Close-in Giant Planets Research Articles

The surface magnetic activity of the weak-line T Tauri stars TWA 7 and TWA 25

ABSTRACT We present an analysis of spectropolarimetric observations of the low-mass weak-line T Tauri stars TWA 25 and TWA 7. The large-scale surface magnetic fields have been reconstructed for both stars using the technique of Zeeman Doppler imaging. Our surface maps reveal predominantly toroidal and non-axisymmetric fields for both stars. These maps reinforce the wide range of surface magnetic fields that have been recovered, particularly in pre-main sequence stars that have stopped accreting from the (now depleted) central regions of their discs. We reconstruct the large scale surface brightness distributions for both stars, and use these reconstructions to filter out the activity-induced radial velocity jitter, reducing the RMS of the radial velocity variations from 495 to 32 m s −1 for TWA 25, and from 127 to 36 m s −1 for TWA 7, ruling out the presence of close-in giant planets for both stars. The TWA 7 radial velocities provide an example of a case where the activity-induced radial velocity variations mimic a Keplerian signal that is uncorrelated with the spectral activity indices. This shows the usefulness of longitudinal magnetic field measurements in identifying activity-induced radial velocity variations.

Metastable Helium Reveals an Extended Atmosphere for the Gas Giant HAT-P-18b

Abstract The metastable helium line at 1083 nm can be used to probe the extended upper atmospheres of close-in exoplanets and thus provide insight into their atmospheric mass loss, which is likely to be significant in sculpting their population. We used an ultra-narrow band filter centered on this line to observe two transits of the low-density gas giant HAT-P-18b, using the 200″ Hale Telescope at Palomar Observatory, and report the detection of its extended upper atmosphere. We constrain the excess absorption to be 0.46% ± 0.12% in our 0.635 nm bandpass, exceeding the transit depth from the Transiting Exoplanet Survey Satellite (TESS) by 3.9σ. If we fit this signal with a 1D Parker wind model, we find that it corresponds to an atmospheric mass loss rate between 8.3 − 1.9 + 2.8 × 10 − 5 M J Gyr−1 and 2.63 − 0.64 + 0.46 × 10 − 3 M J Gyr−1 for thermosphere temperatures ranging from 4000 K to 13,000 K, respectively. With a J magnitude of 10.8, this is the faintest system for which such a measurement has been made to date, demonstrating the effectiveness of this approach for surveying mass loss on a diverse sample of close-in gas giant planets.

The Linkage between the Core Mass and the Magnetic Field of an Extrasolar Giant Planet from Future Radio Observations

Abstract Close-in gas giants are expected to have a strong magnetic field of ∼10–100 G. Magnetic fields in extrasolar giant planets are detectable by future radio observations in ≳10 MHz and the spectropolarimetry of atomic lines. In contrast, the elusive interiors of exoplanets remain largely unknown. Here we consider the possibility of inferring the existence of the innermost cores of extrasolar giant planets through the detection of planetary magnetic fields. We simulated the long-term thermal evolution of close-in giant planets with masses of 0.2–10 M Jup to estimate their magnetic field strengths. A young, massive gas giant tends to have a strong magnetic field. The magnetic field strength of a hot Jupiter is insensitive to its core mass, whereas the core strongly affects the emergence of a planetary dynamo in a hot Saturn. No dynamo-driven magnetic field is generated in a hot Saturn with no core or a small one until ∼10–100 Myr if metallization of hydrogen occurs at ≳1–1.5 Mbar. The magnetic field strength of an evolved gas giant after ∼100 Myr is almost independent of the stellar incident flux. Detecting the magnetic field of a young, hot Saturn as a good indicator of its core may be challenging because of the weakness of radio signals and the shielding effect of plasma in Earth’s ionosphere. Hot Jupiters with ≳0.4 M Jup can be promising candidates for future ground-based radio observations.

Decaying Orbit of the Hot Jupiter WASP-12b: Confirmation with TESS Observations

Abstract Theory suggests that the orbits of some close-in giant planets should decay due to tidal interactions with their host stars. To date, WASP-12b is the only hot Jupiter reported to have a decaying orbit, at a rate of 29 ± 2 ms yr−1. We analyzed data from NASA’s Transiting Exoplanet Survey Satellite (TESS) to verify that WASP-12b’s orbit is indeed changing. We find that the TESS transit and occultation data are consistent with a decaying orbit with an updated period of 1.091420090 ± 0.000000041 days and a decay rate of 32.53 ± 1.62 ms yr−1. We find an orbital decay timescale of . If the observed decay results from tidal dissipation, the modified tidal quality factor is , which falls at the lower end of values derived for binary star systems and hot Jupiters. Our result highlights the power of space-based photometry for investigating the orbital evolution of short-period exoplanets.

