Transit Light Curves Research Articles

A regularisation technique to precisely infer limb darkening using transit measurements: Can we estimate stellar surface magnetic fields?

Abstract The high-precision measurements of exoplanet transit light curves that are now available contain information about the planet properties, their orbital parameters, and stellar limb darkening (LD). Recent 3D magneto-hydrodynamical (MHD) simulations of stellar atmospheres have shown that LD depends on the photospheric magnetic field, and hence its precise determination can be used to estimate the field strength. Among existing LD laws, the uses of the simplest ones may lead to biased inferences, whereas the uses of complex laws typically lead to a large degeneracy among the LD parameters. We have developed a novel approach in which we use a complex LD model but with second derivative regularisation during the fitting process. Regularisation controls the complexity of the model appropriately and reduces the degeneracy among LD parameters, thus resulting in precise inferences. The tests on simulated data suggest that our inferences are not only precise but also accurate. This technique is used to re-analyse 43 transit light curves measured by the NASA Kepler and TESS missions. Comparisons of our LD inferences with the corresponding literature values show good agreement, while the precisions of our measurements are better by up to a factor of 2. We find that 1D non-magnetic model atmospheres fail to reproduce the observations while 3D MHD simulations are qualitatively consistent. The LD measurements, together with MHD simulations, confirm that Kepler-17, WASP-18, and KELT-24 have relatively high magnetic fields (>200 G). This study paves the way for estimating the stellar surface magnetic field using the LD measurements.

An Analytic Characterization of the Limb Asymmetry—Transit Time Degeneracy

Atmospheres are not spatially homogeneous. This is particularly true for hot, tidally locked exoplanets with large day-to-night temperature variations, which can yield significant differences between the morning and evening terminators—known as limb asymmetry. Current transit observations with the James Webb Space Telescope (JWST) are precise enough to disentangle the separate contributions of these morning and evening limbs to the overall transmission spectrum in certain circumstances. However, the signature of limb asymmetry in a transit light curve is highly degenerate with uncertainty in the planet’s time of conjunction. This raises the question of how precisely transit times must be measured to enable accurate studies of limb asymmetry, in particular with JWST. Although this degeneracy has been discussed in the literature, a general description of it has not been presented. In this work, we show how this degeneracy results from apparent changes in the transit contact times when the planetary disk has asymmetric limb sizes. We derive a general formula relating the magnitude of limb asymmetry to the amount by which it would cause the apparent time of conjunction to vary, which can reach tens of seconds. Comparing our formula to simulated observations, we find that numerical fitting techniques add additional bias to the measured time, of generally less than a second, resulting from the occultation geometry. We also derive an analytical formula for this extra numerical bias. These formulae can be applied to planning new observations or interpreting literature measurements, and we show examples for commonly studied exoplanets.

Exomod: A Python Library for Exoplanet Transit Light Curve Fitting and Stacking with Background Simulation and Optimization

Abstract From the light curve taken during exoplanet transit, important parameters such as the radius ratio of the star-planet, impact parameter, inclination, and relative tangential velocity could be derived. A module was developed in the form of a Python library based on modeling using background simulation and fitting by utilizing global and local optimization, such as differential evolution and the Broyden–Fletcher–Goldfarb–Shanno (BFGS) method. For more accurate fitting, the effects of linear limb darkening on exoplanets are also included. The performance testing for the program was done by using dummy data to test its accuracy, followed by validation tests using WASP-12b transit curves to find out any discrepancies between our model and real exoplanet data. While performing a characterization test on WASP-12b, we found an interesting result regarding its impact parameter and the exoplanet’s velocity, which might be an interesting subject for further analysis.

