Signs of magnetic star-planet interactions in HD 118203 TESS detects stellar variability that matches the orbital period of a close-in eccentric Jupiter-sized companion

Context. Planetary systems with close-in giant planets can experience magnetic star-planet interactions that modify the activity levels of their host stars. The induced activity is known to strongly depend on the magnetic moment of the interacting planet. Therefore, such planet-induced activity should be more readily observable in systems with close-in planets in eccentric orbits, since those planets are expected to rotate faster than in circular orbits. However, no evidence of magnetic interactions has been reported in eccentric planetary systems to date. Aims. We intend to unveil a possible planet-induced activity in the bright ( V = 8.05 ± 0.03 mag) and slightly evolved star HD 118203, which is known to host an eccentric ( e = 0.32 ± 0.02) and close-in ( a = 0.0864 ± 0.0006 au) Jupiter-sized planet. Methods. We characterized the planetary system by jointly modelling 56 ELODIE radial velocities and four sectors of TESS photometry. We computed the generalized Lomb-Scargle periodogram of the TESS, ELODIE, and complementary ASAS-SN data to search for planet-induced and rotation-related activity signals. We studied the possible origins of the stellar variability found, analysed its persistence and evolution, and searched for possible links with the eccentric orbital motion of HD 118203 b. Results. We found evidence of an activity signal within the TESS photometry that matches the 6.1-day orbital period of its hosted planet HD 118203 b, which suggests the existence of magnetic star-planet interactions. We did not find, however, any additional activity signal that could be unambiguously interpreted as the rotation of the star, so we cannot discard stellar rotation as the actual source of the signal found. Nevertheless, both the evolved nature of the star and the significant orbital eccentricity make the synchronous stellar rotation with the planetary orbit very unlikely. Conclusions. The planetary system HD 118203 represents the best evidence that magnetic star-planet interactions can be found in eccentric planetary systems, and it opens the door to future dedicated searches in such systems that will allow us to better understand the interplay between close-in giant planets and their host stars.


Introduction
In the late 1980s, Campbell et al. (1988) presented the first exoplanet candidate that was later found to be a real planet (Hatzes et al. 2003).Soon after, Mayor & Queloz (1995) confirmed the first exoplanet orbiting a Sun-like star, 51 Peg b.Having half the mass of Jupiter and orbiting its star every 4.2 days, 51 Peg b was the prelude to the detection of tens of similar planets through the radial velocity technique (e.g.Butler et al. 1997Butler et al. , 1998;;Santos et al. 2000) and the transit method (e.g. Henry et al. 2000;Charbonneau et al. 2000).Those giant planets orbiting close to their host stars (≲ 0.1 au) are commonly known as hot Jupiters, and they dominated the exoplanet demographics in the early years of exoplanet exploration since they were the easiest to detect.
The Kepler mission (Borucki et al. 2010;Howell et al. 2014) detected thousands of small planets thanks to several statistical validation works that required minimal follow-up observations (e.g.Livingston et al. 2018a,b;Castro González et al. 2020;de Leon et al. 2021;Christiansen et al. 2022).Interestingly, there was not such an explosive increase for the hot Jupiter detections because of two main reasons.First, planet occurrence studies revealed that hot Jupiters are an unusual outcome of planet formation and evolution (e.g.Mayor et al. 2011;Howard et al. 2012).Second, much of the radial velocity follow-up effort was focussed on the newly discovered Neptune-sized and super-Earthsized planets (e.g.Lillo-Box et al. 2020;Dai et al. 2023;Osborn et al. 2023;Passegger et al. 2024), thus leaving thousands of hot Jupiter candidates detected via transit without confirmation 1 .
Jupiter-sized planets, however, have played a major role in our understanding of the properties and formation of planetary systems.Shortly after the first discoveries, following initial suspicions (Gonzalez 1997), Santos et al. (2001Santos et al. ( , 2004) ) found that the fraction of gas giants increases as the stellar host metallicity increases, which favours the traditional core-accretion planet formation theory against the alternative disk instability theory.Also, hot Jupiters provide ideal laboratories to study tidal interactions and magnetic star-planet interactions (MSPIs) that do not exist in our own Solar System.This is because hot Jupiters typically lie inside the Alfvén radius of their host stars, which marks the boundary between the stellar corona and stellar wind (≃ 10 R ⋆ ).At such short orbital distances, the coronal plasma's Alfvén velocity is larger than the stellar wind velocity, which allows for a direct magnetic interaction with the stellar surface.
The possibility of tidal interactions and MSPIs in planetary systems hosting hot Jupiters was first suggested by Cuntz et al. (2000).Magnetic star-planet interactions can be manifested as periodic stellar activity that matches the orbital period of the interacting planet.In contrast, tidal interactions can induce stellar variability with half the orbital period.One of the first signs of MSPIs was observed in HD 192263, which was known to have a hot Jupiter detected via radial velocities by Santos et al. (2000).This planet was put into question by Henry et al. (2002), who detected periodic photometric variations with a very similar period to that of the reported planetary orbit.In a subsequent study, Santos et al. (2003) acquired simultaneous radial velocity and photometric data and found that the photometric variations alternated stable and variable moments.In contrast, the radial velocity variations showed long-term stability in period, phase, and amplitude.This result supported the idea that the radial velocity signal had a planetary origin and that the photometric signal could be produced either by the rotation of the star or by magnetic interactions induced by the hosted planet.Only four months after, Shkolnik et al. (2003) reported the first piece of evidence of MSPIs in HD 179949, which was known to host a 3-day orbit hot Jupiter (Tinney et al. 2001).The authors detected periodic chromospheric activity through Ca II H and K variability that matched the orbital period of the planet, as well as 7-day stellar variability corresponding to the rotation of the star.Since this first discovery, dozens of MSPIs have been reported and analysed (e.g.Shkolnik et al. 2005Shkolnik et al. , 2008;;Walker et al. 2008;Pagano et al. 2009;Pillitteri et al. 2011;Maggio et al. 2015;Cauley et al. 2019).Tidal interactions, however, took longer to be confirmed.One of the first examples was the case of Kepler-91 b, in which Lillo-Box et al. (2014a,b) found evidence of stellar tidal distortions within the Kepler light curve.More recently, Barros et al. (2022) detected for the first time tidal distortions in an exoplanet, and Ilic et al. (2022) found that tidal forces exerted by hot Jupiters can alter the rotation evolution of their host stars.
Direct detections of hot Jupiter's magnetic fields have been attempted through radio observations aiming at observing the electron cyclotron maser instability (Zarka 1998;Treumann 2006).Recently, Ben-Jaffel et al. (2022) reported signatures of magnetization in HAT-P-11 b through a detection of a magnetotail, but previous attempts to detect radio emission from planetary magnetic fields were not successful (e.g.Bastian et al. 2000;Farrell et al. 2003Farrell et al. , 2004;;Winterhalter et al. 2006;George & Stevens 2007, 2008;Lecavelier Des Etangs et al. 2009;Lazio et al. 2010;Vidotto et al. 2012;Zarka et al. 2015).To date, the best approach to probe planetary magnetic fields is through indirect MSPIs.Although they have been only found in systems hosting hot Jupiters, their detection in systems with smaller plan-ets might also be possible in the near future.It will be particularly relevant to detect MSPIs generated by small planets in the habitable zones (HZs) of their stars (Kasting et al. 1993;Kopparapu et al. 2013) since planetary magnetic fields are likely a necessary condition for surface habitability.Interestingly, the starplanet separations where MSPIs can appear begin to coincide with the HZs of M-dwarf and some K-dwarf stars, being the latter recently proposed as the most suitable stars to search for life beyond Earth (Richey-Yowell et al. 2019;Lillo-Box et al. 2022).
In order to understand planetary magnetic fields it is important to study under what conditions they appear.In the Solar System, there is a strong correlation between the magnetic moment of a body and the ratio between its mass and its rotation period (e.g.Kivelson et al. 2002).Similarly, Shkolnik et al. (2003Shkolnik et al. ( , 2005Shkolnik et al. ( , 2008) ) found that the stellar variability induced by MSPIs is also correlated with such a ratio, which suggests that MSPIs are dominated by the planetary magnetic moment as well.This observational evidence is supported by several formalisms (e.g.Lanza 2009Lanza , 2012;;Saur et al. 2013;Strugarek et al. 2015).
The rotation periods of exoplanets are difficult to measure.However, they can be confidently estimated for hot Jupiters since those planets undergo strong and well-known tidal forces that affect both their orbits and rotation velocities.In particular, their orbits tend to circularize and their rotation periods tend to synchronize with the planetary orbital period in very short time scales (i.e. of a few million years ;Hut 1981;Wu 2018).To date, all MSPIs have been found in circular planetary systems, which allowed us to assume that the orbital and rotation periods coincide.However, there are a few exceptions in which hot Jupiters managed to preserve an eccentric orbit because of particular conditions such as planet migration or gravitational interactions induced by an outer companion.In such eccentric systems, the planetary rotation periods are not expected to be synchronized, but rather pseudo-synchronized with the orbital periods (Hut 1981;Correia et al. 2011).This pseudo-synchronization depends on the planet's eccentricity and translates into higher rotation velocities that would generate larger magnetic planetary moments than those in circular systems.Interestingly, eccentric planetary systems also offer a unique opportunity to probe the possible imprint of the orbital geometry into the planet-induced activity signals.Unfortunately, all the attempts to detect MSPIs in eccentric systems have turned out to be unsuccessful (e.g.Hodgson et al. 2014;Figueira et al. 2016).To date, there is only one case of periodic activity (Quinn et al. 2015) and one case of sudden activity enhancement (Maggio et al. 2015) in eccentric systems that could be explained by MSPIs.
In this work, we aim to search for MSPIs in the bright (V = 8.05 ± 0.03 mag) and slightly evolved star HD 118203, which is known to host the eccentric (e = 0.32 ± 0.02) and close-in (a = 0.0864 ± 0.0006 au) transiting Jupiter-sized planet HD 118203 b (da Silva et al. 2006;Pepper et al. 2020).In Sect.2, we describe the observations.In Sect.3, we present our analysis of photometric and spectroscopic time series.In Sect.4, we discuss the results found, and we conclude in Sect. 5.

