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C. A. Murray

Publications and source records attributed to C. A. Murray.

At least 19 recordsLinked to original sources

A Panchromatic JWST Spectrum of a Giant Starspot on the Fully Convective M-dwarf TOI-3884

TOI-3884 b is a rare super-Neptune transiting a fully convective M dwarf that hosts a persistent giant polar spot. Because the planet occults this active region during every transit, the system offers a unique laboratory to directly probe the stellar surface and spot properties. We present seven James Webb Space Telescope (JWST) transits of TOI-3884 b observed with NIRISS and NIRSpec (spanning 0.6--5.3$\mu$m). While all visits show a recurring spot-crossing signature, each transit exhibits a distinct spot-crossing morphology, enabling us to infer a stellar rotation period of $P$=11.102$\pm$0.003d and tightly constrain the pole-on stellar orientation ($i_{*}$=139.2$\pm$0.3$^{\circ}$, $\lambda_{*}$=31.1$\pm$0.4$^{\circ}$) and spot properties ($R_{\rm{spot}}=0.576^{+0.006}_{-0.005}$R$_{*}$, $\phi_{\rm{spot}}$=-84.69$\pm$0.12$^{\circ}$).We leverage this orbital configuration to measure the first empirical panchromatic spectrum of an M dwarf starspot with JWST, establishing a direct observational benchmark for stellar atmosphere models in the fully convective regime. Comparison with 1D NewEra and SPHINX atmosphere models indicates that the spot is 183$\pm$1K cooler than the photosphere, consistent with previous ground-based measurements and expectations for mid M dwarf spot contrasts. While the models reproduce the observed contrasts at wavelengths longer than 1$\mu$m, they significantly underpredict the contrasts at shorter wavelengths. These results demonstrate that M dwarf stellar atmosphere models may not fully capture the wavelength dependence of stellar contamination in transmission spectra and highlight the importance of empirical spot spectra for robust interpretation of planetary atmospheres, particularly in the optical.

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Quantifying the Impact of Starspot-Crossing Events on Retrieved Parameters from Transit Lightcurves

Starspot-crossing events (SCEs) in exoplanet transit lightcurves are becoming increasingly common as we focus on cooler host stars and observe higher precision photometric and spectroscopic lightcurves. In this work, we explore how these events affect our retrievals of transit depths and the accuracy with which we can derive spot properties. We inject and recover synthetic SCEs in photometric lightcurves using starry. We find that for high signal-to-noise ratio SCEs, we constrain the spot longitudes tightly (>80% within 1{\deg} of the true value) but degeneracies complicate retrieving spot contrasts, radii, and latitudes (within 17%, 19%, and 9{\deg} respectively). On average, the difference between injected and recovered transit depths is 0.78% or 78.3 ppm. In most (80%) injections, we recover the transit depth to within 0.6%. For transit depths inflated >1.3% by the transit light source effect (TLSE), fitting for a spot crossing improves the transit depth retrieval over masking the SCE in >95% of cases. However, we find that for spots with small contrasts (<5%) and/or covering fractions (<2%), we are likely to overcorrect for the TLSE, recovering a worse transit depth than simply masking. In addition, even when fitted, we find SCEs can inflate the uncertainties on recovered transit depths significantly, especially for JWST-like precisions. Finally, we present a new method, using SCE observables, of carving out the degenerate spot parameter space that provides informative priors for Markov Chain Monte Carlo sampling, demonstrating this technique on a real SCE observed in Kepler-51d's lightcurve.

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Two warm Earth-sized exoplanets and an Earth-sized candidate in the M5V-M6V binary system TOI-2267

We report two warm Earth-sized exoplanets orbiting the close binary TOI-2267 (M5+M6, separation ~8 au). Data from TESS and ground-based facilities confirm the planets, but we cannot determine which star they orbit. The planets have radii of 1.00+/-0.11 R_Earth (TOI-2267 b, P=2.28 d) and 1.14+/-0.13 R_Earth (TOI-2267 c, P=3.49 d) if around TOI-2267A, or 1.22+/-0.29 R_Earth and 1.36+/-0.33 R_Earth if around TOI-2267B. TESS also shows a candidate signal (TOI-2267.02, P=2.03 d, 0.95+/-0.12 or 1.13+/-0.30 R_Earth). Dynamical analysis shows all three cannot orbit one star; the most stable configuration has planets b and c (near a 3:2 resonance) orbiting one star and the candidate the other. This scenario would make TOI-2267 the most compact binary system known to host planets, with both components harbouring transiting worlds, offering a unique benchmark for studying planet formation and evolution in compact binary.