Evidence of three mechanisms explaining the radius anomaly of hot Jupiters

Context. The anomalously large radii of hot Jupiters are still not fully understood, and all of the proposed explanations are based on the idea that these close-in giant planets possess hot interiors. Most of the mechanisms proposed have been tested on a handful of exoplanets. Aims. We approach the radius anomaly problem by adopting a statistical approach. We want to infer the internal luminosity for the sample of hot Jupiters, study its effect on the interior structure, and put constraints on which mechanism is the dominant one. Methods. We developed a flexible and robust hierarchical Bayesian model that couples the interior structure of exoplanets to the observed properties of close-in giant planets. We applied the model to 314 hot Jupiters and inferred the internal luminosity distribution for each planet and studied at the population level (i) the mass–luminosity–radius distribution and as a function of equilibrium temperature the distributions of the (ii) heating efficiency, (iii) internal temperature, and the (iv) pressure of the radiative–convective–boundary (RCB). Results. We find that hot Jupiters tend to have high internal luminosity with 104 LJ for the largest planets. As a result, we show that all the inflated planets have hot interiors with an internal temperature ranging from 200 up to 800 K for the most irradiated ones. This has important consequences on the cooling rate and we find that the RCB is located at low pressures between 3 and 100 bar. Assuming that the ultimate source of the extra heating is the irradiation from the host star, we also illustrate that the heating efficiency increases with increasing equilibrium temperature and reaches a maximum of 2.5% at ~1860 K, beyond which the efficiency decreases, which is in agreement with previous results. We discuss our findings in the context of the proposed heating mechanisms and illustrate that ohmic dissipation, the advection of potential temperature, and thermal tides are in agreement with certain trends inferred from our analysis and thus all three models can explain various aspects of the observations. Conclusions. We provide new insights on the interior structure of hot Jupiters and show that with our current knowledge, it is still challenging to firmly identify the universal mechanism driving the inflated radii.

Tidal evolution of eccentric binaries driven by convective turbulent viscosity

ABSTRACT Tidal dissipation due to convective turbulent viscosity shapes the evolution of a variety of astrophysical binaries. For example, this type of dissipation determines the rate of orbital circularization in a binary with a post-main-sequence star that is evolving toward a common envelope phase. Viscous dissipation can also influence binaries with solar-type stars, or stars with a close-in giant planet. In general, the effective viscosity in a convective stellar envelope depends on the tidal forcing frequency ωtide; when ωtide is larger than the turnover frequency of convective eddies, the viscosity is reduced. Previous works have focused on binaries in nearly circular orbits. However, for eccentric orbits, the tidal potential has many forcing frequencies. In this paper, we develop a formalism for computing tidal dissipation that captures the effect of frequency-dependent turbulent viscosity and is valid for arbitrary binary eccentricities. We also present an alternative simpler formulation that is suitable for very high eccentricities. We apply our formalisms to a giant branch (GB) star model and a solar-type star model. We find that a range of pseudo-synchronous rotation rates are possible for both stellar models, and the pseudo-synchronous rate can differ from the prediction of the commonly used weak tidal friction theory by up to a factor of a few. We also find that tidal decay and circularization due to turbulent viscosity can be a few orders of magnitude faster than predicted by weak tidal friction in GB stars on eccentric, small pericentre orbits, but is suppressed by a few orders of magnitude in solar-type stars due to viscosity reduction.

TOI-677b: A Warm Jupiter (P = 11.2 days) on an Eccentric Orbit Transiting a Late F-type Star

Abstract We report the discovery of TOI-677 b, first identified as a candidate in light curves obtained within Sectors 9 and 10 of the Transiting Exoplanet Survey Satellite (TESS) mission and confirmed with radial velocities. TOI-677 b has a mass of = , a radius of = , and orbits its bright host star (V = 9.8 mag) with an orbital period of d, on an eccentric orbit with . The host star has a mass of = , a radius of = , an age of Gyr and solar metallicity, properties consistent with a main-sequence late-F star with K. We find evidence in the radial velocity measurements of a secondary long-term signal, which could be due to an outer companion. The TOI-677 b system is a well-suited target for Rossiter–Mclaughlin observations that can constrain migration mechanisms of close-in giant planets.

