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M. Gillon

Publications and source records attributed to M. Gillon.

At least 163 records · Page 9Linked to original sources

Discovery of three new transiting hot Jupiters: WASP-161 b, WASP-163 b and WASP-170 b

We present the discovery by the WASP-South transit survey of three new transiting hot Jupiters, WASP-161 b, WASP-163 b and WASP-170 b. Follow-up radial velocities obtained with the Euler/CORALIE spectrograph and high-precision transit light curves obtained with the TRAPPIST-North, TRAPPIST-South, SPECULOOS-South, NITES, and Euler telescopes have enabled us to determine the masses and radii for these transiting exoplanets. WASP-161\,b completes an orbit around its $V=11.1$ F6V-type host star in 5.406 days, and has a mass and radius of $2.5\pm 0.2$$M_{Jup}$ and $1.14\pm 0.06$ $R_{Jup}$ respectively. WASP-163\,b has an orbital period of 1.609 days, a mass of $1.9\pm0.2$ $M_{Jup}$, and a radius of $1.2\pm0.1$ $R_{Jup}$. Its host star is a $V=12.5$ G8-type dwarf. WASP-170\,b is on a 2.344 days orbit around a G1V-type star of magnitude $V=12.8$. It has a mass of $1.7\pm0.2$ $M_{Jup}$ and a radius of $1.14\pm0.09$ $R_{Jup}$. Given their irradiations ($\sim10^9$ erg.s$^{-1}$.cm$^{-2}$) and masses, the three new planets sizes are in good agreement with classical structure models of irradiated giant planets.

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WASP-147b, 160Bb, 164b and 165b: two hot Saturns and two Jupiters, including two planets with metal-rich hosts

We report the discovery of four transiting hot Jupiters, WASP-147, WASP-160B, WASP-164 and WASP-165 from the WASP survey. WASP-147b is a near Saturn-mass ($M_P = 0.28 M_{J}$) object with a radius of $ 1.11 \, R_{J}$ orbiting a G4 star with a period of $ 4.6 $ d. WASP-160Bb has a mass and radius ($ M_p = 0.28 \, M_J $, $ R_p = 1.09 \, R_J$) near-identical to WASP-147b, but is less irradiated, orbiting a metal-rich ([Fe/H] = 0.27) K0 star with a period of $3.8$ d. WASP-160B is part of a near equal-mass visual binary with an on-sky separation of 28.5 arcsec. WASP-164b is a more massive ($M_P = 2.13 \, M_J$, $R_p = 1.13 \, R_J$) hot Jupiter, orbiting a G2 star on a close-in ($P=1.8$ d), but tidally stable orbit. WASP-165b is a classical ($M_p = 0.66 \, M_J$, $R_P = 1.26 \, R_J$) hot Jupiter in a $3.5$~d period orbit around a metal-rich ([Fe/H] = 0.33) star. WASP-147b and WASP-160Bb are promising targets for atmospheric characterization through transmission spectroscopy, while WASP-164b presents a good target for emission spectroscopy.

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The 0.8-4.5$μ$m broadband transmission spectra of TRAPPIST-1 planets

The TRAPPIST-1 planetary system represents an exceptional opportunity for the atmospheric characterization of temperate terrestrial exoplanets with the upcoming James Webb Space Telescope (JWST). Assessing the potential impact of stellar contamination on the planets' transit transmission spectra is an essential precursor step to this characterization. Planetary transits themselves can be used to scan the stellar photosphere and to constrain its heterogeneity through transit depth variations in time and wavelength. In this context, we present our analysis of 169 transits observed in the optical from space with K2 and from the ground with the SPECULOOS and Liverpool telescopes. Combining our measured transit depths with literature results gathered in the mid/near-IR with Spitzer/IRAC and HST/WFC3, we construct the broadband transmission spectra of the TRAPPIST-1 planets over the 0.8-4.5 $μ$m spectral range. While planets b, d, and f spectra show some structures at the 200-300ppm level, the four others are globally flat. Even if we cannot discard their instrumental origins, two scenarios seem to be favored by the data: a stellar photosphere dominated by a few high-latitude giant (cold) spots, or, alternatively, by a few small and hot (3500-4000K) faculae. In both cases, the stellar contamination of the transit transmission spectra is expected to be less dramatic than predicted in recent papers. Nevertheless, based on our results, stellar contamination can still be of comparable or greater order than planetary atmospheric signals at certain wavelengths. Understanding and correcting the effects of stellar heterogeneity therefore appears essential to prepare the exploration of TRAPPIST-1's with JWST.