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A Benchmark JWST Near-Infrared Spectrum for the Exoplanet WASP-39b

Observing exoplanets through transmission spectroscopy supplies detailed information on their atmospheric composition, physics, and chemistry. Prior to JWST, these observations were limited to a narrow wavelength range across the near-ultraviolet to near-infrared, alongside broadband photometry at longer wavelengths. To understand more complex properties of exoplanet atmospheres, improved wavelength coverage and resolution are necessary to robustly quantify the influence of a broader range of absorbing molecular species. Here we present a combined analysis of JWST transmission spectroscopy across four different instrumental modes spanning 0.5-5.2 micron using Early Release Science observations of the Saturn-mass exoplanet WASP-39b. Our uniform analysis constrains the orbital and stellar parameters within sub-percent precision, including matching the precision obtained by the most precise asteroseismology measurements of stellar density to-date, and further confirms the presence of Na, K, H$_2$O, CO, CO$_2$, and SO$_2$ atmospheric absorbers. Through this process, we also improve the agreement between the transmission spectra of all modes, except for the NIRSpec PRISM, which is affected by partial saturation of the detector. This work provides strong evidence that uniform light curve analysis is an important aspect to ensuring reliability when comparing the high-precision transmission spectra provided by JWST.

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CHEOPS in-flight performance: A comprehensive look at the first 3.5 years of operations

CHEOPS is a space telescope specifically designed to monitor transiting exoplanets orbiting bright stars. In September 2023, CHEOPS completed its nominal mission and remains in excellent operational conditions. The mission has been extended until the end of 2026. Scientific and instrumental data have been collected throughout in-orbit commissioning and nominal operations, enabling a comprehensive analysis of the mission's performance. In this article, we present the results of this analysis with a twofold goal. First, we aim to inform the scientific community about the present status of the mission and what can be expected as the instrument ages. Secondly, we intend for this publication to serve as a legacy document for future missions, providing insights and lessons learned from the successful operation of CHEOPS. To evaluate the instrument performance in flight, we developed a comprehensive monitoring and characterisation programme. It consists of dedicated observations that allow us to characterise the instrument's response. In addition to the standard collection of nominal science and housekeeping data, these observations provide input for detecting, modelling, and correcting instrument systematics, discovering and addressing anomalies, and comparing the instrument's actual performance with expectations. The precision of the CHEOPS measurements has enabled the mission objectives to be met and exceeded. Careful modelling of the instrumental systematics allows the data quality to be significantly improved during the light curve analysis phase, resulting in more precise scientific measurements. CHEOPS is compliant with the driving scientific requirements of the mission. Although visible, the ageing of the instrument has not affected the mission's performance.

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TOI-4336 A b: A temperate sub-Neptune ripe for atmospheric characterization in a nearby triple M-dwarf system

Small planets transiting bright nearby stars are essential to our understanding of the formation and evolution of exoplanetary systems. However, few constitute prime targets for atmospheric characterization, and even fewer are part of multiple star systems. This work aims to validate TOI-4336 A b, a sub-Neptune-sized exoplanet candidate identified by the TESS space-based transit survey around a nearby M-dwarf. We validate the planetary nature of TOI-4336 A b through the global analysis of TESS and follow-up multi-band high-precision photometric data from ground-based telescopes, medium- and high-resolution spectroscopy of the host star, high-resolution speckle imaging, and archival images. The newly discovered exoplanet TOI-4336 A b has a radius of 2.1$\pm$0.1R$_{\oplus}$. Its host star is an M3.5-dwarf star of mass 0.33$\pm$0.01M$_{\odot}$ and radius 0.33$\pm$0.02R$_{\odot}$ member of a hierarchical triple M-dwarf system 22 pc away from the Sun. The planet's orbital period of 16.3 days places it at the inner edge of the Habitable Zone of its host star, the brightest of the inner binary pair. The parameters of the system make TOI-4336 A b an extremely promising target for the detailed atmospheric characterization of a temperate sub-Neptune by transit transmission spectroscopy with JWST.

