# Is the orbit of the exoplanet WASP-43b really decaying? TESS and MuSCAT2
observations confirm no detection

Z. Garai,1,2,3,20 T. Pribulla,1,2,3 H. Parviainen,4,5 E. Pallé,4,5 A.
Claret,6,7 L. Szigeti,1,2,20 V. J. S. Béjar,4,5 N. Casasayas-Barris,19 N.
Crouzet,15 A. Fukui,11,4 G. Chen,17 K. Kawauchi,18 P. Klagyivik,16 S.
Kurita,13 N. Kusakabe,9,10 J. P. de Leon,8 J. H. Livingston,8 R. Luque,6 M.
Mori,8 F. Murgas,4,5 N. Narita,4,9,11,12 T. Nishiumi,9,14 M. Oshagh,4,5 Gy. M.
Szabó1,2,20 M. Tamura,8,9,10 Y. Terada,8 N. Watanabe,9,14
1MTA-ELTE Exoplanet Research Group, 9700 Szombathely, Szent Imre h. u. 112,
Hungary
2ELTE Gothard Astrophysical Observatory, 9700 Szombathely, Szent Imre h. u.
112, Hungary
3Astronomical Institute, Slovak Academy of Sciences, 05960 Tatranská Lomnica,
Slovakia
4Instituto de Astrofísica de Canarias, 38200 La Laguna, Tenerife, Spain
5Department Astrofísica, Universidad de La Laguna, 38206 La Laguna, Tenerife,
Spain
6Instituto de Astrofísica de Andalucía, CSIC, Apartado 3004, 18080 Granada,
Spain
7Dept. Física Teórica y del Cosmos, Universidad de Granada, Campus de
Fuentenueva s/n, 10871 Granada, Spain
8Department of Astronomy, Graduate School of Science, The University of Tokyo,
7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
9Astrobiology Center, 2-21-1 Osawa, Mitaka-shi, Tokyo 181-8588, Japan
10National Astronomical Observatory, 2-21-1 Osawa, Mitaka-shi, Tokyo 181-8588,
Japan
11Komaba Institute for Science, The University of Tokyo, 3-8-1 Komaba, Meguro,
Tokyo 153-8902, Japan
12JST, PRESTO, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan
13Department of Earth and Planetary Science, Graduate School of Science, The
University of Tokyo, 7-3-1 Hongo, Bunkyo-ku, Tokyo 113-0033, Japan
14Department of Astronomical Science, The Graduated University for Advanced
Studies, SOKENDAI, 2-21-1, Osawa, Mitaka, Tokyo, 181-8588, Japan
15European Space Agency (ESA), European Space Research and Technology Centre
(ESTEC), Keplerlaan 1, 2201 AZ Noordwijk, The Netherlands
16Institute of Planetary Research, German Aerospace Center, Rutherfordstrasse
2, 12489 Berlin, Germany
17Key Laboratory of Planetary Sciences, Purple Mountain Observatory, Chinese
Academy of Sciences, Nanjing 210023, PR China
18Department of Multi-Disciplinary Sciences, Graduate School of Arts and
Sciences, The University of Tokyo, 3-8-1 Komaba, Meguro, Tokyo 153-8902, Japan
19Leiden Observatory, Leiden University, Postbus 9513, 2300 RA Leiden, The
Netherlands
20MTA-ELTE Lendület Milky Way Research Group, Hungary E-mail:
<EMAIL_ADDRESS>
(Accepted XXX. Received YYY; in original form ZZZ)

###### Abstract

Up to now, WASP-12b is the only hot Jupiter confirmed to have a decaying
orbit. The case of WASP-43b is still under debate. Recent studies preferred or
ruled out the orbital decay scenario, but further precise transit timing
observations are needed to definitively confirm or refute the period change of
WASP-43b. This possibility is given by the Transiting Exoplanet Survey
Satellite (TESS) space telescope. In this work we used the available TESS
data, multi-color photometry data obtained with the Multicolor Simultaneous
Camera for studying Atmospheres of Transiting exoplanets 2 (MuSCAT2) and
literature data to calculate the period change rate of WASP-43b and to improve
its precision, and to refine the parameters of the WASP-43 planetary system.
Based on the observed-minus-calculated data of 129 mid-transit times in total,
covering a time baseline of about 10 years, we obtained an improved period
change rate of $\dot{P}=-0.6\pm 1.2$ ms yr-1 that is consistent with a
constant period well within $1\sigma$. We conclude that new TESS and MuSCAT2
observations confirm no detection of WASP-43b orbital decay.

###### keywords:

methods: observational – techniques: photometric – planets and satellites:
individual: WASP-43b

††pubyear: 2015††pagerange: Is the orbit of the exoplanet WASP-43b really
decaying? TESS and MuSCAT2 observations confirm no detection–Is the orbit of
the exoplanet WASP-43b really decaying? TESS and MuSCAT2 observations confirm
no detection

##  1 Introduction

Transit time variations (TTVs) of known exoplanets can be used to search for a
third body in the planetary systems, but variations of transit times can also
indicate star-planet tidal interaction. This interaction has various forms:
apsidal precession in which the orbit ellipse rotates in its own plane, and
nodal precession in which the orbit normal precesses about the total angular
momentum vector. For eccentric orbits, both will result in long-term
variations of the transit times, and of the transit durations. Typically,
apsidal precession dominates (Miralda-Escudé, 2002; Ragozzine & Wolf, 2009).
In addition to the effects of apsidal precession due to tidal bulges, tidal
effects in close-in planets can lead to tidal decay, and a shift in transit
times (Sasselov, 2003). This tidal decay is also referred to as orbital decay
or tidal inspiraling. The end result of this process is tidal disruption and
disintegration of the planet body.

Tidal decay was considered in several cases, for example, for WASP-18 (Hellier
et al., 2009), KELT-16 (Oberst et al., 2017), WASP-103 (Gillon et al., 2014),
WASP-12 (Hebb et al., 2009) and WASP-43 (Gillon et al., 2012). The full list
of interesting planets from this viewpoint was summarized in Table 1 of Patra
et al. (2020). In the case of WASP-4 a decreasing orbital period was detected
by Bouma et al. (2019), later Bouma et al. (2020) concluded that the system is
accelerating toward the Sun, and the associated Doppler effect should cause
the apparent period change rate. Up to now, WASP-12b is the only hot Jupiter
to have a decaying orbit confirmed by Turner et al. (2021). The confirmation
was a long process started by Maciejewski et al. (2016), who reported as first
the possibility that the orbital period of WASP-12b is changing. Further
observations confirmed the departure of transit times from the linear
ephemeris (Patra et al., 2017; Maciejewski et al., 2018; Bailey & Goodman,
2019). Yee et al. (2020) preferred orbital decay over apsidal precession or
Romer effect. Turner et al. (2021) analyzed, besides the literature data, the
data obtained by TESS (Ricker, 2014) to characterize the system and to verify
that the planet is undergoing orbital decay. The authors highly favor the
orbital decay scenario and obtained a decay rate of $\dot{P}=-32.5\pm 1.6$ ms
yr-1.