Probing the Possible Causes of the Transit Timing Variation for TrES-2b in the TESS Era

Nowadays, transit timing variations (TTVs) are proving to be a very valuable tool in exoplanetary science to detect exoplanets by observing variations in transit times. To study the TTV of the hot Jupiter TrES-2b, we have combined 64 high-quality transit light curves from all seven sectors of NASA's Transiting Exoplanet Survey Satellite along with 60 best-quality light curves from the ground-based facility Exoplanet Transit Database and 106 midtransit times from the previous works. From the precise transit timing analysis, we have observed a significant improvement in the orbital ephemerides, but we did not detect any short-period TTVs that might result from an additional body. The inability to detect short-term TTVs further motivates us to investigate long-term TTVs, which might be caused by orbital decay, apsidal precession, the Applegate mechanism, and the Rømer effect, and the orbital decay appeared to be a better explanation for the observed TTV with ΔBIC = 4.32. The orbital period of the hot Jupiter TrES-2b appears to be shrinking at a rate of ∼–5.58 ± 1.81 ms yr−1. Assuming this decay is primarily caused by tidal dissipation within the host star, we have subsequently calculated the stellar tidal quality factor value to be ∼9.9 × 103, which is 2–3 orders of magnitude smaller than the theoretically predicted values for other hot-Jupiter systems, and its low value indicates more efficient tidal dissipation within the host star. Additional precise photometric and radial velocity observations are required to pinpoint the cause of the change in the orbital period.

Numerical simulations of exocomet transits: Insights from β Pic and KIC 3542116

In recent years, the topic of existence and exploration of exocomets has been gaining increasing attention. The asymmetrical decrease in the star’s brightness due to the passage of a comet-like object in front of the star was successfully predicted. It was subsequently confirmed on the basis of the light curves of stars observed by Kepler and TESS orbital telescopes. Since then, there have been successful attempts to fit the asymmetrical dips observed in the stars’ light curves utilizing a simple 1D model of an exponentially decaying optically thin dust tail. In this work, we propose fitting the photometric profiles of some known exocomet transits based on a Monte Carlo approach to build up the distribution of dust particles in a cometary tail. As the exocomet prototypes, we used the physical properties of certain Solar System comets belonging to the different dynamical groups and moving at heliocentric distances of 0.6 au, 1.0 au, 5.0 au, and 5.5 au. We obtained a good agreement between the observed and modeled transit light curves. We also show that the physical characteristics of dust particles, such as the particle size range, the power index of dust size distribution, the particle terminal velocity, and distance to the host star affect the shape of the transit light curve, while the dust productivity of the comet nucleus and the impact parameter influence its depth and duration. The estimated dust production rates of the transiting exocomets are at the level of the most active Solar System comets.

Exocomet Models in Transit: Light Curve Morphology in the Optical—Near Infrared Wavelength Range

Following the widespread practice of exoplanetary transit simulations, various presumed components of an extrasolar system can be examined in numerically simulated transits, including exomoons, rings around planets, and the deformation of exoplanets. Template signals can then be used to efficiently search for light curve features that mark specific phenomena in the data, and they also provide a basis for feasibility studies of instruments and search programs. In this paper, we present a method for exocomet transit light curve calculations using arbitrary dust distributions in transit. The calculations, spanning four distinct materials (carbon, graphite, pyroxene, and olivine), and multiple dust grain sizes (100–300 nm, 300–1000 nm, and 1000–3000 nm) encompass light curves in VRJHKL bands. We also investigated the behavior of scattering colors. We show that multicolor photometric observations are highly effective tools in the detection and characterization of exocomet transits. They provide information on the dust distribution of the comet (encoded in the light curve shape), while the color information itself can reveal the particle size change and material composition of the transiting material, in relation to the surrounding environment. We also show that the typical cometary tail can result in the wavelength dependence of the transit timing. We demonstrate that multi-wavelength observations can yield compelling evidence for the presence of exocomets in real observations.

TOI-1408: Discovery and Photodynamical Modeling of a Small Inner Companion to a Hot Jupiter Revealed by Transit Timing Variations

We report the discovery and characterization of a small planet, TOI-1408 c, on a 2.2 day orbit located interior to a previously known hot Jupiter, TOI-1408 b (P = 4.42 days, M = 1.86 ± 0.02 M Jup, R = 2.4 ± 0.5 R Jup) that exhibits grazing transits. The two planets are near 2:1 period commensurability, resulting in significant transit timing variations (TTVs) for both planets and transit duration variations for the inner planet. The TTV amplitude for TOI-1408 c is 15% of the planet’s orbital period, marking the largest TTV amplitude relative to the orbital period measured to date. Photodynamical modeling of ground-based radial velocity (RV) observations and transit light curves obtained with the Transiting Exoplanet Survey Satellite and ground-based facilities leads to an inner planet radius of 2.22 ± 0.06 R ⊕ and mass of 7.6 ± 0.2 M ⊕ that locates the planet into the sub-Neptune regime. The proximity to the 2:1 period commensurability leads to the libration of the resonant argument of the inner planet. The RV measurements support the existence of a third body with an orbital period of several thousand days. This discovery places the system among the rare systems featuring a hot Jupiter accompanied by an inner low-mass planet.

