arXiv subjects

Benjamin V. Rackham

Publications and source records attributed to Benjamin V. Rackham.

At least 37 records · Page 2Linked to original sources

arXiv2026

Two temperate Earth- and Neptune-sized planets orbiting fully convective M dwarfs

As the diversity of exoplanets continues to grow, it is important to revisit assumptions about habitability and classical HZ definitions. In this work, we introduce an expanded 'temperate' zone, defined by instellation fluxes between $0.1<S/\mathrm{S}_\oplus<5$, thus encompassing a broader range of potentially habitable worlds. We also introduce the TEMPOS survey, which aims to produce a catalogue of precise radii for temperate planets orbiting M dwarfs with $T_\mathrm{eff}\leq3400\,$ K. This work reports the discovery and characterisation of two planets in this temperate regime orbiting mid-type M dwarfs: TOI-6716\,b, a $0.98\pm0.07\,\mathrm{R}_\oplus$ planet orbiting its M4 host star ($R_\star=0.231\,\pm0.015\mathrm{R}_\odot$, $M_\star=0.223\pm0.011\,\mathrm{M}_\odot$, $T_\mathrm{eff}=3110\pm80\,\mathrm{K}$) with a period $P=4.7185898^{+0.0000054}_{-0.0000041}\,\mathrm{d}$, and TOI-7384 b, a $3.56\pm0.21\,\mathrm{R}_\oplus$ planet orbiting an M4 ($R_\star=0.319\,\pm0.018\mathrm{R}_\odot$, $M_\star=0.318\pm0.016\,\mathrm{M}_\odot$, $T_\mathrm{eff}=3185\pm75\,\mathrm{K}$) star every $P=6.2340258^{+0.0000034}_{-0.0000036}\,\mathrm{d}$. The radii of TOI-6716 b and TOI-7384 b have precisions of $6.8\%$ and $5.9\%$ respectively. We validate these planets with multi-band ground-based photometric observations, high-resolution imaging and statistical analyses. We find these planets to have instellation fluxes close to the inner (hotter) edge of the temperate zone, with $4.4\pm1.1\,\mathrm{S}_\oplus$ and $4.9\pm1.1\,\mathrm{S}_\oplus$ for TOI-6716 b and TOI-7384 b respectively. Also, with a predicted TSM similar to the TRAPPIST-1 planets, TOI-6716 b is likely to be a good rocky-world JWST target, should it have retained its atmosphere.

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arXiv2025

JWST TRAPPIST-1 e/b Program: Motivation and first observations

One of the forefront goals in the field of exoplanets is the detection of an atmosphere on a temperate terrestrial exoplanet, and among the best suited systems to do so is TRAPPIST-1. However, JWST transit observations of the TRAPPIST-1 planets show significant contamination from stellar surface features that we are unable to confidently model. Here, we present the motivation and first observations of our JWST multi-cycle program of TRAPPIST-1 e, which utilize close transits of the airless TRAPPIST-1 b to model-independently correct for stellar contamination, with the goal of determining whether TRAPPIST-1 e has an Earth-like mean molecular weight atmosphere containing CO$_2$. We present our simulations, which show that with the 15 close transit observations, we will be able to detect this atmosphere on TRAPPIST-1 e at $Δ\ln\,Z=5$ or greater confidence assuming we are able to correct for stellar contamination using the close transit observations. We also show the first three observations of our program. We find that our ability to correct for stellar contamination can be inhibited when strong stellar flares are present, as flares can break the assumption that the star does not change meaningfully between planetary transits. The cleanest observation demonstrates the removal of stellar contamination contribution through an increased preference for a flat line over the original TRAPPIST-1 e spectrum, but highlights how minor data analysis assumptions can propagate significantly when searching for small atmospheric signals. This is amplified when using the signals from multiple planets, which is important to consider as we continue our atmospheric search.

