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

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.

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.

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).

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.

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:

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.

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.

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/).