Interpretation of the Transit Light Curve in the Presence of Principal Main Minimum with Allowance for the Eccentricity of the Transit (Planet) Orbit

Interpretation of the Transit Light Curve in the Presence of Principal Main Minimum with Allowance for the Eccentricity of the Transit (Planet) Orbit

TASTE

The discovery of the first transiting hot Jupiters (HJs), giant planets on orbital periods shorter than P ~ 10 days, was announced more than 20 years ago. As both ground- and space-based follow-up observations are piling up, we are approaching the temporal baseline required to detect secular variations in their orbital parameters. In particular, several recent studies have focused on constraining the efficiency of the tidal decay mechanism to better understand the evolutionary timescales of HJ migration and engulfment. This can be achieved by measuring a monotonic decrease in orbital period dP/dt < 0 due to mechanical energy being dissipated by tidal friction. WASP-12b was the first HJ for which a tidal decay scenario appeared convincing, even though alternative explanations have been hypothesized. Here we present a new analysis based on 28 unpublished high-precision transit light curves gathered over a 12-yr baseline and combined with all the available archival data, and an updated set of stellar parameters from HARPS-N high-resolution spectra, which are consistent with a main-sequence scenario, close to the hydrogen exhaustion in the core. Our values of dP/dt = −30.72 ± 2.67 and Q′* = (2.13 ± 0.18) × 105 are statistically consistent with previous studies, and indicate that WASP-12 is undergoing fast tidal dissipation. We additionally report the presence of excess scatter in the timing data and discuss its possible origin.

Nuance: Efficient Detection of Planets Transiting Active Stars

The detection of planetary transits in the light curves of active stars, featuring correlated noise in the form of stellar variability, remains a challenge. Depending on the noise characteristics, we show that the traditional technique that consists of detrending a light curve before searching for transits alters their signal-to-noise ratio and hinders our capability to discover exoplanets transiting rapidly rotating active stars. We present nuance, an algorithm to search for transits in light curves while simultaneously accounting for the presence of correlated noise, such as stellar variability and instrumental signals. We assess the performance of nuance on simulated light curves as well as on the Transiting Exoplanet Survey Satellite light curves of 438 rapidly rotating M dwarfs. For each data set, we compare our method to five commonly used detrending techniques followed by a search with the Box-Least-Squares algorithm. Overall, we demonstrate that nuance is the most performant method in 93% of cases, leading to both the highest number of true positives and the lowest number of false-positive detections. Although simultaneously searching for transits while modeling correlated noise is expected to be computationally expensive, we make our algorithm tractable and available as the JAX-powered Python package nuance, allowing its use on distributed environments and GPU devices. Finally, we explore the prospects offered by the nuance formalism and its use to advance our knowledge of planetary systems around active stars, both using space-based surveys and sparse ground-based observations.

TOI-2266 b: A keystone super-Earth at the edge of the M dwarf radius valley

We validate the Transiting Exoplanet Survey Satellite (TESS) object of interest TOI-2266.01 (TIC 8348911) as a small transiting planet (most likely a super-Earth) orbiting a faint M5 dwarf (V = 16.54) on a 2.33 d orbit. The validation is based on an approach where multicolour transit light curves are used to robustly estimate the upper limit of the transiting object's radius. Our analysis uses SPOC-pipeline TESS light curves from Sectors 24, 25, 51, and 52, simultaneous multicolour transit photometry observed with MuSCAT2, MuSCAT3' and HiPERCAM, and additional transit photometry observed with the LCOGT telescopes. TOI-2266 b is found to be a planet with a radius of 1.54 ± 0.09 R⊕, which locates it at the edge of the transition zone between rocky planets, water-rich planets, and sub-Neptunes (the so-called M dwarf radius valley). The planet is amenable to ground-based radial velocity mass measurement with red-sensitive spectrographs installed in large telescopes, such as MAROON-X and Keck Planet Finder (KPF), which makes it a valuable addition to a relatively small population of planets that can be used to probe the physics of the transition zone. Further, the planet's orbital period of 2.33 days places it inside a ‘keystone planet’ wedge in the period-radius plane where competing planet formation scenarios make conflicting predictions on how the radius valley depends on the orbital period. This makes the planet also a welcome addition to the small population of planets that can be used to test small-planet formation scenarios around M dwarfs.