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Teegarden's Star revisited: A nearby planetary system with at least three planets

The two known planets in the planetary system of Teegarden's Star are among the most Earth-like exoplanets currently known. Revisiting this nearby planetary system with two planets in the habitable zone aims at a more complete census of planets around very low-mass stars. A significant number of new radial velocity measurements from CARMENES, ESPRESSO, MAROON-X, and HPF, as well as photometry from TESS motivated a deeper search for additional planets. We confirm and refine the orbital parameters of the two know planets Teegarden's Star b and c. We also report the detection of a third planet d with an orbital period of 26.13+-0.04 d and a minimum mass of 0.82+-0.17 M_Earth. A signal at 96 d is attributed to the stellar rotation period. The interpretation of a signal at 172 d remains open. The TESS data exclude transiting short-period planets down to about half an Earth radius. We compare the planetary system architecture of very low-mass stars. In the currently known configuration, the planetary system of Teegarden's star is dynamically quite different from that of TRAPPIST-1, which is more compact, but dynamically similar to others such as GJ 1002.

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TESS discovery of a super-Earth orbiting the M dwarf star TOI-1680

We report the discovery by the TESS mission of a super-Earth on a 4.8-d orbit around an inactive M4.5 dwarf (TOI-1680) validated by ground-based facilities. The host star is located 37.14 pc away, with a radius of 0.2100+/-0.0064 R_sun, mass of 0.1800+/-0.0044 M_sun and an effective temperature of 3211+/-100 K. We validated and characterized the planet using TESS data, ground-based multi-wavelength photometry from TRAPPIST, SPECULOOS, and LCO, as well as high-resolution AO observations from Keck/NIRC2 and Shane. Our analyses have determined the following parameters for the planet: a radius of 1.466+0.063/-0.049 R_earth and an equilibrium temperature of 404+/-14 K, assuming no albedo and perfect heat redistribution. Assuming a mass based on mass-radius relations, this planet is a promising target for atmospheric characterization with the James Webb Space Telescope (JWST).

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TOI-2084 b and TOI-4184 b: two new sub-Neptunes around M dwarf stars

We present the discovery and validation of two TESS exoplanets orbiting nearby M dwarfs: TOI-2084b, and TOI-4184b. We characterized the host stars by combining spectra from Shane/Kast and Magellan/FIRE, SED (Spectral Energy Distribution) analysis, and stellar evolutionary models. In addition, we used Gemini-South/Zorro & -North/Alopeke high-resolution imaging, archival science images, and statistical validation packages to support the planetary interpretation. We performed a global analysis of multi-colour photometric data from TESS and ground-based facilities in order to derive the stellar and planetary physical parameters for each system. We find that TOI-2084b and TOI-4184b are sub-Neptune-sized planets with radii of Rp = 2.47 +/- 0.13R_Earth and Rp = 2.43 +/- 0.21R_Earth, respectively. TOI-2084b completes an orbit around its host star every 6.08 days, has an equilibrium temperature of T_eq = 527 +/- 8K and an irradiation of S_p = 12.8 +/- 0.8 S_Earth. Its host star is a dwarf of spectral M2.0 +/- 0.5 at a distance of 114pc with an effective temperature of T_eff = 3550 +/- 50 K, and has a wide, co-moving M8 companion at a projected separation of 1400 au. TOI-4184b orbits around an M5.0 +/- 0.5 type dwarf star (Kmag = 11.87) each 4.9 days, and has an equilibrium temperature of T_eq = 412 +/- 8 K and an irradiation of S_p = 4.8 +/- 0.4 S_Earth. TOI-4184 is a metal poor star ([Fe/H] = -0.27 +/- 0.09 dex) at a distance of 69 pc with an effective temperature of T_eff = 3225 +/- 75 K. Both planets are located at the edge of the sub-Jovian desert in the radius-period plane. The combination of the small size and the large infrared brightness of their host stars make these new planets promising targets for future atmospheric exploration with JWST.