TESS photometry
The star HD 118203 (TOI-1271, TIC 286923464) has been observed by the Transiting Exoplanet Survey Satellite (TESS; Ricker et al. 2015) in sectors 15, 16, 22, and 49 at a 2-min cadence, resulting in a 3-month duty cycle obtained throughout a 2.5-year baseline.In total, 61556 target pixel files (TPFs) were acquired, of which 9502 were discarded as having a non-zero quality flag (QF).In Table 1 we summarize the details of the observations.We downloaded the presearch data conditioned simple aperture photometry (PDCSAP; Smith et al. 2012;Stumpe et al. 2012Stumpe et al. , 2014) ) from the Mikulski Archive for Space Telescopes (MAST)2 , which was processed by the Science Processing Operation Center (SPOC) pipeline (Jenkins et al. 2016).The SPOC module Create Optimal Aperture (COA) selected the photometric aperture that maximized the signal-to-noise of the measured flux, and then estimated the flux fraction inside the aperture that came from the target star (99.96%) in order to correct for possible photometric contamination.In Figure 1, we used tpfplotter3 (Aller et al. 2020) to plot the selected aperture over a TPF of HD 118203, together with all the nearby stars detected in the Gaia Data Release 3 (DR3; Gaia Collaboration et al. 2022).There are no additional sources within the aperture with a magnitude difference ∆G < 6 mag with HD 118203 in the Gaia passband, which implies a negligible contamination (e.g.Castro-González et al. 2022).In October 2019, the Transit Planet Search (TPS) algorithm of the SPOC pipeline detected a periodic flux decrease of 3.86 ppt (parts per thousand) every 6.13 days, which passed all the diagnostic tests described in Twicken et al. (2018).
Both the orbital period and mid-transit time coincide with that of the RV-detected planet HD 118203 b, which confirms its transiting nature.The out-of-transit photometry of this target has a standard deviation of 0.46 ppt, which makes it an ideal target for searching for low-amplitude planet-induced activity signals.