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arXiv2025

TOI-7166 b: A Habitable Zone mini-Neptune planet around a nearby low-mass star

We present the discovery and validation of TOI-7166b, a 2.01+/-0.05R_Earth planet orbiting a nearby low-mass star. We validated the planet by combining TESS and multi-color high-precision photometric observations from ground-based telescopes, together with spectroscopic data, high-contrast imaging, archival images, and statistical arguments. The host star is an M4-type dwarf at a distance of ~35 pc from the Sun. It has a mass and a radius of Ms=0.190+/-0.004M_Sun and Rs=0.222+/-0.005R_Sun, respectively. TOI-7166b has an orbital period of 12.9 days, which places it close to the inner edge of the Habitable Zone of its host star, receiving an insolation flux of Sp=1.07+/-0.08S_Earth and an equilibrium temperature of Teq=249+/-5K (assuming a null Bond albedo). The brightness of the host star makes TOI-7166 a suitable target for radial velocity follow-up to measure the planetary mass and bulk density. Moreover, the physical parameters of the system including the infrared brightness (Kmag = 10.6) of the star and the planet-to-star radius ratio (0.0823+/-0.0012) make TOI-7166b an exquisite target for transmission spectroscopic observations with the JWST, to constrain the exoplanet atmospheric compositions.

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arXiv2025

Separating flare and secondary atmospheric signals with RADYN modeling of near-infrared JWST transmission spectroscopy observations of TRAPPIST-1

Although TRAPPIST-1's temperate planets have the highest transmission signals of any known system, flares contaminate 50-70% of transits at the 1000 ppm level, far above 100 ppm secondary atmospheres. Efforts to mitigate flare contamination and assess impacts on radiation environments are each hampered by a lack of empirical spectral analysis and physics-based modeling. We present spectrotemporal analysis and radiative-hydrodynamic modeling of 5.5 hr of NIRISS and NIRSpec observations of 6 TRAPPIST-1 flares of 2.2-8.7x10^30 erg. Flare lines and continua are characterized using grid searches of RADYN beam-heating models spanning 10$^4\times$ in electron beam parameters. Best-fit models indicate these flares result from moderate-intensity beams with emergent electron fluxes of 10^12 erg s^-1 cm^-2 and energies $\leq$37 keV, although all models over-predict the Paschen jump. These models predict XUV, FUV, and NUV counterparts to the infrared peak fluxes of 8.9-28.9x10^27, 4.3-13.9x10^26, and 3.4-11.4x10^27 erg s^-1, respectively. Scaling the flare rate into the XUV suggests flaring contributes 1.35$_{-0.15}^{+2.0}\times$ quiescence yr$^{-1}$. We bin integrations of similar flare effective temperature to construct fiducial flare spectra from 2000-4500 K in order to develop separate empirical and RADYN-based mitigation pipelines. Both pipelines are applied to all 5.5 hr of R=10 data, resulting in maximum residuals from 1-2.8$μ$m of 100-140 ppm and typical residuals of 54$\pm$14 and 65$\pm$17 ppm for the empirical and RADYN-based pipelines, respectively. Injection testing supports 3$σ$ detection capability for CO2 atmospheres with features of 150-250 ppm, with weak evidence (BF$\approx$3) still obtained at 130 ppm. Our results motivate multi-wavelength observations to improve model fidelity and test high-energy predictions.

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arXiv2025

Horizontal and vertical exoplanet thermal structure from a JWST spectroscopic eclipse map

Highly-irradiated giant exoplanets known as "ultra-hot Jupiters" are anticipated to exhibit large variations of atmospheric temperature and chemistry as a function of longitude, latitude, and altitude. Previous observations have hinted at these variations, but the existing data have been fundamentally restricted to probing hemisphere-integrated spectra, thereby providing only coarse information on atmospheric gradients. Here we present a spectroscopic eclipse map of an extrasolar planet, resolving the atmosphere in multiple dimensions simultaneously. We analyze a secondary eclipse of the ultra-hot Jupiter WASP-18b observed with the NIRISS instrument on JWST. The mapping reveals weaker longitudinal temperature gradients than were predicted by theoretical models, indicating the importance of hydrogen dissociation and/or nightside clouds in shaping global thermal emission. Additionally, we identify two thermally distinct regions of the planet's atmosphere: a "hotspot" surrounding the substellar point and a "ring" near the dayside limbs. The hotspot region shows a strongly inverted thermal structure due to the presence of optical absorbers and a water abundance marginally lower than the hemispheric average, in accordance with theoretical predictions. The ring region shows colder temperatures and poorly constrained chemical abundances. Similar future analyses will reveal three-dimensional thermal, chemical, and dynamical properties of a broad range of exoplanet atmospheres.

