Context. Transit spectroscopy is one of the most commonly used methods to characterize exoplanets’ atmospheres. From the ground, these observations are very challenging due to the terrestrial ...atmosphere and its intrinsic variations, but high-spectral-resolution observations overcome this difficulty by resolving the spectral lines and taking advantage of the different Doppler velocities of the Earth, the host star, and the exoplanet. Aims. We analyze the transmission spectrum around the Na I doublet at 589 nm of the extrasolar planet WASP-69b, a hot Jupiter orbiting a K-type star with a period of 3.868 days, and compare the analysis to that of the well-known hot Jupiter HD 189733b. We also present the analysis of the Rossiter-McLaughlin (RM) effect for WASP-69b. Methods. We observed two transits of WASP-69b with the High Accuracy Radial velocity Planet Searcher (HARPS-North) spectrograph (R = 115 000) at the Telescopio Nazionale Galileo (TNG). We perform a telluric contamination subtraction based on the comparison between the observed spectra and a telluric water model. Then, the common steps of the differential spectroscopy are followed to extract the transmission spectrum. The method is tested with archival transit data of the extensively studied exoplanet HD 189733b, obtained with the HARPS-South spectrograph at ESO 3.6 m telescope, and then applied to WASP-69b data. Results. For HD 189733b, we spectrally resolve the Na I doublet and measure line contrasts of 0.72 ± 0.05% (D2) and 0.51 ± 0.05% (D1), and full width half maximum (FWHM) values of 0.64 ± 0.04 Å (D2) and 0.60 ± 0.06 Å (D1), in agreement with previously published results. For WASP-69b only the contrast of the D2 line can be measured (5.8 ± 0.3%). This corresponds to a detection at the 5σ-level of excess absorption of 0.5 ± 0.1% in a passband of 1.5 Å. A net blueshift of ~ 0.04 Å is measured for HD 189733b and no shift is obtained for WASP-69b. By measuring the RM effect, we get an angular rotation of 0.24-0.01+0.02 rad/day and a sky-projected angle between the stellar rotation axis and the normal of orbit plane (λ) of 0.4-1.9+2.0° for WASP-69b. Similar results to those previously presented in the literature are obtained for the RM analysis of HD 189733b. Conclusions. Even if sodium features are clearly detected in the WASP-69b transmission spectrum, more transits are needed to fully characterize the line profiles and retrieve accurate atmospheric properties.
This text, combining analysis and tools from mathematical probability, focuses on a systematic and novel exposition of a recent trend in pure and applied mathematics. The emphasis is on the unity of ...basis constructions and their expansions (bases which are computationally efficient), and on their use in several areas: from wavelets to fractals. The aim of this book is to show how to use processes from probability, random walks on branches, and their path-space measures in the study of convergence questions from harmonic analysis, with particular emphasis on the infinite products that arise in the analysis of wavelets. The book brings together tools from engineering (especially signal/image processing) and mathematics (harmonic analysis and operator theory).
Key features:
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AU Mic b is a Neptune-sized planet on an 8.47-day orbit around the nearest pre-main sequence (~20 Myr) star to the Sun, the bright (
V
= 8.81) M dwarf AU Mic. The planet was preliminary detected in ...Doppler radial velocity time series and recently confirmed to be transiting with data from the TESS mission. AU Mic b is likely to be cooling and contracting and might be accompanied by a second, more massive planet, in an outer orbit. Here, we present the observations of the transit of AU Mic b using ESPRESSO on the Very Large Telescope. We obtained a high-resolution time series of spectra to measure the Rossiter-McLaughlin effect, to constrain the spin-orbit alignment of the star and planet, and to simultaneously attempt to retrieve the planet’s atmospheric transmission spectrum. These observations allowed us to study, for the first time, the early phases of the dynamical evolution of young systems. We applied different methodologies to derive the spin-orbit angle of AU Mic b, and all of them retrieve values consistent with the planet being aligned with the rotation plane of the star. We determined a conservative spin-orbit angle
λ
value of −2.96
−10.30
+10.44
degrees, indicative that the formation and migration of the planets of the AU Mic system occurred within the disc. Unfortunately, and despite the large signal-to-noise ratio of our measurements, the degree of stellar activity prevented us from detecting any features from the planetary atmosphere. In fact, our results suggest that transmission spectroscopy for recently formed planets around active young stars is going to remain very challenging, if at all possible, for the near future.