ELODIE spectoscopy
HD 118203 was observed by the ELODIE spectrograph (Baranne et al. 1996), which was in operation between 1993 and 2006 at the 1.93 m telescope located at the Observatoire de Haute-Provence, France.ELODIE was a fibre-fed echelle spectrograph placed in a temperature-controlled room, with a resolution power of 42000 and a wavelength range from 389.5 to 681.5 nm split into 67 spectral orders.A total of 43 spectra were acquired between May 2004 and July 2005 with a typical cadence of 1 day and a typical exposure time of 1200 s.These observations were analysed in the discovery paper (da Silva et al. 2006).
In addition, 13 more spectra were acquired right after the publication of da Silva et al. 2006 (between March andJune 2006).
In this work, we analyse all the 56 ELODIE spectra, which have a median signal-to-noise ratio of 43.5 at 555 nm, and are publicly available on the Data & Analysis Center for Exoplanets (DACE)4 .The spectra were reduced through the ELODIE Data Reduction Software (TACOS), which also extracted the RVs and activity indicators such as the full width at half maximum (FWHM) and the contrast of the cross-correlation function (CCF) through the cross-correlation technique (Baranne et al. 1996).We used these indicators to search for planet-induced and rotation-related activity signals.

ASAS-SN photometry
HD 118203 has been monitored by four stations of the All-Sky Survey for Supernovae (ASAS-SN; Shappee et al. 2014;Kochanek et al. 2017).Each station consists of four Nikon telephoto lenses of 14 cm aperture, which are equipped with a 2048 × 2048 pixels CCD camera with a pixel scale of 8.0 arc seconds.The survey pipeline performs aperture photometry through IRAF (Tody 1986) considering a 2-pixel radius aperture and 7-10 pixel radius annulus for the target star and for the reference stars, which are selected from the Photometric All-Sky Survey (APASS, Henden et al. 2012;Henden 2019).We used the ASAS-SN Sky Patrol web interface5 to compute and download the light curves of HD 118203.This target is a high proper motion star (µ α = −85.88± 0.05 mas yr −1 , µ δ = −78.91 ± 0.04 mas yr −1 ; Gaia Collaboration et al. 2022).Hence, given that the ASAS-SN photometry is extracted in a fixed location of the detector, and the typical FWHMs are comparable to the radius of the aperture, we shifted the aperture location over time in order to minimize possible flux losses.HD 118203 is visible from the four stations from 15 November to 1 September.Hence, similarly to Castro-González et al. ( 2023), we computed the photometry of HD 118203 considering the coordinates corrected for proper motion corresponding to the central time of each observing window.Finally, we discarded those epochs in which the flux is below the estimated 5σ detection limit for the target location, as well as those data points with a deviation greater than 5σ of a flattened version of the photometric time series, which could be caused by flares, cosmic rays, or uncorrected instrumental systematics.The median standard deviation of the final ASAS-SN photometry of HD 118203 is 15.5 ppt.
(1) NZQF stands for the number of TESS observations with a non-zero quality flag.4000 4500 5000 5500 6000 6500 7000 7500 Effective temperature, T eff (K) comprehensive stellar characterization is out of the scope of this work, we need to adopt a stellar mass, radius, and effective temperature to determine the orbital and physical properties of HD 118203 b.We chose the spectroscopic values from the catalogue of Stars With ExoplanETs (SWEET-Cat; Sousa et al. 2021).In Table 2 we summarize the main properties of the star.The effective temperature and log g indicate that the star is slightly evolved.In Fig. 2 we place HD 118203 within the Hertzsprung-Russell diagram, which illustrates the star ascending the subgiant branch.

Joint radial velocity and transit model
We inferred the planetary and orbital parameters of HD 118203 b by modelling jointly the TESS photometry and ELODIE RVs described in Sects.2.1 and 2.2, respectively.The RVs are not significantly influenced by the stellar activity, but the TESS photometry shows a clear modulation in all the observed sectors (see Sects.3.4 and 3.5 for a detailed analysis of the variability of both datasets).Hence, we modelled the ELODIE RVs with a simple Keplerian, and the TESS photometry with a model composed of a transit model and a Gaussian Process (GP; Rasmussen &   We implemented the Keplerian model based on the radvel package (Fulton et al. 2018).We considered the parametrization P orb , T 0 , K, √ e cos(w), √ e sin(w) recommended by Eastman et al. (2013), where P orb is the orbital period of the planet, T 0 the time of inferior conjuntion, K the semiamplitude, e the orbital eccentricity, and w the planetary argument of the periastron.We included a linear trend component in order to account for a possible long-period drift.This component is described by the systemic radial velocity of the star (v sys ) and a slope (γ).Finally, in order to model the white noise not taken into account in our model, we included a jitter term (σ ELODIE ) that we added quadratically to the uncertainties of the RV measurements.We implemented the Mandel & Agol (2002) quadratic limb darkened transit model through batman (Kreidberg 2015), which is described by the P orb , T 0 , e, w, the orbital inclination (i), the quadratic limb darkening (LD) coefficients u 1 and u 2 , the planetto-star radius ratio (R p /R ⋆ ), and the semimajor axis scaled to the stellar radius, which we parametrized through P orb and the stellar mass (M ⋆ ) and radius (R ⋆ ) following the Kepler's Third Law.We implemented a GP defined by an approximate Matérn-3/2 kernel through celerite (Foreman-Mackey et al. 2017; Foreman-Mackey 2018), which has been extensively used to model TESS photometry given its simplicity and flexibility.This GP kernel can be written as: where the hyperparameters η σ and η ρ are the characteristic amplitude and timescale of the correlated variations, respectively, and ϵ controls the approximation to the exact Matérn-3/2 kernel.
Since both the amplitude and timescale of the TESS variability can vary from one sector to another (e.g.Murgas et al. 2023), we fitted those parameters independently; that is, we fitted η σ i and η ρ i , where i indicates the sector.We also included an offset (F 0,i ) and a jitter term (σ TESS,i ) for each sector in order to model the white noise not taken into account in our model.We sampled the posterior probability density function of the different parameters involved in our global model by using a Markov Chain Monte Carlo (MCMC) affine-invariant ensemble sampler (Goodman & Weare 2010) as implemented in emcee (Foreman-Mackey et al. 2013).We used 240 walkers (eight times as many as the number of parameters), and performed two consecutive runs.The first run (or burn-in) consisted of 200 000 iterations.After this run, we reset the sampler and initialized the second run (or production) with 100 000 iterations while considering the initial values from the last iteration of the burn-in phase.We finally estimated the autocorrelation time for each parameter and checked that it is at least 50 times smaller than the chain length, which indicates that we collected thousands of independent samples after discarding the burn-in phase.In Table A.1, we include the priors used in the MCMC run, together with the median and 1σ (68.3% credible intervals) of the posterior distributions of the fitted parameters.In Figs. 3 and 4, we show the complete ELODIE and TESS datasets together with the median posterior global model.In Fig. 5, we show the phasefolded ELODIE and TESS data after being subtracted from their corresponding linear trend and GP components.In Fig. B.1, we show the corner plot of the main fitted parameters.

