Transit Timing Variations Signal Research Articles

Characterisation of the TOI-421 planetary system using CHEOPS, TESS, and archival radial velocity data

Context. The TOI-421 planetary system contains two sub-Neptune-type planets (Pb ~ 5.2 days, Teq,b ~ 900 K, and Pc ~ 16.1 days, Teq,c ~ 650 K) and is a prime target to study the formation and evolution of planets and their atmospheres. The inner planet is especially interesting as the existence of a hydrogen-dominated atmosphere at its orbital separation cannot be explained by current formation models without previous orbital migration. Aims. We aim to improve the system parameters to further use them to model the interior structure and simulate the atmospheric evolution of both planets, to finally gain insights into their formation and evolution. We also investigate the possibility of detecting transit timing variations (TTVs). Methods. We jointly analysed photometric data of three TESS sectors and six CHEOPS visits as well as 156 radial velocity data points to retrieve improved planetary parameters. We also searched for TTVs and modelled the interior structure of the planets. Finally, we simulated the evolution of the primordial H-He atmospheres of the planets using two different modelling frameworks. Results. We determine the planetary radii and masses of TOI-421 b and c to be Rb = 2.64 ± 0.08 R⊕, Mb = 6.7 ± 0.6 M⊕, Rc = 5.09 ± 0.07 R⊕, and Mc = 14.1 ± 1.4 M⊕. Using these results we retrieved average planetary densities of ρb = 0.37 ± 0.05ρ⊕ and ρc = 0.107 ± 0.012 ρ⊕. We do not detect any statistically significant TTV signals. Assuming the presence of a hydrogen-dominated atmosphere, the interior structure modelling results in both planets having extensive envelopes. While the modelling of the atmospheric evolution predicts for TOI-421 b to have lost any primordial atmosphere that it could have accreted at its current orbital position, TOI-421 c could have started out with an initial atmospheric mass fraction somewhere between 10 and 35%. Conclusions. We conclude that the low observed mean density of TOI-421 b can only be explained by either a bias in the measured planetary parameters (e.g. driven by high-altitude clouds) and/or in the context of orbital migration. We also find that the results of atmospheric evolution models are strongly dependent on the employed planetary structure model.

The Advantages of Global Photometric Models in Fitting Transit Variations

Estimation of planetary orbital and physical parameters from light-curve data relies heavily on the accurate interpretation of Transit Timing Variation (TTV) measurements. In this letter, we review the process of TTV measurement and compare two fitting paradigms—one that relies on making transit-by-transit timing estimates and then fitting a TTV model to the observed timings, and one that relies on fitting a global flux model to the entire light-curve data set simultaneously. The latter method is achieved either by solving for the underlying planetary motion (often referred to as “photodynamics”), or by using an approximate or empirical shape of the TTV signal. We show that, across a large range of the transit S/N regime, the probability distribution function of the mid-transit time significantly deviates from a Gaussian, even if the flux errors do distribute normally. Treating the timing uncertainties as if they are distributed normally leads, in such a case, to a wrong interpretation of the TTV measurements. We illustrate these points using numerical experiments and conclude that a fitting process that relies on a global flux fitting, rather than the derived TTVs, should be preferred.

Characterization of the HD 108236 system with CHEOPS and TESS Confirmation of a fifth transiting planet

