | TESS S9
$3217$ | $2458559.39915513$ | $+0.0004648924$ | $-0.000459963$ |  $0.6-1.0\ \mu$m | TESS S9
$3218$ | $2458560.18683688$ | $+0.0004597507$ | $-0.0004630294$ |  $0.6-1.0\ \mu$m | TESS S9
$3219$ | $2458560.97725509$ | $+0.0004797756$ | $-0.0004820024$ |  $0.6-1.0\ \mu$m | TESS S9
$3220$ | $2458561.76548315$ | $+0.0004690496$ | $-0.0004596392$ |  $0.6-1.0\ \mu$m | TESS S9
$3221$ | $2458562.55375174$ | $+0.0004630492$ | $-0.0004569487$ |  $0.6-1.0\ \mu$m | TESS S9
$3222$ | $2458563.34272117$ | $+0.000474578$ | $-0.0004586996$ |  $0.6-1.0\ \mu$m | TESS S9
$3223$ | $2458564.13193688$ | $+0.0004401143$ | $-0.000421447$ |  $0.6-1.0\ \mu$m | TESS S9
$3224$ | $2458564.92115668$ | $+0.0004787526$ | $-0.0004844793$ |  $0.6-1.0\ \mu$m | TESS S9
$3225$ | $2458565.70935215$ | $+0.0004918357$ | $-0.000486038$ |  $0.6-1.0\ \mu$m | TESS S9
$3226$ | $2458566.49875766$ | $+0.000457878$ | $-0.0004531755$ |  $0.6-1.0\ \mu$m | TESS S9
$3227$ | $2458567.28771693$ | $+0.000479046$ | $-0.0004815575$ |  $0.6-1.0\ \mu$m | TESS S9
$3228$ | $2458568.07636429$ | $+0.0004715116$ | $-0.000471451$ |  $0.6-1.0\ \mu$m | TESS S9
$4134$ | $2459282.76422855$ | $+0.000445984$ | $-0.0004382528$ |  $0.6-1.0\ \mu$m | TESS S36
$4135$ | $2459283.55349494$ | $+0.0004680825$ | $-0.0004832548$ |  $0.6-1.0\ \mu$m | TESS S36
$4136$ | $2459284.34243336$ | $+0.0005023551$ | $-0.000509186$ |  $0.6-1.0\ \mu$m | TESS S36
$4137$ | $2459285.13027096$ | $+0.0004852793$ | $-0.0004831051$ |  $0.6-1.0\ \mu$m | TESS S36
$4138$ | $2459285.91977053$ | $+0.0004735948$ | $-0.0004618111$ |  $0.6-1.0\ \mu$m | TESS S36
$4139$ | $2459286.70892877$ | $+0.0005314286$ | $-0.0005276405$ |  $0.6-1.0\ \mu$m | TESS S36
$4140$ | $2459287.49727343$ | $+0.0004814359$ | $-0.000498216$ |  $0.6-1.0\ \mu$m | TESS S36
$4141$ | $2459288.28588867$ | $+0.0004538875$ | $-0.0004737029$ |  $0.6-1.0\ \mu$m | TESS S36
$4142$ | $2459289.07496964$ | $+0.0005078695$ | $-0.000492987$ |  $0.6-1.0\ \mu$m | TESS S36
$4143$ | $2459289.86351056$ | $+0.0004664274$ | $-0.0004644744$ |  $0.6-1.0\ \mu$m | TESS S36
$4144$ | $2459290.65262719$ | $+0.0005161349$ | $-0.0005024358$ |  $0.6-1.0\ \mu$m | TESS S36
$4145$ | $2459291.44091157$ | $+0.0005141344$ | $-0.0005178709$ |  $0.6-1.0\ \mu$m | TESS S36
$4146$ | $2459292.23014503$ | $+0.0004648569$ | $-0.0004685227$ |  $0.6-1.0\ \mu$m | TESS S36
$4150$ | $2459295.38506316$ | $+0.0005516386$ | $-0.0005686305$ |  $0.6-1.0\ \mu$m | TESS S36
$4151$ | $2459296.17521974$ | $+0.0004610964$ | $-0.0004679605$ |  $0.6-1.0\ \mu$m | TESS S36
$4152$ | $2459296.9630376$ | $+0.0004828338$ | $-0.0004728424$ |  $0.6-1.0\ \mu$m | TESS S36
$4153$ | $2459297.75137559$ | $+0.0005018343$ | $-0.000503573$ |  $0.6-1.0\ \mu$m | TESS S36
$4154$ | $2459298.53984262$ | $+0.0004852697$ | $-0.0004830355$ |  $0.6-1.0\ \mu$m | TESS S36
$4155$ | $2459299.32941899$ | $+0.0004804281$ | $-0.0004758144$ |  $0.6-1.0\ \mu$m | TESS S36
$4156$ | $2459300.11844447$ | $+0.0004893952$ | $-0.0004878233$ |  $0.6-1.0\ \mu$m | TESS S36
$4157$ | $2459300.90763443$ | $+0.0004986904$ | $-0.0005087346$ |  $0.6-1.0\ \mu$m | TESS S36
$4158$ | $2459301.69651184$ | $+0.0004741549$ | $-0.0004809383$ |  $0.6-1.0\ \mu$m | TESS S36
$4159$ | $2459302.48452828$ | $+0.0004956919$ | $-0.0004803605$ |  $0.6-1.0\ \mu$m | TESS S36
$4160$ | $2459303.27444271$ | $+0.0005392028$ | $-0.0005249785$ |  $0.6-1.0\ \mu$m | TESS S36
$4161$ | $2459304.06362531$ | $+0.0004885187$ | $-0.0004994962$ |  $0.6-1.0\ \mu$m | TESS S36
$4162$ | $2459304.85196345$ | $+0.000436011$ | $-0.0004488881$ |  $0.6-1.0\ \mu$m | TESS S36
$4163$ | $2459305.64011759$ | $+0.000536406$ | $-0.0005166219$ |  $0.6-1.0\ \mu$m | TESS S36