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arXiv2025

What's in Your Transit? Towards Reliably Getting $5\times$ More Science from Exoplanet Transit Data

Exoplanetary science heavily relies on transit depth ($D$) measurements. Yet, as instrumental precision increases, the uncertainty on $D$ appears to increasingly drift from expectations driven solely by photon-noise. Here we characterize this shortfall (the Transit-Depth Precision Problem, TDPP), by defining an amplification factor, $A$, quantifying the discrepancy between the measured transit-depth uncertainty and the measured baseline scatter on a same time bin size. While in theory $A$ should be $\sim\sqrt{3}$, we find that it can reach values $\gtrsim$10 notably due to correlations between $D$ and the limb-darkening coefficients (LDCs). This means that (1) the performance of transit-based exoplanet studies (e.g., atmospheric studies) can be substantially improved with reliable priors on LDCs and (2) low-fidelity priors on the LDCs can yield substantial biases on $D$--potentially affecting atmospheric studies due to the wavelength-dependence of such biases. For the same reason, biases may emerge on stellar-density and planet-shape/limb-asymmetry measurements. With current photometric precisions, we recommend using a 3$^{\rm rd}$-order polynomial law and a 4$^{\rm th}$-order non-linear law, as they provide an optimal compromise between bias and $A$, while testing the fidelity for each parametrization. While their use combined with existing LDC priors (10-20% uncertainty) currently implies $A\sim10$, we show that targeted improvements to limb-darkening models can bring $A$ down to $\sim2$. Improving stellar models and transit-fitting practices is thus essential to fully exploit transit datasets, and reliably increasing their scientific yield by $5\times$, thereby enabling the same science with up to $25\times$ fewer transits.

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arXiv2025

Testing the performance of cross-correlation techniques to search for molecular features in JWST NIRSpec G395H observations of transiting exoplanets

Cross-correlations techniques offer an alternative method to search for molecular species in JWST observations of exoplanet atmospheres. In a previous article, we applied cross-correlation functions for the first time to JWST NIRSpec/G395H observations of exoplanet atmospheres, resulting in a detection of CO in the transmission spectrum of WASP-39b and a tentative detection of CO isotopologues. Here we present an improved version of our cross-correlation technique and an investigation into how efficient the technique is when searching for other molecules in JWST NIRSpec/G395H data. Our search results in the detection of more molecules via cross-correlations in the atmosphere of WASP-39b, including $\rm H_{2}O$ and $\rm CO_{2}$, and confirms the CO detection. This result proves that cross-correlations are a robust and computationally cheap alternative method to search for molecular species in transmission spectra observed with JWST. We also searched for other molecules ($\rm CH_{4}$, $\rm NH_{3}$, $\rm SO_{2}$, $\rm N_{2}O$, $\rm H_{2}S$, $\rm PH_{3}$, $\rm O_{3}$ and $\rm C_{2}H_{2}$) that were not detected, for which we provide the definition of their cross-correlation baselines for future searches of those molecules in other targets. We find that that the cross-correlation search of each molecule is more efficient over limited wavelength regions of the spectrum, where the signal for that molecule dominates over other molecules, than over broad wavelength ranges. In general we also find that Gaussian normalization is the most efficient normalization mode for the generation of the molecular templates.