Context. The HD 108236 system was first announced with the detection of four small planets based on TESS data. Shortly after, the transit of an additional planet with a period of 29.54 d was serendipitously detected by CHEOPS. In this way, HD 108236 (V = 9.2) became one of the brightest stars known to host five small transiting planets (Rp < 3 R⊕). Aims. We characterize the planetary system by using all the data available from CHEOPS and TESS space missions. We use the flexible pointing capabilities of CHEOPS to follow up the transits of all the planets in the system, including the fifth transiting body. Methods. After updating the host star parameters by using the results from Gaia eDR3, we analyzed 16 and 43 transits observed by CHEOPS and TESS, respectively, to derive the planets’ physical and orbital parameters. We carried out a timing analysis of the transits of each of the planets of HD 108236 to search for the presence of transit timing variations. Results. We derived improved values for the radius and mass of the host star (R★ = 0.876 ± 0.007 R0 and M★ = 0.867-0.046+0.047M⊙). We confirm the presence of the fifth transiting planet f in a 29.54 d orbit. Thus, the HD 108236 system consists of five planets of Rb = 1.587±0.028, Rc = 2.122±0.025, Rd = 2.629 ± 0.031, Re = 3.008 ± 0.032, and Rf = 1.89 ± 0.04 [R⊕]. We refine the transit ephemeris for each planet and find no significant transit timing variations for planets c, d, and e. For planets b and f, instead, we measure significant deviations on their transit times (up to 22 and 28 min, respectively) with a non-negligible dispersion of 9.6 and 12.6 min in their time residuals. Conclusions. We confirm the presence of planet f and find no significant evidence for a potential transiting planet in a 10.9 d orbital period, as previously suggested. Further monitoring of the transits, particularly for planets b and f, would confirm the presence of the observed transit time variations. HD 108236 thus becomes a key multi-planetary system for the study of formation and evolution processes. The reported precise results on the planetary radii – together with a profuse RV monitoring – will allow for an accurate characterization of the internal structure of these planets.

A search for transit timing variations within the exomoon corridor using Kepler data

ABSTRACT An exomoon will produce transit timing variations (TTVs) upon the parent planet and their undersampled nature causes half of such TTVs to manifest within a frequency range of two to four cycles, irrespective of exomoon demographics. Here, we search through published Kepler TTV data for such signals, applying a battery of significance and robustness checks, plus independent light-curve analyses for candidate signals. Using the original transit times, we identify 11 (ostensibly) single-planets with a robust, significant and fast (PTTV < 4 cycles) TTV signal. However, of these, only five are recovered in an independent analysis of the original photometry, underscoring the importance of such checks. The surviving signals are subjected to an additional trifecta of statistical tests to ensure signal significance, predictive capability and consistency with an exomoon. KOI-3678.01, previously validated as Kepler-1513b, is the only case that passes every test, exhibiting a highly significant (>20σ) TTV signal with a periodicity, amplitude and shape consistent with that caused by an exomoon. Our analysis finds that this planet is $8.2_{-0.5}^{+0.7}$ R⊕ orbiting at $0.53_{-0.03}^{+0.04}$ au around a late G-type dwarf. After forecasting the planetary mass, we expect it to be capable of maintaining at least a 0.3 M⊕ exomoon for 5 Gyr, and the TTV signal corresponds to a moon mass as low as 0.75 Lunar masses. We thus encourage follow-up observations and dynamical analysis of this unique signal, but caution skepticism until such data can be obtained.

Generalized Peas in a Pod: Extending Intra-system Mass Uniformity to Non-TTV Systems via the Gini Index

It has been demonstrated that planets belonging to the same close-in, compact multiple-planet system tend to exhibit a striking degree of uniformity in their sizes. A similar trend has also been found to hold for the masses of such planets, but considerations of such intra-system mass uniformity have generally been limited to statistical samples wherein a majority of systems have constituent planetary mass measurements obtained via analysis of transit timing variations (TTVs). Since systems with strong TTV signals typically lie in or near mean motion resonance, it remains to be seen whether intra-system mass uniformity is still readily emergent for nonresonant systems with non-TTV mass provenance. We thus present in this work a mass uniformity analysis of 17 non-TTV systems with masses measured via radial velocity measurements. Using the Gini index, a common statistic for economic inequality, as our primary metric for uniformity, we find that our sample of 17 non-TTV systems displays intra-system mass uniformity at a level of ∼2.5σ confidence. We provide additional discussion of possible statistical and astrophysical underpinnings for this result. We also demonstrate the existence of a correlation (r = 0.25) between characteristic solid surface density (Σ0) of the minimum-mass extrasolar nebula and system mass Gini index, suggesting that more-massive disks may generally form systems with more-unequal planetary masses.