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A low-density hot Jupiter in a near-aligned, 4.5-day orbit around a $V$ = 10.8, F5V star

We report the independent discovery and characterisation of a hot Jupiter in a 4.5-d, transiting orbit around the star TYC 7282-1298-1 ($V$ = 10.8, F5V). The planet has been pursued by the NGTS team as NGTS-2b and by ourselves as WASP-179b. We characterised the system using a combination of photometry from WASP-South and TRAPPIST-South, and spectra from CORALIE (around the orbit) and HARPS (through the transit). We find the planet's orbit to be nearly aligned with its star's spin. From a detection of the Rossiter-McLaughlin effect, we measure a projected stellar obliquity of $λ= -19 \pm 6^\circ$. From line-profile tomography of the same spectra, we measure $λ= -11 \pm 5^\circ$. We find the planet to have a low density ($M_{\rm P}$ = 0.67 $\pm$ 0.09 $M_{\rm Jup}$, $R_{\rm P}$ = 1.54 $\pm$ 0.06 $R_{\rm Jup}$), which, along with its moderately bright host star, makes it a good target for transmission spectroscopy. We find a lower stellar mass ($M_*$ = $1.30 \pm 0.07$ $M_\odot$) than reported by the NGTS team ($M_*$ = $1.64 \pm 0.21$ $M_\odot$), though the difference is only $1.5$ $σ$.

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WASP-189b: an ultra-hot Jupiter transiting the bright A star HR 5599 in a polar orbit

We report the discovery of WASP-189b: an ultra-hot Jupiter in a 2.72-d transiting orbit around the $V = 6.6$ A star WASP-189 (HR 5599). We detected periodic dimmings in the star's lightcurve, first with the WASP-South survey facility then with the TRAPPIST-South telescope. We confirmed that a planet is the cause of those dimmings via line-profile tomography and radial-velocity measurements using the HARPS and CORALIE spectrographs. Those reveal WASP-189b to be an ultra-hot Jupiter ($M_{\rm P}$ = 2.13 $\pm$ 0.28 $M_{\rm Jup}$; $R_{\rm P}$ = 1.374 $\pm$ 0.082 $R_{\rm Jup}$) in a polar orbit ($λ= 89.3 \pm 1.4^\circ$; $Ψ= 90.0 \pm 5.8^\circ$) around a rapidly rotating A6IV-V star ($T_{\rm eff}$ = 8000 $\pm$ 100 K; $v_* \sin i_*$ $\approx$ 100 km\, s$^{-1}$). We calculate a predicted equilibrium temperature of $T_{\rm eql}$ = 2641 $\pm$ 34 K, assuming zero albedo and efficient redistribution, which is the third hottest for the known exoplanets. WASP-189 is the brightest known host of a transiting hot Jupiter and the third-brightest known host of any transiting exoplanet. We note that of the eight hot-Jupiter systems with $T_{\rm eff}$ $>$ 7000 K, seven have strongly misaligned orbits, and two of the three systems with $T_{\rm eff}$ $\geq$ 8000 K have polar orbits (the third is aligned).

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Monitoring of the activity and composition of comets 41P/Tuttle-Giacobini-Kresak and 45P/Honda-Mrkos-Pajdusakova

We report on photometry and imaging of the Jupiter Family Comets 41P/Tuttle-Giacobini-Kresak and 45P/Honda-Mrkos-Pajdusakova with the TRAPPIST-North telescope. We observed 41P on 34 nights from February 16, 2017 to July 27, 2017 pre- and post-perihelion (r$_h$=1.04 au), while we collected data for comet 45P from February 10 to March 30 after perihelion (r$_h$=0.53 au). We computed the production rates of the daughter species OH, NH, CN, C$_3$ and C$_2$ and we measured the dust proxy, Af$ρ$, for both comets. The peak of water production rate of 41P was (3.46$\pm$0.20)$\times$10$^{27}$ molecules/s on April 3, 2017 when the comet was at 1.05 au from the Sun. We have shown that the activity of 41P is decreasing by about 30% to 40% from one apparition to the next. We measured a mean water production rate for 45P of (1.43$\pm$0.62)$\times$10$^{27}$ molecules/s during a month after perihelion. Our results show that these Jupiter Family Comets had low gas and dust activity and no outburst was detected. Relative abundances, expressed as ratios of production rates and Af$ρ$ parameter with respect to OH and to CN, were compared to those measured in other comets. We found that 41P and 45P have a typical composition in term of carbon bearing species. The study of coma features exhibited by the CN gas species allowed the measurement of the rotation period of 41P, showing a surprisingly large increase of the rotation period from (30$\pm$5) hrs at the end of March to (50$\pm$10) hrs at the end of April, 2017 in agreement with recent observations by other teams.