TOI-6883.01: A Single-transit Planet Candidate Detected from TESS

A new candidate exoplanet, proposed in ExoFOP by authors, it was promoted from TIC 393818343 to TOI-6883.01 at coordinates R.A.(J2000)20:41:10.01 decl.(J2000) + 3:38:17.87 in the Delphinus constellation and its distance is (93.73 ± 0.35) pc from Earth. The target star is a Sun-type having G0 class according to Skiff spectral classification and it has photometric magnitude V(Johnson) = 9.5 mag. We analyzed the transit light curve using Transit Exoplanet Survey Satellite’s ExoMAST tool, and evaluated the Lightcurve Analysis Tool for Transiting Exoplanets-report by excluding false positives, studying the background, satellite and centroid motion, and analyzing the pixels in sector 55 to define the source goodness. The candidate exoplanet transit has a duration of TD = 3.957 hr, Depth = 0.1196% and mid-transit time occurs at TBJD = 2811.24. Only one event was observed, so the orbital period cannot be evaluated.

Effects of tidal deformation on planetary phase curves

With the continuous improvement in the precision of exoplanet observations, it has become feasible to probe for subtle effects that can enable a more comprehensive characterization of exoplanets. A notable example is the tidal deformation of ultra-hot Jupiters by their host stars, whose detection can provide valuable insights into the planetary interior structure. In this work we extend previous research on modeling deformation in transit light curves by proposing a straightforward approach to account for tidal deformation in phase curve observations. The planetary shape is modeled as a function of the second fluid Love number for radial deformation h2f. For a planet in hydrostatic equilibrium, h2f provides constraints on the interior structure of the planet. We show that the effect of tidal deformation manifests across the full orbit of the planet as its projected area varies with phase, thereby allowing us to better probe the planet’s shape in phase curves than in transits. Comparing the effects and detectability of deformation by different space-based instruments (JWST, HST, PLATO, CHEOPS, and TESS), we find that the effect of deformation is more prominent in infrared observations where the phase curve amplitude is the largest. A single JWST phase curve observation of a deformed planet, such as WASP-12 b, can allow up to a 17σ measurement of h2f compared to 4σ from transit-only observation. This high-precision h2f measurement can constrain the core mass of the planet to within 19% of the total mass, thus providing unprecedented constraints on the interior structure. Due to the lower phase curve amplitudes in the optical, the other instruments provide ≤ 4σ precision on h2f depending on the number of phase curves observed. We also find that detecting deformation from infrared phase curves is less affected by uncertainty in limb darkening, unlike detection in transits. Finally, the assumption of sphericity when analyzing the phase curve of deformed planets can lead to biases in several system parameters (radius, dayside and nightside temperatures, and hotspot offset, among others), thereby significantly limiting their accurate characterization.

Simultaneous multicolour transit photometry of hot Jupiters HAT-P-19b, HAT-P-51b, HAT-P-55b, and HAT-P-65b