An Updated Ephemeris for K2-138 d

Abstract K2-138 d (EPIC 245950175 d) is one of five planets in a chain of 3:2 mean motion resonances discovered by Christiansen et al. in K2 Campaign 12. An additional planet, confirmed with the Spitzer Space Telescope by Hardegree-Ullman et al., is not in the resonant chain. The near first-order resonances, coupled with the planets being locked in a set of three-body Laplace resonances, make this system a unique target to study for transit timing variations (TTVs). As the predicted transit timing amplitude (∼7 minutes) was below the typical transit timing uncertainty (∼10 minutes) of the K2 data, Christiansen et al. were unable to detect TTVs for K2-138 d in the K2 time series. Here, we describe new observations that allow us to refine the ephemeris for K2-138 d and perform a brief search for TTVs. Our efforts result in a refined orbital period that is 19 times more precise than previously available measurements, but our data are insufficient to confirm a TTV signal for K2-138 d.

The Transit Timing and Atmosphere of Hot Jupiter HAT-P-37b

Abstract We perform transit timing variation (TTV) and transmission spectroscopy analyses of the planet HAT-P-37b, which is a hot Jupiter orbiting a G-type star. Nine new transit light curves are obtained and analyzed together with 21 published light curves from the literature. The updated physical parameters of HAT-P-37b are presented. The TTV analyses show a possibility that the system has an additional planet that induced the TTVs amplitude signal of 1.74 ± 0.17 minutes. If the body is located near the 1:2 mean-motion resonance orbit, the sinusoidal TTV signal could be caused by the gravitational interaction of a sub-Earth-mass planet with mass of 0.06 M ⊕. From the analysis of an upper-mass limit for the second planet, a Saturn-mass planet with orbital period less than 6 days is excluded. The broadband transmission spectra of HAT-P-37b favors a cloudy atmospheric model with an outlier spectrum in the B filter.

Orbital Period Refinement of CoRoT Planets with TESS Observations

CoRoT was the first space mission dedicated to exoplanet detection. Operational between 2007 and 2012, this mission discovered 37 transiting planets, including CoRoT-7b, the first terrestrial exoplanet with a measured size. The precision of the published transit ephemeris of most of these planets has been limited by the relative short durations of the CoRoT pointings, which implied a danger that the transits will become unobservable within a few years due to the uncertainty of their future transit epochs. Ground-based follow-up observations of the majority of the CoRoT planets have been published in recent years. Between Dec. 2018 and Jan. 2021, the TESS mission in its sectors 6 and 33 re-observed those CoRoT fields that pointed towards the Galactic anti-center. These data permitted the identification of transits from nine of the CoRoT planets, and the derivation of precise new transit epochs. The main motivation of this study has been to derive precise new ephemerides of the CoRoT planets, in order to keep these planets’ transits observable for future generations of telescopes. The TESS data were analyzed for the presence of transits and the epochs of these re-observed transits were measured. The original CoRoT epochs, epochs from ground-based follow-up observations and those from TESS were collected. From these data, updated ephemerides are presented for nine transiting planets discovered by the CoRoT mission in its fields pointing towards the Galactic anti-center. In three cases (CoRoT-4b, 19b and 20b), transits that would have been lost for ground observations, due to the large uncertainty in the previous ephemeris, have been recovered. The updated ephemerides permit transit predictions with uncertainties of less than 30 min for observations at least until the year 2030. No significant transit timing variations were found in these systems.