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WASP-128b: a transiting brown dwarf in the dynamical-tide regime

Massive companions in close orbits around G dwarfs are thought to undergo rapid orbital decay due to runaway tidal dissipation. We report here the discovery of WASP-128b, a brown dwarf discovered by the WASP survey transiting a G0V host on a $2.2\,\mathrm{d}$ orbit, where the measured stellar rotation rate places the companion in a regime where tidal interaction is dominated by dynamical tides. Under the assumption of dynamical equilibrium, we derive a value of the stellar tidal quality factor $\log{Q_\star'} = 6.96 \pm 0.19$. A combined analysis of ground-based photometry and high-resolution spectroscopy reveals a mass and radius of the host, $M_\star = 1.16 \pm 0.04\,M_\odot$, $R_\star = 1.16 \pm 0.02\,R_\odot$, and for the companion, $M_\mathrm{b} =37.5 \pm 0.8\,M_\mathrm{Jup}$, $R_\mathrm{b} = 0.94 \pm 0.02\,R_\mathrm{Jup}$, placing WASP-128b in the driest parts of the brown dwarf desert, and suggesting a mild inflation for its age. We estimate a remaining lifetime for WASP-128b similar to that of some ultra-short period massive hot Jupiters, and note it may be a propitious candidate for measuring orbital decay and testing tidal theories.

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Activity induced variation in spin-orbit angles as derived from Rossiter-McLaughlin measurements

One of the most powerful methods used to estimate sky-projected spin-orbit angles of exoplanetary systems is through a spectroscopic transit observation known as the Rossiter-McLaughlin (RM) effect. So far mostly single RM observations have been used to estimate the spin-orbit angle, and thus there have been no studies regarding the variation of estimated spin-orbit angle from transit to transit. Stellar activity can alter the shape of photometric transit light curves and in a similar way they can deform the RM signal. In this paper we discuss several RM observations, obtained using the HARPS spectrograph, of known transiting planets that all transit extremely active stars, and by analyzing them individually we assess the variation in the estimated spin-orbit angle. Our results reveal that the estimated spin-orbit angle can vary significantly (up to 42 degrees) from transit to transit, due to variation in the configuration of stellar active regions over different nights. This finding is almost two times larger than the expected variation predicted from simulations. We could not identify any meaningful correlation between the variation of estimated spin-orbit angles and the stellar magnetic activity indicators. We also investigated two possible approaches to mitigate the stellar activity influence on RM observations. The first strategy was based on obtaining several RM observations and folding them to reduce the stellar activity noise. Our results demonstrated that this is a feasible and robust way to overcome this issue. The second approach is based on acquiring simultaneous high-precision short-cadence photometric transit light curves using TRAPPIST/SPECULOOS telescopes, which provide more information about the stellar active region's properties and allow a better RM modeling.

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Discovery of WASP-174b: Doppler tomography of a near-grazing transit

We report the discovery and tomographic detection of WASP-174b, a planet with a near-grazing transit on a 4.23-d orbit around a $V$ = 11.9, F6V star with [Fe/H] = 0.09 $\pm$ 0.09. The planet is in a moderately misaligned orbit with a sky-projected spin-orbit angle of $λ$ = 31$^{\circ}$ $\pm$ 1$^{\circ}$. This is in agreement with the known tendency for orbits around hotter stars to be misaligned. Owing to the grazing transit the planet's radius is uncertain, with a possible range of 0.8-1.8 R$_{\rm Jup}$. The planet's mass has an upper limit of 1.3 M$_{\rm Jup}$. WASP-174 is the faintest hot-Jupiter system so far confirmed by tomographic means.