Apsidal precession
As shown in Sect.3.2, the RVs of HD 118203 show a longterm linear trend that might be caused by an outer massive companion.This potential companion could perturb the orbit of HD 118203 b and cause apsidal precession.Determining whether the orbit of HD 118203 b precesses is of crucial importance to be able to interpret the possible links between the eccentric orbital motion of HD 118203 b and the photometric variations of its host star.We used the RVs to study whether there is any change in the argument of the periastron of the HD 118203 b orbit.To that end, we modelled the RVs following the procedure described in Sect.3.2, but parametrizing the argument of the periastron as w 0 + dw × (t − t 0 ), being w 0 and dw free parameters, t the observing times, and t 0 the dataset mid-point.We obtain w 0 = 152.7 ± 3.1 deg and dw = -0.01 ± 0.15 deg.Hence, being dw consistent with zero, we conclude that the orbit of HD 118203 b does not significantly precesses throughout a 750-day time span.

Stellar variability in TESS photometry
The TESS photometry of HD 118203 shows a clear variability that can be seen in the four observed sectors (Fig. 4).In order to analyse such photometric variations, we removed all the transit signatures of HD 118203 b.Given that the duration of the transits is ≃5.7 hours, we masked all data points located three hours before and after each mid-transit time.

Search for periodic signals
We computed the generalized Lomb-Scargle periodogram (GLS; Zechmeister & Kürster 2009)6 of the masked photometry in order to identify possible periodic sinusoidal-like signals.As a result, we obtain a maximum power period of 10.5 days in S15, 6.0 days in S16, 6.1 days in S22, and 6.1 days in S49, all of them with a False Alarm Probability (FAP)7 lower than 0.1%.Thus, in three of the four observed sectors the TESS photometry shows a periodic sinusoidal-like signal with the same periodicity as the HD 118203 b orbit (≃6.1 days; see Table A.1). Regarding S15, the first half of the light curve (just before the downlink gap) is dominated by a parabolic trend, but the second half shows a clear ≃6-day periodicity, which stands out in the periodogram as the second highest peak.In order to know if this signal is significant, we detrended the S15 photometry for the parabolic trend, which is most likely the cause of the 10.5-day periodicity.To do so, we modelled the photometry with a second-order polynomial.The periodogram of the detrended photometry reveals a maximum power period of 6.2 days, also with FAP < 0.1%.This result confirms that all the observed TESS sectors show a sinusoidallike signal with a ≃6.1-day periodicity, which coincides with the orbital period of the confirmed planet.We also ran the GLS over the complete TESS dataset and different combinations of sectors, and in all cases we detected the signal.
We studied whether the GLS-detected ≃6.1-day signal describes a true periodic photometric variability, or if it could be an alias of the masked transits.To do so, we computed the GLS periodograms of the window functions of each sector.We find no peaks at the ≃6.1-day periodicity detected within the original periodograms, and instead, we find maximum power periods of 16.1 days in S15, 15.8 days in S16, 18.0 days in S22, and 16.0 days in S49.Those periodicities correspond to 67% (i.e.two-thirds) of their corresponding sector lengths, which suggests that they could be related to the observing baselines.Alterna-tively, they could also be related to the beat period between the ≃6.1-day transit gap separations and the length of each observing chunk before and after downlink.We filled the masked transit regions with mock data and checked whether the ≃6.1-day periodicity and the 16-to-18 days periodicities of the window functions remain.To do so, we first performed a cubic spline interpolation over the TESS photometry filtered through a median filter with a 5-hour kernel size.Then, we filled the masked regions with 2-min cadence data generated according to the white noise properties of each sector; that is, we used Gaussian distributions with mean values centred on the interpolation models and standard deviations obtained from the flattened photometry.In Fig. B.2, we show an example of the generated mock photometry.The GLS periodograms of the filled datasets show maximum power periods of 6.1 days (S15), 6.0 days (S16), 6.1 days (S22), and 6.1 days (S49), all of them with FAP < 0.1%.Similarly, the GLS periodograms of the window functions of the filled datasets show the same maximum power periods as those of the window functions of the masked datasets (see Fig. B.3).This analysis confirms that the ≃6.1-day signal found is not related to the data sampling (i.e. it is not an alias of the masked transits), and instead, it describes a true periodic photometric variability.In Fig. 6, we show the sector-by-sector TESS photometry, the GLS periodograms of the original time series and their window functions, and the photometry folded in phase to the orbital period of HD 118203 b.

Persistence and evolution of the ≃6.1-day signal
We studied whether the ≃6.1-day signal remains invariant or suffers changes from one orbit to another.To do so, we split the photometry of each sector into two chunks (i.e.before and after the downlink gap), which correspond to ≃1.5 orbits.Hereinafter we refer to them as SXCY, where X denotes the sector and Y denotes its corresponding chunk (i.e. 1 or 2).We repeated the GLS analysis over each chunk and detected the ≃6.1-day signal in six of them.No significant signals were detected either in S15C1 or in S16C2.In Fig. 7, we plot each chunk folded in phase with the orbital period of HD 118203 b, in which we can appreciate how the ≃6.1-day signal appears and disappears from one orbit to another in S15 and S16.
Figure 7 also reveals that the ≃6.1-day signal experiences a strong and quick evolution.The magnitude of such evolution can be quantified in terms of the signal amplitude and shape.For example, the signal amplitude in S22C1 and S22C2 is decreased by ≃50% with respect to that of S15C2 or S16C1.Also, the signal shape in S22 is inverted with respect to that of the other three sectors (i.e. in S15C2, S16C1, S49C1, and S49C2, the periodic transits of HD 118203 b occur before reaching the maximum flux emission, but in S22 the transits occur in the descendant region).Hence, in summary, we find that the ≃6.1-day signal appears and disappears suddenly, and when it shows up it undergoes strong changes in both amplitude and shape.