Photometric follow-up observations and transit timing analysis of HAT-P-37b

Abstract We performed follow-up photometric observations on exoplanetary system HAT-P-37 from 2011 February to 2019 September. The nine new transit light curves of the R and V bands are presented in this work. Based on the new light curves and published literature data, the physical and orbital parameters of HAT-P-37 are refined. In addition, mid-transit times are obtained to update the linear ephemeris, Tc[0] = 2456478.57916 ± 0.00077 [BJDTDB], P = 2.7974415 ± 0.0000025 d. Moreover, the transit timing variations (TTVs) have an rms of 57 s and there is no significant TTV signal. According to dynamic analysis, we excluded the possibility of perturbers with a mass larger than 200M⊕, when located in 1 : 3, 1 : 2, 2 : 3 (interior) or 3 : 2, 2 : 1, 5 : 2, 3 : 1 (exterior) orbital resonance, respectively.

Systematic search for long-term transit duration changes in Kepler transiting planets

ABSTRACT Holczer, Mazeh, and collaborators (HM+16) used the Kepler 4-yr observations to derive a transit-timing catalog, identifying 260 Kepler objects of interest (KOI) with significant transit timing variations (TTV). For KOIs with high enough S/Ns, HM+16 also derived the duration and depth of their transits. In this work, we use the duration measurements of HM+16 to systematically study the duration changes of 561 KOIs and identify 15 KOIs with a significant long-term linear change of transit durations and another 16 KOIs with an intermediate significance. We show that the observed linear trend is probably caused by a precession of the orbital plane of the transiting planet, induced in most cases by another planet. The leading term of the precession rate depends on the mass and relative inclination of the perturber, and the period ratio between the two orbits, but not on the mass and period of the transiting planet itself. Interestingly, our findings indicate that, as a sample, the detected time derivatives of the durations get larger as a function of the planetary orbital period, probably because short-period planetary systems display small relative inclinations. The results might indicate that short-period planets reside in relatively flattened planetary systems, suggesting these systems experienced stronger dissipation either when formed or when migrated to short orbits. This should be used as a possible clue for the formation of such systems.

New constraints on the planetary system around the young active star AU Mic

AU Microscopii (AU Mic) is a young, active star whose transiting planet was recently detected. Here, we report our analysis of its TESS light curve, where we modeled the BY Draconis type quasi-periodic rotational modulation by starspots simultaneously to the flaring activity and planetary transits. We measured a flare occurrence rate in AU Mic of 6.35 flares per day for flares with amplitudes in the range of 0.06% < fmax < 1.5% of the star flux. We employed a Bayesian Markov chain Monte Carlo analysis to model the five transits of AU Mic b observed by TESS, improving the constraints on the planetary parameters. The measured planet-to-star effective radius ratio of Rp∕R⋆ = 0.0496 ± 0.0007 implies a physical radius of 4.07 ± 0.17 R⊕ and a planet density of 1.4 ± 0.4 g cm−3, confirming that AU Mic b is a Neptune-size moderately inflated planet. While a single feature possibly due to a second planet was previously reported in the former TESS data, we report the detection of two additional transit-like events in the new TESS observations of July 2020. This represents substantial evidence for a second planet (AU Mic c) in the system. We analyzed its three available transits and obtained an orbital period of 18.859019 ± 0.000016 d and a planetary radius of 3.24 ± 0.16 R⊕, which defines AU Mic c as a warm Neptune-size planet with an expected mass in the range of 2.2 M⊕ < Mc < 25.0 M⊕, estimated from the population of exoplanets of similar sizes. The two planets in the AU Mic system are in near 9:4 mean-motion resonance. We show that this configuration is dynamically stable and should produce transit-timing variations (TTV). Our non-detection of significant TTV in AU Mic b suggests an upper limit for the mass of AU Mic c of <7 M⊕, indicating that this planet is also likely to be inflated. As a young multi-planet system with at least two transiting planets, AU Mic becomes a key system for the study of atmospheres of infant planets and of planet-planet and planet-disk dynamics at the early stages of planetary evolution.