Evolution of atmospheric escape in close-in giant planets and their associated Ly α and H α transit predictions

ABSTRACT Strong atmospheric escape has been detected in several close-in exoplanets. As these planets consist mostly of hydrogen, observations in hydrogen lines, such as Ly α and H α, are powerful diagnostics of escape. Here, we simulate the evolution of atmospheric escape of close-in giant planets and calculate their associated Ly α and H α transits. We use a 1D hydrodynamic escape model to compute physical properties of the atmosphere and a ray tracing technique to simulate spectroscopic transits. We consider giant (0.3 and 1 Mjup) planets orbiting a solar-like star at 0.045 au, evolving from 10 to 5000 Myr. We find that younger giants show higher rates of escape, owing to a favourable combination of higher irradiation fluxes and weaker gravities. Less massive planets show higher escape rates (1010–1013 g s−1) than those more massive (109–1012 g s−1) over their evolution. We estimate that the 1-Mjup planet would lose at most 1 per cent of its initial mass due to escape, while the 0.3-Mjup planet, could lose up to 20 per cent. This supports the idea that the Neptunian desert has been formed due to significant mass-loss in low-gravity planets. At younger ages, we find that the mid-transit Ly α line is saturated at line centre, while H α exhibits transit depths of at most 3–4 per cent in excess of their geometric transit. While at older ages, Ly α absorption is still significant (and possibly saturated for the lower mass planet), the H α absorption nearly disappears. This is because the extended atmosphere of neutral hydrogen becomes predominantly in the ground state after ∼1.2 Gyr.

Close-in giant-planet formation via in-situ gas accretion and their natal disk properties

Aims. The origin of close-in Jovian planets is still elusive. We examine the in-situ gas accretion scenario as a formation mechanism of these planets. Methods. We reconstruct natal disk properties from the occurrence rate distribution of close-in giant planets, under the assumption that the occurrence rate may reflect the gas accretion efficiency onto cores of these planets. Results. We find that the resulting gas surface density profile becomes an increasing function of the distance from the central star with some structure at r ≃ 0.1 au. This profile is quite different from the standard minimum-mass solar nebula model, while our profile leads to better reproduction of the population of observed close-in super-Earths based on previous studies. We compute the resulting magnetic field profiles and find that our profiles can be fitted by stellar dipole fields (∝r−3) in the vicinity of the central star and large-scale fields (∝r−2) at the inner disk regions, either if the isothermal assumption breaks down or if nonideal magnetohydrodynamic effects become important. For both cases, the transition between these two profiles occurs at r ≃ 0.1 au, which corresponds to the period valley of giant exoplanets. Conclusions. Our work provides an opportunity to test the in-situ gas accretion scenario against disk quantities, which may constrain the gas distribution of the minimum-mass extrasolar nebula.

On the Mass Function, Multiplicity, and Origins of Wide-orbit Giant Planets

Abstract A major outstanding question regarding the formation of planetary systems is whether wide-orbit giant planets form differently than close-in giant planets. We aim to establish constraints on two key parameters that are relevant for understanding the formation of wide-orbit planets: (1) the relative mass function and (2) the fraction of systems hosting multiple companions. In this study, we focus on systems with directly imaged substellar companions and the detection limits on lower mass bodies within these systems. First, we uniformly derive the mass probability distributions of known companions. We then combine the information contained within the detections and detection limits into a survival analysis statistical framework to estimate the underlying mass function of the parent distribution. Finally, we calculate the probability that each system may host multiple substellar companions. We find that (1) the companion mass distribution is rising steeply toward smaller masses, with a functional form of N ∝ M −1.3±0.03, and consequently, (2) many of these systems likely host additional undetected substellar companions. Combined, these results strongly support the notion that wide-orbit giant planets are formed predominantly via core accretion, similar to the better studied close-in giant planets. Finally, given the steep rise in the relative mass function with decreasing mass, these results suggest that future deep observations should unveil a greater number of directly imaged planets.