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A super-Earth and a mini-Neptune near the 2:1 MMR straddling the radius valley around the nearby mid-M dwarf TOI-2096

Several planetary formation models have been proposed to explain the observed abundance and variety of compositions of super-Earths and mini-Neptunes. In this context, multitransiting systems orbiting low-mass stars whose planets are close to the radius valley are benchmark systems, which help to elucidate which formation model dominates. We report the discovery, validation, and initial characterization of one such system, TOI-2096, composed of a super-Earth and a mini-Neptune hosted by a mid-type M dwarf located 48 pc away. We first characterized the host star by combining different methods. Then, we derived the planetary properties by modeling the photometric data from TESS and ground-based facilities. We used archival data, high-resolution imaging, and statistical validation to support our planetary interpretation. We found that TOI-2096 corresponds to a dwarf star of spectral type M4. It harbors a super-Earth (R$\sim1.2 R_{\oplus}$) and a mini-Neptune (R$\sim1.90 R_{\oplus}$) in likely slightly eccentric orbits with orbital periods of 3.12 d and 6.39 d, respectively. These orbital periods are close to the first-order 2:1 mean-motion resonance (MMR), which may lead to measurable transit timing variations (TTVs). We computed the expected TTVs amplitude for each planet and found that they might be measurable with high-precision photometry delivering mid-transit times with accuracies of $\lesssim$2 min. Moreover, measuring the planetary masses via radial velocities (RVs) is also possible. Lastly, we found that these planets are among the best in their class to conduct atmospheric studies using the James Webb Space Telescope (JWST). The properties of this system make it a suitable candidate for further studies, particularly for mass determination using RVs and/or TTVs, decreasing the scarcity of systems that can be used to test planetary formation models around low-mass stars.

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Precise near-infrared photometry, accounting for precipitable water vapour at SPECULOOS Southern Observatory

The variability induced by precipitable water vapour (PWV) can heavily affect the accuracy of time-series photometric measurements gathered from the ground, especially in the near-infrared. We present here a novel method of modelling and mitigating this variability, as well as open-sourcing the developed tool -- Umbrella. In this study, we evaluate the extent to which the photometry in three common bandpasses (r', i', z'), and SPECULOOS' primary bandpass (I+z'), are photometrically affected by PWV variability. In this selection of bandpasses, the I+z' bandpass was found to be most sensitive to PWV variability, followed by z', i', and r'. The correction was evaluated on global light curves of nearby late M- and L-type stars observed by SPECULOOS' Southern Observatory (SSO) with the I+z' bandpass, using PWV measurements from the LHATPRO and local temperature/humidity sensors. A median reduction in RMS of 1.1% was observed for variability shorter than the expected transit duration for SSO's targets. On timescales longer than the expected transit duration, where long-term variability may be induced, a median reduction in RMS of 53.8% was observed for the same method of correction.

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Two temperate super-Earths transiting a nearby late-type M dwarf

In the age of JWST, temperate terrestrial exoplanets transiting nearby late-type M dwarfs provide unique opportunities for characterising their atmospheres, as well as searching for biosignature gases. We report here the discovery and validation of two temperate super-Earths transiting LP 890-9 (TOI-4306, SPECULOOS-2), a relatively low-activity nearby (32 pc) M6V star. The inner planet, LP 890-9b, was first detected by TESS (and identified as TOI-4306.01) based on four sectors of data. Intensive photometric monitoring of the system with the SPECULOOS Southern Observatory then led to the discovery of a second outer transiting planet, LP 890-9c (also identified as SPECULOOS-2c), previously undetected by TESS. The orbital period of this second planet was later confirmed by MuSCAT3 follow-up observations. With a mass of 0.118$\pm$0.002 $M_\odot$, a radius of 0.1556$\pm$0.0086 $R_\odot$, and an effective temperature of 2850$\pm$75 K, LP 890-9 is the second-coolest star found to host planets, after TRAPPIST-1. The inner planet has an orbital period of 2.73 d, a radius of $1.320_{-0.027}^{+0.053}$ $R_\oplus$, and receives an incident stellar flux of 4.09$\pm$0.12 $S_\oplus$. The outer planet has a similar size of $1.367_{-0.039}^{+0.055}$ $R_\oplus$ and an orbital period of 8.46 d. With an incident stellar flux of 0.906 $\pm$ 0.026 $S_\oplus$, it is located within the conservative habitable zone, very close to its inner limit. Although the masses of the two planets remain to be measured, we estimated their potential for atmospheric characterisation via transmission spectroscopy using a mass-radius relationship and found that, after the TRAPPIST-1 planets, LP 890-9c is the second-most favourable habitable-zone terrestrial planet known so far. The discovery of this remarkable system offers another rare opportunity to study temperate terrestrial planets around our smallest and coolest neighbours.