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arXiv2025

Gravity-sensitive Spectral Indices in Ultracool Dwarfs: Investigating Correlations with Metallicity and Planet Occurrence using SpeX and FIRE Observations

We present a near-infrared spectroscopic analysis (0.9--2.4~$μ$m) of gravity indices for 56 ultracool dwarfs (M5.5--L0), including exoplanet hosts SPECULOOS-2, SPECULOOS-3, and LHS 3154, with 59 spectra from SpeX and FIRE and literature data for TRAPPIST-1. Using gravity-sensitive spectral features (FeH at 0.99, 1.20, and 1.55~$μ$m; VO at 1.06~$μ$m; the H-band continuum; KI at 1.17 and 1.25$μ$m), we investigate links between gravity classification, metallicity, and planet occurrence. All four planet hosts show intermediate-gravity signatures despite field-age indicators. A volume-corrected logistic regression finds no significant association between gravity class and planet occurrence. Among individual indices, FeH_z (0.99~$μ$m) is the most promising tracer of planet-hosting status, with a tentative $2σ$ correlation that may reflect observational biases. More robustly, FeH_z shows a $3.3σ$ anti-correlation with [Fe/H]. A Kruskal--Wallis test finds no metallicity difference across gravity classes, suggesting the FeH_z--[Fe/H] trend is not due to bulk metallicity. We propose this relation reflects the interplay of age, gravity, and composition, with higher-metallicity objects being systematically younger and lower-gravity, reducing FeH absorption. While only hinting at a connection between gravity-sensitive features and planet occurrence among late-M dwarfs, these results highlight the need for caution when using spectral diagnostics to interpret ultracool dwarf planet hosts.

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arXiv2025

Flares on TRAPPIST-1 reveal the spectrum of magnetic features on its surface

TRAPPIST-1 is an M8 dwarf hosting seven known exoplanets and is currently one of the most frequently observed targets of the James Webb Space Telescope (JWST). However, it is notoriously active, and its surface is believed to be covered by magnetic features that contaminate the planetary transmission spectra. The radiative spectra of these magnetic features are needed to clean transmission spectra, but they currently remain unknown. Here, we develop a new approach for measuring these spectra using time-resolved JWST/NIRISS observations. We detect a persistent post-flare enhancement in the spectral flux of TRAPPIST-1. Our analysis rules out lingering flare decay as the cause of the flux enhancement and, thus, points to structural changes on the stellar surface induced by flares. We suggest that the flaring event triggers the disappearance of (part of) a dark magnetic feature, producing a net brightening. This suggestion is motivated by solar data: flare-induced disappearance of magnetic features on the solar surface has been directly detected in high spatial resolution images, and our analysis shows that this process produces changes in solar brightness very similar to those we observe on TRAPPIST-1. The proposed explanation for the flux enhancement enables, to our knowledge, the first measurement of the spectrum of a magnetic feature on an M8 dwarf. Our analysis indicates that the disappearing magnetic feature is cooler than the TRAPPIST-1 photosphere, but by at most a few hundred kelvins.

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arXiv2025

The Pandora SmallSat: A Low-Cost, High Impact Mission to Study Exoplanets and Their Host Stars

The Pandora SmallSat is a NASA flight project aimed at studying the atmospheres of exoplanets -- planets orbiting stars outside our Solar System. Pandora will provide the first dataset of simultaneous, multiband (visible and NIR), long-baseline observations of exoplanets and their host stars. Pandora is an ambitious project that will fly a 0.44 m telescope in a small form factor. To achieve the scientific goals, the mission requires a departure from the traditional cost-schedule paradigm of half-meter-class observatories. Pandora achieves this by leveraging existing capabilities that necessitate minimal engineering development, disruptive and agile management, trusted partnerships with vendors, and strong support from the lead institutions. The Pandora team has developed a suite of high-fidelity parameterized simulation and modeling tools to estimate the performance of both imaging channels. This has enabled a unique bottom-up approach to deriving trades and system requirements. Pandora is a partnership between NASA and Lawrence Livermore National Laboratory. The project completed its Critical Design Review in October 2023 and is slated for launch into Sun-synchronous, low-Earth orbit in Fall 2025.