Exploiting the transit timing capabilities of Ariel

The Transit Timing Variation (TTV) technique is a powerful dynamical tool to measure exoplanetary masses by analysing transit light curves. We assessed the transit timing performances of the Ariel Fine Guidance Sensors (FGS1/2) based on the simulated light curve of a bright, 55 Cnc, and faint, K2-24, planet-hosting star. We estimated through a Markov-Chain Monte-Carlo analysis the transit time uncertainty at the nominal cadence of 1 second and, as a comparison, at a 30 and 60-s cadence. We found that at the nominal cadence Ariel will be able to measure the transit time with a precision of about 12s and 34s, for a star as bright as 55 Cnc and K2-24, respectively. We then ran dynamical simulations, also including the Ariel timing errors, and we found an improvement on the measurement of planetary masses of about 20-30% in a K2-24-like planetary system through TTVs. We also simulated the conditions that allow us to detect the TTV signal induced by an hypothetical external perturber within the mass range between Earth and Neptune using 10 transit light curves by Ariel.

Transit timing variation signature of planet migration: the case of K2-24

The convergent migration of two planets in a gaseous disc can lead to mean motion resonance (MMR) capture. In addition, pairs of planets in or near MMRs are known to produce strong transit timing variations (TTVs). In this paper, we study the impact of disc-induced migrations on the TTV signal of pairs of planets that enter a resonant configuration. We show that disc-induced migration creates a correlation between the amplitude and the period of the TTVs. We study the case of K2-24, a system of two planets whose period ratio indicates that they are in or near the 2:1 MMR, with non-zero eccentricities and large-amplitude TTVs. We show that a simple disc-induced migration cannot reproduce the observed TTVs. Moreover, we propose a formation scenario in which the capture in resonance during migration in a disc with strong eccentricity damping is followed by eccentricity excitation during the dispersal of the disc. This is assisted by a third planet whose presence has been suggested by radial velocity observations. This scenario accounts for the eccentricities of the two planets and their period ratio, and it accurately reproduces the amplitude and period of the TTVs. It allows for a unified view of the formation and evolution history of K2-24, from disc-induced migration to its currently observed properties.

An Independent Analysis of the Six Recently Claimed Exomoon Candidates

Abstract It has been recently claimed that KOIs-268.01, 303.01, 1888.01, 1925.01, 2728.01, and 3320.01 are exomoon candidates, based on an analysis of their transit timing. Here, we perform an independent investigation, which is framed in terms of three questions: (1) Are there significant transit timing variations (TTVs)? (2) Is there a significant periodic TTV? (3) Is there evidence for a nonzero moon mass? We applied rigorous statistical methods to these questions alongside a reanalysis of the Kepler photometry and find that none of the Kepler objects of interest (KOIs) satisfy our three tests. Specifically, KOIs-268.01 and 3220.01 pass none of the tests and KOIs-303.01, 1888.01, and 1925.01 pass a single test each. Only KOI-2728.01 satisfies two, but fails the cross-validation test for predictions. Further, detailed photodynamical modeling reveals that KOI-2728.01 favors a negative-radius moon (as does KOI-268.01). We also note that we find a significant photoeccentric effect for KOI-1925.01 indicating an eccentric orbit of at least e > (0.62 ± 0.06). For comparison, we applied the same tests to Kepler-1625b, which reveals that (1) and (3) are passed, but (2) cannot be checked with the cross-validation method used here, due to the limited number of available epochs. In conclusion, we find no compelling evidence for exomoons among the six KOIs. Despite this, we were able to derive exomoon mass upper limits versus semimajor axis, with KOI-3220.01 leading to particularly impressive constraints of M S/M P < 0.4% [2σ] at a similar semimajor to that of the Earth–Moon.