The case of WASP-43b is still under debate. The investigation of its possible
orbital decay started with the orbital period change rate of $\dot{P}=-95\pm
36$ ms yr-1, reported by Blecic et al. (2014). In the same year, Murgas et al.
(2014) and Chen et al. (2014) revised the period change rate and obtained a
value of $\dot{P}=-150\pm 60$ ms yr-1 and $\dot{P}=-90\pm 40$ ms yr-1,
respectively. Further estimation of a period change rate of $\dot{P}=-30\pm
30$ ms yr-1 was presented by Ricci et al. (2015). This result left open the
question of the period change of WASP-43b. In the next year a possible orbital
change rate of $\dot{P}=-28.9\pm 7.7$ ms yr-1 was presented and the orbital
decay scenario was preferred by Jiang et al. (2016), on the other hand Hoyer
et al. (2016) ruled out the orbital decay based on additional transit
observations, obtaining a period change rate of $\dot{P}=0.0\pm 6.6$ ms yr-1.
Stevenson et al. (2017) added three Spitzer Space Telescope transit
observations and found no evidence for orbital decay, moreover the obtained
change rate was positive ($\dot{P}=+9.0\pm 4.0$ ms yr-1). Similarly, Patra et
al. (2020) increased the time baseline by adding three transits and found that
the period of WASP-43b has changed slightly. They found a period change rate
of $\dot{P}=+14.4\pm 4.6$ ms yr-1. The authors noted that this result could be
only a statistical fluke, and this will be clearer after more observations in
the future. Thus, the possible orbital decay of the exoplanet WASP-43b is
still an open question, and precise transit timing observations are needed to
definitively confirm or refute the orbital decay scenario. This possibility is
given by the TESS space telescope. TESS provides high-precision photometric
transit observations, which we used for searching for TTVs.

In this paper we aimed at refining the system parameters based on TESS and
MuSCAT2 data and to calculate the period change rate of WASP-43b. We combined
TESS data and multi-color ground-based observations, because multi-color
photometric transit observations can ameliorate the degeneracy between the
planet-to-star radius ratio and the orbit inclination angle. The first
parameter is passband dependent, but the second parameter is passband
independent (Csizmadia et al., 2013; Espinoza & Jordán, 2015; Parviainen et
al., 2020). The paper is organized as follows. In Section 2 a brief
description of instrumentation and data reduction is given. Data analysis and
model fitting are detailed in Section 3. Our results are described in Section
4. We summarize our findings in Section 5.

##  2 Observations and data reduction

WASP-43b was observed with TESS in Sector No. 9, from 2019-02-28 to 2019-03-26
and also in Sector No. 35, from 2021-02-09 to 2021-03-07. The data were
downloaded from the Mikulski Archive for Space Telescopes111See
https://mast.stsci.edu/portal/Mashup/Clients/Mast/Portal.html. in the form of
Simple Aperture Photometry (SAP) fluxes. Sector No. 9 contains 15 602 data-
points, Sector No. 35 13 661 data-points, i.e., we used 29 263 TESS data-
points in total during our analysis. The number of transits observed in Sector
No. 9 is 26, while from Sector No. 35 we obtained 24 transits, i.e., we used
50 TESS transits in total during the analysis (see Table 1 for the TESS
observational log). These data were obtained from 2-min integrations, but in
comparison with Pre-search Data Conditioning Simple Aperture Photometry
(PDCSAP) fluxes, long-term trends were not removed. The downloaded SAP fluxes
were detrended using our pipeline, described later in this section.

Table 1: Log of TESS photometric observations of WASP-43 used in our analysis (sorted by TESS sectors). Table shows time interval of observations, number of observed transits, and number of data points obtained from the TESS database. TESS Sector | Time interval of observations | Transits | Data points
---|---|---|---
No. 09 | 2019-02-28 – 2019-03-26 | 26 | 15 602
No. 35 | 2021-02-09 – 2021-03-07 | 24 | 13 661
Total | – | 50 | 29 263

The multi-color photometric observations were performed using the Carlos
Sánchez Telescope (TCS) on the island of Tenerife (Spain). The TCS is a 1.52 m
diameter Cassegrain type $f/13.8$ telescope, installed on an equatorial
mount222See http://research.iac.es/OOCC/iac-managed-telescopes/telescopio-
carlos-sanchez/.. The photometric detector, called MuSCAT2, is installed in
the Cassegrain focus of the telescope. The number "2" means that this is
already the second such instrument. MuSCAT2 is a four-color dichroic
instrument, with four $1024\times 1024$ CCD cameras, made by Princeton
Instruments, having a field of view of $7.4^{\prime}\times 7.4^{\prime}$ with
a pixel scale of $0.44^{\prime\prime}$ per pixel. Three dichroic mirrors
separate incoming light into the four CCDs, enabling simultaneous operation of
the cameras. No filter wheel is applied, every CCD has only one filter.
Modified Sloan filters $g$, $r$, $i$, and $z_{s}$ are used with the
transparencies from 400 to 550 nm for the $g$ filter, from 550 to 700 nm for
the $r$ filter, from 700 to 820 nm for the $i$ filter, and from 820 to 920 nm
for the $z_{s}$ filter, see Fig. 1. More details about this instrument can be
found in Narita et al. (2019).

Figure 1: Relative transmittance of the TESS instrument and the modified Sloan
$g$, $r$, $i$, and $z_{s}$ filters, installed on the MuSCAT2 instrument. The
tabulated data were obtained from the web
(https://heasarc.gsfc.nasa.gov/docs/tess/the-tess-space-telescope.html) and by
personal communication from Norio Narita (narita@g.ecc.u-tokyo.ac.jp),
respectively.