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A Study of Flares in the Ultra-Cool Regime from SPECULOOS-South

We present a study of photometric flares on 154 low-mass ($\leq 0.2 \textrm{M}_{\odot}$) objects observed by the SPECULOOS-South Observatory from 1st June 2018 to 23rd March 2020. In this sample we identify 85 flaring objects, ranging in spectral type from M4 to L0. We detect 234 flares in this sample, with energies between $10^{29.2}$ and $10^{32.7}$ erg, using both automated and manual methods. With this work, we present the largest photometric sample of flares on late-M and ultra-cool dwarfs to date. By extending previous M dwarf flare studies into the ultra-cool regime, we find M5-M7 stars are more likely to flare than both earlier, and later, M dwarfs. By performing artificial flare injection-recovery tests we demonstrate that we can detect a significant proportion of flares down to an amplitude of 1 per cent, and we are most sensitive to flares on the coolest stars. Our results reveal an absence of high-energy flares on the reddest dwarfs. To probe the relations between rotation and activity for fully convective stars, we extract rotation periods for fast rotators and lower-bound period estimates of slow rotators. These rotation periods span from 2.2 hours to 65 days, and we find that the proportion of flaring stars increases for the very fastest rotators. Finally, we discuss the impact of our flare sample on planets orbiting ultra-cool stars. As stars become cooler, they flare less frequently; therefore, it is unlikely that planets around the very reddest dwarfs would enter the `abiogenesis' zone or drive visible-light photosynthesis through flares alone.

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TOI-2257 b: A highly eccentric long-period sub-Neptune transiting a nearby M dwarf

Thanks to the relative ease of finding and characterizing small planets around M dwarf stars, these objects have become cornerstones in the field of exoplanet studies. The current paucity of planets in long-period orbits around M dwarfs make such objects particularly compelling as they provide clues about the formation and evolution of these systems. In this study, we present the discovery of TOI-2257 b (TIC 198485881), a long-period (35 d) sub-Neptune orbiting an M3 star at 57.8pc. Its transit depth is about 0.4%, large enough to be detected with medium-size, ground-based telescopes. The long transit duration suggests the planet is in a highly eccentric orbit ($e \sim 0.5$), which would make it the most eccentric planet that is known to be transiting an M-dwarf star. We combined TESS and ground-based data obtained with the 1.0-m SAINT-EX, 0.60-m TRAPPIST-North and 1.2-m FLWO telescopes to find a planetary size of 2.2 $R_{\oplus}$ and an orbital period of 35.19 days. In addition, we make use of archival data, high-resolution imaging, and vetting packages to support our planetary interpretation. With its long period and high eccentricity, TOI-2257 b falls in a novel slice of parameter space. Despite the planet's low equilibrium temperature ($\sim$ 256 K), its host star's small size ($R_* = 0.311 \pm{0.015}$) and relative infrared brightness (K$_{mag}$ = 10.7) make it a suitable candidate for atmospheric exploration via transmission spectroscopy.

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A large sub-Neptune transiting the thick-disk M4V TOI-2406

Large sub-Neptunes are uncommon around the coolest stars in the Galaxy and are rarer still around those that are metal-poor. However, owing to the large planet-to-star radius ratio, these planets are highly suitable for atmospheric study via transmission spectroscopy in the infrared, such as with JWST. Here we report the discovery and validation of a sub-Neptune orbiting the thick-disk, mid-M dwarf star TOI-2406. We first infer properties of the host star by analysing the star's near-infrared spectrum, spectral energy distribution, and Gaia parallax. We use multi-band photometry to confirm that the transit event is on-target and achromatic, and we statistically validate the TESS signal as a transiting exoplanet. We then determine physical properties of the planet through global transit modelling of the TESS and ground-based time-series data. We determine the host to be a metal-poor M4V star, located at a distance of 56 pc, with a sub-solar metallicity $(\mathrm{[Fe/H] = -0.38 \pm 0.07})$, and a member of the thick disk. The planet is a relatively large sub-Neptune for the M-dwarf planet population, with $\mathrm{R_p = 2.94 \pm 0.17} \mathrm{R_\oplus}$ and $\mathrm{P = 3.077}$ d, producing transits of 2% depth. We note the orbit has a non-zero eccentricity to 3$\mathrmσ$, prompting questions about the dynamical history of the system. This system is an interesting outcome of planet formation and presents a benchmark for large-planet formation around metal-poor, low-mass stars. The system warrants further study, in particular radial velocity follow-up to determine the planet mass and constrain possible bound companions. Furthermore, TOI-2406 b is a good target for future atmospheric study through transmission spectroscopy, particularly in the category of warm sub-Neptunes.