ABSTRACT Accurate physical parameters of exoplanet systems are essential for further exploration of planetary internal structure, atmospheres, and formation history. We aim to use simultaneous multicolour transit photometry to improve the estimation of transit parameters, to search for transit timing variations (TTVs), and to establish which of our targets should be prioritized for follow-up transmission spectroscopy. We performed time series photometric observations of 12 transits for the hot Jupiters HAT-P-19b, HAT-P-51b, HAT-P-55b, and HAT-P-65b using the simultaneous four-colour camera MuSCAT2 on the Telescopio Carlos Sánchez. We collected 56 additional transit light curves from TESS photometry. To derive transit parameters, we modelled the MuSCAT2 light curves with Gaussian processes to account for correlated noise. To derive physical parameters, we performed EXOFASTv2 global fits to the available transit and radial velocity data sets, together with the Gaia DR3 parallax, isochrones, and spectral energy distributions. To assess the potential for atmospheric characterization, we compared the multicolour transit depths with a flat line and a clear atmosphere model. We consistently refined the transit and physical parameters. We improved the orbital period and ephemeris estimates, and found no evidence for TTVs or orbital decay. The MuSCAT2 broad-band transmission spectra of HAT-P-19b and HAT-P-65b are consistent with previously published low-resolution transmission spectra. We also found that, except for HAT-P-65b, the assumption of a planetary atmosphere can improve the fit to the MuSCAT2 data. In particular, we identified HAT-P-55b as a priority target among these four planets for further atmospheric studies using transmission spectroscopy.

Kernel-, mean-, and noise-marginalized Gaussian processes for exoplanet transits and H0 inference

ABSTRACT Using a fully Bayesian approach, Gaussian process regression is extended to include marginalization over the kernel choice and hyperparameters. In addition, Bayesian model comparison via the evidence enables direct kernel comparison. The calculation of the joint posterior was implemented with a transdimensional sampler which simultaneously samples over the discrete kernel choice and their hyperparameters by embedding these in a higher dimensional space, from which samples are taken using nested sampling. Kernel recovery and mean function inference were explored on synthetic data from exoplanet transit light-curve simulations. Subsequently, the method was extended to marginalization over mean functions and noise models and applied to the inference of the present-day Hubble parameter, H0, from real measurements of the Hubble parameter as a function of redshift, derived from the cosmologically model-independent cosmic chronometer and lambda-cold dark matter-dependent baryon acoustic oscillation observations. The inferred H0 values from the cosmic chronometers, baryon acoustic oscillations, and combined data sets are $H_0= 66 \pm 6,\, 67 \pm 10,\, \mathrm{ and}\,69 \pm 6\,\mathrm{km}\, \mathrm{s}^{-1}\, \mathrm{Mpc}^{-1}$, respectively. The kernel posterior of the cosmic chronometers data set prefers a non-stationary linear kernel. Finally, the data sets are shown to be not in tension with ln R = 12.17 ± 0.02.

Analytical Lightcurves for Transiting Exomoons

Transit photometry has remained the most effective technique to detect and characterize exoplanets. As thousands of exoplanets have been discovered in the last few decades, the possibility of the existence of exomoons in some of these systems can not be avoided. However, the detection of exomoons has still remained elusive, owing to their much smaller expected size compared to their planetary host. With the advent of next generation space telescopes and large ground based telescopes, the possibility to detect them is imminent in near future. In such scenario, a comprehensive analytical formalism to model the transit lightcurves of a transiting exomoon hosting system will be necessary to confirm their detection and study their physical and dynamical characteristics. Here, I present such an analytical formulation, that can be used to simulate the transit lightcurves for an exoplanetary system hosting transiting exomoons. This formalism uses the physical and orbital properties of the three-body star-planet-moon system, to solve their orbital dynamics, and model the transit lightcurves for every possible physical scenarios. In this report, various aspects of this analytical formalism has been discussed, and the model lightcurves for a few of the practical scenarios have been presented.

TESS ve yer-tabanlı gözlemler ışığında WASP-12b'nin güncellenmiş yörünge küçülme oranı

We investigate the orbital decay behavior of the well-studied hot Jupiter WASP-12\,b orbiting its late-F host star on a 1.09-day orbit by analyzing its transit timings. Thanks to precise photometric data covering nearly 15 years of observations from the space and the ground since the discovery of the planet, including a transit light curve of our own, it became possible to study this behaviour in its details. This work updates the orbital period to a new value of 
 $P = 1.0914202527 \pm 0.000000039\,\text{days}$ and agrees with the previous finding that the planetary orbit has been shrinking with an updated rate of $-31.03 \pm 0.94\,\text{ms yr}^{-1}$. This corresponds to an orbital decay timescale of $\tau =P/|\dot{P}| = 3.04 \pm 0.09\,\text{Myr}$ that we attribute to the strong tidal interactions between the host-star and the planet. We also update the reduced stellar tidal quality factor as $Q_{*}^{\prime} = (1.72 \pm 0.39) \times$ $10^{5}$, which corresponds to the lower bound of the previously reported values of the parameter.