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arXiv2025

Stellar Models Also Limit Exoplanet Atmosphere Studies in Emission

Stellar contamination has long been recognized as a major bottleneck in transmission spectroscopy, limiting our ability to accurately characterize exoplanet atmospheres-particularly for terrestrial worlds. In response, significant observational efforts have shifted toward emission spectroscopy as a potentially more robust alternative, exemplified by initiatives such as the 500-hour JWST Rocky Worlds Director's Discretionary Time (DDT) program. However, the extent to which emission spectroscopy may be affected by stellar effects remains mostly unexplored, in stark contrast with the extensiveexploration and mitigation work for transmission spectroscopy. In this study, we assess the impact of imperfect knowledge of stellar spectra on exoplanet atmospheric retrievals from emission spectroscopy. At 12.8 um, none of the considered bare surface types-basalt, ultramafic, Fe-oxidized, and granitoid-can be reliably distinguished when accounting for the 3 sigma model precision between SPHINX and PHOENIX. At 15.0 um, only the granitoid surface is distinguishable from all others above this threshold. These results show that stellar model uncertainty alone substantially limits our ability to constrain surface composition from photometric data, even before including other sources of uncertainty such as stellar radius. Also, we find that current 15 um eclipse depth estimations using different stellar models introduce a 60 ppm difference for M8 and 20 ppm for M5 stars. This model discrepancy leads to a degeneracy in retrieved planetary albedos and weakens constraints on the presence of an atmosphere. We therefore recommend that future JWST secondary eclipse observations systematically include stellar mid-infrared spectroscopy to mitigate these uncertainties.

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arXiv2025

TOI-1846b: A super-Earth in the radius valley orbiting a nearby M dwarf

We present the discovery and validation of a super-Earth planet orbiting the M dwarf star TOI-1846 (TIC 198385543). The host star(Kmag = 9.6)is located 47 pc away and has a radius of Rs=0.41+/-0.01R_Sun,a mass of Ms=0.40+/-0.02M_Sun and an effective temperature of Teff=3568+/-44K. Our analyses are based on joint modelling of TESS photometry and ground-based multi-color photometric data. We also use high-resolution imaging and archival images, as well as statistical validation techniques to support the planetary system nature. We find that TOI-1846b is a super-Earth sized planet with radius of Rp=1.79+/-0.07R_Earth and a predicted mass of Mp=4.4+1.6-1.0M_Earth (from the Chen & Kipping relation) on a 3.9 d orbit, with an equilibrium temperature of Teq=589+/-20K (assuming a null Bond Albedo) and an incident flux of Sp=17.6+/-2.0S_Earth. Based on the two RV measurements obtained with the TRES spectrograph and high-resolution imaging, a non-planetary transiting companion is excluded. With a radius of ~1.8R_Earth, TOI-1846b is within the sparsely populated radius range around 2R_Earth known as the radius gap (or radius valley). This discovery can contribute to refining the precise location of the radius valley for small planets orbiting bright M dwarfs, thereby enhancing our understanding of planetary formation and evolution processes.

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arXiv2025

Hubble's Multi-Year Search for Exospheres in the TRAPPIST-1 System Reveals Frequent Microflares

Ly-$α$ observations provide a powerful probe of stellar activity and atmospheric escape in exoplanetary systems. We present here an analysis of 104 HST/STIS orbits monitoring the TRAPPIST-1 system between 2017 and 2022, covering 3--5 transits for each of its seven planets. We rule out transit depths $\gtrsim20\%$, which translates into an upper limit on the escape rate of $1064~EO_H$/Gyr for planet b ($1~EO_H$ is the Earth-ocean-equivalent hydrogen content), in agreement with recent claims that planet b should be airless. These upper limits are $\sim$3 times larger than expected from the photon noise due to a large baseline scatter, which we ultimately link to TRAPPIST-1's intrinsic Ly-$α$ variability from frequent ``microflares.'' While JWST observations of TRAPPIST-1 in the near infrared have shown that $\sim10^{30}$-erg flares occur every $\sim$6 hours, we report here $\sim10^{29}$-erg flares on sub-hour timescales in the HST/STIS and also Very Large Telescope (VLT) $g^{'}$ observations. The FUV and optical amplitudes ($\sim$400$\%$ vs $\sim$3$\%$, respectively) for flares with similar waiting-times indicate flare temperatures of 11000$^{+4200}_{-3100}$~K over 0.011$^{+0.03}_{-0.01}$\% of the stellar disk. Finally, our multi-year baseline reveals a variability with $P = 3.27 \pm 0.04$ days, providing further validation of the previously reported 3.295-day rotation period for TRAPPIST-1. These results highlight the importance of accounting for stellar microvariability when searching for exospheres around active M dwarfs.