The observations of WASP-43 were carried out with telescope defocusing. Mainly
the CCD camera equipped with the $g$ filter was used for guiding the
telescope. We used MuSCAT2 transit observations of WASP-43b from five nights
in total. These observations were carried out before TESS observations. The
evening dates of the MuSCAT2 observations are the followings: 2018-01-09,
2018-01-18, 2018-02-18, 2018-04-03, and 2019-01-02. We obtained 3690, 4877,
4306, and 3182 data-points in the passbands $g$, $r$, $i$, and $z_{s}$,
respectively (see Table 2 for the MuSCAT2 observational log). The multi-color
photometric observations were reduced using the dedicated MuSCAT2 photometry
pipeline following Parviainen et al. (2020). The pipeline works under the
Python3333See https://www.python.org/download/releases/3.0/. environment and
it is based on NumPy (van der Walt et al., 2011), SciPy (Virtanen et al.,
2020), AstroPy (Astropy Collaboration et al., 2013), and Photutils (Bradley et
al., 2019) packages. During the first step the pipeline makes dark and flat
corrections of the scientific frames. After this step the astrometric solution
is performed using the Astrometry.net software (Lang et al., 2010). Finally,
the pipeline calculates aperture photometry. During this step the target star
and up to 14 comparison stars in 10 apertures are calculated, which means that
up to 150 absolute light curves are created per measurement and filter. During
the next step we first identified the target star per measurement and filter,
subsequently other stars were used as comparison stars and the relative light
curve of the target star was calculated. We tried every comparison star and
every aperture. In all cases the scatter of the corresponding relative light
curve was determined and the best three comparison stars with the best
apertures, which produced the lowest scatter of the corresponding relative
light curve of the target star, were selected. As the final step we prepared
the relative transit light curve per measurement and filter by using the best
three comparison stars with the best apertures as an average comparison star.

Table 2: Log of MuSCAT2 multi-color photometric observations of WASP-43 used in our analysis (sorted by evening dates). Table shows number of scientific frames per passband ($N_{\mathrm{passband}}$), obtained during the given observing night and the applied exposure times in seconds ($Exp_{\mathrm{passband}}$). Evening date | $N_{\mathrm{g}}/Exp_{\mathrm{g}}$ | $N_{\mathrm{r}}/Exp_{\mathrm{r}}$ | $N_{\mathrm{i}}/Exp_{\mathrm{i}}$ | $N_{\mathrm{z_{s}}}/Exp_{\mathrm{z_{s}}}$
---|---|---|---|---
2018-01-09 | 2086/5 | 2078/5 | 2076/5 | 1425/8
2018-01-18 | 835/13 | 835/13 | 835/13 | 835/13
2018-02-18 | 328/30 | 898/10 | 626/15 | 481/20
2018-04-03 | 441/9 | 441/9 | 441/9 | 441/9
2019-01-02 | –/– | 625/15 | 328/30 | –/–
Total | 3690/– | 4877/– | 4306/– | 3182/–

The MuSCAT2 multi-color light curves were first normalized to unity. After
that, the linear trend, due to the second-order extinction, was removed from
the photometric data. As a next step we cleaned the light curves from
outliers. We used a $3\sigma$ clipping, where $\sigma$ is the standard
deviation of the light curve. Subsequently, we converted all remaining time-
stamps from Modified Julian Date in Universal Time Coordinated
($\mathrm{MJD}_{\mathrm{UTC}}$), which is the used output-time-stamp format of
the MuSCAT2 photometry pipeline (i.e., $\mathrm{JD}-2~{}400~{}000.5$), to
Barycentric Julian Date in Barycentric Dynamical Time
($\mathrm{BJD}_{\mathrm{TDB}}$), using the online applet UTC2BJD444See
http://astroutils.astronomy.ohio-state.edu/time/utc2bjd.html. (Eastman et al.,
2010).

The downloaded TESS data were treated similarly as MuSCAT2 data. The SAP
fluxes were first normalized to unity. During the next step TESS data were cut
into segments, each covering one orbital period. Each segment of the data was
fitted with a linear function. During the fitting procedure the part of the
data covering the transit was excluded from the fit. Consequently, the linear
trend was removed from each chunk of data (including the transit data). This
detrending method can effectively remove the long-term variability (mainly
variability of the host star due to spots and rotation) while it does not
introduce any nonlinear trend to the data, see Fig. 2 and, e.g., Garai (2018).
Outliers were cleaned similarly as in the case of the MuSCAT2 observations.
Since TESS uses as time-stamps Barycentric TESS Julian Date (i.e.,
$\mathrm{BJD}_{\mathrm{TDB}}-2~{}457~{}000.0$), during the next step we
converted all TESS time-stamps to $\mathrm{BJD}_{\mathrm{TDB}}$.

During the modeling tests (See Sect. 3.1) we recognized that mainly in the
case of MuSCAT2 data the linear detrending is not enough, also correlated
noise is present in the data. To better detrend the data and to remove
correlated noise we applied the following procedure. We first detrended the
MuSCAT2 data using higher-order polynomial, then we fitted every single light
curve, including TESS transits, using the Levenberg-Marquardt method
implemented in the non-linear least-squares minimization and light-curve
fitting package, called lmfit555See https://lmfit.github.io/lmfit-py/.. The
following free parameters and priors were adjusted: the mid-transit time
$T_{\mathrm{c}}$ = $N$(2 455 528.868634, 0.000046)
$\mathrm{BJD}_{\mathrm{TDB}}$ (Hoyer et al., 2016), the planet-to-star area
ratio $(R_{\mathrm{p}}/R_{\mathrm{s}})^{2}$ = $N$(0.026, 0.001) calculated
based on Hoyer et al. (2016), the transit duration $T_{\mathrm{dur}}$ =
$N$(0.061, 0.001) in units of phase (Esposito et al., 2017), the impact
parameter $b$ = $N$(0.689, 0.013) in units of stellar radius (Esposito et al.,
2017), and the light-curve normalization factor $l_{\mathrm{norm}}$ = $U$(1.0,
0.5) in fluxes. The quadratic limb darkening coefficients were calculated for
the MuSCAT2 $g$, $r$, $i$, and $z_{\mathrm{s}}$ passbands based on the
spherical PHOENIX-COND models (Claret, 2018) and then linearly interpolated
using the stellar parameters of $T_{\mathrm{eff}}=4500\pm 100$ K, log
$g=4.5\pm 0.2$ cgs, and Fe/H = $-0.01\pm 0.15$ dex, see Esposito et al.
(2017). For the TESS passband the quadratic limb-darkening coefficients were
linearly interpolated from the Table 5666See https://cdsarc.unistra.fr/viz-
bin/nph-Cat/html?J/A+A/618/A20/table5.dat., published by Claret (2018). These
coefficients were fixed during the fitting procedure (see Sect. 3.1), as well
as the orbital period of WASP-43b adopted from Hoyer et al. (2016), i.e.,
$P=0.813473978$ d. We assumed circular orbit of WASP-43b.