Links with the orbital motion of HD 118203 b
We studied whether the ≃6.1-day photometric signal is linked to the orbital motion of HD 118203 b.That is, we compared the observed photometric variations with the location and angular velocity of HD 118203 b throughout its eccentric orbit.
We divided the complete phase-folded PDCSAP photometry into 100 bins of ≃1.5 hours long, for which we estimated the flux derivative.In order to mitigate the short-term variations induced by the photometric scatter, we previously filtered the phase-folded photometry through a median filter with a kernel size of 701 cadences (i.e.≃10% of the orbital phase) and then computed the flux differences of the filtered photometry.In Table 3, we include the orbital phase fraction in which the photometric flux increases ( f inc ) 8 .We find that those fractions roughly  Notes.f inc is the orbital phase fraction in which the TESS photometric flux increases.( f inc ) vis and ( f inc ) hid represent the same fraction but limited to the phases where a hypothetical co-rotating and small active region would be visible and hidden from Earth, respectively.ϕ max and ϕ min are the phase offsets between the subplanetary point and the maximum and minimum flux emission, respectively.R and p-value measure the correlations between the TESS flux derivative of HD 118203 and the orbital angular velocity of HD 118203 b.
In S15C2, S16C1, S49C1, and S49C2, the flux keeps increasing throughout 70-90% of the time that the hypothetical co-rotating active region would be visible from Earth.On the contrary, in S22C1 the flux decreases during 85% of the visible phase, and in S22C2 the increasing and decreasing regions last similar.We also computed the phase offset between the subplanetary point (i.e.time of mid-transit) and the maximum (ϕ max ) and minimum (ϕ min ) flux emission based on the fitted orbital parameters and the filtered photometry.The results are included in Table 3.We find that no flux extreme coincides with the subplanetary point, and instead, there are offsets between -0.35 and 0.25 orbital phases.
In order to visualize the aforementioned results, in the left panels of Figs. 8 and 9 we represent the orbital motion of HD 118203 b based on the fitted parameters in Sect.3.2, and in the centre panels of the same figures we show the phase-folded binned and filtered photometry.
Based on Kepler's second law, we computed the angular velocity of HD 118203 b as: where r is the distance between the star and the planet, and d p and d a are the distances between the star and the periapsis and apoapsis, respectively.We studied whether this quantity is correlated with the absolute photometric derivative.A certain degree of correlation would be expected in a scenario in which the active regions are moving over the stellar surface synchronized with the eccentric orbital motion of HD 118203 b.We note that there is a geometric factor that also affects the flux derivative.However, we cannot take it into account since it depends on the unknown size, location, evolution, and amount of active regions generating the variations.Hence, we warn the reader to just take this analysis as a first approach to quantify a possible link between the eccentric orbital motion of this planet and the photometric variations generated by hypothetical active regions co-rotating with it.In order to make the comparison, we previously normalized each quantity through the total accumulated variations, which we estimated by using the trapezoidal rule.We quantified the existence of possible correlations by means of the Pearson product-moment correlation coefficient and its associated p-value (Rodgers & Nicewander 1988), which we include in Table 3.We find a low degree of correlation (R < 0.3) for S15C2, S16C1, S22C1, and S49C2, and we find a moderate degree of correlation (0.30 < R < 0.50) for S22C2 and S49C1, with R coefficients of 0.33 and 0.34, and p-values of 7.3 × 10 −4 and 6.3 × 10 −4 , respectively.In the right panels of Figs. 8 and 9, we Comparison between the derivative of the phase-folded PDCSAP photometric variations of HD 118203 and the angular velocity of HD 118203 b.The orange circles correspond to binned data of 7% the orbital phase.In all panels: The green and magenta squares represent the periapsis and apoapsis of the orbit, respectively, and the white and grey backgrounds represent the orbital regions in which a hypothetical stellar co-rotating active region would be visible and not visible from Earth, respectively.
show the absolute photometric derivatives and the angular velocity of HD 118203 b resolved in phase, where we can visualize the moderate correlation found in S22C2 and S49C1 as well as the lack of correlation in the remaining sectors.

Stellar variability in ELODIE spectroscopic data
We computed the GLS periodogram of the ELODIE RVs and activity indicators described in Sect.2.2.The RVs periodogram shows a maximum power period of 6.1 days with a FAP of 10 −20 % that corresponds to the orbital period of HD 118203 b.The FWHMs periodogram shows a maximum power period of 110.3 days with a FAP of 10 −6 % that suggests the existence of a periodic activity signal.This signal has no counterpart either in the RVs or in the contrasts of the CCFs, the latter being devoid of any signal with FAP < 10%.We also computed the GLS periodogram of the window function of the observations in order to determine whether the detected peaks could be related to the sampling of the data.We find a maximum power period of 93.8 days, which is relatively close to the periodicity detected in the FWHMs.In Fig. 10, we show the computed periodograms together with the ELODIE time series folded in phase to their corresponding maximum power periods.

Stellar variability in ASAS-SN photometry
We computed the GLS periodograms of the ASAS-SN photometry acquired by the four cameras.The periodograms of three of them show no significant periodic signals; that is, there are no peaks with FAP < 10%.The periodogram of the camera bd, however, shows a peak at 477 days with a FAP of ≃ 10 −5 %, but no peak appears at the 110.3-day signal found in the ELODIE FWHMs.We also computed the GLS periodogram of the window function.It shows a maximum power period of 366 days, which is possibly related to a yearly alias due to the seasonal visibility of the target.In Fig. 11, we show the computed periodograms together with the ASAS-SN photometry folded in phase to its maximum power 477-day period.