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arXiv2025

A transiting giant planet in orbit around a 0.2-solar-mass host star

Planet formation models suggest that the formation of giant planets is significantly harder around low-mass stars, due to the scaling of protoplanetary disc masses with stellar mass. The discovery of giant planets orbiting such low-mass stars thus imposes strong constraints on giant planet formation processes. Here, we report the discovery of a transiting giant planet orbiting a $0.207 \pm 0.011 M_{\odot}$ star. The planet, TOI-6894 b, has a mass and radius of $M_P = 0.168 \pm 0.022 M_J (53.4 \pm 7.1 M_{\oplus})$ and $R_P = 0.855 \pm 0.022 R_J$, and likely includes $12 \pm 2 M_{\oplus}$ of metals. The discovery of TOI-6894 b highlights the need for a better understanding of giant planet formation mechanisms and the protoplanetary disc environments in which they occur. The extremely deep transits (17% depth) make TOI-6894 b one of the most accessible exoplanetary giants for atmospheric characterisation observations, which will be key for fully interpreting the formation history of this remarkable system and for the study of atmospheric methane chemistry.

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arXiv2025

ExoMiner++: Enhanced Transit Classification and a New Vetting Catalog for 2-Minute TESS Data

We present ExoMiner++, an enhanced deep learning model that builds on the success of ExoMiner to improve transit signal classification in 2-minute TESS data. ExoMiner++ incorporates additional diagnostic inputs, including periodogram, flux trend, difference image, unfolded flux, and spacecraft attitude control data, all of which are crucial for effectively distinguishing transit signals from more challenging sources of false positives. To further enhance performance, we leverage multi-source training by combining high-quality labeled data from the Kepler space telescope with TESS data. This approach mitigates the impact of TESS's noisier and more ambiguous labels. ExoMiner++ achieves high accuracy across various classification and ranking metrics, significantly narrowing the search space for follow-up investigations to confirm new planets. To serve the exoplanet community, we introduce new TESS catalog containing ExoMiner++ classifications and confidence scores for each transit signal. Among the 147,568 unlabeled TCEs, ExoMiner++ identifies 7,330 as planet candidates, with the remainder classified as false positives. These 7,330 planet candidates correspond to 1,868 existing TESS Objects of Interest (TOIs), 69 Community TESS Objects of Interest (CTOIs), and 50 newly introduced CTOIs. 1,797 out of the 2,506 TOIs previously labeled as planet candidates in ExoFOP are classified as planet candidates by ExoMiner++. This reduction in plausible candidates combined with the excellent ranking quality of ExoMiner++ allows the follow-up efforts to be focused on the most likely candidates, increasing the overall planet yield.

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arXiv2025

TOI-6478 b: a cold under-dense Neptune transiting a fully convective M dwarf from the thick disc