Influence of general-relativity effects, dynamical tides, and collisions on planet–planet scattering close to the star

Context.Planet–planet (P–P) scattering is an efficient and robust dynamical mechanism for producing eccentric exoplanets. Coupled to tidal interactions with the central star, this phenomenon can also explain close-in giant planets on circularized and potentially misaligned orbits.Aims.We explore scattering events occurring close to the star and test if they can reproduce the main features of the observed orbital distribution of giant exoplanets on tight orbits.Methods.In our modeling we exploited a numerical integration code based on the Hermite algorithm and including the effects of general relativity, dynamical tides, and two-body collisions.Results.We find that P–P scattering events occurring in systems with three giant planets initially moving on circular orbits close to their star produce a population of planets similar to that presently observed, including eccentric and misaligned close-in planets. The contribution of tides and general relativity is relevant in determining the final outcome of the chaotic phase.Conclusions.Even if two-body collisions dominate the chaotic evolution of three planets in crossing orbits close to their star, the final distribution shows a significant number of planets on eccentric orbits. The highly misaligned close-in giant planets are instead produced by systems where the initial semimajor axis of the inner planet was around 0.2 au or beyond.

A high binary fraction for the most massive close-in giant planets and brown dwarf desert members

ABSTRACT Stellar multiplicity is believed to influence planetary formation and evolution, although the precise nature and extent of this role remain ambiguous. We present a study aimed at testing the role of stellar multiplicity in the formation and/or evolution of the most massive, close-in planetary and substellar companions. Using past and new direct imaging observations, as well as the Gaia DR2 catalogue, we searched for wide binary companions to 38 stars hosting massive giant planets or brown dwarfs (M > 7 MJup) on orbits shorter than ∼1 au. We report the discovery of a new component in the WASP-14 system, and present an independent confirmation of a comoving companion to WASP-18. From a robust Bayesian statistical analysis, we derived a binary fraction of $79.0^{+13.2}_{-14.7}$ per cent between 20 and 10 000 au for our sample, twice as high as for field stars with a 3σ significance. This binary frequency was found to be larger than for lower-mass planets on similar orbits, and we observed a marginally higher binary rate for inner companions with periods shorter than 10 d. These results demonstrate that stellar companions greatly influence the formation and/or evolution of these systems, suggesting that the role played by binary companions becomes more important for higher-mass planets, and that this trend may be enhanced for systems with tighter orbits. Our analysis also revealed a peak in binary separation at 250 au, highlighting a shortfall of close binaries among our sample. This indicates that the mechanisms affecting planet and brown dwarf formation or evolution in binaries must operate from wide separations, although we found that the Kozai–Lidov mechanism is unlikely to be the dominant underlying process. We conclude that binarity plays a crucial role in the existence of very massive short-period giant planets and brown dwarf desert inhabitants, which are almost exclusively observed in multiple systems.

The Hot Jupiter Period–Mass Distribution as a Signature of in situ Formation

Abstract More than two decades after the widespread detection of Jovian-class planets on short-period orbits around other stars, their dynamical origins remain imperfectly understood. In the traditional narrative, these highly irradiated giant planets, like Jupiter and Saturn, are envisioned to have formed at large stello-centric distances and to have subsequently undergone large-scale orbital decay. Conversely, more recent models propose that a large fraction of hot Jupiters could have formed via rapid gas accretion in their current orbital neighborhood. In this study, we examine the period–mass distribution of close-in giant planets, and demonstrate that the inner boundary of this population conforms to the expectations of the in situ formation scenario. Specifically, we show that if conglomeration unfolds close to the disk’s inner edge, the semimajor axis–mass relation of the emergent planets should follow a power law a ∝ M −2/7—a trend clearly reflected in the data. We further discuss corrections to this relationship due to tidal decay of planetary orbits. Although our findings do not discount orbital migration as an active physical process, they suggest that the characteristic range of orbital migration experienced by giant planets is limited.