The obliquity of a terrestrial planet is an important clue about its formation and critical to its climate. Previous studies using simulated photometry of Earth show that continuous observations over ...most of a planet's orbit can be inverted to infer obliquity. However, few studies of more general planets with arbitrary albedo markings have been made and, in particular, a simple theoretical understanding of why it is possible to extract obliquity from light curves is missing. Reflected light seen by a distant observer is the product of a planet's albedo map, its host star's illumination, and the visibility of different regions. It is useful to treat the product of illumination and visibility as the kernel of a convolution. Time-resolved photometry constrains both the albedo map and the kernel, the latter of which sweeps over the planet due to rotational and orbital motion. The kernel's movement distinguishes prograde from retrograde rotation for planets with non-zero obliquity on inclined orbits. We demonstrate that the kernel's longitudinal width and mean latitude are distinct functions of obliquity and axial orientation. Notably, we find that a planet's spin axis affects the kernel – and hence time-resolved photometry – even if this planet is east–west uniform or spinning rapidly, or if it is north–south uniform. We find that perfect knowledge of the kernel at 2–4 orbital phases is usually sufficient to uniquely determine a planet's spin axis. Surprisingly, we predict that east–west albedo contrast is more useful for constraining obliquity than north–south contrast.
We have observed several relatively deep transits of the white dwarf WD 1145+017 with the Gran Telescopio Canarias (GTC) in the wavelength range 480 to 920 nm. The observations covered approximately ...one hour on 2016 January 18 and two hours on 2016 January 20. There was variable extinction of the white dwarf during much of that time, but this extinction was punctuated by four sharp transits with depths ranging from 25% to 40%. The spectrum was dispersed with a grism and the flux data were ultimately summed into four bands centered at 0.53, 0.62, 0.71, and 0.84 μm. After careful normalization, we find that the flux light curves in all four bands are consistently the same, including through the deepest dips. We use these results to compute Ångström exponents, α, for the particles responsible for the extinction and find |⟨ α ⟩| ≲ 0.06, assuming that the extinction is relatively optically thin. We use the complex indices of refraction for common minerals to set constraints on the median sizes of possible dust grains and find that particle sizes ≲0.5 μm can be excluded for most common minerals.
We report the first detection of sodium absorption in the atmosphere of the hot Jupiter WASP-52b. We observed one transit of WASP-52b with the low-resolution Optical System for Imaging and ...low-Intermediate-Resolution Integrated Spectroscopy (OSIRIS) at the 10.4 m Gran Telescopio Canarias (GTC). The resulting transmission spectrum, covering the wavelength range from 522 nm to 903 nm, is flat and featureless, except for the significant narrow absorption signature at the sodium doublet, which can be explained by an atmosphere in solar composition with clouds at 1 mbar. A cloud-free atmosphere is stringently ruled out. By assessing the absorption depths of sodium in various bin widths, we find that temperature increases towards lower atmospheric pressure levels, with a positive temperature gradient of 0.88 + or - 0.65 Kkm super(-1), possibly indicative of upper atmospheric heating and a temperature inversion.
Aims. Most hot Jupiters are expected to spiral in toward their host stars because the angular momentum of the orbital motion is transferred to the stellar spin. Their orbits can also precess as a ...result of planet-star interactions. Calculations show that both effects might be detected for the very-hot exoplanet WASP-12 b using the method of precise transit-timing over a time span of about 10 yr. Methods. We acquired new precise light curves for 29 transits of WASP-12 b, spannning four observing seasons from November 2012 to February 2016. New mid-transit times, together with those from the literature, were used to refine the transit ephemeris and analyze the timing residuals. Results. We find that the transit times of WASP-12 b do not follow a linear ephemeris with a 5σ confidence level. They may be approximated with a quadratic ephemeris that gives a change rate in the orbital period of (−2.56 ± 0.40) × 10-2 s yr-1. The tidal quality parameter of the host star was found to be equal to 2.5 × 105, which is similar to theoretical predictions for Sun-like stars. We also considered a model in which the observed timing residuals are interpreted as a result of the apsidal precession. We find, however, that this model is statistically less probable than the orbital decay.