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Dust modelling and a dynamical study of comet 41P/Tuttle-Giacobini-Kresak during its 2017 perihelion passage

Thanks to the Rosetta mission, our understanding of comets has greatly improved. A very good opportunity to apply this knowledge appeared in early 2017 with the appearance of the Jupiter family comet 41P/TGK. We performed an observational campaign with the TRAPPIST telescopes that covered almost the entire period of time when the comet was active. In this work we present a comprehensive study of the evolution of the dust environment of 41P based on observational data from January to July, 2017. Also, we performed numerical simulations to constrain its origin and dynamical nature. To model the observational data set we used a Monte Carlo dust tail model, which allowed us to derive the dust parameters that best describe its dust environment as a function of heliocentric distance. In order to study its dynamical evolution, we completed several experiments to evaluate the degree of stability of its orbit, its life time in its current region close to Earth, and its future behaviour. From the dust analysis, we found that comet 41P has a complex emission pattern that shifted from full isotropic to anisotropic ejection sometime during February 24-March 14 in 2017, and then from anisotropic to full isotropic again between June 7-28. During the anisotropic period, the emission was controlled by two strongly active areas, where one was located in the southern and one in the northern hemisphere of the nucleus. The total dust mass loss is estimated to be $\sim7.5\times10^{8}$ kg. From the dynamical simulations we estimate that $\sim$3600 yr is the period of time during which 41P will remain in a similar orbit. Taking into account the estimated mass loss per orbit, after 3600 yr, the nucleus may lose about 30$\%$ of its mass. However, based on its observed dust-to-water mass ratio and its propensity to outbursts, the lifetime of this comet could be much shorter.

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New transiting hot Jupiters discovered by WASP-South, Euler/CORALIE and TRAPPIST-South

We report the discovery of eight hot-Jupiter exoplanets from the WASP-South transit survey. WASP-144b has a mass of 0.44 Mj, a radius of 0.85 Rj, and is in a 2.27-d orbit around a V = 12.9, K2 star which shows a 21-d rotational modulation. WASP-145Ab is a 0.89 Mj planet in a 1.77-d orbit with a grazing transit, which means that the planetary radius is not well constrained. The host is a V = 11.5, K2 star with a companion 5 arcsecs away and 1.4 mags fainter. WASP-158b is a relatively massive planet at 2.8 Mj with a radius of 1.1 Rj and a 3.66-d orbit. It transits a V = 12.1, F6 star. WASP-159b is a bloated hot Jupiter (1.4 Rj and 0.55 Mj) in a 3.8-d orbit around a V = 12.9, F9 star. WASP-162b is a massive planet in a relatively long and highly eccentric orbit (5.2 Mj, P = 9.6 d, e = 0.43). It transits a V = 12.2, K0 star. WASP-168b is a bloated hot Jupiter (0.42 Mj, 1.5 Rj) in a 4.15-d orbit with a grazing transit. The host is a V = 12.1, F9 star. WASP-172b is a bloated hot Jupiter (0.5 Mj; 1.6 Rj) in a 5.48-d orbit around a V = 11.0, F1 star. It is likely to be the best planet of those reported here for atmospheric characterisation. WASP-173Ab is a massive planet (3.7 Mj) with a 1.2 Rj radius in a circular orbit with a period of 1.39 d. The host is a V = 11.3, G3 star, being the brighter component of the double-star system WDS23366-3437, with a companion 6 arcsecs away and 0.8 mags fainter. One of the two stars shows a rotational modulation of 7.9 d.

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The HARPS search for southern extra-solar planets. XLIII. A compact system of four super-Earth planets orbiting HD 215152

We report the discovery of four super-Earth planets around HD 215152, with orbital periods of 5.76, 7.28, 10.86, and 25.2 d, and minimum masses of 1.8, 1.7, 2.8, and 2.9 M_Earth respectively. This discovery is based on 373 high-quality radial velocity measurements taken by HARPS over 13 years. Given the low masses of the planets, the signal-to-noise ratio is not sufficient to constrain the planet eccentricities. However, a preliminary dynamical analysis suggests that eccentricities should be typically lower than about 0.03 for the system to remain stable. With two pairs of planets with a period ratio lower than 1.5, with short orbital periods, low masses, and low eccentricities, HD 215152 is similar to the very compact multi-planet systems found by Kepler, which is very rare in radial-velocity surveys. This discovery proves that these systems can be reached with the radial-velocity technique, but characterizing them requires a huge amount of observations.