Origin of the ≃6.1-day TESS photometric signal
Close-in giant planets can modify the activity levels of their host stars through MSPIs (Cuntz et al. 2000;Shkolnik et al. 2003Shkolnik et al. , 2005Shkolnik et al. , 2008;;Walker et al. 2008;Pagano et al. 2009;Pillitteri et al. 2011;Maggio et al. 2015;Cauley et al. 2019).The commonly considered criterion to confirm those interactions consists of detecting a periodic activity signal that matches the orbital

Normalized flux
Fig. 11: GLS periodogram of the ASAS-SN photometry acquired by the camera bd (solid orange) and its window function (dotted grey).The red circle indicates the maximum power frequency.The green dotted vertical line highlights the ≃6.1-day orbital period of HD 118203 b, and the magenta dotted vertical line indicates the ≃110-day periodicity found in the ELODIE FWHMs.The horizontal dotted lines correspond to the 10 (orange), 1 (blue), and 0.1% (green) FAP levels.The right panel illustrates the phasefolded photometry to the maximum power period.The grey data points correspond to a 35-day binning.period of the hosted planet, as well as another periodic signal induced by the rotation of the star.In this work, we have found evidence of periodic stellar variability in the TESS photometry of HD 118203 that matches the orbital period of its hosted giant planet HD 118203 b (i.e.≃6.1 days; Sect.3.4).We searched for possible rotation-induced activity in the ELODIE activity indicators (Sect.3.5) and ASAS-SN photometry (Sect.3.6) and found significant signals at ≃110 and ≃477 days, respectively.However, given the disparity of results in both datasets, the nonrepeatability of the signals found, and the relative closeness of the ELODIE periodicity to the highest peak of the window function periodogram, we consider that we do not have enough evidence to confidently confirm the rotation period of HD 118203.
With a mass of ≃1.3 M ⊙ , HD 118203 must have been a Ftype star during its main sequence (MS) phase.Such a mass coincides with the Kraft break (Kraft 1967).Stars with lower masses are known to have large convective envelopes that provoke angular momentum loss due to magnetized stellar winds.In contrast, stars with higher masses are known to have very thin convective envelopes, so they can keep rotating quickly during the MS phase.As stars leave the MS, their cores contract and their envelopes expand, resulting in an increase in their moments of inertia that leads to a decrease in the surface rotation rate as the star evolves across the subgiant branch.Besides, stars with masses above the Kraft break develop convective envelopes so that wind-driven angular momentum loss affects both MS rotational regimes in evolved stages (e.g.van Saders & Pinsonneault 2013).This has been empirically shown by do Nascimento et al. (2012), who found that subgiants with masses both above and below the Kraft break show rotation periods of several tens of days.Therefore, whether HD 118203 underwent significant magnetic braking during its MS phase, or remained rotating rapidly because of a thin convective envelope, both models and theory indicate that its rotation period would have been increased during its subgiant phase.
Another factor that might also affect the rotation velocity of this star is the presence of a close-in massive giant planet.However, the energy dissipation due to tidal forcing is much lower in stars than in their hosted planets (e.g.Fabrycky & Tremaine 2007;Correia et al. 2011;Beaugé & Nesvorný 2012).This has been observationally proved for G-type stars with tightly orbiting giant planets, which show similar rotation periods to those of G-type stars without close-in companions (Akeson et al. 2013).F-type stars, however, are less studied in this regard, but we know they should be more prone to reach a synchronization state since radiative envelopes dissipate more energy than convective envelopes (e.g.Lanza et al. 2011), and, as discussed above, they are much less slowed down by magnetized winds.Interestingly, to date, the only star thought to be tidally locked to the orbit of its hosted hot Jupiter is an MS F-type star, τ Boo (Butler et al. 1997;Henry et al. 2000).Therefore, the natural question that arises here is whether HD 118203 may be a new case of a tidally locked star to its hosted hot Jupiter.If so, the tidal locking configuration must have been strong enough to avoid the influence of the braking forces experienced by the star when ascending the subgiant branch.The tidal theory shows that the equilibrium state of planetary systems with gas giants in eccentric orbits is not a synchronous state, but rather a pseudo-synchronous state that depends on the orbital eccentricity (Hut 1981;Correia et al. 2011).According to Eq. ( 42) in Hut (1981), the pseudo-synchronization in the HD 118203 planetary system corresponds to a rotation period of 3.73 days.Such pseudo-synchronized rotation is expected to have occurred quickly for the hosted giant planet HD 118203 b (i.e. a few million years), but much more slowly for the host star HD 118203 (in the case that this rotational state was actually reached).Therefore, being HD 118203 a subgiant star, either coming from an MS star with a thick or narrow convective envelope, we expect that it underwent the well-studied rotation period increase when ascending the subgiant branch.In a hypothetical and unusual case in which the rotation of HD 118203 could have been dominated by the tidal forces exerted by its hot Jupiter during its MS phase, the star would be pseudosynchronized at 3.73 days, being a hypothetical 6.1-day rotation a non-equilibrium state for this system.Hence, although we do not have observational evidence of the rotation period of HD 118203, we argue that it being 6.1 days is very unlikely, which makes MSPIs the most likely scenario to explain the observed TESS activity signal.This argument agrees with literature estimates of the spectroscopic projected rotational velocity in case the stellar rotation axis is orthogonal to the line of sight.That is, da Silva et al. (2006) and Luck (2017) computed values of 5 and 7 km s −1 , respectively, while a projected velocity of 17 km s −1 would be required for the rotation of the star to be the 6.1day signal found.In the case of a pseudo-synchronized 3.73-day rotation, a 27 km s −1 projected rotational velocity would be required.In the following, we discuss how the TESS signal properties unveiled in Sects.3.4.2and 3.4.3match the MSPIs and rotation scenarios.