As a next step we ran a Markov chain Monte Carlo (MCMC) analysis with the
affine-invariant sampler implemented in the emcee777See
https://emcee.readthedocs.io/en/stable/. package (Foreman-Mackey et al.,
2013). During this step we also modeled correlated noise using a Gaussian
process regression method with the SHOTerm plus JitterTerm kernel, with a
fixed quality factor $Q=1/\sqrt{2}$, implemented in the CELERITE888See
https://celerite.readthedocs.io/en/stable/. package (Kallinger et al., 2014;
Foreman-Mackey et al., 2017; Barros et al., 2020). The regression is done by
using $\log\sigma$ (free), $\log Q$ (fixed), $\log\omega_{0}$ (free), and
$\log S_{0}$ (free) hyperparameters with bounds on the values of these
parameters to be inputted by the user. We first fixed the transit shape, i.e.,
the parameters $(R_{\mathrm{p}}/R_{\mathrm{s}})^{2}$, $T_{\mathrm{dur}}$, $b$,
and the mid-transit time $T_{\mathrm{c}}$ from the lmfit result and set free
the three hyperparameters for a preliminary MCMC analysis. The posteriors of
the hyperparameters obtained from this analysis were used to define the priors
for the next MCMC analysis as twice the uncertainty computed from the
posterior distribution. Finally, we ran the MCMC analysis again with free
transit model parameters and free hyperparameters. As the very last step we
removed correlated noise from the data. We can note that TESS data changed
negligibly with this procedure, however MuSCAT2 data were significantly
detrended. These detrended MuSCAT2 light curves of WASP-43b transits are
depicted in Fig. 3.

To quantify and compare the quality of individual detrended light curves we
used a quantity, which is called photometric noise rate ($PNR$), adopted from
Fulton et al. (2011). It is defined as:

$PNR=\frac{rms}{\sqrt{\Gamma}},$ (1)

where the root mean square ($rms$) is derived from the light curve residuals
and $\Gamma$ is the median number of cycles, including exposure time and
readout time999Readout time of MuSCAT2 CCD cameras is about 1.35 s, while in
the case of TESS CCD camera it is about 0.3 s., per minute. MuSCAT2 $PNR$
values are summarized in Fig. 3 and TESS transit light curves are qualified
with $PNR$ in Table 3. We can see that the MuSCAT2 photometry in
$z_{\mathrm{s}}$ passband has always the worst quality, the best quality
measurement was taken on 2019-01-02 in $r$ passband. TESS light curves have
stable quality with $PNR\approx 0.26$ % min-1, which is comparable to the
MuSCAT2 measurement taken on 2018-01-18 in $g$ passband.

Figure 2: Detrended and normalized TESS data taken from the Mikulski Archive
for Space Telescopes in the form of SAP fluxes. Figure 3: Detrended MuSCAT2
data, plotted in chronological order starting from the top, and offset in
relative flux for clarity. On the right side of the graph the quality of
individual light curves is quantified using $PNR$ (in % min-1) for comparison
purposes (see the last paragraph of Sect. 2).

##  3 Data analysis

###  3.1 Transit modelling

We analyzed the detrended TESS and MuSCAT2 photometry data using the RMF
(Roche ModiFied) code. The software was prepared only recently based on the
ROCHE code, which is devoted to the modeling of multi-data set observations of
close eclipsing binary stars, such as radial velocities and multi-color light
curves (Pribulla, 2012). The RMF code was already used with success, e.g., in
Szabó et al. (2020). The code can simultaneously model multi-color light
curves, radial velocities, and broadening functions, or least-squares
deconvolved line profiles of binary stars and transiting exoplanets. Its
modification to be used with the transiting exoplanets uses the Roche surface
geometry with the planet gravity neglected for the host star (rotationally
deformed shape) and spherical shape for the planet. The model can handle
eccentric orbits, misaligned rotational axes of the components, stellar
oblateness, gravity darkening due to rapid rotation using the analytical
approach of Espinosa Lara & Rieutord (2011), Doppler beaming effect, advanced
limb-darkening description, and third light. The synthesis of the broadening
functions assumes solid-body rotation. The synthesis of the observables is
performed in the plane of the sky using pixel elements. The effectiveness of
the integration is increased by the adaptive phase step being more fine during
the eclipses/transits.

During the analysis procedure we used the following parameters: the mid-
transit time $T_{\mathrm{c}}$, the orbital period $P_{\mathrm{orb}}$, the
orbit inclination angle $i$ with respect to the plane of the sky, the ratio of
the host radius to the semi-major axis $R_{\mathrm{s}}/a$, the passband-
dependent planet-to-star radius ratio $R_{\mathrm{p}}/R_{\mathrm{s}}$, the
eccentricity $e$, the longitude of the periastron passage $\omega$, the
passband-dependent third light $l_{3}$, defined as $l_{3}/(l_{1}+l_{2})$, and
the passband-dependent light-curve normalization factor $l_{\mathrm{norm}}$.
The stellar limb darkening is described by the four-parameter limb-darkening
model of Claret (2018) with the critical foreshortening angle when the
intensity drops to zero101010Parameter $\mu=\cos\theta$, where $\theta$ is the
so-called foreshortening angle, which is angle between the line of sight and a
normal to the stellar surface. For $\mu<\mu_{\mathrm{crit}}$ the stellar flux
is assumed to be zero, see Claret (2018)., interpolating for local gravity and
temperature for each pixel. The limb-darkening coefficients ($a_{1}$, $a_{2}$,
$a_{3}$, $a_{4}$, and $\mu_{\mathrm{crit}}$) were calculated for the $g$, $r$,
$i$, $z_{\mathrm{s}}$, and TESS passbands, using the tabulated transmittance
of the MuSCAT2 filters and TESS instrument, and using the same spherical
PHOENIX-COND models as in Claret (2018). The limb-darkening coefficients were
linearly interpolated from the calculated tables of coefficients for the
stellar parameters of $T_{\mathrm{eff}}=4500\pm 100$ K, log $g=4.5\pm 0.2$
cgs, and Fe/H = $-0.01\pm 0.15$ dex, see Esposito et al. (2017). These
coefficients were fixed during the fitting procedure. We note that prior this
treatment we ran several test modelings with quadratic and four-parameter limb
darkening coefficients allowed to float. Since we always got unphysical fitted
coefficients far from the tabulated theoretical values, we decided to keep
fixed these coefficients during the fitting procedure and to use the four-
parameter model, because there is no significant difference in fitted
parameters while applying either the quadratic or the four parameter approach,
but the latter one represents better the distribution of specific intensities,
because it improves the description of both the stellar limb and the central
parts. The unphysical fitted limb-darkening coefficients could be due to the
high impact parameter of the system, $b=0.689\pm 0.013$ (Esposito et al.,
2017), which means that the transit chord is located in such a disk region,
where $\mu$ values are from a very narrow interval. In addition, the
eccentricity $e$ was set to zero and the longitude of the periastron passage
$\omega$ was fixed at $90^{\circ}$, i.e., we assumed circular orbit of
WASP-43b. Finally, we also fix the $l_{3}$ parameters. In the case of MuSCAT2
apertures there is no third light contamination. TESS has larger aperture than
MuSCAT2, therefore the third light contamination possibility is also larger.
Since we used SAP fluxes, which are not corrected by the dilution factor, we
used the CROWDSAP111111CROWDSAP is a keyword on the header of the fits files
containing the light curves. It represents the ratio of the target flux to the
total flux in the TESS aperture. crowding metric value to determine the
$l_{3}$ parameter for the TESS aperture. In the case of WASP-43b this gives
$l_{3,\mathrm{\textit{TESS}}}=0.0008$.