Exomoon indicators in high-precision transit light curves

Context. While the Solar System contains about 20 times more moons than planets, no moon has been confirmed around any of the thousands of extrasolar planets discovered so far. Considering the large computational load required for the statistical vetting of exomoon candidates in a star–planet–moon framework, tools for an uncomplicated identification of the most promising exomoon candidates could be beneficial to streamline follow-up studies. Aims. Here we study three exomoon indicators that emerge if well-established planet-only models are fitted to a planet–moon transit light curve: transit timing variations (TTVs), transit duration variations (TDVs), and apparent planetary transit radius variations (TRVs). We re-evaluate under realistic conditions the previously proposed exomoon signatures in the TTV and TDV series. Methods. We simulated light curves of a transiting exoplanet with a single moon, taking into account stellar limb darkening, orbital inclinations, planet–moon occultations, and noise from both stellar granulation and instrumental effects. These model light curves were then fitted with a planet-only transit model whilst pretending there were no moon, and we explored the resulting TTV, TDV, and TRV series for evidence of the moon. Results. The previously described ellipse in the TTV-TDV diagram of an exoplanet with a moon emerges only for high-density moons. However, low-density moons distort the sinusoidal shapes of the TTV and the TDV series due to their photometric contribution to the combined planet–moon transit. Sufficiently large moons can nevertheless produce periodic apparent TRVs of their host planets that could be observable. We find that Kepler and PLATO have similar performances in detecting the exomoon-induced TRV effect around simulated bright (mV = 8) stars. Although these stars are rare in the Kepler sample, they will be abundant in the PLATO sample. Moreover, PLATO’s higher cadence yields a stronger TTV signal. We detect substantial TRVs of the Saturn-sized planet Kepler-856 b although an exomoon could only ensure Hill stability in a very narrow orbital range. Conclusions. The periodogram of the sequence of transit radius measurements can indicate the presence of a moon. The TTV and TDV series of exoplanets with moons could be more complex than previously assumed. We propose that TRVs could be a more promising means to identify exomoons in large exoplanet surveys.

Simultaneous TESS and NGTS transit observations of WASP-166 b

ABSTRACT We observed a transit of WASP-166 b using nine Next Generation Transit Survey (NGTS) telescopes simultaneously with the Transiting Exoplanet Survey Satellite (TESS) observations of the same transit. We achieved a photometric precision of 152 ppm per 30 min with the nine NGTS telescopes combined, matching the precision reached by TESS for the transit event around this bright (T = 8.87) star. The individual NGTS light-curve noise is found to be dominated by scintillation noise and appears free from any time-correlated noise or any correlation between telescope systems. We fit the NGTS data for TC and Rp/R*. We find TC to be consistent to within 0.25σ of the result from the TESS data, and the difference between the TESS and NGTS measured Rp/R* values is 0.9σ. This experiment shows that multitelescope NGTS photometry can match the precision of TESS for bright stars, and will be a valuable tool in refining the radii and ephemerides for bright TESS candidates and planets. The transit timing achieved will also enable NGTS to measure significant transit timing variations in multiplanet systems.

Impossible moons - transit timing effects that cannot be due to exomoon

Exomoons are predicted to produce transit timing variations (TTVs) upon their host planet. Unfortunately, so are many other astrophysical phenomena - most notably other planets in the system. In this work, an argument of reductio ad absurdum is invoked, by deriving the transit timing effects that are impossible for a single exomoon to produce. Our work derives three key analytic tests. First, one may exploit the fact that a TTV signal from an exomoon should be accompanied by transit duration variations (TDVs), and that one can derive a TDV floor as a minimum expected level of variability. Cases for which the TDV upper limit is below this floor can thus be killed as exomoon candidates. Second, formulae are provided for estimating whether moons are expected to be "killable" when no TDVs presently exist, thus enabling the community to estimate the value of deriving TDVs beforehand. Third, a TTV ceiling is derived, above which exomoons should never be able to produce TTV amplitudes. These tools are applied to a catalog of TTVs and TDVs for two and half thousand Kepler Objects of Interest, revealing over two hundred cases that cannot be due to a moon - remarkably then a large fraction of the known TTV amplitudes are consistent with being caused by a moon. These tests are also applied to the exomoon candidate Kepler-1625b i, which comfortably passes the criteria. These simple analytic results should provide a means of rapidly rejecting putative exomoons and streamlining the search for satellites.