TESS signal properties
In Sect.3.4.2,we found that the ≃6.1-day photometric signal is not a persistent phenomenon (see Fig. 7).Interestingly, this is an expected behaviour for MSPIs.Shkolnik et al. (2008) found evidence of synchronous stellar activity in HD 179949 and υ And during 75% of the monitored time, while in the remaining 25% only the rotation of the star showed up.This on/off nature of MSPIs had been previously predicted by the models of Cranmer & Saar (2007).The authors found that the complex nature of the multipole fields may cause MSPI-induced activity not to repeat exactly from one orbit to another, and sometimes it can even disappear completely.We note, however, that while being expected for MSPIs, this behaviour does not completely rule out the rotation of the star as the source of the variability.Stellar rotation is a periodic phenomenon, but the rotation-induced activity signals are quasiperiodic since the active regions move on the stellar surface and appear and disappear throughout the magnetic cycle timescale.The typical stellar magnetic cycles last several years (e.g.Suárez Mascareño et al. 2016), but some stars have also been found to have a quick spot evolution, showing variations throughout time scales of a few days (e.g.Namekata et al. 2019).Therefore, we consider that the strong changes in amplitude and shape experienced by the ≃6.1-dayTESS signal are most likely explained by MSPIs, although we cannot completely discard the possibility that they could be caused by the rotation of the star with quick-evolving spots.
In Sect.3.4.3,we studied the possible existence of links between the ≃6.1-day photometric signal and the orbital motion of HD 118203 b.We found that the flux variations span the complete orbit, which suggests that the total active area generating those variations occupies a considerable amount of the stellar surface.Hence, the observed photometric properties do not allow us to identify a link with the orbital location of the planet under the assumption of a small co-rotating spot on the stellar surface.However, we also found that in five of the six analysed chunks the flux mostly increases (S15C2, S16C1, S49C1, and S49C2) or decreases (S22C1) when such a hypothetical big active area would be visible from Earth.Hence, if we consider an MSPI scenario, the photometry of S15C2, S16C1, S49C1, and S49C2 would be best explained by the presence of bright and extensive spots co-rotating with HD 118203 b, while in S22 such co-rotating spots would be dark.This possible alternation caused by MSPIs has been previously noticed by Walker et al. (2008).Previous works reporting MSPIs also found that the stellar activity extremes tend to be shifted with respect to the subplanetary point, which is interpreted as the co-rotating active regions advancing or delaying with respect to the planet location (e.g.Shkolnik et al. 2008).Depending on the system, those offsets can vary significantly (e.g.Cauley et al. 2019 found a 0.46 phase offset for υ And, a 0.92 phase offset for HD 189733, and offsets in between for other two systems).Interestingly, we have found similar offsets for HD 118203.
In Sect.3.4.3,we also studied whether the eccentric orbital motion of HD 118203 b has an imprint in the observed TESS variability.To date, only two eccentric systems had been reported to possibly have MSPIs, Kepler-432 (Quinn et al. 2015;Ciceri et al. 2015) and HD 17156 (Maggio et al. 2015).However, the periodic variability of Kepler-432 was found to be invariant during the whole photometric observations so that both MSPIs and tidal interactions could explain them (Quinn et al. 2015).Regarding HD 17156, the occasional nature of the activity enhancement makes it also compatible with accretion onto the star of material tidally stripped from the planet (Maggio et al. 2015).Therefore, HD 118203 b represents the best evidence of MSPIs in eccentric planetary systems, which makes it an ideal target to probe a possible eccentricity imprint in the observed photometric variations.We searched for a possible correlation between the stellar flux derivative ( d f dt ) and the planetary angular velocity ( dθ dt ), given that the projected area of active regions connected to, and co-moving with the planet, would change according to the eccentric orbital motion of the planet.Unfortunately, we could not confirm the existence of clear links between the photometric variations of HD 118203 and the eccentric orbital motion of HD 118203 b.

Orbital eccentricity as a possible booster of MSPIs
As discussed before, given the closeness of this gas giant to its host star, and the significant orbital eccentricity, the rotation period of HD 118203 b is expected to be pseudo-synchronized at ≃3.73 days.This prediction indicates that the eccentric orbit of this hot Jupiter could be responsible for a higher planetary magnetic moment than for a similar circular system.In particular, HD 118203 b would have a ≃ 40% larger magnetic moment than if it was in a circular synchronized orbit.Shkolnik et al. (2005Shkolnik et al. ( , 2008) ) found that circular planetary systems with hot Jupiters with M p sin(i) / P rot > 0.4 M J day −1 tend to undergo MSPIs, while below that value only 20 % of their studied systems showed MSPIs.For HD 118203 b, we estimate a M p / P rot of 0.61 M J day −1 , while in a hypothetical circular orbit, the ratio would be 0.37 M J day −1 .Hence, the estimated ratio for the eccentric case is well above the 0.4 M J day −1 value where MSPIs are expected to be found, while in a hypothetical circular orbit, the estimated ratio corresponds to a region of the parameter space where MSPIs are not expected to be always found.This suggests that the unusually high eccentricity of HD 118203 b could be critical for the generation of the potential MSPIs found.