Influence of stellar structure, evolution, and rotation on the tidal damping of exoplanetary spin-orbit angles

Context. It is debated whether close-in giant planets can form in-situ and if not, which mechanisms are responsible for their migration. One of the observable tests for migration theories is the current value of the obliquity, that is, the angle between the stellar equatorial plane and the orbital plane. However, after the main migration mechanism has ended, the obliquity and the semi-major axis keep on evolving due to the combined effects of tides and magnetic braking. The observed correlation between effective temperature and measured projected obliquity in well-characterised systems has been taken as evidence of such mechanisms being at play. Aims. Our aim is to produce an improved model for the tidal evolution of the obliquity, including all the components of the dynamical tide for circular misaligned systems. This model is developed to take into account the strong variations in structure and rotation of stars during their evolution, and their consequences for the efficiency of tidal dissipation. Methods. Our model uses an analytical formulation for the frequency-averaged dissipation in convective layers for each mode, depending only on global stellar parameters and rotation. It also includes the effect of magnetic braking in the framework of a double zone stellar model. Results. For the orbital configurations of typical hot Jupiters, the obliquity is generally damped on a much shorter timescale than the semi-major axis. The final outcome of tidal evolution is also very sensitive to the initial conditions, with Jupiter-mass planets being either quickly destroyed or put on more distant orbits, depending on the initial ratio of planetary orbital momentum to stellar spin momentum. However, we find that everything else being the same, the evolution of the obliquity around low-mass stars with a thin convective zone is not slower than around those with a thicker convective zone. On the contrary, we find that more massive stars, which remain faster rotators throughout their main-sequence, produce more efficient dissipation.

The Influence of a Stellar Flare on the Dynamical State of the Atmosphere of the Exoplanet HD 209458b

By applying an one-dimensional aeronomic model of the upper atmosphere of the close-in giant planet HD 209458b, we study the reaction of the planetary atmosphere to an additional heating caused by the influence of a stellar flare. It is shown that the absorption of additional energy of the stellar flare in the extreme ultraviolet leads to local atmospheric heating, accompanied by formation of two shock waves, propagating in the atmosphere. We discuss possible observational manifestations of the shocks and feasibility of their detection.

Do Close-in Giant Planets Orbiting Evolved Stars Prefer Eccentric Orbits?

Abstract The NASA Kepler and K2 Missions have recently revealed a population of transiting giant planets orbiting moderately evolved, low-luminosity red giant branch stars. Here, we present radial velocity (RV) measurements of three of these systems, revealing significantly non-zero orbital eccentricities in each case. Comparing these systems with the known planet population suggests that close-in giant planets around evolved stars tend to have more eccentric orbits than those around main sequence stars. We interpret this as tentative evidence that the orbits of these planets pass through a transient, moderately eccentric phase where they shrink faster than they circularize due to tides raised on evolved host stars. Additional RV measurements of currently known systems, along with new systems discovered by the recently launched NASA Transiting Exoplanet Survey Satellite (TESS) mission, may constrain the timescale and mass dependence of this process.

A Secular Resonant Origin for the Loneliness of Hot Jupiters

Abstract Despite decades of inquiry, the origin of giant planets residing within a few tenths of an astronomical unit from their host stars remains unclear. Traditionally, these objects are thought to have formed further out before subsequently migrating inwards. However, the necessity of migration has been recently called into question with the emergence of in situ formation models of close-in giant planets. Observational characterization of the transiting subsample of close-in giants has revealed that “warm” Jupiters, possessing orbital periods longer than roughly 10 days more often possess close-in, co-transiting planetary companions than shorter period “hot” Jupiters, that are usually lonely. This finding has previously been interpreted as evidence that smooth, early migration or in situ formation gave rise to warm Jupiter-hosting systems, whereas more violent, post-disk migration pathways sculpted hot Jupiter-hosting systems. In this work, we demonstrate that both classes of planet may arise via early migration or in situ conglomeration, but that the enhanced loneliness of hot Jupiters arises due to a secular resonant interaction with the stellar quadrupole moment. Such an interaction tilts the orbits of exterior, lower-mass planets, removing them from transit surveys where the hot Jupiter is detected. Warm Jupiter-hosting systems, in contrast, retain their coplanarity due to the weaker influence of the host star’s quadrupolar potential relative to planet–disk interactions. In this way, hot Jupiters and warm Jupiters are placed within a unified theoretical framework that may be readily validated or falsified using data from upcoming missions, such as TESS.