Validating AU Microscopii d with Transit Timing Variations

AU Mic is a young (22 Myr), nearby exoplanetary system that exhibits excess transit timing variations (TTVs) that cannot be accounted for by the two known transiting planets nor stellar activity. We present the statistical “validation” of the tentative planet AU Mic d (even though there are examples of “confirmed” planets with ambiguous orbital periods). We add 18 new transits and nine midpoint times in an updated TTV analysis to prior work. We perform the joint modeling of transit light curves using EXOFASTv2 and extract the transit midpoint times. Next, we construct an O−C diagram and use Exo-Striker to model the TTVs. We generate TTV log-likelihood periodograms to explore possible solutions for d’s period, then follow those up with detailed TTV and radial velocity Markov Chain Monte Carlo modeling and stability tests. We find several candidate periods for AU Mic d, all of which are near resonances with AU Mic b and c of varying order. Based on our model comparisons, the most-favored orbital period of AU Mic d is 12.73596 ± 0.00793 days (T C,d = 2458340.55781 ± 0.11641 BJD), which puts the three planets near 4:6:9 mean-motion resonance. The mass for d is 1.053 ± 0.511 M ⊕, making this planet Earth-like in mass. If confirmed, AU Mic d would be the first known Earth-mass planet orbiting a young star and would provide a valuable opportunity in probing a young terrestrial planet’s atmosphere. Additional TTV observations of the AU Mic system are needed to further constrain the planetary masses, search for possible transits of AU Mic d, and detect possible additional planets beyond AU Mic c.

Revisiting the Transit Timing and Atmosphere Characterization of the Neptune-mass Planet HAT-P-26 b

We present a transit-timing variation (TTV) and planetary atmosphere analysis of the Neptune-mass planet HAT-P-26 b. We present a new set of 13 transit light curves from optical ground-based observations and combine them with light curves from the Wide Field Camera 3 on the Hubble Space Telescope, the Transiting Exoplanet Survey Satellite, and previously published ground-based data. We refine the planetary parameters of HAT-P-26 b and undertake a TTV analysis using 33 transits obtained over seven years. The TTV analysis shows an amplitude signal of 1.98 ± 0.05 minutes, which could result from the presence of an additional ∼0.02 M Jup planet at a 1:2 mean-motion resonance orbit. Using a combination of transit depths spanning optical to near-infrared wavelengths, we find that the atmosphere of HAT-P-26 b contains % H2O with a derived temperature of K.

TransitFit: combined multi-instrument exoplanet transit fitting for JWST, HST, and ground-based transmission spectroscopy studies

ABSTRACT We present transitfit1, a package designed to fit exoplanetary transit light curves. transitfit offers multi-epoch, multi-wavelength fitting of multi-telescope transit data. transitfit allows per-telescope detrending to be performed simultaneously with transit parameter fitting, including custom detrending. Host limb darkening can be fitted using prior conditioning from stellar atmosphere models. We demonstrate transitfit in a number of contexts. We model multi-telescope broad-band optical data from the ground-based SPEARNET survey of the low-density hot-Neptune WASP-127b and compare results to a previously published higher spectral resolution GTC/OSIRIS transmission spectrum. Using transitfit, we fit 26 transit epochs by TESS to recover improved ephemeris of the hot-Jupiter WASP-91b and a transit depth determined to a precision of 111 ppm. We use transitfit to conduct an investigation into the contested presence of TTV signatures in WASP-126b using 180 transits observed by TESS, concluding that there is no statistically significant evidence for such signatures from observations spanning 27 TESS sectors. We fit HST observations of WASP-43 b, demonstrating how transitfit can use custom detrending algorithms to remove complex baseline systematics. Lastly, we present a transmission spectrum of the atmosphere of WASP-96b constructed from simultaneous fitting of JWST NIRISS Early Release Observations and archive HST WFC3 transit data. The transmission spectrum shows generally good correspondence between spectral features present in both data sets, despite very different detrending requirements.