The joint model optimization was done by the steepest descend method, using
the numerical derivatives of the observables with respect to the parameters.
The optimization was run until the $\chi^{2}$ improvement was smaller than
0.00005. To obtain realistic estimates of the parameter uncertainties 2000
Monte Carlo experiments were performed. The artificial data-sets were created
from the best fitting model at the times of observations adding a random
Gaussian noise equal to the standard deviation of the data with respect to the
fit. We aimed at compensating the fixed limb-darkening coefficients, therefore
uncertainty of the parent star’s effective temperature and surface gravity,
which strongly affect limb darkening, were propagated to the modeling as
Gaussian priors. The distribution of the parameters were analyzed to obtain
the final values and the standard errors. The best-fitting parameter values
correspond to quantile 0.50 (median) and the uncertainties to quantils $\pm
0.341$.

Table 3: The list of the observed (’O’) mid-transit times of WASP-43b, derived using the joint model parameter values (see Table 4). During this fitting procedure only the mid-transit time and the light-curve normalization factor parameters were adjusted. The uncertainties in the fitted parameters were estimated based on the covariance matrix method. The quality of individual TESS light curves is also quantified using $PNR$ for comparison purposes (see the last paragraph of Sect. 2). Transit | ’O’ times [$\mathrm{BJD}_{\mathrm{TDB}}$] |  $PNR$ [% min-1] | Source
---|---|---|---
No. 01 | $2458128.732027\pm 0.000080$ | See Fig. 3 | MuSCAT2
No. 02 | $2458137.680280\pm 0.000120$ | See Fig. 3 | MuSCAT2
No. 03 | $2458168.592124\pm 0.000068$ | See Fig. 3 | MuSCAT2
No. 04 | $2458212.519760\pm 0.000070$ | See Fig. 3 | MuSCAT2
No. 05 | $2458486.660595\pm 0.000064$ | See Fig. 3 | MuSCAT2
No. 06 | $2458545.23075\pm 0.00020$ | 0.2710 | TESS
No. 07 | $2458546.04416\pm 0.00022$ | 0.2620 | TESS
No. 08 | $2458546.85750\pm 0.00020$ | 0.2749 | TESS
No. 09 | $2458547.67129\pm 0.00021$ | 0.2826 | TESS
No. 10 | $2458548.48448\pm 0.00022$ | 0.2648 | TESS
No. 11 | $2458549.29790\pm 0.00020$ | 0.2884 | TESS
No. 12 | $2458550.11120\pm 0.00020$ | 0.2988 | TESS
No. 13 | $2458550.92453\pm 0.00021$ | 0.2684 | TESS
No. 14 | $2458551.73864\pm 0.00022$ | 0.2494 | TESS
No. 15 | $2458552.55170\pm 0.00021$ | 0.2683 | TESS
No. 16 | $2458553.36520\pm 0.00020$ | 0.2694 | TESS
No. 17 | $2458554.17893\pm 0.00021$ | 0.2529 | TESS
No. 18 | $2458554.99224\pm 0.00020$ | 0.2757 | TESS
No. 19 | $2458558.24619\pm 0.00021$ | 0.2767 | TESS
No. 20 | $2458559.05960\pm 0.00020$ | 0.2652 | TESS
No. 21 | $2458559.87291\pm 0.00020$ | 0.3016 | TESS
No. 22 | $2458560.68623\pm 0.00021$ | 0.2763 | TESS
No. 23 | $2458561.49990\pm 0.00020$ | 0.2584 | TESS
No. 24 | $2458562.31369\pm 0.00020$ | 0.2547 | TESS
No. 25 | $2458563.12719\pm 0.00022$ | 0.2864 | TESS
No. 26 | $2458563.94020\pm 0.00020$ | 0.2710 | TESS
No. 27 | $2458564.75415\pm 0.00021$ | 0.2727 | TESS
No. 28 | $2458565.56763\pm 0.00020$ | 0.2796 | TESS
No. 29 | $2458566.38034\pm 0.00020$ | 0.2949 | TESS
No. 30 | $2458567.19410\pm 0.00020$ | 0.2866 | TESS
No. 31 | $2458568.00806\pm 0.00020$ | 0.2798 | TESS
No. 32 | $2459256.20649\pm 0.00020$ | 0.2494 | TESS
No. 33 | $2459257.02070\pm 0.00021$ | 0.2538 | TESS
No. 34 | $2459257.83368\pm 0.00021$ | 0.2450 | TESS
No. 35 | $2459258.64749\pm 0.00020$ | 0.2502 | TESS
No. 36 | $2459259.46044\pm 0.00021$ | 0.2690 | TESS
No. 37 | $2459260.27437\pm 0.00021$ | 0.2585 | TESS
No. 38 | $2459261.08729\pm 0.00021$ | 0.2620 | TESS
No. 39 | $2459261.90120\pm 0.00021$ | 0.2618 | TESS
No. 40 | $2459262.71463\pm 0.00022$ | 0.2481 | TESS
No. 41 | $2459263.52811\pm 0.00020$ | 0.2549 | TESS
No. 42 | $2459264.34187\pm 0.00020$ | 0.2441 | TESS
No. 43 | $2459265.15498\pm 0.00021$ | 0.2630 | TESS
No. 44 | $2459265.96887\pm 0.00022$ | 0.2696 | TESS
No. 45 | $2459266.78191\pm 0.00021$ | 0.3170 | TESS
No. 46 | $2459272.47657\pm 0.00021$ | 0.2544 | TESS
No. 47 | $2459273.28930\pm 0.00020$ | 0.2695 | TESS
No. 48 | $2459274.10301\pm 0.00020$ | 0.2851 | TESS
No. 49 | $2459274.91692\pm 0.00020$ | 0.2735 | TESS
No. 50 | $2459275.73038\pm 0.00020$ | 0.2596 | TESS
No. 51 | $2459276.54350\pm 0.00020$ | 0.2639 | TESS
No. 52 | $2459277.35728\pm 0.00020$ | 0.2694 | TESS
No. 53 | $2459278.17090\pm 0.00021$ | 0.2469 | TESS
No. 54 | $2459278.98399\pm 0.00022$ | 0.2713 | TESS
No. 55 | $2459279.79781\pm 0.00020$ | 0.2644 | TESS