Revisiting the HIP 41378 System with K2 and Spitzer

Abstract We present new observations of the multiplanet system HIP 41378, a bright star (V = 8.9, K s = 7.7) with five known transiting planets. Previous K2 observations showed multiple transits of two Neptune-sized bodies and single transits of three larger planets (R P = 0.33R J , 0.47R J , 0.88R J ). K2 recently observed the system again in Campaign 18 (C18). We observe one new transit each of two of the larger planets d/f, giving maximal orbital periods of 1114/1084 days, as well as integer divisions of these values down to a lower limit of about 50 days. We use all available photometry to determine the eccentricity distributions of HIP 41378 d & f, finding that periods ≲300 days require non-zero eccentricity. We check for overlapping orbits of planets d and f to constrain their mutual periods, finding that short periods (P < 300 days) for planet f are disfavored. We also observe transits of planets b and c with Spitzer/Infrared Array Camera (IRAC), which we combine with the K2 observations to search for transit timing variations (TTVs). We find a linear ephemeris for planet b, but see a significant TTV signal for planet c. The ability to recover the two smaller planets with Spitzer shows that this fascinating system will continue to be detectable with Spitzer, CHEOPS, TESS, and other observatories, allowing us to precisely determine the periods of d and f, characterize the TTVs of planet c, recover the transits of planet e, and further enhance our view of this remarkable dynamical laboratory.

TESS Full Orbital Phase Curve of the WASP-18b System

Abstract We present a visible-light full orbital phase curve of the transiting planet WASP-18b measured by the TESS mission. The phase curve includes the transit, secondary eclipse, and sinusoidal modulations across the orbital phase shaped by the planet’s atmospheric characteristics and the star–planet gravitational interaction. We measure the beaming (Doppler boosting) and tidal ellipsoidal distortion phase modulations and show that the amplitudes of both agree with theoretical expectations. We find that the light from the planet’s dayside hemisphere occulted during secondary eclipse, with a relative brightness of ppm, is dominated by thermal emission, leading to an upper limit on the geometric albedo in the TESS band of 0.048 ( ). We also detect the phase modulation due to the planet’s atmosphere longitudinal brightness distribution. We find that its maximum is well aligned with the substellar point to within 2.°9 ( ). We do not detect light from the planet’s nightside hemisphere, with an upper limit of 43 ppm ( ), which is 13% of the dayside brightness. The low albedo, lack of atmospheric phase shift, and inefficient heat distribution from the day to night hemispheres that we deduce from our analysis are consistent with theoretical expectations and similar findings for other strongly irradiated gas giant planets. This work demonstrates the potential of TESS data for studying the full orbital phase curves of transiting systems. Finally, we complement our study by looking for transit timing variations (TTVs) in the TESS data combined with previously published transit times, although we do not find a statistically significant TTV signal.

A periodic configuration of the Kepler-25 planetary system

We study proximity of the Kepler-25 planetary system to a periodic configuration, which is known to be the final state of a system that undergoes smooth migration resulting from the planet-disc interaction. We show that the system is close to the periodic configuration of 2:1 mean motion resonance (MMR) what indicates that its past migration was neither disturbed significantly by turbulence in the disc nor the orbits were perturbed by planetesimals that left after the disc dispersal. We show that, because of the TTV model degeneracy, a periodic configuration is difficult to be found when the standard modelling of the transit timing variations (TTVs) is used. The TTV signal of a periodic configuration (with anti-aligned apsidal lines) may be misinterpreted as an aligned non-resonant system. We demonstrate that the standard MCMC modelling of the Kepler-25 TTVs is very sensitive to an a~priori information on the eccentricities (prior probability distributions). Wide priors (of the order of the ones typically used in the literature) result in favouring the aligned non-resonant configurations with small planets' masses and moderate eccentricities, while for the narrower priors the most likely are the anti-aligned resonant systems with larger masses and very low eccentricities.