WASP-52b is a low-density hot Jupiter orbiting a moderately active K2V star. Previous low-resolution studies have revealed a cloudy atmosphere and found atomic Na above the cloud deck. Here we report ...on the detection of excess absorption at the Na doublet, the H
α
line, and the K D
1
line. We derived a high-resolution transmission spectrum based on three transits of WASP-52b, observed with the ultra-stable, high-resolution spectrograph ESPRESSO at the Very Large Telescope array. We measured a line contrast of 1.09 ± 0.16% for Na D
1
, 1.31 ± 0.13% for Na D
2
, 0.86 ± 0.13% for H
α
, and 0.46 ± 0.13% for K D
1
, with a line FWHM range of 11–22 km s
−1
. We also found that the velocity shift of these detected lines during the transit is consistent with the planet’s orbital motion, thus confirming their planetary origin. We did not observe any significant net blueshift or redshift that could be attributed to planetary winds. We used activity indicator lines as control but found no excess absorption. However, we did notice signatures arising from the Center-to-Limb variation (CLV) and the Rossiter-McLaughlin (RM) effect at these control lines. This highlights the importance of the CLV + RM correction in correctly deriving the transmission spectrum, which, if not corrected, could resemble or cancel out planetary absorption in certain cases. WASP-52b is the second non-ultra-hot Jupiter to show excess H
α
absorption after HD 189733b. Future observations targeting non-ultra-hot Jupiters that show H
α
could help reveal the relation between stellar activity and the heating processes in the planetary upper atmosphere.
ABSTRACT We present the discovery of a transiting exoplanet candidate in the K2 Field-1 with an orbital period of 9.1457 hr: K2-22b. The highly variable transit depths, ranging from ∼0% to 1.3%, are ...suggestive of a planet that is disintegrating via the emission of dusty effluents. We characterize the host star as an M-dwarf with Teff 3800 K. We have obtained ground-based transit measurements with several 1-m class telescopes and with the GTC. These observations (1) improve the transit ephemeris; (2) confirm the variable nature of the transit depths; (3) indicate variations in the transit shapes; and (4) demonstrate clearly that at least on one occasion the transit depths were significantly wavelength dependent. The latter three effects tend to indicate extinction of starlight by dust rather than by any combination of solid bodies. The K2 observations yield a folded light curve with lower time resolution but with substantially better statistical precision compared with the ground-based observations. We detect a significant "bump" just after the transit egress, and a less significant bump just prior to transit ingress. We interpret these bumps in the context of a planet that is not only likely streaming a dust tail behind it, but also has a more prominent leading dust trail that precedes it. This effect is modeled in terms of dust grains that can escape to beyond the planet's Hill sphere and effectively undergo "Roche lobe overflow," even though the planet's surface is likely underfilling its Roche lobe by a factor of 2.
Context. The TESS and PLATO missions are expected to find vast numbers of new transiting planet candidates. However, only a fraction of these candidates will be legitimate planets, and the candidate ...validation will require a significant amount of follow-up resources. Radial velocity (RV) follow-up study can be carried out only for the most promising candidates around bright, slowly rotating, stars. Thus, before devoting RV resources to candidates, they need to be vetted using cheaper methods, and, in the cases for which an RV confirmation is not feasible, the candidate’s true nature needs to be determined based on these alternative methods alone. Aims. We study the applicability of multicolour transit photometry in the validation of transiting planet candidates when the candidate signal arises from a real astrophysical source (transiting planet, eclipsing binary, etc.), and not from an instrumental artefact. Particularly, we aim to answer how securely we can estimate the true uncontaminated star-planet radius ratio when the light curve may contain contamination from unresolved light sources inside the photometry aperture when combining multicolour transit observations with a physics-based contamination model in a Bayesian parameter estimation setting. More generally, we study how the contamination level, colour differences between the planet host and contaminant stars, transit signal-to-noise ratio, and available prior information affect the contamination and true radius ratio estimates. Methods. The study is based on simulations and ground-based multicolour transit observations. The contamination analyses were carried out with a contamination model integrated into the PYTRANSIT v2 transit modelling package, and the observations were carried out with the MuSCAT2 multicolour imager installed in the 1.5 m Telescopio Carlos Sanchez in the Teide Observatory, in Tenerife. Results. We show that multicolour transit photometry can be used to estimate the amount of flux contamination and the true radius ratio. Combining the true radius ratio with an estimate for the stellar radius yields the true absolute radius of the transiting object, which is a valuable quantity in statistical candidate validation, and enough in itself to validate a candidate whose radius falls below the theoretical lower limit for a brown dwarf.
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