###  3.2 Timing analysis

To analyze the possible shift in transit times, which can indicate the orbital
decay of WASP-43b, we constructed the so-called observed-minus-calculated
(O-C) diagram for mid-transit times. We used 50 TESS transits, 5 MuSCAT2
transits and literature data, which amount to 74 additional transits. To
obtain the ’O’ times of the mid-transits we modeled each TESS and MuSCAT2
transit event individually using the RMF code. During this procedure we fixed
every parameter to its best value from the joint model except for two
parameters: the mid-transit time and the light-curve normalization factor. The
list of the fitted mid-transit times obtained from this modeling is presented
in Table 3. The uncertainties in the fitted parameters were estimated based on
the covariance matrix method. The literature data were taken directly in the
form of mid-transit times. We used 68 mid-transit times compiled by Hoyer et
al. (2016), see references therein, 3 mid-transit times obtained by Stevenson
et al. (2017), and 3 mid-transit times of WASP-43b observed by Patra et al.
(2020). We used 129 transit events in total, covering a time baseline of about
10 years. The first mid-transit time in our data-set,
$\mathrm{BJD}_{\mathrm{TDB}}$ = 2 455 528.86863, corresponds to 08:50:49.63 UT
on 2010-11-28. To calculate the ’C’ times of the mid-transits we used the
linear ephemeris formula as:

$T_{0}=T_{\mathrm{c}}+P_{\mathrm{orb}}\times E,$ (2)

were $T_{0}$ corresponds to the ’C’ value, $T_{\mathrm{c}}$ is the reference
mid-transit time, $P_{\mathrm{orb}}$ is the orbital period, and $E$ is the
epoch of observation, i.e., the number of the orbital cycle calculated from
$T_{\mathrm{c}}$. We used the jointly fitted parameter values for
$T_{\mathrm{c}}$ and $P_{\mathrm{orb}}$ to calculate $T_{0}$ values (see Sect.
4.1). In such a way we could construct the O-C diagram of WASP-43b mid-transit
times. For this purpose we used the environment of the OCFIT121212See
https://github.com/pavolgaj/OCFit. code (Gajdoš & Parimucha, 2019). The
software is simple thanks to a very intuitive graphic user interface. As
first, we fitted the O-C data with a linear function using the OCFIT package
FitLinear. The free parameters of the linear model are the reference mid-
transit time $T_{\mathrm{c}}$ and the orbital period $P_{\mathrm{orb}}$.
Subsequently, the O-C data were fitted with a quadratic function, also offered
by the OCFIT code, within the package called FitQuad. The free parameters of
the quadratic model are the reference mid-transit time $T_{\mathrm{c}}$, the
orbital period $P_{\mathrm{orb}}$, and the quadratic coefficient $Q$, which
follows from the quadratic ephemeris formula of:

$T_{0}=T_{\mathrm{c}}+P_{\mathrm{orb}}\times E+Q\times E^{2},$ (3)

where the quadratic coefficient $Q$ can be expressed as:

$Q=\frac{1}{2}P_{\mathrm{orb}}\times\dot{P},$ (4)

where $\dot{P}$ means the orbital period change with time $t$, i.e., this is
the so-called orbital period change rate: $\dot{P}=\mathrm{d}P/\mathrm{d}t$.
$\dot{P}$ is a dimensionless quantity, but it can be expressed in s yr-1 or in
ms yr-1. The uncertainties in the fitted parameters of $P_{\mathrm{orb}}$,
$T_{\mathrm{c}}$, and $Q$ were derived within the OCFIT packages FitLinear and
FitQuad applying the covariance matrix method.

##  4 Results

###  4.1 System parameters from the TESS and MuSCAT2 data

We summarize the fitted and derived parameters of the planetary system in
Table 4. The phase-folded and binned transit light curves of the exoplanet
WASP-43b, overplotted with the best-fitting RMF models are presented in Fig.
4. The posterior probability distributions are depicted in Fig. 5. WASP-43b is
a dense gaseous planet despite its close-in orbit, which is due to the low
effective temperature of the host star ($T_{\mathrm{eff}}=4403^{+46}_{-53}$
K), and, consequently, to the relatively low equilibrium temperature of the
planet ($T_{\mathrm{eq}}=1426.7\pm 8.5$ K, see Esposito et al. (2017)). The
radius of WASP-43b is very close to the radius of the planet Jupiter, i.e.,
$R_{\mathrm{p}}=1.037^{+0.022}_{-0.019}$ $\mathrm{R}_{\mathrm{Jup}}$, but the
mass of the planet is about 2-times the mass of Jupiter, i.e.,
$M_{\mathrm{p}}=1.997^{+0.072}_{-0.073}$ $\mathrm{M}_{\mathrm{Jup}}$. The
combination of these two parameters results in a planet density, which is
about 1.6-times the density of the planet Jupiter
($\rho_{\mathrm{p}}=2.10^{+0.31}_{-0.32}$ $\mathrm{g.cm}^{-3}$). WASP-43b had
the closest orbit to its host star among hot Jupiters at the time of its
discovery. The semi-major axis of the planet is
$a=0.01507^{+0.00026}_{-0.00027}$ a.u.

Table 4: An overview of the best-fitting and derived parameters of the WASP-43 planetary system (host and planet b), obtained from the TESS and MuSCAT2 data. The final fitted values correspond to quantile 0.50 (median) and the uncertainties to quantils $\pm 0.341$ in the parameter distributions obtained from 2000 Monte Carlo experiments. The values of $T_{\mathrm{eff}}$ and log $g$ are distributions of Gaussian priors for limb darkening. The $T_{\mathrm{c}}$ and $P_{\mathrm{orb}}$ parameter values are preliminary, see Sect. 4.2 and Table 5 for improved values. The planet-to-star radius ratio parameter value for all passbands combined was calculated as weighted average of TESS and MuSCAT2 $R_{\mathrm{p}}/R_{\mathrm{s}}$ values with weights of $1/\sigma^{2}$, where $\sigma$ is the uncertainty in each passband. Notes: Gaia DR2 = Gaia Collaboration et al. (2018), E2017 = Esposito et al. (2017). Parameter | Value | Source
---|---|---
Gaia ID | 3767805209112436736 |  Gaia DR2
RA [h:m:s] (J2000) | 10:19:38.0 |  Gaia DR2
Dec [deg:m:s] (J2000) | -09:48:22.6 |  Gaia DR2
Parallax [mas] | $11.499\pm 0.043$ |  Gaia DR2
$T_{\mathrm{eff}}$ [K] | $4403^{+46}_{-53}$ | This work
log $g$ [dex] | $4.500^{+0.011}_{-0.012}$ | This work
$V$ [mag] | 12.4 | E2017
$G$ [mag] | 11.9 |  Gaia DR2
$M_{\mathrm{s}}$ [$M_{\odot}$] | $0.688\pm 0.037$ | E2017
$R_{\mathrm{s}}$ [$R_{\odot}$] | $0.6506\pm 0.0054$ | E2017
$K$ [$\mathrm{m.s}^{-1}$] | $551.0\pm 3.2$ | E2017
$T_{\mathrm{c}}$ [$\mathrm{BJD}_{\mathrm{TDB}}$] | $2~{}455~{}528.869175^{+0.000061}_{-0.000063}$ | This work
$P_{\mathrm{orb}}$ [d] | $0.813473949^{+0.000000019}_{-0.000000021}$ | This work
$i$ [deg] | $81.684^{+0.039}_{-0.033}$ | This work
$R_{\mathrm{s}}/a$ | $0.21127^{+0.00056}_{-0.00063}$ | This work
$R_{\mathrm{p}}/R_{\mathrm{s}}$ (TESS passband) | $0.16015^{+0.00040}_{-0.00042}$ | This work
$R_{\mathrm{p}}/R_{\mathrm{s}}$ ($g$ passband) | $0.16630^{+0.00120}_{-0.00110}$ | This work
$R_{\mathrm{p}}/R_{\mathrm{s}}$ ($r$ passband) | $0.16412^{+0.00051}_{-0.00064}$ | This work
$R_{\mathrm{p}}/R_{\mathrm{s}}$ ($i$ passband) | $0.16740^{+0.00120}_{-0.00100}$ | This work
$R_{\mathrm{p}}/R_{\mathrm{s}}$ ($z_{\mathrm{s}}$ passband) | $0.16530^{+0.00150}_{-0.00180}$ | This work
$R_{\mathrm{p}}/R_{\mathrm{s}}$ (all passbands) | $0.16224\pm 0.00031$ | This work
$R_{\mathrm{p}}$ [$\mathrm{R}_{\mathrm{Jup}}$] | $1.037^{+0.022}_{-0.019}$ | This work
$M_{\mathrm{p}}$ [$\mathrm{M}_{\mathrm{Jup}}$] | $1.997^{+0.072}_{-0.073}$ | This work
$\rho_{\mathrm{p}}$ [$\mathrm{g.cm}^{-3}$] | $2.10^{+0.31}_{-0.32}$ | This work
$a$ [a.u.] | $0.01507^{+0.00026}_{-0.00027}$ | This work