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The discoveries of WASP-91b, WASP-105b and WASP-107b: two warm Jupiters and a planet in the transition region between ice giants and gas giants

We report the discoveries of three transiting exoplanets. WASP-91b is a warm Jupiter (1.34 $M_{\rm Jup}$, 1.03 $R_{\rm Jup}$) in a 2.8-day orbit around a metal-rich K3 star. WASP-105b is a warm Jupiter (1.8 $M_{\rm Jup}$, 0.96 $R_{\rm Jup}$) in a 7.9-day orbit around a metal-rich K2 star. WASP-107b is a warm super-Neptune/sub-Saturn (0.12 $M_{\rm Jup}$, 0.94 $R_{\rm Jup}$) in a 5.7-day orbit around a solar-metallicity K6 star. Considering that giant planets seem to be more common around stars of higher metallicity and stars of higher mass, it is notable that the hosts are all metal-rich, late-type stars. With orbital separations that place both WASP-105b and WASP-107b in the weak-tide regime, measurements of the alignment between the planets' orbital axes and their stars' spin axes may help us to understand the inward migration of short-period, giant planets. The mass of WASP-107b (2.2 $M_{\rm Nep}$, 0.40 $M_{\rm Sat}$) places it in the transition region between the ice giants and gas giants of the Solar System. Its radius of 0.94 $R_{\rm Jup}$ suggests that it is a low-mass gas giant with a H/He-dominated composition. The planet thus sets a lower limit of 2.2 $M_{\rm Nep}$ on the planetary mass above which large gaseous envelopes can be accreted and retained by proto-planets on their way to becoming gas giants. We may discover whether WASP-107b more closely resembles an ice giant or a gas giant by measuring its atmospheric metallicity via transmission spectroscopy, for which WASP-107b is a very good target.

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Three sub-Jupiter-mass planets: WASP-69b & WASP-84b transit active K dwarfs and WASP-70Ab transits the evolved primary of a G4+K3 binary

We report the discovery of the transiting exoplanets WASP-69b, WASP-70Ab and WASP-84b, each of which orbits a bright star ($V\sim10)$. WASP-69b is a bloated Saturn-mass planet (0.26 $M_{\rm Jup}$, 1.06 $R_{\rm Jup}$) in a 3.868-d period around an active, $\sim$1-Gyr, mid-K dwarf. ROSAT detected X-rays $60 \pm 27"$ from WASP-69. If the star is the source then the planet could be undergoing mass-loss at a rate of $\sim$10$^{12}$ g s$^{-1}$. This is 1 to 2 orders of magnitude higher than the evaporation rate estimated for HD 209458b and HD 189733b, both of which have exhibited anomalously-large Lyman-$α$ absorption during transit. WASP-70Ab is a sub-Jupiter-mass planet (0.59 $M_{\rm Jup}$, 1.16 $R_{\rm Jup}$) in a 3.713-d orbit around the primary of a spatially-resolved, 9-to-10-Gyr, G4+K3 binary, with a separation of 3.3$'$ ($\geq$800 AU). WASP-84b is a sub-Jupiter-mass planet (0.69 $M_{\rm Jup}$, 0.94 $R_{\rm Jup)}$ in an 8.523-d orbit around an active, $\sim$1-Gyr, early-K dwarf. Of the transiting planets discovered from the ground to date, WASP-84b has the third-longest period. For the active stars WASP-69 and WASP-84, we pre-whitened the radial velocities using a low-order harmonic series. We found this reduced the residual scatter more than did the oft-used method of pre-whitening with a fit between residual radial velocity and bisector span. The system parameters were essentially unaffected by pre-whitening.

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Atmospheric reconnaissance of the habitable-zone Earth-sized planets orbiting TRAPPIST-1

Seven temperate Earth-sized exoplanets readily amenable for atmospheric studies transit the nearby ultracool dwarf star TRAPPIST-1 (refs 1,2). Their atmospheric regime is unknown and could range from extended primordial hydrogen-dominated to depleted atmospheres (refs 3-6). Hydrogen in particular is a powerful greenhouse gas that may prevent the habitability of inner planets while enabling the habitability of outer ones (refs 6-8). An atmosphere largely dominated by hydrogen, if cloud-free, should yield prominent spectroscopic signatures in the near-infrared detectable during transits. Observations of the innermost planets have ruled out such signatures (ref 9). However, the outermost planets are more likely to have sustained such a Neptune-like atmosphere (refs 10,11). Here, we report observations for the four planets within or near the system's habitable zone, the circumstellar region where liquid water could exist on a planetary surface (refs 12-14). These planets do not exhibit prominent spectroscopic signatures at near-infrared wavelengths either, which rules out cloud-free hydrogen-dominated atmospheres for TRAPPIST-1 d, e and f, with significance of 8, 6 and 4 sigma, respectively. Such an atmosphere is instead not excluded for planet g. As high-altitude clouds and hazes are not expected in hydrogen-dominated atmospheres around planets with such insolation (refs 15,16), these observations further support their terrestrial and potentially habitable nature.