Summary and conclusions
The close-in (a = 0.0864 ± 0.0006 au) and eccentric (e = 0.32 ± 0.02) Jupiter-sized planet HD 118203 b was discovered by da Silva et al. ( 2006) through 43 RVs acquired with the ELODIE spectrograph.Recently, the TESS satellite revealed that HD 118203 b transits its bright host star (Pepper et al. 2020).Having a magnitude of V = 8.05 ± 0.03, HD 118203 is among the 10 brightest stars to have a transiting giant planet.Close-in giant planets such as HD 118203 b may influence the activity levels of their host stars through magnetic star-planet interactions (MSPIs), which may induce stellar variability modulated by the orbital period of the interacting planet.Since the first claims (Santos et al. 2003;Shkolnik et al. 2003), dozens of signs of MSPIs have been reported (e.g.Shkolnik et al. 2005Shkolnik et al. , 2008;;Walker et al. 2008;Pagano et al. 2009;Pillitteri et al. 2011;Maggio et al. 2015).However, a key regime remained unexplored: eccentric planetary systems.Eccentric systems hosting close-in giant planets such as HD 118203 are very scarce since at those close distances gas giants suffer a quick circularization process (Hut 1981).Previous studies focussed on detecting MSPIs in eccentric systems were unsuccessful, and to date, there are only two possible cases of MSPIs in eccentric systems (Quinn et al. 2015;Maggio et al. 2015).However, eccentric systems can give us important insights on MSPIs.
In this work, we analysed the complete ELODIE dataset (43 RVs from the discovery paper and 13 more public RVs) and four TESS sectors of HD 118203 with the primary objective of searching for activity signals potentially induced by its hosted close-in giant planet, and the secondary objective of refining the orbital and physical properties of the planetary system.
We found evidence of an activity signal within the TESS photometry that matches the orbital period of HD 118203 b (i.e.≃6.1 days), which could be the result of magnetic interactions between the planet and its host star.In order to confirm such interactions, the commonly considered criterion consists of independently detecting the rotation period of the star.To do so, we analysed the ELODIE activity indicators and complementary ASAS-SN photometry but found no compelling evidence of an additional rotation-induced activity signal.However, given the evolved nature of the star and the significant orbital eccentricity, we argue that MSPIs is the most likely scenario to explain the observed TESS variability.This argument agrees with literature estimates of the spectroscopic projected rotational velocity.
We analysed the persistence and evolution of the signal and found that it appears and disappears in time scales comparable to a planetary orbit.Also, when active, it experiences strong changes in both amplitude and shape.We interpret this behaviour as a possible manifestation of the on/off nature of MSPIs found by Shkolnik et al. (2008).However, it does not completely rule out the rotation scenario since the star could have a quick spot evolution that could cause those sudden changes (e.g.Namekata et al. 2019).We also studied the existence of links between the TESS variability and the orbital motion of HD 118203 b.Unfortunately, the observed variations are complex and cannot be interpreted as a single small spot moving over the stellar surface, which implies that there is a geometric factor that we cannot consider in our analysis.Overall, we found a moderate degree of correlation between the flux derivative of HD 118203 and the angular velocity of HD 118203 b in two chunks of the TESS photometry but found no correlations in the remaining four chunks.We also found that the rotation period of the planet is expected to be pseudo-synchronized with the planetary orbital period with a 3.73-day periodicity.Interestingly, such a spin velocity is expected to generate a planetary magnetic moment able to produce strong MSPIs, but in a hypothetical circular scenario in which the planetary rotation and orbital periods were synchronized, the generated magnetic moment could not be enough to produce such interactions (Shkolnik et al. 2005(Shkolnik et al. , 2008)).This suggests that the unusually high eccentricity of HD 118203 b could be critical for the generation of the potential MSPIs found.
Regarding the secondary objective of the work, we significantly improved the transit ephemeris of this planetary system thanks to the inclusion of two new sectors of TESS data separated 2.5 years from the last observations.As an example, for the year 2028, we compute a propagated uncertainty in the midtransit time of just 1 minute, in contrast with the 27 minutes uncertainty reported in the current most accurate characterization (Pepper et al. 2020).Obtaining accurate ephemeris for very bright targets is very valuable for the community since those targets will be most likely scheduled for atmospheric studies.
Similar to previous studies such as Walker et al. (2008) and Pagano et al. (2009), this work reports new signs of MSPIs detected photometrically in a planetary system hosting a hot Jupiter, whose confirmation via rotation period determination should be attempted through precise photometric or spectroscopic follow-up observations.In this regard, the PLATO mission (Rauer et al. 2014) will play a major role thanks to the expected long-term and continuous precise photometric monitoring of the sky.Also, state-of-the-art high-resolution spectrographs such as HARPS-N (Cosentino et al. 2012) and CARMENES (Quirrenbach et al. 2014) could be very useful to determine the rotation period of this star, either through direct observations of the stellar chromospheric activity or through the Rossiter-McLaughlin effect (Rossiter 1924;McLaughlin 1924).To date, HD 118203 represents the best evidence that magnetic star-planet interactions can be found in eccentric planetary systems, and it opens the door to future dedicated searches in such systems that will allow us to better understand the interplay between close-in giant planets and their host stars.

Fig. 1 :
Fig. 1: TESS target pixel file of HD 118203.The orange grid is the selected aperture and the red circles correspond to the nearby Gaia DR3 sources scaled to their G magnitudes.

Fig. 2 :
Fig. 2: Location of HD 118203 in the Hertzsprung-Russell diagram.The black curve represents the main sequence, and the coloured curves are the PARSEC 2.1s tracks from Bressan et al. (2012, 2013) for stars with Z = 0.04 ([M/H] ≈ +0.3).

Fig. 6 :
Fig. 6: GLS periodograms of the TESS photometry time series and their window functions.Left panels: TESS photometry time series of HD 118203.The red dashed line within the S15 panel indicates the degree 2 polynomial fit used to de-trend the data.The orange circles correspond to 1.8-day binned data.Centre panels: GLS periodograms of the time series (solid black) and their window functions (dotted grey).In the S15 panel, the periodogram over the de-trended data is represented in red.The green circles and boxes indicate the maximum power frequencies and the vertical magenta dashed lines indicate the orbital period of HD 118203 b.Right panels: TESS photometry time series folded to the HD 118203 b orbital period as obtained from our global fit.The phase is referred to the planet's time of inferior conjunction.The orange circles correspond to binned data of 10% the orbital phase.

Fig. 7 :
Fig. 7: TESS PDCSAP split into eight chunks and folded in phase with the orbital period of HD 118203 b.Large circles correspond to 50-min binned data for better visualization of the photometric variations.

Fig. 8 :
Fig.8: Links with the orbital motion of HD 118203 b.Left panels: Orbital path of HD 118203 b, which follows the anticlockwise direction.The circles represent the location of HD 118203 b every ≃1.5 hours and are coloured in red, blue, or white, depending on whether the photometric flux increases, decreases, or remains stable during that time lapse, respectively.Centre panels: TESS PDCSAP photometry of HD 118203 folded in phase with the orbital period of HD 118203 b and binned with ≃5% phase bins.The cyan line corresponds to the filtered photometry through a median filter with a kernel size of 701 cadences.The blue, red, and white vertical lines indicate whether the photometry increases, decreases, or remains stable in time lapses of ≃1.5 hours.Right panels: Comparison between the derivative of the phase-folded PDCSAP photometric variations of HD 118203 and the angular velocity of HD 118203 b.The orange circles correspond to binned data of 7% the orbital phase.In all panels: The green and magenta squares represent the periapsis and apoapsis of the orbit, respectively, and the white and grey backgrounds represent the orbital regions in which a hypothetical stellar co-rotating active region would be visible and not visible from Earth, respectively.

Fig. 10 :
Fig. 10: GLS periodograms of the ELODIE time series and window function.Left panels: Time series of the ELODIE RVs, activity indicators described in Sect.2.2, and window function of the observations.Centre panels: GLS periodogram of the time series and the window function.The red circle indicates the maximum power frequencies.The green dotted vertical lines highlight the ≃6.1-day orbital period of HD 118203 b.The magenta dotted vertical lines indicate the ≃110-day periodicity found in the ELODIE FWHMs.The horizontal dotted lines correspond to the 10 (orange), 1 (blue), and 0.1% (green) FAP levels.Right panels: ELODIE time series and window function folded to the maximum power periods.

Table 1 :
Summary of the TESS observations of HD 118203.