Based on the joint TESS and MuSCAT2 observations we obtained an orbital period
of $P_{\mathrm{orb}}=0.813473949^{+0.000000019}_{-0.000000021}$ d and
$T_{\mathrm{c}}=2~{}455~{}528.869175^{+0.000061}_{-0.000063}$
$\mathrm{BJD}_{\mathrm{TDB}}$. We refined this ephemeris in Sect. 4.2 based on
the whole O-C data-set of mid-transit times, therefore this result is
considered as a preliminary orbital period and reference mid-transit time. We
note, however, that this ephemeris was also necessary during the timing
analysis – the O-C diagram of the mid-transit times (see Fig. 6) was
calculated based on this $P_{\mathrm{orb}}$ and $T_{\mathrm{c}}$, using the
Eq. 2. The orbit inclination angle value, $i=81.684^{+0.039}_{-0.033}$ deg,
obtained by the RMF code, is in a $3\sigma$-agreement with the parameter
values presented, e.g., by Hellier et al. (2011) and by Ricci et al. (2015),
i.e., $i=82.6^{+1.3}_{-0.9}$ deg and $i=81.92\pm 0.54$ deg, respectively.
Hoyer et al. (2016) obtained $i=82.11\pm 0.10$ deg, which is out of this
$3\sigma$-agreement interval. We found the value of
$R_{\mathrm{s}}/a=0.21127^{+0.00056}_{-0.00063}$, which is equal to
$a/R_{\mathrm{s}}=4.733^{+0.012}_{-0.014}$. This parameter value corresponds
within $3\sigma$ to the parameter values presented, e.g., by Ricci et al.
(2015) and by Esposito et al. (2017), i.e., $a/R_{\mathrm{s}}=4.82\pm 0.11$
and $a/R_{\mathrm{s}}=4.97\pm 0.14$, respectively. Hoyer et al. (2016)
obtained $a/R_{\mathrm{s}}=4.867\pm 0.023$, which is about $5.8\sigma$
difference.

In the case of the planet-to-star radius ratio parameter, we obtained the
best-fitting value of $R_{\mathrm{p}}/R_{\mathrm{s}}$ = $0.16224\pm 0.00031$
for all passbands combined, which is comparable, e.g., with the value of
$R_{\mathrm{p}}/R_{\mathrm{s}}$ = $0.1588\pm 0.0040$, published by Esposito et
al. (2017). Several transmission spectroscopy observations targeted also
WASP-43, see e.g., Chen et al. (2014), Kreidberg et al. (2014), Murgas et al.
(2014), or Ricci et al. (2015). The passband-dependent planet-to-star radius
ratio parameter values derived during the joint analysis are in a $3\sigma$
agreement with these transmission spectra. Mainly the TESS passband value fit
well the existing measurements.

Figure 4: Phase-folded transit light curves of WASP-43b in TESS and MuSCAT2
$g$, $r$, $i$, and $z_{s}$ passbands, overplotted with the best-fitting RMF
models (black lines). We binned the data only for better visualization of the
transit shape, but we fitted individual data-points (1 gray bin-point
represents 50 data-points). During the joint modeling procedure all individual
light curves per filter were combined and fitted simultaneously. Figure 5:
Posterior probability distributions of WASP-43b, obtained from 2000 Monte
Carlo experiments. The diagonal panels show the 1D distributions and the other
panels show the 2D distributions and illustrate the parameter degeneracies.

###  4.2 Transit timings and ephemeris refinement

Figure 6: Observed-minus-calculated (O-C) diagrams of WASP-43b mid-transit
times. The left-hand panel shows the whole O-C data-set sorted by the sources
and fitted with a linear/quadratic function using the OCFIT code. The right-
hand panel focuses on the O-C data-points derived based on the TESS data for
better visibility.

The whole O-C data-set of mid-transit times used during our analysis is
presented in Fig. 6 (left-hand panel). In this graph we can see the 68 data-
points, collected by Hoyer et al. (2016), the 3 data-points, observed by
Stevenson et al. (2017), the 3 data-points presented by Patra et al. (2020),
the 50 data-points derived from the TESS observations, plotted also separately
in Fig. 6 (right-hand panel), and the 5 data-points derived from the MuSCAT2
observations in this work, i.e., 129 data-points in total. As first, these O-C
data were fitted with a linear function. This fit is shown in Fig. 6 (left-
hand panel). Based on the linear fit we obtained a refined linear ephemeris
of:

$T_{0}=2~{}455~{}528.868607(51)~{}\mathrm{BJD}_{\mathrm{TDB}}+0.813474101(18)~{}\mathrm{d}\times
E.$ (5)

Subsequently, the O-C data-set of mid-transit times was fitted with a
quadratic function. This fit is also depicted in Fig. 6 (right-hand panel). We
can see that the quadratic trend is not significant at the first glance. Based
on this quadratic fit we obtained a quadratic ephemeris of:

$T_{0}=2~{}455~{}528.868590(60)~{}\mathrm{BJD}_{\mathrm{TDB}}+0.813474135(70)~{}\mathrm{d}\times
E+Q\times E^{2},$ (6)

where the quadratic coefficient is $Q=(-0.8\pm 1.5)\times 10^{-11}$ d,
confirming the negligible quadratic trend in the O-C data-set of mid-transit
times. Based on the Eq. 4 we can easily calculate the period change rate
$\dot{P}$ from $Q$. We obtained a dimensionless value of $\dot{P}=(-2.0\pm
3.7)\times 10^{-11}$, which we can convert to $\dot{P}=-0.6\pm 1.2$ ms yr-1.
The result is negative, but is not significant, confirming the previous
results about no detection. In comparison with the results presented by Hoyer
et al. (2016), i.e., $\dot{P}=0.0\pm 6.6$ ms yr-1, derived by Stevenson et al.
(2017), i.e., $\dot{P}=+9.0\pm 4.0$ ms yr-1, and obtained by Patra et al.
(2020), i.e., $\dot{P}=+14.4\pm 4.6$ ms yr-1, our result is more precise
thanks to the high quality TESS observations and to the longer time baseline.
The quality of the linear and quadratic fit was expressed as Bayesian
Information Criterion ($BIC$), which is defined as:

$BIC=\chi^{2}+k\ln N,$ (7)

where $k$ is the number of free parameters of the model and $N$ is the number
of data-points. There is no significant difference between the two Bayesian
Information Criterions, i.e., $BIC=266.1$ in the case of the linear fit and
$BIC=269.9$ in the case of the quadratic fit, which means that it is not
justified to use the quadratic fit.

Since we did not detect significant orbital period change rate of WASP-43b, we
can adopt the values presented in Eq. 5 as a final solution for the reference
mid-transit time and orbital period of the planet, i.e.,
$T_{\mathrm{c}}=2~{}455~{}528.868607\pm 0.000051$
$\mathrm{BJD}_{\mathrm{TDB}}$ and $P_{\mathrm{orb}}=0.813474101\pm
0.000000018$ d. In comparison with the ephemeris obtained from the joint TESS
and MuSCAT2 analysis (see Table 4), using the whole O-C data-set of mid-
transit times we improved the parameter $T_{\mathrm{c}}$ by a factor of 1.23
and the parameter $P_{\mathrm{orb}}$ by a factor of 1.16. This result confirms
the previously published parameter values, see Table 5 for examples.

Table 5: The finally adopted ephemeris of WASP-43b, improved based on the whole O-C data-set of mid-transit times, and its comparison with two previously published ephemeris. Notes: H2011 = Hellier et al. (2011), H2016 = Hoyer et al. (2016). Parameter | Value | Source
---|---|---
$T_{\mathrm{c}}$ [$\mathrm{BJD}_{\mathrm{TDB}}$] | $2~{}455~{}528.868607\pm 0.000051$ | This work
$P_{\mathrm{orb}}$ [d] | $0.813474101\pm 0.000000018$ | This work
$T_{\mathrm{c}}$ [$\mathrm{BJD}_{\mathrm{TDB}}$] | $2~{}455~{}528.86774\pm 0.00014$ | H2011
$P_{\mathrm{orb}}$ [d] | $0.8134750\pm 0.0000010$ | H2011
$T_{\mathrm{c}}$ [$\mathrm{BJD}_{\mathrm{TDB}}$] | $2~{}455~{}528.868634\pm 0.000046$ | H2016
$P_{\mathrm{orb}}$ [d] | $0.813473978\pm 0.000000035$ | H2016

##  5 Conclusions

Using the O-C data-set of mid-transit times, derived from 129 transits of
WASP-43b, we have re-estimated the orbital period change rate of the
exoplanet. The obtained result, $\dot{P}=-0.6\pm 1.2$ ms yr-1, is consistent
with a constant period well within $1\sigma$. It confirms the previous results
about no detection, but in comparison with the previous results, our result is
more precise thanks to the high quality TESS observations and to the longer
time baseline. By extending the observations to more than 730 days, i.e.,
covering a time baseline of about 10 years, we could improve the $\dot{P}$
parameter by a factor of about 3.8 in comparison with the latest published
result. Thus, we see no evidence to support previous claims of a decaying
orbit for WASP-43b. As a by-product of the data analysis, we also derived the
system parameters of WASP-43b. Several of them were refined in comparison with
the previously published parameters. Thanks to combination of the high quality
TESS and multi-color MuSCAT2 observations we could estimate, for example, the
orbit inclination angle parameter and the combined planet-to-star radius ratio
parameter precisely and without parameter degeneration. The derived parameter
values are mostly in $3\sigma$ agreement with the results of existing studies.
Since we did not detect significant period change rate of the planet, a new
linear ephemeris of WASP-43b was derived using the whole O-C data-set of mid-
transit times.

## Acknowledgements

We thank Dr. S. Hoyer from the Laboratoire d’Astrophysique de Marseille (LAM)
in France for the helpful discussions. We also thank the anonymous reviewer
for the helpful comments and suggestions. This work was supported by the
ERASMUS+ grant No. 2017-1-CZ01-KA203-035562, by the VEGA grant of the Slovak
Academy of Sciences No. 2/0031/18, by an ESA PRODEX grant under contracting
with the ELTE University, by the GINOP No. 2.3.2-15-2016-00003 of the
Hungarian National Research, Development and Innovation Office, and by the
City of Szombathely under agreement No. 67.177-21/2016. This article is based
on observations made with the MuSCAT2 instrument, developed by ABC, at
Telescopio Carlos Sánchez operated on the island of Tenerife by the IAC in the
Spanish Observatorio del Teide. This work is partly financed by the Spanish
Ministry of Economics and Competitiveness through grants No.
PGC2018-098153-B-C31. This work is partly supported by JSPS KAKENHI grant Nos.
JP18H01265 and JP18H05439, and JST PRESTO grant No. JPMJPR1775. This work is
partly supported by JSPS KAKENHI grant No. JP17H04574. This work was partly
supported by Grant-in-Aid for JSPS Fellows, grant No. JP20J21872. M.T. is
supported by MEXT/JSPS KAKENHI grant Nos. 18H05442, 15H02063, and 22000005.
A.C. acknowledges financial support from the State Agency for Research of the
Spanish MCIU through the ”Center of Excellence Severo Ochoa” award for the
Instituto de Astrophysics of Andalusia (SEV-2017-0709). We acknowledge funding
from the European Research Council under the European Union’s Horizon 2020
research and innovation program under grant agreement No 694513.

## Data availability

The data underlying this article will be shared on reasonable request to the
corresponding author. The reduced light curves presented in this work will be
made available at the CDS (http://cdsarc.u-strasbg.fr/).

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