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The First Post-Kepler Brightness Dips of KIC 8462852

We present a photometric detection of the first brightness dips of the unique variable star KIC 8462852 since the end of the Kepler space mission in 2013 May. Our regular photometric surveillance started in October 2015, and a sequence of dipping began in 2017 May continuing on through the end of 2017, when the star was no longer visible from Earth. We distinguish four main 1-2.5% dips, named "Elsie," "Celeste," "Skara Brae," and "Angkor", which persist on timescales from several days to weeks. Our main results so far are: (i) there are no apparent changes of the stellar spectrum or polarization during the dips; (ii) the multiband photometry of the dips shows differential reddening favoring non-grey extinction. Therefore, our data are inconsistent with dip models that invoke optically thick material, but rather they are in-line with predictions for an occulter consisting primarily of ordinary dust, where much of the material must be optically thin with a size scale <<1um, and may also be consistent with models invoking variations intrinsic to the stellar photosphere. Notably, our data do not place constraints on the color of the longer-term "secular" dimming, which may be caused by independent processes, or probe different regimes of a single process.

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High-precision multi-wavelength eclipse photometry of the ultra-hot gas giant exoplanet WASP-103 b

We present sixteen occultation and three transit light curves for the ultra-short period hot Jupiter WASP-103 b, in addition to five new radial velocity measurements. We combine these observations with archival data and perform a global analysis of the resulting extensive dataset, accounting for the contamination from a nearby star. We detect the thermal emission of the planet in both the $z'$ and $K_{\mathrm{S}}$-bands, the measured occultation depths being 699$\pm$110 ppm (6.4-$σ$) and $3567_{-350}^{+400}$ ppm (10.2-$σ$), respectively. We use these two measurements together with recently published HST/WFC3 data to derive joint constraints on the properties of WASP-103 b's dayside atmosphere. On one hand, we find that the $z'$-band and WFC3 data are best fit by an isothermal atmosphere at 2900 K or an atmosphere with a low H$_2$O abundance. On the other hand, we find an unexpected excess in the $K_{\mathrm{S}}$-band measured flux compared to these models, which requires confirmation with additional observations before any interpretation can be given. From our global data analysis, we also derive a broad-band optical transmission spectrum that shows a minimum around 700 nm and increasing values towards both shorter and longer wavelengths. This is in agreement with a previous study based on a large fraction of the archival transit light curves used in our analysis. The unusual profile of this transmission spectrum is poorly matched by theoretical spectra and is not confirmed by more recent observations at higher spectral resolution. Additional data, both in emission and transmission, are required to better constrain the atmospheric properties of WASP-103 b.

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The structure of Chariklo's rings from stellar occultations

Two narrow and dense rings (called C1R and C2R) were discovered around the Centaur object (10199) Chariklo during a stellar occultation observed on 2013 June 3. Following this discovery, we planned observations of several occultations by Chariklo's system in order to better characterize the physical properties of the ring and main body. Here, we use 12 successful occulations by Chariklo observed between 2014 and 2016. They provide ring profiles (physical width, opacity, edge structure) and constraints on the radii and pole position. Our new observations are currently consistent with the circular ring solution and pole position, to within the $\pm 3.3$ km formal uncertainty for the ring radii derived by Braga-Ribas et al. The six resolved C1R profiles reveal significant width variations from $\sim 5$ to 7.5 km. The width of the fainter ring C2R is less constrained, and may vary between 0.1 and 1 km. The inner and outer edges of C1R are consistent with infinitely sharp boundaries, with typical upper limits of one kilometer for the transition zone between the ring and empty space. No constraint on the sharpness of C2R's edges is available. A 1$σ$ upper limit of $\sim 20$ m is derived for the equivalent width of narrow (physical width <4 km) rings up to distances of 12,000 km, counted in the ring plane.

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