Magnetic activity and radial velocity filtering of young Suns: The weak-line T Tauri stars Par 1379 and Par 2244

We report the results of our spectropolarimetric monitoring of the weak-line T-Tauri stars (wTTSs) Par 1379 and Par 2244, within the MaTYSSE (Magnetic Topologies of Young Stars and the Survival of close-in giant Exoplanets) programme. Both stars are of a similar mass (1.6 and 1.8 M$_{\odot}$) and age (1.8 and 1.1 Myr), with Par 1379 hosting an evolved low-mass dusty circumstellar disc, and with Par 2244 showing evidence of a young debris disc. We detect profile distortions and Zeeman signatures in the unpolarized and circularly polarized lines for each star, and have modelled their rotational modulation using tomographic imaging, yielding brightness and magnetic maps. We find that Par 1379 harbours a weak (250 G), mostly poloidal field tilted $65^{\circ}$ from the rotation axis. In contrast, Par 2244 hosts a stronger field (860 G) split 3:2 between poloidal and toroidal components, with most of the energy in higher order modes, and with the poloidal component tilted $45^{\circ}$ from the rotation axis. Compared to the lower mass wTTSs, V819 Tau and V830 Tau, Par 2244 has a similar field strength, but is much more complex, whereas the much less complex field of Par 1379 is also much weaker than any other mapped wTTS. We find moderate surface differential rotation of $1.4\times$ and $1.8\times$ smaller than Solar, for Par 1379 and Par 2244, respectively. Using our tomographic maps to predict the activity related radial velocity (RV) jitter, and filter it from the RV curves, we find RV residuals with dispersions of 0.017 kms$^{-1}$ and 0.086 kms$^{-1}$ for Par 1379 and Par 2244, respectively. We find no evidence for close-in giant planets around either star, with $3\sigma$ upper limits of 0.56 and 3.54 M$_{\text{jup}}$ (at an orbital distance of 0.1 au).

The effect of close-in giant planets’ evolution on tidal-induced migration of exomoons

Hypothetical exomoons around close-in giant planets may migrate inwards and/or outwards in virtue of the interplay of the star, planet and moon tidal interactions. These processes could be responsible for the disruption of lunar systems, the collision of moons with planets or could provide a mechanism for the formation of exorings. Several models have been developed to determine the fate of exomoons when subject to the tidal effects of their host planet. None of them have taken into account the key role that planetary evolution could play in this process. In this paper we put together numerical models of exomoon tidal-induced orbital evolution, results of planetary evolution and interior structure models, to study the final fate of exomoons around evolving close-in gas giants. We have found that planetary evolution significantly affects not only the time-scale of exomoon migration but also its final fate. Thus, if any change in planetary radius, internal mass distribution and rotation occurs in time-scales lower or comparable to orbital evolution, exomoon may only migrate outwards and prevent tidal disruption or a collision with the planet. If exomoons are discovered in the future around close-in giant planets, our results may contribute to constraint planetary evolution and internal structure models.

The GAPS Programme with HARPS-N at TNG

In the framework of the GAPS project, we are conducting an observational programme aimed at the determination of the orbital obliquity of known transiting exoplanets. The targets are selected to probe the obliquity against a wide range of stellar and planetary physical parameters. We exploit high-precision radial velocity (RV) measurements, delivered by the HARPS-N spectrograph at the 3.6m Telescopio Nazionale Galileo, to measure the Rossiter-McLaughlin (RM) effect in RV time-series bracketing planet transits, and to refine the orbital parameters determinations with out-of-transit RV data. We also analyse new transit light curves obtained with several 1-2m class telescopes to better constrain the physical fundamental parameters of the planets and parent stars. We report here on new transit spectroscopic observations for three very massive close-in giant planets: WASP43b, HATP20b and Qatar2b orbiting dwarf K-type stars with effective temperature well below 5000K. We find lambda = 3.5pm6.8 deg for WASP43b and lambda = -8.0pm6.9 deg for HATP20b, while for Qatar2, our faintest target, the RM effect is only marginally detected, though our best-fit value lambda = 15pm20 deg is in agreement with a previous determination. In combination with stellar rotational periods derived photometrically, we estimate the true spin-orbit angle, finding that WASP43b is aligned while the orbit of HATP20b presents a small but significant obliquity (Psi=36 _{-12}^{+10} deg). By analyzing the CaII H&K chromospheric emission lines for HATP20 and WASP43, we find evidence for an enhanced level of stellar activity which is possibly induced by star-planet interactions.