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Development of the SPECULOOS exoplanet search project

SPECULOOS (Search for habitable Planets EClipsing ULtra-cOOl Stars) aims to perform a transit search on the nearest ($<40$pc) ultracool ($<3000$K) dwarf stars. The project's main motivation is to discover potentially habitable planets well-suited for detailed atmospheric characterisation with upcoming giant telescopes, like the James Webb Space Telescope (JWST) and European Large Telescope (ELT). The project is based on a network of 1m robotic telescopes, namely the four ones of the SPECULOOS-Southern Observatory (SSO) in Cerro Paranal, Chile, one telescope of the SPECULOOS-Northern Observatory (SNO) in Tenerife, and the SAINT-Ex telescope in San Pedro Mártir, Mexico. The prototype survey of the SPECULOOS project on the 60~cm TRAPPIST telescope (Chile) discovered the TRAPPIST-1 system, composed of seven temperate Earth-sized planets orbiting a nearby (12~pc) Jupiter-sized star. In this paper, we review the current status of SPECULOOS, its first results, the plans for its development, and its connection to the Transiting Exoplanet Survey Satellite (TESS) and JWST.

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SPECULOOS -- Ultracool Dwarf Transit Survey: Target List and Strategy

One of the most promising avenues for the detailed study of temperate Earth-sized exoplanets is the detection of such planets in transit in front of stars small and nearby enough to make possible their thorough atmospheric characterisation with next generation telescopes like the James Webb Space telescope (JWST) or Extremely Large Telescope (ELT). In this context, the TRAPPIST-1 planets form an unique benchmark system that has gathered the interest of a large scientific community. The SPECULOOS survey is an exoplanet transit survey, that targets a volume-limited (40 pc) sample of ultracool dwarf stars. We define the SPECULOOS target list as the sum of three non-overlapping sub-programs incorporating the latest type objects (T_eff < 3000K): Program1: 365 dwarfs that are small and nearby enough to make possible the detailed atmospheric characterisation of an `Earth-like' planet with the upcoming JWST, Program2: 171 dwarfs of M5-type and later for which a significant detection of a planet similar to TRAPPIST-1b should be within reach of the exoplanet transit survey TESS, and Program3: 1121 dwarfs later than M6-type that aims to perform a statistical census of short-period planets around ultracool dwarf stars. Our compound target list includes 1657 photometrically classified late-type dwarfs. 260 of these targets are classified for the first time as possible nearby ultracool dwarf stars. Our general observational strategy is to monitor each target for 100 to 200hr with our telescope network, by efficiently using the synergy with TESS for our Program2 and a fraction of the targets of Program1. We expect to detect up to a few dozens temperate, rocky planets, a handful of them being amenable for atmospheric characterisation with JWST and other future giant telescopes which will improve drastically our understanding of the planetary population of the latest-type stars.

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Global Analysis of the TRAPPIST Ultra-Cool Dwarf Transit Survey

We conducted a global analysis of the TRAPPIST Ultra-Cool Dwarf Transit Survey - a prototype of the SPECULOOS transit search conducted with the TRAPPIST-South robotic telescope in Chile from 2011 to 2017 - to estimate the occurrence rate of close-in planets such as TRAPPIST-1b orbiting ultra-cool dwarfs. For this purpose, the photometric data of 40 nearby ultra-cool dwarfs were reanalysed in a self-consistent and fully automated manner starting from the raw images. The pipeline developed specifically for this task generates differential light curves, removes non-planetary photometric features and stellar variability, and searches for transits. It identifies the transits of TRAPPIST-1b and TRAPPIST-1c without any human intervention. To test the pipeline and the potential output of similar surveys, we injected planetary transits into the light curves on a star-by-star basis and tested whether the pipeline is able to detect them. The achieved photometric precision enables us to identify Earth-sized planets orbiting ultra-cool dwarfs as validated by the injection tests. Our planet-injection simulation further suggests a lower limit of 10 per cent on the occurrence rate of planets similar to TRAPPIST-1b with a radius between 1 and 1.3 $R_\oplus$ and the orbital period between 1.4 and 1.8 days.

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