Growing numbers of exoplanet detections continue to reveal the diverse nature of planetary systems. Planet formation around late-type M dwarfs is of particular interest. These systems provide practical laboratories to measure exoplanet occurrence rates for M dwarfs, thus testing how the outcomes of planet formation scale with host mass, and how they compare to Sun-like stars. Here, we report the discovery of TOI-6478b, a cold ($T_{\text{eq}}=204\,$K) Neptune-like planet orbiting an M5 star ($R_\star=0.234\pm0.012\,\text{R}_\odot$, $M_\star=0.230\pm0.007\,\text{M}_\odot$, $T_{\text{eff}}=3230\pm75\,$K) which is a member of the Milky Way's thick disc. We measure a planet radius of $R_b=4.6\pm0.24\,\text{R}_\oplus$ on a $P_b=34.005019\pm0.000025\,$d orbit. Using radial velocities, we calculate an upper mass limit of $M_b\leq9.9\,\text{M}_\oplus$ ($M_b\leq0.6\,\text{M}_{\text{Nep}})$, with $3\,σ$ confidence. TOI-6478b is a milestone planet in the study of cold, Neptune-like worlds. Thanks to its large atmospheric scale height, it is amenable to atmospheric characterisation with facilities such as JWST, and will provide an excellent probe of atmospheric chemistry in this cold regime. It is one of very few transiting exoplanets that orbit beyond their system's ice-line whose atmospheric chemical composition can be measured. Based on our current understanding of this planet, we estimate TOI-6478b's spectroscopic features (in transmission) can be $\sim2.5\times$ as high as the widely studied planet K2-18b.

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arXiv2024

Stellar Contamination Correction Using Back-to-Back Transits of TRAPPIST-1 b and c

Stellar surface heterogeneities, such as spots and faculae, often contaminate exoplanet transit spectra, hindering precise atmospheric characterization. We demonstrate a novel, epoch-based, model-independent method to mitigate stellar contamination, applicable to multi-planet systems with at least one airless planet. We apply this method using quasi-simultaneous transits of TRAPPIST-1 b and TRAPPIST-1 c observed on July 9, 2024, with JWST NIRSpec PRISM. These two planets, with nearly identical radii and impact parameters, are likely either bare rocks or possess thin, low-pressure atmospheres, making them ideal candidates for this technique, as variations in their transit spectra would be primarily attributed to stellar activity. Our observations reveal their transit spectra exhibit consistent features, indicating similar levels of stellar contamination. We use TRAPPIST-1 b to correct the transit spectrum of TRAPPIST-1 c, achieving a 2.5x reduction in stellar contamination at shorter wavelengths. At longer wavelengths, lower SNR prevents clear detection of contamination or full assessment of mitigation. Still, out-of-transit analysis reveals variations across the spectrum, suggesting contamination extends into the longer wavelengths. Based on the success of the correction at shorter wavelengths, we argue that contamination is also reduced at longer wavelengths to a similar extent. This shifts the challenge of detecting atmospheric features to a predominantly white noise issue, which can be addressed by stacking observations. This method enables epoch-specific stellar contamination corrections, allowing co-addition of planetary spectra for reliable searches of secondary atmospheres with signals of 60-250 ppm. Additionally, we identify small-scale cold (2000 K) and warm (2600 K) regions almost uniformly distributed on TRAPPIST-1, with overall covering fractions varying by 0.1% per hour.

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arXiv2024

Reliable Transmission Spectrum Extraction with a Three-Parameter Limb Darkening Law

Stellar limb darkening must be properly accounted for to accurately determine the radii of exoplanets at various wavelengths. The standard approach to address limb darkening involves either using laws with coefficients from modelled stellar spectra or determining the coefficients empirically during light curve fitting of the data. Here, we test how accurately three common laws -- quadratic, power, and a three-parameter law -- can reproduce stellar limb darkening at different wavelengths and across a broad range of stars. We show that using a quadratic limb darkening law, which is most frequently employed by the community, leads to wavelength-dependent offsets in retrieved transmission spectra. For planets with high impact parameters ($b$ larger than about 0.5) the amplitude of these offsets can reach 1\% of the transit depth which is some cases is comparable to and can even exceed the expected signals from the planetary atmosphere. Furthermore, the quadratic law causes an offset in the value of the impact parameter when it is determined by fitting the broadband transit light curves. In contrast, using the Kipping--Sing three-parameter law leads to robust retrievals. We advocate the use of this law in retrievals, especially for transits with large impact parameters.

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